Glasses and Amorphous Materials

1 Classical Glass Technology Michael Cable Division of Ceramics, Glasses and Polymers, School of Materials, University of Sheffield, Sheffield, U.K.

List of 1.1 1.1.1 1.1.2 1.1.3 1.1.4 1.1.5 1.2 1.2.1 1.2.2 1.2.3 1.2.4 1.2.5 1.2.5.1 1.2.5.2 1.2.5.3 1.2.5.4 1.2.5.5 1.2.6 1.2.7 1.3 1.3.1 1.3.2 1.3.2.1 1.3.2.2 1.3.3 1.3.4 1.3.4.1 1.3.4.2 1.3.4.3 1.3.4.4 1.3.4.5 1.4 1.4.1 1.4.2

Symbols and Abbreviations The Historical Development of Glass Technology Introduction The Beginnings of Glass Technology The Eighteenth Century The Nineteenth Century The Twentieth Century Choice of Glass Compositions Properties Important to the User Properties Important to the Glass Maker Choice of Glass Composition Composition-Property Relations Models for Composition-Property Relations The Viscosity-Temperature Relation Liquidus Temperature Specific Heat Thermal Conductivity Summary The Modern Approach to Choice of Glass Composition Choice of Raw Materials The Melting of Glasses Introduction Energy Requirements Enthalpy of Reaction Sensible Heat Preparations The Stages of Melting Batch Heating The Initial Melting Reactions Refining The Homogenizing of Glass Melts Modern Furnaces Glass Forming Introduction The Manufacture of Containers

Materials Science and Technology Copyright © WILEY-VCH Verlag GmbH & Co KGaA. Allrightsreserved.

3 6 6 6 8 11 13 18 18 20 21 22 23 24 25 26 26 29 29 32 32 32 33 33 34 34 35 35 37 45 53 59 62 62 64

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1.4.3 1.4.4 1.4.4.1 1.4.4.2 1.4.4.3 1.4.5 1.4.5.1 1.4.5.2 1.4.6 1.4.6.1 1.4.6.2 1.4.6.3 1.4.6.4 1.4.6.5 1.5 1.5.1 1.5.2 1.6

1 Classical Glass Technology

The Production of Lamp Bulb Envelopes The Manufacture of Flat Glass Introduction Sheet Glass Processes Float Glass Rod and Tubing The Danner Process Vertical Drawing Processes Glass Fibers Introduction The Physics of Fiber Drawing The Technology of Fiber Production Continuous Fibers Non-Circular Rod Tube and Fiber Polishing Mechanical Polishing Acid Polishing References

69 70 70 71 74 78 78 79 80 80 80 81 82 83 83 83 84 85

List of Symbols and Abbreviations

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List of Symbols and Abbreviations A A Ao a a0 a0 at b b B B Ca Cs C ro CEQ Ct C c ct Ac d D E Ex E2 £* Ft F (a) F(p) g gt G H h h / kB k / L m M

amplitude of wave parameter in Vogel-Tammann-Fulcher equation initial amplitude of wave radius or semi-major axis of elliptical inclusion initial radius of sphere constant term in Eqs. (1-1), (1-2) and (1-4) coefficient for term i in Eqs. (1-1) and (1-2) coefficient in Eq. (1-43) semi-minor axis of elliptical inclusion parameter in Vogel-Tammann-Fulcher equation rate of production of bottles dissolved concentration in liquid at radius a concentration of gas inside bubble uniform dissolved concentration in liquid far from bubble equilibrium concentration of silica in liquid in contact with silica grain concentration of dissolved silica in liquid at time t dimensionless concentration (0 < C < 1) specific heat concentration of component i concentration difference driving dissolution equilibrium thickness of Float glass ribbon diffusivity dimensionless equilibrium shape of deformed inclusion approximate dimensionless equilibrium shape of deformed inclusion parameter used to define approximate dimensionless equilibrium shape of deformed inclusion activation energy for viscous flow dimensionless dissolved concentration of gas i net surface tension force over unit length net force due to pressure over unit length gravitational acceleration mole fraction of gas i in a bubble rate of shear enthalpy height of Float glass ribbon above surface of tin bath depth of glass melt parameter describing initial behaviour of a multi-component bubble Boltzmann constant constant in Eqs. (1-19), (1-20), (1-42) and (1-44) linear dimension length of orifice number of components in system mass rate of flow through orifice

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1 Classical Glass Technology

n n n n n N p p Ap R R R s sa 5 aH 5 T T{ t U V w X X x y z z

number of degrees of freedom number of moles of a component refractive index number of terms in series number of bubbles of given size per unit volume of melt total number of bubbles per unit volume of melt pressure number of moles of silica in silicate liquid pressure difference or excess pressure due to surface tension gas constant dimensionless radius of sphere radius of atom or molecule natural strain natural strain of a-axis for inclusion differing in viscosity from surrounding liquid natural strain of a-axis when inclusion h a s same viscosity as matrix parameter defining eventual behaviour of multi-component bubble temperature interfacial temperature time velocity vector volume wall thickness value of a property mole fraction of a constituent diameter of bubble thickness of reaction product layer volume of product per unit volume of sphere number of moles of silica

a a a a OL{ P y S X X X X Xo XR rj

angle absorption coefficient mass fraction reacted thermal diffusivity Ostwald solubility coefficient for gas i rate of growth parameter for sphere auxiliary parameter in Appen's property calculations concentration boundary layer thickness wavelength of electromagnetic radiation wavelength of wave on liquid thermal conductivity dimensionless viscosity parameter true thermal conductivity apparent thermal conductivity due to radiant heat transfer viscosity

List of Symbols and Abbreviations

q> q> 0 ©0 9 90 Q a o \jj s

effective solubility of gas in liquid auxiliary parameter in Appen's property calculations temperature in °C temperature constant in Vogel-Tammann-Fulcher equation angle coefficient in Eq. (1-6) mass density surface tension or interfacial energy Stefan-Boltzmann constant auxiliary parameter in Appen's property calculations eccentricity of ellipse

1 Classical Glass Technology

1.1 The Historical Development of Glass Technology 1.1.1 Introduction

Glass making is an extremely old technology, the history of which has often been recounted, see for example Douglas and Frank (1972), but is constantly in need of revision as archaeological evidence keeps advancing our understanding of various aspects and throwing up new puzzles. Here we consider only how the general advance of science and the evolution of glass making have interacted with each other. Few events earlier than the middle of the seventeenth century deserve detailed discussion; until that time chemistry and physics were too primitive to be able to assist development of high temperature processes like glass or ceramic manufacture or iron making. But before proceeding it is salutary to remind ourselves of the brilliant technical achievements occasionally produced in distant ages: first, skill in glass melting such as the Wilsford bead (Guido et al., 1984) and the sealing-wax red glass from Nimrud (Cable and Smedley, 1987 b) and the glass of the Lycurgus cup (Brill, 1965) required; second, virtuosity in after working of the cold glass such as the Roman diatreta ware (Wiedman, 1954), the Portland or Barberini vase, and the modelling of the Lycurgus cup. These remind us that technological advance has often come about by intuition and intelligent trial and error experimentation rather than by applying scientific methods or knowledge. Even in recent times advances in scientific understanding have often been stimulated by technical advances rather than the converse. Several notable cornerstones of modern science depended on the availability of glass apparatus and from mediaeval times

onwards glass was the pre-eminent choice of alchemists and chemists for their apparatus. Even if borosilicate glass for laboratory apparatus (Pyrex) is a twentieth century invention, the relatively fragile glass apparatus then available was essential to many laboratory operations in earlier times. One of the events having an obvious claim to mark the beginning of modern science was Galileo's work on the motion of the planets which would have been impossible without astronomical telescopes needing glass lenses. Isaac Newton's pioneering work in optics, begun in 1666, also required prisms, lenses and mirrors. Other basic investigations which required glass apparatus were the classic investigations of the properties of gases (Boyle's law and Charles's law), thermometry, barometry and the development of microscopes. 1.1.2 The Beginnings of Glass Technology The earliest written records of glass making are some famous clay tablets, dating from around 650 BC, from the library of Assur-bani-pal, see Douglas and Frank (1972), but these are incompletely understood because we have no dictionary to explain the technical terms. Many centuries passed before written accounts of glass making contained any useful insight besides recipes to be followed by rote. The earliest development in glass making of which we have a reasonably documented description seems to be the invention of glass of lead by Ravenscroft around 1673-1676 (Moody, 1988, 1989). From very distant times it had been common to make much European glass using sand and an alkali flux obtained from plant ash. By mediaeval times it was known that leaching the ash and purifying the alkali by evaporation had several advantages in melting the glass. Unfortunately this also

1.1 The Historical Development of Glass Technology

made glass of simpler compositions richer in alkali, to the serious detriment of chemical durability. When Ravenscroft was called their rescue the holders of the monopoly on glass in England were in danger of losing their privilege because of customer dissatisfaction with the chemical durability of their product. Ravenscroft rescued them by developing a glass of lead (not the same as modern English lead crystal). This is the earliest work that we know where an investigation was deliberately made to find how to modify glass properties by adjusting composition. However, this could not have been done by scientific methods because chemistry was still on a mystical basis and the techniques of analysis needed did not exist. Some of the shortcomings of chemical knowledge of those times are indicated by the many years that Isaac Newton devoted to chemical studies which had a negligible influence, unlike his profound insights into gravitation and light. His Optics (1704) was the first important scientific book to be published in any vernacular language rather than Latin. It was not only directly concerned with the properties of glass but also the first to expound the modern scientific method of proposing hypotheses, devising experiments to test them and reporting the results before theorizing further. It is interesting to speculate how much further he might have developed optics if he had been able to experiment with glasses of distinctly different refractive indices and dispersions. The primitive state of glass technology may have let him down but led him to invent the reflecting astronomical telescope. The most influential of all books on glass was Antonio Neri's L'Arte Vetraria which first appeared in AD 1612 and was soon translated into both Latin and several other vernacular languages (Turner,

1962), generally with a commentary by the translator as exemplified by Merret's Art of Glass (1662) and Kunckel's Glasmacherkunst (1679). Although these give much useful information they are little more than recipe books: insight into the reasons why particular things should be done or avoided is rare. The beginnings of a sound glass science needed a better understanding of both chemistry and physics. Developments in chemistry were needed to permit the analysis of both glasses and raw materials as well as to understand the difference between elements such as sodium and potassium or calcium and magnesium. Science lacked a proper understanding of heat, which was thought of as some kind of chemical element though, as knowledge developed, it had to be treated as one with a negative mass. As a result melting and solidification and also glass formation could not be understood. The only important glass properties that could easily be measured were density and refractive index. This gives an unduly pessimistic a picture of what practitioners of the useful arts could achieve. For example, in those days glass makers did have some simple quality control tools for their ash, probably depending more on taste than anything else because sodium and potassium salts have different tastes as do carbonate, chloride, sulphate and nitrate; there are published comments such as "the bitterest is the best for making glass". Assessment of silica was a bigger problem and it was often assumed that all whitish stones which would neither dissolve in acid nor be affected by heat but struck a spark with steel were chemically equivalent and equally suitable for making glass. The reasons for this situation are clear: no other analytical tools were available. Another century was to pass before much progress was possible with any of

1 Classical Glass Technology

these crucial factors. Given what we now know about the sensitivity of glass properties to changes in composition, it sometimes seems amazing that any good quality glass was regularly made. Few glass makers can have enjoyed placid lives, a situation possibly not very different from today. The other main problems were associated with furnaces. First there was the problem of what to build them from, secondly, how to attain sufficiently high temperatures and, thirdly, how to measure and control temperature; even at the end of the last century it was normal to speak of degrees of heat when talking about high temperature processes. It was realised at an early stage that drying the wood used as fuel had important advantages; the net calorific value of wood decreases almost linearly with moisture content and becomes zero at about 70% H 2 O, so that air dried wood still containing around 20% moisture is much inferior to that which has been thoroughly dried. It is also clear that in those times glasses were regularly made which needed melting temperatures much above the 1200°C which used to be assumed to be the maximum melting temperature attainable (Cable and Smedley, 1987 a). The introduction of coal as the main fuel required significant changes in the design of furnaces to allow for its different combustion characteristics but this was done, as so often, by trial and error without real scientific insight. Up to those times two types of furnace had been developed (Newton, 1985). One was the southern European 'beehive' type exemplified by the famous woodcuts in Agricola's book, Fig. 1-1 (Hoover and Hoover, 1912). The other from northern Europe was a rectangular chamber frequently built with four smaller furnace chambers as wings on the corners, the plan looking like a butterfly, see Fig. 1-2.

Figure 1-1. The traditional southern European beehive type of furnace; from Agricola. The wood fire was central at ground level and charged through the opening shown; the exhaust gases passed over the pots and out of the working holes. Straight sided pots were more common than the vases shown.

Techniques of glass melting and forming processes remained virtually unchanged from the practices of several preceding centuries. 1.1.3 The Eighteenth Century

Several branches of chemistry and physics made very rapid advances towards the end of the eighteenth century. Some of the essential physical properties of gases were already known; Boyle's law was demonstrated in 1660 but Charles's law

1.1 The Historical Development of Glass Technology

0

5m

Figure 1-2. A northern European wood fired furnace showing the four small wing furnaces. Vertical section through the middle and plan view just above the level of the siege. Two fires were made, one at each end of the hearth. After Bosc D'Antic and other French

not until 1787. The experiments that were needed for these investigations would have been impossible without glass apparatus. A clear appreciation and separation of the chemical and physical aspects of heat and combustion came much later. Physicists had the evidence to abandon phlogiston towards the end of the 18th century but a considerably longer time elapsed before all chemists also came to a modern view of heat. There were, however, some notable publications about glass making in the second half of the century. The glass

making sections of the great Diderot and D'Alembert Encyclopedic (1765 -1772) contain more than a hundred beautifully drawn and engraved plates, which are well known, as well as very detailed descriptions of the processes, which are unjustly neglected. The text of the Diderot and D'Alembert Encyclopedic gives the most detailed account of glass making practices ever published and makes clear that much skill and experience was involved but very little science. The plates were republished with a significantly different and obviously more modern text in the Encyclopedic Methodique (1791). Figures 1-3 and 1-4 show examples of these plates which illustrate the two long established methods of making window glass, the crown process and the cylinder process. The crown process used a large gather formed like a shallow bowl which was transferred to a punty then reheated and spun by hand so that centrifugal force made it open up into an almost flat circular disk with excellent fire polished surfaces; the main disadvantages of crown glass were the thickened central bullion where the punty was attached and the fact that the disk was always somewhat saucer shaped. The glass, when homogeneous, was nevertheless of uniform thickness, generally in the range 1 to 2.5 mm (Cable and Swan, 1988). Cylinder glass was made by blowing a cylinder, cutting off the ends, cracking it longitudinally, then reheating it and opening out the cylinder into a flat sheet in a separate furnace. This operation required the use of a kind of wooden rake to open out the cylinder. The effect of this tool on the glass and of contact with the slab on which it lay always produced slightly rippled surfaces, although the sheet could be quite flat overall. Cylinder glass could provide considerably larger panes than

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1 Classical Glass Technology Tig.z

Figure 1-3. Reheating and spinning the gather in making crown glass: from the Diderot Encyclopedia.

crown. Crown glass could make good but slightly convex or concave mirrors but cylinder glass was rarely good enough to make looking glasses. The Collected Works of Paul Bosc D'Antic (1780) cover a range of subjects but glass making is the major part. In a fascinating introduction and a lengthy essay written in 1760 which is supplemented (in the established way) by additional commentaries written in 1780, he writes for the first time about glass making in the modern way referring, where possible, to the latest scientific literature. However, D'Antic was a man of complex personality and some influence at the court of Louis XVI (as physician to the King) but of dubious practical achievement because he was dis-

Figure 1-4. Steps in making cylinder glass; from the Diderot Encyclopedia.

missed from his position as Director at Saint Gobain in 1761 after only two years in that post. A clash of personalities may have contributed to D'Antic's downfall. His vivid style of writing suggests that he may have been vain and opinionated, a view clearly shared by Delaunay Deslandes, his deputy and successor as Director, who may not be an entirely impartial witness but whose distinguished 31 years in that post demonstrates his own technical

1.1 The Historical Development of Glass Technology

expertise and tends to lend credence to his strictures on D'Antic (Barton, 1989). 1.1.4 The Nineteenth Century

Enormous advances were made during the last century. The title of most eminent glass technologist of all time should probably be awarded to Joseph Fraunhofer (1787-1826) who as a more or less self educated orphan was in 1806, at the age of 19, employed at the Optical Institute in Benediktbeuern, where he assisted the elderly Guinand in developing the stirring of glass melts to produce optical glasses capable of making good achromatic doublets. Fraunhofer soon supplanted Guinand and spent the whole of his regrettably short career in this post, making his enormous contributions to astronomical optics, especially spectral analysis and diffraction, whilst engaged in the manufacture of astronomical telescopes. Although none of the telescopes made by Fraunhofer himself still exists, one made to the same design by his immediate successors is still to be seen at the Harvard College Observatory. One of Fraunhofer's (1817) published papers shows that he had developed a test for the chemical durability of glasses using sulphuric acid and also implies that he was the discoverer of the mixed alkali effect, that is to say recognizing that a mixture of alkalis often gives properties quite different from what one would have predicted from measuring properties of glasses containing only each alkali alone. Although chemistry was advancing rapidly, Fraunhofer would have been hindered by lack of pure materials and inability to analyse them or his glasses. These problems were rather less severe for Michael Faraday, the most creative of all scientists to have spent some of his time working as glass technologist, who had better resources close to hand.

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Faraday (1791-1867) was asked by the Board of Longitude and the Royal Society to find how to make good quality optical glasses to enable better instruments to be made and worked on this project from 1825 to 1830 when, having had reasonable success and not seeing how to make much further progress, he asked to be released to continue his work with electricity. Faraday (1830) described his methods but his work failed to have any practical impact on glass manufacture, largely because the system of controlling glass making, to ensure that the taxes were paid, and the way in which taxes were levied made experimentation by glass makers too difficult and expensive for most of them to contemplate. The small scale of his operations may also have failed to impress glass makers (Cable and Smedley, 1989). William Vernon Harcourt (1789-1871) was an important pioneer about whose work we know too little. Vernon Harcourt was a Church of England clergyman who was influential in founding first the Yorkshire Philosophical Society (his father was Archbishop of York at the time) and then the British Association for the Advancement of Science; the early history of the latter has been recounted by Morrell and Thackray (1981). During much of his long life he spent a great deal of time in making unusual glasses using a hydrogen furnace that he had invented (Vernon Harcourt 1844). His interest was to extend the range of optical properties available to allow better optical instruments to be made, latterly in conjunction with Prof. Stokes who undertook the optical measurements (Stokes, 1871). He used at least 29 elements in his glasses and was the first person ever to use at least 13 of them in glasses, see Fig. 1-5. He produced good samples of titanate, borate and phosphate glasses. Unfortunately his work, like Faraday's, led to no practical

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1 Classical Glass Technology

Li

Be

B

Na

Mg

Al

K

Ca

Ti

V

Cr

Sr

Mo

Ba

W

Mn

Fe-

Co

Ni

Cu

Si

Zn

P

F

S

As

Cd Au

0

TI

Sn

Sb

Pb

Bi

II

Figure 1-5. Periodic table of the elements showing those used in his glasses by Vernon Harcourt. Those which he was the first to use are marked by a bold outline; the others shown had previously been used in glasses.

U

applications. The punitive tax on glass had been abolished in 1845 so that was not the reason in this instance. Perhaps glass makers were unwilling to take seriously the results of such small scale laboratory experiments by an amateur or to consider using such unusual ingredients. The real beginnings of glass technology had to wait for the arrival on the scene of Abbe and Schott who began the first really fruitful investigations of property-composition relations in 1881, again with the intention of improving optical instruments, initially microscopes. Their success owed much to the collaboration of Carl Zeiss and his son Roderich in developing methods of large scale high quality lens manufacture which were soon also applied to the production of photographic lenses: Schott and Zeiss remain influential names today. The results of their pioneering investigations were described in detail by Hovestadt (1900) and an English translation by Everett (1902) soon appeared. The basic engineering industries developed rapidly during the nineteenth century, making possible advances in many other fields which required the large scale production of components and machines or high standards of accuracy; the development of electrical machines playing an especially important part. It is an interesting

coincidence that the Siemens Brothers had important roles in both electrical machinery and in glass melting. The tank furnace, which made possible continuous large scale production of molten glass, and machines for mechanized production of containers and flat glass were inventions crucial to the glass industry which together revolutionized it. The earliest patent for a regenerative glass melting furnace appears to have been granted to Robert Stirling in 1816 but this patent was never published, or exploited. Nevertheless it seems that Wilhelm Siemens knew of this work (Maurer and Bischoff, 1930). Attempts to make glass melting continuous had begun as early as 1840 when Joseph Crosfield obtained a patent for a reverberatory furnace in which batch was placed on an inclined surface and ran down into a pot as it melted. Chance Brothers in Smethwick obtained a patent for a tank about this time but, even if tried, there is no record of it being successful. The regenerative tank furnace was brought to success by two of the Siemens Brothers, of whom there were five, Friedrich, Hans, Karl, Werner, and Wilhelm, who between them worked in England and Russia as well as Germany but remained in regular contact. Friedrich had worked on regenerative furnaces in Eng-

1.1 The Historical Development of Glass Technology

land in 1857 and, jointly with Wilhelm, obtained an English patent for a regenerative system of firing a gas furnace in 1861. The regenerator as a means of heat recovery brought both higher temperatures and better fuel economy. The first successful glass tank was built by Friedrich in Dresden in 1867; on examining its plans one is surprised to see how little the main features changed during the ensuing years. The use of the tank for melting glass then spread rapidly. At about the same time Friedrich also devised a three compartment pot which allowed continuous melting and working on a smaller scale but it was never successfully exploited. A fascinating history of these developments has been written by Stein (1958). The introduction of iron mold was an important step forward in the glass industry. Magoun obtained an American patent for their use in 1847 and their usage was soon accepted. The first major development in mechanization occurred in United States where the machine pressing of glass made great progress between about 1820 and 1860. Soon after this the possibilities of the press and blow process for hollow ware were seen. In 1865 Gillinder of Pittsburgh was granted a patent for a combined press plunger and blow pipe with which he could press the top of a water jug and then blow the body. Following this line of thought Arbogast in 1881 developed the pressing of the neck and parison of a bottle in one mold followed by its transfer to another mold for blowing to the final shape, which he patented in 1882. This reversal of the traditional way of making containers in which the mouth was the last part to be shaped and hence called the finish was crucial to the subsequent development of all mechanized processes. The first blow and blow machine for containers was invented by Ashley, in England, in 1886. Although

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Owens began work on bottle manufacture around 1898, his major work took place in the early years of the present century, so his story will be taken up later. 1.1.5 The Twentieth Century

In the early years of the century the possibility of solids reacting together was becoming widely recognized and some of the earliest systems studied were of interest to glass makers. For example, Cobb (1910) published some studies of reactions involving sodium carbonate, calcium carbonate, and alumina with silica. Gustav Tammann (1861-1938) did much to develop scientific studies of glasses, including melting reactions, over an extended period. One of the most notable pioneers was W. E. S. Turner (1881-1963) who, at the beginning of the first World War, was already an ambitious university physical chemist. The early stages of the war showed him how badly the British glass industry needed scientific advice and research for which it had been relying on Germany and this led to him found the Society of Glass Technology in 1915 and the Department of Glass Technology at Sheffield University a year later. This was the first University Department to have glass technology as its special field of teaching and research. For forty years from its foundation the department was organized and financed in a way very unusual for those times but probably now widely thought very commendable, relying heavily on funding coming directly from the glass industry and being run by a joint University-Industry committee. The first successful attempt to produce an approximate theory to describe the kinetics of solid state reactions was by Jander (1927) who used data for systems including carbonates and silica to support his theory. This developed an interest in

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1 Classical Glass Technology

studies of glass making reactions among chemists as well as glass technologists. Science saw rapid advances in all fields. More and more elements became readily available and could be incorporated into glasses to investigate their possible uses. Correspondingly ever wider ranges of applications have called for novel glasses with properties not previously known or studied. Important novel families of glasses have been developed: these include inorganic non-oxide glasses such as the chalcogenides sharing many general structural similarities with oxides; quite unexpected inorganic systems of which the halide, especially fluoride, glasses are the most notable; metallic glasses and organic glasses, the last of which are no longer given only grudging recognition by glass scientists. All of these are discussed in later chapters of this volume. One of the most significant developments for glass technology was the Griffith (1920) theory for the strength of brittle materials which proposed that surface flaws were the controlling factor (see Sec. 13.3). Griffith himself tested his theory on glass bulbs deliberately scratched with a diamond. This at once aroused interest in the strength of glasses and provided a sound theoretical underpinning for previously ill defined and poorly understood studies of glass strength. It thus had an enormous beneficial influence on such work and on attempts to improve the practical strength of glasses. A notable practical result was the elegant demonstration by Thomas (1960) that strength is not necessarily dependent on sample size. The X-ray diffraction analysis of crystal structures was a particularly exciting field which had an enormous impact on glass science in the first quarter of the century. The most influential event in glass science was probably Zachariasen's (1932) publi-

cation of his random network hypothesis of oxide glass structures (see Sec. 5.1.1). This derived from early studies of crystal structures by X-ray diffraction which had led Zachariasen consider how one could build up extended structures in which all bonding requirements were met and nearest neighbor coordination maintained without imposing the exact long range order that a crystal demands. Although this is a static geometrical model of glass structures it has remained useful and fruitful to the present time, although it is now generally thought that models based on rates of cooling required to avoid crystallization are more universally valid (Turnbull and Cohen, 1960); however, they do not yield such a rich harvest of ideas about composition-property relations. The next most exciting development in structural studies probably was the ability to use high magnification electron microscopy to examine sub-liquidus phase separation after about 1960. Developments in technology also saw enormous strides in many fields, some considered to be in the realms of fantasy, if thought about at all in earlier times. An interest in lighting, initially for purely economic reasons, had led Count Rumford to invent photometry two hundred years ago (Brown, 1979) and twentieth century developments in lighting again called for major improvements by glass technologists, for example, in glasses for sealing to wire leads and others resistant to sodium vapour, then more recently glasses suitable for the envelopes of quartz-halogen lamps. An interesting review of the development of lamp manufacture in Germany has recently been published by Tober (1990 a, b). Radio equipment made rather different demands for the development of glasses and television demanded consideration of Xray absorption, the improvement of glass

1.1 The Historical Development of Glass Technology

homogeneity and development of high quality pressing for large face plates. Solid state electronics and microelectronics have had yet other requirements, mainly for electrical and mechanical properties. Some of the ways in which glasses played a part in these advances have been recorded in an impressive history of one of Britain's most successful industrial research laboratories, the General Electric Company's Hirst Research Centre, by Clayton and Algar (1989). The vast expansion of architectural uses and automobile manufacture put flat glass production under great stress and must have played an important part in the decisions to invest very large sums in the development of the Float glass process. The industry's major developments were in flat glass manufacture, automatic production processes for containers and lamp bulbs, and the development of fibers for insulation and for textiles. The first improvement in flat glass production was the Sieverts process which mechanized the blowing of hand gathered cylinders and somewhat increased their size but the Lubbers process of 1903 was more important. This mechanized the blowing of large cylinders, up to about 12 m long and 0.6 to 0.8 m in diameter, but these still had to be split then opened up in a flattening furnace. This increased the size of sheets that could be made and the scale of production but not the quality. Better flatness had to await the success of drawing flat sheet directly from the melt. Patents for sheet glass processes date back to the 1850s but then had no chance of success. Fourcault, who had obtained a Belgian patent for a sheet drawing process in 1902, was the first to succeed but did not manage to produce continuously drawn sheet glass until 1916, during the First World War. Colburn obtained a United States patent in 1903 and a French one in 1905 but likewise did not achieve

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success until the Libbey Owens company was established in 1916. The 1920s saw advances in other methods of drawing flat glass and in polished plate manufacture. The Pittsburgh sheet process was first operated in the United States in 1928 and brought to Europe in 1930. The Pilkington continuous process for grinding both sides of the cast plate ribbon at the same time was a notable engineering achievement of the 1930s. However, the most important large scale development was the invention of the Float process in the 1950s which made the very expensive plate process redundant. By a remarkable coincidence the Float process was being worked on simultaneously by both Ford in the United States and Pilkington in Britain but Pilkington submitted their patent applications only a few months before Ford and thus won the race which neither of them had consciously been running. Some of the problems encountered and solved by Pilkington Brothers in making the process work have been described by Pilkington (1969). Considerably quicker success attended the inventors of machines for making bottles. Michael J. Owens joined E. D. Libbey when Libbey moved his bottle factory from Boston, Massachusetts, and reopened in Toledo, Ohio, in 1888. By 1894 Owens had developed a paste mold machine which could make lamp chimneys and he began work on a bottle making machine in 1898. By 1903 Owens had produced a successful six arm rotary machine which differed from most others in the way in which it was supplied with glass. Semiautomatic machines which had to be supplied with gobs by a skilled gatherer already existed and persisted until about 1960. Owens solved the gathering problem by using his parison mold for this purpose. The parison mold dipped into a pool of relatively fluid glass

16

1 Classical Glass Technology

and was filled by suction; a second mold was then used for blowing, just as in the press and blow process. Further models followed and by 1920 improved and very effective machines which used six, ten, fifteen, and twenty sets of molds had been been put on the market. However, the Owens machine had important disadvantages, some technical and some commercial. The major technical problem (which was never solved) was the cut-off scar on the base of the container where the hot glass had been severed by a knife as the parison mold was lifted from the pool of glass. The Owens machine was very large and this was a disadvantage. Apart from its actual physical dimensions and weight, hence heavy power consumption (despite its continuous rotation), it also required large number of sets of molds for every article made. It was therefore suitable for long runs producing millions of one type of container but much less suited to producing a range of different products on a less ambitious scale. Commercial disadvantages included the high initial cost, the strict licensing arrangements and the heavy royalty payments required. Many smaller manufacturers therefore were not willing to use the Owens machine. This stimulated work on feeder fed blow and blow machines. The glass industry has been very fortunate in its engineering pioneers. The Owens machine was brought almost to perfection by about 1920: it then remained almost unchanged but was an important bottle producer until about 1960 when it was supplanted by machines supplied by gob feeders; the most successful of these likewise established its main features at an early stage. The most important advance needed by container manufacture was the successful development of forehearths and gob feed-

ers capable of supplying accurately made gobs of good quality glass to the forming machines. This was necessary for any other type of machine to compete with the Owens. The Homer Brooke feeder was first used in 1903 but was not very successful because it used a cup to collect the glass from a steady stream and thermal homogeneity was impossible to maintain. The crucial advance here was made in 1922 by Karl Peiler, a Massachusetts Institute of Technology graduate, when he introduced the first of the modern type of Hartford feeder which used a reciprocating vertical plunger and surrounding tube to control the flow of glass and produce separate gobs one at a time from the orifice. This made possible the successful development of gob-fed machines for container manufacture and took away from the Owens machine the one major advantage that it had enjoyed since its invention. Containers are now almost universally made by the Individual Section, or IS, machine which was invented in 1925 by Henry Ingle of the Hartford Empire Company. Nearly all previous machines had been conceived as using molds on a circular table which rotated, at first only intermittently, to execute the necessary sequence of operations. Most machines, other than the Owens, used two tables, one for parisons and one for blow molds. The major novelties of the IS machine were to have molds which are stationary, apart from opening and closing, only the neck ring holding the glass being moved, which greatly decreased essential operating power consumption, and to make each section essentially independent of the others, which allowed interruption of part of the machine, for example to change a mold, without having to stop the whole operation, a feature unique to the IS. Although numerous improvements have been made to con-

1.1 The Historical Development of Glass Technology

trol methods and mechanisms in recent years, for example the development of the narrow mouth press and blow process for containers in addition to the original blow and blow and wide mouth press and blow methods, the IS remains identifiably the original machine and the most efficient yet widely exploited. None of the numerous alternative machines developed in the last sixty years has long survived direct competition with the IS, one of the important reasons being that having the molds stationary, except for opening and closing, allows much more efficient mold cooling to be installed. The Heye company in Germany has developed a machine of great technical promise but it has yet to become a major competitor of the IS. Although processes were needed for the large scale manufacture of rod and tube, which had long been drawn by hand, their development did not need the same imaginative leap to entirely new methods as had containers. The Danner process, developed in 1912, is remarkably like the traditional hand made process with glass being continuously fed onto the outer surface of an inclined rotating mandrel from which it is drawn off. The Philips process is similar but draws the glass from inside a hollow mandrel. Corning developed both upward and downward drawing processes and the Velio process is also a downward drawing one. The large scale production of glass fiber for insulation and for textiles was another important twentieth century development. One of the puzzling facts of the early days of glass technology was the high strength of fine fibers and this must have influenced attempts to exploit them. Reaumur, who attempted to convert bottles to glass ceramic about 270 years ago, also realized that sufficiently fine glass fibers would be capable of being woven. Some novelty fab-

17

rics of the nineteenth century used glass fibers interwoven with silk. The evolution of a separate branch of the industry devoted to fibers dates from the 1930s when the Owens-Corning company was established and has ever since been the leader in this field. Other important advances which have received little public attention include high quality dimensionally accurate pressing for television screen face plates, car headlight lenses and some optical components. The development of small tank furnaces, partly lined with platinum and using platinum stirrers, for the continuous production of very homogeneous optical glass also played a vital part in satisfying the needs of the optical industries. Optical instruments benefited from vigorous research into expanding the ranges of combinations of optical properties available in glasses. During the last twenty years this has been matched by advances in lens design resulting from use of computers. Previously lens design and the evaluation of aberrations depended on extremely tedious manual ray tracing for every modification envisaged. Computer ray tracing so accelerated the evaluation of lens designs that major improvements in performance have been realized in the recent past. A number of notable developments have come from the Corning research laboratories, the earliest being Pyrex borosilicate glass for laboratory ware and other purposes needing good thermal shock resistance or chemical durability. Some years later the Corning ribbon machine made possible the very large scale production of lamp bulb envelopes and Corning also developed a process for spinning television tube components. On a more scientific level the Corning laboratories saw the invention of optical wave guides (also devel-

18

1 Classical Glass Technology

oped by the STL laboratories in England); photosensitive glasses, the exploitation of which by S. D. Stookey and his colleagues led to glass ceramics (see McMillan, 1979) (see Vol. 11, Chap. 4 of this series); photochromic glasses and more recently polychromatic glass which can have multicoloured images developed in it. Another Corning success was the exploitation of phase separation in borosilicate glasses to make Vycor which is produced by making and forming an easily melted alkali borosilicate glass then heat treating it to cause phase separation. After that it is leached in acid to leave a microporous skeleton of almost pure silica which can be fired again to densify it. This makes possible the manufacture of some articles very difficult to form when working directly with pure silica. It also provides microporous structures for other applications. The last two decades have seen the need for glasses with much smaller transmission losses than previously imagined to be feasible, for use in optical communication systems and this has been one of the most fruitful research and development fields (see Chap. 15). This has led to the development of halide glasses made in systems never before considered capable of producing glasses or worth investigation (see Chap. 8). Subsequent developments have led to studies of other possible optical communication devices including optical switches and amplifiers; this has encouraged detailed studies of glasses with nonlinear optical properties (see Chap. 12). Glasses are usually good electrical insulators but can be made with a very wide range of electrical properties including semi-conduction and fast ion conduction. The most exciting discovery of the past few years in the ceramic field has been 'high temperature' superconductors, meaning those which superconduct at liquid nitro-

gen temperatures. This property depends on a particular type of crystal structure and there is no sign that glasses can show such behavior. However, it has been shown that such superconductors can be made as glasses and then converted to the crystalline superconducting form by the usual glass-ceramic techniques (Zeng et al., 1989). Where this can be done it is much simpler than the usual ceramic techniques of preparation.

1.2 Choice of Glass Compositions Choosing a glass composition is a more complicated exercise than may at first appear. One must first establish the properties important to the final user, next consider those properties important to the glass maker, then achieve a balance between these and lastly determine what choice of batch materials will produce either the best quality or, perhaps, the cheapest glass meeting the quality requirements. Table 1-1 gives some examples of the range of compositions used for various purposes. 1.2.1 Properties Important to the User

Many glass properties vary fairly smoothly with composition across a considerable range. The user of a glass for any particular purpose therefore wishes to choose the glass which will be the best for his application. This requires decisions about the most important properties and a search for the glass coming closest to the desired values. Which properties are important depends very much on the application. From a designer's point of view, strength would nearly always be the first to be considered. However, because the practical strength of glasses is determined more by surface flaws than anything else,

19

1.2 Choice of Glass Compositions

Table 1-1. Typical glass compositions (wt.%). Type of glass Containers Mid 19th C bottle Mid 20th C bottle Late 20th C bottle Pharmaceutical Ampoule Ampoule Flat glass Float (UK) Fourcault sheet Lead crystal English European Laboratory ware Pyrex Kavalier Vycor As melted After leaching Sealing glasses Molybdenum Tungsten Fibers E glass Textile Mineral wool C glass Incandescent lamp Envelope Pinch Pinch Sodium vapor lamp Inner coating Inner coating Inner coating Outer casing

Na 2 O

K2O

CaO

MgO

ZnO

BaO

PbO

4.7 14.5 13.5

0.9 0.3 0.4

20.5 9.9 11.0

5.4 0.3 1.5

0 0 0

0 0 0

0 0 0

4.4 1.0 1.0

0 0 0

62.5 73.7 72.3

9.0 12.8

3.0 0

0 3.9

0 1.1

0 2.3

6.5 0

0 0

9.0 8.1

8.0 1.4

64.5 70.2

13.0 12.3

0.6 0.7

8.4 8.8

3.9 3.6

0 0

0 0

0 0

1.0 1.8

0 0

72.6 72.1

5.1 1.0

7.2 14.9

0 0

0 0

0 0

0 0

30.0 24.0

1.0 0.1

0 0

56.5 60.0

4.1 7.6

0.5 7.7

0.3 7.4

0.2 0.3

0 0

0 0

0 0

2.2 0.6

11.9 0

80.8 76.4

6.6 0.2

0 0

0 0

0 0

0 0

0 0

0 0

3.5 0.8

26.9 4.0

62.7 95.0

4.8 4.0

0.7 1.8

0.9 0

0 0

0 0

4.6 0

0 0

4.8 2.0

8.4 16.9

75.5 75.3

0.5 1.0 3.5 8.5

0 1.1 0

19.0 18.0 10.4 14.0

3.5 4.5 10.3 3.0

0 0 0 0

0 0 0 0

0 0 0 0

15.0 14.6 13.5 4.0

7.0 7.4 0 5.0

55.0 54.3 45.6 65.0

16.3 12.9 5.1

1.0 0.9 7.2

5.5 0.4 0

3.4 0 0

0 0 0

2.0 0 0

0 22.6 30.0

1.4 0.5 1.0

0 0 0

70.3 61.8 56.5

14.0 6.5 0 15.0

0 0 0 1.0

6.0 10.0 5.0 6.4

0 0

0 0

0 0 10.0 2.3

0 0

24.0 23.7 32.5 1.5

48.0 37.0 24.0 0.5

8.0 22.6 0 69.1

0

0

3.7

0

0 0

A12O3 B 2 O 3 SiO2

Other

Fe 2 O 3 SO3 SO 3

SO 3 ,Fe 2 O 3 SO 3 , Fe 2 O 3

F2 15.5Fe 2 O 3

28.5 P 2 O 5

Totals may be less than 100% because of rounding off or omission of some minor constituents (e.g. refining agents or decolorizers).

strength can generally be taken to be weakly dependent on composition and omitted from the specification. So far as strength is concerned commercial glasses can usually be considered as being either pure silica or "the rest" and only two sets of strength data need be considered.

The next most important property, which may not always come immediately to mind, often is resistance to corrosion. Good glasses are generally stable, already being oxides, but can be leached by water or other chemicals, something which is only rarely desirable. Chemical durability

20

1 Classical Glass Technology

is strongly dependent on composition, especially alkali and alumina contents, and thus should always be included. Next we come to the properties essential for the specific application. These may include refractive index, electrical resistivity, thermal expansion, transparency to or absorption of radiation, softening temperature, and so on. These properties fall into two classes, those for which a specific value is needed, like refractive index in an optical glass or thermal expansion for a sealing glass, and those that need to be better than some particular limit, like chemical durability or thermal expansion when thermal shock resistance is important. 1.2.2 Properties Important to the Glass Maker

Apart from the criteria set by the final user, several properties are very important to the glass manufacturer. The viscositytemperature characteristic is crucially important to efficient forming; Fig. 1-6 shows

1

1

I

i

|\

1

\

-\

1

1

1

|

1

1

1

1

1

\

AA

\

\

\2

\3

10

\

A

- y 5

1 500

•

\

^

:

:

k I

1

i

I

1000

I

1

I

i

i

1500

i

i

i

i

2000

Temperature in °C

Figure 1-6. Viscosity-temperature relations for some common types of glasses. 1) vitreous silica, 2) a glass for fibers, 3) a container glass, 4) sodium disilicate, 5) lead crystal.

some typical viscosity curves for different types of glasses and shows that a wide range of working temperatures can be required. Also the liquidus temperature must be below the temperature at which the melt must be held to begin forming operations. The actual devitrification characteristics may be less important but it can be useful to know whether crystal growth may be rapid if it does occur. The glass manufacturer also wants to have a glass as easy as possible to melt, refine, and homogenize but these factors are not capable of being specified in terms of standard properties. Some glasses contain significant proportions of elements which can exist in more than one valence state and these may need their oxidation states to be controlled. The most familiar example is the decolorizing of glass in which iron is oxidized, as far as possible, to the ferric state which gives a paler tint than the same concentration of iron reduced to ferrous. On the other hand, to make a heat absorbing glass one would wish to reduce the iron to ferrous which has a broad absorption peak in the near infrared. Control of oxidation is generally achieved largely by the selection of oxidizing or reducing materials added to the batch but partly by control of furnace atmosphere. In small scale laboratory melting oxidation can be controlled by bringing the melt to equilibrium with a specific atmosphere but this is not necessary and would be difficult to achieve in large scale manufacture. The batch materials can considerably influence ease of melting, degree of segregation during melting, volatilization losses, refining, and homogeneity of the glass. Both control of oxidation and overall melting performance can also be affected by minor constituents, that is to say cations or anions added at levels usually below 1%, which control oxidation through mutual

1.2 Choice of Glass Compositions

interactions or have beneficial effects on melting, refining, and homogeneity. The interactions between iron and arsenic, antimony or cerium can play an important part in decolorizing. Sulfate is the most commonly used refining agent: arsenic is often efficient but now rarely used because of legal controls on its use and halides can be effective. The glass maker will usually expect to be allowed to modify slightly the user's composition specification to optimize these factors. 1.2.3 Choice of Glass Composition Taking account of all the properties referred to above can easily produce a list of ten or more factors important to either the user or the glass maker. Finding a glass to satisfy all these requirements may not be easy. However, the task is easier if only some of the properties need to have specific values and the others need only to be within some given limit. The number of constraints to be met is the most important reason for the complexity of most commercial glasses many of which contain at least six major constituents: soda, potash, lime, magnesia, alumina, and silica. It is in fact gratifying that so many different glasses can be made without requiring a much longer list of constituents although most of the elements have some specific use. The most commonly used other oxides include Li 2 O, ZnO, B 2 O 3 , BaO, and PbO. If one tries to select a glass from a binary system only two degrees of freedom are available: 1) which particular system to choose (e.g. Na 2 O-SiO 2 , K 2 O-SiO 2 or Li 2 O-SiO 2 ) and 2) the specific composition. The composition may be chosen so that one property, such as thermal expansion coefficient, has the desired value but all other properties are then already fixed. If a third component is added it becomes

21

possible to keep the same thermal expansion but adjust composition to match one more property. With a four component glass three properties can be matched, and so on, see Fig. 1-7. Looked at formally it may be seen that trying to match a particular set of n properties requires n degrees of freedom or, since every composition must add up to 100%, n + 1 components. If the number of constraints exceeds the degrees of freedom it is impossible to satisfy all the desired requirements. In that case it will be necessary to accept a compromise. Choice of a glass composition used to rely heavily on the glass technologist's experience and intuition, requiring first the selection of a composition, then checking its properties, then making another guess and repeating the process until the desired result was obtained: this could be a tedious process. Any exercise of this

Figure 1-7. Property value surfaces for two different properties (Y and Z) in a four component system (A-B-C-D). All compositions along the line XX have the same values of Yand Z; a third property can also be matched by choosing a particular composition along this line.

22

1 Classical Glass Technology

kind is made much easier if models exist to describe the relations between properties and composition. This can clearly greatly reduce the number of steps needed and the necessity for numerous trial melts and measurement their properties. 1.2.4 Composition-Property Relations

Most research on composition-property relations has been restricted to systems with no more than three components. The major exceptions have been when an investigation was undertaken with the intention of producing a model for predicting properties from composition. Several factors have influenced this; the most important are the scientist's normal wish to work with as simple a system as is worth investigating and the difficulty of representing data for more than three components in a two dimensional diagram, as illustrated just above. The latter was a very serious problem before the ability of computers to work in multi-dimensional space was exploited. This is clearly seen in the invaluable comprehensive collection of composition-property data assembled in six volumes by Mazurin and his colleagues (1973-1981), which is limited to three components. Some of the problems of dealing with more complex glasses can be appreciated by consulting books such as Volf (1961) where much insight into the reasons for the complexity of several types of glass may be obtained but information on the specific effects of various individual components helpful in designing a new glass may be sparse. One of the most familiar examples of developing new compositions to solve manufacturing problems is sheet glass. The upward drawing of sheet glass was first brought into production by Fourcault during the first World War. Because of the

inherent instability of drawing a flat sheet, these processes have very strict requirements for viscosity in the drawing chamber and the rate of cooling of the sheet. As a result the soda-lime glasses originally used had to be held very close to their liquidus temperatures and were subject to devitrification. This remained a serious problem for some years. Eventually it was discovered that partial replacement of lime by magnesia greatly alleviated the problem by somewhat lowering liquidus but also giving much slower crystal growth. The classic work on the subject is by Swift (1947), see Fig. 1-8. Ever since then flat glass compositions have contained about 8% CaO and 3.5% MgO. Another important problem concerned the glass used in electric lamp bulbs through which the wires carrying the current are sealed. This glass must have suitable thermal expansion for sealing to the wires, appropriate softening point and

1000 Temperature in °C

Figure 1-8. Devitrification characteristics of flat glass compositions with 0, 2, and 4% MgO. Full lines are for devitrite and dashed ones for cristobalite; after Swift (1947).

1.2 Choice of Glass Compositions

good electrical resistivity up to at least normal lamp operating temperatures. The second requirement implies a glass of fairly high soda content but this clashes with the third. Using a lead glass similar in composition to English lead crystal met those requirements and far more glass of this type is today used in lamps than for making decorative products. 1.2.5 Models for Composition-Property Relations

Most experimental work has obviously led to data allowing the prediction of properties from the composition. Fortunately simple additive equations are quite successful for several important properties over the range of compositions most often used. Much effort was devoted to such work by a number of pioneer glass technologists; one of the oldest such investigations being that of Winkelmann and Schott (1894). Such models are entirely empirical and often of unknown accuracy and limited validity. Properties for which there are widely accepted models of this kind include thermal expansion, room temperature density, refractive index, Young modulus, Poisson ratio, dielectric constant, surface tension, specific heat, and thermal conductivity. One of the most attractive features of Scholze's (1977) well known book is the inclusion of a considerable number of these models and some comparisons of their predictions and ranges of validity. The classic models nearly all assume that a property is a simple linear function of composition and capable of calculation from an equation of the type X = Zaici

(1-1)

or = a0

a, ct

(1-2)

23

where X is the property value, a{ coefficients for each constituent and c{ the concentration of each constituent present. Concentrations are often expressed as weight percentages, which are generally the most convenient to use: in principle molar percentages ought to be better, especially when oxides of very different molar masses are concerned but, with linear approximations, the accuracy is not always improved by converting to moles. Sometimes, because m components give only m — 1 degrees of freedom, compositions are expressed by the ratios of the other constituents to the silica content when Eq. (1-2) must be used; the coefficient a0 then represents the notional property value for pure silica. If the regression analysis fitted the data very closely there would be no point in using more than the necessary number of coefficients; that is to say m — \. Sometimes, when the fit is acceptable but clearly not perfect, using m coefficients and having one more degree of freedom in the curve fitting exercise can yield a slightly better result. Before computers were available, processing the data and obtaining the best set of coefficients was a very tedious task and this clearly made the evaluation of complex models too daunting a task for most investigators. Occasionally the inverse of the property was found to give a better correlation but few other refinements were widely tried. It is unfortunate that present understanding of the structures of glasses still does not provide a more scientific basis for dealing with accurate composition-property relationships. The most important advances of recent years have been in the more sophisticated models and methods of analysis made possible by the development of computer hardware and software. One of the earliest useful attempts to work from

24

1 Classical Glass Technology

Their original measurements and analysis were restricted to a range of compositions including soda, potash, lime, magnesia, alumina, and silica but were later extended to include small proportions of several other oxides. In separate exercises they also dealt with lead crystal glasses (Lakatos et al., 1977, 1978, 1979) and glasses for insulating fibers (Lakatos et al., 1981). Geologists are interested in the viscosities of silicates, though not to the precision 1.2.5.1 The Viscosity-Temperature wanted by glass technologists; two interRelation esting papers on the estimation of viscosity It should be no surprise to find that visin systems of geological interest have been cosity has received more attention than published but, so far as is known, no one most other properties. One of the first athas compared their predictions with those tempts to produce a simple useful method already discussed. Bottinga and Weill was that of Okhotin (1954) whose work is (1972) reviewed viscosity data for a wide discussed by Braginskii (1973). range of compositions and pointed out the One of the most notable exercises has considerable scatter when plotted as In 77 been the work of Lakatos et al. (1972versus mole fraction silica (XSiO2) but 1981). They made their own set of very chose best fit straight lines for several segcareful viscosity measurements on a set of ments with boundaries at XSiO2 = 0.35, carefully selected glasses and then analysed 0.45, 0.55, 0.65, 0.75, and 0.81. They then the results. This work was initially inused a simple linear additive relation to tended only to cover a fairly narrow range estimate In 77 at 50 °C intervals from 1200 of compositions close to those used for to 1700°C for each of these ranges for containers and flat glass (Lakatos et al., 11 oxides (SiO2, TiO 2 , FeO, MnO, MgO, 1972 a) but experience has shown that it CaO, SrO, BaO, Li 2 O, Na 2 O, and K 2 O); can be extrapolated considerably outside alumina was dealt with in terms of six aluthe original field with reasonable accuracy. minate compounds of Na, K, Mg, Ca, Ba, Their particular success was to find that and Mn (e.g. MgAl2O4). They include a the constants A, B, and <90 in the Vogelreasonably detailed comparison of their Tamman-Fulcher equation for viscosity predictions with reported data; this indilogrj = -A + B/(0-0o) (1-3) cates excellent agreement at highest temperatures and growing discrepancies at can be well represented by simply additive lower temperatures, as might be expected. terms for each of the oxides present. Thus They report that 77% of their results lay for a glass with m components and hence within +0.25 In rj units and 99% within m — 1 degrees of freedom, ±0.75 units. Shaw (1972) based his work partly on (1-4) : = 1 to m - j Bottinga and Weill but used a different ap(1-5) proach to temperature dependence which, (1-6) according to the examples that are quoted,

a rather sounder base was the work of Huggins and Sun (1943) who used molar volumes rather than simple factors for density itself. Huggins used his approach for optical constants as well as density. The following sections discuss some of the particular properties of greatest interest to glass technologists and illustrate some of the difficulties that can arise.

1.2 Choice of Glass Compositions

gives a somewhat better fit than Bottinga and Weill. Natural logarithm of viscosity is again assumed to be a simple sum of the contributions by each oxide but temperature dependence is assumed to be of simple Arrhenius form, lnrj = \nrio + E*/T

(1-7)

and the activation energy £* also described by a simple additive relation for the mole fraction of each oxide multiplied by an appropriate coefficient obtained from calculations made for each pseudobinary silicate system. This assumption about the form of the viscosity-temperature curve means that extrapolation to lower temperatures and much higher viscosities cannot be relied on. The apparent activation energy for viscous flow in a typical soda-limesilica glass increases by a factor of about 2.5 between 1400 °C and 600 °C, so this is a considerable weakness in seeking to use Shaw's model at lower temperatures. It is possible that either of these methods may give as good or better results, at high temperatures, than the models usually used for compositions outside the range usually used by the glass industry, but glass technologists are often more interested in lower temperatures and higher viscosities than are dealt with by these models. 1.2.5.2 Liquidus Temperature

Liquidus temperature is the one important property for which difficulties must be expected to arise. Liquidus shows sharp minima as well as inflexions and maxima across sections of most systems and multiple linear regression analysis might not be expected to succeed. That is certainly the conclusion reached on examining the attempt of Lakatos et al. (1974, 1976 a) to calculate liquidus by simple linear regression; his model fits quite well data used to

25

obtain the factors but gives large errors for many other compositions, as might be expected when his range of compositions was narrow. One possible solution to that problem is to divide the system into different regions and treat each one separately. Doing this in terms of primary phase fields as suggested by Babcock (1977) has obvious merit for liquidus temperature. The author has confirmed that this method gives liquidus temperatures in the soda-limealumina-silica system (Silverman, 1939) to within + 8 °C for most of the compositions used in the original analysis; the largest discrepancy being 18 °C. Simply as an exercise in curve fitting, dividing any curve into short segments is likely to allow it to be acceptably described by a series of straight lines. However, narrowing the composition field for which a given model is evaluated, which will improve accuracy within that field, is likely to incur larger errors on extrapolating beyond its limits. This is certainly true when a complex curve is modelled by several separate segments. The possibility of improving liquidus temperature predictions has recently been investigated by Backman et al. (1990). This work attempted to predict liquidus temperatures in the soda-lime-silica system using thermodynamically based models as well as empirical regression analysis and also measured the liquidus temperatures of 50 complex glasses with 10 components. In planning the work it was expected that it might be possible to derive coefficients for each of the minor constituents which would give reasonable values of the liquidus of these complex glasses by estimating the change from its value for the pure soda-lime base glass. In fact a multiple regression analysis for the whole body of data proved the best of the models examined, partly because accurate thermody-

26

1 Classical Glass Technology

namic modelling is not possible even for the basic soda-lime-silica system because some of the essential data are lacking. Yet this best model still give errors of a hundred degrees or so for some compositions. When one considers how many experiments are needed to establish even a fairly straightforward ternary phase diagram, it would have been a surprise if data for only fifty complex glasses had produced a sufficiently refined model.

approximation which works reasonably well only because so many glasses fall in a rather narrow range of compositions. A better model has recently been proposed by Richet (1987); this allows the temperature dependence to differ for each oxide. However, his analysis covers temperatures only up to about 950 °C and thus may not be as accurate at the temperatures used for glass forming operations as might be hoped.

1.2.5.3 Specific Heat

1.2.5.4 Thermal Conductivity

Specific heat is often needed by workers concerned with melting or forming processes. Because it is difficult to measure temperatures during forming, determining the total heat content of the glass after dropping it into a calorimeter is often the only measurement easily made. If a good model for specific heat is available the average temperature of the glass is readily calculated from such data. Specific heat varies with temperature, the rate of increase falling off as temperature rises; it is zero at OK and approaches an asymptotic limit of about 3 R per atom (R being the gas constant) at very high temperatures. It is therefore important to specify whether the value at a particular temperature or the average over a wide temperature interval is needed. For the purpose just mentioned the latter is required and is also the information obtained directly from the classic kind of experiment in which a sample at a known temperature is dropped into a calorimeter. The first simple model was published by Sharp and Ginther (1951) and then somewhat improved by Moore and Sharp (1958) who still assumed that all glasses show the same temperature dependence. However, examination of the reliable data available shows that to be a rather crude

Heat transfer is a vital part of glass melting and glass forming operations as well as annealing and thermal toughening. The thermal conductivity is thus frequently required. Unfortunately it is one of the most difficult properties to evaluate. The true thermal conductivity is fairly easy to measure near room temperature and factors for calculating it from glass composition have been published by Russ (1928) and Ratcliffe (1963). Scholze (1977) discusses these and shows that, at least for the examples that he examines, Russ's rather more complex calculation gives the better agreement with experiment. An important complication is the partial transparent of most glasses to thermal radiation. Any element inside a body of glass at sufficiently high temperature can both transmit and partially absorb radiation. If the glass is at steady state any element which absorbs radiation must also re-emit as much as it absorbs and this step by step process across the whole body could transmit large heat fluxes even in a material of zero true conductivity. The two limits of this process are 1) the absorption coefficient is so low that a negligible fraction of the radiation is absorbed by the body or 2) the absorption coefficient is so high that the depth of penetration of the radiation is

1.2 Choice of Glass Compositions

negligible. In the former case the methods usually used for radiant transfer across empty space may be used; in the latter the problem is properly treated as simple conduction but most glasses fall in the intermediate range. The infrared transmission of most glasses varies very significantly with wavelength over the range important for radiant heat transfer, which may be estimated by Wien's law, according to which any particular position on the normalized black body radiant energy versus wavelength (A) distribution curve is defined by XT=k{

(1-8)

the value of k{ depending on the point on the spectrum. The following three values will suffice to make the points needed for our present purpose; Maximum intensity: k{ = 2898 (in jimK) 90% at longer wavelengths k{ = 2\95 90% at shorter wavelengths k{ = 9375 Most colourless silicate glasses transmit well from about 350 nm to about 4.5 \im. This means that the maximum intensity of black body radiation falls within the range over which a glass transmits at temperatures from 370 °C to 8000 °C and a significant fraction of the radiation may be transmitted by a silicate glass at any temperature above 215°C. Clearly the role of radiant transfer will be important in many processes with glasses. Fortunately the difficulties of dealing with radiation by using quite different mathematical arguments from those used for conduction can often be avoided by inserting an effective conductivity into the usual conduction equations. This effective conductivity is defined by X = X0

(1-9)

where Xo is the true conductivity and XR is the radiation conductivity.

27

This concept was first put forward by Schuster (1903) who showed that, for a parallel beam of radiation travelling through a partially transparent grey body, the net heat flux density due to the emission and reabsorption of radiation could be written

=

(8n2aT3/a)dT/dx

(1-10)

which by analogy with conduction gives XR = Sn2aT3/a

(1-11)

where n is the refractive index of the medium, a the Stefan-Boltzmann constant and a the absorption coefficient of the material (see Chap. 12). Making this calculation for radiation in three dimensions gives XR =

16n2aT3/3a

(1-12)

It is thus assumed that the total heat flux will be given by the sum of the contributions of true conduction and radiation so that the calculations can be made as if the process is one of conduction only but the conductivity to be used is as defined by Eqs. (1-9) and (1-12). One difficulty immediately arises over the evaluation of XR; coloring agents and impurities such as iron make a strongly dependent on wavelength for many glasses so that evaluation of the best value to represent the equivalent grey body may not be easy. As the absorption spectrum can be quite strongly influenced by temperature of the glass, merely measuring the room temperature absorption spectrum is not sufficient in many cases. When radiation is important the effective conductivity becomes steeply temperature dependent above about 600 °C and it may be more than an order of magnitude greater than the true conductivity at 1200°C. The increase with temperature is often less than the T 3 term indicates because of the changes in a and it may show inflexions, see Fig. 1-9.

28

1 Classical Glass Technology

Temperature in °C

Figure 1-9. Typical effective thermal conductivities of colourless flint and green container glasses compared with the true conductivity over a range of temperatures. After Genzel (1953).

A further complication arises when the optical thickness of the glass is considered. Whatever the actual thickness of the glass, the validity of using radiation conductivity depends on the optical thickness a x. If the optical thickness is less than about 0.1 radiant transfer plays a small enough role to be ignored: if it is greater than about a x = 3, there is a central region not directly influenced by conditions at the boundaries and heat transfer in the central part of the glass may be dealt with using the calculated radiation conductivity and ignoring boundary effects. However, if the optical thickness lies between these limits the effective conductivity becomes a function of the actual dimensions of the glass body, the conditions at the boundaries and the rate of heating or cooling. As Schuster demonstrated, temperature gradients near any boundary at which transparency to radia-

tion changes always deviate from those found in the bulk of the body: in a material of zero true conductivity there would be a discontinuity in temperature which true conduction smooths out in practice. Figure 1-10 shows some predictions of steady state temperature distributions in thick bodies of glass made by Walther et al. (1953). As a result effective conductivity is not easily estimated for many real situations, especially in bodies of intermediate thickness. Radiation does, however, play a vital and relatively straightforward role in the transfer of heat in the molten glass inside a melting tank and a negligible role in a typical glass no more than a few millimetres thick being rapidly cooled or heated. One of the most authoritative reviews of these matters is by Gardon (1961) and Table 1-2 gives a selection of thermal conductivities for sheet glass taken from Gardon's review; it can be seen how much geometry and cooling rate influence the values even at a temperature where radiation is just beginning to be important.

1500

1400

Q.

1200 -

0.2

0.4

0.6

0.8

1.0

Depth in m

Figure 1-10. Predicted temperature distributions in a bath of glass with black body radiation from gas above and black body refractories at the bottom. The values of the absorption coefficient a in m" 1 are shown on the curves: after Walther et al. (1953).

1.2 Choice of Glass Compositions

Table 1-2. Thermal conductivity of flat glass at 600 °C according to conditions of measurement or process. Conditions

Effective conductivity <(Win- 1 ^ 1 )

Measured in steady state: 4.5 mm wall of cylinder 6 mm slab 9 mm wall of cylinder 18 mm wall of cylinder 25 mm thick slab 50 mm thick slab Measured by periodic flow: 83 mm radius cylinder Theoretical estimates: True conductivity Radiation conductivity in thick body Best values for use in calculations: Slow cooling of 6 mm slab Thermal toughening of 6 mm slab

0.84 1.59 1.63 2.30 1.67-2.09 2.59 3.47 0.837 5.19 1.34 1.00

29

puter models in designing new glass compositions. Existing models do, however, give valuable assistance in providing useful approximations which should generally need little further experimentation to reach a suitable final composition. Turkdogan (1983) deals extensively with slags as well as glasses and provides a useful addition to the sources of data usually consulted by glass researchers. Tables 1-3 and 1-4 give a selection of factors often used for the prediction of glass properties using simple additive relations; however, these are of unspecified accuracy and limited ranges of validity so readers are recommended to consult the original sources or Scholze (1977) before using them. 1.2.6 The Modern Approach to Choice of Glass Composition

1.2.5.5 Summary

The various examples given in the last few sections show that the development of improved property-composition models is not just a matter of improved statistical analysis of the data. Since most, but not all, properties of glasses vary smoothly, even if rapidly, with composition it will often be possible to represent properties within limited areas by linear regressions. However, higher order terms often become necessary as the composition field is broadened. Also, as Lakatos et al. (1975) showed in their work on chemical durability, higher order terms are sometimes necessary even for quite restricted ranges of compositions. Another problem with entirely empirical models is that coefficients obtained for one particular set of data are valid only for that particular analysis. Much more work is needed on properties like liquidus, chemical durability, electrical conductivity, and specific heat before it will be possible to rely entirely on com-

Basically two things are needed to make the design of glass compositions easier. One is the development of better multidimensional computer models for more properties and wider ranges of compositions. The other is to approach the problem from the converse of the traditional direction, that is to specify the properties and then deduce the composition, or range of compositions, coming closest to meeting that specification. Huff and Call (1973) outlined the possibilities of developing procedures for computing compositions from specifications of properties by using optimization techniques. Westerlund et al. (1983) have published a more detailed account of procedures for this purpose provided that the required compositionproperty models exist and giving the models that they used. A typical application of this program would specify six points on the viscosity-temperature curve, thermal expansion, Young modulus, Poisson ratio, chemical durability, density and refractive

30

1 Classical Glass Technology

Table 1-3. Appen's factors for calculating density, refractive index, thermal expansion coefficient, Young modulus and surface tension for multi-component glasses. Property

Equation Unit of Cj Li 2 O Na 2 O K2O MgO CaO ZnO SrO BaO PbO A12O3 B2O3 SiO 2

Density

Refractive index

Thermal expansion

Young Modulus

Surface tension

(1-1) mol%

(1-1) mol%

(1-1) mol%

(1-1) mol%

(1-1) mol%

27.0 39.5 46.5 6.0 13.0 5.0 16.0 20 13.0 to 19 -3.0 -5.0 to 0.0 0.5 to 3.8

8.0 5.95 4.1 9.2 11.15 6.0 9.65 6.25 4.3 11.4 1.0 to 18.0 6.5 to 7.1

450 295

11.0 20.2 34.1 12.5 14.4 14.5 18 22.0 20.0 to 23.6 40.4 18.4 to 34.0 26.1 to 27.25

1.695 1.590 1.575 1.610 1.730 1.710 1.770 1.880 2.5 to 2.35 1.520 1.47 to 1.710 1.458 to 1.475

520 510 450 490 470 580 290

Sources: Appen (1949, 1954, 1956), Appen et al. (1961) Calculation of values of variable factors Density in g cm'3 Silica: c (SiO2) < 67, a (SiO2) = 26.1: c (SiO2) > 67, a(SiO2) = 23.75 + 0.035 c(SiO2). Boric oxide: calculate cp = QT c(R 2 O) + E C ( R O ) - C ( A 1 2 O 3 ) ) / C ( B 2 O 3 ) then select a(B 2 O 3 ) according to the following: c (SiO2) 44 to 64; 0.33 < cp < 1, a (B 2 O 3 ) = 24.7 + 3.1/cp; l4, a(B 2 O 3 ) = 18.5. c(SiO 2 ) 71 to 80: 0.333 1.6, a(B 2 O 3 ) = 18.5. Lead oxide: calculate y = c (SiO2) + c (B 2 O 3 ) + c (A12O3) then select as follows: 50 < y < 80, a (PbO) = 14.0 + 0.12 y; y > 80, a (PbO) = 23.6. Refractive index Silica: c (SiO2) < 67, a (SiO 2 ) = 1.475; c (SiO 2 ) > 67, a (SiO 2 ) = 1.5O85-O.OOO5 c (SiO 2 ). Boric oxide: calculate cp as above then select as follows: c(SiO2) 44 to 64: cp <0.333, a(B2O3) = 1.470; 0.333 <4, a(B 2 O 3 ) = 1.710. c(SiO 2 ) 71 to 80: cp < 0.333, a(B 2 O 3 ) = 1.470; 0.333 < cp < 0.5, a (B2O3) = 1.760-0.12/cp; l 1.6, a (B 2 O 3 ) = 1.710. Lead oxide: calculate y as above then select as follows: 50 < y < 80, a (PbO) = 2.685-0.0067 y; y > 80, a (PbO) = 2.350. Thermal expansion in 10~8 K'1

(20 to 400°C)

Silica: c(SiO 2 )<67, «(SiO2) = 3.8; c(SiO 2 )>67, c(SiO2) = 10.5-0.1 c(SiO2). Boric oxide: calculate ij/ = {c (Na2O) + c (K2O) + c (BaO) - c (A12O3) + 0.7 (c (CaO) + c (SrO) + c (PbO)) + + 0.3 (c (Li2O) + c (MgO) + c (ZnO))} /c (B2O3) then a (B2O3) = -1.25 i// except for xfj > 4 when the value is a(B 2 O 3 ) = -5.0. Lead oxide: a (PbO) = 13.0 for a) alkali-free glasses, b) alkali lead silicate glasses with X C ( R 2O) < 3> c) other glasses with E c (RO) + S c (RmOB)]/J] c (R2O) < 3; for other glasses not meeting conditions a) to c) it is a (PbO) = 11.5 + 0.5 X c (R2O).

31

1.2 Choice of Glass Compositions Table 1-4. Factors for calculating viscosity and room temperature thermal conductivity. Property Equation

Viscosity (1-2)

Thermal conductivity (1-1)

Unit of c{ Author

wt./wt SiO 2 Lakatos et al. (1976 b)

wt.% Iluss(1928)

A Li 2 O Na 2 O K2O MgO CaO ZnO BaO PbO A12O3 B2O3 (B 2 O 3 ) 2 SiO2 Constant (a0)

-3.180 -1.620 0.660 5.890 0.640 1.60 0.260 -0.500 -0.870 -4.650 16.27 — 1.713

B - 1 1 518 - 6 601 - 541 5 621 - 6 063 - 376.0 - 2 103 - 2 544 1 521 - 1 5 511 40 999 __ 6 237.01

To - 1 329 50.0 -236 -212 771 96.0 109 82.0 140 1203 - 2 765 — 149.4

10.70 13.40 4.55 8.80 8.65 11.85 11.70 6.25 3.70 3.00 -

_ 0.3448 0.3448 0.2564 0.2564 0.1695 0.1408 0.1000 0.3125 0.4255 — 0.4348 -

Viscosity The terms are summed to give the values of A, B and To to be put into the Vogel-Tammann-Fulcher equation, log(?//dPa s) = —A-\-B/(0 — 0o); note that there are both first and second order terms for B 2 O 3 . Thermal conductivity First calculate the notional volume percentage of each oxide from f f = 100 ct vt/Y, ct vn then sum the vi (1/Af) terms to obtain the reciprocal of the conductivity I/A'. To obtain the true room temperature conductivity (Wm" 1 K) take the reciprocal of this (Xf) and multiply by 418.7.

Young Modulus in kbar Silica: c (SiO2) < 67, a (SiO2) = 6.5; c (SiO2) > 67, a (SiO2) = 5.3 + 0.018 c (SiO2). Boric oxide: calculate cp as above and select as follows: 2, a(B 2 O 3 ) = 18. Surface tension in mNm~l

(1300°C)

* These oxides can have very variable effects on surface tension in different glass melts, even the sign of the term may change.

32

1 Classical Glass Technology

index. Weighting factors can be used to emphasize the influence of the most important properties. Indeed Westerlund et al. (1983) have taken the method two useful stages further. The first is to work with batch materials, not just glass composition; the second is to include raw material prices, allowing optimization of batch costs as suggested by Kiessling and Dressel (1979). 1.2.7 Choice of Raw Materials

Selecting the cheapest batch is not always the best choice because choice of batch can have very important effects on melting and glass quality which are not recognized by computer models. Nevertheless, the ability to examine the possibilities of savings in cost of the batch is a very useful tool and has been successfully exploited (Hatakka, 1986). As already indicated, choice of raw materials can have significant effects on ease of melting and glass quality as well as costs. Even though the commonest glasses use natural minerals and the cheapest of manufactured chemicals, the raw materials often cost more than twice as much as the fuel used in melting. This is a tribute to the efforts of the industry to achieve the most efficient use of the fuel and shows that using the cheapest raw materials is an attractive idea. However, this is not always the best choice. The overall melting cost depends on ease of melting and refining and the quality of the glass, also on furnace life. Sometimes a rather more expensive batch material proves worthwhile because of its influence on these other factors. West-Oram (1979) gave an extensive and very informative review of glass batch materials. Choice of batch materials may also be influenced by the need to control oxidation of the melt. For this purpose the Batch

Redox Number is often useful. Manring and Hopkins (1958) proposed that factors for oxidizing or reducing power could be assigned to each batch material and then summed in the traditional way to obtain a value that would describe the state of oxidation of the melt produced. These factors were based on a simple assumption about the reducing action of carbon but modified in the light of experience. The factors were given and their use also illustrated by Simpson and Myers (1978). The more recent modification of this concept in terms the chemical oxygen demand does not seem to have important advantages. Glass melting is discussed next. Here it is sufficient to note that what is called melting is complex and it is not always easy to predict what will produce the best result. The possibilities of including accurate predictions about melting, refining, or homogenizing in a computer data base are at present remote.

1.3 The Melting of Glasses 1.3.1 Introduction

It is important to recognize that glass makers do not use the word melting in its strict scientific sense; most glasses are melted at temperatures below the melting points of their major refractory constituent, most often silica. If a glass can be produced by normal melting that will nearly always be the preferred method on grounds of cost and scale of production: when it will produce a satisfactory product there is little reason to choose a more restricted and expensive method. However, alternatives to normal melting are very active research topics at present. Sol-gel and chemical vapour deposition techniques have important parts to play in high technology applications; these tech-

33

1.3 The Melting of Glasses

niques are usually expensive and limited to small scale production, they are discussed in the next chapter. It has often been said that sol-gel methods can save energy in the manufacture of refractory glasses, such as pure silica, because considerably lower temperatures are used and this is true when the energy consumption of only the final stage is considered. But when the energy consumed in making the starting materials for the sol-gel process is considered, that method is seen overall to use a great deal more energy and the prices of the raw materials demonstrate this. Similar statements are sometimes made about large scale electric melting. The efficiency of using the energy supplied in a well designed electric melting furnace should be more than twice that achieved in a good combustion heated furnace but the efficiency of using the energy in a well designed glass tank is considerably better than that achieved in a fuel fired electricity generating station. Therefore it is not generally more efficient to convert the thermal energy of gas or oil to electricity before using it. However, electric furnaces have other advantages for certain purposes, such as the melting of glasses containing some important volatile constituents, or if the electricity is produced hydroelectrically. Determining the economics of large scale glass production must consider all of the relevant factors including capital and running costs of the furnace. Electric furnaces are discussed in detail by Stanek (1977).

ing the raw materials at room temperature, heating them to these high temperatures but eventually cooling the glass produced to room temperature uses a great deal of heat much of which is apparently wasted. The efficient use of this energy must thus be examined. The energy required has two basic components, the heat of reaction and the sensible heat needed to raise the glass to the maximum temperature used. 1.3.2.1 Enthalpy of Reaction

Accurate data for glass melting reactions themselves are rare. It is therefore necessary to treat the glass as a mixture of appropriate compounds for which the basic data are available and assume that the heats of mixing of the silicate liquids are zero. Heats of mixing are not in fact zero but probably small enough for this procedure to be acceptable. For a simple sodalime-silica batch comprising carbonates one might use Na 2 CO 3 + SiO2 -• -+Na 2 SiO 3 + CO 2 T+2!iJ 1

(1-13)

Na 2 SiO 3 + SiO2 -> ->Na 2 Si 2 O 5 +zliJ 2

(1-14)

CaCO 3 -+CaO + CO2T

(1-15)

CaO + SiO2 -• CaSiO3 + AH4

(1-16)

The overall enthalpy of melting is then obtained by adding together the correct mole fractions of these energies to make up the correct glass compositions (1-17) AHM = nx AH1 + n2 AH2 + n3 AH3 + ...

1.3.2 Energy Requirements

Silicate glasses are usually melted at temperatures of around 1400-1600°C and forming operations need the melt to be held at a certain viscosity, which usually means temperatures of 1050-1200°C. Tak-

The data usually used and the methods of calculation employed are those given by Kroger (1953) and Kroger et al. (1958).

34

1 Classical Glass Technology

1.3.2.2 Sensible Heat Specific heat varies with temperature as well as composition so it is important to use the average over the proper temperature range. For glasses of the most common types the factors discussed in the previous section may be used. For many glasses the average specific heat to raise to melting temperature is close to l k J k g " 1 so that a rough estimate of the sensible heat is easily made. Calculations of this kind yield results similar to those given in Table 1-5 and some interesting observations arise from these values. First, the sensible heat considerably exceeds the enthalpy of reaction; when the glass is to be cooled again to room temperature this implies that energy could be saved by using as low a melting temperature as possible, for example, just above the liquidus, but this is a false conclusion. Second, it seems that lead crystal should be the easiest to melt of the glasses mentioned and this is true but the laboratory ware borosilicate is by far the most difficult to melt. Clearly the theoretical energy required for melting does not tell us about the ease of melting the glass. Ease of melting is determined by the kinetics of the important reactions and the dissolution of silica grains in essentially isothermal conditions is generally the slowest of these. Looking at the silica contents of these

Table 1-5. Theoretical heat required for glass melting inkJkg-1. Type

Lead crystal Borosilicate Container Flat

Heat of reaction 400 410 475 700

Total heat to raise to: 1200°
1500°C

1830 1820 2125 2420

2250 2250 2620 2940

glasses gives us a much better idea of how readily they melt; lead crystal has around 56wt.% SiO2 and Pyrex about 80wt.% SiO2 whilst the others will have about 72wt.% SiO2. Logic suggests that the use of raw materials which take part in exothermic glassforming reactions should be beneficial and some ingenious ideas based on the use caustic soda or soda-lime have been put forward from time to time, for example by Pugh (1968). Because of the exothermic reactions involving sodium hydroxide, it is dangerous to cast soda-rich glasses or fusions into water. However, the implied smaller enthalpy of melting is no guarantee of faster practical melting, quicker refining or better homogeneity, as shown by Cable and Siddiqui (1980). One of their findings was that mixing NaOH and CaCO 3 allows the reaction 2NaOH + CaCO 3 -> -> Na 2 CO 3 + Ca(OH) 2

(1-18)

to proceed almost to completion before any other begins. On the other hand, the major contribution of the sensible heat does mean that preheating of the batch can bring appreciable savings if it can be achieved. However, preheating must stop below the temperature at which the batch begins to react and form a sticky mass which will clog any apparatus in which it is reacting; this temperature can be below 500 °G 1.3.3 Preparations In both laboratory and large scale glass making it is a serious mistake to neglect batch preparation. The use of carefully prepared and homogeneous batch can have a great influence on the quality of the glass produced. It is not intended to discuss batch preparation and handling in detail

35

1.3 The Melting of Glasses

here, just to point out some of the important factors. Glass batches usually contain several, often seven or more, materials in a wide range of relative proportions and, perhaps, different particle sizes, which makes their mixing difficult. When these materials have a range of densities, shapes and frictional properties, it is difficult to achieve good mixing or, once attained, to prevent segregation before the batch is melted. Long mixing times, such as often used in the ceramic industry, are rarely desirable. There is ample evidence that the quality of the batch put into the furnace has an important influence on the quality of the glass produced. Even if the batch is well mixed some tendency to segregation during melting is inevitable. Much thought and experience goes into the design and operation of a successful batch mixing, transport and charging system on an industrial furnace. On a laboratory scale care over accuracy of weighing out materials, mixing and preventing segregation is equally beneficial. It can be claimed that the scientific principles of mixing solids are reasonably well understood and largely concern generating random diffusive motion in an assembly of particles. This can only occur when the particles are already in motion caused by stirring or tumbling the bulk of the material. However, the theory is little help in practice when particles having very different properties are concerned. Different sizes, shapes, and so on mean that different particles always have some tendency to behave differently under the influence of gravity. Hence the motion which is being used to achieve mixing always has some tendency to provoke segregation at the same time. It is easy to mix glass batch too long or to cause segregation by vibration or free fall between mixing and charging into the furnace. Deliberate addition of a

few percent of water can be very helpful in retarding batch segregation. Papers by Poole (1963) and Fletcher (1963), together with several others in the same issue of Glass Technology give some very useful insight into these matters. 1.3.4 The Stages of Melting Glass melting comprises a number of rather complex stages in which different physical and chemical phenomena predominate. It is therefore useful to consider it in several stages but it must never be forgotten that these overlap in time and space and considerably influence each other. Figure 1-11 shows the most useful way of dividing the whole process; each of these stages is considered in the sections that follow.

1500 i -

Q

Temperature

1000 Dissolve sand | BAICH-hHLb

• /I

500 -

"Ij\

Remove bubbles ~|SEED-FF

Homogenize

I 2

3

Time in h

Figure 1-11. Schematic diagram of the stages of glass melting. Region (i) is where the batch has not yet reached reaction temperature and (ii) shows the time occupied by vigorous reaction.

1.3.4.1 Batch Heating Melting reactions can be detected in common silicate batches at about 400 °C

36

1 Classical Glass Technology

but usually are not sufficiently rapid to be important until the temperature reaches about 600 °C. Some subsidiary processes, such as evaporation of moisture or the melting of minor constituents with lower melting points, may of course take place at lower temperatures. Glass batches are largely made from materials with poor thermal conductivities and the question of how to heat the batch deserves examination. This may be confirmed by taking a simple example. Suppose that a furnace is producing 120 tonnes of glass a day, which is equivalent to supplying 100 kg of batch per minute, and that the batch is charged as a continuous blanket 4 m wide and 0.15 m thick which hence must advance at a rate of 0.083 m min" x . If this were a slab of solid material with both of its surfaces suddenly heated to 1400 °C the time for its centre to reach 600 °C by simple conduction would, according to the classic theory, be given by at/I2 = 0.33. Here the half thickness / is 0.075 m and the thermal diffusivity of the batch may be estimated at about a = 2.8 x 10~7 m 2 s" 1 . The time needed for all of the batch to begin to react would thus be about HOmin during which time the blanket would advance 9.2 m down the furnace and it might travel as much as 20 m before melting was complete. This is clearly a serious overestimate of the length of furnace occupied by melting batch. Several factors cause this serious error. First, the thermal properties of the batch vary with temperature, largely due to them reacting; second, the batch blanket does not remain of constant thickness as reaction occurs; third, flow of liquid produced by reaction and convection of hot gases can both increase the rate of heat transfer. Jack and Jacquest (1958) studied the implications of the simple constant property model considered above and showed that

minimum melting length would be given by a particular blanket thickness for a given output. Measurements by Ito et al. (1954) in a layer of batch 150 mm thick charged on to a melt in a pot 1 m in diameter found that it took 60 min for all of the batch to reach 1000°C and thus react vigorously: our simple model predicts that it should take about 200 min for the centre to reach 1000 °C. Daniels (1973) found that the centre of a batch layer initially 40 mm thick charged on to glass at 1400°C reached 1000 °C in 24 min. Comparing these two observations suggests that the rule of time proportional to square of thickness expected for simple conduction in a solid does not apply to melting batch: if 24 min were correct for 40 mm one would predict 340 min for 150 mm. It is difficult to measure the thermal properties of reacting batch but some useful data were obtained by Kroger and Eligehausen (1959) who measured the temperature difference between the inner and outer walls of an annular space filled with batch when it was heated by a central axial heating element. When operating at steady state this is a standard method for determining conductivity; the energy input gives the heat flux and the measured temperatures allow the thermal conductivity to be calculated. Several important bold assumptions are made in applying exactly the same simple analysis to reacting batch but the data obtained are the best estimates that we have. Figure 1-12 shows the general trends found for measurements made during both heating and cooling after the batch had been converted to glass. The values for the latter are more influenced by radiant transfer. It can be seen that the apparent conductivity of batch changes little until reaction begins but then increases rapidly as temperature rises.

37

1.3 The Melting of Glasses

This brief discussion should have demonstrated that, although rarely discussed in the literature, how to charge batch into a large scale furnace to get the most rapid melting and also minimum melting segregation is a complex question of considerable importance. Batch is a good insulating material which greatly restricts heat transfer into the melt below it and thus to the under side of the batch layer. Covering the whole of the melting area with a uniform layer of batch may give the thinnest batch layer, which by itself should accelerate melting, but seriously restricts the melting of the bottom of the batch layer unless a powerful convection current of other energy source beneath the batch layer provides the necessary heat input. Optimizing the extent of cover of the melting area by batch piles, logs or blanket is a subtle matter. There is some discussion of this topic in Trier (1984). Some electric melting furnaces, for example the Gell type, rely entirely on the insulating properties of the batch to prevent heat loss from the top of the melt (Gell, 1956). 1.3.4.2 The Initial Melting Reactions

The rates at which the various materials in a batch tend to react together depend on temperatures as well as time. It is, of course, essential for the reacting materials to be in contact with each other and good contact cannot be guaranteed until some liquid has formed and is able to percolate around the solid grains still present. If the initial reactions occur in the solid state their particle sizes and efficiency of mixing must be important; reactions occurring at a solid surface must depend on the surface area available and thus on particle size. Varying the particle size for a given rate of heating can thus affect the extent to which some of the possible reactions occur. The

200

400

600

800

1000

1200

1400

Temperature in °C

Figure 1-12. Estimates of the apparent thermal conductivities of reacting batch during heating and of the glass produced; after Kroger and Eligehausen (1957).

dependence of reaction rates on temperature also means that behavior can be modified by rate of heating. We have already seen that different parts of a batch layer cannot all be heated at the same rate, so some complications may be expected for that reason. As a result one cannot produce one reaction scheme which will always apply in a particular system and this is the reason for some of the discrepancies between the findings of different authors who have studied similar batches but used different methods or conditions. This is easily illustrated for potash-red lead-sand batches. Figure 1-13 shows the average reaction paths found for two somewhat different compositions in this system. There is no reason why the earliest reactions should have been greatly influenced by the difference in final glass composition, yet the results shown suggest this. However, both sets of results may be described fairly well by assuming the following general scheme: 1) All the potash reacts to form a potassium silicate. 2) This potassium silicate reacts with the red lead.

38

1 Classical Glass Technology Si0o

PbO

Figure 1-13. Average compositions of the liquid phase during melting of lead crystal glass according to Rosenkrands and Simmingskold (1962) and Bezborodov and Appen (1933). Idealized reaction sequences are shown dashed. The two investigations used different experimental methods, see text.

3) The potassium lead silicate dissolves the remaining silica to achieve the final glass composition. The important difference is in the composition of the potassium silicate first formed. According to Rosenkrands and Simmingskold (1962) it is the metasilicate, K 2 SiO 3 , but Bezborodov et al. (1933) found it to be the tetrasilicate, K 2 Si 4 O 9 ; the difference is explained by the experimental procedures used in the two cases. Rosenkrands and Simmingskold took small samples from a typical large pot melt being made in normal conditions but Bezborodov et al. used heat treatment of laboratory samples in 100 °C steps from 200 °C to 1200°C, keeping the sample at each temperature long enough for reaction to have almost ceased. This clearly explains why their results show much more silica reacted in the early stages than those of Rosenkrands and Simmingskold. Both sets of experiments agree about the main points: reaction first produces whatever product is most easily formed (a potassium silicate) which then undergoes a further se-

quence of reactions, ending with the slowest step (dissolving residual silica). Melting inevitably produces a range of compositions which can differ greatly in composition, density and viscosity and thus may easily segregate. Mixing these to make a homogeneous glass can be difficult, especially if density and viscosity difference have encouraged serious melting segregation. Few books discuss glass melting reactions; Bezborodov (1968) is a notable exception. If one or more of the raw materials, early liquid phases or the final melt has a strong tendency to lose a component by evaporation this can aggravate the difficulties of producing a homogeneous melt. Alkalis, sulphur, lead, boron and halogens are amongst the most volatile constituents. The kinetics of volatilization can be influenced by several factors including diffusion in the melt, transport in the gas phase and reaction with the atmosphere, see Cable (1978). Laboratory Studies The discussion above compared results obtained in the laboratory with some typical of industrial practice. The former type of experiment is convenient when it can be employed but, as we shall see, does not yield all the information that would be helpful. However, direct experiment on an industrial scale is difficult to organize and control and also very expensive, especially when the results are not directly beneficial. There is therefore a role for both the application of standard laboratory techniques and for empirical melting studies: both are needed to obtain the maximum insight that can be expected. The most obviously useful laboratory techniques are thermogravimetric analysis (at constant temperature),

1.3 The Melting of Glasses

differential thermogravimetry (with steadily rising temperature) and differential thermal analysis or its close analog differential scanning calorimetry. Thermogravimetry records only weight changes and so can record decomposition of carbonates, sulphates, nitrates and so on but cannot identify the fraction of silica reacted. Differential thermal analysis or scanning calorimetry are more versatile because they record evolution or absorption of energy, whatever its cause, but they likewise do no directly identify the process concerned. Constant temperature thermogravimetry should be the simplest kind of experiment to interpret and approximate theoretical models for solid state reactions in two component systems are available. Three are well known and widely used, the Jander model, the Ginstling and Brounshtein model and the Valensi- Carter model. Jander's (1927) equation was based on a qualitatively correct analysis of diffusion between two flat slabs of reacting solids which maintain constant volume. The important feature being that control by diffusion would make the thickness y of the flat layer of reaction product increase as y2 = kt

(1-19)

If the spherical shell on an idealized particle of radius a0 is assumed to behave like a flat slab and a is the mass fraction reacted, this transforms into [l-(l-a)ll3]2

= kt/a20

(1-20)

When examined quantitatively for a sphere the equation becomes /n)Dt/a2

(1-21)

where q> is the effective solubility; note that it appears as cp2.

39

Ginstling and Brounshtein (1950) improved this model to take the spherical symmetry into account but their analysis still ignores the motion of the boundary and any change in volume of the system and yields l-(2/3)a-(l-a)2/3 =

(1-22)

The Valensi-Carter (Valensi, 1935, 1936, 1950; Carter, 1961 a, b) model does allow for a change of volume as well as spherical or cylindrical symmetry. For spherical particles it gives [1 + (z - 1 ) a] 2 / 3 + (z -1) (1 - a) 2/3 = = z + 2(l-z)(pDt/a2 (1-23) where z is the volume of product per unit volume of the material in the sphere. The limited validity of all these equations has recently been examined by Cable and Frade (1991) who conclude that they are useful for seeing whether a reaction is diffusion-controlled but not at all suitable for estimating other parameters such as diffusivity. No good models exist for multicomponent systems or for ones with liquid present, where convection of that liquid is very likely to affect the reaction. Neither do any satisfactory theories exist for differential thermogravimetry. The main use of this kind of experiment is to indicate the temperature ranges where various reactions may be rapid and to amplify the information available from differential thermal analysis. In principle the area under the peak of a differential thermal analysis trace gives the quantity of heat evolved or absorbed. In practice it is extremely difficult to establish the base line with sufficient accuracy to make quantitative evaluation possible, largely because the thermal properties of the material change whilst it is reacting and the sample may also either swell or shrink at the same time. It is easy to show that better accuracy may be ex-

40

1 Classical Glass Technology

pected when a small sample is used and modern sets of apparatus are therefore often designed for no more than 50 mg. However, when one considers the size of particle often used in glass batches and the complexity of the mixtures concerned, it is clear that obtaining an accurate and reproducible result is by no means easy especially if it was intended to investigate the effects of minor constituents. Very finely divided powders must be used and one is thus unable to study the known effect of particle size on reaction kinetics with such apparatus. The latest improvements in the apparatus have not, in fact, helped workers studying reactions in glass or ceramic systems. One of the classic investigations of reactions in the soda-silica system is the differential thermal analysis work of Wilburn and Thomasson (1958, 1960). The second part of this investigation was concerned with the influence of minor additions on sodium carbonate-silica reactions. These workers necessarily used small samples and finely divided materials which were heated at 10 °C a minute. Their results for the basic system indicate differences according the particle size. Their main findings were that an endothermic reaction can begin around 550 °C, possibly influenced by but not due to the quartz inversion at 573 °C; that there is an important exothermic reaction at about 700 °C and an endothermic reaction at 780 °C. Glass was only detected (by the presence of an annealing peak) in samples heated to above 780 °C which agreed with the formation of some eutectic liquid. With coarser materials (0.156-0.210 mm) the main loss of CO 2 occurred at about 850 °C, the melting point of sodium carbonate, thus suggesting only limited solid state reaction in that case. The second paper investigated the effects of NaF, NaNO 3 , (NH 4 ) 2 SO 4 , and Na2SiF6

on Na 2 CO 3 -SiO 2 reactions. They found that the main effects could be summarized by putting each material into one of three groups: 1) Production of a liquid at a lower temperature by eutectic melting of the minor addition with sodium carbonate (NaCl, NaF, Na 2 SiF 6 ); 2) Reaction between the minor component and a major one producing a new compound which might or might not assist melting ((NH 4 ) 2 SO 4 , Na 2 SiF 6 ); 3) the minor phase melting to form a liquid at a lower temperature (NaNO3). Other studies of this kind were reported by Wilburn et al. (1965). Such work is evidently very useful but far from sufficient to reveal everything about glass making reactions. Devising other experiments that will reveal useful information is often a greater challenge than making the experiment. Cable and Martlew (1971, 1984, 1985, 1986) studied the corrosion of silica rods by a variety of liquids, and found that adding relatively small proportions of silica to molten sodium carbonate evolved proportions of carbon dioxide equivalent to the formation of the metasilicate, Na 2 SiO 3 . The various results available suggest the following kind of scheme as a basic model but it does not always show the exact sequence of reactions even in this apparently simple system. Na 2 CO 3 zSiO 2 (1-24) Na 2 O SiO2 + CO 2 t + (z - l)SiO 2 N a 2 O S i O 2 + ( z - l ) S i O 2 -+ -» Na 2 O • 2 SiO2 + (z - 2) SiO2

(1-25)

Na 2 O • 2 SiO2 + (z - 2) SiO2 -> (i _26) -> Na 2 O • n SiO2 + (z - n) SiO 2 , n « 2.5 Na 2 O • n SiO2 + (z - n) SiO2 -> -• Na 2 O • p SiO2 + (z - p) SiO2

(1-27)

1.3 The Melting of Glasses

Na 2 O • p SiO2 + (z - p) SiO2 -• Na 2 O • z SiO2

(1-28)

The value of n in the above equations may be the disilicate-silica eutectic composition and p the composition of liquid in equilibrium with silica according to the phase diagram (see below). This range of liquids differs considerably in density and viscosity so that segregation under the influence of gravity may easily occur. There may also be a definite tendency for undissolved silica to float to the surface of the melt. Of course these reactions overlap in time and space so that it may be very difficult to identify them beyond the second step. A recent study of melting reactions in 3 g soda-lime-silica batches by Sheckler and Dinger (1990) found a complex series of reactions clearly sensitive to silica particle size, when mixed with very fine soda and limestone but, they, unfortunately, do not specify their rate of heating which was probably 10 °C per minute. The samples were held for 5 minutes at each of seven temperatures from 775 to 865 °C and cooled for examination. Silica was the only compound to persist throughout this range but numerous others had a transient presence. For example, some double sodium calcium carbonate was always formed yet sodium disilicate was present only up to 790 °C and wollastonite occurred above 805 °C but only with the finest grade of silica (< 53 |im) in both cases. On the other hand, Na 2 O • 2CaO • 3SiO 2 formed towards the top end of the temperature range with all three grades of silica used. An intermediate carbonate, 5 CaO • SiO2 • CO 3 , was found for two grades of silica but not the finest. The authors correctly conclude that no existing model of melting can correctly predict the behavior to be found in even a relatively simple three component system. This behaviour depends on heating

41

rate (which cannot be uniform throughout a typical volume of batch) as well as on particle size. Most batches contain more sand, usually the most refractory constituent, than any other component and this must be dissolved by the liquid phase or phases. Dissolving the quartz which did not react during the early vigorous reactions often occupies the majority of the batch-free time. The dissolution of residual silica is normally controlled by diffusion in the melt with equilibrium conditions at the silica-melt interface (Kreider and Cooper, 1967; Hlavac and Nademlynska, 1969). Thus, even if the rest of the liquid were homogeneous, this would produce inhomogeneities in the form of silica-rich haloes around each sand grain, see the photographic demonstration of this by JebsenMarwedel (1956) and by Cable and Bower (1965). Figure 1-14 indicates what happens in the simple binary soda-silica system. Suppose that we choose to melt a glass with 34% soda at 1400 °C. The phase diagram shows that the liquid in contact with the sand grains will contain 12.7% Na 2 O and the concentration difference driving dissolution will be equivalent to Ac = 213% Na 2 O. Even when all the sand grains have just disappeared the melt must contain regions of compositions covering at least the range from about 13 to 35% Na 2 O. One useful way of minimizing the problem of silica dissolution is to use silicate minerals like feldspars or nepheline syenite to decrease the proportion of silica that must be supplied as quartz. This also has the advantage of decreasing the amounts of alkali that must be added as the expensive carbonates. It is usually a mistake to use oxides as raw materials simply to save the trouble of doing the necessary batch calculations because many of those that are stable (e.g. MgO, A12O3) are

42

1 Classical Glass Technology I 1600

I

I

I

I

I

I

j

-

AC _y

1400

/ /

o 1200

-

1000

-

CD Q.

I

\

V

800 I

I 40

I

i 60

I

| 80

100

wt. % SiCL

Figure 1-14. The driving force for dissolution of residual sand grains in a binary melt with 34% soda when melted at 1400 °C, assuming equilibrium at the silicamelt interface.

One of the most notable contributions not mentioned is that of Kroger who, with his colleagues, made a detailed thermogravimetric study of reactions in soda-lime-silica batches between 1933 and 1957. Some of the problems encountered in such work may be illustrated by a brief examination of Kroger's work. Such experiments reveal how quickly the carbonates decompose but nothing directly about the reaction of the silica or other refractory oxides. The only theoretical models available to interpret the results were the admittedly approximate equations derived for solid state reactions in binary systems which are often acceptable up to about 50% mass fraction reacted but not beyond (Frade and Cable, 1991 a). These did not fit Kroger's data which were for three component mixtures and reaction in the presence of liquid but he found that the following equation generally yielded straight lines, (1-29)

not at all reactive; materials that decompose on heating together are much more suitable. The above example shows that further mixing and diffusion beyond the batch-free time will be essential to produce homogeneous glass. Unfortunately diffusivities are low and mixing by diffusion alone will be effective only over distances of fractions of a millimetre even after many hours. Flow can stretch and intermingle different layers and considerably accelerate mixing; this is discussed under homogenizing. This brief discussion does scant justice to the work of numerous other experimenters who have studied various aspects of glass melting reactions but the processes are so complex and our theoretical framework for trying to understand them so inadequate that it is impossible to give an informative brief summary of their work.

He showed that this equation is equivalent to assuming

= k'l(yt)

(1-30)

but did not further justify this model. However, quite a lot of results showed an inflexion, and it may be very misleading to assume that this indicates a change in the reaction. This empirical analysis was however useful in demonstrating the temperature dependence of reaction rate and the sudden increase in it as soon as eutectic liquid has formed. Estimating how much silica has reacted is a difficult task. Some workers have attempted to do this by measuring the size of the differential thermal analysis peak due to the quartz inversion but this is not easy to make quantitative. Azm and Moore (1953) used an X-ray diffraction method to follow reactions in several soda-lime-silica

43

1.3 The Melting of Glasses

batches at temperatures between 900 and 1400°C, see Fig. 1-15 and confirmed that initial reaction is rapid even at 900 °C but at that temperature becomes extremely slow once about half the silica has reacted. Raising the temperature accelerates the initial reaction but, more important, increases the proportion of silica which reacts quickly. It is interesting to note that the liquidus temperature of this glass is about 1040 °C and that its primary crystalline phase is devitrite but it is near to the /J-wollastonite border; when a considerable proportion of silica has yet to dissolve it might produce Na 2 O 2CaO • 3 SiO 2 . This does not mean that it would be impossible to react all the silica at temperatures below 1040 °C but such reaction would be accompanied by the formation of one or more of these crystalline phases and such a reaction would proceed only slowly. This doubtless explains why the extent of reaction after 48 h was only about 57% at 900 °C and 78% at 1000°C but had risen steeply to 98% at 1100°C. From what we have already seen the course of reaction does not involve just one simple step; not surprisingly, Azm and Moore failed to find a simple model to describe the overall kinetics. More insight was shown by Botvinkin (1936) than some other workers when he suggested that one might be able to describe the progress of reaction by a modified boundary layer model

da/dt=DAt(CEQ-Ct)/S

(1-31)

where D is diffusivity, At the surface area of silica available at time t, CEQ the equilibrium silica concentration at the relevant temperature and Ct the actual concentration of silica in the liquid at time t. However, this still leaves some problems over the value of CEQ for a complex glass and determining At as well as severe complications in trying both to estimate Ct and to

1300°C

1200°C

10

20

30

40

50

Time in h

Figure 1-15. Variation of fraction of quartz reacted with time in small melts of a sodium carbonate-calcium carbonate-sand batch (11.2% Na 2 O, 10.0% CaO) at different temperature; Azm and Moore (1953).

predict the boundary layer thickness S. Today this remains a very difficult field in which to make sound theoretical progress, even for interpreting simple model experiments like those of Cable and Martlew (1971, 1984a, b, 1986). Empirical Melting Studies Because of the difficulties pointed out above, there is a place for observations made directly on glass melts. Whenever complex phenomena can be observed, seeing what happens (or appears to happen) can be a powerful stimulus to thought and understanding. Relying only on instruments which give strictly limited and predetermined information can be misleading. Simple qualitative and quantitative experiments involving batch melting thus have a useful role to play. One of the most important questions to be asked of any experiment is how to scale up the results to predict what will happen on a large scale. This

44

1 Classical Glass Technology

is impossible with standard laboratory methods of thermal analysis. It might be possible if melting were studied on a range of melt or batch charge sizes. The experiment recognized as useful to some degree by all glass makers is the batch-free time. This is simply the time needed to dissolve all of the original batch ingredients, silica usually being the slowest to dissolve completely. Because of the poor heat transfer properties of batch, if for no other reason, batch-free time must depend on the size of the sample. Another factor determined by the size of the sample is the influence of the gases evolved during reaction on the atmosphere in which melting effectively occurs. In a reasonably large sample the atmosphere is determined almost entirely by the gases given off by the reactions. However, with a very small sample mixing of these gases with the surrounding atmosphere may be so quick as prevent this. Where the influence of atmosphere is not important samples as small as 1 g may give useful information but, if the atmosphere and oxidation of the melt do matter, samples weighing less than about 50 g are not likely to give useful information. One obvious problem with measurements of batch-free time is the tendency for segregation to occur and another the sticking of some silica grains to the crucible walls above the level of the melt or the floating of some grains on the surface around the meniscus. In both cases those grains may take much longer to dissolve than any others and they should be discounted. Potts et al. (1944) used a slightly inclined furnace and rotated the melt so that grains near the meniscus were washed down and stirred into the melt, thereby decreasing the scatter of the batch-free time measurements. In one of the early classic investigations Preston and Turner (1940) showed a simple

linear relation between sand grain size and batch-free time which can be interpreted in the following disarmingly simple but inexact way. Assume that the inverse of batchfree time gives the average reaction rate just as the total surface area of a given mass of similar shaped particles is proportional to the inverse of particle size; the observed linear relation, with an intercept close to what can be justified by the time to heat to reaction temperature, can thus be taken to mean that rate of reaction is proportional to the surface area of silica available. This seems to be an unexceptionable conclusion but is not generally valid as shown by the other classic series of experiments by Potts (1939, 1941) and his colleagues at Owens Illinois (Potts et al, 1944). They found that batch-free time can go through a minimum when particle sizes are varied, the minimum being where all particle sizes are matched, see Fig. 1-16. The increase in batch-free time seen here for very fine sand was not observed by Preston and Turner because they used very finely divided chemical reagent sodium and calcium carbonates so that their silica was always coarser than the other materials. That the increase in batch-free time for very fine silica was largely due to segregation and inadequate contact between different types of particle is supported by results of Manring and Bauer (1964) whose experiments with dry batches also showed such a minimum but when water was added, so that soda-rich solution could coat all the sand grains, the minimum disappeared and the finest sand again gave the shortest batch-free time as shown in Fig. 1-17. Interesting experiments by Boffe and Letocart (1962), who used graded sands, showed that the real behavior is quite complex. The average rate of the initial reac-

1.3 The Melting of Glasses !

I

I

I

I

I

Sand

/ 300 -

/

Lime //

/ 200

/

Soda

/ /

/

/

•

s Cd CQ

-

100 -

I

0

0

I 0.2

I

I

0.4

I

I

0.6

Average particle grain size in mm

Figure 1-16. The effect of varying one at a time the particle sizes of the three raw materials on the batchfree times of small melts of a soda-lime-silica glass at 1427 °C; after Potts et al. (1944).

45

tions must be approximately proportional to the surface area of silica available but the final stage of dissolving the last few silica grains must depend on the size of the largest grains, even if there are only a few of them. Hence batch-free time is not always a simple function of either surface area of silica or of average particle size, as shown in Fig. 1-18. Hot stage microscopy can be very informative. Thus Manring et al. (1964) showed that molten sodium carbonate can prefer to wet cullet rather than sand grains and this led them to make some suggestions about how cullet should be charged into a furnace. In glass melting studies it is often much more difficult to devise a useful experiment than to carry out experiments by one of the standard but not very relevant laboratory methods. 1.3.4.3 Refining

A typical batch to produce 100 kg of glass weighs about 120 kg and thus evolves around 20 kg of combined gases during

sz o 05 CQ

10 -

0

0.2

0.4

0.6

Average sand grain size in mm

Figure 1-17. Comparison of batch-free times at 1482 °C of dry and moist batches of a soda-silica glass (25.6% Na 2 O) when using different sand particle sizes with a constant soda fraction (about 0.256 mm); after Manring and Bauer (1964).

Specific surface in m 2 kg' 1

Figure 1-18. The relation between specific surface of silica and batch-free time for melts made using graded sands. The anomalous values near the middle of the diagram are for sands containing small proportions of large grains; after Boffe and Letocart (1962).

46

1 Classical Glass Technology

melting. The majority of this gas is carbon dioxide from carbonates which, at a melting temperature of 1400 °C and 1 atm, occupies nearly 1500 times as large a volume as the melt produced. It cannot be surprising that vigorous gas evolution during the early stages of melting sometimes causes a melt to boil over the pot which contains it. Much of this gas is given off at somewhat lower temperatures during the course of the batch reactions and it provides the majority of the atmosphere in which the glass is produced. The presence of oxidizing or reducing agents in the batch can therefore have a considerable effect on the degree of oxidation of the freshly made melt. Much of the gas escapes easily by forming large bubbles which coalesce and quickly reach the surface where they burst. However, when the vigorous reactions have ceased the melt contains some residual dissolved gases, but may not be saturated with them, and also a considerable number of smaller bubbles some of which cannot rise rapidly through the melt. Refining is the elimination of these bubbles which are only easy to study beyond the batch-free time. Many melts contain less than 1 vol.% of bubbles at the batch-free time but the average size may be less than 1 mm and the number sufficient to make the glass almost opaque. Several factors influence the number of bubbles and their size distribution but a fairly typical number at the batchfree time would be 500 per mL, and the size distribution would range from about 25 jam up to 1 mm diameter. These small bubbles are called seed and normally represent a very tiny fraction of all those produced during melting. Bubbles bigger than about 2 mm in diameter are called blisters. The number and size distribution depend on the type of glass, choice of batch materials, refining agents used and size of sand

grains as well as melting temperature and size of melt. It is not easy to observe bubbles in a melt at high temperature so the majority of our information about refining is based on measurements made on samples cooled to room temperature. Such samples have to be prepared with care if reliable information is to be obtained from them. One of the main problems concerns relaxation of the glass during cooling. Near to melting temperature the viscosity of the melt is sufficiently low for a bubble to expand or shrink to maintain equlibrium internal pressure as temperature changes. Thus, assuming ideal behavior,

PiVJT1=p2V2/T2

(1-32)

or, if x is the diameter of the bubble, Pixl/T1=p2xl/T2

(1-33)

The pressure in the melt outside the bubble will be only slightly higher than the external atmosphere pressure p0 because the hydrostatic head will be small, so Eq. (1-33) may be written

•2a/pox2)xl/T2

(1-34)

Only if the bubbles are less than about 50 jim in diameter does surface tension a have a measurable effect on their behavior. Many bubbles will therefore maintain equilibrium pressure and shrink according to x 2 /x 1 = (T2/T1)1>3

(1-35)

On cooling the melt will eventually become too viscous for flow to occur and the bubble becomes frozen into the effectively solid glass. The size will now remain almost constant on further cooling but the internal pressure will change according to •2a/pox)/T2

(1-36)

1.3 The Melting of Glasses

The viscosity at which the glass becomes effectively solid in this respect is near the upper end of the annealing range and bubbles containing non-condensable gases usually have internal pressures close to 0.30 atm at room temperature. Figure 1-19 shows the behavior expected of bubbles on cooling provided there is no reaction of the contents with the surrounding glass. This question has recently been examined in detail by Cable and Frade (1991). If glass is cast then quenched below the annealing range some bubbles can behave in a startlingly different fashion. Consider a sphere of glass 100 mm in diameter which is rapidly cooled to room temperature and which before cooling contained one tiny bubble near its centre. The outer skin of the sphere may become solid at about 500 °C when the average temperature of the still fluid interior is perhaps 750 °C. As the sphere cools further the inner core is still able to flow under stresses down to about

500 °C, by which stage it will have wanted to contract by about an additional 4.6 mL (taking the volume coefficient of thermal expansion to be 3.5xl0~ 5 ). The glass is close to incompressible so that the sphere should be highly stressed, tensile in the centre and compressive on the outside, unless now annealed. However, since it contains a seed near the centre, the work needed to expand this is much less than the stored strain energy, so the bubble is expanded and its internal pressure decreases as the glass relaxes and much of the stress is relieved. This is why Rupert's drops sometimes contain relatively large bubbles. Only bubbles nearest the slowest cooling part of the glass are expanded in this way. Of course the real behavior is more complex and the volume of the bubble perhaps no more than a third of the volume estimated. The Role of Buoyancy in Refining Rise to the surface is the most obvious way in which seed might be removed once the vigorous melting reactions have stopped. Jebsen-Marwedel (1936) used model calculations for a typical range of bubble diameters, temperatures and viscosities, to show that it was doubtful whether this could be the only mechanism at work. Stokes's law is one of the classic exercises in hydrodynamics and shows that the terminal velocity Vs of an isolated solid sphere of diameter x in a large body of liquid is given by

Pressure

1.0 -

Vs=(l/lS)(Ql-Q2)x2g/r1 400

800

47

1200

Temperature in °C

Figure 1-19. Approximate changes in size and internal pressure in a bubble in a body of glass which is being cooled relatively slowly.

(1-37)

where QX and Q2 are the densities of solid and liquid and g is gravitational acceleration. Jebsen-Marwedel plotted a very clear diagram showing how this velocity varied with temperature and bubble diameter for a typical viscosity-temperature relation.

48

1 Classical Glass Technology

Bastick (1956) took this argument one step further by demonstrating that measurements of how total number of bubbles varied with time yielded a temperature dependence steeper than that predicted by allowing for the known changes in viscosity of the melt and variation in size of a bubble according to the perfect gas laws, see Fig. 1-20. Note that Bastick extrapolated his measured data back to a common

100

200

300

400

Time in min

Figure 1-20. Variation of rate of refining with temperature according to Bastick (1956). The rate changes more steeply with temperature than would be expected from the known dependence of viscosity.

intercept at zero time but, although this is an interesting observation, it is an unwise thing to rely on because the phenomena occurring during the shortest times (batch heating and gas-evolving reactions) are clearly different from those occurring later. Bastick used the slopes of the lines in his figures to show that combining Eqs. (1-35) and (1-37) would lead one to expect rate of disappearance by rise to the surface to be given by

= (im(Ql-Q2)x2g/t1 = = kx(T)2/r,(T)

(1-38)

Putting in the known variation of glass melt viscosity rj1 and x(T) showed that k was not a constant but increased as temperature rose. A possible explanation is

that the refining agents present made bubbles expand more than expected, thus increasing doubts about the role of rise. The fact that the Rybczynski-Hadamard analysis for a fluid sphere shows the terminal velocity (FB) of a fluid sphere of very low viscosity in a liquid of much higher viscosity to be given by VB = (3/2) Vs= (1/12)(Q 1 -Q 2 )x 2 g/f 1

(1-39)

does not affect this argument. Hornyak and Weinberg (1984) confirmed that bubbles in a glass melt obeyed Eq. (1-39). Hearing Bastick describe these experiments and his deductions from them led Cable (1958) to make similar experiments which then included measuring the size distributions of the seed as well as their total numbers in all samples. He reasoned as follows. The spatial distribution bubbles of particular size must be close to uniform at some time soon after the vigorous reactions have finished but before the batchfree time. Bubble formation may not cease until the melt is batch free but may be assumed unimportant from this time onward. If the melt is static all bubbles will rise towards the surface at a rate given by Eq. (1-39), so that the fraction disappeared at any particular time will be in proportion to the distance risen divided by the depth of the melt h. If the number of bubbles of a given size present per unit volume at the assumed beginning of the process is n 0 , the decay in number at longer times should be

n = no(l-k'x2t/h)

(1-40)

k! being obtained from Eq. (1-39) with t measured from the time when the random spatial distribution existed. When a range of sizes is present the total number of bubbles should be obtained by summing Eq. (1-40) for all sizes,

N=Yno-{k'lh)tY o

o

(1-41)

1.3 The Melting of Glasses

49

As indicated the summation must be made only for the sizes still remaining and cut off at

c' = (*/W 2

(1-42)

Bubbles obeying such a law could easily produce an exponential decay of total number with time as the average size and average rate of disappearance will both decrease with time. However, analysis of the recorded data shows the relation between n and t not to be linear but closer to log n = log n0 — b t

C/)

c o

(1-43)

Since d(logn)/dt = (l/n)(dn/dt% the predicted slope of such a graph should be b = x2/[h/k-x2t]

(1-44)

Figure 1-21 shows the predictions of this equation for appropriate times together with two sets of experimental data. It can be seen that bubbles large enough to disappear by rise and bursting do so but smaller bubbles disappear faster than expected and the discrepancy gets larger as the size becomes smaller; there is no indication that rate of disappearance approaches zero for x = 0 and rate of disappearance is, fortunately, less sensitive to bubble size than this theory indicates. Also note that the general features of the behavior are very similar for melts with and without refining agents. This model ignores convection of the melt. Horizontal velocities would affect the path followed by a bubble but not the time taken to rise to the surface but vertical velocities will affect time to rise and be able to burst at the surface. The internal circulation caused by thermal convection in a pot or tank must therefore have some effect. However, any flow system in a pot or crucible must have as much downward flow as upward and it is difficult to see how

0

0.1 Seed diameter in mm

Figure 1-21. Comparison of calculated rate of disappearance at 1400 °C of seed by rise to the surface (shaded area) and actual observations in small melts of a soda-lime-silica glass: without (•) and with (•) refining agent (0.50% As2O3); after Cable (1960).

thermal convection would accelerate the removal of most bubbles. Another possible mechanism is coalescence which is evidently important whilst the vigorous early reactions take place but is most unlikely to occur in such viscous liquids when small bubbles are on average a considerable number of diameters apart. Refining agents, that is minor constituents added to the batch to accelerate refining, have been known for a long time. The most important are sulfates, arsenic oxide, antimony oxide, and halides, especially chloride. Sulfate is the most used today. If refining were governed by rise to the surface they could only act by either affecting the density and viscosity of the melt or by making the bubbles bigger. At the levels used (< 1%) their effects on the properties

50

1 Classical Glass Technology

of the melt are too small to accept that explanation; the kind of analysis just described allows for any effect of bubble size and thus shows that refining agents affect the rate of disappearance of bubbles of the same size. Some other explanation must be found. The Role of Mass Transfer Since large volumes of gas are evolved during the melting reactions, most of which happen before the reacting batch has reached maximium temperature, the melt may or may not be saturated with gases and interaction between bubble and gases dissolved in the melt may make bubbles either grow or dissolve. The former would accelerate rise to the surface, assisting larger bubbles most, and the latter would make rise to the surface unnecessary. The first reliable evidence that mass transfer does occur between bubble and melt was reported by Appen and Polyakova (1938). These workers showed that the composition of the gas in bubbles in samples taken from a melt at different times changes during the course of refining. Bubbles from a melt without refining agents were largely carbon dioxide, as might be expected from the batch materials, but changes occurred when a refining agent had been added. At first the bubbles were still rich in carbon dioxide but they soon became rich in oxygen and later rich in nitrogen. Appen and Polyakova had to use primitive methods of gas analysis and their results represented a considerable experimental feat. Slavyanskii (1957) reported a larger body of similar data by Russian workers also obtained by the same methods. Since about 1960 it has been possible to analyse nanolitre and picolitre quantities of gas by several techniques and numerous

workers have confirmed and extended these early data for samples taken from melts then analysed at room temperature, see for example Cable and Naqvi (1975), Cable etal. (1969) and Mulfinger (1974, 1976). The relation between the rate of change of gas composition, the amount of refining agent used and the change in refining behavior, see Cable and Naqvi (1975), is very convincing qualitative evidence that refining agents do act by mass transfer. However, these data do not show whether growth or dissolution is the crucial process, or whether both are generally involved. The conditions in which bubbles are formed and in which refining occurs are far from equilibrium and simple models assuming that conditions around the bubble are at equilibrium may give seriously misleading predictions. Direct observation of bubbles during refining would be the best way to determine what happens but accurate observation in conditions typical of refining is difficult although several workers have measured bubble behavior in model experiments. The first notable experiments which demonstrated that bubble growth or dissolution is possible were by Greene and Gaffney (1959); Greene and Kitano (1959); Greene and Lee (1965); Greene and Platts (1969); Greene and Davis (1974). This work confirmed that oxygen bubbles subsequently formed and reheated in well refined glass could shrink in the conditions used. Also that equimolar proportions of SO2 and O 2 could easily dissolve. These experiments also showed that complete dissolution of a bubble is much influenced by low impurity levels in the initial gas or by gases dissolved in the melt, some of which will diffuse into the bubble in the early stages. Solinov and Pankova (1965) reported some data for bubble growth which showed that adding arsenic retarded

1.3 The Melting of Glasses

bubble growth but these were not typical refining bubbles. Nemec (1974, 1977a,b, 1980) has also published a considerable body of data on bubble growth. Cable and Haroon (1970) tried a different experiment in freshly made melts, one without and one with refining agent. They injected a few relatively large bubbles of carbon dioxide at 1200 °C, left the melts for a few minutes, cooled and annealed them, then recovered these bubbles, measured them and also analysed their contents. These bubbles had become enriched in oxygen but also shrunk, more in the melt containing the refining agent than in the other, showing that the refining agent had made transfer of CO 2 into the melt faster than transfer of O 2 from the melt into the bubble in those conditions. Both growth and dissolution can clearly occur in melts under different conditions, one of the obvious factors being the temperature dependence of gas solubilities in the melt, most gases becoming more soluble as temperature falls. However the melt is not at equilibrium during the short period of time which determines the conditions for refining and the age of the melt may affect behavior even at constant temperature. The widely accepted picture is that growth occurs at maximum melting temperature but that resorption allows dissolution of residual bubbles on cooling near the end of melting. This may often be true but will not apply to isothermal laboratory melts on which many studies have been made. Theoretical Models for Mass Transfer Two approaches are possible and both have some range of validity. The diffusioncontrolled change in size of a sphere is a very difficult problem to solve even when the spherical symmetry of the system is

51

maintained. As a result it is a considerable challenge to deal with a bubble assumed to be stationary in the melt and this is one model. The other is to use standard boundary layer approximations for a freely rising bubble. The latter should apply for relatively fluid melts and fairly large bubbles but must eventually fail for a dissolving bubble even if valid in its early stages. The classic model for a stationary bubble takes over the result of Carslaw and Jaeger (1959) for heat transfer in a region internally bounded by a bubble which has a constant temperature on its surface. This leads to da/dt=D[(CO0-Ca)/Cs](1-45)

-[I/a-

where C^ is the assumed uniform concentration of gas in the melt, Ca the value at the surface of the bubble and C s the concentration of gas inside the bubble. This equation is valid only for very low solubility and hence very slow change in bubble size; it also assumes that the bubble contains only one gas, which we know not to be true. Even this equation is difficult to integrate and both of the two not very satisfactory approximations obtained by assuming either I/a g> l/(nD t)lj2, a2 = a2 + 2D[(C^-Ca)/Cs]t

(1-46)

or l/(7i D 0 1 / 2 M M a = a0 +

(2/T^2)D1/2

[(C*, - Ca)/Cs] t^2

have often been used; the latter can be cast into the same form as Jander's Eq. (1-21). The motion of the boundary changes the area through which mass transfer can occur and also distorts the concentration profile in the liquid around the bubble. A change in composition of the bubble means that concentrations of the various gases at the surface of the bubble also

52

1 Classical Glass Technology

change with time; this further complicates solution of a realistic model of the process. Adding surface tension for small bubbles and the fact that Sieverts' law rather than Henry's law may be needed to describe conditions at the interface for water vapour increases the complexities. These complications mean that numerical methods must be used to obtain valid results and this family of problems in diffusion-controlled bubble growth and dissolution have been studied in detail by Cable and Frade (1987a,b,c,d, 1988) for both one component and multi-component bubbles. Growth of a one component bubble from zero initial size must follow R = 2p(Dt)1/2

(1-48)

as shown by Scriven (1959), where R is the dimensionless radius and the growth rate constant is a function of, but not in general equal to, (CO0 — Ca)/Cs. This also represents the asymptotic behavior of a bubble growing from finite initial size and most bubbles closely follow this regime for R > 5. Dissolving bubbles, on the other hand, are always in a transient regime and the only valid simple approximation for one component dissolving bubbles applies only for very low solubility and is Ri = l-D[(C^-Ca)/Cs]t

(1-49)

Over most of the range of values of solubility the form of JR (t) is sensitive to the values of the parameters. Multi-component bubbles can show several interesting features. Bubbles which continue to grow will always eventually achieve a constant composition which can be estimated from the properties of the particular case. If the bubble initially had this composition it would behave like a one component bubble but one with any other initial composition can show com-

plex transient behavior. It may, according to the deviation from equilibrium bubble composition, initially exhibit either shrinkage or accelerated growth: it seems that only one change in the sign of dR/dt is possible with a given bubble but this is difficult to demonstrate rigorously. Multicomponent bubbles which eventually dissolve can show either positive or negative values of dR/dt at the beginning, for the same reasons as with growing bubbles, but do not generally tend to an asymptotic constant composition because they cannot achieve a pseudo-steady state. Although it is difficult to predict the details of behavior there are simple rules for deciding whether the initial value of dR/dt will be positive or negative and for deciding whether the bubble will in the end grow or dissolve (Cable and Frade, 1987 d). If the dissolved concentration of each gas i is defined in terms of Fi = (C — C (oo))J C s , gt(0) is the mole fraction of each gas initially in the bubble and oct is the Ostwald solubility coefficient for that gas, the initial sign of dR/dt will be the same as that of I = I.(Fo.t-*igi(0))

(1-50)

whilst its final behavior is controlled by S = ItFOti/ai

(1-51)

If S is positive the bubble will grow, if S is negative it will dissolve. The asymptotic composition of a growing bubble could often be determined experimentally but the solubilities, diffusivities and saturations of each of the gases involved will rarely be known with sufficient accuracy to make a theoretical prediction. However, the bubble must have the most mobile species tending to diffuse into the bubble as its major constituent. The observation that seed eventually become rich in nitrogen towards the end of refining cannot be attrib-

1.3 The Melting of Glasses

uted to bubble growth because nitrogen normally behaves like an inert gas of low solubility and diffusivity. Bubbles which become rich in nitrogen late in their lives must be dissolving, the other gases which find it easier to diffuse out leaving the bubble rich in nitrogen. This does not exclude the possibility that other bubbles grew because those may have risen to the surface and burst by that stage of refining. It is interesting that Cable and Frade (1987d) could not match the observed CO 2 ->O 2 -> N 2 composition cycle or any plausible set of values of solubilities, diffusivities and dissolved concentrations. The theory confirms the finding of Greene and his students that a tiny impurity content in the initial gas or a very small residual content of other gases dissolved in the melt can greatly retard complete dissolution of a bubble and shows that it is not easy to tell which of these factors has affected any particular bubble. The standard boundary layer model for freely rising bubbles was applied to bubbles in glass by Onorato et al. (1981), using plausible model values for the properties of the gases but there is again a lack of accurate data for these parameters and also for experimental data to which the model is known to apply. It is difficult to claim that our knowledge of refining glass melts is qualitatively clearly understood and only in need of data for solubilities and diffusivities to resolve all the problems. Why, for example, does it seem to be frequently true that too little refining agent makes refining worse and that too much also makes performance fall off again? This appears to be related to the rate of conversion from carbon dioxide to oxygen; with too little refining agent this is not observed to happen, with too much it is retarded. The usually accepted model, proposed by Otto Schott,

53

assumes a process such as (1-52) and that it tends to go further to the right as temperature falls so that the melt is supersaturated at the maximum melting temperature and less than saturated on cooling to near working temperature. However, this does not explain why refining agents function in isothermal melts. Nor does it account for the more rapid transfer of carbon dioxide out of the bubble than of oxygen in observed by Cable and Haroon (1970). Refining requires that the melt around a bubble can rapidly absorb or desorb a small amount of gas; this may not necessarily require an increased equilibrium solubility, a transient kinetic effect would suffice. 1.3.4.4 The Homogenizing of Glass Melts The discussion of melting reactions has made it clear that a range of liquids which vary considerably in density, viscosity, reactivity, volatility and other properties will be formed at different stages of melting. These must be mixed together to attain the degree of homogeneity required of most glasses. Differences in refractive index lead to optical distortion and, as a result, optical glasses must have higher standards of homogeneity than any other material made on a large scale. Differences in thermal expansion can cause considerable and increasing internal stress as a glass cools from the glass transition range which can make inhomogeneous glasses very fragile at room temperature and this implies high standards of homogeneity in many glasses where optical properties are not the most important. Likewise not all properties are simple additive functions of composition so that accurate and reproducible measurements of many properties need samples of good homogeneity.

54

1 Classical Glass Technology

Diffusive Mixing In the end mass transfer working at an atomic level must make glass composition as uniform as can be achieved. Although the classic Stokes-Einstein relation between viscosity and diffusivity > = kBT/(6nrjR)

(1-53)

applies only to liquids comprised of large spherical molecules of radius JR, not to typical glass melts, it is sufficient to show that mass transfer diffusivities are very low in glass melts even at melting temperatures. Effective diffusivities for mass transfer are strongly dependent on both composition and temperature; values will not often exceed 10~ 1 0 m 2 s~ 1 . Unaided diffusion will require extremely long times to homogenize a viscous liquid. If an inhomogeneity could be represented as a slab of thickness 2 /, with a concentration of solute C o , immersed in a large bulk of material with uniform concentration C^, its centre concentration would decay with time according to

Table 1-6. Dimensionless times for the decay of concentration at the centre of inhomogeneities of thickness or diameter 2 /.

OAAC0 Isolated: Slab Cylinder Sphere Regular array: Alternate layers

-erf(//2(Dr)

)

(1-54)

If it were a cylinder the radial diffusion would proceed rather faster according to C(0) = 1 - e x p ( - l2/(4Dt))

(1-55)

if it were a sphere the result would be 12

C(0) = erf 1/2{Dt) ' - (2/^/n) (1/2 JDt) • •exp(-/ 2 /(4£>£))

(1-56)

All of these involve the dimensionless time Dt/l2 which shows that real time is inversely proportional to diffusivity and directly proportional to square of size. Table 1 -6 shows the predicted times for the maximum concentration to decay to a tenth and a hundredth of its original value for these cases. It can be seen that the geome-

0.05 AC0 0.01 AC0

31.67 2.37 0.854

126.8 4.87 1.42

3185 24.87 4.34

1.031

1.31

1.97

try has a very significant effect; a point which is reinforced by imagining that the flat slab has been stretched and folded numerous times to make a laminar structure with alternate layers of the two compositions. If these layers are assumed to be of equal thickness the dimensionless concentration is given by (-i)n (1-57) exp

1/2

2

Time (Dt/l ) to decay to:

Type of inhomogeneity

Dt

-

Jf2

cos

2/

and the concentration on the centre line of a layer by C(0)=^ exp

Dt

Jl2

(1-58)

This series converges rapidly for (Dt)/l2 >0.2; for short times the following is more convenient, ,. ^_Q.

Figure 1-22 compares the rates of decay of the central concentrations in an isolated layer and in one in a regular array: the

1.3 The Melting of Glasses

advantage of the latter is clear. The decay of the latter is much quicker for two reasons: 1) the maximum distance over which diffusion must occur is greatly reduced and 2) stretching and folding that layer p times to make one layer of thickness 2 / into a series of layers each of thickness only 2 l/p brings an extra advantage. These relations make clear that there are only three ways in which homogenizing by diffusion can be accelerated: 1) by increasing diffusivity by raising temperature, 2) by decreasing duffusion distances and 3) by decreasing the initial concentration difference which must be reduced. The first of these can only be achieved by raising temperature, which is only possible within specific limits; the second is the most attractive and achieved by stirring; the third is very important but often forgotten in general discussions; choice of batch materials and melting schedules can be very influential here. Preventing the development of inhomogeneity is better than trying to cure it afterwards.

1

102

10

10 3

2

Dimensionless time, Dt/I

Figure 1-22. Predicted decay by diffusion of the centre concentration for a single slab of inhomogeneity of thickness 2 / embedded in a melt and for a layer in a regular array of alternate layers and glass matrix each of the same thickness.

Convective Mixing Glass melts are sufficiently viscous for flow to nearly always be governed by viscous drag and so in the laminar flow regime. This is very convenient when wishing to describe and calculate flow patterns but the predictability of the flows implies that the degree of randomness required for good mixing is difficult to achieve. However, as is shown below, simple shear can assist homogenizing of viscous liquids. It can redistribute inhomogeneities on a large scale by convective flow so that diffusion distances are decreased and in doing so individual inhomogeneities can be dispersed, stretched and made thinner. Three cases need to be examined. The Deformation of Homogeneous Inclusions A homogeneous inclusion is one which is assumed to have the same viscosity as its surroundings although differing in other properties. Its deformation is thus a relatively simple exercise in analysis of flow patterns. The most useful model to consider is steady laminar flow with a constant velocity along a straight flow path but a velocity gradient at right angles, such as will occur in flow along a rectangular open channel. The inhomogeneities that concern us are generally much thinner than the overall body of fluid and it is reasonable to assume that the local velocity distribution is represented by a straight line although, in many cases, this will be part of a parabola. Consider a rectangular element of length / lying at an angle a0 to the direction of flow. Its two ends will be moving at different velocities so that it is stretched out and rotated, see Fig. 1-23. This model has been evaluated by several authors including Mohr (1960), McKelvey (1962) and Cooper (1966a,b).

56

1 Classical Glass Technology h cot a.

Ght

Figure 1-23. The geometry of deformation by simple shear of a layer initially lying at an angle <x0 to the velocity vector U.

The most important facts are that the layers are rotated to become almost parallel to the direction of flow but that the rate of stretching approaches zero as this occurs. For the two dimensional case where the velocity vector U lies along the x axis and dU/dx = 0 but dU/dy = G and the liquid is assumed incompressible, this leads to

large amounts of shear may be required merely to make these the same thickness as they were to start with. However much shear is applied there will always be a narrow range of angles for which matters will be made worse but sufficient shear means that these will occur infrequently. Of course, with almost perfect laminar flow, acceleration of the flow will attenuate inhomogeneities in an easily predictable way. The simplest way of achieving this is to make the melt flow through a reduced cross section, such as the throat of a furnace or the orifice of a gob feeder, when all the constituent parts of stream will be reduced in the same proportions as the cross section of the whole flow. However, if the stream expands again, as on exit from the throat, little may have been achieved. Unfortunately this is not likely to assist diffusive mixing very much because of the short

(1-60) b _ 1 Yo ~ [1 + G t sin 2 a 0 + G2t2 sin2 a o ] 1 / 2 Note that only the product Gt, the total shear, appears and neither of these variables is itself important. Some of the predictions of this equation are shown in Fig. 1-24. The decrease in thickness with amount of shear is roughly a double exponential of G t for favorably oriented layers and a factor of ten reduction in thickness is easily achieved but a factor of a hundred is hardly possible. If attenuation by a factor of more than about twenty is required, it is necessary to change the flow pattern and the orientation of the layers relative to the velocity vector. Note particularly that some layers in a randomly oriented array will be compressed rather than attenuated;

0.01 0

20

40

Total shear, Gt

Figure 1-24. Predicted changes in layers of initial thickness b0 by simple shear for a range of initial orientations according to Eq. (1-60) which ignores differences in viscosity.

57

1.3 The Melting of Glasses

Deformation of Inhomogeneous Inclusions Here this term means inclusions which differ in viscosity from their surrounding matrix. Most inclusions in glass will fall into this category. A rigid inclusion would not deform at all although it would rotate, so intuition rightly suggests that a more viscous inclusion should deform less than one of low viscosity subject to the same stresses. This problem can be elegantly treated by a method devised by Eshelby (1957, 1959) to deal with elastic inclusions which he kindly demonstrated to the author in 1968. By this method a simple relation can be deduced to describe the difference in deformation of a homogeneous two dimensional inclusion and an inhomogeneous one when both have been subjected to the same (but unspecified) amount of shear. Since deformation may be large it is defined in terms of the natural strain 5 f

d a

1

a = In s= J—

(1-61)

flo

The other parameter introduced is the relation between the two viscosities defined by * = (*1i-*iM)/tiM

(1-62)

where the subscripts refer to the inclusion (i) and the matrix (M). The relation between the deformation of the inclusions in the two cases is given by s a +(A/2) tanhs a = :

(1-63)

where sa is the elongation of the longer axis of, for example, the cross section of a long cylinder being deformed at right angles to its major axis, and saH is the deformation in the homogeneous case (k = 0). For the two

dimensional case and an incompressible liquid, the minor axis of the inclusion must decrease by the same factor as the major axis increases. Figure 1-25 shows how viscosity affects deformation according to this model; it can be seen that an inclusion of lower viscosity deforms rather more than a homogeneous one but increasing viscosity soon causes a considerable decrease in the deformation. This analysis is best used in two steps; the model in the previous section is used to obtain an explicit relation between shear and deformation for the homogeneous case and Eq. (1-63) used to determine the difference in deformation between the homogeneous and inhomogeneous cases. One important inference to be drawn from this is that any furnace will be unable to deal with inclusions significantly more viscous than those that usually occur; feasible changes in furnace operating conditions are likely to have very little effect: only removing the source of the viscous inclusions will cure the problem, Three dimensional inclusions were studied by Bilby et al. (1975) and Howard and Brierley (1976); the general features of these are very similar to Eshelby's original analysis. 1

fB '

J

I -J

I

I

^° w

8

£ o

x

\ \ \

0.1

1

1

-

X

\2 0

0.01 -

6

\

^

\

wNX

S\

\

\

\

0.002

1

1

i

0.1

l

l

'

20

\

X

CD O>

|

1

•

- — — .

in th

residence time in the narrow part of the system. The combined effects of shear and reduction in cross section were discussed by Rhiel (1976).

1

1

10" 2

\k

\

\ \ \

I 10" 3

i ^X

i

10~ 4

b/bQ for homogeneous case

Figure 1-25. Results of Eshelby's analysis of the difference in deformation of homogeneous and inhomogeneous (in the sense of viscosity) elliptical inclusions subject to simple shear; values on the diagram are viscosity ratios, see text.

58

1 Classical Glass Technology

Deformation Limited by Surface Tension Both of the above models assume that inclusions are, in principle, infinitely deformable and that only the total shear G t affects the result. This is not true when an interfacial tension exists, as is the case with gas bubbles. Here there is a discontinuity in pressure and normal stress at the interface because of the additional pressure which is given by Ap =
(1-64)

where a is the surface or interfacial tension and a and b are the principal radii of the curved surface. When this term is not trivial, because of the magnitude of a or the small values of the radii, a sphere reaches an equilibrium shape which depends on the rate of shear and this equilibrium shape may be more important than the rate at which it is approached. The classic analysis, limited to small deformations, was undertaken by Taylor (1934) and led to a-b = E1 a+b

=

16i?r

(1-65)

defined as cpa = n/4 + 0, the value of 9 is given by tan 2 6 = 19Griia0/{20&)

(1-67)

This shows that the equilibrium rotation increases with both rate of shear and viscosity of the inclusion. The shape is defined in terms of deviations from spherical shape as a/a o = l + ea and

b/ao = l— eb

(1-68)

which is related to the equilibrium values by

(1-69) £

E2 = ( e a " b)/(2 + sa + fib) «(e a - e b )/2 The equilibrium elongation of the longer axis (a) is given by E2 = E1cos2 6

(1-70)

Figure 1-26 shows some predictions based on Cox's theory which confirm that a high viscosity ratio, which makes the equilibrium angle soon approach 90° as rate of shear increases, is associated a very limited degree of deformation. A gas bubble thus is the most sensitive indicator of the stress around it as the glass melt solidified. Cox's

Since the second term can have values lying only between 1 and 1.1875, Taylor considered that the approximation = GrjMa0/a

(1-66)

would usually be satisfactory. A number of other authors re-examined this question within the last twenty years and some published results are incorrect. An analysis which gave the rate of deformation as well as the equilibrium shape was published by Cox (1969). Although limited to small deformations this analysis, involving spherical harmonics, is valid for any value of viscosity ratio. If the equilibrium angle relative to the shear vector is

Rate of shear parameter, E

Figure 1-26. The dependence of equilibrium shape on shear rate for elliptical inclusions where deformation is limited by interfacial energy according to Cox's model. The ratio of the major axes is plotted against rate of shear expressed by E1 (Eq. (1-65)). The values on the curves are viscosity ratios (inclusion/matrix).

1.3 The Melting of Glasses

theory shows the time dependence of shape to be approximately a sine wave superimposed on an exponential. Study of the shapes and orientations of bubbles in glass is capable of yielding information about the stress fields existing in the glass as it became effectively solid somewhat above annealing temperature. However, one of the most obvious types of such bubbles, namely the very long thin bubbles sometimes found in drawn sheet or rod and tube confirm their orientation to be essentially parallel to the main stress vector but their shapes are not elliptical, the tips being too pointed. However, this section is not in the plane of maximum shear. An exact analysis of this case remains to be undertaken.

1.3.4.5 Modern Furnaces

Glass making has evolved over a long period, the most significant advances being within the last century. Most glass is made in tank furnaces which appear from the outside to be merely large rectangular chambers. In fact they must be very sophisticated devices to meet the different needs of melting, refining, and homogenizing. Melting rates and requirements for refining and homogeneity vary considerably with the product and this leads to many apparently small differences in design and construction which nevertheless have important effects on performance. The design of a particular furnace can often be considered in two separate parts, the tank full of molten glass and the combustion space, with the only essential link between the two being the exchange of heat. The overall size of the melting end of the tank depends on the glass quality needed, the properties of the glass and the required output. Since the energy is transmitted through the free

59

surface of the melt it is usual to estimate the surface area of the tank in terms of daily output per unit surface area, which implicitly recognizes the energy input per unit area from the combustion space. Values in the range 1.3 to 2.2 t m~ 2 d" 1 are common. The ratio of length to breadth (L/B) depends on several factors, two of the most important are 1) a length sufficient to establish the desired longitudinal temperature profile and thus the required internal circulation of the melt and 2) the width must be large enough to allow efficient combustion of the fuel (in a crossfired tank) but not so great as to threaten the stability of the crown which is a free standing arch. As a result small furnaces (about 20 m2) often have L/B about 1.2 but larger furnaces have greater values of L/B, say 2.3 for a 90 m 2 furnace. The depth of the melt should be such as to prevent the melt at the bottom becoming to cool and thus too viscous to flow easily, allow the required internal circulation but also avoid the bottom refractories becoming too hot and thus easily corroded. The depth must thus take account of the transparency of the melt to infrared radiation. Depths from about 0.75 to 1.3 m are common but rarely exceed 1.0 m for strongly infrared absorbing glasses. Most tanks have a throat, a central passage at the bottom of the chamber, between melting end and working end. This helps to prevent unmelted batch or only partially melted glass being carried into the working end and also allows the melt to cool before entering the forehearths which supply the forming machines. Because of the cooling of the melt as it passes through the throat there is a tendency for a return flow of denser glass to develop from working end to melting end. Sunken throat designs which control this are often used. The tank may also in-

60

1 Classical Glass Technology

elude weirs or bubblers or supplementary electrodes to control the flow of the melt and, in the last case, also to increase energy input and melting rate. The combustion space must match the length and width of the melting area but its dimensions must allow the insertion of ports for fuel (if gas is used) and combustion air of a size and number sufficient to supply the necessary energy and establish the desired temperature distribution. Because there is a minimum effective flame length for any particular type of fuel and burner system small tanks often have a horseshoe or U-shaped flame, the entry and exit ports both being in the end wall of the furnace where the batch is normally charged. Such furnaces must have a dog house to charge the batch at the side. These factors are discussed by Trier (1984). Figure 1-27 shows a schematic diagram of a modern container glass tank and Fig. 1-28 a flat glass furnace. The main differences are in size and the absence of a bridge wall and throat in the flat glass furnace in which it is necessary to develop a better internal circulation. Energy distribution and hence temperatures inside the tank are carefully controlled ro retain partly melted batch near the dog house and to control the internal circulation of the melt, which is complex. The energy distribution is most easily controlled with cross fired tanks having several pairs of ports along the side walls. The internal circulation plays a very important part in mixing and homogenizing the glass. Since perfect homogeneity is rarely attainable, considerable effort goes into stretching out inhomogeneities and aligning them parallel to the direction of flow. Some of the important differences between furnaces for container glass and flat glass are due to the higher standard needed in this respect to minimize optical distortion in flat glass.

Figure 1-27. Layout of a typical gas fired modern tank furnace for container glass. Partially sectioned plan view and vertical section across the melting chamber, a) melting end, b) working end, c) throat, d) forehearths, e) combustion space, f) port neck, g) air regenerator, h) gas regenerator, i) crown.

The electrical resistivity of glass is sufficiently low at high temperatures to pass an electric current and heat the glass by the Joule effect. Heating by electricity avoids having to deal with very large volumes of combustion gases and their possible problems of controlling furnace emissions; it needs no regenerators or recuperators, although batch gases are still produced. It also uses the energy input much more efficiently inside the furnace but this does not necessarily make electric melting cheaper. Many electric furnaces are very similar in general appearance to combustion fired ones because the requirements for melting,

61

1.3 The Melting of Glasses

frvi

fT^l

ts^

IXN K ^ l ^ l k ^

^r^ i

IN.XWSN^XXX-'

Kkuuvvvvuv^^vv.uT

QDDDDDD

_Q O Q O

Q Q Q Q c

fl

c

—

,

d

e 0 1

1

10

20 m

1

Figure 1-28. Layout of a modern gas fired Float glass furnace showing sections just above the surface of the melt, vertical section along the center line and transverse section of the melting chamber, a) melting end, b) doghouse, c) working end or conditioning chamber, d) Float bath, e) regenerators, f) combustion space, g) port.

refining and homogenizing remain the same. The electrodes immersed in the glass are usually of molybdenum but graphite was used by some of the pioneers such as Borel (1958). Electric furnaces are discussed at length by Stanek (1977) and by Trier (1984). Electric furnaces are especially useful for small scale melting and for the melting of glasses which contain volatile constituents such as fluorides. One ingenious furnace of this type is that due to Gell (1956) which uses the very poor thermal conductivity of the batch cover to render a crown unnecessary in normal operation, see Fig. 1-29. This can also trap and recycle condensible volatiles evolved where the melting reactions take place. The complex internal flow of the melt means that the residence time distribution of glass inside the furnace is quite broad.

Figure 1-29. Layout of a small 'cold top' electric glass melting furnace using molybdenum plate electrodes set along the side walls. The insulation provided by the batch cover makes a crown unnecessary whilst operating normally.

62

1 Classical Glass Technology

This can be investigated experimentally when changing from one glass composition to another, or by introducing a new constituent as a tracer into the batch, and monitoring its concentration in the output. Such measurements show that some of the new glass usually appears six to eight hours after the batch was charged, the maximum concentration often occurs after 20 to 30 hours but a few percent of the glass is still inside the furnace after 150 to 200 hours. Understanding this behavior is very important in furnaces where the color or composition of the glass must be changed from time to time. Furnace design and operation probably owe more to accumulated experience than scientifically based analysis but some firms do now spend large amounts on the study of models, especially for flow patterns in the melt. The highest standards of homogeneity are required of optical glasses which, for about the last forty years, have been melted in small special tank furnaces which are partly lined with platinum and use mechanical stirring to achieve the attenuation of inhomogeneities necessary to satisfy quality standards. Given these conditions, making optical glass does not require long times and the average residence time for optical glass may be no more than about ten hours. Good homogeneity is much more difficult to attain in pots than in tanks because of the differences in flow within the melt. Mechanical stirring must be used in pots and crucibles if high standards are to be achieved. The author and his students have studied methods of measuring homogeneity (Cable and Bower, 1965; Cable and Walters, 1980; Afghan and Cable, 1983; Aylward et al., 1986) and made detailed studies intended to devise simple stirrers suitable for laboratory melts, see for example Cable and Hakim (1973). Very detailed

model studies were made by Sadeghi (1980) and these led to a very effective simple stirrer the performance of which in glass melts has recently been investigated by Joanni (1989); Joanni et al. (1989). These can make optical quality glass of many compositions on a very small scale, something that used to be considered impossible. Stirrers are sometimes used in full size furnaces but represent a rather different challenge because of the differences in geometry and throughput flow as well as the very high cost of making and installing them. Simple stirrers are quite often used in forehearths where they may do more for thermal than for chemical homogeneity.

1.4 Glass Forming 1.4.1 Introduction

Glass forming involves simultaneous fluid flow and heat transfer. Flow normally depends on the newtonian behavior of glass melts, which means that velocity may be assumed exactly proportional to the stress applied. However, the rapid change of temperature, and hence viscosity, as the glass cools during forming as well as often the complex geometry makes mathematical analysis of most glass forming operations a difficult task. The need to deal with both flow and heat transfer makes resort to numerical methods necessary for most problems of interest. The equations to be solved are usually easy to set up but problems often arise in setting realistic boundary conditions, especially for heat transfer, and in determining the effective thermal conductivity. In general flow occurs under quite low stressses and glass making machinery rarely needs to be massively built. In most cases the removal of heat from the glass is

1.4 Glass Forming

the slower and controlling process. The initial viscosity of the glass must be high enough to prevent excessive flow under gravity but not so great that high stresses are needed to complete the shaping as the glass cools. In the interests of efficiency the glass must then be cooled to become essentially solid as soon as possible after reaching the required shape. Table 1-7 gives some typical values of the viscosities at which various processes occur but some of these are rather crude estimates because so many operations do not take place in isothermal conditions. Two important features of industrial glass forming operations are that 1) it is normal to complete the whole process from raw materials to the finished product in one continuous cycle of operations and 2) mechanized glass forming operations are suited only to the production of large numbers of articles. The first of these arises partly from the brittle nature, poor thermal shock resistance of large pieces and other typical properties of glasses, partly from the fact that cooling and then reheating is a very inefficient use of energy. Very few large scale operators buy previously melted glass and then re-process it; it is however normal to remelt rejects produced during manufacture and many large scale producers also buy cullet (waste glass) to add to their batches. The second arises from the delicate non-equilibrium conditions under which molds, for example, must function for efficient processing. Molds can be preheated before fitting to a machine but cannot be brought beforehand to the actual non-isothermal conditions in which they operate efficiently. Forming processes can be classified in several different ways. Two of the more important aspects are: 1) whether a continuous stream of glass is used (flat glass, tube, fibers) or separate gobs formed (containers,

63

Table 1-7. Approximate viscosity values for glass forming operations in dPa s. Operation

logfa/dPas)

Melting 1.5 to 2.5 Seal glass to glass 3.5 Seal glass to metal 3.8 Forming gobs for containers 3.6 to 4.2 Drawing Fourcault sheet 4.0 to 4.4 Pressing 4.0 to 6.3 Surface of parison during forming 4.0 to 8.0 Glass at tip of Danner mandrel 5.5 Surface of bottle during blowing 5.7 to 10.0 Sinter glass powder to solid body 6.0 Littleton softening point 7.65 Sinter glass powder to porous body 8.0 to 8.8 Thick tube collapse under vacuum 11.0 Deform under gravity 11.3 Dilatometric softening point Mg 11.3 to 11.7 Lehr belt marks base of container 11.7 Annealing 12.0 to 14.0 Stress release occurs in a few seconds 12.8 Temperature for matching glass and metal expansion curves for seals 14.0 to 14.5 Stress release too slow to be useful 14.6

television screens) and 2) whether or not molds are used to shape the glass. Some processes, like container manufacture, require that the temperatures in one place, such as a particular point on a mold, keep repeating a certain time-temperature cycle whilst others, such as drawing tube or forming flat glass, require the temperature at a particular point to be as constant as possible but temperatures vary rapidly with position. In both instances the glass itself changes temperature rapidly as it flows during forming and the optimum conditions can only be established whilst the process is operating. Different types of process have different preferred viscositytemperature relations. Even with today's sophisticated controls it can take several hours to optimize operating conditions after making a change, such as fitting a new set of molds; frequent changes in operat-

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1 Classical Glass Technology

ing conditions are thus very undesirable. Glass manufacturers usually expect to make very large numbers of individual articles between changes in operating conditions. Making quantities that represent only a few hours production (which could still mean more than 50000 containers) is inefficient and expensive because of the production lost during stoppages and the rejects produced whilst achieving optimum conditions. 1.4.2 The Manufacture of Containers

Forming by blowing in a split mold using compressed air permits complex shapes to be made and this has long been the preferred method for making most containers. The manufacture of containers by a skilled workman manipulating a gather on a blow pipe was practised for nearly two thousand years and required a complex series of operations to form a parison by rolling on a marver, using gravity to stretch or compress the length of the parison and blowing a little from time to time; the parison was then put into the blow mold and blown to the final shape. The pressure available when blowing by mouth is very low and too high a viscosity risks flow being very slow and possibly not complete; automatic machines use an effective pressure of only about 2 atm. Forming the mouth followed breaking the container off the blow pipe and reheating the neck; this led to the mouth being known as the finish. One of the early successes of pioneers in container production was to demonstrate that the process could be done in two steps using two body molds, a parison mold and a final blow mold. Of course the mouth now has to be formed first and held in a neck ring whilst performing the other operations but it is still called the finish. Although the whole process has many neces-

sary individual steps the essential seven are: 1) form a gob and feed it to the parison mold, 2) form the mouth or finish of the container, 3) form the parison, 4) transfer the parison to the blow mold, 5) blow the container to its final form, 6) cool in the blow mold until sufficiently rigid to keep its shape and 7) open the mold and remove the container. The container must then be annealed. The gob must be supplied in as near to an isothermal a state as is possible and at a viscosity sufficiently high to prevent too rapid flow under gravity whilst still ready to flow when blown. The viscosity for gob formation depends on the particular process and article being made but is usually around log r\ = 3.7 to 4.2 (dPa s). Later stages of the operations are less easy to characterize in terms of viscosity because the glass is being rapidly cooled and steep gradients of both temperature and viscosity exist within it; however the viscosity of the surface layers must be the most important value. As mentioned in the historical review, nearly all containers are now made on individual section (IS) machines. These are made up by coupling a row of identical sections which work independently of each other, except that feeding the gobs to each section in turn must clearly be coordinated. A machine may have only four or five sections but up to sixteen is known. All the parison molds sit along one side of the machine and all the blow molds along the other. These molds open and close as required but are otherwise stationary. The neck ring is swung vertically through 180° to transfer the parison to the blow mold. Figure 1-30 illustrates the steps in forming a bottle on an IS machine. Many of the details of construction of the IS and other machines then widely used are discussed by Giegerich and Trier (1964). Bollert et al.

1.4 Glass Forming

/! S

Figure 1-30. Schematic diagram of the blow-blow operation of the IS machine. The top row shows stages in parison forming and the bottom row blowing in the blow mold. In the center the neck ring is seen in the position occupied during parison formation. The parison is transferred to the blow mold by rotating the arm through 180° (position shown dashed). 1) gob entering mold, 2) blow down to ensure proper formation of neck, 3) blowing of parison complete, 4) parison enclosed by blow mold, 5) blowing just begun, 6) mold opened for bottle to be removed.

(1987) more recently reviewed the evolution of the IS machine and some of its most recent refinements. The majority of containers have necks which are relatively narrow compared with their bodies so it is normal to drop the gob into the inverted parison mold. Two differ-

65

ent methods of forming the parison may then be used, blow and blow or press and blow. When first developed the press and blow process was limited to wide mouthed articles like jam jars but it is now used for many narrow necked containers. If the parison is made by the blow and blow process the mold is at once covered by a blow head and compressed air applied to ensure that the mouth is properly formed; any distortion of the sealing surface will often make that container unusable. As soon as the mouth has been formed the opening is covered by a baffle plate and the parison blown to fill its mold. Failure to blow at least a small bubble as soon as possible risks the glass around the plug forming the inside of the mouth becoming too viscous to be blown at all. In the press and blow process a central metal plunger is used to form the central cavity in the parison and to ensure that the neck ring is properly filled. This process has several advantages which include being able to make the central cavity an exact shape and some simplification of the steps needed to form the parison. If the glass in the parison does not have the desired wall thickness as well as external contour, it may not give the required wall thickness distribution in the final article. Although the machine most widely used for the manufacture of containers was designed and brought into service many years ago, recent years have seen important improvements in it and in the containers produced. Reducing the weight of glass in a given type of container has several obvious advantages and such progress is steadily continuing, as demonstrated by Fig. 1-31 which shows how the weight of the standard English one pint (568 mL) milk bottle has changed over the recent past. Once formed the parison is transferred to the blow mold and blown in the same

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1 Classical Glass Technology

600

500 -

400 O) c o

300 -

<1960

1965

1975

1985

1995

Year Figure 1-31. Changes in the weight of the standard English 568 ml milk bottle over the years. The development of the narrow mouth press and blow process has been an important factor. By courtesy of PLMRedfearn Glass.

gap between glass and mold, or the parison may be deliberately left for a period enclosed by the blow mold before beginning to blow. The mold surfaces are quite hot and simply introducing the air gap decreases heat transfer to the mold by a considerable factor. Whilst it is reheating the parison stretches under gravity and this must not be permitted to go too far. Figure 1-32 shows typical examples of temperature profiles in a parison at different stages. It is extremely difficult to study the flow of the glass during parison formation. Direct observation is impossible and it is necessary to resort to computing by finite element methods, solving for both heat transfer and fluid flow, or to use physical models. Interesting studies using model liquids were undertaken by Reinhardt (1965) and Schmid and Hertel (1968).

1000

way with both processes. On the IS machine the arm carrying the neck ring swings vertically through 180° to carry the parison to the blow mold which at once closes around it. A very important stage of foming the bottle or jar is reheating of the surface of the glass once blowing of the parison is finished. Reheat occurs when the surface of the parison is no longer in close contact with the metal mold and not having heat extracted so rapidly. The steep internal temperature gradient ensures that heat continues to flow towards the surface; as it is no longer being lost at the previous rate this heat accumulates just below the surface and the thin surface layer of the glass which has been cooled most by contact with the mold gains in temperature and becomes less viscous. To assist reheating the parison mold may be opened a fraction to make sure that there is a small air

0.2

0.4

0.6

0.8

1.0

Fraction of wall thickness

Figure 1-32. Typical temperature distributions in the wall of a pressed parison at different stages of its formation: 1) just after beginning of pressing, 2) at the beginning of reheat, 3) at the end of reheat.

67

1.4 Glass Forming

Giegerich (1960) devised a simple scheme for comparing the main stages of the forming cycle on different machines and published some data which indicate why the IS machine has become so favored. The actual construction and operation of the Emhart IS, or any other machine, has innumerable complexities but it is possible to give a simple outline of the main features of the process by Giegerich's method. Figure 1-33 shows Giegerich's method of analysis. A gob is dropped into the inverted parison mold at t = 0. All the operations necessary to form the mouth and blow the parison are included in the parison forming time £P, then the mold is slightly opened to assist reheating for a time tR which includes the time needed to transfer the parison to the blow mold and close that mold. A time tB is needed for blowing in the blow mold, followed by a cooling time tc before the mold is opened and the container removed. The time between the delivery of successive gobs to the same mold is tG and the total time needed to make one article is tT. If the process were operating as efficiently as possible the idle time tY between removing one parison from the parison mold and supplying the next gob would be negligible and the total time would be divided equally between parison and blow molds. The idle or wasted time in each cycle may therefore be defined as tY=tG~\l2tT

(1-71)

Although part of the time tG—(tP-\-tR) *S needed to cool the parison mold it may be considered wasted; so may most of the cooling time tc for the blow mold as well as the time that it is actually empty. When times are measured in seconds, the actual productivity in bottles per minute is, B = 60/t G

(1-72)

Gob 1

Bottle 2

Figure 1-33. Schematic diagram of Giegerich's method of analysing container machine operations, see text.

whilst the ideal productivity would be B max =120/t T

(1-73)

Giegerich showed that tP increased more or less linearly with gob weight and the data for most machines fell very close to the same line. When total time (tT) was plotted against parison forming time (tP) all machines again showed similar behavior. However, the IS machine showed shorter reheat times (tR) than any other gob fed machine, although the suction fed Owens machine was slightly better from this point of view. However, when the various productivity figures were compared, the IS machine clearly outperformed most others and achieved about 80% of the maximum possible value whilst some other machines commonly used up to about 20 years ago worked at little more than half the maximum value. One of the most important aspects of container manufacture is the heat transfer between glass and metal mold. Perfect contact between the two would assist rapid heat transfer but implies that the glass adheres to the mold which would be disastrous. However, the perfect contact model

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1 Classical Glass Technology

is the one to start with. If two relatively thick isothermal slabs of the same material at temperatures TA and TB were brought into perfect contact the interface temperature would be T{ = (TA + TB)/2. If the slabs have different thermal properties the dimensionless interface temperature T* should be given by £BCB)] 1 / 2

(1-74)

Although not given a particular name in English, the parameter XQC is called the Temperaturleitzahl in German. When typical values for the properties of glass (A) and cast iron (B) are taken and TA assumed to be 1100°C and TB 550 °C, the calculated value of T{ is found to be about 585 °C. It is important that this should not exceed the sticking temperature of the glass to the mold material which is often about 600620 °C; such intimate contact would be good for heat transfer but prevent removal of the glass from the mold or, at least, badly damage the surface of the glass. The fact that the glass contracts as it cools whilst the metal expands on heating helps to prevent sticking. However it is found on analysing glass-mold heat transfer that the heat transfer coefficient at the interface is strongly time dependent. This considerably complicates attempts to calculate temperatures and viscosities within the glass during forming. Figure 1-34 shows some data for the variation of glass to mold heat transfer during pressing reported by McGraw (1961). The mold surface of course cannot be absolutely smooth and clean, indeed it is usual practice to apply mold dopes to the inner surfaces of the mold to aid release of the glass and improve surface finish; these may contain graphite and oils which carbonize. Trier (1955) reported some interesting results of varying parison mold contact

1 0.4

0.8

Contact time in s

Figure 1-34. Variation glass-mold heat transfer coefficient during a pressing operation according to measurements by McGraw (1961).

times and total cycle times on a semi-automatic machine without changing any other parameters. These show that a proper balance must be maintained between heat removed from the glass and heat removed from the mold, see Fig. 1-35. Too short a total cycle time makes the mold overheat so that the glass sticks and too long a cycle time makes the mold too cool so that the glass is chilled and will not flow properly. Too short a time in the parison mold leaves the glass too fluid allowing it to distort too much under gravity but too long a parison forming time leaves it too viscous to be blown in the blow mold. Current cycle times on an IS machine would be considerably shorter than those seen here. The design of molds to ensure the desired rates of heat extraction from different parts and thus the temperature distribution over the inner surface is a complex matter. One of the most obvious features is that a considerable proportion of the heat transferred from the glass is lost again from the inner surface of the mold by forced convection cooling whilst the mold is open and empty. The inner surface temperature

1.4 Glass Forming 16

I

I

I

12 -

r

CD

o eg c o o

i

Sticks to mold _

I

450°C

-•

~-~ — —

/ * 6 1 (re

,

/ /•600°C

/ /

/

/•450

j /

1.4.3 The Production of Lamp Bulb Envelopes

I

Parison too viscous

610°C / 435°C y ^j

4 -

^avy surface

Parison too fluid

I

1

i

16

i

1

24

69

i

32

Total cycle time in s

Figure 1-35. The effects of varying parison mold glass contact time and total cycle time on parison formation on a semi-automatic machine. Some mold surface temperature readings are also shown. After Trier (1955).

typically varies by about 80 °C during the whole cycle of operations. Drilling cooling passages in the wall of the mold, parallel to the long axis of the container, is one of the ways in which the efficiency of the IS machine has been improved in recent years. The only easy measurement of the heat extracted from the glass during forming is to drop into a calorimeter 1) a gob, 2) a parison at transfer and 3) a just completed bottle. If good specific heat data are available these results can give the average temperatures of the whole article at each stage. Data of Giegerich indicate that the heat loss during forming of a container on an IS machine was equivalent to a fall in average temperature of about 320 to 400 °C with the loss during parison formation being rather greater than during blowing, which points out the necessity of reheating before blowing the parison.

The manufacture of bulbs for incandescent electric lamps is a very important branch of the glass industry. These differ from most other kinds of hollow ware in having much thinner walls, usually somewhat less than 1 mm. These are made by a rather different process which also uses a special machine. Thin walled articles of this kind, including some drinking glasses are made using paste molds. A paste mold is one which does much less damage to the surface of the glass during manufacture. This is achieved by using a mold with a relatively soft and porous lining which is used saturated with water so that the glass vaporizes the water when it is introduced into the mold and the glass is prevented from coming into close contact with the mold by a cushion of steam. This method is restricted to thin walled articles because of the limit on the heat that can be used in evaporating the water. The molds are usually relatively thin iron shells which are lined with a carbon layer produced by applying a layer of cork granules mixed with additives which is carbonized before use. The molds have a short life and the ware is normally rotated in the mold throughout blowing, partly to obtain as uniform and circular a section as possible also to avoid mold seams. Such bulbs are made at very high rates of production on the Corning ribbon machine the main features of which are shown in Fig. 1-36; the most notable features are the mounting of the blow heads and blow molds on two separate bands like caterpillar tracks, one above the other, whilst the continuous ribbon of glass carrying the bulbs advances between them.

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1 Classical Glass Technology

n u n n n n n n( J n

(n n n n 1

M

TOO Figure 1-36. Schematic diagram of the Corning ribbon machine for making lamp bulbs. A stream of glass (a) passes between two rollers (b) which shape it slightly; it then falls onto a band of metal plates (c) each with a central hole through which the glass sags under gravity to begin parison formation. Blow heads (d) mounted on the upper belt press against the upper surface of the glass ribbon and begin to blow at (e). The paste molds (f) mounted on the lower belt close around the parison at (g) and the bulb then blown in the rotating mold. At (h) the blow heads are lifted away and the blow molds open leaving the bulbs suspended from the ribbon from which they are cracked off and collected at (i). The ribbon is then crushed and returned to be used as cullet.

1.4.4 The Manufacture of Flat Glass 1.4.4.1 Introduction

The requirements of buildings and vehicles make flat glass production one of the largest sections of the industry. As mentioned in the introduction, the crucial advances in flat glass manufacture occurred during the present century: the first successful processes for continuous drawing of sheet coming into production between about 1916 and 1930, to be followed by the development of the Float process in the fifties and sixties. Cast plate glass, made by grinding and polishing thick cast plate, was invented around AD 1680 but its large scale manufacture was greatly improved largely by Pilkington Brothers between 1920 and 1940; however, it has now been entirely replaced by Float glass. Although they are also now obsolescent it is worth

briefly outlining the important sheet drawing processes which are still in use. Whether drawn upwards or downwards a stream of any liquid, even one of high viscosity, is inherently unstable. Any attempt to draw a thin sheet of viscous liquid, for example using a knife blade dipped into a pool, shows that it at once necks and tends towards a circular section. Even a circular jet will break up unless rapidly cooled and made effectively solid. The break up of a circular jet is a classic and complex problem of hydrodynamics but some useful analytical approximations exist. By taking the simplest useful approximations for the equations governing the behavior of a circular jet Levich (1962) estimated the time to break up (TB) for either a low viscosity jet or a viscous jet. For a viscous jet of radius a this is approximately (1-75)

1.4 Glass Forming

which means that if its velocity is U9 the critical (break up) length is about LB= 5 Ur]a/a

(1-76)

High velocity, high viscosity and large diameter will all help to increase this length. It is clear that rapid increase in viscosity to make the glass essentially solid (rj >1012 dPa s) within say a quarter of the initial isothermal break up length will achieve reasonable stability of the process. Such an analysis done beforehand would have encouraged a pioneer of flat glass manufacture to proceed but emphasizes that very rapid cooling is necessary, something not favored, from the heat transfer point of view, by a large thickness. Because of its shape, forming and preserving the desired width and thickness of a sheet is a bigger problem than controlling a circular jet. Mathematical modelling of the drawing of a sheet from a pool at first looks relatively simple because it can be treated as a two dimensional problem symmetrical about the center line of the sheet. As the glass is so much more viscous than the air it can be assumed that shear stress and so velocity gradient go to zero at the surfaces. However, the positions of the surfaces where these boundary conditions apply are not known; indeed finding them is the main purpose of the exercise. The foot of the sheet could, for example, be assumed to be of hyperbolic or exponential form but, in practice, it may bulge into what is called the onion just above the surface of the melt. This therefore is a difficult problem to solve properly even if the conditions are assumed isothermal. When the heat transfer and rapid change of viscosity with position, which are essential features of the real process, are introduced the difficulties are considerably multiplied. The need for rapid cooling, in conditions where the effective conductivity is very lit-

71

tle greater than the true conductivity of the glass (largely because the sheet is usually of small optical thickness), is one of the main factors limiting the maximum thickness of glass that can be produced. Thin sheet must be drawn off at a higher speed and thus subject to greater stresses so that the danger of the sheet breaking is one of the limitations on minimum thickness. However, the critical factors controlling complex industrial processes are not always the most obvious ones. The most comprehensive description and discussion of sheet glass manufacturing processes is the book by Goerk (1966); a useful review is given by Hynd (1984). 1.4.4.2 Sheet Glass Processes The Fourcault Process Fourcault (1862-1919), the first inventor to make his process work, overcame the major difficulties by inventing the debiteuse (a word not translated into English) which is a kind of refractory clay boat which floats in the glass. It has in its base a slot of approximately elliptical shape, through which the glass will flow up. This rate of flow may be increased by pushing the debiteuse down into melt. If this stream is gripped and pulled up at the same volume rate of flow, without it being able to wet and fill the inside of the debiteuse, a sheet can be formed. Rectangular water cooled iron boxes extending across the whole width of the drawing chamber are placed very near to the surfaces of the sheet and not far above the top of the debiteuse to cool the glass sufficiently quickly to control its tendencies to neck down and try to form a circular jet or become unstable. The outer edges will cool more quickly than the rest so that the still deformable sheet is held between two almost rigid side strips from very close to the top of the debiteuse.

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1 Classical Glass Technology

As soon as the surfaces of the sheet are sufficiently cool it is gripped very lightly by the first of a series of pairs of rollers (at least 12), which used to be covered with asbestos, and is drawn vertically upwards. The height of the first pair of rollers above the surface of the melt must have an important influence on the stability of the process. The minimum height of these depends on the rate of cooling and the upward velocity of the sheet. The main disadvantage of the Fourcault process is that the slot in the clay debiteuse is subject to forced convection corrosion and eventually threads of corrosion product, which obviously lie on the surfaces of the sheet, are drawn up and impair the optical quality. Because of the large difference in refractive index between glass and air, small surface imperfections cause the maximum optical distortion and the parallel lines that result are called piano or music lines. As a result the debiteuse must be changed at rather frequent intervals, often around 60 days. Not surprisingly, the waviness of the surfaces is usually least near the center and wide strips from the edges are sometimes cut off and discarded when the best quality sheet is required. Accurate control of temperatures is vital in such a process and this means that control of the convection of the air in the drawing chamber and in the vertical drawing tower is important. The rate of cooling in the middle part of the tower must be controlled carefully to achieve a reasonable degree of annealing before the glass is cut into sheets at the top of the tower. Figure 1-37 shows the essential components of the Fourcault system. The glass sheet may be up to 3 m wide but around 1.8 or 2.3 m is more common. The range of thicknesses (or substance) that can be produced is surprisingly large, from about 0.6 to 14 mm, but the whole of the

>5

El Figure 1-37. The essential components of the Fourcault sheet drawing process. The upper diagram shows a vertical section through the middle of the drawing chamber, the lower one a plan view and sections of the debiteuse (slightly larger scale). 1) Debiteuse, 2) water cooling box, 3) push rod holding debiteuse, 4) control for adjusting immersion of debiteuse, 5) drawing rollers.

potential range is not usually exploited and a range from about 0.7 to 6 mm is more typical. To exploit the whole range of thicknesses requires that the width of the slot in the debiteuse be varied. Drawing speeds can vary from around 3.5 m min" 1 for thin glass to 0.2 m m m " 1 for thick glass; surface distortion is difficult to avoid with sheet near to the maximum thickness. The height of the drawing tower rarely exceeds 6 m and this can mean that thick glass is not well annealed. The main controls over thickness being produced in a given installation are 1) the temperature of the drawing chamber, 2) the speed of drawing, 3) the depth of immersion of the debiteuse and 4) the positions of the water cooling boxes.

1.4 Glass Forming

73

The Pittsburgh Process The main difference in the Pittsburgh or Pennvernon process is that the debiteuse is replaced by a draw bar which is totally immersed in the melt so that the corrosion products eventually formed and drawn off lie buried near the centre of the sheet and do not cause the obvious defects seen on the surfaces of Fourcault glass. The immersed draw bar has its upper surface 60 to 80 mm below the surface of the glass and helps to stabilize the foot of the sheet. The shape has many variants; it sometimes has a central slot in it through which chilled glass from the just below the point of drawing can sink, mix with the rest, and be reheated. Two different ways of quickly cooling the edges have been used. The original method is to have edge cooling cups or forks about 250 mm in diameter and 100 mm deep, each with a radial slot from edge to center, so that the cup encircles and quickly chills the edge of the sheet very close to the surface of the bath, thereby making two almost rigid side strips. The other is to use air cooled edge rolls, ribbed or knurled, which actually grip the sheet immediately above the surface of the bath to form the two almost solid side strips, which are driven upwards at a controlled rate from this position. This method was originally part of the Colburn process and provides the closest control of the edges of the sheet during drawing. Figure 1-38 shows a typical Pittsburgh drawing chamber. Note that the actual drawing position is more or less isolated from the rest of the furnace chamber by the L-blocks. The Pittsburgh process is otherwise very similar to the Fourcault. Although capable of giving better surface quality than the Fourcault process the Pittsburgh process is not quite so versatile in range of thickness and requires more

Figure 1-38. Sketch of a Pittsburgh sheet drawing chamber showing 1) the skimmer block, 2) the immersed draw bar, 3) the edge rolls, 4) one of the water coolers, 5) one L-block, 6) the lowest pair of drawing rolls) and 7) the sheet of glass.

accurate control of temperatures and glass level. The maximum width of the sheet (including the edge strips) is about 3.05 m but 2.1 to 2.75 m is the common range. The thickness of the sheet made by this process is usually in the range 2.0 to 9.5 mm. Production of thinner glass is difficult partly because drawing speeds are generally rather higher than for the Fourcault process. The largest single sheets produced on the cutting floor are 3.0 m long (for 6 mm thickness) but a common size supplied to customers is 1840 x 1220 mm. The Libbey-Owens-Ford Process The vertical drawing of sheet is rather inconvenient from an engineering point of view. The height of the tower should be determined by rates of cooling need for annealing but given the need to handle all the glass at a considerable height above ground level, is obviously fixed and partly determined by engineering factors. Colburn, inventor of this process, who first made it succeed and founded the LibbeyOwens company in 1916, avoided this

74

1 Classical Glass Technology

problem by bending the sheet horizontally over a polished air cooled metal roller just before it became too viscous for this to be done. The feasibility of doing so may have been suggested by the opening and flattening of the cylinders long practised in the hand and Lubbers processes. The roller is about 0.2 m in diameter and approximately 0.7 m above the surface of the bath. Colburn also introduced air cooled edge rolls to control the stability of the point of drawing and the width of the sheet by producing two chilled strips along the edges of the sheet. Figure 1-39 shows a schematic diagram of a Libbey-Owens-Ford drawing chamber. The total length of the horizontal chamber can be much longer than the maximum feasible height of a Fourcault or Pittsburgh drawing tower and may be as much as 60 m; this permits good annealing of even the thickest sheet. The Libbey-Owens-Ford process can make glass up to about 3.5 m wide and is capable of a wide range of thicknesses, from about 0.6 mm to 25 mm, but 2 m wide and 1.0 to 10.0 mm thick represents a more typical range of production. Drawing speeds are higher than for the other two processes, about 2.5 m min" 1 for 2 mm

Figure 1-39. The layout of the Libbey-Owens sheet drawing process. 1) the conditioning chamber of the tank, 2) auxiliary burner, 3) the edge rolls, 4) water cooling box to chill sheet, 5) the bending roll, 6) water cooler.

and 0.7 m min 1 being typical. Lemaire (1965) published some interesting studies of temperature distributions and flow patterns in a Libbey-Owens drawing chamber. Downward Drawing Processes Several methods of drawing a stream downwards have been developed in recent years and are used to make much thinner sheet than the other processes can easily produce, such as that used for microscope slides. The most obvious is analogous to the Fourcault process with a stream of glass being drawn down from a slot in a platinum bushing but the surface quality is not as good as with the Float process. However, another method which avoids irregularities that would be produced by slight imperfections in the edges of the slot has been developed by Corning Glass Works. Molten glass is fed into one end of a trough with an inclined base to give a steadily decreasing depth; the upper edges also deviate very slightly from the horizontal. A proper combination of these geometrical features can make the rate of overflow the same along the whole length of the trough. The two streams flowing down each side meet at the central ridge along the bottom of the trough and the resultant sheet is gripped just below by edge rolls and is then drawn away by other rollers lower down. The melt in the trough has a viscosity of about 4 x 104 dPa s and coolers increase this to about 3 x 105 dPa s as it leaves the ridge or root at the bottom of the trough. Hynd (1984) gave some details of this process and it is mentioned by Dumbaugh et al. (1991). 1.4.4.3 Float Glass In the past high quality flat glass for mirrors, vehicle or shop windows and such

1.4 Glass Forming

like had to be made by mechanically grinding and polishing cast plate. Large scale manufacture involved considerable engineering difficulties and made the process costly; a continuous plate glass line was about 600 m long and used about 1.7 MW of electrical energy solely for grinding the glass. The development of the Float process has rendered polished plate obsolete. The idea of floating glass on a bath of molten metal, for a variety of purposes, some misconceived, can be traced back for about a century but older inventors lacked the insight and the sophisticated engineering skills needed to develop a successful process. The physical basis of the modern Float process is beautifully simple: a broad stream of glass is allowed to spread out and come to equilibrium whilst floating on a bath of molten metal. It is then cooled until almost rigid and lifted off. Both surfaces of the glass can have almost ideally flat and smooth firepolished surfaces so that grinding and polishing are unnecessary. A fascinating review of the evolution of flat glass manufacture and the early development of the Float process has been given by Pilkington (1969) and another account is by Hynd (1984). The Physical Principles of the Process The metal must be denser than the glass, which is not a problem: the other requirements are not so easily met. On considering the range of viscosities over which the deformation of the glass can occur and be controlled, it is clear that the metal must have a melting point below 600 °C and a boiling point above 1050°C. Both the molten metal and the atmosphere above it have very low viscosities compared with the glass which will therefore spread out to come to equilibrium under a balance between hydrostatic and surface tension

forces, so long as the atmosphere and molten metal are not vigorously disturbed. The cross section of a continuous ribbon is thus similar to a two dimensional sessile drop which, if sufficiently wide, will have a broad flat central region. Figure 1-40 shows the two factors which control the thickness of the sheet. The balance of the interfacial tensions gives a net force over unit length of this section of F(a) = ag + <jgm-Gm

(1-77)

which is balanced by the forces due to the hydrostatic pressures. If the thickness of the sheet is d and its depth of immersion in the molten metal bath (d — /*), Archimedes principle requires that Qgd

= Qm(d-h)

(1-78)

If one imagines that the left part of the ribbon has been removed, as shown in the Figure, it is necessary to apply forces to keep the remaining part in equilibrium. There are two contributions to this: 1) the hydrostatic pressure in the glass which increases linearly from x = 0 to d and 2) the pressure in the molten metal which acts in the opposite direction but only from x = h to d. The net force due to these over a section of unit length is (1-79)

Figure 1-40. The forces controlling the equilibrium thickness of Float glass, see text.

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1 Classical Glass Technology

and equating F(o) with F(p) gives i-am

=

{Qgd2l2-Qm{d-h)2l2)g (1-80)

from which (d — h) can be eliminated through Eq. (1-78). On rearrangement this yields the equilibrium thickness d, (1-81) The other basic model is to calculate the time needed for a surface irregularity to be smoothed out. This may be determined by considering the decay of a sine wave disturbance of the surface. Three different mechanisms could be involved, 1) viscous flow due to gravity, 2) viscous flow due to surface tension forces and 3) surface diffusion. These would in turn predominate on decreasing scales with gravity controlling the behavior of long waves and surface diffusion only becoming controlling when the wavelength approaches atomic scale. The gravitational driving force is just the difference in hydrostatic pressure due to the amplitude (A) of the wave,

Ap=Agg

(1-82)

Since the amplitude itself represents the driving force, an exponential decay, A=.

(1-83)

may be expected. In a very viscous liquid the constant k in Eq.(1-83) is QgX/(4nrj) for control by gravity (Lamb, 1932). The driving force for flow when surface tension governs is the excess pressure due to curvature of the surface which, for a surface curved in only one plane, is Ap = a/a if a is the radius of curvature. For a sine wave this also leads to exponential decay (Mullins, 1970) A =A0Qxp( — (na/Xrj)t)

(1-84)

Gravity thus causes rapid decay of long waves but surface tension governs short waves. The two processes have the same rate of decay when X2rit = 4n2a/Qg

(1-85)

and waves of this critical wavelength are the slowest to decay. For typical glass properties Xcrit is about 23 mm and such a wave decays to 1.5% of its initial amplitude in 100 s if the viscosity is 104 dPa s. Cassidy and Gjostein (1970) confirmed that the decay of corrugations on glass of wavelengths around 5 to 15 \xm was controlled by surface tension and that more complex profiles become simple sine waves as they decay, experiment and theory agreeing quite well. In practice it is found that about one minute is needed at about 1050 °C (viscosity 104 dPa s) to achieve optical quality flatness. Chemistry of the Float Process The molten metal must have a low vapor pressure ( < 1 0 N m ~ 2 at 1050°C) otherwise condensation towards the cool end of the Float bath may be troublesome. Chemical interaction between the molten metal and the glass must be minimal. On examining the properties of all molten metals it is found that only gallium, indium, and tin satisfy these requirements (lead has too high a vapor pressure) and that tin is best in terms of vapor pressure and availability. Tin has the highest boiling point, which is above 2500 °C, and is the metal always used. Pure tin easily reacts with the oxygen in the air to form solid oxides but reacts less with the glass. It is therefore necessary to have a reducing atmosphere in the Float bath; 97% N 2 , 3% H 2 is commonly used. Very low levels of oxygen or sulfur impurity in the tin are sufficient to cause problems due to formation of stannous oxide or

1.4 Glass Forming

sulphide. If these compounds are formed they can condense near the cool end of the bath, be reduced to metal by the atmosphere, and form specks of tin adhering to the upper surface of the ribbon; because of its higher solubility sulfur is the greater problem. The glass itself contains a significant proportion of sulfur, as sulfate added to aid melting and refining, some dissolved water and some variable valence elements, chiefly iron, capable of being oxidized or reduced to absorb or evolve oxygen. A very delicate control of these factors is therefore required. Sodium is the most reactive major constituent of the glass and is also the most mobile ion within it. It is thus likely that reactions between sodium in the glass and the tin bath will be the most significant and some aspects of this have been discussed by Miiller et al. (1989). Float Glass Technology The overall layout of the process derives from the continuous casting of plate glass. A controlled stream of glass is delivered by the melting furnace onto the molten tin bath and drawn along it to the other end where it is lifted off. The glass is fed onto the molten tin at about 1050°C, allowed to become flat, cooled until too viscous to flow easily or be damaged (about lO^dPas), then lifted off it at the other end at about 600 °C. The melting tank may be up to about 65 m long and l l m wide with the melt about 1.3 m deep and capable of producing as much as 6000 tonnes a week. Energy consumption in the melting tank is now around 5800 kJ kg" *. A smaller conditioning section approximately 9 m wide and 25 m long is attached to the end of the melting tank; in it the glass is cooled and brought to a uniform temperature suitable for forming the stream which is fed onto

77

the Float bath. The Float bath may be about 5 m wide and 35 m long and the molten tin needs to be only about 100 mm deep. On leaving the Float bath the ribbon passes through an annealing furnace. At the end of the line the curved meniscus regions are removed then the ribbon is cut into whatever size sheets are required, taking into account any defects that have been detected before cutting it. One of the major problems of Float glass development was the production of a range of thicknesses. The natural equilibrium thickness of the ribbon is about 7 mm, which is very fortunate because the largest market used to be for 1/4 in (6.3 mm) polished plate. As was soon discovered, nature tries to insist on achieving this equilibrium thickness and attempts to control thickness simply by drawing faster have a greater effect on width than on thickness. The first method of making thinner glass was to allow the ribbon to spread out to equilibrium width and cool it to a viscosity of around 10 8 dPas (700 °C) at which position the edges were gripped by edge rolls; further downstream the ribbon was reheated to around 106 dPa s (850 °C) and stretched to the required thickness, with some reduction in width, by adjusting the rate of drawing. The roof of the Float bath thus needs to be fitted with both electric heaters and cooling panels to permit the adjustment of the longitudinal temperature distribution. This method permits glass of high quality to be produced at thicknesses down to 3 mm. Subsequently other methods were developed. At high furnace loads the drag force of the tin can be used to confine stretching largely to the cooler end of the Float bath, where width and thickness are decreased in the same proportions, instead of acting only at the hot end where thickness hardly changes. Another variant uses several pairs of

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1 Classical Glass Technology

driven toothed wheels along the length of the Float bath to prevent excessive reduction in width; these wheels, which press on the edges of only the upper surface of the ribbon, are about 300 mm in diameter and 20 mm wide and mounted on long cooled shafts. They are especially useful in producing a wide ribbon at high loads. Glass thicker than the natural equilibrium thickness is produced by using graphite guides, which are not wetted by the glass, to prevent lateral spreading. This allows glass up to about 25 mm thick to be produced. Several types of process have been developed which permit coatings to be applied to the ribbon in the cooler end of the Float bath, or soon after its emergence from the tin bath. The Electrofloat process uses an electrolytic method to produce a surface layer on the top of the ribbon inside the Float bath by ion exchange. These processes are especially useful in making glasses with controlled heat transmission characteristics. Some information about them is given by Hynd (1984). Coatings are also discussed by Kirkbride and Williams (1991). 1.4.5 Rod and Tubing

A circular jet is inherently unstable, as pointed out in discussing flat glass manufacture, but drawing a circular rod or tube has fewer problems than maintaining a flat sheet. Rod and tube are made by very similar methods and have been little analysed in the literature, nor has their technology been discussed in detail. Although upward and downward drawing processes exist, those in which the rod or tube is drawn off sideways from the end of an inclined rotating mandrel are more widely used, rotation being necessary to cancel the effect of gravity. To make tubing it is necessary to have a mandrel with a central hole and to blow

air down it at a pressure only slightly greater than atmospheric. Rod is made in the same way but without the central air flow. 1.4.5.1 The Danner Process The Danner process may be regarded as the mechanization of hand drawing with a steady stream of glass falling on to the rotating blow pipe or mandrel at about 103 dPa s and running down to form a uniform layer then being drawn away from the lower end at about 5 x 104 dPa s and carried onto a horizontal series of rollers. The refractory sleeve of the mandrel is about 800 mm long and around 200 mm diameter; it is mounted on a heat resisting steel shaft about 50 mm in diameter. The nose of the mandrel may be of heat resistant steel, especially for tubing, because it can be machined and maintained to greater dimensional accuracy than a refractory nose. The mandrel rotates at around 8 rpm and is inclined at about 15° to the horizontal so that the glass will flow towards the tip. The tube is drawn away from the nose approximately in line with the axis of the mandrel and led onto a horizontal track about 50 m long where it is supported by rollers, see Fig. 1-41. Towards the end of the track, when quite cool, the tube is lightly gripped by two caterpillar driving belts which draw it away at the desired rate. These driving belts may be slightly angled across the line of draw so that the tube is rotated in the contrary sense to the rotation of the mandrel. As a result of these twisting forces the mass of glass just beyond the tip of the mandrel may look remarkably asymmetrical. The tube is cut into lengths just beyond these driving belts. One of the few detailed descriptions of the process is due to Sibilia (1939) and an approximate theoretical model was developed by Yamauchi (1977).

1.4 Glass Forming

Figure 1-41. Schematic diagram of a Danner tube drawing machine enclosed by a gas fired muffle chamber.

Since tube drawing does not use a mold control of both viscosity and the main parameters of the process must be very precise if accuracy of tube dimensions is required. Bajorat and Weiss (1965) reported data on some of the factors affecting the dimensions of Danner tube; their most detailed data being for tube of 37 mm OD with a 0.9 mm thick wall being drawn at 25 m min ~1 with the mandrel rotating at 8.1 rpm and an air pressure of 2.9 x 10 ~ 3 atm. The measurements concerned both the magnitude and the frequency of variations in air pressure, pipe rotation and drawing speed. For example, air pressure fluctuations of up to 4% lasting for 0.2 to 0.4 s had no measurable effect on tube diameter but a variation persisting for 2 to 4 s had a clear effect. Douglas (1938) showed that the rate of expansion of a long tube under internal pressure can be calculated by analogy with the elastic strain of a solid tube. If the tube is of external radius a and wall thickness w its rate of expansion under a pressure difference ZIP is given by

da/dt = a2AP/(4wrj)

(1-86)

Bajorat and Weiss (1965) reported that a 1% change in diameter was caused by a

79

1.6% change in pressure lasting for 2 s; putting these values into the equation gives a viscosity of 4.2 x 104 dPa s, which is close to the viscosity of the glass at the tip of the mandrel and confirms the reasonableness of their findings. Variations in the rotation of the mandrel can trap bubbles where the stream of glass falls on to the mandrel and may also lead to ovality of the tube. The Philips process is very like the Danner but uses glass drawn from the inside of a heat resistant steel mandrel and may thus avoid contamination of the inside of the tube by corrosion products, which must eventually happen with the refractory mandrel of the Danner process. 1.4.5.2 Vertical Drawing Processes

The upward or downward drawing processes appear more straightforward but, like vertically drawn sheet, suffer from producing the tube or rod at a considerably higher or lower level than that at which the glass is melted, unless the tube is curved round. The Koroljov process is based on the Fourcault process with a central blowing nozzle fitted below the centre of the debiteuse and can produce tubing up to 175 mm diameter. The Schuller and Corning processes also function by drawing vertically upwards from a refractory ring immersed in a pool of glass with the tube passing through a circular cooler just above the pool from which the tube is drawn; the Schuller method uses a circular ring with holes which blow air down on to the tube but the Corning process uses a water cooler. The Velio process uses a stream of glass which flows out of the bottom of a forehearth orifice and is spread out by a cone suspended on the end of a hollow shaft through which air is blown; the formed tube is gently curved round to be drawn along a horizontal track. There is

80

1 Classical Glass Technology

also a Corning downward drawing process in which the glass flows over the inner rim of a circular channel and is pulled downwards. There is an inner concentric water cooled truncated cone through the centre of which air may be blown but this cone acts chiefly as a cooler and is not in contact with the glass at any time. The literature on tube and rod drawing is sparse; Giegerich and Trier (1964) report most of what is available. 1.4.6 Glass Fibers 1.4.6.1 Introduction

Manufacture of fibers has been an important branch of the glass industry for about sixty years but within the last decade fibers of an entirely new kind have become very important, namely those used for optical communication systems. The first fibers used for optical communication were of very pure silica but these are incompatible with most other glasses because of their very low thermal expansion, unusually high softening point and very high viscosity. Thus, apart from trying to develop glasses with even better optical properties, silica fibers were rather difficult to use in some applications and most recent research has been devoted to heavy metal halide glasses (see Chap. 8). Such fibers are made by specialized methods based on the same principles as those used for other fibers but differing in many details and are not considered here. Some of the most interesting aspects of glasses for optical fibers have recently been discussed by Parker (1989), and a full treatment will be found in Chap. 15. The more traditional kinds of fibers are widely used for low density insulation, for reinforcement of polymers, and in some kinds of textiles. Such fibers have small di-

ameters, typically from 5 to 20 jim, and a very high surface to volume ratio; as a result they need to be made from glasses of better than average chemical durability. The standard type of glass developed for this purpose is called E-glass which means a glass with specific properties rather than a specified composition; a typical composition may include a little fluoride, see Table 1-1. This glass has a liquidus temperature of about 1140°C and, because it has very little alkali to act as a flux during melting, needs melting temperatures of 1550 to 1600°C. Despite its low alkali content it is not very resistant to attack by mineral acids and C-glass was developed for the improved acid durability needed for some purposes; it has some alkali but about 10% more silica than E-glass, see Table 1-1. The two main products are continuous fibers and staple or short curled lengths. The latter are mainly used for low density insulating mat which is bonded by spraying on an organic binder. Continuous fibers may be chopped into short lengths and also used for mat but can be made into a large variety of rovings (untwisted bundles of filaments) or yarn (twisted bundles of filaments) and used in many different ways, including being woven into cloth. A high proportion of all the continuous fiber made is used as reinforcing for polymer composite materials. 1.4.6.2 The Physics of Fiber drawing

The simple criteria developed to describe the stability of a liquid jet introduced when discussing the drawing of flat glass are directly relevant here. It may be recalled that a very viscous circular jet of radius a leaving an orifice would break up in a time of about TB=5rja/a

(1-87)

1.4 Glass Forming

if a is the surface tension. A fairly typical nozzle radius for fiber drawing would be a = 0.5 mm and assuming a viscosity of about 104 dPa s, a jet of that size would break up in about 20 ms. However, the fiber is drawn away at such a speed that its radius is much decreased immediately below the orifice and its radius is so small that it cools and becomes rigid in less than the critical time, without needing special measures to achieve sufficiently rapid cooling as is essential in producing flat glass. The hydrodynamics of fiber drawing is nevertheless very interesting. In the conditions used in making glass fibers it may be assumed that the flow through the nozzle itself is governed by Poiseuille's law, that is to say the mass rate of flow M through an orifice of radius a will be nAPa4 M =Q SrjL

(1-88)

where AP is the pressure difference causing flow (the hydrostatic head) and L the length of the nozzle. Drawing the fiber more quickly reduces its final diameter without increasing the mass flow rate; it is generally better to control the flow by having a short relatively small diameter orifice rather one a longer one of greater diameter. The viscosity range used for fiber drawing is quite narrow; if less than about 500 dPa s at the orifice the jet breaks up into drops; if greater than about 1000dPas the stresses become too high and breakage is frequent. Although drawing the fiber from the nozzle might appear to be very simple it shows some unexpected features. It is possible to observe four different profiles just below the orifice in the range of conditions that might be used for fiber drawing: 1) the fiber diameter decreases steadily (approximately exponentially) with distance from

81

the rim of the orifice, 2) the jet emerges as a stream of the same diameter as the orifice, 3) the stream of glass bulges out, rather like the onion in Fourcault sheet drawing, immediately below the orifice, or 4) a thin fiber forms from a base distinctly smaller than the size of the orifice. Burgman (1970) investigated these and showed that they could be related to Reynolds number. Glicksman (1968) made calculations of the rate of cooling of a fiber then used these results to predict how fiber diameter would change with distance from the orifice and obtained good agreement between measured and predicted profiles. 1.4.6.3 The Technology of Fiber Production

Staple fibers may be produced directly by several methods. One common method uses two rows of platinum alloy nozzles in the bottom of a forehearth which has adjacent downward pointing steam jets on each side to accelerate and attenuate the filaments. Because both glass and steam have similar kinematic viscosities in these conditions there is a major interaction between the two flows and the turbulent flow of the steam also curls the fibers and makes them break into fairly short lengths. As the fibers fall on to a collecting belt they are sprayed with a binder to form mat suitable for insulation. The fiber diameter is likely to vary between about 5 and 30 jim. The Hager-Rosengarth process uses centrifugal forces produced by a thin stream of glass falling on to the centre of a rotating disk to produce fibers. The disk rotates at 3000-4000 rpm and produces fairly long fibers (about 500 mm) of diameter around 20 jim which are carried away by a current of air and often laid down to make a mat. The TEL process is a rather similar one in which a stream of glass falls into the center of a shallow dish or spinner made of heat

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1 Classical Glass Technology

resistant steel which has several thousand apertures about 1 mm in diameter drilled around its circumference. The spinner rotates at about 3000 rpm and jets of glass fly horizontally out of the apertures to meet the combustion gases of a series of burners set around the perimeter of the spinner and pointing vertically downwards. The relatively thick jets leaving the spinner are thus reheated and further extruded to make the final fibers about 6jnm in diameter and about the same length as given by the Hager process. These are collected in a similar way. Some additional details of the processes are given by Giegerich and Trier (1964). 1.4.6.4 Continuous Fibers

The glass for manufacturing continuous fibers is generally melted in a small tank at about 1580°C and fed directly to the fiber drawing heads but it may be formed into 19 mm diameter marbles which are then fed directly into a separate drawing chamber, thus separating melting from fiber production. Although making marbles, cooling to room temperature and reheating, wastes a considerable amount of heat, the remelting and drawing is easy to control and is still the favored method for a few types of fiber. Continuous fibers are made by a process which relies on pulling the fiber away from a nozzle and using the velocity of drawing to attenuate the fiber to the desired diameter. The crucial nozzle dimensions are usually in the range of diameter 1 to 2.5 mm and length of the cylindrical part which controls flow rate 3 to 6 mm. The velocity of drawing may be more than 25 000 times the average velocity in the nozzle and the final fiber diameter as little as 6 jum; drawing speeds may be as high as 2500 mmin" 1 . Avoiding bubbles or crystalline inclusions in the glass is

thus very important. The large reduction in cross section also means that fibers are sometimes drawn under stresses not far short of the fracture stress and breakages may occur. The electrically heated platinum alloy bushing from which the fibers are drawn has several hundred nozzles (usually in multiples of 200) spaced as close together as convenient and is heated by the Joule effect. Having to stop the drawing for any reason, correct the defect and then restart drawing is a tedious operation; avoidable manufacturing defects are guarded against very carefully. A bushing has a working life of about 12 months and weighs 2 to 4 kg so that replacing it is a major expense. The drawing of a large number of fibers from a bushing creates a considerable flow of the air adjacent to the bushing and it is normal to supply an appropriate flow of clean air through inlets. The fibers are then sprayed with water before being coated with size by passing over a size applicator; this is often a rotating cylinder partially immersed in a bath of size. Next the fibers are gathered together by passing over a gathering shoe or wheel which may form one or several strands of yarn. The gathering shoe needs to be wetted to prevent the size adhering to it. Finally the strand is wound on a suitable core to make a cylindrical cake which is then dried and is ready for the final user. To make the strand easy to unwind it is wound on as a helix traversing from end to end of the bobbin. One important function of the size is to act as a surface lubricant to minimize damage by glass to glass abrasion during drawing and winding but it is very common for it to be formulated to act as a keying agent when the fiber is to be used in some kind of polymer composite; many different types of size exist for the latter use. The high drawing velocities mean that problems can

1.5 Polishing

sometimes arise over the rheological properties and wetting of the fiber by the size. An expert and detailed account of continuous fiber production is given by Loewenstein (1983). 1.4.6.5 Non-Circular Rod Tube and Fiber

Because glass flows as a perfectly newtonian liquid in most conditions it is possible to extrude preforms of many shapes and preserve their cross section, except for slight rounding off of sharp corners, provided that the extrusion is done at relatively high viscosity and fairly high stresses which minimize the effect of surface tension. The production of solid sections of a variety of shapes, such as rectangular and also hollow ones with internal ribs and partitions, was reported by Humphrey (1965). More recently Roeder and EgelHess (1987) have described the continuous extrusion of tubes with complex inner cross sections.

1.5 Polishing Most glass working operations are performed with hot fluid glass but polishing is the most important operation often necessary on cold glass. The Float process has made polishing unnecessary on large pieces of flat glass but it is still needed for high quality optical components and in preparing small samples for many kinds of laboratory measurements. Some glasses may also be polished by chemical rather than mechanical means but chemical polishing is not used when very accurate surface profiles are required. 1.5.1 Mechanical Polishing

Mechanical polishing is a rather slow and expensive process which consumes

83

large amounts of mechanical energy. The standard procedure is to wet grind the surface using in succession several grades of a suitable hard abrasive powder, each finer than the last, until a very fine frosted granular texture free from any pits or scratches left by the coarser grades is produced. The rate of removal decreases as the particle size and consequently chip size decrease. The liquid used at this stage is nearly always water and iron wheels are generally used. Large scale grinding of plate glass used to use quartz, which is a little harder than the glass but smaller scale operations usually use silicon carbide. Diamond wheels may be used for more rapid grinding or when making curved surfaces of specific radii but are much more costly. Having obtained a sufficiently fine texture the final stage of polishing uses a different very finely divided polishing agent in a similar way. Plate glass polishing used to use iron oxide but small scale operations frequently use specially prepared ceria on a cloth or felt covered wheel which is damp rather than wet. This eventually produces the required smooth and shiny surface. Polishing is an old art but one which is incompletely understood. The early stages of grinding to the necessary contour clearly operate by pressing the particles of grinding agent against the glass and breaking off chips of glass. The surface is formed by many small cracks which spread out and join together but also penetrate into the glass beneath. The use of several successively finer grades of abrasive is necessary to minimize the depth affected by this damage and thus avoid leaving sub-surface damage below the polished surface. The obvious simple physical model of polishing is to assume that the glass always behaves as an isotropic brittle material; using finer and finer grades of grinding and polishing agents is then assumed to produce essen-

84

1 Classical Glass Technology

tially similar surface texture on an ever smaller scale until the scale of the roughness is rather less than the wavelength of light and no longer gives scattering at the interface. Such a view has often been put forward in the past, for example by Newton in 1695 (see Thomson, 1922 and Preston, 1921). However, we now know that glass can flow on a small scale at room temperature: diamond pyramid micro-indentation tests can make permanent impressions in glasses, as in metals, so the possibility of some local flow cannot be ignored. A theory of flow in polishing was first elaborated by Beilby (1921) but has found few adherents. Its most obvious defect is that it attributes polishing entirely to flow of the surface layer but all quantitative studies show that polishing does remove material. It is now widely agreed that some chemical interaction between glass, polishing agent and liquid medium must be considered. This view was shared by Preston (1930) only a few years after his earlier championing of the abrasion theory. However, no theory yet put forward seems to be capable of explaining all the observations made in glass polishing studies. One of the most obvious pieces of evidence for a chemical interaction is that polishing efficiency is clearly not determined simply by particle size and hardness: most of the effective polishing agents are oxides of variable valence elements. The staining of the surface that can occur during polishing with iron oxide, chromium oxide, and ceria is another interesting demonstration of some chemical interaction. The liquid medium also has a definite influence and the pH of the medium can considerably affect both rate of removal of material and surface finish (Compton, 1989). One recent attempt to interpret the polishing of glasses is by Koucky and Matusek (1984) but, de-

spite its importance to the optical industry, mechanical polishing of glass remains only partially understood. 1.5.2 Acid Polishing

For many years it has been the practice of the lead crystal industry to polish cut (abraded) glass chemically by using hydrofluoric acid, the one readily available reagent capable of easily dissolving silicate glasses. It has also been known for a considerable time that etching away the surface layers of glass containing flaws which weaken it can increase the strength (Proctor, 1962). Such etching does not necessarily produce a polished surface, especially when the products of reaction are not removed, and commercial etchants of this type are often used for badging or otherwise producing frosted surfaces. Ammonium fluoride may be present in these mixtures. In recent years there have been many studies concerned with the safety of the operation and the disposal of the residues from the mixtures of hydrofluoric and sulfuric acids normally used but few concerned with details of the chemistry and the influence of the acid on the glass, however, some of these matters were discussed by Maskill and Ferguson (1950). A lengthy discussion by Kausch (1973) gives extensive descriptions of typical installations and useful information about the construction of baths and accessories sufficiently resistant to hydrofluoric and sulfuric acids for industrial use. Vacek and Kopackova (1977) concentrate more on some of the chemical aspects of the process. The essential step in the process may be considered to be 2 H + + SiF62~

n)H 2 O

(1-89)

1.6 References

When polishing glasses which contain lead or barium with a medium using sulfuric acid, the sulfates of these elements are also precipitated because they are considerably less soluble than the fluorides. Extraction of other alkali and alkaline earth ions also tends to neutralize the acid. It is thus necessary to replenish both acids from time to time as well as to dispose of the sludge which is formed. The low pH of the solution encourages the process ^ ^ 2 H + + SiF62~ -> H2SiF6 -> 2HF + SiF4 to proceed to the right and the evolution of both HF and SiF4 as vapors is an important health hazard which must be strictly controlled. The rate at which glasses are etched by hydrofluoric acid based solutions is strongly dependent on glass composition and Loftier (1954, 1957, 1964) used this to develop techniques for identifying various types of cord and ream by examining in an interferometer sections first polished and then acid etched, different types of cord giving different characteristic etching contours. Cable and Hakim (1973) used this technique to obtain a quantitative index of homogeneity.

1.6 References Abou el Azm, A.M.A., Moore, H. (1953), J. Soc. Glass Tech. 37, 129-154, 155-167, 168-181, 182189, 190-210. Afghan, M., Cable, M. (1980), Proc. XIII Internat. Glass Congress, Albuquerque. Amsterdam, New York, Oxford: North Holland, pp. 3-8. Anon. (1791), Encyclopedic Methodique. Paris: C. J. Panckcoucke, Vol. 8. Appen, A. A. (1949), Proc. Acad. Set USSR 69, 841 844. Appen, A. A. (1954), Silikattech. 5, 11-12. Appen, A. A. (1956), Proc. IV Internat. Glass Congress. Paris: Imprimerie Chaix, pp. 36-40. Appen, A. A., Polyakova, L. B. (1938), StekoL Prom. 1 (7), 18-21.

85

Appen, A. A., Kozlovskaya, E.I., Gan, E X . (1961), J. Appl. Chem. USSR 34, 975-981. Aylward, N.H., Cable, M., Wang, S.S. (1986), Proc. XIV Internat. Glass Congress, New Delhi. Calcutta: Indian Ceramic Society. Vol. 2, pp. 280-287. Babcock, C.L. (1977), Silicate Glass Technology Methods. New York/London/Sydney/Toronto: Wiley, Interscience. Backman, R., Cable, M., Karlsson, K., Pennington, N. P. (1990), Final Report EURAM Contract MA/ 1E/009/C; Glastech. Ber. 63K, 460-469. Bajorat, H., Weiss, W. (1965), Glastech. Ber. 38, 147152. Barton, XL. (1989), Glass Technol. 30, 115-116. Bastick, R. E. (1956), Compte Rendu Symposium sur L'Affinage du Verre. Paris: Union Scientifique Continentale du Verre, pp. 127-138. Beilby, G.T. (1921), Aggregation and Flow of Solids. London: MacMillan. Bezborodov, M. A. (1968), Synthesis and Structure of Glasses (in Russian). Minsk: Nauka i Tekhnika. Bezborodov, M. A., Appen, A. A., Korsukhina, T. E, Chodikel, E.P., Shinke, G. A. (1933), J. Soc. Glass Tech. 17, 305-319. Bilby, B. A., Eshelby, J. D., Kundu, A. K. (1975), Tectonophys. 28, 265-274. Bollert, X, Griffel, H., Seidel, H.-G. (1987), Glastech. Ber. 60, 406-410. Boffe, M., Letocart, G. (1962), Glass Technol. 3,117123. Borel, E. (1958), Fusion Electrique du Verre. Neuchatel: Paul Attinger. Bosc D'Antic, P. (1789), Oeuvres Paris 2 vols. Botvinkin, O.K. (1936), New Work on the Physical Chemistry of Glass (in Russian). Moscow and Leningrad. Bottinga, Y, Weill, D.F. (1972), Amer. J. Sci. 272, 438-475. Braginskii, K. I. (1973), Glass and Ceramics 30, 451454. Brill, R. H. (1965), Proc. VIIInternat. Glass Congress, Brussels. Part 2, Paper No. 223, pp. 1-13. Brown, S. C. (1979), Benjamin Thomson, Count Rumford. Cambridge, Mass.: MIT Press. Burgman, X A. (1970), Glass Technol. 1, 110-116. Cable, M. (1958), J. Soc. Glass Tech. 42, 20-31. Cable, M. (1960), Glass Technol 1, 144-154. Cable, M. (1978), in: Borate Glasses: Structure Properties and Applications: Pye, L. D., Frechette, V.D., Kreidl, N.X (Eds.). New York/London: Plenum Press, pp. 399-411. Cable, M., Bower, C. (1965), Glass Technol. 6, 197205. Cable, M., Clarke, A.R., Haroon, M.A. (1969). Glass Technol. 10, 15-21. Cable, M., Frade, X R. (1987 a), J. Mater. Sci. 22, 149-154. Cable, M., Frade, XR. (1987 b), /. Mater. Sci. 22, 919-924.

86

1 Classical Glass Technology

Cable, M., Frade, J.R. (1987 c), J. Mater. Sci. 22, 1894-1900. Cable, M., Frade, J.R. (1987d), Glastech. Ber. 60, 355-362. Cable, M., Frade, J. R. (1988), Proc. Roy. Soc. Lond. A420, 247-265. Cable, M., Frade, J. R. (1991), submitted to J. Amer. Ceram. Soc. Cable, M., Hakim, J. (1973), Glass Technol. 14, 90100. Cable, M., Haroon, M. A. (1970), Glass Technol. 11, 48-53. Cable, M., Martlew, D. (1971), Glass Technol. 12, 142-147. Cable, M., Martlew, D. (1984), Glass Technol. 25, 24-30; 139-144. Cable, M., Martlew, D. (1985), Glass Technol. 26, 212-217. Cable, M., Martlew, D. (1986), Trans. J. Brit. Ceram. Soc. 85, 95-100. Cable, M., Naqvi, A. A. (1975), Glass Technol. 16, 2-11. Cable, M., Siddiqui, M.Q. (1980), Glass Technol. 21, 193-198. Cable, M., Smedley, J. W. (1987 a), Glass Technol. 28, 94-98. Cable, M., Smedley, J. W. (1987b), in: Early Vitreous Materials. Bimson, M., Freestone, I. C. (Eds.). London: British Museum Laboratory Occasional Papers No. 56, pp. 151-164. Cable, M., Smedley, J.W. (1989), Glass Technol. 30, 39-46. Cable, M., Swan, H.T. (1988), Glass Technol. 29, 144-149. Cable, M., Walters, S. D. (1980), Glass Technol. 21, 279-283. Carslaw, H. S., Jaeger, J. C. (1959), The Conduction of Heat in Solids. Oxford: Clarendon Press. Carter, R. E. (1961 a), /. Chem. Phys. 34, 2010-2015. Carter, R. E. (1961 b), J. Chem. Phys. 35, 1137-1138. Cassidy, D.C., Gjostein, N.A. (1970), /. Amer. Ceram. Soc. 53, 161-168. Clayton, R., Algar, J. (1989), The GEC Research Laboratories 1919-1984. London: Peter Peregrinus. Cobb, J.W. (1910), J. Soc. Chem. Ind. 29, 69-1 A, 250259, 335-336, 399-404, 608-614, 799-802. Compton, S. (1989), The polishing of ophthalmic crown glass. Ph. D. Thesis, University of Sheffield. Cooper, A.R. (1966 a), Glass Technol. 7, 2-11. Cooper, A. R. (1966 b), Chem. Engng. Sci. 21, 87-94. Cox, R.G. (1969), J. Fluid Mech. 37, 601-623. Daniels, M. (1973), Glastech. Ber. 46, 40-46. Diderot, D., D'Alembert, J. (1765), Encyclopedie ou Dictionnaire Raisonnee. Paris, Neufchastel: Plates vol IV Glacerie: (1772) Ibid vol XVII Verrerie. Douglas, R.W (1938), /. Soc. Glass Tech. 22, 206213; 259. Douglas, R.W, Frank, S. (1972), A History of Glassmaking. Henley on Thames: G. T. Foulis.

Dumbaugh, W H., Bocko, P. L., Fehlner, F P. (1991), in: High Performance Glasses: Cable, M., Parker, J. M. (Eds.). Glasgow: Blackie. Eshelby, I D . (1957), Proc. Roy. Soc. Lond. A241, 276-296. Eshelby, J.D. (1959), Proc. Roy. Soc. Lond. A 252, 561-569. Everett, J. D., Everett, A. (1902), Jena Glass & its Scientific and Industrial Applications. London: Macmillan. Faraday, M. (1830), Phil. Trans. Roy. Soc. Lond. 128, 1-57. Fletcher, W W (1963), Glass Technol. 4, 152-158. Fraunhofer, J. (1817), Reprinted in (1866), Bayer. Kunst und Gewerbeblatt 1-19, 34-49. Gardon, R. (1961), /. Amer. Ceram. Soc. 44, 305-312. Gell, P. A. M. (1956), J. Soc. Glass Tech. 40, 482-494. Genzel, L. (1953), Glastech. Ber. 26, 69-71. Giegerich, W. (1960), Glastech. Ber. 3, 441-449. Giegerich, W, Trier, W (1964), Glasmaschinen. Berlin, Gottingen, Heidelberg: Springer. Ginstling, A.M., Brounshtein, V.I. (1950), J. Appl. Chem. USSR (Consultants Bureau Translation) 23, 1327-1338. Glicksman, L.R. (1968), Glass Technol. 9, 131-138. Goerk, H. (1966), Tazeni Plocheni Skla. Prague: SNTL. Greene, C.H., Davis, D.H. (1974), Proc. X Internat. Glass Congress, Kyoto. Tokyo: Ceramic Society of Japan, Part 3, pp. 59-62. Greene, C.H., Gaffney, R. (1959), J. Amer. Ceram. Soc. 42,211-212. Greene, C. H., Kitano, I. (1959), Glastech. Ber. 32K, V, 44-48. Greene, C.H., Lee, H.A. (1965), /. Amer. Ceram. Soc. 48, 528-533. Greene, C.H., Platts, D. R. (1969), /. Amer. Ceram. Soc. 52, 106-109. Griffith, A. A. (1920), Trans. Roy. Soc. Lond. A 221, 163-198. Guido, M., Henderson, X, Cable, M., Bayley, X, Biek, L. (1984), Proc. Prehist. Soc. 50, 245-254. Hatakka, L. (1986), Glass 63, 449-450. Hlavac, X (1983), The Technology of Glass and Ceramics. Amsterdam: Elsevier. Hlavac, X, Nademlynska, H. (1969), Glass Technol. 10, 54-58. Hoover, H. C , Hoover, L. H. (1912), De Re Metallica (translation), London: Mining Magazine (1950) reprint, New York: Dover. Hornyak, E.X, Weinberg, M.C. (1984), Comm. Amer. Ceram. Soc. C 244-246. Hovestadt, H. (1900), Jenaer Glas und seine Verwendung in Wissenschaft und Technik. Jena: G. Fischer. Howard, I.C., Brierley, P. (1976), Int. J. Engng. Sci. 14, 1151-1159. Huff, N. T., Call, A. D. (1973), J. Amer. Ceram. Soc. 56, 55-57. Huggins, M.L., Sun, K.-H. (1943), J. Amer. Ceram. Soc. 26, 4-11.

1.6 References

Humphrey, R. A. (1965), Proc. VHInternat. Congress on Glass, Brussels. Charleroi: INdV, Paper No. 77, pp. 1-8. Hynd, W. C. (1984), in: Glass Science and Technology, Vol. 2, Processing I. Kreidl, N. X, Uhlmann, D. R. (Eds.). New York/London: Academic Press, Chap. 2. Ito, T., Hosoi, T., Suganuma, M., Uno, T. (1954), Res. Rept. Asahi Glass Co. 4, 98-106. Jack, H. R. S., Jacquest, I T. (1958), Symposium sur la Fusion du Verre, Brussels. Charleroi: Union Scientifique du Verre, pp. 339-360. Jander, W. (1927), Z. anorg. allgem. Chem. 163,1-30. Jebsen-Marwedel, H. (1936), Glastechnische Fabrikationsfehler, 1st ed. Berlin: Springer. Jebsen-Marwedel, H. (1956), Glastech. Ber. 30, 122129. Joanni, E. (1989), Homogenization of Laboratory Scale Glass Melts, PhD. thesis, University of Sheffield. Joanni, E., Smedley, I W , Cable, M. (1989), Proc. XV Internat. Glass Congress, Leningrad. Leningrad: Nauka. Vol. 3 a, 66-71. Kausch, J.C. (1973), Sprechsaal 106, 401-408, 522531, 627-630, 667-669. Kiessling, B., Dressel, H. (1979), Silikattech. 30, 210213. Kirkbride, B. X, Williams, G. (1991), in: High Performance Glasses. Cable, M., Parker, XM. (Eds.). Glasgow: Blackie. Koucky, X, Matusek, M. (1984), Glass Technol 25, 240-243. Kreider, K. G., Cooper, A.R. (1967), Glass Technol. 8, 11-13. Kroger, C , Fingas, G. (1933), Z. anorg. allgem. Chem. 213, 482-483. Kroger, C. (1948), Glastech. Ber. 22, 86-93. Kroger, C. (1953), Glastech. Ber. 26, 202-214. Kroger, C , Eligehausen, H. (1959), Glastech. Ber. 32, 362-372. Kroger, C , Marwan, F. (1955), Glastech. Ber. 28, 51-57; 89-98. Kroger, C , Marwan, F. (1956), Glastech. Ber. 29, 257-289. Kroger, C , Marwan, F. (1957), Glastech. Ber. 30, 222-229. Kroger, C , Vogel, E. (1955), Glastech. Ber. 28, 426437; 468-474. Kroger, C , Ziegler, G. (1952), Glastech. Ber. 25, 307324. Kroger, C , Ziegler, G. (1953), Glastech. Ber. 26, 346353. Kroger, C , Ziegler, G. (1954), Glastech. Ber. 27,199212. Kroger, C , Janetzko, W, Kreitlow, G. (1958), Glastech. Ber. 31,221-228. Kunckel, X (1679), Ars Vitraria Experimentalis, 1st ed. Frankfurt, Leipzig: Johann Bielcke. Lakatos, X, Johansson, L.-G., Simmingskold, B. (1972 a), Glass Technol. 13, 88-95.

87

Lakatos, T., Johansson, L.-G., Simmingskold, B. (1972 b), Glastekn. Tidskr. 27, 25-28. Lakatos, T., Johansson, L.-G., Simmingskold, B. (1972 c), Glastekn. Tidskr. 27, 11-SO. Lakatos, T., Johansson, L.-G., Simmingskold, B. (1973), Glastekn. Tidskr. 28, 69-73. Lakatos, T., Johansson, L.-G., Simmingskold, B. (1974), Glastekn. Tidskr. 29, 43-47. Lakatos, T., Johansson, L.-G., Simmingskold, B. (1975), Glastekn. Tidskr. 30, 7-8. Lakatos, T., Johansson, L.-G., Simmingskold, B. (1976 a), Glastekn. Tidskr. 31, 31-35. Lakatos, T., Johansson, L.-G., Simmingskold, B. (1976b), Glastekn. Tidskr. 31, 51-54. Lakatos, T., Johansson, L.-G., Simmingskold, B. (1977), Glastekn. Tidskr. 32, 31-35. Lakatos, T., Johansson, L.-G., Simmingskold, B. (1978), Glastekn. Tidskr. 33, 55-59. Lakatos, T., Johansson, L.-G., Simmingskold, B. (1979), Glastekn. Tidskr. 34, 9-10. Lakatos, T., Johansson, L.-G., Simmingskold, B. (1981), Glastekn. Tidskr. 36, 51-55. Lamb, H. (1945), Hydrodynamics 6th. ed. New York: Dover, pp. 623-628. Lemaire, E. (1965), Proc. VII Internat. Congress on Glass, Brussels. Vol. 2, Paper No. 223, 1-10. Levich, V. I. (1962), Physicochemical Hydrodynamics. Englewood Cliffs, New Jersey: Prentice Hall. Loewenstein, K. L. (1983), The Manufacturing Technology of Continuous Glass Fibres, 2nd ed. Amsterdam, Oxford, New York: Elsevier. Loffler, X (1954), Glastech. Ber. 27, 381-392. Loffler, X (1957), Glastech. Ber. 30, 457-463. Loffler, X (1964), Glastech. Ber. 37, 548-553. Manring, W.H., Bauer, W.C. (1964), Glass Ind. 45, 413-416; 449-451. Manring, W. H., Hopkins, E. W. (1958), Glass Ind. 39, 139-142; 170. Maskill, W, Ferguson, D. (1950), /. Soc. Glass Tech. 34, NR 115-121. Maurer, E., Bischoff, W. (1930), Stahl und Eisen 55, 477-484. Mazurin, O.V., Strel'tsina, M.V., Shvaiko-Shvaikovskaya, T.P. (1973-1981), Properties of Glass and Glass-forming Melts (in Russian), Six vols. Leningrad: Nauka. McGraw, D. A. (1961), / Amer. Ceram. Soc. 44, 353363. McKelvey, XM. (1962), Polymer Processing. New York: John Wiley. McMillan, P. W. (1979), Glass Ceramics, 2nded. London, New York, San Francisco: Academic Press. Merret, C. (1662), The Art of Glass. London: printed by A. W. for Octavian Pulleyn. Mohr, W. D. (1960), in: Processing of Thermoplastic Materials. Bernhard, E. C. (Ed.). New York: Reinhold, Chap. 3. Moody, B.E. (1988), Glass Technol. 29, 198-210. Moody, B.E. (1989), Glass Technol. 30, 191-192.

88

1 Classical Glass Technology

Moore, J., Sharp, E. E. (1958), /. Amer. Ceram. Soc. 41, 461-463. Morrell, I, Thackray, A. (1981), Gentlemen of Science. Oxford: Clarendon Press. Mulfinger, H. O. (1974), Glastekn. Tidskr. 29, 81-95. Mulfinger, H.O. (1976), Glastech. Ber. 49, 232-245. Muller, R, Lim, S.-K., Gebhardt, R, Kiistner, D. (1989), Glastech. Ber. 62, 369-376. Mullins (1959), J. Appl. Phys. 30, 77-83. Nemec, L. (1974), Glass TechnoL 15, 153-161. Nemec, L. (1977 a), Proc. XI Internat. Glass Congress, Prague. Praha: CVTS, Vol. 4, 155-165. Nemec, L. (1977 b), /. Amer. Ceram. Soc. 69, 436440. Nemec, L. (1980), Glass TechnoL 21, 139-144. Neri, A. (1612), L'Arte Vetraria. Pirenze: nella Stampa de'Giunti. Newton, I. (1704), Optics. London: (Reprint (1952) New York: Dover). Newton, R.G. (1985), Glass TechnoL 26, 93-103. Okhotin, M.V. (1954), Steklo Keram. 11 (1), 7-11. Onorato, P.I.K., Weinberg, M.C., Uhlmann, D.R. (1981), J. Amer. Geram. Soc. 64, 676-682. Parker, X M. (1989), Ann. Rev. Mater. Sci. 19, 21 -41. Pilkington, L.A.B. (1969), Proc. Roy. Soc. Lond. A 314, 1-25. Poole, J.P. (1963), Glass TechnoL 4, 143-152. Potts, J.C. (1939), /. Soc. Glass Tech. 23, 129-150. Potts, J.C. (1941), J. Amer. Ceram. Soc. 24, 43-50. Potts, J.C, Brookover, G., Burch, O.G. (1944), /. Amer. Ceram. Soc. 27, IIS-ISX. Preston, RW. (1921-1922), Trans. Opt. Soc. Amer. 23, 141. Preston, R W. (1930), J. Soc. Glass Tech. 14,127-132. Preston, E., Turner, W.E.S. (1940), /. Soc. Glass Tech. 24, 124-138. Proctor, B. (1962), Phys. Chem. Glasses 3, 7-27. Pugh, A.C.P. (1968), Glastekn. Tidskr. 23, 95-104. Ratcliffe, E. H. (1963), Glass TechnoL 4, 113-128. Reinhardt, H.P. (1965), Proc. VII Internat. Congress on Glass, Brussels. Charleroi: Institut Nationale du Verre. Vol. 1, Paper No. 73, 1-10. Rhiel, P.P. (1976), Glastech. Ber. 49, 217-226. Richet, P. (1987), Chem. Geol. 62, 111-124. Roeder, E., Egel-Hess, W. (1987), Glastech. Ber. 60, 177-181. Rosenkrands, B., Simmingskold, B. (1962), Glass TechnoL 3, 46-51. Russ, A. (1928), Sprechsaal61, 887-891; 907-913. Sadeghi, J.J. (1980), Ph.D. Thesis, University of Sheffield. Schmid, W, Hertel, H. (1968), Glastech. Ber. 41, 395408. Scholze, H. (1977), Glas: Natur, Struktur und Eigenschaften, 2nd ed. Berlin, Heidelberg, New York: Springer. Schuster, A. (1903), Phil. Mag. Series 65, 243-257'. Scriven, L. E. (1959), Chem. Engng. Sci. 10, 1-13. Sharp, D.E., Ginther, L. B. (1951), J. Amer. Ceram. Soc. 34, 260-271.

Shaw, H.R. (1972), Amer. J. Sci. 272, 870-893. Sheckler, C. A., Dinger, D. R. (1990), J. Amer. Ceram.

Soc. 73, 24-30. Sibilia, V. E. (1939), /. Soc. Glass Tech. 23, 292-307. Silverman, A. (1939), /. Amer. Ceram. Soc. 22, 378384. Simpson, W, Myers, D. (1978), Glass TechnoL 19, 82-84. Slavyanskii, V. T. (1957), Gases in Glass (in Russian). Moscow: Gos. Izdat. Oboronoi Prom., pp. 87115. Solinov, F.G., Pankova, N. A. (1965), Proc. VII Internat. Glass Congress, Brussels. Charleroi: Institut Nationale du Verre. Paper No. 341, pp. 1-11. Stanek, J. (1977), Electric Melting of Glass. Amsterdam, Oxford, New York: Elsevier. Stein, G. (1958), in: Gunther, R., Glass Tank Furnaces (English translation). Sheffield: Society of Glass Technology. Stokes, G. G. (1871), Brit. Assoc. Reports 41, 38-44. Swift, H.R. (1947), /. Amer. Ceram. Soc. 30, 170174. Taylor, G.I. (1934), Proc. Roy. Soc. Lond. A146, 501-523. Thomas, W.R (1960), Phys. Chem. Glasses 1, 4-18. Thomson, E. (1922), J. Opt. Soc. Amer. 6, 843-847. Tober, H. (1990 a), Glastech. Ber. 63, 78-84. Tober, H. (1990 b), Glastech. Ber. 63, 172-182. Trier, W. (1955), Glastech. Ber. 28, 336-351. Trier, W. (1984), Glasschmelzofen. Berlin, Heidelberg, New York, Tokyo: Springer. Turkdogan, E. T. (1983), Physicochemical Properties of Molten Slags and Glasses. London: Metals Society. Turnbull, D., Cohen, M. (1960), in: Modern Aspects of the Vitreous State, Vol. 1. Mackenzie, J. D. (Ed.). London: Butterworth, pp. 38-62. Turner, W.E.S. (1962), Glass TechnoL 3, 201-213. Vacek, M., Kopackova, J. (1977), Proc. XI Internat. Glass Congress, Prague. Praha: CVTS, Vol. 5, pp. 253-263. Valensi, G. (1935), C. R. Acad. Sci. Paris, 201, 602604. Valensi, G. (1936), C. R. Acad. Sci. Paris, 202, 309312. Valensi, G. (1950), /. Chim. Phys. 47, 489-505. Vernon Harcourt, W. (1844), Brit. Assoc. Reports 14, 82-85. Volf, M.B. (1961), Technical Glasses. London: Pitman. Walther, A., Eller, J., Dorr, E. (1953), Glastech. Ber. 26, 133-146. Westerlund, T., Hatakka, L., Karlsson, K. (1983), /. Amer. Ceram. Soc. 6, 574-579. West-Oram, R G. (1979), Glass TechnoL 20, 222-245. Wiedmann, K. (1954), Glastech. Ber. 27, 33-40. Wilburn, F. W, Thomasson, C. V. (1958), /. Soc. Glass Tech. 42, 158-175. Wilburn, RW, Thomasson, C.V. (1960), Phys. Chem. Glasses 1, 52-69.

1.6 References

Wilburn, F.W., Metcalf, S.A., Warburton, R.S. (1965), Glass Technol. 6, 107-114. Winkelmann, A., Schott, O. (1894), Ann. Phys. Chem. 51, 697-714, 730-746. Yamauchi, H. (1977), Proc. XI Internat. Glass Congress, Prague. Praha: CVTS, Vol. 5, 147-158. Zachariasen, W.H. (1932), /. Amer. Chem. Soc. 54, 3841=3851. Zeng, R.J., Cable, M., Harris, E.A. (1989), Supercond. Sci. Technol. 2, 47-51.

General Reading Babcock, G.L. (1977), Silicate Glass Technology Methods. New York: Wiley. Douglas, R. W, Franck, S. (1972), A History of Glassmaking. London: Foulis Co.

89

Giegerich, W, Trier, W. (1964), Glasmaschinen. Berlin, Gottingen, Heidelberg: Springer. Hlavac, J. (1983), The Technology of Glass and Ceramics. Amsterdam, Oxford, New York: Elsevier. Morey, G. W. (1954), The Properties of Glass, 2nd ed. New York: Reinhold. Rawson, H. (1967), Inorganic Glass Forming Systems. London, New York: Academic Press. Rawson, H. (1980), Properties and Applications of Glass. Amsterdam, Oxford, New York: Elsevier. Shand, E.B. (1958), Glass Engineering Handbook. New York: McGraw. Scholze, H. (1977), Glas, Natur, Struktur und Eigenschaften, 2nd ed. Berlin, Heidelberg, New York: Springer. Tooley, F. V. (Ed.) (1961), Handbook of Glass Manufacture, Vol. I and II, 2nd ed. New York: Ogden. Uhlmann, D.R., Kreidl, N.J. (1984), Glass Science and Technology, Vol. 2, Processing, I. New York: Academic Press. Zarzycki, J. (1991), Glasses and the Vitreous State. Cambridge: Cambridge Univ. Press.

2 Special Methods of Obtaining Glasses and Amorphous Materials Jerzy Zarzycki Laboratory of Science of Vitreous Materials, University of Montpellier, Montpellier, France

List of 2.1 2.1.1 2.1.2 2.1.3 2.2 2.2.1 2.2.2 2.3 2.3.1 2.3.2 2.3.3 2.4 2.4.1 2.4.2 2.4.3 2.4.4 2.5 2.6 2.7 2.7.1 2.7.1.1 2.7.1.2 2.7.1.3 2.7.2 2.7.3 2.7.3.1 2.7.3.2 2.7.3.3 2.7.4 2.7.4.1 2.7.4.2 2.7.5 2.7.5.1 2.7.5.2

Symbols and Abbreviations Introduction Glasses and Amorphous Materials The Concept of "New Glasses" Different Routes to Non-Crystalline Solids Melt Quenching Techniques Unconventional Melting Ultrafast Quenching Vapor Quenching Techniques Evaporation Sputtering Reactive Deposition Solid-State Methods Radiation Damage Effects of Intense Shock Waves Slow Mechanical Actions Diffusion Effects Electrochemical Methods - Anodic Oxidation Pyrolysis Solution Methods; "Sol-Gel" Processing of Glasses Methods of Gel Formation Gel Formation from Alkoxides Gel Formation from Sols Redispersion Methods Aging Effects Drying The Role of Capillary Forces Obtaining Monolithic Gels Structural Aspects Curing-Sintering Viscous Flow Sintering Devitrification Kinetics - Use of TTT Diagrams Forming Processes Bulk Glass Thin Films

Materials Science and Technology Copyright © WILEY-VCH Verlag GmbH & Co KGaA. Allrightsreserved.

93 94 94 94 95 95 95 95 98 98 98 99 100 100 100 101 101 102 102 102 103 103 105 106 107 107 108 108 110 110 Ill Ill 112 112 112

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2.7.5.3 2.7.5.4 2.7.6 2.7.7 2.8

2 Special Methods of Obtaining Glasses and Amorphous Materials

Fibers Hollow Glass Microspheres Advantages and Disadvantages of the Sol-Gel-Process Future Trends References

113 113 114 114 116

List of Symbols and Abbreviations

List of Symbols and Abbreviations

c

D E P r

r

critical point fractal dimension Young's modulus critical stress concentration coefficient pressure radius of the pore reduced time

V

fracture surface energy specific surface energy viscosity Poisson's number

CVD DCCA HSE ICF NMR rf SAXS TTT

chemical vapor deposition drying control chemical additives hypercritical solvent evacuation inertial confinement fusion nuclear magnetic resonance radio frequency small angle X-ray scattering time-temperature-transformation

7

n

93

94

2 Special Methods of Obtaining Glasses and Amorphous Materials

2.1 Introduction 2.1.1 Glasses and Amorphous Materials Glasses, in the current sense of the term, are essentially non-crystalline materials obtained by fusing together silica (sand) with Na and Ca oxides (in the form of carbonates), which act as fluxes and lower the processing temperature. The resulting melt is cooled at a sufficient rate to avoid crystallization and then shaped into different forms: flat sheets, containers, fibers. This classical glass technology was the object of the preceding chapter. The glass-making process has evolved over the centuries and now represents a heavy industry with a yearly production of approximately 18 million tons for the European Community and about the same amount for the U.S.A. It is well known, however, that substances other than silica or silicates can exist in a non-crystalline form. Tamman (1933) coined the concept of the "glassy state of matter" to describe this situation, and glasses are often simply identified with non-crystalline materials. This definition is obviously too wide, as it encompasses materials which, though noncrystalline, frankly have different properties (e.g., gels). Furthermore, quenching a liquid is not the only way in which noncrystalline solids can be obtained. It would therefore seem more appropriate to reserve the term of "glasses" only for those noncrystalline solids which present the phenomenon of "glass transition", whatever their origin, and to call the remainder amorphous materials (Zarzycki, 1982 a). This classification however, has not yet been universally adopted. The terms "amorphous" and "non-crystalline" are often considered as synonymous; for instance, Elliott (1990) defines glass as "an amorphous solid which exhibits a glass transition".

2.1.2 The Concept of "New Glasses" Non-crystalline solids, glasses, and amorphous materials alike now play an increasingly important role in modern technology. Besides common glass, which is an indispensable material in today's economy in architecture, transport, lighting, conditioning, etc., there is a whole set of glasses and amorphous materials which enter into more and more sophisticated applications in optics, electronics, optoelectronics, biotechnologies, etc. The concept of "new glasses" emerged progressively and covers materials other than classical glasses. The Japanese experts consider the market for these new materials to be of the order of $ 1 billion in 1987 and estimate that it will reach $ 17 billion by the beginning of the 21st century. It should be noted that in many cases the methods of producing these materials differ so profoundly form classical glass technology that their manufacture is being taken over by firms not traditionally concerned with glass but rather with electronic equipment or chemistry. Most of these glasses are high-tech materials and their production is to be evaluated in tons rather than in millions of tons as is the case of classical glass. The purpose of this chapter is to review the various "unusual" ways of producing glass and amorphous materials. Some of these methods are of purely academic value or are still in the laboratory stages, while others have already gained industrial importance. Previous reviews of this subject have been made by Secrist and Mackenzie (1964) and Scherer and Schultz (1983). Particular attention will be paid here to the obtention of glasses from precursors using methods of soft chemistry which have shown particularly rapid development in recent years.

2.2 Melt Quenching Techniques

2.1.3 Different Routes to Non-Crystalline Solids

To obtain a glass or an amorphous solid, it is necessary either to retain at ambient temperature the disordered state of a liquid or gas, or, alternatively, to destroy (amorphize) the structure of a crystal. It is also possible to produce the disordered structure directly by means of suitable chemical reactions which may or may not be assisted by external fields (electrical or chemical potentials). The following general types of methods are at our disposal: • melt quenching • vapor quenching • crystalline solid disordering (other than melting) • interdiffusion and sintering • electrolysis • pyrolysis • reactions in solution

2.2 Melt Quenching Techniques

95

which leads to melting in an atmosphere of inert gas, often in sealed ampoules. Atmospheric control is also necessary for metallic glasses (see Chapter 9). For halide glasses (see Chapter 8) the melt is obtained by fluorination of corresponding oxides in an atmosphere containing HF. Melting under high pressure has seldom been used in practice. It was applied by Datta et al. (1964) under 1 kbar pressure to produce K 2 CO 3 -MgCO 3 glasses, as well as glasses combining Mn, Pb, or Ca carbonates. Operating under pressures of up to 10 kbar, in an Ar, H 2 O, or CO 2 atmosphere, Roy et al. (1964) produced glasses containing unusually large amounts of dissolved gases (up to 25mol% H 2 O and 4mol% Ar). While the quench in air is average, the quench in a liquid (water, mercury, or liquid nitrogen) is strong and may be used to achieve higher cooling rates. The quenching rate, however, is quickly limited in practice (up to 10 2o C/s) by the formation of an insulating vapor layer at the glass-liquid interface (calefaction effect).

2.2.1 Unconventional Melting

The usual way of obtaining a glass is by quenching a melt obtained by fusion of one or several crystalline substances. When the rate of the decrease in temperature is sufficient to bypass crystallization, the disordered state of the liquid is retained in the solid state (see Chapters 3 and 4). In classical glass technology, where glass formers such as SiO2 or B 2 O 3 are used, air quenching is sufficient, and the composition of the glasses is optimized to avoid the risk of crystallization (devitrification). For oxide glasses the melt can be obtained in air, although control of the Redox conditions may be necessary (see Chapter 1). For chalcogenide glasses (see Chapter 7) the exclusion of oxygen is essential,

2.2.2 Ultrafast Quenching

To achieve higher cooling rates it is necessary to use a contact with a solid of high thermal conductivity, generally a metal such as copper (see also Chapter 2 of Volume 15). The splat-cooling technique (Duwez etal., 1960) consists of projecting a droplet of a melt by the action of a pressure shock wave which propulses the sample towards a curved Cu-plate (Fig. 2-1). The glass is obtained in the form of thin flakes of a few microns in thickness resulting from high-speed conduction cooling (10 5 -10 9 °C/s). The quality of the contact between the liquid and the solid substrate controls the effective cooling rate, as shown by Ruhl (1967).

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2 Special Methods of Obtaining Glasses and Amorphous Materials

Pressurized He • I - High-pressure chamber - Breakable mylar diaphragm (~80um thick) -Low-pressure chamber Ar

-Furnace -Molten sample (~100mg) in crucible Molten jet

Opening

Copper reception strip

Figure 2-1. Duwez-type splat-cooling device (schematic).

-Furnace

Fast-moving hammer Figure 2-2. Hammer-and-anvil splat-cooling device (schematic). Stationary anvil

In another device, designed by Pietrokowsky (1963), a molten droplet is expelled from a crucible and smashed between two metallic plates, one of which is electronically triggered via a photocell by the droplet itself (Fig. 2-2). The advantage of this device is that it produces plates of uniform thickness devoid of holes as in Duwez' device, but quenching speeds are somewhat lower (10 5o C/s). The calculation of limiting cooling speeds in splat cooling was performed by Bletry (1973), and recent devices using laser sources for melting were developed by Krepski et al. (1975) and Veltri et al. (1979). The cooling of a molten droplet between two rapidly rotating steel rollers was used by Zarzycki and Naudin (1967) to produce flakes of B 2 O 3 -PbO-Al 2 O 3 glasses for unmixing kinetics studies (Fig. 2-3). Chen and Miller (1970, 1976) developed a similar device for obtaining metallic glasses, which was also used by Suzuki and Anthony (1974) to examine various binary systems of refractory oxides, some of which formed glasses. All the preceding devices produce small samples suitable only for laboratory examination of structure. The device of Chen and Miller (1976) opened the way to making continuous ribbons of metallic glasses, by the use of a metallic (Cu-Be) wheel spinning at 300-1800 rpm. A liquid stream impinges on the inside of the wheel's toruslike, convex surface. The quenched ribbon slips out of the wheel under the action of the centrifugal force. Ribbons 0.5 mm wide, 20 jam thick, and up to 100 m in length were produced. The technique was further improved by quenching the melt on the outside of the spinning wheel (Fig. 2-4). The liquid is spread in the form of continuous film with quench rates of 1 0 6 - 1 0 8 K s " 1 . Modern devices enable ribbons up to several deci-

97

2.2 Melt Quenching Techniques

C0 2 Laser (250 W)

J— Furnace Molten sample in crucible

Spun-off spherules

\ \

— Laser beam focussed onto the tip of the sample

High-speed (20000 rpm) Rotating sample rod

A Falling droplet

v)

Collecting —\ hopper \ Fast rotating steel rollers

\_

Steel collecting tray

Figure 2-5. Laser spin-melting device (schematic).

Splat Figure 2-3. Rollers splat-cooling device (schematic).

Gas pressure

Furnace Crucible Liquid metal

Quenched glass ribbon

Fast rotating wheel Figure 2-4. Melt-spinning device (schematic).

meters wide to be produced. More details on this important industrial technique will be given in Chapter 9 of this Volume. Reviews on splat cooling are to be found in Anantharaman and Suryanarayana (1971), Jones (1972), and Jones and Suryanarayana (1973). A variant of splat cooling is

laser-film melting, whereby the beam of a CO 2 laser is used to scan the surface of a specimen, producing a molten layer which quickly solidifies in perfect contact with the solid (not molten) substrate (United Technologies Research Center, 1976). In splat-cooling techniques one dimension (the thickness) of the splat or of the ribbon is kept small in order to speed up the heat exchange. It is also possible to subdivide the melt into droplets small enough to achieve a high cooling rate by radiation. In the method of laser-spin melting (Topol et al., 1973) small droplets are produced by spinning the target in the form of a rod at 8000-30000 rpm. The extremity of the target is heated by a CO 2 laser (Fig. 2-5). Cooling rates for droplets 500 jim in thickness were estimated at 4000 °C/s. Various refractory oxides and their mixtures (A12O3, Ga 2 O 3 , La 2 O 3 , Nb 2 O 3 , Ta 2 O 5 , etc.) were obtained in partly non-crystalline form. Other experiments were made in the preparation of glass-melting experiments in migrogravity conditions (Spacelab and Shuttle missions).

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2 Special Methods of Obtaining Glasses and Amorphous Materials

2.3 Vapor-Quenching Techniques Vacuum jar

The formation of non-crystalline solids may also be achieved by depositing one or several components in the vapor state onto a substrate. The vapor may be produced by heating a suitable compound and deposited as such without further modification (nonreactive deposition), or a chemical reaction may intervene (reactive deposition). These processes are typically used for producing thin films for electronic and optical applications. Reactive deposition, however, may also be used to produce either bulk glasses that are difficult to obtain from the melt or hyperpure materials, when are needed (e.g., blanks for optical fibers). 2.3.1 Evaporation

The evaporation method consists of emitting a vapor under vacuum and condensing it onto the specimen (Fig. 2-6). The various techniques differ according to the heating method employed to evaporate the substance: electrical resistance heating, electron beam heating, or high-frequency heating. The operation takes place in a re-

Sample at controlled temperature

Vacuum jar

-Shutter Residual atmosphere (1CTA-10-7Torr)

/N \±l

I

|

Heated evaporation boats

To pumping system Figure 2-6. Thermal evaporator (schematic).

Solid to be sputtered (cathode)

Sputtered atoms Specimen to be coated (anode)

Figure 2-7. Sputtering coating device (schematic).

sidual atmosphere (10 4 - 1 0 7 Torr), and the vapor pressure of the depositing material is kept below 10 ~2 Torr. Single metals can be readily evaporated in this way. For multicomponent systems several separate sources may be used or a metal alloy rapidly evaporated using the "flash" technique. In the case of oxides, their dissociation (e.g., SiO formation in the case of SiO2) may cause difficulties. 2.3.2 Sputtering

In the sputtering method the specimen to be coated and the solid source are both contained in a closed vessel in a low-pressure gas atmosphere (generally Ar), Fig. 2-7). A high d.c. voltage of a few kilo volts is used to produce a glow discharge, with the specimen as anode and the source as cathode. This discharge produces Ar + ions, which after being driven toward the cathode, eject (sputter) the atoms from the cathode. Some of these atoms will condense on the specimen forming a uniform, generally non-crystalline film of a composition close to that of the source material. (For the physics of sputtering, see Townsend et al., 1976.)

2.3 Vapor-Quenching Techniques

The method can be used to deposit both elemental metals or alloys. It is widely used in electronic and optical applications. In glass technology continuous sputtering devices are used to coat glass panes with metal or oxide layers for applications in architecture (light control). The industrial devices use alternating voltages and magnetic fields (magnetron sputtering) to increase the path of the ions and thus their collision frequency, which results in a better yield. A standard work on the deposition of thin films is that of Holland (1956). 2.3.3 Reactive Deposition In reactive-deposition processes a chemical reaction is initiated in the gas phase by supplying sufficient activation energy: thermal, in the form of heat, or electrical, in an rf glow discharge. Heterogeneous and homogeneous processes must be distinguished. For example, SiO2 glass may be produced by homogeneous or heterogeneous oxidation of SiCl4 vapor or by oxidizing the surface of a silicon wafer. In reactive sputtering, if the Ar gas contains O 2 or N 2 , the resulting sputtered film will be the oxide or nitride of the sputtered cathode metal. With an Si cathode, SiO2 or Si 3 N 4 films will be produced. Processes of this kind are extremely important in the electronics industry, where glass films are used for encapsulating integrated circuits and thin dielectric films as both active and positive components. Using these techniques, amorphous films can often be obtained in systems where the obtention of glasses by direct methods is impossible. For general reviews on these applications see Amick et al. (1977) and Pliskin et al. (1967). Chemical Vapor Deposition (CVD) involves a heterogeneous reaction and deposition from organometallic or metal halide

99

vapors at a heated solid substrate. For example, gas mixtures such as SiH 4 , PH 3 , and O 2 , or SiCl4, POC1 3 , and O 2 passing over a heated Si surface at temperatures below 1000°C, SiO 2 -P 2 O 5 glass layers are formed at a rate < 1 jim/min. Most of the work done concerns SiO2, Si 3 N 4 , SiO 2 -P 2 O 5 , SiO 2 -B 2 O 3 , and A12O3 both for low-temperature CVD (450 °C) or high-temperature CVD (850 °C). Glow discharge plasmas (rf or microwave) allow for low-temperature operations (310 °C). This method was used to prepare chalcogenide films and SiJCN}?Hz films. For details see Kern and Rosier (1977). Thermally activated homogeneous oxidation of mixtures of metal halide vapors is performed to obtain large bulk glasses of high purity and quality by vapor-deposition techniques. Metal halides (SiCl4, GeCl 4 , TiCl 4 , BC13, POC13) are generally used as starting compounds as are SiH4 and organometallics (e.g., (CH4)3B). At temperatures above 1500°C, a homogeneous oxidation reaction predominates, and without a catalyzing surface a finely divided glass particulate material called "soot" is obtained. The reaction SiCl4 + O 2 -* SiO2 + 2Cl 2

(2-1)

is obtained by passing a mixture of SiCl4 and O 2 in a burner through a methaneoxygen flame. The high specific surface of the soot (^20m 2 /g) provides a strong driving force for sintering (see Chapter 3). When soot is collected on a target heated at a sufficiently high temperature ( » 1800°C for SiO2), sintering and conversion into solid bubble-free glass occur, (Fig. 2-8). By this process very large glass "boules" (over 500 kg) were obtained for SiO 2 , either in pure form or with additions (TiO2, A12O3, B 2 O 3 ); see Dalton and Nordberg (1941) and Nordberg (1943).

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2 Special Methods of Obtaining Glasses and Amorphous Materials

5iCl^+ 0 2 ( +Dopants) — Burners

\l V ik

Soot-carrying flames

Y//////////////////
Deposited SiO2 "boule"

Slowly rotating substrate held at ~1800°C

Figure 2-8. Flame oxidation process for producing bulk silica (schematic).

Lowering the soot deposition temperature to less than 1500°C helps to retain the more volatile components (e.g., B 2 O 3 ); this results in a porous silica body which can then be sintered in a separate step at a higher temperature (Schultz, 1975). Deposition methods based on these principles are used to prepare preforms for glass optical fibers. These important techniques will be described in Chapter 16 of this Volume.

2.4 Solid-State Methods

particle to the neighboring atoms produces "thermal spikes" of the order of several thousand degrees Kelvin for 10 " 1 ° -10 " 1 1 s which extend to regions of the order of 104 atoms and may produce local melting followed by an ultrafast quench. Exposure of various ceramic materials to neutron doses of approximately 3xlO 2 0 neutrons/cm 2 renders these materials amorphous (Wullaert, 1964; see also Ch. 9, Sec. 9.2.5). The classic work of Primak (1958) has shown that on irradiation quartz and cristobalite are progressively amorphized and that their properties tend toward those of vitreous SiO2. Radioactive materials, e.g., complex uranium oxide minerals, become rnetamictized, i.e., disordered by their own radioactivity (Primak and Bohmann, 1962). Ion implantation may be used to modify the structure of superficial layers of materials. Some results are presented in Chapters 6 and 9. As yet, amorphization by irradiation effects has not been exploited in glass technology, but ion implantation has recently been used to modify oxide glass surfaces (Ch. 6). 2.4.2 Effects of Intense Shock Waves

Non-crystalline solids may be obtained from crystals without passing through the fusion stage. There are several other ways of destroying a regular crystal lattice. 2.4.1 Radiation Damage The collision of energetic particles with the atoms of a crystal produces lattice defects; the effect is cumulative and the process may end in the formation of a noncrystalline solid. Fast neutrons have a low probability of collision, but each collision produces a large number of defects; charged particles have a higher probability of collision but produce less displacements. The transfer of the kinetic energy of the

Powerful pressure shock waves of several hundred kilobars generated during explosions may produce amorphization of crystals without their melting. The external boundaries of the original crystal are conserved and show the absence of flow, but the crystalline lattice is destroyed. Such glasses are called diaplectic or thetomorphic. Impacts of meteorites produce such materials (Chao, 1967), and in particular, it was discovered that the surface of the moon is covered with glassy material. Research on glasses linked with the lunar exploration (Apollo program) was destined to determine whether these materials were

101

2.4 Solid-State Methods

of volcanic origin or the result of continuous meteorite bombardment (Pye et al., 1984). In the laboratory the first diaplectic glasses were produced by De Carli and Jamieson (1959) who amorphized silica with shock waves at pressures exceeding 350 kbar and Milton and De Carli (1963) who obtained diaplectic plagioclase (NaAlSi 3 O 8 -CaAl 2 Si 2 O 8 ) glass with pressures up to 800 kbar. For a review, see Stoffler (1972, 1974). Shock waves are produced in the laboratory by explosions in which a projectile (striking plate) is propelled at a specimen. Upon impact with the specimen, a pressure pulse of several hundred kilobars with a duration of a few microseconds is produced (Fig. 2-9). Methods of calculating pressures and temperatures thus generated were given by Wackerle (1962) and Gibbons and Ahrens (1971). In natural events (meteoritic impacts) much higher pressures are expected, reaching several megabars. This may induce partial or total fusion and even vaporization of the sample. Practical applications are as yet rare. The firm Schott Glasswerk has obtained a patent (Schott, 1968) for shock-produced oxide glasses (B2O3-La2O3-ThO2Nb 2 O 3 -Ta 2 O 5 ) and fluoride glasses (CaF 2 -SrF 2 -LaF 3 -AlF 3 -NaPO 3 ) with elevated refractive indices. The pressures employed were 5-10 kbar. The preceding oxide glasses cannot be obtained by conventional melting, and the fluoride glass has a refractive index superior to that of glass obtained by melting. Another use of shock waves which should lead to important applications in the field of metallic glasses is the explosive compaction of metallic glass particles into homogeneous cylinders or disks, first reported by Cline and Hopper (1979). Such bulk pieces cannot be obtained by sinter-

Sample Heavy steel block

Explosionpropelled projectile Striker plate

Figure 2-9. Shock-amorphization device (schematic).

ing without inducing crystallization, whereas shock-wave treatment preserves the amorphous character of the material. Dynamic compaction of metallic glass powders and ultrasonic welding of ribbons is being developed in Japan (Makino, 1985). For more details, see Matsumoto (1986), Negishi et al. (1985), Toda et al. (1985), and Aoki et al. (1986). 2.4.3 Slow Mechanical Actions The effects of shearing under prolonged mechanical grinding of a crystal can progressively destroy the crystalline order and lead to the formation of a non-crystalline solid. Mechanical alloying processes are used to prepare various metallic glasses (see also Ch. 9, Sec. 9.2.7 and Vol. 15, Ch. 5, Sec. 5.6.3). 2.4.4 Diffusion Effects Interdiffusion effects can be employed to produce non-crystalline materials. Using multilayers formed of superposed crystalline metallic thin films, Johnson et al. (1985) have examined the possibility of producing amorphous interlayers when pure metals characterized by a large negative heat of mixing are brought into contact under suitable kinetic conditions. The couples investigated were Au-La, Zr-Ni and Hf-Ni. Amorphous alloys can also be obtained from intermetallic compounds by hydrogen absorption. Yeh et al. (1983) found this

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2 Special Methods of Obtaining Glasses and Amorphous Materials

phenomenon for metastable Zr 3 Rh and subsequently (Aoki et al., 1985, 1986) for SmNi2 and GdCo 2 Laves phases. The phenomenon is found in many Laves phases consisting of transition metals and rare earth metals such as CeFe 2 , CeCo 2 , CeNi 2 , YNi 2 , etc., even at room temperature under 5MPa hydrogen gas pressure (Masumoto, 1986). The subject of interdiffusion amorphization will be treated in greater detail in Chapter 9.

2.5 Electrochemical Methods Anodic Oxidation Amorphous oxide layers can be grown on the surface of a metal of semiconductor by making it the anode in an electrolytic cell in a variety of aqueous electrolytes (Fig. 2-10). Al, Zr, Nb, and especially Ta will oxidize when a current is passed through the cell under sufficient overvoltage, whereby a glass layer is formed with a thickness of up to several thousand angstroms (Young, 1961; Vermilyea, 1960). Amorphous silica films can be grown on Si substrate (Schmidt and Michel, 1957). Doped silica films have been obtained by Schmidt and Owen (1964) and Crosset and Dieumegard (1973). Anodic oxidation of

D.C. Power supply

GaAs (Hasegawa and O'Handley, 1979) and of InAs, InSb, GaP, and GaAsP (Schnable and Schmidt, 1976) have also been obtained. The technique, however, is not as widely used in the semiconductor industry as thermal oxidation.

2.6 Pyrolysis Pyrolysis is a method in which a suitable compound (the precursor) is subjected to controlled thermal decomposition, the residue being the product to be synthesized. Pyrolysis of organometallic precursors is an established way of producing advanced ceramics, namely polycrystalline SiC and Si 3 N 4 . As far as non-crystalline materials are concerned, pyrolysis is used in the synthesis of glass-like carbons. These were first obtained by pyrolysis of cellulose and then of thermosetting resins. Phenol-aldehyde resins were the starting materials for "vitreous carbon" (Cowlard and Lewis, 1967). "Glassy carbon" was obtained from furfuryl-alcohol resin (Yamada and Sato, 1962) and "vitro-carbon" from acetonefurfural resin. Carbon fibers were manufactured by pyrolyzing spinned phenol resin fibers (Kawamura and Jenkins, 1970). The details of these processes will be discussed in Chapter 10 of this Volume which also contains references to numerous patents.

2.7 Solution Methods; "Sol-Gel" Processing of Glasses Cathode

Sample to be oxidized - (Anode)

Electrolyte Figure 2-10. Anodization cell (schematic).

In polymer technology non-crystalline or partly crystalline materials ("plastics") are currently obtained in a direct way using methods of organic chemistry. This important theme is the subject of Volume 18, "Processing of Polymers".

103

2.7 Solution Methods; "Sol-Gel" Processing of Glasses

There exists, however, a large array set of methods in which inorganic glasses may be synthesized using methods of solution chemistry. Sol-gel processes belong to this last group of syntheses: they are based on the possibility of forming the disordered network of the glass, not directly at high temperatures from a melt, but at low temperatures from suitable compounds by chemical polymerization in a liquid phase. In this way a gel is first formed from which glass may be obtained both by the successive elimination of the interstitial liquid and by the collapse of the resulting solid residue by sintering. This "precursor-based" synthesis of glasses, ceramics, and composites is currently one of the most rapidly progressing fields of materials science and engineering. The "sol-gel" method of preparing glasses is being actively studied in leading laboratories all over the world, and in the last ten years, the number of scientific publications in this field has shown an exponential increase. Current research work in this field is to be found in the Proceedings of the International Workshops on Gels: Gottardi (1982), Scholze (1984), Zarzycki (1986), Sakka (1988), Aegerter (1990); the International Conferences on Ultrastructure Processing: Hench and Ulrich (1984, 1986), Mackenzie and Ulrich (1988), Uhlmann and Ulrich (1990); as well as in the series of symposia "Better Ceramics through Chemistry": Brinker et al. (1964, 1986, 1988). For general reviews, see Sakka (1982), Zarzycki (1984), Rabinovich (1985). The recent books by Klein (1988), Aegerter et al. (1989), and Brinker and Scherer (1990) present different aspects of sol-gel technology. The excellent treatise of Her (1979) should be consulted for details on silica sols and gels.

2,7.1 Methods of Gel Formation The main steps of sol-gel processing are summarized in Fig. 2-11. The different variants developed depend on the way in which the initial gel is obtained and on the forming process. As silica is the essential ingredient of most of the glasses prepared by sol-gel methods, our description will be centered on silica-based gels. There are three ways of obtaining them: (1) Hydrolysis and polycondensation of organo-metallic compounds (alkoxides) dissolved in alcohols in the presence of a limited amount of water. (2) Destabilization of silica sols (e.g., Ludox ®), pure of containing other metal ions added in the form of aqueous solutions of salts. (3) Redispersion of fine dry silica particles in a suitable liquid medium by mechanical (shearing) action to form a sol which gels spontaneously. 2.7.1.1 Gel Formation from Alkoxides Metal alcoholates, also known as metal alkoxides M(OR) n , where M is a metal (e.g., Si) and R an alkyl group (e.g., CH 3 or C 2 H 5 ), react with water and undergo hydrolysis and polycondensation reactions which lead to the progressive formation of a metal oxide. The overall reaction scheme consists of at least two main steps: (2-2) 3 (2-3)

The resulting metal oxide is produced in the form of extremely small particles ( « 2 nm) which may link to form a gel. In reality, the situation is more complex; the reactions (Eqs. (2-2) and (2-3)) proceed simultaneously and are generally incomplete. Hydrolysis may be achieved using a smaller quantity of water than that required by stoichiometry, and a number of radicals R remain unreacted. Polyconden-

104

2 Special Methods of Obtaining Glasses and Amorphous Materials Liquid ingredients

Mixing Reacting

Figure 2-11. Principle of sol-gel processing (from Zarzycki, 1987 a).

sation is incomplete and the final product corresponds rather to the formula (MOyOH),(OR) z

(2-4)

In cases where several different compounds (e.g., M(OR)n, M'(OR)J are reacted, a complexation step may precede reactions Eqs. (2-2) and (2-3). In this way complex networks involving several different cations, (e.g., M, M') may be produced: -M-O-M-O-M-

Bradley et al. (1978) and Andrianov (1955). Since alcoholates and water are immiscible, the reagents are dissolved in alcohol, generally methyl- or ethylalcohol. The use of a common solvent can be avoided, however, by subjecting the alcoholate-water Table 2-1. Alkoxides used in gel synthesis. M

M(OR)n

Si

Si(OCH3)4 Si(OC 2 H 5 ) 4 Al(O-iso C 3 H 7 ) 3 Al(O-sec C 4 H 9 ) 3 Ti(O-C 2 H 5 ) 4 Ti(O-isoC 3 H 7 ) 4 Ti(O-C 4 H 9 ) 4 Ti(O-C 5 H 7 ) 4 B(OCH 3 ) 3 Ge(O-C 2 H 5 ) 4 Zr(O-iso C 3 H 7 ) 4 Zr(O-C 4 H 9 ) 4 Y(O-C 2 H 5 ) 3 Ca(O-C 2 H 5 ) 2

(2-5)

The use of alkoxides of Si, B, Ti, Zr, etc., leads to the formation of complex gels composed of small particles which prefigure the network of corresponding oxide glasses. Table 2-1 gives a list of organometallic compounds most frequently used in the synthesis of glasses by this method. For details on the synthesis of alkoxides and chemistry involving these compounds see

Al Ti

B Ge Zr Y Ca

2.7 Solution Methods; "Sol-Gel" Processing of Glasses

mixture to ultrasound (Tarasevich, 1984). The "sonogels" obtained in this way are more dense due to the absence of the solvent, and their structural properties are different from those of "classical" gels (Zarzycki, 1991). The water necessary for hydrolysis can be taken from the atmosphere (as in the case of thin coatings) or more generally added to the solution in a controlled amount. Other cations may also be introduced in the form of alcoholic or aqueous solutions of salts (nitrates, acetates, etc.). A carefully controlled amount of a catalyst, either an acid (hydrochloric, nitric, or acetic acid) or a base (ammonia, amines, etc.), is added. The gelling time depends on the pH, the temperature, the amount of water, and the nature of the catalyst. The structure of the gel depends very much on the nature of the catalyst used: acid catalysis leads to filamentous structures with a low degree of reticulation of the - M - O - M - chains, while basic catalysis produces more compact spheroidal particles with a higher internal degree of reticulation. 2.7.1.2 Gel Formation from Sols Most colloidal solutions of silica (silica sols) are either prepared by chemical condensation methods, acidifying solutions of Na silicates, K silicates, and NH 4 silicates, or made from hydrolyzable products such as SiCl4 or Si(OR)4, where R is an alkyl group. The formation of silicic acid in aqueous solutions is followed by polymerization of monomers Si(OH)4 when its concentration exceeds 100 ppm, which is the limiting solubility in water at 25 °C. The polymerization reaction is based on the condensation of silanol groups with the elimination of water. (2-6) -Si-OH + H O - S i - -> - S i - O - S i - + H 2 O

105

Amorphous spheroidal groupings of about 1 to 2 nm are formed by a nucleation process similar to what occurs in the formation of crystalline precipitates. At low pH values, particle growth stops once the size of 2-4 nm is reached. Above pH 7, particle growth continues at room temperature until particles of about 5 10 nm in diameter are formed, and then it slows down. At higher temperatures particles are negatively charged, and they repel each other. Growth continues without aggregation, resulting in the formation of stable sols. Commercial silica hydrosols (e.g., Ludox®, Nalcoag®, Nyalcol ®, Snowtex®) are stable sols with 20-50 wt.% SiO2. They are made up of dense silica particles with an average diameter of between 7 and 21 nm. The pH is between 9 and 11. To obtain a gel from a stable sol, the sol must be destabilized either by a temperature increase or by the addition of an electrolyte. An increase in temperature reduces the amount of intermicellar liquid by evaporation and increases thermal agitation, which in turn induces collisions between particles and their linking in chains by condensation of surface hydroxyls. The sol-gel transition should be distinguished from a precipitation or flocculation mechanism. In the latter mechanisms separate aggregates are formed, whereas a gelling involves a continuous three-dimensional particle network that invades the total volume of the sol (Fig. 2-12). By electrolyte addition the pH of the sol may be modified in order to reduce the electric repulsion between the particles (depending on the zeta potential). This is accomplished by adding an acid to diminish the pH to 5-6 to induce gel formation by aggregation. This conversion of sol into gel is progressive, the growing aggregates (microgel) gradually invading the whole vol-

106

2 Special Methods of Obtaining Glasses and Amorphous Materials

temperature, the gelling time may vary from minutes to months. Sol

2.7.1.3 Redispersion Methods

Figure 2-12. Difference between gelling and precipitation of a sol (schematic).

ume originally occupied by the sol. When about half of the silica has entered the gel phase, a rapid increase in viscosity is noted (Fig. 2-13). The mechanism of interparticle bonding leading to microgels and gels involves the attachment of two neighboring silica particles via the formation of Si-O-Si bonds (Eq. (2-6)). Colloidal particles will form gels only if there are no active forces which would promote coagulation into aggregates with a higher silica concentration than the original sol. Metal cations, especially the polyvalent ones, may lead to precipitation rather than gelling: This is encountered with some multicomponent gels. In that case at least one gelling constituent (generally silica sol) is required. Other constituents may be added in the form of soluble salts (nitrates, sulfates, etc.) or organometallic compounds. By adjusting the temperature, concentration, and especially the pH of the resulting sol, a homogeneous solution is obtained which may then be gelled in a controlled way in order to avoid precipitation. According to the composition, pH, and

Fine dry silica particles such as the commercial "fumed silica" Cab-O-Sil®, or Aerosil® obtained by flame oxidation of SiCl4, can be mechanically redispersed in water using a shear blender. At pH 2-7, a sol is formed which will gel in a few hours. SiO2 particles form agglomerates which are linked by hydrogen bonds. SiO2 dispersions in organic liquids such as chloroform or n-decanol were also prepared; they can be readily gelled by the action of amines or ammonia vapor. Not only pure silica but also SiO 2 -GeO 2 particles, obtained by the method of flame oxidation for mixtures of gaseous SiCl4, TiCl 4 , GeCl 4 , were successfully gelled (Rabinovich, 1985).

J

2

i

-

o"

4> D

o

(S)

A

o

o

Q_

1 -

c* A

TO

Aoo

o

a

0

-

D

A

Q

D

a

° A A*o

A

O

_

A

A

-1

I

0.90 T/Tfgel

1.00

Figure 2-13. Evolution of viscosity of various TMOSalcohol-water mixtures approaching the gelling point as a function of the reduced time T/Tgel (from Mizuno et al., 1985).

2.7 Solution Methods; "Sol-Gel" Processing of Glasses

107

2.7.2 Aging Effects

The freshly prepared "wet" gel consists of a network of particles holding an interstitial liquid - the solvent trapped during the gelling step is water in the case of hydrogels and mixtures of alcohols and water for the alcogels. The interstitial liquid still contains unreacted sol particles, which progressively attach themselves to the network. Furthermore, there is a transport of SiO2 from convex to concave parts due to solubility effects which smooth the inequalities between linked particles and convert the chains into filaments (Fig. 2-14). Additional deposition of SiO2 from solution may further "nourish" and thus stiffen the chains (Fig. 2-15). The syneresis effect then sets in, whereby the network slowly contracts and tends to progressively expel the interstitial liquid in order to reduce the internal interface. With time all these effects bring about a gradual increase in the Young's modulus, E, of the wet gel (Fig. 2-16); the gel stiffens progressively, even if evaporation of the interstitial liquid is prevented. Freshly gelled wet silica gel is an extremely fragile material, which behaves as a brittle solid with conchoidal fracture. Gels prepared from Si alkoxides are predominantly elastic while those from colloidal solutions (Ludox®) show partly visco-elastic or viscoplastic properties. Fig. 2-17 shows the critical stress concentration coefficient Klc of some SiO2 gels, and Fig. 2-18 the corresponding fracture surface energy.

Neck formation

Figure 2-14. Strengthening of particle chains by deposition of silica at the necks due to differential solubility effect (from Zarzycki et al, 1982).

Secondary deposition

Figure 2-15. Strengthening of chains during aging by secondary deposition of silica (from Zarzycki et al., 1982).

106

105

u

L

Days

H

Figure 2-16. Evolution of Young's modulus, E, as a function of time for a Ludox gel (v: Poisson's number) (from Zarzycki, 1988).

300 200 100

2.7.3 Drying

The drying stage is necessary to free the solid network of the gel from the accompanying interstitial liquid phase.

0

1

2

3 Days

A

5

Figure 2-17. Evolution of critical stress intensity factor K1C as a function of time for a Ludox gel (from Zarzycki, 1988).

108

2 Special Methods of Obtaining Glasses and Amorphous Materials

0.1

T(Nm"

-0.05

0

1

2

3 Days

A

5

6

Figure 2-18. Evolution of the fracture surface energy as a function of time for a Ludox gel (from Zarzycki, 1988).

uid-air interface and inversely proportional to the radius r of the pore; 6 is the contact angle at the liquid-solid-air boundary line. Considerable stresses may be generated in this way: Ap = 7.3 xlO 7 Nm " 2 for a pore radius r = 2 nm filled with water, assuming perfect wetting (Fig. 2-19). Differential stresses due to adjacent pores then induce breaking if the tensile strength is exceeded. A detailed treatment of drying, comprising the analysis of stress redistribution due to interstitial liquid transfers was recently proposed by Scherer (1988).

2.7.3.1 The Role of Capillary Forces

Elimination of the liquid phase leads to dry gels, namely xerogels. When a "wet" gel is dried, the following sequence of events is generally observed on a macroscopic scale: • progressive shrinkage and hardening • stress-development • fragmentation The chief difficulty is encountered in the preparation of bulk glass, where specimens of gel without any cracks are required. This problem, occurring in monolithic gels, was recently the object of intensive research. Cracking during the drying stage is the result of non-uniform shrinkage of the drying body, a well-known phenomenon in ceramic technology. The stresses arise not only from the local differences in expansion coefficients due to variable water content but primarily from the action of capillary forces which become operative when the pores start to empty and a liquid-air interface is present in the form of menisci distributed in the pores of the drying gel. The magnitude of these forces is given by Laplace's formula: Ap = (2y cos9)/r

(2-7)

The change in pressure Zip is proportional to the specific surface energy y of the liq-

2.7.3.2 Obtaining Monolithic Gels

In practice, a very long drying time is necessary to preserve "monolithicity". This may reach hundreds of hours even for small specimens with surface areas of a few square centimeters. Much effort has therefore been spent to find more economical ways of drying gels and still preserving their integrity. All actions which tend to minimize the capillary stress and increase the mechanical resistance of the network should enhance the probability of keeping the gel

108r

Q_

a o

10£

10°

101 Pore radius in nm

102

Figure 2-19. Capillary pressure Ap in a drying gel as a function of pore-radius when the interstitial liquid is (a) water (b) alcohol (after Zarzycki et al., 1982).

2.7 Solution Methods; "Sol-Gel" Processing of Glasses

monolithic. The following measures are possible: • Strengthening the gel by reinforcement (aging) • Enlarging the pores • Tending toward monodispersity of the pores • Reducing the surface tension of the liquid • Making the surface hydrophobic • Evacuating the solvent by freeze-drying • Operating in hypercritical conditions where the liquid-vapor interface vanishes The last two methods are the most efficient ways of eliminating the destructive action of the surface tension of the liquid suppressing the liquid-vapor interface. Hypercritical solvent evacuation (HSE) consists in treating the gel in an autoclave in hypercritical conditions for the solvent. It is directly applicable to alcogels produced from alkoxides. Hydrogels cannot be directly treated in this way as under hypercritical conditions for water, silica is solubilized. This has prompted the importance of the alkoxide method. Redispersion methods, on the other hand, permit the obtention of wet gels with large pores by a double redispersion treatment. These pores facilitate solvent evacuation without the danger of cracking in the gels (Rabinovitch, 1985). The HSE process is schematized in Fig. 2-20, which shows the equilibrium curve between the liquid and the gas phase of the solvent. In order to ensure the continuity of the liquid-gas transition, the path of the thermal treatment must not cross the equilibrium curve. To circumvent the critical point C, a path such as a, b, d, e may theoretically be used. In practice this path is modified in the following way: the open container which contains the gel is placed inside an autoclave, and to obtain hypercritical conditions, a given quantity of solvent (e.g.,

109

Temperature Figure 2-20. Principle of hypercritical solvent evacuation (from Zarzycki, 1984).

methanol) is added to the autoclave. The autoclave is then closed and electrically heated. When the critical temperature of methanol is exceeded, slow decompression followed by successive flushings with dry argon eliminate the last traces of alcohol. The autoclave is then cooled down and the gel removed at ambient temperature (path a,d,e). The gel, which contains air-filled pores, is termed aerogel A number of experiments has shown that monolithicity depends on many variables: • the speed of heating • the proportion of the additional solvent • the concentrations of organometallic compounds and • the water of hydrolysis • the geometry of the sample and its size • the previous aging of the gel Monolithic samples can be obtained with 100% certainty when these variables are optimized (Zarzycki, 1982). The aerogels are hydrophobic due to partial surface esterification and contain an appreciable percentage of adsorbed organic radicals. Their mechanical resistance, however, is sufficient for these radicals to be eliminated by subsequent

110

2 Special Methods of Obtaining Glasses and Amorphous Materials

thermal treatment without loss of monolithicity, and they can finally be converted into a clear glass of excellent optical quality. Aerogels can be made with an exceedingly high porosity (close to 99%) and a pore size of a few nanometers, which makes them excellent thermal insulators. For silica aerogels thermal conductivity of the order of 0.01 W m " 1 K " 1 has been demonstrated. Their refraction index may be close to 1, and they can be made translucent hence their application in Cerenkov radiation detectors. (For these and other applications, see Fricke, 1986.) Another method consists in adding a suitable substance to the sol before gelling that will influence the subsequent behavior of the sol during drying. The most successful of these drying control chemical additives (DCCA) is formamide (Hench, 1986). Its effect seems to be a tendency toward the formation of gels with smaller but more uniform pores which favor drying in monolithic form. 2.7.3.3 Structural Aspects

The gelling process, the structure of the resulting wet gels, and that of the xero- and aerogels have been the object of numerous studies on various systems, the detailed description of which is outside the scope of the present article. The use of small-angle X-ray scattering (SAXS) combined with spectroscopic methods (IR, Raman, NMR) and electron microscopy has permitted the various aggregation theories to be tested, and the results of these methods have led to structural models. Gelling may be explained either using Flory's theory, familiar in polymer chemistry, or by percolation theories, which are more in favor with the physicists. The structure of growing aggregates and of the

resulting gels may be described using fractal concepts (Mandelbrot, 1983). A fractal cluster has a structure which becomes increasingly wispy as its dimensions increase. In particular, its mass scales as r D , where r is the radius of the cluster, and D the "fractal dimension" which is smaller than three. The fractal dimension D may be obtained by a variety of methods. See, for example, Zarzycki (1987 b) for a synthetic presentation. 2.7.4 Curing-Sintering

The final structure of the dry gel will depend on the structure of the wet gel originally formed in solution; it is a contracted or a distorted version of the latter. The constituent particles are coated with residual OH groups which are partly eliminated during the transition from a particulate texture to a continuous solid. They may be detected and analyzed by conventional infrared spectroscopic techniques. To transform the particulate structure of a dried gel into continuous glass, the elementary particles must fuse together, resulting in progressive pore elimination. This is achieved by heating the gel in order to promote diffusion phenomena and viscous flow. During this heat-treatment the residual OH and OR groups will first tend to be eliminated in the form of H 2 O and ROH which is accompanied by an additional polymerization of the system: (2-8) - S i - O R + O H - S i - -> - S i - O - S i + ROH The escape of residual products from closed pores may constitute a problem; the organic residues are finally carbonized at a higher temperature which brings about a coloration of the gel and leaves carbonaceous particles in the glass. It is therefore important to favor the escape of residues

2.7 Solution Methods; "Sol-Gel" Processing of Glasses

before complete closure of the pores, and oxidation treatments are often necessary to eliminate certain organic groups. For pure SiO2 gels this oxidation treatment is carried out at 300-400 °C. It is important to define the heating schedule in each particular case in order to eliminate the unwanted residues without impairing monolithicity before the onset of viscous flow. Occluded OH groups and H 2 O may cause bloating on heating at high temperatures - even if the specimen has remained monolithic up to this stage. Residual OH groups may be eliminated by chlorination treatments if very low OH levels are required in the final glass (e.g., for optical fibers applications). On the other hand, occluded water may be used in foaming processes, e.g., in blowing gel particles into microspheres (see Sec. 2.7.5.4). 2.7.4.1 Viscous Flow Sintering

Densification is essentially a sintering process by which the pores of a dry gel are eliminated, and the initially opaque material progressively converted into clear bulk glass. After elimination of residues, the driving force in this process is supplied by the surface energy of the porous gel. This tends to reduce the interface, thus eliminating the pores, the collapse being governed, in the case of glasses, by Newtonian viscous flow. Extra pressure, as in hot-pressing techniques, may be applied externally to speed up the process (Decottignies et al., 1978). The theoretica aspects of sintering are presented in Chapter 3 of this Volume.

111

tween phenomena which lead to densification and those which promote crystallization. The TTT (time-temperature-transformation) diagrams are a convenient way of studying the problem of devitrification versus compaction in order to define the appropriate thermal treatment (Zarzycki, 1982 b). The TTT diagrams show the time ty required to obtain a determined crystallized fraction y as a function of the temperature T. Treating y as a parameter, a set of Cy curves is obtained which represent the kinetic behavior of the system. In particular, if y0 corresponds to the smallest crystallized fraction detectable by analytical techniques, the curve Cyo represents a frontier not to be crossed during a thermaltreatment schedule if crystallization is to be avoided (generally y0 = 10 ~6 is adopted, see Chapter 3). The relative positions of the thermaltreatment path during densification and the Cyo curve of the gel determine the possibility of obtaining glassy or crystallized materials at the end of the compaction program. For example, (Fig. 2-21) if there is no danger of devitrification using path (a) for

2.7.4.2 Devitrification Kinetics Use of TTT Diagrams

During densification crystallize (devitrify) at successful conversion therefore depends on

the gel will tend to the same time. The of gel into glass a competition be-

Time Figure 2-21. Use of TTT diagrams for determining sintering heat treatment without crystallization (from Zarzycki, 1982 b. Reprinted by permission of the American Ceramic Society).

112

2 Special Methods of Obtaining Glasses and Amorphous Materials

a gel corresponding to Cl9 this will no longer be true for the curve of C 2 , the same path would lead to crystallized material. The solution would then be either to shorten the sintering time, e. g., by applying a suitable external pressure (path (b)), or to increase the temperature for a short time using the technique of "flash-pressing" (path (c)). In the case of gels the position of the curves C strongly depends on the impurities of the material and, in the first instance, of water content which influences the viscosity, as well as the surface energy of the material. 2.7.5 Forming Processes In the classical process, the resulting melt is generally immediately formed into the desired end products: sheet glass, hollow ware, or fibers. In sol-gel technology the various forming operations have to occur before or during the gelling stage (e.g., molding an object, forming a thin coating, or spinning a fiber); the drying-curing and sintering stages simply consolidate the original shape produced at low temperatures (Fig. 2-11). The nature of the processes during gelling and subsequent drying, which are of a diffusional nature, favors, however, those configurations in which at least one of the dimensions is small: Thin films, fibers, and small particles (or shells) are current examples, and it is significant that the first established industrial applications of the sol-gel route were precisely in the field of thin coatings. 2.7.5.1 Bulk Glass It is possible to produce bulk pieces of glass if cracking of gels during drying is avoided. This problem of obtaining monolithic gels has been extensively studied in

recent years - hypercritical solvent evacuation and drying chemical control additives (DCCA) have proved effective against cracking. In the laboratory, pure SiO2 glasses, as well as those combining SiO2 with other oxides (e.g., B 2 O 3 , TiO 2 , GeO 2 , P 2 O 5 , ZrO 2 , etc.) were successfully prepared. Glasses containing oxides of alkali and alkaline-metals sometimes prove more difficult to obtain because of the tendency of gels to devitrify during the sintering stages. The difficulty linked with monolithicity can be avoided if hot-pressing techniques are used to compact gels in a granular form; this, however, limits the size of the specimens. In industrial practice the early attempt in 1970 by Owens-Illinois (USA) at commercializing bulk gel-made glass was discontinued because of the high cost. However, the manufacture of sizeable glass pieces of pure SiO2 for optical applications has been reported (Hench, 1986). Advanced glasses for optical-fiber preforms (SiO2 doped by GeO 2 , P 2 O 5 , or B 2 O 5 ) have been successfully made, but the corresponding industrial applications have not yet followed. 2.7.5.2 Thin Films At the present time, the main industrial applications recognized for sol-gel methods are in the production of thin glass coatings by Schott Glass (FRG). They use the alkoxide method to modify the spectral transmission of flat glass for architectural applications (Schroeder, 1969; Dislich, 1971, 1988). In the method of dip coating (Fig. 2-22), a sheet of glass is first immersed in a tank containing a dilute solution of suitable alkoxide precursors and then slowly withdrawn at a constant rate. This leaves a superficial film of equal thickness which is then reacted with water vapor from the

2.7 Solution Methods; "Sol-Gel" Processing of Glasses

surrounding atmosphere to induce hydrolysis and polymerization. The glass is then dried and baked in an oven at ^500°C; successive layers of several hundred angstroms may be applied up to a total thickness of « 3000 A, Thicker films tend to craze or peel away. Other methods consist in applying an even initial liquid film by spinning (e.g., for optical components of circular shape) or spraying. Solar reflective TiO 2 coatings containing Pd or Au are manufactured by these methods. Antireflective coatings, contrast-enhancing coatings and protective coatings for optical surfaces against laser damage as well as electrically conductive layers have also been produced in this manner (Mukherjee and Lowdermilk, 1982; Dislich, 1988; Pettit et al., 1988). An interesting application of thicker solgel films of about one micron, which may be superficially patterned by pressing, is reported for the production of supports for recording disks for audio-visual purposes (Fig. 2-23), (Tohge et al, 1988).

7"~5OO°C

Glass sheet Film -=

H20 Vap. ROH Vap.

(a)

W////////////////M*--Gel

113

film

<=—Glass substrate

^-Stamper (b)

\

Electric furnace

(c)

////A Wn^BnfIIh7fIIhTfIJhTfIJhWI\<-Glass

(d)

film with fine pattern

Figure 2-23. Patterning process of gel coatings (from Tohge et al., 1988).

2.7.5.3 Fibers Continuous glass fibers may be produced by sol-gel methods. On approaching gelling point, the solution is drawn into a gel fiber, which is then converted into glass by heating. The composition of the starting solution must be carefully adjusted to render it spinnable. In general low water content for hydrolysis and an acid catalyst are thus required. The cross section of the fibers prepared in this way may not be circular. The process requires strict viscosity control. Pure SiO2 fibers as well as those of SiO 2 -Al 2 O 3 , SiO 2 -ZrO 2 , SiO 2 -ZrO 2 Na 2 O and SiC^-A^C^-I^C^ systems have been prepared (Sakka, 1988 b; Sowman, 1988; La Course, 1988). 2.7.5.4 Hollow Glass Microspheres

a b c Figure 2-22. Thin-film deposition by dip-coating process (schematic).

Hollow glass microspheres are used as fillers in plastic resins or paints and also in a more sophisticated version as targets for inertial confinement fusion (ICF) in ther-

114

2 Special Methods of Obtaining Glasses and Amorphous Materials

monuclear fusion research. They are produced from gels which are first dried, then crushed and sieved. The resulting powder is subsequently fed into an electrical vertical drop tower furnace where the gel particles, falling freely, are blown and vitrified into spherical shells by residual gas contained in the gel. Shells of up to 1000 jim with uniform wall thickness of 0.4-20 Jim were produced for ICF experiments (Downs et al, 1988). 2.7.6 Advantages and Disadvantages of the Sol-Gel Process As the sintering operation is carried out at temperatures much lower than those required for the melting of glass-forming components - practically in the vicinity of the transition temperature - the process is particularly attractive for the production of those glasses which require high melting temperatures (e. g., SiO2 glass can be made at 1200 °C instead of at 2000 °C). The second important characteristic of the process is that final homogeneity is directly obtained in solution on a molecular scale. This can be compared to the difficulties of obtaining homogeneous glasses in the classical way, particularly when one of the components is more volatile or when the resulting melts possess a high viscosity which hinders efficient mixing of the constituents. In some cases it is then necessary to remelt the original batch several times to reach the necessary compositional uniformity. This in turn increases the likelihood of contamination from crucible walls, particularly at high temperatures, or during repeated crushing procedures. In the sol-gel route the wet gel may, in principle, be obtained with a degree of purity which depends only on the starting ingredients. The degree of purity of the final glass will depend on the sintering pro-

cess, which is performed at lower temperatures, and thereby reduces the risk of contamination. A substantially lower elaboration temperature, excellent homogeneity obtained directly, and a high degree of purity are the main advantages attributable to the sol-gel process. Is this enough to make the process competitive with the classical glass-melting practice? The lower elaboration temperature, from which energy saving might be expected, is largely offset by the high cost of the initial ingredients necessary for making the gel. In addition, organometallic precursors are not always available at present for the more exotic cations that might be required in some cases, and the initial formulation of the solution leading to a proper gel (without flocculation) can be a very difficult task indeed. The subsequent treatment of the gel, the drying-curing and sintering stages, are also more complicated and time-consuming in practice than the direct melting and fining involved in classical glass processing. Furthermore, they are specific to a given composition and the process has to be "tailored" for each new glass, which requires a complete preliminary study in each case. It seems therefore that the sol-gel process can only be competitive in areas of advanced technology (high-tech areas), and that neither window nor bottle glass will ever be made industrially in this way.

2.7.7 Future Trends

What really differentiates the sol-gel route from the classic igneous route is essentially the fact that an inorganic gel is a two-phase system where each of the two phases can be influenced separately by the preparative methods.

2.7 Solution Methods; "Sol-Gel" Processing of Glasses

In the classical method of obtaining glasses, the structural disorder is produced by progressive breakdown at high temperature of different crystalline components, and the resulting melt is a collection of more or less polymerized anions and fractions of chains with interdispersed accompanying cations. For a given melt the distribution of these entities depends essentially on the equilibrium conditions in the melt, i.e., on the temperature and atmosphere of the furnace which controls the oxidation-reduction changes. This hightemperature situation is preserved during quench, and the polyanionic distribution reflects the equilibrium conditions in the melt. Apart from systems which undergo phase separation (either in the liquid or sub-liquidus), the quenched melt is a onephase system with frozen-in local compositional fluctuations. The equilibrium conditions cannot be influenced to a great extent except by initial compositional changes. On the other hand, if we consider the processes which lead to the constitution of a gel, the various steps by which the disor-

115

dered network is built up are essentially chemical polymerization, polycondensation, cross-linking, etc., processes familiar in polymer chemistry. In this way elementary particles, filaments, etc., are produced which progressively link up to produce first a colloidal solution - a sol - and then a gel, when these elements unite into a reticulated network spanning the volume offered. A gel is essentially a system constituted of two phases: a solid backbone immersed in an interstitial liquid. The two phases are intimately mixed on a very fine scale. It is possible to change the nature of this second phase by various operations (Fig. 2-24). In the drying process the liquid was simply replaced by a gas-solvent vapor and air leading to aerogels. Using exchange processes, one liquid may be substituted for another; e.g., water may be replaced by alcohol to enable hypercritical treatment of aquagels. Foreign reactants may be diffused into gels via the interstitial liquid whereby chemical reactions, precipitation, etc., may be produced

Interstitial liquid Backbone

Solvent exchange ^

Hypercritical drying Aerogel

Reaction

-Sintering •

— Drying Dry gel

Figure 2-24. Examples of exchange methods combined with sol-gel processing to obtain composite materials (from Zarzycki, 1987 a).

116

2 Special Methods of Obtaining Glasses and Amorphous Materials

within the second phase or also within the backbone if this is done during gel formation. Infiltration of foreign substances into dry gels permits the air pockets (pores) to be filled, e.g., by colored or index matching substances. In this way a whole range of glass composites may be obtained on a very fine scale, depending on the backbone configuration. The range of the scale may descend to a few nanometers, hence the name nanocornposites, which was proposed for this class of materials (Roy et al., 1984, 1986). For example, gels containing suitable dyes may be prepared for advanced nonlinear optical applications. On the other hand, the preparation of gels with a complex backbone combining inorganic and organic systems, opens up new and unlimited possibilities of synthesis of hybrid amorphous materials, which are intermediate between pure inorganic glasses and organic polymers. This is the field of "organically modified silicates" (Ormosils), which has barely begun to be explored (Schmidt, 1985). Attempts to apply the sol-gel techniques to obtain chalcogenide glasses are reported where the inherent heterogeneity of meltobtained glasses could be improved, or new systems produced. Halide gels are also being investigated initially and thus completely new sol-gel systems are likely to be explored in the near future.

2.8 References Aegerter, M.A. (Ed.) (1990), 5 th Intern. Workshop "Glasses and Ceramics from Gels" Rio de Janeiro, 1989. J. Non-Cryst. Sol. 121, 1-492. Aegerter, M. A., Jafelici, Jr. M., Souza, D.F., Zanotto, E. D. (Eds.) (1989), Sol-gel Science and Technology. Singapore: World Scientific, pp. 1-505. Amick, J. A., Schnable, G.L., Vossen, XL. (1977), /. Vac. Sci. Technol. 14, 1053-1063.

Anantharaman, T. R., Suryanarayana, C. (1971), J. Mater. Sci. 6, 1111-1135. Andrianov, K. A. (1955), Organic Silicon Compounds, Moscow: State Scientific Publishing House for Chemical Literature; Translation 59-11239: Washington D.C., U.S.A.: U.S. Dept. of Commerce. Aoki, K., Shirakawa, K., Masumoto, T. (1985), Sci. Rep. Ritu A-32, 239. Aoki, K., Yamamoto, T., Masumoto, T. (1986), Sci. Rep. Ritu A-33, 163. Aoki, K., Toda, Y, Fukamishi, K., Masumoto, T. (1986), Sci. Rep. Ritu A-33, 149. Bletry, I (1973), J. Phys. D 6, 256-275. Bradley, D.C., Mehrotra, R.C., Gaur, D.P. (1978), Metal Alkoxides. New York: Academic Press. Brinker, C.J., Scherer, G.W. (1990), Sol-Gel Science. San Diego: Academic Press. Brinker, C.J., Clark, D.E., Ulrich, D. R. (Eds.) (1984), Better Ceramics Through Chemistry, Vol. 32. Amsterdam: North Holland. Brinker, C. I, Clark, D.E., Ulrich, D. R. (Eds.) (1986), Better Ceramics Through Chemistry II, Vol. 73. Pittsburgh: MRS. Brinker, C. I, Clark, D. E., Ulrich, D. R. (1988), Better Ceramics Through Chemistry III. Pittsburgh: MRS. Chao, E. C.T (1967), Science 156, 192-202. Chen, H. S., Miller, C. E. (1970), Rev. Sci. Instrum. 41, 1237. Chen, H. S., Miller, C. E. (1976), Mat. Res. Bull. 11, 49-54. Cline, C.F., Hopper, R. (1979), Scripta Metall. 11, 1137. Cowlard, F. C , Lewis, J.C. (1967), /. Mater. Sci. 2, 507. Crosset, M., Dieumegard, D. (1973), J. Electrochem. Soc. 120, 526. Dalton, R.H., Nordberg, M. E. (1941), U.S. Patent 2239551, April 21. Datta, R.K., Roy, D. M., Faile, S.P., Tuttle, O.F. (1964), J. Am. Ceram. Soc. 47, 153. DeCarli, P. S., Jamieson, D.C. (1959), J. Chem. Phys. 31, 1675-1676. Decottignies, M., Phalippou, I, Zarzycki, J. (1978), /. Mater. Sci. 13, 2605-2618. Dislich, H. (1971), Glastechn. Ber. 44, 1-8. Dislich, H. (1988), "Thin Films from the Sol-Gel Process", in: Sol-gel Technology for Thin Films, Fibers, Preforms, Electronics and Specialty Shapes: Klein, L. C. (Ed.). New Jersey: Noyes Publ., pp. 50-79. Downs, R.L., Ebner, M. A., Miller, W.J. (1988), "Hollow Glass Microspheres by Sol-Gel Technology", in: Sol-Gel Technology for Thin Films, Fibers, Preforms, Electronics and Specialty Shapes: Klein, L. C. (Ed.). New Jersey: Noyes Publ., pp. 330-381. Duwez, P., Willens, R. H., Klement, W. Jr. (1960), /. AppL Phys. 31, 1136-1173. Elliott, S. R. (1990), Physics of Amorphous Materials, 2nd. ed. Harlow: Longman. Fricke, J. (Ed.) (1986), Aerogels, Berlin: Springer.

2.8 References

Gibbons, R. V., Ahrens, I J. (1971), J. Geophys. Res. 76, 5489-5498. Gottardi, V. (Ed.) (1982), "1st Intern. Workshop Glasses and Glass-Ceramics from Gels, Padova 1981", J. Non-Cryst. Sol. 48, 1-230. Hasegawa, R., O'Handley, R.C. (1979), J. Appl. Phys.50, 1551-1556. Hench, L. L. (1986), "Use of Drying Control Chemical Additives (DCCAs) in Controlling Sol-Gel Processing", in: Science of Ceramic Chemical Processing: Hench, L. L., Ulrich, D. R. (Eds.). New York: Wiley, pp. 52-64. Hench, L. L., Ulrich, D. G. (Eds.) (1984), Ultrastructure Processing of Ceramics, Glasses and Composites. New York: Wiley, pp. 1-564. Hench, L. L., Ulrich, D. G. (Eds.) (1986), Science of Ceramic Chemical Processing. New York: Wiley, pp. 1-593. Holland, J. (1956), Vacuum Deposition of Thin Films. New York: Wiley. Her, R. K. (1979). The Chemistry of Silica. New York: Wiley, pp. 1-866. Johnson, W.L., Dolgin, B., Van Rossum, M. (1985), in: Glass-Current Issues. Wright, A. R, Dupuy, J. (Eds.). Dordrecht: Martinus Nijhoff Publ., pp. 172-187. Jones, H. (1972), J. Sheffield Univ. Metall. Soc. 11, 50-57. Jones, H., Suryanarayana, C. (1973), J. Mater. Sci. 8, 705-753. Kawamura, K., Jenkins, G.M. (1970), J. Mater. Sci. 5, 262. Kern, W, Rosier, R. S. (1977), J. Vac. Sci. Technol. 14, 1082. Klein, L. C. (Ed.) (1988), Sol-Gel Technology for Thin Films, Fibers, Preforms, Electronics and Specialty Shapes. New Yersey: Noyes Publ., pp. 1-407. Krepski, R., Swyler, K., Carleton, H. R., Herman, H. (1975), J. Mater. Sci. 10, 1452-1454. La Course, WC. (1988), "Continuous Filament Fibers by the Sol-Gel Process", in: Sol-Gel Technology for Thin Films, Fibers, Preforms, Electronics and Specialty Shapes: Klein, L. C. (Ed.). New Jersey: Noyes Publ., pp. 184-189. Mackenzie, J.D., Ulrich, D.G. (Eds.) (1988), Ultrastructure Processing of Advanced Ceramics. New York: Wiley, pp. 1-1014. Makino, Y. (1985), in: Current Topics on Non-Crystalline Solids: Baro, M.D., Clavaguera, N. (Eds.). Singapore: World Scientific, pp. 87-100. Mandelbrot, B. B. (1983). The Fractal Geometry of Nature. New York: Freeman. Masumoto, T. (1986), in: Current Topics on NonCrystalline Solids: Baro, M.D., Clavaguera, N. (Eds.). Singapore: World Scientific, pp. 73-86. Milton, D. X, De Carli, P. S. (1963), Science 140, 670671. Mizuno, T., Phalippou, X, Zarzycki, X (1985), Glass Technology 26, 39-45.

117

Mukherjee, S.P., Lowdermilk, WH. (1982), J. NonCryst. Sol. 48, 177-184; Appl. Opt. 21, 293-296. Negishi, T., Ogura, X, Ishii, H., Masumoto, T., Goto, T., Fukuoka, K., Syono, Y. (1985), J. Mater. Sci. 20, 399-406. Nordberg, M.E. (1943), U.S. patent 2326059, August 3. Pettit, R.B., Ashley, C. S., Reed, S.T., Brinker, C.X (1988), "Antireflective Films from the Sol-Gel Process", in: Sol-Gel Technology for Thin Films, Fibers, Preforms, Electronics and Specialty Shapes. Klein, L. C. (Ed.), New Jersey: Noyes Publ., pp. 80-110. Pietrokowsky, P. (1963), Rev. Sci. Instr. 34, 445. Pliskin, W. A. (1977), /. Vac. Sci. Technol. 14, 10641081. Pliskin, W A., Kerr, D. R., Perri, J. A. (1967), Phys. Thin Films 4, 257-324. Primak, W. (1958), Phys. Rev. 110, 1240-1254. Primak, W, Bohmann, M. (1962), Prog. Ceram. Sci. 2, 103-177. Pye, L.D., O'Keefe, J.A., Frechette, V.D. (Eds.) (1984), "Natural Glasses, Proc. Intern. Conf. on Glass in Planetary and Geological Phenomena". New York: Alfred (1983); J. Non-Cryst. Sol. 67, 1-662. Rabinovich, E. M. (1985), /. Mater. Sci. 20, 42594297. Roy, D. M., Faile, S. P., Tuttle, O. F. (1964), Am. Ceram. Soc. Bull. 43, 291 (Abstract only). Roy, R., Suwa, Y, Komarneni, S. (1986), in: Science of Ceramic Chemical Processing: Hench, L. L., Ulrich, D. R. (Eds.). New York: Wiley, pp. 247258. Roy, R., Komarneni, S., Roy, D.M. (1984), "Multiphasic Ceramic Composites Made by Sol-Gel Technique", in: Better Ceramics Through Chemistry, Vol.32: Brinker, C.X, Clark, D. E., Ulrich, D.R. (Eds.). Mat. Res. Soc, p. 347. Ruhl, R.C. (1967), Mat. Sci. Eng. 1, 313-320. Sakka, S. (1982), pp. 129-169, in: Treatise on Materials Science and Technology, Vol. 22. Tomozawa, M., Doremus, R. H. (Eds.). New York: Academic Press. Sakka, S. (Ed.) (1988 b), "4th Intern. Workshop Glasses and Glass-Ceramics from Gels, Kyoto, 1987", /. Non-Cryst. Sol. 100, 1-554. Sakka, S. (1988), "Fibers from the Sol-Gel Process", in: Sol-Gel Technology for Thin Films, Fibers, Preforms, Electronics and Specialty Shapes: Klein, L. C. (Ed.). New Jersey: Noyes PubL, pp. 140-161. Scherer, G. W. (1988), "Theory of Drying Gels", in: Ultrastructure Processing of Advanced Ceramics: Mackenzie, X D., Ulrich, D. R. (Eds.). New York: Wiley, pp. 295-302. Scherer, G. W, Schultz, P. C. (1983), in: Glass Science and Technology, Vol. 1: Uhlmann, D.R., Kreidl, N.X (Eds.). New York: Academic Press, pp. 4 9 103. Schmidt, H. (1985), /. Non-Cryst. Sol. 73, 681.

118

2 Special Methods of Obtaining Glasses and Amorphous Materials

Schmidt, P. R, Michel, W. (1957), J. Electrochem. Soc. 104, 230. Schmidt, P.F., Owen, A. E. (1964), J. Electrochem. Soc. Ill, 682. Schnable, G. L., Schmidt, P. F. (1976), J. Electrochem. Soc. 123, 310 C. Scholze, H. (Ed.) (1984), "2nd Intern. Workshop Glasses and Glass-Ceramics from Gels, Wiirzburg, 1983", /. Non-Cryst. Sol. 63, 1-300. Schott, Jenaer Glaswerk (1968), French Patent 1537617. Schroeder, H. (1969), Physics of Thin Films 5, 87142. Schultz, P.C. (1975), U.S. Patent 3 859073, January 7. Secrist, D. R., Mackenzie, I D . (1964), in: Modern Aspect of the Vitreous State, Vol. 3: Mackenzie, I D . (Ed.). London: Butterworths, p. 149-165. Sowman, H. G. (1988). "Alumina Boria-Silica Ceramic Fibers from the Sol-Gel Process", in: Sol-Gel Technology for Thin Films, Fibers, Preforms, Electronics and Specialty Shapes. Klein, L. C. (Ed.), New York: Noyes PubL, pp. 162-183. Stoffler, D. (1972), Fortschr. Mineral. 49, 50-113. Stoffler, D. (1974), Fortschr. Mineral. 51, 256-289. Suzuki, T., Anthony, A. (1974), Mat. Res. Bull. 9, 745-754. Tamman, G. (1933), Der Glaszustand. Leipzig: Voss. Tarasevich, M. (1984), Am. Ceram. Bull. 63, 500 (abstract only). Toda, Y, Ogura, T., Masumoto, T., Fukuoka, F., Syono, Y (1985), in: Proc. Intern. Conf. of Rapidly Quenched Metals V: Steeb, S., Warlimont, H. (Eds.). New York: Elsevier, p. 1755. Tohge, N., Matsuda, A., Minami, T., Matsuno, Y, Katayama, S., Ikeda, Y (1988), / Non-Cryst. Sol. 100, 501-505. Topol, L. E., Hengsteinberg, D. H., Blander, M., Happe, R.A., Richardson, N.L., Nelson, L. S. (1973), /. Non-Cryst. Sol. 12, 377-390. Townsend, P.D., Kelly, J.C., Hartley, N.E.W. (1976), "Ion Implantation, Sputtering and Their Applications". New York: Academic Press. Uhlmann, D. R., Ulrich, D.G. (Eds.) (1990), Ultrastructure Processing of Ceramics, New York: Wiley. United Technologies Research Center (1976), in: Machine Design, April 18, 6; Optical Spectra, April, 22. Veltri, R.D., Breinan, E.M., McCarthy, G.P., Galasso, F. S. (1979), /. Mater. Sci. 14, 3000-3002. Vermilyea, D.A. (1960), in: Non-Crystalline Solids: Frechette, V.D. (Ed.). New York: Wiley, p. 328347. Wackerle, J. (1962). J. Appl. Phys. 33, 922-937. Wullaert, R.A. (1964), in: Effects of Radiation on Materials and Components. New York: Van Nostrand Reinhold, pp. 277-402.

Yamada, S., Sato, H. (1962), Nature 193, 261. Yeh, X. L., Samwer, K., Johnson, W. L. (1983), Appl. Phys. Lett. 42, 242. Young, L. (1961), Anodic Oxide Films. New York: Academic Press. Zarzycki, J. (1982 a), Les Verres et VEtat Vitreux. Paris: Masson. Zarzycki, J. (1982 b), "Nucleation in Glasses from Gels", in: Advances in Ceramics 4, 204. Columbus: Amer. Cer. Soc. Zarzycki, J. (1984), "Processing of Gel Glasses", in: Glass Science and Technology, Vol. 2. Uhlmann, D.R., Kreidl, N.J. (Eds.). New York: Academic, pp. 209-249. Zarzycki, J. (Ed.) (1986), "3rd Intern. Workshop Glasses and Glass-Ceramics fom Gels, Montpellier, 1985". J. Non-Cryst. Sol. 82, 1-436. Zarzycki, J. (1987 a), "Advanced Glass by Sol-Gel Process", in: Proc. First Intern. Symposium on New Glass., Tokyo, Japan. Tokyo: The Association of New Glass Industries (Ed.), pp. 35-42. Zarzycki, I (1987 b), /. Non-Cryst. Sol. 95-96, 173. Zarzycki, J. (1988), J. Non-Cryst. Sol. 100, 359-363. Zarzycki, J. (1991), "Sonogels - Development and Perspectives", in: Ultrastructure Processing of Ceramics: Uhlmann, D. R., Ulrich, D. G. (Eds.). New York: Wiley (in press). Zarzycki, I, Naudin, F. (1967), Phys. Chem. Glasses 8, 11-18. Zarzycki, I, Prassas, M., Phalippou, J. (1982), /. Mater. Sci. 17, 3371-3379 (Published by Chapman and Hall).

General Reading Brinker, C. Y, Scherer, G. W (1990), Sol-Gel Science, San Diego: Academic Press. Gottardi, V. (Ed.) (1982), /. Non Cryst. Sol. 48, 1 230. Hermann, H., (Ed.) (1981), Ultrarapid Quenching of Liquid Alloys, Vol. 20, Treatise on Materials Science and Technology, New York: Academic Press Weeks, R. A., Kinser, D. L., Kordas, G., (Eds.) (1985), J. Non Cryst. Sol. 71, 1-456. Weeks, R. A., Kinser, D. L. (Eds.) (1989), Diffusion and Defect Data 53 (4), 920. Zarzycki, J. (1991), Glasses and The Vitreous State. Cambridge: Cambridge University Press. See also the following references listed in Sec. 2.8: Brinker et al. (1984), Brinker et al. (1986), Hench and Ulrich (1984), Hench and Ulrich (1986), Holland (1956), Her (1979), Mackenzie and Ulrich (1988), Pye et al. (1984), Sakka (1988 b), Scholze (1984), Zarzycki (1986).

3 Glass Formation and Relaxation George W. Scherer E.I. DuPont de Nemours & Co.,Wilmington, DE, U.S.A.

List of 3.1 3.2 3.2.1 3.2.1.1 3.2.1.2 3.2.2 3.2.2.1 3.2.2.2 3.2.3 3.2.3.1 3.2.3.2 3.2.3.3 3.2.3.4 3.2.3.5 3.3 3.3.1 3.3.2 3.4 3.4.1 3.4.1.1 3.4.1.2 3.4.1.3 3.4.1.4 3.4.1.5 3.4.2 3.4.3 3.4.3.1 3.4.3.2 3.4.3.3 3.4.4 3.4.4.1 3.4.4.2 3.5 3.5.1 3.5.1.1

Symbols and Abbreviations Introduction Glass Formation from the Melt Nucleation of Crystals Homogeneous Nucleation Heterogeneous Nucleation Crystal Growth Interface Control Diffusion Control Kinetics of Glass Formation Critical Cooling Rate Nonisothermal Analyses Simplified Model Heterogeneous and Transient Nucleation Factors Favoring Glass Formation Sintering and Crystallization Sintering Competition Between Sintering and Crystallization The Glass Transition Phenomenology Cooling Rate Dependence of Tg Fictive Temperature Hysteresis Nonlinearity Nonexponential Relaxation Function Thermodynamic Aspects Theories of Relaxation Rheological Models Kinetic Models Relaxation Models Phenomenological Models Tool's Equation Narayanaswamy's Theory Viscoelasticity Elasticity, Stress Relaxation, and Creep Elasticity

Materials Science and Technology Copyright © WILEY-VCH Verlag GmbH & Co KGaA. Allrightsreserved.

121 124 124 125 125 126 127 127 128 129 130 131 132 133 134 134 134 136 137 138 138 139 141 141 142 144 146 146 148 150 151 151 153 155 156 156

120

3 Glass Formation and Relaxation

3.5.1.2 3.5.1.3 3.5.2 3.5.2.1 3.5.2.2 3.5.3 3.5.3.1 3.5.3.2 3.5.3.3

Creep and Stress Relaxation Viscosity Temperature Dependence Equilibrium Liquid Nonequilibrium Liquid Calculation of Thermal Stresses Glass-to-Metal Seals Tempering Annealing

157 159 160 160 162 163 164 166 169

3.6

References

171

List of Symbols and Abbreviations

List of Symbols and Abbreviations A a a (T) B b cp D d Dc DL E AE en / /(0) g {v) G Ag AgD Agn Agv Gd H h h(T) h hf Iv Jt J2 K K (T) kB kn Kp / Ltj mt Mp n n n* N1

constant coefficient, radius shift function constant coefficient isobaric heat capacity transport coefficient dimension of space kinetic coefficient for transport across interface lattice diffuson coefficient Young modulus activation energy embryo containing n monomers interface site factor function of 0 function of v shear modulus free energy change activation barrier for transport free energy of formation of an embryo of n monomers free energy difference between unit volumes of crystal and liquid delayed elastic strain enthalpy Planck constant function of T magnetic field molar heat of fusion rate of homogeneous nucleation shear compliance or creep compliance dilatational compliance bulk modulus function of temperature Boltzmann constant rate constants for the addition and removal of a monomer constant thickness of seal phenomenological transport coefficients number of neighbors in "up" position relaxation function of property p number of pores per unit volume of liquid phase stiffness ratio number of embryos larger than r* number of monomers remaining in the liquid phase

121

122

"d

nv P q r r, r* Re R s

s sc s

f

T t TiV % TK TL Tn Tr TR Ts TK u V V

vm

w wk W*

w,w0

X

x, y, z

z Z 1 ? —Z N

a

P y

3 Glass Formation and Relaxation

Avogadro number refractive index of a liquid in equilibrium at Tx number of embryos with n monomers number of molecules of nucleating phase per unit volume pressure cooling rate heating rate distance vector biaxial relaxation function radius, critical radius critical cooling rate ideal gas constant interfacial area configurational entropy entropy of fusion temperature time fictive temperature for volume V fictive temperature glass transition temperature Kauzmann temperature liquidus temperature time corresponding with the "nose" method temperature corresponding with the "nose" method reduced temperature room temperature setting temperature temperature of crossover experiment growth rate volume volume fraction molar volume width of seal weighting factors thermodynamic barrier to nucleation relaxation rate, primary relaxation rate nonlinearity parameter stress axes number of molecules set of order parameters thermal expansion coefficient exponent with a value between 0 and 1 constant near unity interfacial energy (solid/liquid; liquid/vapor)

List of Symbols and Abbreviations

5 height of hierarchical energy barriers s volumetric strain rj viscosity 9 contact angle between crystal a n d nucleating heterogeneity x isothermal compressibility X j u m p distance size of the diffusing species Aji potential barrier per molecule hindering rearrangement v vibration frequency, Poisson ratio FITP Prigogine-Defay ratio Q relative density, density of sites o hydrostatic (or dilatational) stress G{ spin state T duration of period of transient nucleation T relaxation time TU uniaxial relaxation time 0X (t\
Adam-Gibbs cooperatively rearranging subsystem Kohlrausch-Wiliam- Watts partial fictive temperatures structural relaxation thermorheologically simple time-temperature-transformation viscoelasticity Vogel-Fulcher-Tamman

123

124

3 Glass Formation and Relaxation

3.1 Introduction When a liquid is cooled below the liquidus temperature (TL) it enters a state of metastable equilibrium. If the thermodynamic barrier to nucleation can be overcome, a crystal of the equilibrium phase is formed and the volume of the system decreases discontinuously, as shown in Fig. 3-1. In Section 3.2 we briefly review the theory of nucleation and growth, and establish the parameters that control the degree of crystallization during cooling. The goal is to predict the critical cooling rate, which is the minimum cooling rate that prevents the formation of a detectable degree of crystallinity. Of course, as indicated in the preceding chapter, glasses are formed in many ways other than cooling from the melt. In Section 3.3 we examine the problem of form-

Equilibrium liquid Metastable liquid Glass transition £

Glass

ing a glass object by sintering of a powder compact or gel. The degree of crystallization that occurs during sintering is relatively insensitive to thermal history, but does depend strongly on pore size and applied pressure. If nucleation does not occur, the liquid remains in metastable equilibrium below TL and continues to contract at the high rate corresponding to the thermal contraction coefficient of the equilibrium liquid. At lower temperatures the atomic mobility of the liquid decreases, and eventually the atoms become trapped in fixed positions. This occurs over a range of temperature called the glass transition region, which is discussed at length in Section 3.4. The glass transition temperature (Tg) is generally defined as the point of intersection of lines extrapolated from the glass and metastable liquid ranges (see Fig. 3-1). In the glass transition range, the properties of the liquid vary with time at a rate that is readily detected by human observers. This has important implications for stress development during cooling (especially for glasscontaining composites), because the viscosity that controls the rate of stress relaxation is a function of time as well as temperature. This problem is discussed in Section 3.5.

Crystal

3.2 Glass Formation from the Melt Figure 3-1. Volume change during cooling of a liquid. If nucleation of crystals occurs easily, the volume decreases discontinuously at the liquidus temperature, TL. Otherwise, the liquid remains in metastable equilibrium until reaching the glass transition temperature, where structural rearrangement is kinetically arrested. Further contraction results from the decreasing amplitude of vibration of the atoms around fixed positions (as in the crystal), so the slopes are similar for the glass and crystal.

A glass is typically formed by homogenizing the components in the liquid state at a temperature well above TL, then cooling below Tg. The cooling rate must be great enough so that no significant quantity of crystals can form. The critical rate depends on the kinetics of nucleation and growth, so we begin by discussing the standard theories for those processes.

3.2 Glass Formation from the Melt

3.2.1 Nucleation of Crystals

stituted into Eq,(3-3), the critical radius is found to be

3.2.1.1 Homogeneous Nucleation The barrier to nucleation arises from the interfacial energy (ySL) between the crystal and liquid phases. The free energy change (Ag) on growing a spherical crystal to a radius r is given by (Uhlmann and Chalmers, 1965; Christian, 1975):

Ag=-(4n/3)r3Agv

(3-1)

where Agv is the difference in free energy between unit volumes of the crystal and liquid. Since energy is expended to form the interface, the high surface-to-volume ratio of small crystals inhibits their growth. The break-even point occurs at the critical radius (r*), where dAg dr

= 0

(3-2)

Crystals with radii smaller than r* are called embryos, and they tend to shrink because dAg/dr>0 when r
(3-3)

The interfacial energy can be related to the molar heat of fusion, Ahf, by (Turnbull, 1964)

" - '

"U,

(3-4)

where NA is Avogadro's number and Vm is the molar volume. The free energy change can be approximated by (Hoffman, 1958)

Agv*Ah(Tr(l-Tt)/Vm

125

(3-5)

where Tr is the reduced temperature, Tr = T/7J. As we shall see, the maximum nucleation rate occurs in the range 0.5 < Tr <0.7, so when Eqs.(3-4) and (3-5) are sub-

r*^4{VJNA)^

(3-6)

which is just 4 formula units for the crystallizing compound, so r * ^ l nm. However, at small undercooling (TL—T), the liquid and crystal are in equilibrium, so Agv = 0 and the radius of the critical nucleus is infinite; thus, homogeneous nucleation (where crystals form directly from the liquid) only becomes favorable at large undercoolings. Growth of embryos is assumed to occur by reactions of the type (3 ?) K '" " where en is an embryo containing n "monomers" (e.g., formula units) and the kn are constants for the addition and removal of a monomer. If equilibrium were established, the number of embryos with n monomers (Nn) would be

Nn=NlQxp(-Agn/kBT)

(3-8)

where Nt is the number of monomers remaining in the liquid phase and Agn is the free energy of formation of an embryo of n monomers. However, there is no equilibrium, because embryos larger than the critical size (ft* monomers, or radius r*) grow rapidly and are removed from the system. Instead, a steady state develops, where the rate of the forward reaction in Eq. (3-7) becomes independent of time and n. The nucleation rate increases during the transient period (of length T) while the steady-state distribution of embryos is developing. The t Thompson and Spaepen (1979) find that Hoffman's approximation is appropriate for materials with a large change in cp at TL, but it does not work well for metals; they recommend replacing the factor of Tx with 2 Tr/(1 + Tt). Takahashi and Yoshio (1973) also find that Eq. (3-5) is not accurate for alkali disilicates; better results are obtained by neglecting the factor of T .

126

3 Glass Formation and Relaxation

kinetics of transient nucleation are very well described by the theory due to Kashchiev (1969), a fact that has been verified by experiment (James, 1974) and by computer simulations (Kelton et al, 1983). Substituting Eq.(3-6) into Eq.(3-1) we find the free energy of the critical nucleus, which is the thermodynamic barrier to nucleation: Ag{r*) = W* =

"5 A

(3.9)

The rate of formation of critical nuclei, or rate of homogeneous nucleation (Iv) is given by (James, 1985; Zanotto and James, 1985) ;n v vexp where nv is the number of molecules or formula units of nucleating phase per unit volume, v is a vibration frequency, v& kBT/h, where k is Boltzmann's constant and h is Planck's constant; AgD is the activation barrier for transport across the nucleus/liquid interface, and W* is the thermodynamic barrier to nucleation defined in Eq. (3-9). It is conventionally assumed that transport at the interface is related to a diffusion coefficient, D = v X1 exp ( - AgD/kB T)

(3-11)

where X is a jump distance, of the order of atomic dimensions. It is further assumed that D can be related to the viscosity (rj) by the Stokes-Einstein equation D=

kBT

(3-12)

so that W* exp

-

(3-13)

The validity of Eq. (3-13) has been extensively investigated. James (1985) gives an excellent account of this work. Rowlands

and James (1979) concluded from a study of nucleation in lithium disilicate glasses that the temperature dependence of the nucleation rate was well represented by the theory, except at very large undercoolings, but the magnitude of the measured rate was 20 orders of magnitude larger than predicted! Later it was shown (Zanotto and James, 1985) that the temperature dependence was indeed predicted correctly by Eq. (3-13), if viscosity values and nucleation rates were measured in the same glass; however, the magnitude of Iv was still grossly in error. Finally, James (1985) showed that the magnitude could also be brought into agreement by allowing for a weak (and physically reasonable) temperature dependence in y^. 3.2.1.2 Heterogeneous Nucleation In most real systems, crystals result from heterogeneous nucleation, where foreign material provides a surface that facilitates the formation of a critical nucleus. As indicated in Fig. 3-2, a nucleating agent (such as laboratory dirt, which is largely composed of aluminosilicates) is effective if it provides a low-energy interface with the crystal. In that case the energy invested to form the nucleus is smaller and the rate of t Weinberg and Zanotto (1989 a) argue that the use of the Stokes-Einstein equation, Eq. (3-12), is unjustified. Based on the very successful theory of Kashchiev (1969), they propose that the temperaturedependence of the transient time x gives a better representation of the kinetics of transport at the crystal/ liquid interface. Using measured values of x and Iv, they find that the predicted and measured values of the nucleation rate are not in agreement at large undercoolings. However, Kelton et al. (1983) found in their computer simulations that the temperature dependence of the transient time was not the same as for transport at the interface, and the difference was in the right direction to account for the results reported by Weinberg and Zanotto, so the standard theory is probably correct after all, even with the use of the Stokes- Einstein approximation.

127

3.2 Glass Formation from the Melt

Unfavorable

contamination by particles is most likely to occur at the surface, and these heterogeneities can be potent nucleating agents.

yr > yY sv SL

3.2.2 Crystal Growth 3.2.2.1 Interface Control

The standard theory for crystal growth is discussed in several good reviews (Jackson etal., 1967; Uhlmann, 1969, 1972 a). When growth is controlled by attachment of atoms to the interface, the growth rate (u) can be written

Crystal: Liquid i Vapor •

Figure 3-2. Schematic illustration of homogeneous and heterogeneous nucleation; 6 is the contact angle between the crystal and the nucleating heterogeneity.

nucleation is faster. For a nucleus in the form of a spherical cap growing on a flat substrate, the barrier to heterogeneous nucleation is given by (Uhlmann and Chalmers, 1965) (3-14) where / (0) = (2 + cos 6) (1 - cos 0)2/4

(3-15)

and 6 is the contact angle between the crystal and the nucleating heterogeneity, as illustrated in Fig. 3-2. The function f(6\ shown in Fig. 3-3, substantially reduces the barrier to nucleation when the contact angle is small (<90°). This allows nucleation to occur at relatively small undercoolings, where homogeneous nucleation is improbable. Heterogeneities are responsible for the appearance of crystals at small undercoolings, and for the occurrence of crystallization originating at the surface of a body of glass. As illustrated in Fig. 3-2, a free surface is an unfavorable site for homogeneous nucleation, because of the high energy of the solid/vapor interface. However,

where Dc is the kinetic coefficient governing the rate of transport at the crystal/liquid interface, / is the interface site factor (i.e., the fraction of sites on the interface to which an atom can attach), and the quantity in brackets is the thermodynamic factor determining the probability that an atom on the crystal surface will remain there, rather than jumping back into the liquid; Vm is the molar volume, .Rg is the ideal gas constant, and Agv is the same free energy that appears in Eq. (3-1). The coefficient Dc is generally identified with D in

0

20

40

60

80

100

120

e Figure 3-3. Function f(0), defined in Eq. (3-15), causes drastic reduction in barrier to nucleation when contact angle 6 is small.

128

3 Glass Formation and Relaxation

Eq.(3-ll) and approximated using the Stokes-Einstein equation, as in Eq.(3-12). A material with an entropy of fusion (Asf=Ahf/TL) less than 2Rg is expected to develop a rough liquid/crystal interface (Jackson et al, 1967), so the interface site factor will be near unity. In such cases, for small undercoolings Eq. (3-16) reduces to

Dc\ (As, RgT

(3-17)

where the second equality follows from Eq. (3-5). If the entropy of fusion is > 4 Rg, the crystal/liquid interface is smooth, and attachment is relatively difficult. If growth occurs at the ledge of a screw dislocation, then / increases in proportion to the undercooling:

ceeds, the rejected layer increases in thickness, so that diffusion must occur over greater and greater distances; consequently, the growth rate decreases with time according to uocr112

(3-20)

Once a diffusion layer forms, as indicated in Fig. 3-4, any perturbation that forms on the interface enters a region where the undercooling is greater, so it grows faster. This situation is called constitutional supercooling (Chalmers, 1964), and it accounts for the instability of smooth interfaces in systems crystallizing under diffusion control. Such systems typically exhibit dendritic ("tree-like") or spherulitic morphologies; the latter consists of den-

(3-18) If growth advances by formation of diskshaped nuclei on the smooth interface, the growth rate has the form

TL-T greater at tip of bump a)

B where A and B are constants (Hillig, 1966). b)

3.2.2.2 Diffusion Control In many systems, growth is not controlled by attachment kinetics. In rapidly crystallizing materials, such as metals, growth may be limited by the rate of transport of the heat of fusion away from the interface. In multicomponent systems (which includes most oxides of commercial or geological significance), the limiting step may be diffusion of solute. The rejected heat or solute builds up at the interface and decreases the driving force for crystallization (viz., the undercooling); growth will stop unless it diffuses away. As growth pro-

c)

Figure 3-4. Schematic illustration of diffusion-limited growth. Solute accumulating at the crystal/liquid interface reduces the driving force (TL—T) for growth; a perturbation on the interface enters a region with a greater undercooling, so it grows faster, leading to breakdown of the planar interface. The same phenomenon occurs when heat, rather than solute, is the diffusing species.

129

3.2 Glass Formation from the Melt

dritic needles with a common point of origin. An important feature of dendritic growth is that the growth rate is constant, rather than obeying Eq. (3-20). The reason is that the tip of the dendrite continually moves into "uncontaminated" liquid, so that diffusion occurs through a layer whose thickness is constant, rather than increasing (Christian, 1975).

1 -

i

i

A

0.8 ~

i

'•

-

0.6

0.4 -

0.2

\

''

o -

3.2.3 Kinetics of Glass Formation A variety of schemes have been proposed to account for the ability of certain compositions to form glasses; many are discussed in reviews by Uhlmann and Yinnon (1983) and Gutzow et al. (1985). Rules based on the ratios of the sizes of the atoms, the strengths of the bonds, or other structural features seem to work for certain groups of materials, but always fail for others. Such approaches are logically unsatisfactory, because glass formation is a kinetic phenomenon: even silica will crystallize if cooled too slowly, and water will vitrify if cooled fast enough. The answer to whether a given material is a glass former is not "yes" or "no". The answer is always "yes, in principle", because any liquid will form a glass if it is cooled rapidly enough. Dietzel and Wickert (1956) identified the quality of a glass-former by the reciprocal of its maximum crystallization rate. This would be reasonable if the nucleation behavior of various liquids were comparable, but it is not. The growth rate is not related to the interfacial energy that controls the nucleation barrier, so a liquid that crystallizes easily might be hard to nucleate. Turnbull (1969) suggested that the condition for glass formation should be the absence of any nucleation: (3-21)

i

• * u(max) / •

I p (max)

/

v\lvdt
i

0.5

;

\

\ 0.6

0.7

0.8

0.9

1.1

T/Tr

Figure 3-5. Rates of nucleation and crystal growth in SiO2, calculated from standard theory, using parameters given by MacFarlane (1982).

where V is the volume of the sample. This is a rigorous definition, certainly, as it ensures that a material that is called a glass is truly free of any crystallinity. However, when this proposal was investigated by Vreeswijk et al. (1974) their calculations predicted that SiO2 would have to be cooled 1010 times faster than GeO 2 to form a glass, and that As 2 O 3 would have to be quenched at 10 7o C/s. These results are clearly inconsistent with experimental evidence. The reason for the failure of this approach is indicated in Fig. 3-5: for many materials, the temperature ranges where the nucleation and growth rates are significant do not overlap. It may be virtually impossible to avoid forming a nucleus, but those nuclei that do form may not be able to grow to any meaningful «i™ 1" ^ Note that the situation is quite different on cooling and reheating. During cooling, the concentration of critical nuclei is near zero as the liquid passes through the temperature of the maximum growth rate. However, once it has been cooled through the range where the nucleation rate is high, many nuclei are available to grow during reheating.

130

3 Glass Formation and Relaxation

3.2.3.1 Critical Cooling Rate The most comprehensive method of predicting glass formation was introduced by Uhlmann (1972 b). The idea is to construct a time-temperature-transformation (TTT) curve as in Fig. 3-6: the curve defines the time required at any temperature to produce a particular volume fraction of crystallization, v. Uhlmann chose a fraction of v = 10" 6, on the basis that it represents the limit of detectability of crystallinity by current techniques; the results are not sensitive to this choice of v, as we shall see. Thus, a glass is implicitly defined as a material that contains an insignificant quantity of crystal. The TTT curve is used to calculate the critical cooling rate (Rc\ which is the minimum rate that results in a glassy product (i.e., one having a crystalline content < v). There is no clear-cut separation between glass-formers and non-glass-formers; instead, the glass-forming tendency of a liquid is quantified in terms of Rc.

The TTT curve is calculated using the Johnson-Mehl-Avrami theory (Christian, 1975), which relates v to the rates of nucleation (Iv) and growth (u): (3-22) 4 71

> = 1 — exp I —

Under isothermal conditions, when Iv and u are constant, this reduces to v = l — exp

« log t Figure 3-6. Schematic illustration of a TTT curve. The abscissa indicates the time required at each temperature to produce a volume fraction of crystals of v. The critical cooling rate (Rc) is the minimum rate that avoids crossing the curve. The "nose" of the curve, at time tn and temperature Tn, corresponds to the fastest rate of transformation. The nose method uses the approximation JRC «(TL — Tn)/tn, where TL is the liquidus temperature.

lv u i

(3-23)

or, when v is small, to v& —.

(3-24)

This expression can be modified (Christian, 1975) to account for those cases when the growth rate is not constant (e.g., under diffusion control, when u oc t~1/2) or is anisotropic (e.g., when crystals grow in the form of needles or plates). It must also be modified when heterogeneous or transient nucleation are important; these situations are discussed below. The TTT curve can be constructed using Eq. (3-24), together with measured or calculated values for Iv and u. The curve then represents isothermal crystallization, but we are interested in crystallization during constant cooling. A conservative estimate of the critical cooling rate is obtained by the "nose method": K*(TL-Tn)/tn

r

J/Jjudr df

(3-25)

where Tn and tn are the temperature and time corresponding to the nose of the TTT curve (see Fig. 3-6). The nose of the curve represents the fastest rate of transformation of liquid into crystal, and Eq. (3-25) gives the cooling rate that would be required if that crystallization rate applied over the whole temperature range from TL to Tn. The values of Rc found in this way,

131

3.2 Glass Formation from the Melt

using measured values for u, rj, and W*9 are generally in order-of-magnitude agreement with experiment (Uhlmann and Yinnon, 1983). Similar agreement has been obtained by other workers (e.g., Davies, 1976; Ramachandrarao et al., 1977; Tanner and Ray, 1979; Vil'kovskii, 1988) who used this approach to calculate Rc for metallic glassformers. 3.2.3.2 Nonisothermal Analyses An improved estimate of Rc can be obtained by taking proper account of the transformation rate at each temperature during a constant cooling treatment, rather than using the nose method. A simple way of adapting an isothermal TTT diagram to describe constant cooling is an averaging method suggested by Grange and Kiefer (1941): it is assumed that on cooling through a small temperature interval from T± at time t1to T2 at time t2, the amount of crystallization is equal to that produced isothermally at temperature (T1 + T2)/2 in a time period of t2-tv Onorato and Uhlmann (1976) adapted this method to calculate curves appropriate for cooling at a constant (dT/dt = constant) or logarithmic (dT/d (In t) = constant) rate, with the results shown in Fig. 3-7. The descending curves in Fig. 3-7 a represent constant cooling rates, and the one that barely misses the nose of the curve corresponds to Rc. When the constant cooling rate is taken into account, a smaller value of Rc is found, as expected, but the difference is typically less than a factor often. Note that Rc is relatively insensitive to the assumed value of v: a change o f ~ 5 x l 0 5 i n i ; causes a change by a factor of ~20 in Rc. Fig. 3-7 b shows that a logarithmic cooling rate (encountered in the cooling of many large bodies) produces a curve that falls between the isothermal TTT and the constant rate curve.

b) I

~

1500 U00 £ 1300 •1200 1100 1000

Figure 3-7. a) Isothermal TTT for v = 10" 6 and constant-rate cooling curves for v = 10" 6 and v =0.5-0.9; calculated for lunar glass 79155 (multicomponent silicate); b) Isothermal TTT and nonisothermal curves assuming constant (continuous) or logarithmic cooling rates, all for v =0.01; calculated for lunar glass 15286. From Uhlmann and Yinnon (1983).

A more rigorous nonisothermal analysis, suggested by Hopper et al. (1974), allows prediction of the distribution of crystal sizes following a given cooling treatment, or inference of the cooling rate from measurement of the size distribution. For the calculation of Rc it reduces to Eq. (3-22). A simpler method was suggested by MacFarlane (1982), based on the concept of additivity. This means that the rate of transformation depends on the current state of the system (i.e., v and T), and not

132

3 Glass Formation and Relaxation

on the thermal history. Then it can be shown (Cahn, 1956) that (3-26) where h and g are functions only of T and v9 respectively. MacFarlane (1982) noted that Eq.(3-24) can be written in the form (3-27)

Then, when additivity is valid, for a cooling rate ofq = dT/dt = constant, Eq. (3-27) becomes /^ ~QX

- 0I

At'

Y K(T(t'))J)

f

(3-Z5)

dT

'Y

which is readily evaluated. However, as Cahn (1956) explained, Eq.(3-26) is not generally valid when both Iv and u are temperature-dependent, so it cannot describe concurrent homogeneous nucleation and growth. However, it is valid when growth occurs from a constant number of nuclei, as might happen when heterogeneous nucleation dominates. (It is also valid when Iv and u have identical temperature dependences, Iv oc w, but no example of this circumstance is known or expected. See Fig. 3-5, for an example of typical temperature dependence.) Weinberg and Zanotto (1989 b) compared the prediction of Eqs. (3-22) and (3-28) and found that the predictions of v were very different when homogeneous nucleation was assumed. However, since Rc depends on t?1/4, an error of 103 in v causes less than an order of magnitude error in Rc. 3.2.3.3 Simplified Model Actually, it is easier to measure Rc directly than to obtain all the data necessary to calculate it, even using the nose method. Therefore, Uhlmann et al. (1979) have de-

veloped various simplified methods to predict JRC from limited data. One method is to calculate tn from Eq. (3-24), using Eq. (3-16) for u and Eq. (3-13) for Iv; Agv is approximated using Eq. (3-5), and the transport coefficients are approximated using the Stokes-Einstein equation, Eq. (3-12). Further, based on experience with a wide range of materials, it is recognized that the temperature of the nose occurs near r n *0.77T L

(3-29)

With these approximations, Eqs. (3-24) and (3-25) lead to (Uhlmann and Yinnon, 1983) RCK

^-exp(-0.212b)(3-30)

where a = 0.04 J/cm 3 K, rjn is the viscosity at 0.77 TL, and b is related to the nucleation barrier at a reduced temperature of T=0.8: b=

0.8fe B T L

(3-31)

The cooling rates calculated from Eq. (3-30) were found to be in order-of-magnitude agreement with experiment, so the results were almost as good as when the more rigorous analysis was used. Of course, it is essential to make a good choice for the value of b, because a 15-20% change in b results in a 10-fold change in Rc. The performance of the simplified analysis is surprisingly good, considering that it assumes that nucleation occurs homogeneously and that crystal growth is interface-controlled. The presence of heterogeneous nucleation changes only the magnitude of the nucleation barrier, not the form of the equations, but it does have a profound effect on the transformation rate,

3.2 Glass Formation from the Melt

as we shall see. The reproducibility of experimental measures of Rc indicates that heterogeneous nucleation is minimal or that the samples are contaminated in a consistent way. In many of the systems studied, growth is certainly diffusion-controlled, so the implication (Uhlmann and Yinnon, 1983) is that Eq. (3-16) is reasonably accurate in predicting the rate of dendritic growth in the vicinity of Tn. This would certainly not be expected a priori. However, it is worth noting that Magill et al. (1973) have shown that the crystal growth rates for a variety of organic glass formers can be collapsed onto a single master curve by plotting

u(T)/u(Tmax) versus

133

320

0.95

310

0.90

0.85

Homogeneous, 0.80 nucleation only

250

-U

-3

- 1 0 1 2 Log t (mini

Figure 3-8. Continuous cooling curves for homogeneous 4- bulk heterogeneous nucleation in o-terphenyl with contact angles as indicated, as well as for homogeneous nucleation only. Curves calculated from Eq. (3-22). From Uhlmann and Yinnon (1983).

(T-TJ/(TL-TJ,

where Tmax is the temperature of the maximum growth rate and T^ is a parameter (which may be related to the glass transition temperature). Moreover, Dearnley (1983) has shown that growth rate data for a variety of minerals (basalts, plagioclase, and diopside) can be described by the same curve. The organic systems probably grow under interface control, but the latter almost certainly exhibit diffusion control; nevertheless, in spite of a range of several hundred degrees in TL, all of these materials show similar temperature dependence for w. 3.2.3.4 Heterogeneous and Transient Nucleation

The effect of heterogeneous nucleation on the TTT curve has been examined by Onorato and Uhlmann (1976) and by Yinnon and Uhlmann (1981). The latter study used Eqs. (3-13) and (3-14) to calculate the effect of heterogeneities with various contact angles, 9. The TTT diagrams were constructed using Eq. (3-22) together with measured crystal growth rates for anorthite (CaO • A12O3 • 2SiO 2 ) and the or-

ganic glass-former o-terphenyl. As shown in Fig. 3-8, heterogeneities with #<100° cause drastic reductions in the critical cooling rate, because they allow nucleation in the temperature range where crystal growth is rapid. When heterogeneities with a range of contact angles are present, those with the smallest 6 are depleted first during cooling and those with larger 9 become more important at greater undercoolings. Uhlmann (1972 b) concluded that transient effects in nucleation would have a negligible effect on the calculation of Rc, because the transient period (of duration T) is generally short compared to (TL — Tn)/ Rc. Gutzow et al. (1985) used the theory of Kashchiev (1969) for transient nucleation to modifiy Eq. (3-24). For isotropic isothermal growth, they obtained 3v

(3-32)

The transient effects were found to be important when very potent heterogeneous nuclei were present, in which case high critical cooling rate were required. Kelton and Greer (1986) used a numerical method to simulate cluster growth directly, rather than

134

3 Glass Formation and Relaxation

using the Johnson-Mehl-Avrami analysis. They found that transient nucleation effects were insignificant for lithium disilicate, which is a good glass-former (Rc « 3.8 K/s), and were minor for (Au 85 Cu 15 ) 77 Si 9 Ge 14 , which is a relatively poor glass former (Rc«104 K/s). However, for Au 81 Si 19 , calculations including transient nucleation effects gave R c ^ 1 0 5 K / s , while steady-state calculations gave Rc « 2.4 x 107 K/s. Thus, when the critical cooling rate is high, transient effects become important, and ignoring them leads to a very pessimistic estimate of Rc. (See also Vol. 15, Chap. 9, Sec. 9.3.3.) 3.2.3.5 Factors Favoring Glass Formation Kinetic analyses suggest that the following factors are most important in reducing the critical cooling rate (Uhlmann and Yinnon, 1983): 1) High viscosity at the melting point or liquidus temperature (as is characteristic of silicate liquids) or a viscosity that rises rapidly with undercooling (as in organic glass-formers), since Iv and u are both inversely related to rj. 2) A high value of Tg/TL, since glass formation requires cooling from TL to Tg (this is clearly closely related to factor 1). 3) No heterogeneous nucleation. 4) A high barrier to homogeneous nucleation. 5) A large difference in composition between the crystal and liquid, since this makes crystal growth difficult. This condition, along with a small ratio of Tg to TL, is often met at eutectic compositions. Metallic glasses are most often found near eutectics. 6) Asymmetric molecules (as in o-terphenyl) that inhibit crystal growth. (See also Vol. 15, Chap. 9, Sees. 9.3.2 and 9.3.3.)

3.3 Sintering and Crystallization As explained in Chapter 2, glasses are formed in many ways other than cooling from the melt. One method that has achieved considerable importance in recent years is sol-gel processing, where wetchemical techniques are used to prepare an inorganic gel that is sintered to obtain a dense ceramic (Brinker and Scherer, 1990). In this section we discuss the factors that determine whether the sintered product crystallizes or remains glassy. This problem is closely related to that considered in the previous section, except that the glassy state is approached from below during heating of the gel, rather than from above, as during quenching of a melt. 3.3.1 Sintering A porous glass contains an excess energy equal to yLV S, where yLV is the liquid/vapor interfacial energy and S is the interfacial area. If the body is heated to a temperature at which the atoms have sufficient mobility, this energy provides a driving force for densification. The reduction of porosity through viscous flow or diffusion driven by surface energy is called sintering. This process is used to produce a variety of glassy objects, as described by Rabinovich (1985). In sol-gel processing, the surface area of the body is so enormous (typically 300-1000 m 2 /g) that the driving force is sufficient to permit sintering at very low temperatures. This raises the possibility of producing glasses that tend to crystallize or phase separate when prepared from the melt. For example, Yamane and Kojima (1981) made clear glasses in the strontium silicate system; since these compositions fall within a stable immiscibility region extending above 2000 °C, such glasses are virtually impossible to prepare by melting.

3.3 Sintering and Crystallization

On the other hand, sodium silicate glasses that are readily prepared by melting cannot be sintered, because crystallization of the porous gel is too rapid (Prassas and Hench, 1984). In glassy materials, sintering occurs by viscous flow. The kinetics of the process were first modeled by Frenkel (1945), who suggested that the energy gained by reduction in surface area must be equal to the energy dissipated in viscous flow. A variety of models have been developed based on that principle, differing principally in the geometry assumed for the pores (Mackenzie and Shuttleworth, 1949; Scherer, 1977). These models and their application to gels have been recently reviewed (Scherer, 1987; Brinker and Scherer, 1990). The prediction of these models, which is remarkable insensitive to the geometrical assumptions, is that the densification rate is given approximately by

135

(Scherer, 1984 b)

4na3

(3-34)

Sintering of crystalline materials is more complicated, because transport can occur simultaneously by diffusion through the crystal lattice, along grain boundaries, or across the surface of the particles, or by evaporation and condensation. As indicated in Fig. 3-9, there is a grain boundary at the point of contact (called a neck) between sintering crystalline particles, because the crystal planes do not generally align. Densification occurs when the centers of the particles move toward one another, and this requires that material be removed from the grain boundary and transported to the pore. This can be achieved only by diffusion along the grain boundary or through the lattice. Surface diffusion and evaporation/condensation reduce the surface area by moving material ,1/3 de to the neck (a process called coarsening), (3-33) 0.3 < Q < 0.9 dt but as indicated in Fig. 3-10, these processes do not cause densification. where Q is the relative density of the porous A large number of models have been body (i.e., the volume fraction of porosity = 1 — Q) and rj is the viscosity. The geomet- proposed to describe the kinetics of sintering when diffusion follows one or more ric parameter, n, is the number of pores per paths, and Ashby (1974) has developed unit volume of the liquid phase; for a body "maps" that indicate which process domicomposed of spherical particles of radius a, nates in a given range of temperature. For there is roughly one pore per particle, so

Path 2: Lattice diffusion Path 5: Lattice diffusion Path 3: Evaporation

Path 1: Surface Diffusion Path 4: Boundary diffusion

Figure 3-9. Schematic illustration of sintering of crystalline particles showing possible paths for transport of matter. For densification to occur, atoms must be removed from the grain boundary (dashed line) at the plane of contact (neck) between the particles.

136

3 Glass Formation and Relaxation Densification

Coarsening

ceramics can be made from amorphous aerogels, but only if the amount of crystallization during sintering is less than 5-10 vol%. To find a thermal treatment that will produce densification of a glass without excessive crystallization, it is necessary to combine the TTT diagram discussed in the previous section with information about the kinetics of viscous sintering.

Figure 3-10. Densification results when atoms move from the grain boundary to the pore. Coarsening occurs when atoms move from the surface of the particle toward the neck; the centers of the particles do not move toward one another.

our purposes, it is sufficient to consider a widely used model for densification produced by diffusion from the grain boundary through the lattice (Coble, 1961). The densification rate is given by 336 DL-

(3-35)

dt

where a is the radius of the particle, D L , is the lattice diffusion coefficient, y sv is the solid/vapor interfacial energy, and X is the size of the diffusing species. To compare the sintering rates permitted by viscous flow and diffusion, we use the Stokes-Einstein equation, Eq. (3-12), to replace DL with the viscosity, rj. Then, assuming that the surface energies are similar, Eqs. (3-33) to (3-35) lead to 2

dt

diffusion

dg dt

(3-36) flow

This indicates that sintering of crystalline materials is slower than sintering of glass, unless the particles are a few times larger than a molecule. Clearly, then, it is advantageous to densify a porous body before it crystallizes, if that is possible. A practical application of this principle is the demonstration by Thomas (1974) that dense glass

3.3.2 Competition Between Sintering and Crystallization From Eqs. (3-33) and (3-34) it can be seen that the time to achieve densification by viscous sintering is approximately TS * 1.6arj/yLY

(3-37)

Knowing rj (T) one can calculate the sintering time for a given particle size and plot it together with a TTT curve, as in Fig. 3-11. If the sintering curve does not cross the TTT curve, the sample can be sintered before it crystallizes. This variant on the TTT diagram was proposed by Uhlmann et al. (1975), who were interested in inferring the thermal history of a sample from examination of its microstructure. It is also useful if one seeks a sintering treatment that will be complete before significant crystallization occurs. Whereas a melt must be quenched to obtain a glass, a porous glass or gel must be heated to a temperature where viscous flow can occur. This generally means that the sample must pass through the temperature range where the nucleation rate is greatest, and the presence of abundant nuclei facilitates the crystallization that we seek to avoid. In fact most gels sinter in the vicinity of the glass transition temperature (Brinker and Scherer, 1990), where nucleation may be rapid; fortunately, growth in that temperature range is generally slow. Glass powders sinter at higher tempera-

3.4 The Glass Transition

137

U00 Breccias with crystallinities between 1% and 90% 1300

Completely crystalline breccias

Figure 3-11. Curve indicating sintering time (SINTERS) combined with isothermal TTT curves for various volume fractions of crystallization for a lunar glass. A breccia is a rock containing sharp fragments embedded in a finegrained matrix. The objective of this study (Uhlmann et al., 1975) was to infer the thermal history of the sample from the degree of crystallinity and extent of sintering.

6 8 log10 t (s)

tures (because the particle size, a, in Eq.(3-37) is larger), so they may have a significant growth rate as well as a high content of nuclei. The general guideline is that the particle size should be as small as possible, so that sintering can proceed at a temperature where the crystal growth rate is small. Of course, one should avoid heterogeneous nuclei, but even these are not important if the temperature is kept low enough. If the crystallization rate is fast even at temperatures too low for sintering, the densification rate can be accelerated by applying pressure (with a piston, for instance). However, to be effective, the applied pressure must be comparable to the capillary pressure, 2yLY/a, that drives sintering; for gels, this is on the order of 10100 MPa. In gels, the viscosity may be much lower than in a melted glass with the same oxide content, because gels tend to have high concentrations of hydroxyl (~ 0.1-0.3% OH). Therefore, the viscosity of a gel can be varied by low-temperature treatments that reduce the OH content, and one might expect this to have an impact on the ease of

sintering without crystallization. Zarzycki (1982) considered the question and concluded that chemical impurities that change rj will have the same effect on the rate of sintering and crystallization, since both processes are proportional to t/rj. Zarzycki found some evidence that OH could affect the barrier to homogeneous nucleation (probably by reducing ySL), but the differences in crystallinity among the silica gels he examined was attributed to heterogeneous nucleation.

3.4 The Glass Transition We have seen that a liquid can be cooled below the liquidus temperature if the rates of nucleation and growth are small enough. At moderate undercoolings the liquid is in metastable equilibrium, which means that physical properties such as specific volume, V9 are functions of temperature (T) and pressure (P), independent of time. Following small changes in state (caused, for example, by sudden heating or

138

3 Glass Formation and Relaxation

cooling) the properties of the liquid gradually approach their equilibrium t values. The time-dependent variation in physical properties as the liquid approaches equilibrium is called structural relaxation or physical aging. The glass transition is a region of temperature (corresponding to a viscosity of t] ^ l O ^ - l O 1 3 Pas) in which the rate of relaxation is slow enough to be readily detectable by human observers. The process of structural relaxation is nonlinear and nonexponential, and this gives rise to a rich phenomenology that is described in the next subsection. The same behavior is found in every class of liquid, including network oxides (e.g., soda-limesilicates), fluorides (e.g., the heavy metal fluorides being considered for optical telecommunications), salts (e.g., 0.4Ca(NO3)2 • •O.6KNO3), molecular liquids (e.g., o-terphenyl), polymers (e. g., polycarbonate), and metals (e.g., Si 15 5 Cu 6 Pd 7 8 5 ). More detailed discussions of relaxation in glassforming liquids are presented in the books Relaxation in Viscous Liquids and Glasses (Brawer, 1985) and Relaxation in Glasses and Composites (Scherer, 1986 b). After a brief look at the thermodynamic implications of the glass transition, we review a variety of theories that attempt to explain the kinetics of relaxation based on different views of the microscopic nature of the relaxation processes. The most powerful tool for prediction of the kinetics of relaxation is a theory proposed by Narayanaswamy (1971) that makes no assumption about the microscopic processes of relaxation. In the "f In the remainder of this chapter we are exclusively concerned with relaxation processes that occur below the liquidus. When we refer to the equilibrium state of a liquid it is understood to mean the metastable equilibrium state of the undercooled liquid. Of course, large excursions in T or P can result in transformation to the true equilibrium structure - the crystal by nucleation and growth, but we exclude such cases from consideration.

final subsection we discuss that theory and its application to such practical problems as tempering, annealing, and fabrication of glass-to-metal seals. 3.4.1 Phenomenology

The glass transition is characterized by a change in the temperature dependence of properties such as volume (V) and enthalpy (H) during cooling. As illustrated in Fig. 3-12, the volumetric thermal expansion coefficient (av = d In V/dT) and isobaric heat capacity (cp = dH/dT) decrease near Tg from a high value characteristic of the equilibrium liquid (avl9 cpl) to a small value characteristic of solid glass (ayg, cpg). In the glass, the atoms are frozen into fixed positions, and the properties change only because the temperature affects the amplitude of vibration of the atoms around those positions. Stronger temperature dependence is found in the liquid, because the atoms are free to diffuse, so changes in temperature can produce different atomic configurations in addition to changes in vibrational amplitude. As the temperature is lowered toward Tg, the mobility of the atoms decreases and relaxation times (T) on the order of seconds or minutes are required for the liquid to achieve the equilibrium configuration. If the temperature is dropping at the rate of a few degrees per minute, it is evident that the structure will not be able to remain in equilibrium; the liquid will be trapped in a configuration characteristic of a temperature near Tg. 3.4.1.1 Cooling Rate Dependence of Tg

The higher the cooling rate (q = dT/dt), the higher the glass transition temperature, as indicated in Fig. 3-12. This is easy to understand if the process of cooling is regarded as a sequence of temperature jumps of size A T followed by isothermal holds of

3.4 The Glass Transition

139

V

(B) slow cool and heat at rate I a I 1

B

Figure 3-12. Change in property p (illustrated for specific volume V and enthalpy if) during cooling of a glass-forming liquid. As the cooling rate (q) increases, so does the glass transition temperature (Tg). Lower part of plot shows slope of curves in upper plot:

oc = d(\nV)/dT and cp = dH/dT; vg

pg

subscripts / and g refer to properties of equilibrium liquid and glass, respectively.

Temperature

length At=AT/q. The liquid remains in equilibrium as long as At is much longer than the relaxation time, which is proportional to the viscosity (Rekhson et al., 1971; Mazurin, 1977): xp = t1/Kp

(3-38)

where Kp is a constant and xp is the relaxation time for the property p that is being measured; for the relaxation of volume in oxides, Kp » 2.5 x 109 Pa. At high temperatures, T
quantified by Copper (1985), who identifies the glass transition with the temperature where 1 dT

dT

(3-39)

Expressions that are more useful for quantitative predictions of Tg (q) are discussed in Section 3.4.4.2. 3.4.1.2 Fictive Temperature

A convenient way of characterizing the structure of the nonequilibrium liquid is by the value of the fictive temperature (Tf), which is defined in Fig. 3-13. The continuous curve represents the change in property p during constant cooling of a glassforming liquid, until it reaches temperature 7\ at time t0. If a line is drawn from the

140

3 Glass Formation and Relaxation

Constant cooling rate Quench

a.

t Tt

Tf(tn)Tf(t0)

Temperature Figure 3-13. The fictive temperature (Tf) is found by extrapolating a line with the glassy slope from any point on the nonequilibrium curve to its point of intersection with the curve of the equilibrium liquid. The continuous curve shows the path of property p during constant cooling, arriving at temperature Tx at time t0; if a line with the glassy slope is extrapolated from temperature Tx, the fictive temperature is found to be Tf (t0). If a sample were equilibrated at temperature T{ (t0) and then quenched to Tlt it would have the same value of p as the continuously cooled sample. During an isothermal hold at Tx, property p relaxes toward its equilibrium value, and T{ relaxes toward T,.

Figure 3-14. At high temperatures the liquid is in equilibrium and Tf = T, but on cooling into the glass transition region p lies above its equilibrium value and correspondingly Tf lags behind T. In the glassy state, T{ reaches a constant minimum value, which is called Tg.

nonequilibrium curve with the slope dp/dT characteristic of the glass (i.e., the "glassy slope"), it intersects the extrapolated equilibrium curve at the fictive temperature, Tt (t0). If another sample were equilibrated at temperature Tf (t0), then quenched to Tx, p for that sample would change along a line with the glassy slope, so the quenched sample would have the same value of p as the continuously cooled sample. Since the structure of the sample is assumed to be unchanged during the quench, the implication is that the structure of the continuously cooled sample is the same as that of a liquid in equilibrium at Tf. As we shall see, this is not strictly true: two samples with the same value of p do not necessarily have the same structure. However, the fictive temperature is a sim-

ple and useful measure of the structural state of the glass. If the sample is held isothermally at 7\, p relaxes toward its equilibrium value, which lies on the extrapolation of the equilibrium curve (heavy dashed line in Fig. 3-13). The fictive temperature decreases to Tf (tx) at time t1, and eventually becomes equal to Tx when the sample reaches equilibrium. The relationship between Tf and Tg is illustrated in Fig. 3-14. In the equilibrium liquid, the fictive temperature is equal to the actual temperature, but as the liquid is cooled into the glass transition region T{ decreases more slowly than T. By the time the liquid has frozen into the glassy state, Tf has reached the lowest possible value (for that cooling rate), and that value is called 71.

3.4 The Glass Transition

3.4.1.3 Hysteresis Fig. 3-12 indicates that the properties of a glass exhibit hysteresis during reheating through the glass transition range. At first the reheating curve bends toward the equilibrium curve, as we might expect, but then it crosses that curve and approaches equilibrium from below. Low atomic mobility prevents the structure from reaching equilibrium until the temperature is raised above Tg; then relaxation is rapid and the slope of the reheating curve is actually greater than that of the equilibrium curve. As shown in the lower portion of Fig. 3-12, the sudden approach to equilibrium causes an overshoot in cp (or <xv) on reheating. If the heating rate is much faster than the preceding cooling rate, the overshoot is particularly dramatic. On the other hand, if the reheating rate is relatively slow, there is plenty of time for relaxation during heating, so p(T) bends strongly toward the equilibrium curve. As shown in Fig. 3-15, this causes an undershoot in dp/dT below Tg, and relatively little overshoot. 3.4.1.4 Nonlinearity The kinetics of structural relaxation are most clearly revealed in experiments using temperature jumps, as shown schemat-

ically in Fig. 3-16, If a liquid in equilibrium at temperature T± is instantaneously cooled to T2, property p changes immediately because of the reduced vibrational amplitude of the atoms; thus, dp/dT has the value characteristic of the glass. During an isothermal hold at T2, there is a further change in p with time as the configuration approaches equilibrium. In terms of the fictive temperature, we could say that the sample arrives at T2 with Tf = T1, and relaxes until Tf = T2. A similar experiment can be performed by suddenly heating a liquid to T2 after equilibrating at T3. Structural relaxation is slower in this case, because the sample arrives at T2 with a structure characteristic of the lower temperature (Tf = T3). Therefore, the atoms have less mobility than those in the sample quenched from Tt, which arrives at T2 with a structure characteristic of the higher temperature. This is an illustration of the nonlinearity of structural relaxation: the rate of relaxation depends on the size and direction of the temperature jump, because TP depends on the structure of the liquid. The phenomenon is clearly illustrated in the data of Hara and Suetoshi (1955) for the relaxation of the density of window glass following jumps of 30 °C from above and below (see Fig. 3-17). If the temperature

j \ + qh (fast)

dT

q (slow)

141

qh (fast) »\q

\» qh (slow)

Figure 3-15. Hysteresis in dp/dT, where p is a property of the glass-forming liquid and T is temperature; if p is enthalpy, then this plot represents the heat capacity, cp. The overshoot on reheating is greater when the heating rate (qh) is greater than the preceding cooling rate (qc). If qh<\qc\ there is relatively little overshoot, but there is an undershoot below 71.

142

3 Glass Formation and Relaxation Glassy

slope

Equilibrium slope \

Pro erty p

bo

\

yf

\/ )h—

"eqm

/T

OH

I Temperature

Time

Figure 3-16. Approach to equilibrium following instantaneous jump to temperature T2 following equilibration at Tx or T3. During the jump (left side of figure), the change in property p reflects changes in the vibrational amplitude of atoms in fixed positions; time-dependent changes at temperature T2 (right side of figure) result from relaxation of the atomic configuration. 2.504

ation function of property p (Narayanaswamy, 1971):

l~p(oo,T)

Mp =

(3-40)

Structural relaxation in nonexponential, which means that Mp cannot be accurately represented by an equation of the form 2.492

200

Figure 3-17. Change in density with time at 530 °C for soda-lime-silicate glass previously equilibrated at 560 °C (•) and 500 °C (o). The temperature jump is 30 °C for both samples, but the sample quenched from the higher temperature relaxes faster. Data of Hara and Suetoshi (1955).

:

where t is the time following a jump to temperature T. Empirically, the relaxation function can be represented by a sum of exponential terms, t

Mp = jump is very small, then the configurational change is also small, and the relaxation appears linear; however, nonlinearity is clearly seen for oxide glasses following jumps as small as 7°C (Rekhson and Mazurin, 1974). 3.4.1.5 Nonexponential Relaxation Function

The shapes of the curves in Fig. 3-17 or the right side of Fig. 3-16 define the relax-

(3-41)

exp(--

(3-42)

where the xk are independent relaxation times and the wk are weighting factors, or by the stretched exponential, Mp = exp

-

(3-43)

where the exponent /? has a value between 0 and 1; a smaller value of /? corresponds to a broader distribution of relaxation times. (As written, the preceding equations apply only to linear relaxation; for temperature

jumps of more than a few degrees, it is necessary to take account of the time dependence of rp by replacing t/zp with j dt/ xp. This is discussed in Section 3.4.4.) Eq. (3-43) was originally used by Kohlrausch (1847) to describe creep of metals under mechanical stress, and later was applied for modeling of creep and stress relaxation in oxides by DeBast and Gilard (1963, 1965). Williams and Watts (1970) found it useful for describing dielectric relaxation. It is now often called the Kohlrausch-William-Watts of KWW function and, as we shall see, it emerges from a wide variety of theoretical models of the glass transition. If it is approximated by a sum of exponential terms, as in Eq. (3-42), exp

Hi

p

expl-

(3-44)

k= l

the distribution of weighting factors varies with the exponent /? as shown in Fig. 3-18. To describe structural relaxation, typical values of /? are in the range of 0.6 to 0.8 (Mazurin, 1977), whereas /?^0.5 for stress relaxation (Rekhson and Ginzburg, 1976). Although the KWW function has some theoretical support, it does not provide a perfect description of the relaxation function when the data cover several orders of magnitude in t/xp, either for stress relaxation (Kurkjian, 1963), or structural relaxation (Scherer, 1986 a). The nonexponential character of structural relaxation is most clearly illustrated in a crossover experiment of the type shown in Fig. 3-19. The sample is quenched from temperature 7\ to T2 and held there until the refractive index reaches nd = a, which is the index of a liquid in equilibrium at temperature Tx; thus, the fictive temperature for the sample is now Tf = Tx. Then the sample is immediately transferred to a furnace at temperature Tx and nd is measured as a function of time

3.4 The Glass Transition

143

l(f

10°

0.6

-o.i 10' l

(x /T

°Sio p *>

Figure 3-18. Distribution of relaxation times obtained when the KWW function is represented by sum of exponential terms, as in Eq. (3-44); ft = 1 corresponds to a single relaxation time. As p decreases the distribution broadens, but always remains skewed to short times.

(Fig. 3-19b). Since a -1.51493 is the equilibrium index at that temperature we would expect nd to remain constant, but it clearly decreases (apparently moving away from equilibrium) before relaxing toward the equilibrium value. As noted by Ritland (1954), this demonstrates that a glass with a fictive temperature of Tf = Tx does not necessarily have the same structure as a liquid at equilibrium at Tx. Macedo and Napolitano (1967) concluded that the relaxation process must consist of at least two processes that relax exponentially: a fast process with relaxation time rf and a slow process with relaxation time TS. During the hold at T2, the fast process relaxes almost to equilibrium (C) while the slow process barely rises above B, but the average of the two produces an index of a. When the sample is exposed to Tx9 the fast process effectively experiences a downward quench from equilibrium at T2, while the slow process is effectively up-quenched. The dashed lines in Fig. 3-19 b represent the paths of these two processes during the isothermal hold at Tx9 and the solid curve shows their aver-

144

3 Glass Formation and Relaxation

a)

*d T

2

C

\

C

i a i \— 4

B (

m a

.i. ••-

\

TEMPERATURE

TIME

(t)

1.51600

b)

1

Fast component 1.51493 + .00103 exp( - tl 7.77)

75 i

^ ^

50 t i *

25 _

Z O P

nd = a

1.51500 1.51493 1.51475 -

w Pi

+' **

50 --

\ Average Curve

Calculated

t

25 .

^pp 1.51400 -

S/ow component 1.51493 - 0.0111 exp (- tl 64.4)

4 t

1.51375 0

30

60

TIME

90

120

150

Figure 3-19. Scheme of crossover experiment used by Macedo and Napolitano (1967). a) Sample quenched from temperature T± to T2 shows instantaneous increase in refractive index from A to B, followed by relaxation toward equilibrium at C; a is index of liquid at equilibrium at Tx. When index reaches a, sample is transferred to furnace at Tx and change in index with time is followed, b) Refractive index (sodium d-line) versus time at Tx (o); solid curve is average of two dashed curves with relaxation times of rf = 7.77 and TS = 64.4 minutes.

180

(MINUTES)

age (assuming that each process contributes equally to the refractive index). Note that both processes approach directly toward equilibrium, but their average value moves away and then returns. If the relaxation process were simply exponential, the index could not move away from equilibrium.

3.4.2 Thermodynamic Aspects

Fig. 3-20 illustrates a phenomenon that is called the Kauzmann paradox. Kauzmann (1948) noted that the configuration entropy (Sc)-of the equilibrium liquid decreases so strongly with temperature that it would fall below the entropy of the cor-

3.4 The Glass Transition

Equilibrium liquid

s

d

responding crystal if extrapolated below temperature TK. This unacceptable situation is prevented by the glass transition, which freezes the configuration and "locks in" Sc at a value characteristic of the equilibrium liquid at Tg. What is disturbing is that the thermodynamic catastrophe is apparently prevented by the coincidental intervention of a kinetic phenomenon - the glass transition. Moreover, the interval between the Kauzmann temperature (TK) and Tg is often quite small, even at moderate cooling rates (Angell, 1988), so one could imagine cooling at such a slow rate that Tg would drop below TK. Kauzmann (1948) suggested that crystallization would always occur before TK, but that does not seem to be true in every case (Angell et al., 1986). Various theories propose that the reduction in Sc is arrested by thermodynamic phase transitions of first order (Grest and Cohen, 1981) or second order (Gibbs and DiMarzio, 1958), while Stillinger (1988) argues plausibly that no phase transition is likely. The existence of a phase transition must be regarded as an open question, but it is clear that an adequate theory of the glass transition must provide a resolution for this paradox.

145

Figure 3-20. The configurational entropy of the equilibrium liquid is dropping so fast that the entropy would fall below that of the crystal at temperatures < TK. This thermodynamic catastrophe is averted by the glass transition, which freezes the configurational entropy. This apparent coincidence (i.e., a kinetic escape from a thermodynamic problem) is called the Kauzmann paradox.

Davies and Jones (1953) considered the thermodynamic implications of having a single order parameter, such as Tf, that determines the state of a glass. They showed that the Prigogine-Defay ratio,

must have a value of unity if only a single order parameter exists. In Eq. (3-45), Acp is the difference in heat capacity between the equilibrium liquid and the glass, and Ax and A a are the corresponding differences in isothermal compressibility and volumetric thermal expansion coefficient, respectively; Vm is the molar volume. Data collected by Moynihan and Lesikar (1981) indicate that nTP has a value of ~ 2-5 for a variety of glass-forming liquids, so none can be characterized by a single order parameter. Gupta (1988 a) suggested that the fictive pressure could be used as a second order parameter. Irreversible thermodynamics can be used to develop a theory of relaxation based on the existence of an arbitrary number of order parameters (Moynihan and Gupta, 1978; Berg and Cooper, 1978). These models (discussed in Section 3.4.3.2) lead to a relaxation function in the form of

146

3 Glass Formation and Relaxation

a sum of exponential terms, so they can be made to agree with experimental observations; unfortunately, the theory offers no clue as to the nature of the order parameters, nor the temperature dependence of the relaxation times. 3.4.3 Theories of Relaxation A wide variety of theories of relaxation have been developed based on distinct microscopic models, and only a few of the more important ones are presented here. This material is drawn from a more extensive review by Scherer (1990). It is convenient to categorize theories of relaxation as rheological models, which predict the temperature-dependence of the relaxation time (zp), kinetic models, which describe the form of the relaxation function (Mp), and relaxation models, which endeavor to explain both. The principal features that a complete theory must explain are nonlinearity (i.e., dependence of xp on structure) and nonexponentiality. The latter property is well described by the KWW equation, Eq. (3-43), and there is now an astounding number of models based on different physical principles that lead to that expression. Theorists have exploited two means of obtaining nonexponential relaxation: requiring cooperative relaxation or invoking heterogeneity (distributions of density or energy, or randomly situated acceptor/donor sites). In real glasses, both these factors are likely to be important, particularly near Tg, and a few theories have attempted to embrace both. Phenomenological models, which make no assumptions about the molecular-scale processes involved in relaxation, are discussed in detail in Section 3.4.4.

3.4.3.1 Rheological Models As indicated by Eq. (3-38), the relaxation time is proportional to the viscosity, so models for xp are equivalent to models for rj. That is why the term "rheological" is used to describe theories that account for the temperature dependence of xp. One of the most famous of these is the free volume theory developed by Cohen and Turnbull (1959, 1961, 1970). The idea is that flow occurs by movement of molecules into voids of a size greater than some critical size. That is, the molecules rattle around in the cage created by the surrounding molecules, until density fluctuations create a hole large enough to jump into. The free volume (v{) is somewhat vaguely defined, but it represents roughly the space not occupied by the core volumes (v0) of the molecules. According to this model the viscosity can be written as (Scherer, 1984 a)

TJ(a,-a )dr

(3-46)

g

where y is a constant (close to unity), Tfv is the fictive temperature for the volume, To is the temperature where v{ = 0, and oq and ocg are the expansion coefficients for the liquid and glass, respectively. The free volume depends on the actual atomic configuration, rather than the equilibrium configuration, so v{ is written in terms of the fictive temperature, rather than the actual temperature. At equilibrium (T{ = T), if al — ocg is constant, Eq. (3-46) reduces to the empirical Vogel-Fulcher-Tamman (VFT) equation: T-Tn

(3-47)

147

3.4 The Glass Transition

where rj0, A, and To are constants. The VFT equation is the most successful 3-parameter expression for describing r\ (T). In a liquid out of equilibrium, it is clear that Eq. (3-46) can account for nonlinearity, since it implies that TP = TP(T{). However, it fails to explain experiments of the sort represented in Fig. 3-21. In addition to measuring the equilibrium viscosity, Mazurin et al. (1979, 1981) have measured the isostructural viscosity: the sample is equilibrated at a high viscosity, then quenched to a slightly lower temperature where the viscosity can be measured before a significant amount of relaxation occurs; thus, they obtain the temperature dependence of rj when Tf is constant. The measurements made on a variety of oxide glasses indicate that the isostructural viscosity obeys the Arrhenius equation, AE

(3-48)

where Rg is the ideal gas constant and AE is an activation energy. The equilibrium viscosity obeys the VFT equation, Eq. (3-47), and the concave form of that curve corresponds to an apparent activation energy, AEA(T% that increases as the temperature decreases. Typically, the isostructural activation energy is about half of AEA(Tf). Note that Eq. (3-46) indicates that rj is constant when Tf is constant, so it cannot account for the isostructural data. The free volume model also fails to predict the change in Tg with applied pressure (Goldstein, 1963; Angell and Sichina, 1976). Recent developments of the free volume theory that correct some of these defects are discussed in the section on relaxation models. An entirely different picture of viscous flow, developed by Adam and Gibbs (1965), traces its motivation back to Kauzmann (1948). Gibbs and DiMarzio (1958)

17 NBS 710 ISOSTRUCTURAL

16

/

Tf =522X1 15

14

1

13

o 11

10

10

12

13

14

15

io4/r(K) Figure 3-21. Viscosity of soda-lime-silicate glass NBS 710 under equilibrium (Tf = T) and isostructural (T{ = constant) conditions measured by Mazurin et al. (1979). Isostructural data obtained by equilibrating at very high viscosity (10 135 Pa s) then quenching and measuring f]{T) before significant structural relaxation could occur. Curves calculated using AdamGibbs model for viscosity (Scherer, 1984 a).

presented a statistical mechanical theory that predicted a second order phase transition at the Kauzmann temperature TK to an ideal glass with configurational entropy (Sc) equal to zero, thus avoiding the thermodynamic catastrophe. This transition cannot be observed in practice, because TK lies below Tg, so the laboratory glass transition is merely a kinetic manifestation of an unattainable thermodynamic transition. Adam and Gibbs (AG) argued that the increase in viscosity as T-> Tg could be attributed to the loss of configurations available to the liquid. Their model is based on the idea that relaxation requires cooperative rearrangement of a group of z molecules. As the temperature drops and

148

3 Glass Formation and Relaxation

the liquid becomes denser, movement of one molecule disturbs an increasingly large number of its neighbors; i.e., z increases as T decreases. AG assumed that the barrier to rearrangement increased in proportion to z (AE = z A\x, where zl^u is the potential barrier per molecule hindering rearrangement), and determined the temperature dependence of z in terms of S c . Their result is , = T0

exp

(3-49)

where S* is the configurational entropy of the smallest cooperatively rearranging subsystem (CRS); it is generally assumed that the latter must contain 2 configurations, so S?^/c B ln2. Eq. (3-39) has several appealing features. First, it provides an escape from the Kauzmann paradox: even if there is no phase transition, Sc can never fall below zero, because xp diverges as that point is approached; thus, even in an infinitely long experiment, Sc = 0 can only be approached asymptotically. In fact, to avoid the paradox it seems inevitable that either there is a phase transition or the relaxation time is a function of S" 1 , or both. Second, it is clear how the relaxation time (or viscosity) depends on the fictive temperature, since we can write (Howell et al., 1974; Scherer, 1984 a) fH

TV

Ac

(3-50)

to the Kauzmann temperature (i.e., the temperature where Sc extrapolates to zero). If TfH is constant, then so is S c , and Eqs. (3-38) and (3-49) yield Arrhenius behavior for the isostructural viscosity. In fact, the curves shown in Fig. 3-21 for both the equilibrium and isostructural viscosity were calculated from the AG equation. In addition to its ability to reproduce the form of rj (T), the AG equation is much more successful than the free volume model at predicting the effect of pressure on Tg (Goldstein, 1963; Angell and Sichina, 1976). Gupta (1987) has shown that it is also in qualitative accord with the observation that some liquids decrease in viscosity when subjected to compressive pressure (Sharma et al., 1979; Mysen et al., 1980; Angell etal., 1982). 3.4.3.2 Kinetic Models The order parameter model begins with the assumption that the free energy (g) depends on a set of order parameters (Zl9Z2, ... Zjy), in addition to T and P (Moynihan and Gupta, 1978; Berg and Cooper, 1978). The parameters Z- are not identfied with specific physical characteristics, such as free volume. According to the principles of nonequilibrium thermodynamics, the rate of relaxation may be written as dAZt At

(3 51)

"

j

k

1

where Acp = cpl — cpg; we have assumed that Sc(TK) = 0 and that the configurational entropy is governed by the fictive temperature of the enthalpy, H. At equilibrium we can approximate (Angell and Sichina, 1976) Acp ^const/7; so that Eqs. (3-49) and (3-50) lead to the VFT equation, Eq.(3-47), with To identified with TK. This is consistent with the observation that the value of To found empirically is often close

where we have defined the affinities At = —dg/dZt, as well as AZi=Zi—Zie (where Zie is the equilibrium value of Zt) and atj = —dAJdZj. The constants L(j are phenomenological transport coefficients, equivalent to relaxation frequencies \/xk. Eq. (3-51) leads to the following relaxation function for the response of property p to a change in variable x: (3-52)

3.4 The Glass Transition

This approach leads to some important conclusions about the nature of these relaxation functions; for example, MVT = MHP 7^ MVP. That is, the relaxation of the volume in response to a change in temperature is different from its response to a change in pressure, but is equivalent to the response of the enthalpy to a change in pressure. A particularly interesting version of the order parameter model, introduced by Gupta (1988 b), is based on the idea that the free energy of the system is related to the spatial gradients in the order parameters. For a single parameter this leads to a relaxation equation of the form

where T 0 and D are constants. Eq. (3-53) leads to a continuous distribution of relaxation times for Z. This theme recurs in many of the models discussed below: inhomogeneity in the structure of the liquid gives rise to nonexponential relaxation. A group of models based on the formalism of chemical reactions is discussed in an excellent review by Blumen et al. (1986). One class of model involves direct transfer of energy from a donor to an acceptor site. If the sites are uniformly distributed, relaxation is found to occur by a simple exponential decay; however, if randomness is introduced into the structure through an inhomogeneous distribution of sites, the decay becomes nonexponential. Let the energy transfer rate w (r) depend on the distance r between donor and acceptor; neglecting back-transfer, the probability of decay of the donor at rD to an acceptor at rA is ~rD)] (3-54) and this leads to a relaxation function of the form M.(t,r D ) = ]

'jlf{t,rA,rD)y\

(3-55)

149

where g^ is the probability of having j acceptors at one site. For isotropic multipolar interactions, the transfer rate is given by w(r) = a lVs

(3-56)

When this is used in Eq. (3-55), the relaxation function reduces to the KWW function, Eq. (3-43), with ft = d/s (where d is the dimension of space) and xp = aj [VdpQr(l-d/s)]s/d, where Vd is the volume of the unit sphere in d dimensions, p is the concentration of acceptor sites, Q is the density of sites, and F is the gamma function. If the sites are assumed to be distributed on fractals, the fractal dimension (df) replaces d in the preceding results. Another type of model assumes that donors or acceptors make random walks on a lattice and react instantly on meeting (Blumen et al., 1986). This produces simple exponential relaxation in 3 dimensions, but the KWW function if the random walk is performed on a fractal. Thus, the nonexponential relaxation results in this case from geometric randomness. Alternatively, the randomness can be introduced by allowing a distribution of waiting times before each step of the random walk, and this also leads to nonexponential relaxation. In hierarchical models, a diffusing particle must surmount a series of barriers of height 5; given an excitation AE=j5, the particle can move among j levels. The randomness introduced through the energy levels leads to nonexponential relaxation at low temperatures, but at high temperatures where the particle can move freely among the levels, the relaxation reverts to simple exponential decay. This is consistent with the relaxation behavior of real liquids. Ngai et al. (1986) have developed a coupling model They assume that the system consists of primary species with a relaxation rate Wo that controls the initial re-

150

3 Glass Formation and Relaxation

sponse to an impulse. After a characteristic time (co ~ 1 ), coupling between the primary species modifies the relaxation rate,

W{T,t): ^•"-V/KO"-.

«:»i

<3 57)

-

The relaxation function is found from dM p_ _ = dt

-W(T,t)Mp

(3-58)

which leads to Eq. (3-43) with xp = \fia>l~p/ W0]1/fi. An example of the process envisioned in this model is the relaxation of a polymer, where the coupling comes from entanglement of chains, which interferes with the movement of a single chain only after an initial lag (Ngai et al., 1988). This model makes no assertions about the temperature or structure dependence of the relaxation process. It has been applied to the analysis of structural relaxation by making additional assumptions about those factors (Rendell et al., 1987), but Rekhson (1987) has challenged those assumptions. 3.4.3.3 Relaxation Models Nonlinear, nonexponential relaxation kinetics follow simply from the requirement that relaxation involve cooperative movement. This is consistent with the qualitative similarity seen in the relaxation kinetics of every class of liquid. That is, such behavior cannot be dependent on the details of bonding or structure, but must follow from some general phenomenon. A particularly nice example of this idea is the facilitated Ising model studied by Fredrickson and Brawer (1986) and Fredrickson (1986). Consider a set of Ising spins on a square lattice that are subjected to a magnetic field (h) that tends to make the spins flip down. A spin is allowed to flip only if two of its nearest neighbors are

"up", so the rearrangement is cooperative. To establish a connection with real glasses, the up and down spins could be imagined to represent regions of high and low density, respectively. As shown in Fig. 3-22, the smallest CRS in this model contains 4 configurations, rather than 2, as is often assumed in application of the AG model. The rate (Wt) at which a spin at site i flips from state ai to — o{ [where ot can be + 1 (up) or - 1 (down)] is

where co is an attempt frequency and mt is the number of neighbors in the "up" position. Monte Carlo simulations of this model indicate that it relaxes according to Eq. (3-43), with /? decreasing slightly with temperature. The relaxation time obeys the the AG equation, Eq.(3-49) [the configurational entropy is known exactly for this model]. The latter result requires a high degree of cooperativity: Fredrickson (1988) has extended this model to three dimensions, allowing a spin to flip when n neighbors are "up", and finds that the AG equation applies when n = 3, but not when n = 2. The beauty of the facilitated Ising model is that it assumes only a simple form of cooperativity, yet it reproduces the essential features of relaxation in viscous liquids.

\i

Figure 3-22. Smallest cooperatively rearranging subsystem (CRS) in the 2-spin facilitated Ising model has 4 configurations, since spins a and b can both flip.

3.4 The Glass Transition

Brawer (1984) has developed a much more specific model of relaxation that assumes that a local region of the liquid must be excited to a transition state with high energy and low density before that region can relax to a higher density. In this model, the size of the CRS is assumed to be independent of temperature. The most difficult problem in analyzing such a model is accounting for the overlap of the regions. Suppose the CRS has a radius of 10 atoms: then any single atom lies within ~ 103 such regions centered on different neighboring atoms, and it may participate in a rearrangement with any of those regions. This problem was ignored in the derivation of the AG equation. Brawer avoids it by limiting consideration to the earliest stage of relaxation (i.e., 1 — Mp<^ 1), when relatively few regions have transformed and the effect of overlap is negligible. The existence of density (or energy) fluctuations in the fluid produces a distribution of relaxation times, because the regions in a higher state of excitation relax first. The relaxation is nonlinear, because the distribution of energies depends on the temperature history. Thus, the model has all of the right features. Cohen and Grest (1979) and Grest and Cohen (1981) have developed a version of free volume theory that involves percolation of "liquid-like cells" (for a lucid discussion of percolation, and its connection to this theory, see Zallen (1983)). An atom vibrates in a cage in a solid-like manner unless the cage contains a sufficient amount of volume (v > vc\ in which case it is called liquid-like; free volume (vi = v — vc) is freely exchanged between liquid-like cells. Diffusion requires that vi exceed the molecular volume (vm); a cluster in which v{ >vm is liquid, rather than liquid-like. As the amount of free volume increases, the number of liquid-like cells increases to the point that a contiguous network (i.e., a percola-

151

tion cluster) appears, which gives macroscopic fluidity to the material. The free energy of the system is written explicitly in terms of the communal entropy, which is the contribution to the entropy resulting from the freedom of atoms in liquid-like cells to move within liquid clusters (i.e., it represents the accessible configurations of the system). The communal entropy biases the distribution of free volume so as to increase the number of liquid-like cells and suppress solid-like cells. This leads to a discontinuous change in the probability (px) of liquid-like cells as the temperature is reduced, which corresponds to a first order phase transition. The viscosity of the system is still given by Eq. (3-46), but an explicit expression for v{ is obtained that has a sufficiently complicated temperature dependence (involving 3 parameters) to account fully for actual viscosity data. Since the viscosity depends only on vf, this model still does not account for the isostructural viscosity. The above mentioned model was extended (Grest and Cohen, 1980) to account for structural relaxation by using Eq. (3-40) with p = Pi and xp given by Eq. (3-46); this allows for nonlinear exponential relaxation. Nonexponential behavior was obtained by assuming (Cohen and Grest, 1984) that each cluster relaxes independently at a rate proportional to its surfaceto-volume ratio (since relaxation involves diffusion of volume across the boundary of the liquid-like regions). This leads to a relaxation function in the form of Eq. (3-43). 3.4.4 Phenomenological Models 3.4.4.1 Tool's Equation

Phenomenological models (discussed in detail by Scherer, 1986 b) have been developed that permit accurate calculation of the changes in properties of liquids during

152

3 Glass Formation and Relaxation

arbitrary thermal cycles. Great success has been obtained in the use of these models to predict stresses in composites, such as glass-to-metal seals, and in annealing and tempering of glass, as explained in Section 3.5. The first important step in the development of these models was taken by Tool (1945, 1946), who proposed, by analogy to viscoelastic stress relaxation, that structural relaxation of property p should obey pe(T)-p(T,t) dt

(3-60)

where pe(T) = p(T,oo) is the equilibrium value of the property at temperature T. Consider the relaxation following an instantaneous jump from temperature 7\ to T2. It is clear from Fig. 3-23 that the current value of p can be written as

a g (T 2 -T f (0)

p(T2,t)

(3-61 a)

i2

if

it

Temperature Figure 3-23. Relaxation of property p following jump from temperature Tx to T2; pe is the equilibrium value, a} and ocg are the values of dp/dT in the liquid and glassy states, respectively. The sample arrives at T2 at time t = 0 and relaxes toward p(T 2 , oo) = pe(T2).

(3-61 b) so (3-62) With Eqs. (3-61 b) and (3-62), Eq. (3-60) can be written in the form known as Tool's equation: (3-63)

dt

Tool's most important contribution was the suggestion that the effect of structure be incorporated by writing the relaxation time as , = T0

exp(-A1T-A2Tf)

(3-64)

Although this formula lacks theoretical justification, it was found to be quite effective in accounting for the nonlinearity of relaxation.

Ritland (1954) showed that Eqs. (3-63) and (3-64) can be used to predict the effect of cooling rate on Tg. The glass transition temperature corresponding to cooling rates q± and q2 can be shown to be related by (3-65) 1 In or dTa d\n\q\

(3-66)

Thus Tg increases logarithmically with the cooling rate, a result that was experimentally verified by Ritland (1954). The principal weakness of Tool's theory is that it uses only a single parameter, Tf, to represent the state of the glass. Ritland (1956) was the first to perform a crossover

3.4 The Glass Transition

153

experiment of the type shown in Fig. 3-19, and he did it to demonstrate that the structure is dependent on thermal history, so that glasses with a given value of property p (and hence a given Tf) are not structurally identical. The problem was clearly recognized, but was not resolved for another 15 years.

form of the VFT equation, Eq.(3-47), is needed to represent a wider temperature interval. If the relaxation function Mp is represented by Eq. (3-42), then the fictive temperature can be decomposed into "partial fictive temperatures" (PFT) (Rekhson, 1986; Scherer, 1986b)

3.4.4.2 Narayanaswamy's Theory

Tf= f> f c T f f c

A major stride was taken by Narayanaswamy (1971) who generalized Tool's theory by allowing for a distribution of relaxation times. (An essentially identical model was later proposed independently by Kovacs et al., 1979.) He obtained the following expression for the fictive temperature:

where each of the Tfk relaxes in a simple exponential manner with relaxation time ik (i.e., they individually obey Tool's equation). This is formally equivalent to the order parameter model described in Section 3.4.3.2, with each PFT representing an order parameter. When there is more than one, the Prigogine-Defay ratio, Eq. (3-45), will be greater than unity, as is found experimentally. Rekhson (1986) has shown how the crossover experiment can be understood in terms of the independent relaxation of the PFT. The measured property value reflects the average Tf, but the thermal history of the sample determines the distribution of PFT, and many different distributions can yield the same average. The two relaxation processes indicated in Fig. 3-19 b correspond to two partial fictive temperatures. Narayanaswamy's theory has been extensively tested [see e.g., Moynihan et al. (1976 b), Mazurin (1977), and Scherer (1986 b)] on many types of liquids, and it displays all of the necessary features. Nonexponentiality follows from use of Eqs. (3-42) or (3-43) to represent the relaxation function. The KWW function (introduced in this context by Moynihan et al., 1976 a) has been most useful, typically with 0.6 <
(3-67) 0

where £ is the reduced time defined by (3-68) 0

T

p

and xr is the value of i p at some reference temperature. If the relaxation function is represented by a single relaxation time, as in Eq. (3-41), it can be shown (Scherer, 1986b) that Eq.(3-67) reduces to Tool's equation, Eq. (3-63). Narayanaswamy wrote the relaxation time in terms of the Arrhenius equation as xAE ,=

T0

exp

(l-x)AEl

(3-69)

where x, the nonlinearity parameter, divides the temperature dependence between the temperature and fictive temperature. This gives a better representation of the temperature dependence off/ or TP than Eq. (3-64), but still it is useful only over a limited range of temperature (typically ~100°C for a silicate glass). A function with the

(3-70)

154

3 Glass Formation and Relaxation

575 540 494 420 (a)

0

40 80 120 240 280 320 t (min)

4

8

12 16

20

40

80 120 160 200 t (min)

78

(b)

0

100

90

Figure 3-24. Calculated curves and measured values (points) for change in length of specimen of soda-limesilicate glass (Tg = 524 °C): a) thermal history; b) isothermal holds at 494 °C (curve 1, lower time scale) and 540 °C (curve 2, upper time scale); c) entire thermal cycle. From Mazurin et al. (1975).

80

70

(c)

400

450

500

ample of the success of this theory is presented in Fig. 3-24: part a shows the thermal cycle, including cooling, reheating, and isothermal holds; part b shows the relaxation during the holds; part c shows the dilatometer curve for the entire cycle. The calculated curves in parts b and c are in excellent agreement with the data.

550

Experiments including temperature jumps, crossover, and continuous cooling can all be modelled quantitatively in this way, unless the range of temperatures examined is too broad. The origin of this limitation is not certain, but the most likely causes are (1) changes in the distribution of relaxation times (or, equivalently, changes

3.5 Viscoelasticity

in the exponent /? in the KWW equation) with temperature, and (2) the narrow range of applicability of the Arrhenius equation, Eq. (3-69). The first problem has been addressed by several models (Mazurin and Startsev, 1981; Scherer, 1986 a) but that seems to be less important than using a correct form for the relaxation time. A particularly effective modification (Scherer, 1984 a) is to represent xp by the AdamGibbs equation, using Eqs. (3-49) and (3-50). If, following Hodge (1987), we adopt the approximation J C p ^ c o n s t / T suggested by Angell and Sichina (1976), the relaxation time has the form

fit is equally good with Eq. (3-49) or (3-69), but the AG equation yields parameters that have physically reasonable values (e.g., pre-exponential factors with the correct order of magnitude). This version of the theory also provides an excellent description of the nonlinear relaxation behavior of the facilitated Ising model (Fredrickson and Brawer, 1986). Moynihan et al. (1974, 1976 b) showed that Eqs. (3.67) to (3-69) lead to an expression analogous to Eq. (3-66) for the dependence of T on cooling rate, q: dln(l/T g ) AE

,=?0exp

T(l-T K /T f )

(3-71)

At equilibrium, when T{ = % Eq. (3-71) has the form of the VFT equation, Eq. (3-47), with To identified with the Kauzmann temperature, TK, so it can correctly represent the shape of the equilibrium curve. Under isostructural conditions (Tf = constant), Eq.(3-71) has the form of the Arrhenius equation, Eq. (3-48), in keeping with experimental observations (see Fig. 3-21). In addition, Eq. (3-71) offers a theoretical foundation for the incorporation of the fictive temperature into rp9 and provides an expression for the nonlinearity parameter, x, (Hodge, 1987): : = 1-T K /T f

(3-72)

As noted by Howell et al. (1974), the AG equation is unique in that the parameters that control the shape of the equilibrium curve also dictate the slope of the isostructural curve. Hodge (1987) has found that incorporating the AG equation into Narayanaswamy's model gives a better fit than Eq. (3-69) to the enthalpy relaxation of polymers annealed far below Tg. In other cases (Scherer, 1984 a, 1986 a; Opalka, 1987; Crichton and Moynihan, 1988) the

155

(3-73)

Again, the shift in Tg with q depends on the temperature dependence of the equilibrium viscosity. Based on numerical evaluation of Eq. (3-67) with xp given by the AdamGibbs equation, Scherer (1984 a) concluded that the shift could be written in the general form dln(T.) iL —

(3-74)

Narayanaswamy (1988) has presented a rigorous analysis of the implications of Eq. (3-67) for the shift of Tg with q. The expressions derived by Ritland (1954) and Moynihan et al. (1974, 1976 b) were shown to be exact, regardless of the form of the relaxation function. Narayanaswamy finds that Eq. (3-74) is not exact, although it is numerically accurate.

3.5 Viscoelasticity The theory of viscoelasticity is presented in several texts, so only the essential elements are reviewed here. A mathematically rigorous treatment of viscoelasticity (VE) is given by Christensen (1982). A more readable discussion, with the emphasis on or-

156

3 Glass Formation and Relaxation

2e

c)

a)

Figure 3-25. Modes of deformation of a unit cube: a) pure shear causes change of shape without change of volume; b) triaxial stress causes change of volume and, if the normal stresses are not all equal, change of shape; c) under uniaxial stress, the Poisson effect causes a strain in the directions normal to the applied stress, ex = —vaz.

ganic polymers, is provided by Ferry (1961). Scherer (1986b) presents the theory of VE, and shows how it can be combined with Narayanaswamy's theory of structural relaxation (1971) to calculate thermal stresses. This section is based on that book.

stress is applied, as in Fig. 3-25 b, there is a volumetric strain (e) given by AV

which is related to the hydrostatic (or dilatational) stress (a) by

3.5.1 Elasticity, Stress Relaxation and Creep

(3-77)

where

3.5.1.1 Elasticity The mathematical relation between stress and strain is called a constitutive equation. For an isotropic elastic material, such as glass, the constitutive equation requires only two parameters: the shear modulus (G) and bulk modulus (X), or Young's modulus (E) and Poissorfs ratio (v). A pure shear stress (Fig. 3-25 a) causes a change in shape without any change in volume, and the strain is related to the stress by azx = 2Gszx

(3-76)

(3-75)

The subscripts on atj and e^- indicate that axis i is normal to the plane on which the stress acts, and the stress acts in the direction of axis j ; for shear, i # j . When triaxial

(3-78) By definition, tensile stresses are positive; pressure (P) obeys the opposite sign convention, and is defined by P=-(crx + ay + oz)/3

(3-79)

If the stresses (ax, oy,oz) are not all equal, there is a change in shape as well as volume. For example, when the stress is uniaxial (Fig. 3-25 c), the stress and strain are related by az = Esz

(3-80)

In this case the stress can be shown to be 2/3 shear and 1/3 dilatation. The axial compression causes the cube to expand in

3.5 Viscoelasticity

157

the x and y directions; this is called the Poisson effect, and the strains are related by 8x = 8y = -V8z

(3-81)

For a general state of stress, the elastic constitutive equations can be written as (Timoshenko and Goodier, 1970) a)

1 ~E

(3-82 a)

1

(3-82 b) (3-82 c)

The constitutive parameters are interrelated as follows:

3(l-2v) E 2(1 9KG E= 3K + G 3K-2G v = 2(2K + G)

(3-83 a) (3-83 b)

Figure 3-26. Mechanical models of viscoelastic relaxation: a) the Maxwell element consists of a spring, corresponding to the elastic shear modulus G, and a dashpot (representing a piston moving through oil), corresponding to the shear viscosity \\\ b) dilatational relaxation is most simply represented by a spring, corresponding to the elastic bulk modulus K, in series with a Voigt element, which consists of a spring in parallel with a dashpot; the spring in the Voigt element limits the amount of volumetric contraction.

and the dashpot contributes the viscous flow. The compliance of this element is given by . , 1

(3-83 c) (3-83 d)

3.5.1.2 Creep and Stress Relaxation Stress causes flow of a viscoelastic (VE) material, so the constitutive parameters are functions of time. For instance, when a constant shear stress is applied, the shear strain is

t IT

(3-85)

If the viscosity is infinite (a fair approximation to the glassy state), the response is purely elastic (J1 = 1/2G); but if the viscosity is low, the elastic strain is negligible compared to the viscous strain. From Eqs. (3-84) and (3-85) it is clear that the viscous strain is comparable to the elastic strain when t = z, where T is the Maxwell relaxation time, (3-86)

If the Maxwell element is subjected to a constant strain, the stress relaxes accordwhere J1 is the shear compliance; the reing to sponse of a VE material to a constant stress is called creep, so J t is also called the tfz* = G«GiW (3-87) creep compliance. The simplest model for where the shear relaxation function is given viscoelastic behavior is the Maxwell eleby ment shown in Fig. 3-26 a. The spring provides the instantaneous elastic response G1(t) = 2Ge-«t (3-88)

6» =
(3-84)

158

3 Glass Formation and Relaxation

At the instant that the strain is imposed, G1 (0) = 2 G, so Eqs. (3-87) and (3-88) indicate that the initial stress is the same as that in the purely elastic material, Eq. (3-75); the stress then decreases to zero as the sample flows in the direction of the applied stress. A VE material also relaxes under a purely hydrostatic load, but the volume cannot change very much, so the stress generally cannot relax to zero. When a constant hydrostatic stress is applied, the volumetric strain is given by

\ = aJ2(t)

(3-89)

where J 2 (0 *s the dilatational compliance. The simplest mechanical model representing dilatational relaxation is shown in Fig. 3-26 b. The compliance of this model is 1 3KD

xD = rjD/3KD

(3-91)

Note that the viscosity that controls volume relaxation is not necessarily the same as the shear viscosity; experimental evidence indicates that rjD is several times larger than r\, but has the same temperature dependence. These simple mechanical models faithfully represent the essential features of VE response, but the behavior of actual materials is more complex in detail. The shear relaxation function of oxide glasses must be represented by a distribution of relaxation times (which could be represented by a group of Maxwell elements in parallel), } E wk exp

G1(t) = 2 G e x p \ - l -

(3-93)

DeBast and Gilard (1963) showed that Eq. (3-93) gave a very good representation of the relaxation behavior of a soda-limesilicate glass, and Rekhson and Ginzburg (1976) showed stress relaxation in a wide variety of glasses could be described by Eq. (3-93) with /? = 0.5. This is only a good approximation, however, and very precise data cannot be adequately fit by Eq. (3-93). For example, Kurkjian's data (1963) for shear relaxation in a soda-lime-silicate glass require Eq. (3-92) with N = 6. The shear compliance of an oxide glass is given by

(3-90)

where the dilatational relaxation time is given by

N

or the KWW function,

(

t -

(3-92)

where 4>l (t) is a function that can be represented by a sum of exponential terms or the KWW function; thus, ^ ( 0 ) = ! and 0i (0 -~* 0 at t -> oo. Even when Gt and cj)1 (t) are both given by the same functional form, the relaxation times for relaxation and creep are not related in a simple way. The most convenient way to calculate G± from Jx, or vice versa, is to use the Laplace transform (Scherer, 1986 b). The second term in Eq. (3-94) describes the delayed elastic strain and Gd is the delayed elastic shear modulus. The three contributions to the shear strain can be understood schematically as follows. When the stress is first imposed, the instantaneous elastic response results from bond stretching with no change in the configuration of the molecules; the delayed elastic response results from gradual disentanglement of chains or clusters of molecules; viscous flow occurs as those structural elements slide past one another.

3.5 Viscoelasticity

When the stress is removed, the bonds immediately snap back to their natural length, so the elastic strain is recovered instantly. The delayed elastic strain is also completely recovered as the structure returns to its equilibrium configuration; this requires about the same period of time as the strain took to develop. The viscous strain does not recover. The dilatational compliance of an oxide can be written as z w

3K

3K D L

4>Z2V{t)] " /J

-t/Tu

ation time only by a factor of 3/2 (1 + v) « 1.2. For purposes of stress analysis, the dilatational relaxation can be entirely ignored, unless the sample is triaxially constrained, in which case shear deformation is inhibited. 3.5.1.3 Viscosity It can be shown that the shear viscosity is related to the shear relaxation function by

(3-95)

where 4>2 (t) is a function that can be represented by a sum of exponential terms or the KWW function. Corsaro (1976 a) showed that the dilatational relaxation of B 2 O 3 could be described by using the KWW function for (j)2 (t) with j8 = 0.60. The final strain was about three times greater than the instantaneous elastic strain, J2(ty/ j 2 (oo) = 0.30. He further showed (Corsaro, 1976 b) that, because of the nonexponential nature of the relaxation, the crossover effect (discussed in Section 3.4.1.5) could be produced by subjecting a sample to a series of pressure jumps. Since the dilatational modulus relaxes to a substantial fraction (typically ~ l / 3 ) of its original value, while the shear modulus goes to zero, it is not surprising that the relaxation of uniaxial or biaxial stresses is dominated by the shear behavior. For example, for a material whose shear response is given by Eq. (3-88) and which exhibits no dilatational relaxation at all (J 2 = 1/3K), the response to a constant uniaxial strain &z is (Scherer and Rekhson, 1982 a) (3-96)

Thus, shear deformation allows the uniaxial stress to relax to zero even though the stress is partially hydrostatic. The uniaxial relaxation time, TU , exceeds the shear relax-

159

(3-97) where x is an average relaxation time. If Gx is given by Eq. (3-92) (3-98) k =1

and if Gx is given by Eq. (3-93) (DeBast and Gilard, 1963), (3-99) where F is the gamma function. Comparing Eqs. (3-86) and (3-97) we see that the Maxwell relaxation time is the average relaxation time for the glass. Indeed, experimental studies confirm that the viscosity obtained from direct measurements (i.e., in creep experiments) agrees with the values found by integrating stress relaxation data, according to Eq. (3-97). Comparing Eqs. (3-38) and (3-97) we see that the structural relaxation time and the stress relaxation time are proportional to one another, but experiment (Rekhson, 1975) indicates that Kp is about an order of magnitude smaller than G, so stress relaxation is a much faster process. This is what makes it possible to measure the isostructural viscosity (Mazurin et al., 1979): a measurable amount of creep occurs before structural relaxation produces a significant change in 7^.

160

3 Glass Formation and Relaxation

From Eqs. (3-84) and (3-94) it can seen that the shear strain rate in a creep experiment approaches the limit (3-100) If the applied stress is uniaxial (as is typically the case) rather than pure shear, the corresponding relation is At

3rj

(3-101)

Thus, the viscosity can be measured from the slope of a plot of strain versus time; it is only necessary to wait until the delayed elastic strain is fully developed. Oxide liquids exhibit Newtonian viscosity, which means that the viscosity does not depend on the magnitude of the stress that is applied. This also means that the relaxation time governing stress relaxation and creep is independent of the applied stress, so oxides are linearly viscoelastic. This is in contrast to the nature of structural relaxation in the same materials: the rate of structural relaxation depends on the size and direction of the temperature jump; the stress relaxation rate is the same for tensile or compressive stresses. Actually, this is only approximately true: if the stress is large enough to affect the structure of the liquid significantly, nonlinear effects appear. However, the stresses required to produce nonlinearity are large: for a soda-lime-silicate glass it can be shown (Scherer, 1986 b) that a pressure of 12MPa is thermodynamically equivalent to a temperature change of 1 °C. Nonlinearity is evident following temperature jumps of ~ 5 °C, so the same should be expected under applied pressures >60MPa. Indeed, Simmons et al. (1982) found non-Newtonian behavior under tensile stresses of that magnitude. Li and Uhlmann (1970) showed that alkali silicate

glasses exhibited non-Newtonian behavior under shear stresses exceeding ~ 100 MPa. In both cases, the viscosity decreased by an order of magnitude or more. This is consistent with molecular dynamics calculations which indicate that catastrophic changes in the structure of liquids occur under high stresses: the atoms arrange into layers that slide relatively easily. Particularly interesting effects are observed under purely hydrostatic loads. It is expected (intuitively, and particularly where the free volume model applies) that hydrostatic compression will increase the viscosity. However, Sharma et al. (1979) found that the viscosity of GeO 2 decreases under high compressive loads. It is known (Mysen et al., 1980) that network silicates exhibit this behavior when the average silicon atom has less than one nonbridging bond. Thus, highly modified networks, such as Na 2 O • SiO2 (with two nonbridging bonds per Si), show "normal" behavior (viz., rj increasing with pressure), but germania (with no nonbridging bonds) does not. This experimental result is supported by molecular dynamics calculations (Angell et al, 1982). 3.5.2 Temperature Dependence

The rates of relaxation and creep are strongly temperature-dependent. We first examine how the VE response varies in isothermal experiments at various temperatures, when the liquid remains in thermodynamic equilibrium during the experiment. Then we consider cases in which structural relaxation and stress relaxation occur simultaneously. 3.5.2.1 Equilibrium Liquid

Since the relaxation time is proportional to the viscosity, the rate of stress relaxation increases rapidly with temperature. For ex-

3.5 Viscoelasticity

161

and plot the data for T3 against log [t a (T3)], those data coincide with the other sets. In this way the shift function, a(T\ can be used to create a single master curve from all the data. This is possible for any materials whose relaxation function retains the same shape at all temperatures when plotted against \ogt. A material that exhibits this behavior is said to be thermorheologically simple (TRS). In terms of Eq. (3-92), TRS behavior is obtained when all of the relaxation times have the same temperature dependence (xk oc t] for all h) and the weighting factors

ample, if a constant shear strain is applied to a glass, the shear relaxation function varies with temperature as shown in Fig. 3-27. If the data are plotted against log £, as in Fig. 3-27 b, curves for different temperatures are identical in shape, but shifted along the abscissa. The distance, which we shall call log [#(71)], between points A and B is the same as that between points D and E. If the data for temperature 7\ are plotted against log t + log [a (T±)] = log [t a {T±)]9 they coincide with the data for temperature T2. Similarly, if we call the (negative) distance between points C and B log[a(T 3 )],

0.8

a)

25

1 0.8 0.6 2G

0.4 0.2 0

b)

0.001

0.01

1

i

i

0.1

1

10

log t

100

Figure 3-27. Shear stress relaxation function of thermorheologically simple material at several temperatures: a) relaxation rate increases with temperature; b) when plotted versus log t, the curves have the same shape, but are shifted along the abscissa.

162

3 Glass Formation and Relaxation

are constant [w k ^w k (T)]t. If the relaxation function is represented by Eq. (3-93), TRS requires that the exponent /? be independent of temperature. In either case, the shift function represents the temperature dependence of the average relaxation time, (3-102) where, Tr is the reference temperature, the temperature of the data set onto which all of the others are shifted. In relaxation studies it is conventional to introduce the reduced time, (3-103) When T= TT, then £ = t; in general, £ is the time that would be required at Tr to relax to the same extent that occurs in time t at temperature T. Thermorheological simplicity was first noted by Leaderman (1943) in a study of organic polymers, and has been widely observed in oxides (see discussion in Scherer, 1986 b). It must be recognized that TRS is only approximately true: the distribution of relaxation times seems to become narrower at temperatures well above Tg. However, for oxides, TRS provides an excellent approximation at least within + 50°C of Tg, and this proves to be very helpful in analysis of thermal stresses, as we shall see in Section 3.5.3. 3.5.2.2 Nonequilibrium Liquid Hopkins (1958) pointed out that nonisothermal stress relaxation in a TRS mate-

t In principle, each of the relaxation times could have different temperature dependence and the weighting factors could change in such a way that the relaxation function retains the same shape. This seems improbable.

rial could analyzed by writing the reduced time in the form At1

= \a[T(t')]dt' (3-104) o

and replacing t with I; in the stress relaxation functions. During an isothermal test, £/T (Tr) = t/z; if T= Tr, then £ = t. This is an inescapable consequence of TRS of equilibrium liquids; however, it is not obvious that TRS will hold if the changing temperature causes the liquid to drift out of equilibrium. That is, the form of the relaxation function might change under nonequilibrium conditions. This proposition was tested in an ingenious experiment by DeBast and Gilard (1963), in which they measured structural relaxation and uniaxial stress relaxation simultaneously on the same sample. The equilibrium relaxation was found to obey a At)

MO)

-<-($]

(3-105)

with /? = 0.54. Nonequilibrium experiments were performed by equilibrating the sample at T1? then changing the temperature (by ~30°C) to T2 and simultaneously applying a load. Using measured values of rj (t) and assuming TU OC rj, they could predict the course of relaxation using

The calculated curves were found to be in excellent agreement with the relaxation function measured following the temperature jump. A similar study Rekhson et al. (1977) included changing loads as well as changing temperature; using measured values for rj (t% they obtained excellent agreement between calculated and measured creep strains. Thus, TRS does apply in nonequilibrium situations.

163

3.5 Viscoelasticity

3.5.3 Calculation of Thermal Stresses

this case, the true strain exceeds the free strain in layer A, so it is forced into compression, while layer B is stretched into tension. This type of thermal stress results from thermal expansion mismatch between dissimilar layers, and is common in composites. Another type of thermal stress results from temperature gradients within a compositionally uniform material; then layers A and B are the same material, but their free strains are different because each is cooled (or heated) by a different amount. This type of stress develops during rapid cooling of a liquid; it is exploited to strengthen glass objects by creating compressive stresses at the surface in a process called tempering (see Sec. 13.5.1). Such stresses are relieved by heat treatments near Tg, a process called annealing that allows VE relaxation; mismatch stresses cannot be removed by annealing, because new stresses develop on cooling from the annealing temperature.

Thermal stresses are of great importance in many applications of glasses, and the magnitudes of those stresses are dependent on both structural and stress relaxation. We briefly review the analysis of stresses caused by thermal expansion mismatch in composites, such as glass-to-metal seals, and the stresses that arise during rapid cooling of a liquid as it transforms into a glass. The origin of thermal stresses is illustrated in Fig. 3-28. Let layers A and B represent glass and metal components of a composite that shrink by different amounts when cooled by AT. The strains efA and efB are the free strains that occur if the materials are not bonded together; for example, if aA is the linear thermal expansion coefficient of A, then efA = ocA A T. When the layers are bonded together, then cooled, they are obliged to contract by the same amount, so the true strain, £A = £B, is a weighted average of the free strains. In

Free Strain A

A

True Strain A

£

fB

L a

e r

L a y e r

B

A

B

L a y e r

L a y e r

L a y e r

L a

A

B

A

Initial

y

Cooled

y e r

Joined

Figure 3-28. Stress caused by mismatch in thermal expansion: when layers A and B are cooled, they tend to contract by different amounts. The free strains, s{A and siB, are proportional to the thermal expansion coefficients of the layers. When the layers are joined, as in a composite, the true strain is the same in each, and is a weighted average of the free strains.

164

3 Glass Formation and Relaxation

3.5.3.1 Glass-to-Metal Seals As a simple example of mismatch stresses in composites, we consider the sandwich seal shown in Fig. 3-29. To calculate the stress we begin with the elastic constitutive equations, modified to allow for the free strain. These equations have the form (Timoshenko and Goodier, 1970) 1

(3-107)

where the subscript i is G and M in the glass and metal layers, respectively. The symmetry of the problem requires that ax = oy, and sx = 8y; since there is no constraint perpendicular to the faces of the plates, az = 0. The force on the edge of each plate is axi 11 w, and the net force across the composite must be zero, so we require ^G'GW + ^MIMW = 0

(3-108)

The result is that the stress in the glass in the plane of the plate is

J (^G-^

(3-109)

where (3-110)

KG =

and n is a weighting factor called the stiffness ratio, given by lr

n=

W2

EM

(3-111)

Thus, the stress depends on the difference between the free strains in the layers. The free strain is calculated from the setting temper amre (Ts), the temperature below which the glass behaves elastically, to room temperature (TR). Typically such a composite is joined at a high temperature, where the glass layer flows readily, and

Figure 3-29. Planar composite called a sandwich seal consists of a plate of glass between two plates of metal (or conversely); total thickness of glass and metal layers is /M and / G , respectively, and width of seal is w.

stresses develop as the temperature enters the glass transition range. Choosing an appropriate value for Ts is something of an art, because the transition from liquid to elastic behavior does not happen suddenly at a given temperature, but develops continuously over a range of temperature. This problem does not arise in the VE analysis that we consider next. A rigorous calculation of the stresses in the sandwich seal can be obtained by starting with the VE constitutive equations, but they are complicated functions of time. Fortunately, for TRS materials the VE equations take on a simple form after application of the Laplace transform, and problems of thermal expansion mismatch can be solved in a straightforward way (discussed in detail in Scherer, 1986 b). If the uniaxial stress relaxation function for the glass is assumed to be given by Eq. (3-96), then Eq. (3-109) is replaced by (Scherer and Rekhson, 1982 b) TR

J

xG

r

t(TR)

dr/-i

— KoJexp - 1 f•(a G -oc M )dT

(3-112)

This differs from Eq. (3-109) in that the free strain is calculated from the temperature

3.5 Viscoelasticity

To where cooling starts, and the transition from liquid to glassy behavior is controlled by the relaxation time T G , given by T

*G=WT4

"

. ,

(3-H3)

[Calculations using a more realistic relaxation function for the glass lead to expressions more complicated than Eq. (3-112), but the average relaxation time for the composite is still given by Eq. (3-113).] The relaxation time for the composite depends on the stiffness ratio (a fact first recognized and explained by Rekhson and Mazurin, 1977) for the following reason. Suppose the sandwich consists of a very thin glass layer and thick metal layer, so that n is small. As the composite cools and the glass begins to stiffen, the larger metal component exerts a high stress on the glass, and forces it to flow, so the stress relaxes quickly. When n is small the glass cannot resist flowing under the force exerted by the metal until the viscosity becomes very high. On the other hand, if the glass layer is much thicker than the metal (n is large), the metal cannot exert much stress on the glass; then the glass 15

165

barely flows at all, and the stress relaxes slowly. This means that the effective setting temperature for the composite depends on ft, with Ts being lower when n is small, Rekhson (1979) (with experimental assistance from V. Ginzburg) studied the stresses in a series of sandwich seals made of the same materials, but with different stiffness ratios, and obtained the remarkable results shown in Fig. 3-30. Whereas the elastic solution predicts that the stress in the glass rises as the glass layer becomes thinner (because the elastic layer forces it to deform more), the data show the opposite trend. The reason is that the stiffness ratio controls the temperature at which the glass stops flowing, so the setting temperature changes with n. The elastic analysis provides no way to predict the magnitude of this effect, so the stresses are calculated assuming that Ts is independent of n. By taking account of both structural relaxation and viscoelasticity, Rekhson (1979) was able to predict the trend in stress with stiffness ratio (see curve 1 in Fig. 3-30). This result shows the importance of accounting for viscoelastic behavior in thermal stress analyses involving glass.

r-

10

20

30 lGl

40 I

60

Figure 3-30. Stress in sandwich seal (<JXG) at room temperature versus thickness ratio of glass and elastic layers (lG/lM), according to experiment (circles) and elastic solution, Eq. (3-109) (curve 2). Curve 1 is calculated taking account of both structural relaxation and viscosity. In these seals, the elastic layer is alumina. From Rekhson (1979).

166

3 Glass Formation and Relaxation

10 Figure 3-31. Stress in sandwich seal (GXG) at room temperature versus stiffness ratio, n. VE analysis assuming single relaxation time, Eq. (3-112), yields curve 1; assuming three relaxation times (a good approximation to the measured relaxation function) yields curve 2. Both curves allow for structural relaxation in calculation of expansion coefficient and relaxation time, and agree with measured stresses (circles). Curve 3 calculated from VE analysis assuming three relaxation times, but ignoring structural relaxation.

When the VE analysis is used (Scherer and Rekhson, 1982 b; Scherer, 1986 b), the stresses are correctly predicted, as indicated in Fig. 3-31. Curves 1 and 2 represent VE calculations in which the uniaxial relaxation function of the glass is represented by one or three exponential terms, respectively, and they both give good agreement with the measured stresses. Both curves were calculated using Narayanaswamy's (1971) theory to account for the effects of structural relaxation on the thermal expansion coefficient and relaxation time. Curve 3 is obtained from the three-term relaxation function, but ignoring structural relaxation, and it is seriously in error. These results demonstrate two important facts: 1) it is essential to allow for the VE behavior of the glass to predict thermal stresses with accuracy, but it is acceptable to use a simplified expression for the relax-

ation function of the glass; 2) the VE analysis will be accurate only if proper account is taken of structural relaxation. 3.5.3.2 Tempering Tempering is a quenching treatment used to impart strength to a glass by creating high compressive stresses at the surface of the body (see Sec. 13.5.1). We include a brief discussion of tempering here, because the magnitude of the residual stress is controlled by viscoelastic and structural relaxation. The process is discussed in an excellent review by Gardon (1980). The residual stress distribution in a tempered plate is approximately parabolic, with tension
3.5 Viscoelasticity

The stored elastic energy in a tempered plate is also beneficial in the event of fracture, since it causes fragmentation into roughly cubic pieces, rather than the bladelike pieces created when an untempered plate breaks. Consider a plate of elastic material being quenched from a high temperature by air jets directed at its faces; as indicated in Fig. 3-32, a parabolic temperature distribution develops. The origin of the stresses can be understood from Fig. 3-28: B is the cooler surface layer and A is the hotter interior of the plate; the surface is stretched into tension, because the interior will not let it contract freely. As the plate cools, the interior and exterior both approach room temperature (7^), so the differential strain disappears and the stresses fade away. In a viscoelastic plate, if the initial temperature is

167

high enough, stress relaxation is so fast that the temperature distribution becomes established without creating any significant stresses. However, as the plate cools it becomes glassy, so that we have a stressfree elastic plate containing a temperature gradient (see Fig, 3-32 b, curve (2)), Suppose that the surface is at temperature Ts
L: (D and© \

CD a n d ©

Tension Compression

a) Elastic plate

b) Viscoelastic plate

Figure 3-32. Stress distribution during quenching of a plate of (a) elastic or (b) viscoelastic material. The stress, GZ (x), in the elastic plate is proportional to the parabolic temperature gradient, T(x), which is already parabolic by the time the surface has cooled to temperature Tx; az disappears when the plate reaches room temperature, TR (curve ®). In the viscoelastic plate, the stresses relax rapidly at high temperatures, so the temperature distribution is established without creating any corresponding stress (curves © and (J)). However, as the plate cools it solidifies; then as temperature becomes uniform at TR, the midplane contracts more than the surface, resulting in residual compression (curve (3)).

168

3 Glass Formation and Relaxation

pression; in extreme cases, the transient' tension can cause fracture during cooling. This effect is indicated in Fig. 3-33: the maximum tempering is achieved only when the starting temperature exceeds ~ 650 °C, where stress relaxation is too fast to allow significant transient stresses. If the starting temperature is <550°C, the plate behaves like the elastic material in Fig. 3-32, and no residual stress is obtained. The preceding discussion ignored the influence of structural relaxation during quenching. In fact, the difference in cooling rate between the interior and surface of the plate causes a gradient in fictive tempera-

(Annealed glass)

5

2.5U -

^ o

2.512

o a>

Q. 2.510L ._ U)

c
a

2

2.508 --

2.506

\ \

Density N N "Stress-Free" \ as temperecT density p2 J P\ i

i

i

i

i

0.5

i

i

i

0.5 X/X n

-0.73 cm-

3000 Heat transfer coefficient cal/cm 2 °Csec

Figure 3-34. Density distributions in tempered glass shown by heavy curves, average densities by thin horizontal lines. Numbers identify specimens in order of increasing temper: 5, 4, 3, 1, 2; no. 1 represents commercial "full temper". Gardon (1978).

2500

S 5 Ok

I

2000

1500

1000 500 (natural convection)

500

600

700

800

Initial Temperature T' Figure 3-33. Degree of temper is a photoelastic measure of the tension at the midplane of a plate. In this study by Gardon (1965, 1980) it is shown to increase with quenching rate (characterized by the heat transfer coefficient), which increases the temperature gradient in the plate. If the starting temperature To is > 650 °C, the parabolic temperature gradient is established without significant stress, and the maximum tempering stress is achieved; no tempering is possible if T 0 <550°C, because the plate is elastic. Solid symbols represent samples that cracked because of transient tensile stresses at the surface.

ture, as well as true temperature. The magnitude of this effect is shown in Fig. 3-34: in the tempered plate, measurements of refractive index indicate that the density is high near the surface, but when the plate is broken into fragments to relieve the stress, the opposite trend appears. In the unbroken plate, the compressive stresses raise the density of the surface, but when the stresses are removed, the gradient in fictive temperature is revealed; the higher Tf produced by faster cooling at the surface corresponds to a lower density. Many models have been developed to predict the development of tempering stresses, and these are reviewed by Gardon (1980). The first to correctly incorporate viscoelastic effects was an analysis by Lee et al. (1965), which assumed TRS behavior

3.5 Viscoelasticity

169

in the glass. The result was o-z(x,t) = 3 j o

S

(3-114) f

7[sz(x,t')-aT(x,t

)]df

where R (£) is a biaxial relaxation function, the VE analogue of the quantity Ej 3 (1 — v). This is similar to the expressions for stress in composites given in Section 3.5.3.1, except that the reduced time is a function of position as well as time. The stress relaxes more quickly where the temperature is higher, and, since the stresses through the plate must balance, relaxation transfers the stress to the cooler layers. Thus, the stress that develops in any one layer is related to the stress development in all of the others, and the calculation is complicated. Narayanaswamy and Gardon (1969) compared the VE analysis, Eq. (3-114), to experimentally determined stresses, and found that it could successfully predict the transient stresses. Good predictions of the final stress were obtained only if the initial temperature was high, but in that case most of the stress comes from temperature equalization. Complete agreement with experiment was obtained only when Narayanaswamy (1978) included the effect of structural relaxation on the thermal expansion coefficient and stress relaxation time. As shown in Fig. 3-35, the stress is seriously underestimated if volume relaxation is ignored; neglecting the effect of structural relaxation on the viscosity is less important. This is similar to the comparison of curves 2 and 3 in Fig. 3-31, where accurate calculation of the stress in a composite was shown to require consideration of structural relaxation. For geometries more complicated than a plate, analytical solutions such as Eq. (3-114) are generally not available. Fortu-

500 600 700 800 Initial glass temperature 7^ (°C)

Figure 3-35. Effect of structural relaxation (SR) of density and viscosity (or stress relaxation time) on tempering stress calculated from viscoelastic model: without SR (dashed curve A); with SR (solid curve); structure dependence of viscosity suppressed (o, curve B); structure dependence of density suppressed (n, curve C). From Narayanaswamy (1978).

nately, finite element methods are now available that allow for both structural relaxation (using Narayanaswamy's theory) and viscoelasticity (see discussion in Scherer, 1986 b). Burke (1981) has applied finite element analysis to the problem of tempering, and obtained results in good agreement with the analytical result; the surface compression was found to be 89% greater when structural relaxation was incorporated in the calculation. 3.5.3.3 Annealing

Annealing is a process of controlled cooling that allows reduction of residual thermal stresses. For example, suppose a tempered plate is held near Tg until Tf (x) = Tg throughout the plate, so that the specific volume has its equilibrium value everywhere. If the plate is then cooled slowly enough so that no significant temperature gradients develop, the essentially elastic plate will arrive at room temperature with no residual stress. This is particularly important for optical glasses, because resid-

170

3 Glass Formation and Relaxation

400

1

2 Time t (h)

500 T(°C)

600

Figure 3-36. Stress development during (a) cooling (3°C/min) and (b) annealing (4 h) of glass-toalumina sandwich seal using isothermal holds at (1) 500 °C and (2) 460 °C; inset shows strain versus temperature. Symbols are measured stresses; curves were calculated from VE analysis (Rekhson, 1979; see also Scherer and Rekhson, 1982 b).

3

ual stresses cause birefringence and inhomogeneity in refractive index. The effect of a given heat treatment can be calculated using the phenomenological theory development by Narayanaswamy (1971), and he discusses this application in a very good review (1986). In the case of a plate, the availability of an analytical solution allows the use of variational methods to calculate the optimal cooling schedule for annealing, providing the minimum stress for a given processing time (Narayanaswamy, 1981). Particularly interesting effects occur during annealing of composites, because the glass contracts during structural relaxation, but the elastic component does not. Therefore, structural relaxation causes the mismatch stress to rise, and VE relaxation

concurrently tends to reduce the stress. The results of this competition are illustrated in Fig. 3-36 by Rekhson's (1979) data for a glass-to-alumina sandwich seal. If the hold temperature is not far below Tg, the volume change during structural relaxation is not large and is completed quickly, and the rate of stress relaxation is relatively rapid, so the stress decreases substantially during the anneal (Fig. 3-36 a). At lower hold temperatures the glass is so far from equilibrium that the volume change accumulates throughout the hold, and the slow VE relaxation cannot eliminate the resulting stress; therefore, the net effect of the annealing treatment is an increase in tension (Fig. 3-36 b). If the hold were maintained long enough, the stress would pass

3.6 References

through a maximum at 460 °C (when structural relaxation was complete), and the stress would eventually relax to zero. In some cases, the stress developed during low-temperature annealing can cause fracture of composites. However, judicious use of annealing allows the stress in the composite to be adjusted either upward or downward.

3.6 References Adam, G., Gibbs, J.H. (1965), J. Chem. Phys. 43, 139-146. Angell, C. A. (1988), J. Chem. Phys. Solids 49, 863871. Angell, C. A., Sichina W. (1976), Ann. N. Y Acad. Sci. 279, 53-67. Angell, C.A., Cheeseman, P. A., Tamaddon, S. (1982), Science 218, 885-887. Angell, C. A., MacFarlane, D.R., Oguni, M. (1986), Ann. N. Y Acad. Sci. 484, 241-247. Ashby, M. F. (1974), Ada Metall. 22, 275-289. Berg, J.I., Cooper, A.R., Jr. (1978), J. Chem. Phys. (5^4481-4485. Blumen, A., Klafter, J., Zumofen, G. (1986), Optical Spectroscopy of Glasses. Hingham, MA: Reidel Publ. Co., 199-265. Brawer, S. A. (1984), J. Chem. Phys. 81, 954-975. Brawer, S.A. (1985), Relaxation in Viscous Liquids and Glasses. Columbus, OH: American Ceramics Society. Brinker, C. X, Scherer, G.W. (1990), Sol-Gel Science. New York: Academic Press. Burke, M. A. (1981), Report TR8102, MARC Analysis Research Corp., Palo Alto, CA. Cahn, J. W. (1956), Ada Metall. 4, 572-575. Chalmers, B. (1964), Principles of Solidification. New York: Wiley. Christensen, R. M. (1982), Theory of Viscoelasticity, 2nd. ed. New York: Academic Press. Christian, J. W. (1975), The Theory of Transformations in Metals and Alloys, Part I. New York: Pergamon Press. Coble, R.L. (1961), /. Appl. Phys. 32, 787-792. Cohen, M.H., Grest, G.S. (1979), Phys. Rev., B20, 1077-1098. Cohen, M.H., Grest, G.S. (1984), /. Non-Cryst. Solids 61/62, 749-760. Cohen, M. H., Turnbull, D. (1959), /. Chem. Phys. 31, 1164-1169. Cohen, M. H., Turnbull, D. (1961), J. Chem. Phys. 34, 120-125. Cohen, M. H., Turnbull, D. (1970), /. Chem. Phys. 52, 3038-3041.

171

Cooper, A. R (1985), J. Non-Cryst. Solids 71, 5-17. Corsaro, R. D. (1976a), Phys. Chem. Glasses 17, 1322. Corsaro, R. D. (1976 b), I Am. Ceram. Soc. 59, 115118. Crichton, S.N., Moynihan, C. T. (1988), /. NonCryst. Solids 102, 222-227. Davies, H. A. (1976), Phys. Chem. Glasses 17, 159173. Davies, R. O., Jones, G. O. (1953), Adv. Phys. 2, 370410. Dearnley, R. (1983), Nature 304, 151-152. DeBast, J., Gilard, P. (1963), Phys. Chem. Glasses 4, 117-128. DeBast, X, Gilard, P. (1965), IRSIA Comptes Rendus de Recherches, No. 32. Dietzel, A., Wickert, H. (1956), Glastech. Ber. 29, 1-4. Ferry, XD. (1961), Viscoelastic Properties of Polymers. New York: Wiley. Fredrickson, G.H. (1986), Ann. NY Acad. Sci. 484, 185-205. Fredrickson, G. H. (1988), Ann. Rev. Phys. Chem. 39, 149-180. Fredrickson, G.H., Brawer, S.A. (1986), J. Chem. Phys. 84, 3351-3366. Frenkel, X (1945), /. Phys. (Moscow) 9, 385-391. Gardon, R. (1965), Proc. Vllth. Int. Cong. Glass, Charieroi, Belgium. Paper 79. Gardon, R. (1978), J. Am. Ceram. Soc. 61, 143-146. Gardon, R. (1980), Glass: Science and Technology, Vol. 5: Elasticity and Strength in Glasses. New York: Academic Press, 145-216. Gibbs, J.H., DiMarzio, E.A. (1958), J. Chem. Phys. 28, 373-383; 807-813. Goldstein, M. (1963), /. Chem. Phys. 39, 3369-3374. Grange, R. A., Kiefer, X M. (1941), Trans. ASM 29, 85-115. Grest, G.S., Cohen, M.H. (1980), Phys. Rev. B21, 4113-4117. Grest, G. S., Cohen, M. H. (1981), Advances in Chemical Physics, Vol. 48, New York: Wiley, 455-525. Gupta, P.K. (1987), J. Am. Ceram. Soc. 70, C152C153, Gupta, P.K. (1988a), J. Non-Cryst. Solids 102, 231239. Gupta, P. K. (1988 b), J. Non-Cryst. Solids 102, 250254. Gutzow, I., Kashchiev, D., Avramov, I. (1985), /. Non-Cryst. Solids 73, 411-499. Hara, M., Suetoshi, S. (1955), Rep. Res. Lab. Asahi Glass Co. 5, 126-135. Heyes, D. M., Kim, XX, Montrose, C.X, and Litovitz, T.A. (1980), J. Chem. Phys. 73, 3987-3996. Hillig, W.B. (1966), Acta Metall. 14, 1868-1869. Hodge, I. M. (1987), Macromolecules 20, 2897-2908. Hoffman, X D. (1958), J. Chem. Phys. 29, 1192-1193. Hopkins, I.L. (1958), J. Polym. Sci. 28, 631-633. Hopper, R. W, Scherer, G., Uhlmann, D. R. (1974), /. Non-Cryst. Solids 15, 45-62.

172

3 Glass Formation and Relaxation

Howell, F. S., Bose, R. A., Macedo, P. B., Moynihan, C.T (1974), J. Phys. Chem. 78, 639-648. Huling, J.C., Messing, G.L. (1989), J. Am. Ceram. Soc. 72, 1725-1729. Jackson, K. A., Uhlmann, D. R., Hunt, J. D. (1967), /. Cryst. Growth 1, 1-36. James, P. F. (1974), Phys. Chem. Glasses 15, 95-105. James, P. F. (1985), J. Non-Cryst. Solids 73, 517-540. Kashchiev, E. (1969), Surf. Sci. 14, 209-220. Kauzmann, W. (1948), Chem. Rev. 43, 219-256. Kelton, K.F., Greer, A. L. (1986), J. Non-Cryst. Solids 79, 295-309. Kelton, K . F , Greer, A.L., Thompson, C.V. (1983), J. Chem. Phys. 79, 6261-6276. Kohlrausch, R. (1847), Pogg. Ann. 12, 393. Kovacs, A. I , Aklonis, J. X, Hutchinson, J. M., Ramos, A. R. (1979), J. Polym. Sci., Polym. Phys. Ed. 17, 1097-1162. Kurkjian, C.R. (1963), Phys. Chem. Glasses 4, 128136. Leaderman, H. (1943), Elastic and Creep Properties of Filamentous Materials. Washington, D.C.: Textile Foundation. Lee, E.H., Rogers, T. G., Woo, T. C. (1965), J. Am. Ceram. Soc. 48, 480-487. Li, J. H., Uhlmann, D. R. (1970), /. Non-Cryst. Solids 3, 127-147. Macedo, P.B., Napolitano, A. (1967), /. Res. 71 A, 231-238. MacFarlane, D. R. (1982), /. Non-Cryst. Solids 53, 61-72. Mackenzie, J. K., Shuttleworth, R. (1949), Proc. Phys. Soc. 62, 838-852. Magill, J. H., Li, H. M., Gandica, A. (1973), J. Cryst. Growth 19, 361-364. Mazurin, O. V. (1977), J. Non-Cryst. Solids 25, 130169. Mazurin, O. V., Startsev, Yu. K. (1981), Sov. J. Glass Phys. Chem. 7, 274-279 (Engl. transl). Mazurin, O.V., Rekhson, S.M., Startsev, Yu. K. (1975), Sov. J. Glass. Phys. Chem. 1, 412-416 (Engl. transl.). Mazurin, O.V., Startsev, Yu.K., Potselueva, L.N. (1979), Sov. J. Glass. Phys. Chem. 5, 68-79 (Engl. transl.). Mazurin, O.V., Stolyar, S.V., Potselueva, L.N. (1981), Sov. J. Glass. Phys. Chem. 7, 222-227 (Engl. transl.). Moynihan, C.T, Gupta, P.K. (1978), J. Non-Cryst. Solids 29, 143-158. Moynihan, C.T, Lesikar, A.V. (1981), Ann. N.Y. Acad. Sci. 371, 151-164. Moynihan, C.T, Easteal, A.J., Wilder, J., Tucker, J. (1974), J. Phys. Chem. 78, 2673-2677. Moynihan, C.T, Easteal, A.J., DeBolt, M.A., Tucker, J. (1976a), J. Am. Ceram. Soc. 59, 12-16; 16-21. Moynihan, C.T, Macedo, P. B., Montrose, C.J., Gupta, P.K., DeBolt, M. A., Dill, J.F, Dom, B.E., Drake, P.W, Easteal, A. I , Elterman, P.B.,

Moeller, R. P., Sasabe, H., Wilder, J. A. (1976 b), Ann. N.Y. Acad. Sci. 279, 15-35. Mysen, B.O., Virgo, D., Scarfe, C M . (1980), Am. Miner. 65, 690-710. Narayanaswamy, O. S. (1971), J. Am. Ceram. Soc. 54, 491-498. Narayanaswamy, O. S. (1978), J. Am. Ceram. Soc. 61, 146-152. Narayanaswamy, O. S. (1981), J. Am. Ceram. Soc. 64, 109-114. Narayanaswamy, O. S. (1986), Glass: Science and Technology, Vol. 3: Viscosity and Relaxation. New York: Academic Press, pp. 275-318. Narayanaswamy, O. S. (1988), /. Am. Ceram. Soc. 71, 900-904. Narayanaswamy, O. S., Gardon, R. (1969), J. Am. Ceram. Soc. 52, 554-558. Ngai, K. L., Rendell, R. W, Rajagopal, A. K., Teitler, S. (1986), Ann. N.Y. Acad. Sci. 484, 150-184. Ngai, K.L., Rajagopal, A.K., Teitler, S. (1988), J. Chem. Phys. 88, 5086-5094. Onorato, P.I.K., Uhlmann, D.R. (1976), J. NonCryst. Solids 22, 367-378. Opalka, S.M. (1987), Ph.D. thesis, Rensselaer Polytechnic Inst., Troy, N.Y, USA. Prassas, M., Hench, L. L. (1984), Ultrastructure Processing of Ceramics, Glasses and Composites. New York: Wiley, pp. 100-125. Rabinovich, E. M. (1985), J. Mater. Sci. 20, 42594297. Ramachandrarao, P., Cantor, B., Cahn, R. W. (1977), J. Non-Cryst. Solids 24, 109-120. Rekhson, S.M. (1975), Sov. J. Glass Phys. Chem. 1, 417-421 (Engl. transl.). Rekhson, S.M. (1979), Glass Technol. 20, 27-35; 132-143. Rekhson, S.M. (1986), J. Non-Cryst. Solids 84, 6885. Rekhson, S.M. (1987), J. Non-Cryst. Solids 95/96, 131-148. Rekhson, S. M., Ginzburg, V. A. (1976), Sov. J. Glass Phys. Chem. 2, 422-428 (Engl. transl.). Rekhson, S. M., Mazurin, O. V. (1974), J. Am. Ceram. Soc. 57, 327-328. Rekhson, S.M., Mazurin, O. V. (1977), Glass Technol. 18, 7-14. Rekhson, S.M., Bulaeva, A.V, Mazurin, O.V. (1971), Sov. J. Inorg. Mater 7, 622-623 (Engl. transl.). Rekhson, S. M., Gonchukova, N. O., Chernousov, M. A. (1977), Proc. Xlth Int. Cong. Glass, Prague, Vol.1, 329-338. Rendell, R. W, Ngai, K. L., Fong, G. R., Aklonis, J. J. (1987), Macromolecules 20, 1070-1083. Ritland, H.N. (1954), J. Am. Ceram. Soc. 37, 370378. Ritland, H.N. (1956), J. Am. Ceram. Soc. 39, 403406. Rowlands, E.G., James, P.F. (1979), Phys. Chem. Glasses 20, 1-8.

3.6 References

Scherer, G.W. (1977), /. Am. Ceram. Soc. 60, 236239. Scherer, G.W. (1984a), /. Am. Ceram. Soc. 67, 504511. Scherer, G.W. (1984b), J. Am. Ceram. Soc. 67, 709715. Scherer, G.W (1986a), /. Am. Ceram. Soc. 69, 374381. Scherer, G. W (1986 b). Relaxation in Glass and Composites. New York: Wiley. Scherer, G.W. (1987), Surface and Colloid Science, Vol. 14. New York: Plenum Press, pp. 265-300. Scherer, G.W (1990), /. Non-Cryst. Solids 123, 7 5 89. Scherer, G.W, Rekhson, S.M. (1982a), /. Am. Ceram. Soc. 65, 352-360. Scherer, G.W, Rekhson, S.M. (1982b), J. Am. Ceram. Soc. 65, 399-406. Sharma, S. K , Virgo, D , Kushiro, I. (1979), J. NonCryst. Solids 33, 235-248. Simmons, J. H , Mohr, R. K , Montrose, C. J. (1982), J. Appl Phys. 53, 4075-4080. Stillinger, F. H. (1988), /. Chem. Phys. 88, 7818-7825. Takahashi, K , Yoshio, T. (1973), Yogyo Kyokai-Shi 81, 524-533. Tanner, L. E , Ray, R. (1979), Ada Metall 27,17271747. Thomas, I. M. (1974), U.S. Patent 3 791808 (Feb. 12, 1974). Thompson, C.V., Spaepen, F. (1979), Ada Metall. 27, 1855-1859. Timoshenko, S.P, Goodier, J.N. (1970), Theory of Elasticity, 3rd. ed. New York: McGraw-Hill. Tool, A.Q. (1945), /. Res. 34, 199-211. Tool, A.Q. (1946), J. Am. Ceram. Soc. 29, 240-263. Turnbull, D. (1964), Proc. Int. Conf. on Physics of Non-Crystalline Solids, Delft. Amsterdam: NorthHolland, pp. 41-56. Turnbull, D. (1969), Contemp. Phys. 10, 473-488. Uhlmann, D.R. (1969), Materials Science Research, Vol. 4. New York: Plenum Press, pp. 172-197. Uhlmann, D. R. (1972 a), Advances in Nucleation and Crystallization in Glasses. Columbus, OH: American Ceramics Society, pp. 91-115. Uhlmann, D. R. (1972 b), /. Non-Cryst. Solids 7, 337348. Uhlmann, D . R , Chalmers, B. (1965), Ind. & Eng. Chem. 9, 19-31. Uhlmann, D . R , Yinnon, H. (1983), Glass: Science and Technology, Vol.1: Glass-Forming Systems. New York: Academic Press, pp. 1-47. Uhlmann, D . R , Klein, L , Onorato, P.I.K., Hopper, R.W. (1975), Proc. Lunar Sci. Conf 6th., pp. 693-705.

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Uhlmann, D . R , Onorato, P . I . K , Scherer, G.W. (1979), Proc. Lunar Planet. Sci. Conf. 10th., pp. 375-381. Vil'kovskii, S. S. (1988), Sov. J. Glass Phys. Chem. 14, 463-470 (Engl. transl.). Vreeswijk, J.C.A, Gossink, R.G., Stevels, J. M. (1974), J. Non-Cryst. Solids 16, 15-26. Weinberg, M . C , Zanotto, E. D. (1989 a), J. NonCryst. Solids 108, 99-108. Weinberg, M . C , Zanotto, E.D. (1989b), Phys. Chem. Glasses 30, 110-115. Williams, G , Watts, D.C. (1970), Trans. Faraday Soc. 66, 80-85. Yamane, M , Kojima, T. (1981), J. Non-Cryst. Solids 44, 181-190. Yinnon, H , Uhlmann, D.R. (1981), /. Non-Cryst. Solids 44, 37-55. Zallen, R. (1983), The Physics of Amorphous Solids. New York: Wiley. Zanotto, E . D , James, P. F. (1985), J. Non-Cryst. Solids 74, 373-394. Zarzycki, J. (1982), Advances in Ceramics, Vol. 4. Columbus, OH: American Ceramics Society, pp. 204-216.

General Reading Glass transition: Brawer, S.A. (1985), Relaxation in Viscous Liquids and Glasses. Columbus, OH: American Ceramics Society. Sintering and crystallization of gels: Drinker, C.J, Scherer, G.W (1990), Sol-Gel Science. New York: Academic Press; Chap. 11. Theory of nucleation and growth: Christian, J.W (1975), The Theory of Transformations in Metals and Alloys, Part I. New York: Pergamon Press. Tempering: Gardon, R. (1980), Glass: Science and Technology, Vol. 5: Elasticity and Strength in Glasses. New York: Academic Press; pp. 145-216. Annealing: Narayanaswamy, O.S. (1986), Glass: Science and Technology, Vol. 3: Viscosity and Relaxation. New York: Academic Press: pp. 275-318. Viscoelasticity, glass-to-metal seals: Scherer, G.W (1986 b), Relaxation in Glass and Composites. New York: Wiley. Kinetics of glass formation: Uhlmann, D. R , Yinnon, H. (1983), Glass: Science and Technology, Vol. I: Glass-Forming Systems. New York: Academic Press; pp. 1-47.

4 Models for the Structure of Amorphous Solids Philip H. Gaskell Cavendish Laboratory, University of Cambridge, Cambridge, U.K.

List of 4.1 4.1.1 4.1.2 4.1.3 4.1.4 4.1.5 4.2 4.2.1 4.2.1.1 4.2.1.2 4.2.2 4.2.2.1 4.2.2.2 4.2.2.3 4.2.3 4.2.3.1 4.2.3.2 4.2.4 4.2.4.1 4.2.4.2 4.2.4.3 4.2.4.4

4.3 4.3.1 4.3.2 4.3.3 4.3.3.1 4.3.4 4.3.4.1 4.3.5 4.3.5.1 4.3.5.2

Symbols and Abbreviations Introduction Rationale Background Liquids, Crystals, Glasses, Quasicrystals and "Amorphous" Solids Types of Order Outline Conceptual Models Randomness as the Paradigm Dense Random-Packed Hard Sphere Models Random Networks Crystallographic Order as the Paradigm Simple Microcrystallite Models "Quasi-Crystalline" Models "Paracrystalline" Models Non-Crystallographic Order as the Paradigm "Curved-Space" Models Polytetrahedral Models Constrained Disorder as the Paradigm. Stereo-Chemically Defined Models Similarity to Random Networks Similarity to Paracrystalline Models Local Order as a Consequence of Medium-Range Order Stereo-Chemically Defined Models for Close-Packed Oxides and Amorphous Metals Involving Medium Range Structure-Forming Operations Experimental Structural Techniques Neutron Scattering Techniques - Static Structural Methods X-Ray Scattering Effects of Disorder on Scattering Data "Termination" Smearing Polyatomic Solids Total Distribution Functions and Structure Factors Extraction of Partial Structure Factors Combination of the Results of X-Ray, Neutron and Electron Scattering . . Neutron Scattering with Isotopic Substitution

Materials Science and Technology Copyright © WILEY-VCH Verlag GmbH & Co KGaA. Allrightsreserved.

178 180 180 181 182 183 185 186 186 187 188 188 189 190 190 191 192 193 193 196 196 196

198 199 199 201 202 202 203 203 204 204 205

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4.3.5.3 4.3.5.4 4.3.5.5 4.3.6 4.3.7 4.3.8 4.4 4.4.1 4.4.1.1 4.4.2 4.4.3 4.4.4 4.4.5 4.4.6 4.4.6.1 4.4.7 4.5 4.5.1 4.5.1.1 4.5.1.2 4.5.2 4.5.2.1 4.5.2.2 4.5.3 4.5.4 4.6 4.6.1 4.6.2 4.6.2.1 4.6.2.2 4.6.3 4.6.4 4.6.5 4.6.5.1 4.6.5.2 4.6.6 4.6.7 4.6.8 4.7 4.7.1 4.7.2 4.7.2.1 4.7.2.2

4 Models for the Structure of Amorphous Solids

"Difference" Methods 205 X-Ray Absorption Spectroscopy 206 X-Ray Anomalous Scattering 208 Vibrational Spectroscopy 208 High Resolution Transmission Electron Microscopy 210 Nuclear Magnetic Resonance 212 Modelling Techniques 214 Construction of Atomic Models for Amorphous Solids 214 Physical Models 215 Molecular Dynamics 215 Potential Energy Functions 217 Energy Minimisation 219 Monte Carlo Calculations 219 Validation of the Model: Calculation of Microscopic and Macroscopic Properties 220 Bond Length Distributions 221 Calculation of Dynamical Properties 223 Elemental Tetrahedral Semiconductors 223 Amorphous Ge and Si 224 Local Structure - Diffraction Data 224 Local Structure - Complementary Techniques. Medium-Range Structure . 227 Amorphous Carbon 229 Static Properties 229 Excitations 231 Network Models - Static Properties 233 Models for Amorphous Carbon 236 Amorphous Silica 238 Experimental Situation 238 Local Structure 239 Diffraction Data 239 Complementary Techniques 239 Medium-Range Structure 240 Random Network Models 241 Ordered Models 244 Quasi-Crystalline Models 244 Microparacrystalline Models 244 Simulation of Dynamical Properties 245 Molecular Dynamics Models 247 Monte Carlo Simulations 248 Binary Alkali and Alkaline Earth Silicates, Borates and Phosphates 250 Apologia 250 Local Structure Around "Network Modifiers" in Oxide Glasses 251 Diffraction and EXAFS Data 251 Complementary Techniques 256

4 Models for the Structure of Amorphous Solids

4.7.3 4.7.3.1 4.7.3.2 4.7.4 4.7.4.1 4.7.4.2 4.7.5 4.7.6 4.7.7 4.7.8 4.8 4.8.1 4.8.2 4.8.3 4.9 4.10

Medium-Range Structure Centred on "Network-Modifiers" in Oxide Glasses Diffraction Data Complementary Techniques Speciation Borates Silicates Network Models Molecular Dynamics Microcrystallite Models Stereo-Chemically Defined Models Concluding Remarks Information Content Microscopic and Macroscopic Properties Structural Models - Present and Future Acknowledgements References

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257 257 259 259 259 260 264 265 266 267 269 270 271 273 274 274

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List of Symbols and Abbreviations b ca dhkl n-D E / (Q) F (Q) g (r) g (co) G (r) i (Q) / J (r) k kB M (Q) na N Nc NF N (r) Nj P*p{r) P* (r), P*fi (x) q Q Qn rap Rj S (Q) Tg 7^ (u{ > W{ ( 0 Wap za Z

neutron scattering length concentration of atomic species a distance between crystal planes with Miller indices hkl rc-dimensional energy atomic scattering factor reduced interference function pair distribution function vibrational density of states function reduced radial distribution function interference function intensity, nuclear spin radial distribution function photon or photoelectron wave vector Boltzmann constant modification function atomic fraction of species a coordination number, number of atoms number of constraints number of degrees of freedom running coordination number coordination number of j ' t h atomic shell P a i f correlation function between atomic species a and /? peak shape function phonon scattering vector scattering vector, modulus Q number of bridging oxygens (n) (around Si in this case) interatomic distance between atoms of species a and /? mean bond length of i'th shell radius o f / t h shell of atoms structure factor glass transition temperature melting temperature mean square displacement of atomic species i Debye-Waller factor for atomic species i weighting factor for atoms of species a and p electronic charge on atoms of species a atomic number

5 e X (k)
phase shift dielectric function; e l 9 s2 are real and imaginary parts /c-dependent normalised EXAFS signal potential energy

List of Symbols and Abbreviations

CO

wavelength photoelectron mean free path atomic (number) density average atomic (number) density standard deviation of a scattering angle (conventionally 2 6) frequency

CRN CTF DRP EELS ESR EXAFS fee hep HRTEM IR MASNMR MC MD NMR PE ppm PT RDF SCD TEM TM-m TMS XAFS XANES XAS

continuous random network contrast transfer function dense random packed (model) electron energy loss fine structure electron spin resonance extended X-ray absorption fine structure face centred cubic hexagonal close packed high resolution transmission electron microscopy infra-red magic angle spinning NMR Monte Carlo molecular dynamics nuclear magnetic resonance potential energy parts per million polytetrahedral radial distribution function stereo-chemically defined transmission electron microscopy transition metal-metalloid tetramethyl silane X-ray absorption fine structure X-ray absorption near edge spectroscopy X-ray absorption spectroscopy

X A Q(r) Qo

a (a) 9

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4.1 Introduction 4.1.1 Rationale Knowledge of the structure of a material is central to any adequate understanding of its properties. For most classes of solids, for gases, many polymers - including biological macromolecules - such knowledge exists and there is a well-established link between structure at the atomic level and macroscopic properties. Liquids and glasses can be excluded from this statement. The structure of most glasses is not even understood in simple qualitative, conceptual terms. With the added complications of thermal motion, liquids present even more intractable difficulties. Reasons for this state of affairs are not difficult to find. Translational periodicity implies enormous simplification of the experimental, theoretical and conceptual problems. Experimentally, the phase-related response of atoms in identical unit cells to the stimulus of electromagnetic radiation, for example, results in strong signals of high information content, in energyor reciprocal-space. Theoretical models based on the small cluster of atoms comprising the unit cell are readily constructed and optimised to fit experiment. And the conceptual problem hardly exists; experiment provides many or most of the necessary clues. Glasses, on the other hand, have aperiodic structures and at some level are isotropic. Experimental data are therefore extensively averaged - scrambled, indeed - so that the signal is weak with low information content. Much of the symmetry information is lost. Theoretically, modelling loses its rigour: approximations are inevitable, computations become unwieldy because of the large (strictly infinite) size of the models and are constrained not only by limited experimental information but also by computational uncertainties.

The conceptual problem is perhaps the most unsettling. Many macroscopic properties become intelligible simply by recognising the essential microscopic behaviour at a qualitative level. Sharp lines in the vibrational spectrum of a crystal can be seen as the phase-related response of equivalent atoms in all unit cells. But how does one explain, to oneself or to a student, the residual effects associated with (crystal) momentum in an amorphous solid to which the concept is strictly inapplicable, since there is no unit cell; or, ionic migration, that in the crystal can be thought of in terms of defect-controlled mechanisms, when the glass is "all one big defect"? It is therefore relatively easy to argue that the art of modelling the structure of amorphous solids is central to any understanding of their macroscopic properties. Certainly, further progress in the development of this extensive family of sociallyimportant materials depends on it. A representative atomic model, with accurate interatomic forces, allows us to simulate nature. It then becomes possible to compute physical and chemical behaviour ranging from straightforward properties such as the density, through to electronic, optical and magnetic characteristics. Dynamic events can be followed on the computer including processes that occur on time scales that are impossible to achieve in the laboratory. New materials can be explored, computationally, by formation at quench rates that would not easily be attainable to practice. Techniques for producing and exploring atomic models have grown to represent a major area of computational science. Not principally for the reasons advanced in the previous paragraph - those attractions are largely for the future - but as a response to the experimental problem of translating incomplete, inadequate structural data in-

4.1 Introduction

to meaningful models. For the reasons discussed above, structural information available from an experiment on an amorphous solid is minute compared to that routinely acquired from an experiment on a crystalline powder. In 1983 it seemed "fairly safe to assume that no single experimental structural technique, nor perhaps any combination, will in the near future provide a sufficiently large bank of information that we can 'solve' the structure (of a glass) in the sense that the structures of crystals have been solved" (Gaskell, 1983). This statement may be more arguable now but the need to combine structural data from many techniques, or from a number of related techniques and several materials remains. And the task of combining that information is made easier by cross-reference and adaptation of models that try to represent that data - and is only complete when all of the information is encapsulated in an acceptable model. It is to this area that modelling has been attracted in the past, and has proved its worth. The speed with which computational power is now becoming accessible to the average experimentalist, as well as to the theoretician, implies that this movement will accelerate in the future. Indeed, user-friendly atomic modelling systems must become the essential tool of the experimental scientist or technologist working on materials in future years. This increase in available computational power exerts a new pressure - to develop adequate models that are consistent with experiment, rather than simplified, idealised models whose principal merit is the ease of programming. The challenge of this chapter is to set out the ground rules, to present the knowledge that has been established and that which needs to be gained. The approach is deliberately experimentally biased. Although

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the mechanics of computer generation of models, for example, must form part of this chapter, the major thrust is to depict what experiments - including computer experiments - can tell us, where they are defective and how we need to make them more sophisticated. Secondly, it will be important to pare down the concepts and, not only to deconstruct, but also to reconstruct the bones of new approaches. 4.1.2 Background We begin by restating those characteristics of the glassy or amorphous states of matter that relate directly to structural questions; either by informing those questions or because the characteristics themselves require structural interpretations. By definition, glasses are non-crystalline solids. Conventionally, we regard the glassy state as that persisting below a characteristic glass temperature, Tg9 at which the material becomes metastable both with respect to the global thermodynamic ground state corresponding to the crystal and to the local equilibrium represented by the supercooled liquid. Separating the glass from the super-cooled liquid is a socalled "glass transition" that has resemblance to a thermodynamic second order transition but, operationally, can be regarded as a departure from equilibrium imposed by the increased viscosity of the melt. The transition thus has some characteristics related to the time-dependence of "structural relaxations" including wellknown hysteresis effects in differential scanning calorimetry signals, for instance. Apart from unsettled questions concerning the dynamical interaction responsible for the glass transition, the continuous nature of the transition has implications for structure. In contrast to the essential discontinuity that lies at the heart of the change of

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state from the liquid to the crystalline solid - expressed through the appearance of a nucleus and extension of the crystal/liquid interface, discontinuous changes in energy, volume etc. marking the thermodynamic first order transformation - there is no evidence for any change of state during the glass transition. The structure of the glass and that of the liquid - whatever they may be - have essential similarities. Glass formation may be seen as a process in which crystallization is avoided - a feature that has been stressed by Turnbull (1969). Glasses are formed when the disordered structure characteristic of the liquid is preserved from temperatures above TM, where the disordered state is thermodynamically stable, to temperatures below Tg where the disordered, glassy state is kinetically stable. Crystallization, involving diffusional motion of atoms is, like all such transport processes, "frozen out" below T%. The tendency of the material to crystallize or devitrify has important structural implications, of course. In a real sense this is the obvious reference point for microcrystallite models for glasses, and yet there is still the need to reconcile this approach with structural changes that are implicit in the nucleation of a crystal. A further instability relates to the tendency of many multicomponent glasses to "phase separate". Microphase immiscibility is characteristic of many simple liquids and is well understood in that context in thermodynamic terms. Again, the transition from a single phase liquid at high temperatures to a multiphase immiscible liquid mixture as the temperature is reduced, can be seen as a progressive increase in the relative importance of energetic (ordering) parameters rather than entropic terms. Operationally, the boundaries of immiscibility have been defined in compositiontemperature-time space although a satis-

fying explanation in atomistic terms is still awaited. The implications of immiscibility for structural studies are two-fold. Firstly, there is the experimental problem that single phase glasses exist only over limited composition ranges, so that the experimentalist finds it difficult to explore many otherwise interesting compositions. Secondly, the obvious tendency of some glasses to become unmixed on a scale of micrometres implies - like the crystallization transition - the possibility of separation into two or more phases at an atomic level. "Granularity" at this level is thus by no means foreign, as judged by the behaviour of glasses in macroscopic terms. 4.1.3 Liquids, Crystals, Glasses, Quasicrystals and "Amorphous" Solids

The brief survey of the characteristic properties of glasses shows them to be intermediate between the ordered crystalline state on the one hand and the essentially disordered, time-dependent structure of liquids on the other. Glasses can be thought of as being liquids with diffusional atomic motion subtracted. Studies of the structure of glasses - although of intrinsic value - gain added importance as an entree into the more difficult studies on liquids. Not only are glasses necessarily more ordered than the corresponding melt, by virtue of a reduction in diffusive motion, vibrational motion is also suppressed as a result of lower measurement temperatures. Structural data therefore suffers less thermal broadening. Quasicrystals may provide another link. Several metallic alloys form quasicrystalline and glassy phases so that the relationships between them are currently a matter for considerable interest and speculation. Both phases require special preparation conditions - rapid quenching for in-

4.1 Introduction

stance - to avoid formation of stable or metastable crystalline phases. Both phases are clearly defective. Both may be related to an underlying structural principle - possibly the same structural principle. Sharing the same structural diagnostics - lack of order and metastability - are a whole family of "amorphous solids" typified by evaporated films of, say, Si, Se, H 2 O, and amorphous metals. These may or may not be, strictly, glasses under the above definition. Films deposited from the vapour phase or by atom by atom deposition do not necessarily relate at all to other condensed states of matter except that of the crystal. Structurally, deposited films range from those that may have more resemblance to a loose aggregate of molecules such as certain oxides or sulphides of As or P, or they may form giant frameworks entirely analogous to the network glasses. It has become customary to distinguish amorphous solids from "true" glasses by the presence or otherwise of a glass transition, rather than by any exclusively structural characteristic. Amorphous solids may thus defined by the absence of changes in the heat content near Tg9 although, in practice, such changes may be masked by crystallization. 4.1.4 Types of Order

By definition and from experience, glasses are disordered on some length scale. Experiment shows, however, that the vast majority of glasses have recognisable order over a length scale corresponding to first neighbour distances. How should the order in a structure be specified? Firstly, we recognise that if a complete set of atomic coordinates were, by magic, available to use, we would find this unhelpful - as anyone who has modelled

183

even a 1000-atom cluster knows. Structural information is required in the form of distribution functions, local symmetry, a geometrical description, orientational relationships, distribution of chemical species - features, in fact, that are most useful in discussing the structure of a crystal with a large unit cell. We consider the following facets of a structural description. Positional, or geometrical, order. Assuming that a local arrangement of atoms can be identified - a coordination polyhedron and a central atom - we can specify the extent of order through the mean, (rt >, and standard deviation, a(r£), (and higher moments if necessary) of bond length, bond angle distributions and the number of neighbours - the coordination number. An ordered arrangement implies a narrow distribution of first neighbour distances and, ideally, an identifiable coordination number, Nc - rather than a continuous increase in N(r) with increasing r. Comparison with a compositionallyequivalent crystalline phase may show some correspondence between values for crystals and glasses and this can be taken as further evidence for ordering - although not necessarily for a crystallographic model of ordering. If the parameters for higher order neighbour shells can be extracted - and usually they can, with more difficulty, to second neighbours - then and corresponds to the geometry of say, a tetrahedral unit, then the symmetry of the local unit of structure can be specified, indirectly. Symmetry information can be obtained more directly through measurements of the infra-red or Raman spectra, X-ray absorption near edge structure, NMR etc. and clearly represents an important struc-

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4 Models for the Structure of Amorphous Solids

tural parameter. In many cases, symmetry information alone can be used to decide between alternative models with different local symmetries. In previous paragraphs it has been convenient to discuss structural parameters in terms of a length scale that is implicit in the word "local structure". This can be taken to mean the structural characteristics of the immediate environment of a given atomic species out to perhaps second neighbours. The upper limit is arbitrary but since it is usually only possible to analyse experimental correlation functions without recourse to models, out to second neighbours, then it has a certain aptness. At the other extreme of the length scale, glasses are clearly geometrically disordered and as experiment suggests a limit of about 1.5 to 2.0 nm to be the shortest distance at which deviations from randomness can be seen, then this marks the lower limit of what is often termed the long-range structure. There still remain deviations from a structureless solid but such deviations are confined to compositional inhomogeneities occurring on a length scale of about 2 to 200 nm. From second neighbour distances at 0.4-0.5 nm to 1.5 nm between the limits for local and long range structure - comes the "intermediate range" structure or "medium-range" structure. (Often the terms medium-range structure and medium-range order are used interchangeably, but since the latter, clearly, implies order it seems better to use the more neutral term, structure.) Medium range structure is less easy to define in terms of geometry or symmetry, so that topology generally provides a specification. In amorphous tetrahedral semiconductors, for instance, the network topology expressed as the relative proportions of nmembered rings, represents one of the few ways of clearly distinguishing competing models.

Compositional ordering represents a further structural characteristic. For a polyatomic solid, this may be relevant on all length scales: local (compositional) ordering in an amorphous Co-P alloy represents the distinction between models in which Co atoms preferentially cluster around P and alternatives in which Co-Co and P-P pairs are preferred, or in which the distribution is random - determined only by the relative numbers of each type of atom and their relative atomic radii. Compositional ordering, at local and medium-range structural levels, is also important as in certain polyatomic oxide glasses, and in Si: H "alloys". In crystalline lithium silicates, for example, the silicon-oxygen anions have formal charges that vary with the concentration of Li. Considering the mixture of oxides (Li 2 O) x (SiO 2 )i- x ; the composition with x = 0 corresponds to a structure in which all four oxygens are "bridging" that is, they are linked to two silicons. In NMR terminology this is usually specified by the notation Q4 representing four bridging atoms around the tetrahedral (Quaternary) atoms. As x increases, so does the number of non-bridging oxygens so that the fraction of Q4 atoms decreases with corresponding increases in Qn (n<4). The various silicate "species" are shown in Fig. 4-1 for random and compositionally-ordered silicate glasses. In a random model, all species are expected to be present in proportions governed by the average composition, energy and temperature etc. Experiment, especially NMR measurements, allows some definition of the relative proportions of each species so that anionic "speciation" becomes an important structural characteristic. We can thus specify the extent to which a given composition leans towards competitive models in which the majority of species present corresponds to that of the compositionally-equivalent crystalline phase.

4.1 Introduction

185

immiscibility, corresponding to TM
Figure 4-1. Various silicate species Q" in silicate glasses (schematic), a) Elementary g 3 tetrahedron with 3 bridging and 1 non-bridging oxygens, b) Example of isolated and paired non-bridging oxygens, c) Compositionally ordered glass, d) Random network.

Compositional ordering is also evident in the long-range structure of polyatomic glasses. As with other liquids, complete miscibility of several components is only conditionally possible. For reasons that are not always obvious in structural terms, the thermodynamically stable state of a glass in the liquid or super-cooled liquid states may be multi-phase rather than single phase. The boundaries in compositiontemperature-time space are understood in terms of well-established (thermodynamic) parameters. Experimentally, the multiphase nature of a particular glass becomes obvious as a separation into two or more distinct liquid-like phases on a length scale of a few tens of nanometres upwards. (Complete separation into two immiscible liquids can occur - stable immiscibility when the two-liquid state is preferred at temperatures above TM, but metastable

As a direct result of the limited amount of experimental data obtainable for all amorphous solids and glasses, it becomes necessary to extract all the information obtainable from a given technique or, preferably from a combination of complementary techniques. In order to interpret the data it is crucial to express it in terms of candidate models, then to compare models and experimental data and try to achieve agreement to the limits of accuracy, both of experiment and the simulation technique. Unless comparison is made at this level of detail, then the results can be disappointing and even misleading. Models of many different types can be made to agree with the general features of structural data if the only data available is the total correlation function with a relatively low information content. On the other hand, experimental data of the highest information content currently available - partial pair correlation functions - have not yet been modelled to the accuracy of experiment and of computation. An account of models for the structure of glasses must include, therefore, a critical analysis of the results of particular techniques, and a synthesis of results from other techniques or from other related materials. The strategy for this chapter is to begin (Sec. 4.2) with a discussion of the various conceptual models for amorphous solids starting with extreme models based on randomness on the one hand and crystal-like order on the other. We then pass to models that are ordered but without underlying

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4 Models for the Structure of Amorphous Solids

crystallographic order as the rationale. These are the so-called icosahedral, or curved-space models related, perhaps, to quasicrystallinity. We also try to express in words what is implied in other hybrid models that are less easy to describe: those based on twinning, or on constrained randomness, or stereochemically-constrained models. Section 4.3 discusses some of the experimental structural techniques in outline and presents a summary of the formal definition of structural parameters. Emphasis is placed not so much on the details of the techniques but on the results that are obtainable and their value in providing useful experimental data. Other chapters in this series provide the essential background. Section 4.4 considers how models can be made and tested either by computer simulation techniques such as Monte Carlo or Molecular Dynamics algorithms that exhibit little or no bias towards a particular model. We also consider models that are based on crystals - either as a convenient starting point or as the result of "intuition" and those within which certain structure-forming rules are embedded which restrict the range of possible outcomes. We then examine how these models may be validated by comparison with experimental data and the corrections necessary to allow accurate comparisons. Sections 4.5 to 4.7 is where all the above - which is essentially preamble - is tested against reality. Three case histories are given of structural campaigns. Examples are selected to allow conclusions to be drawn about the nature of the amorphous state in materials such as a-Si, through silica, to the relatively complex polyatomic silicates and similar oxide glasses. The final section attempts to bring together what has been learned and compares this with what can and should be

known, with some suggestions for new approaches. Structures of metallic glasses are treated in Vol. 1, Chap. 4, those of chalcogenide glasses in Chap. 7 of this volume. Structural relaxation is fully treated in Chap. 3, and the special case of structural relaxation in metallic glasses in Chap. 9 of this volume. The diffraction concepts used here are treated in depth in Vol. 2, Chap. 8.

4.2 Conceptual Models The plain experimental facts that glasses and amorphous solids are metastable with respect to crystals, that glasses and amorphous solids can be produced by rapid quenching from the melt or vapour, naturally tend to condition our views on structure. Glasses may be considered to be an approach to the crystalline state or as a departure from the liquid state. Extreme models for the structure of glasses - microcrystallite models or random packing models - encapsulate these two preconceptions. Even if only as a framework for discussion it is useful to try to classify models in terms of the paradigms or patterns they can be said to represent. 4.2.1 Randomness as the Paradigm

Experiment immediately dispels any notion that glasses or amorphous solids can be represented as some kind of completely chaotic "frozen atomic gas". Nearest neighbour distances only rarely show significant departures from values expected for crystals or those obtainable from tables of appropriate atomic radii. This would be expected on the basis of macroscopic properties: densities and enthalpies, for example, differ by only a few percent from values appropriate to crystals, so that a signif-

4.2 Conceptual Models

icant number of broken or extensively strained primary bonds is not expected. All random models for glasses start with atoms in contact in the case of DRP models or with essentially fully interconnected local polyhedral units for random networks. In both cases the first neighbour bond lengths are constrained. 4.2.1.1 Dense Random-Packed Hard Sphere Models Pioneering experiments by Bernal (1964) on the structure of monoatomic liquids have proved to be immensely influential in directing subsequent research on the structures of dense-packed alloys, amorphous halides and, by extension, oxides. Bernal's early experiments moulding ball bearings packed into rubber bladders, which were then kneaded and set in black paint, have since been replaced by computer simulation and 3-D graphics. Although the detail has changed, the basic concepts persist. Bernal showed that non-crystalline aggregates could be produced by constraining the exterior surface to an irregular contour. The interatomic arrangement could then be analysed in terms of five deltahedra, "canonical polyhedra" (Fig. 4-2), with a strong preference for tetrahedra and half octahedra.

187

Later computer modelling by Finney (1970) refined the figures for the relative proportion of each polyhedral type, but with the introduction of soft interaction potentials by Finney and Wallace (1981) in an energy minimization routine, the proportions of large polyhedra dropped significantly. The only major contributions remaining were from tetrahedral and half octahedral interstices. The influence of the DRP model can be gauged by the degree to which its salient features were retained in the modifications required to include new knowledge. An example is the extension of DRP monoatomic models to include additional elements. Models were proposed and tested in which atoms of two or more species were assigned randomly to sites in a monoatomic hard sphere structure. An alternative (Polk, 1972), designed for transition metal-metalloid glasses, incorporates the smaller metalloid in the large Bernal holes (Archimedean antiprisms or trigonal prisms). Recently, similar DRP structures have been simulated by sequential addition to a seed, using spheres of two sizes and realistic potential functions. Models of this type can, in principle, be constructed with polyatomic units of any shape and size. In practice, only rarely have attempts been made to construct

(i) Figure 4-2. Polyhedra formed by packing of equal spheres: i) tetrahedron, ii) octahedron, iii) trigonal prism capped with three half octahedra, iv) Archimedean antiprism capped with two half octahedra, v) tetragonal dodecahedron. After Bernal (1960).

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4 Models for the Structure of Amorphous Solids

models of randomly packed molecules, for example. 4.2.1.2 Random Networks

Closely allied to DRP models are random networks. Indeed the two are mutually interconvertible, by suitable decoration of a DRP model, say. The rationale here is that if a local structural unit can be defined - such as a silicon tetrahedron in amorphous silicon - then the random network is created by connecting such units with no rules other than on each addition of a unit to the existing cluster, their relative orientations shall be unconstrained. Additional restrictions, such as reduction of the number of "dangling" bonds to some arbitrary fraction, choice of ring statistics, or the inclusion of constraints relating to minimum strain energy or to a specified density, may be added at a later stage. Models of this type are very flexible in that the constrained unit can be considered to be as large as experimental data requires. That is, if it is clear that a local structural unit can be defined, random connection of these units then provides a realistic non-crystalline model - even if the size of the "local" structural unit is similar to that of a unit cell. Most, if not all, successful models could be considered to fall within this class. By common usage, though, the term has come to mean a random grouping of n-atom "molecular" units with n in the range 1 to 10. The term "random network" is inextricably linked with Zachariasen (1932) who proposed "that the atomic arrangement in glass is characterized by an extended threedimensional network which lacks symmetry and periodicity" (Fig. 4-3 a). This model gained support as a result of Warren's work on silica by X-ray diffraction (Warren et al., 1936) and the essential features

of the Warren-Zachariasen model persist today. Variations in the composition are easily incorporated as a random addition of species other than Q4 with associated alkali or alkaline earth cations, Fig. 4-3 b. That any random network can extend indefinitely to form a "continuous" random network, CRN, does not appear to have been proved. Phillips (1979) has suggested that continuity may be only conditionally possible - the key parameter being the relation between the number of mechanical degrees of freedom per atom, 7VF, and the relevant number of constraints, Nc. By defining constraints to mean the forces acting on an atom from its neighbours - given by the number of independent terms in a valence force field, Phillips suggests that Nc = NF represents the condition for "ideal" glass-forming compositions. In the chalcogenides NC = NF for a composition where the average number of bonds per atom is 2.4 - corresponding to As 2 S 3 . Amorphous Si, on the other hand, is "over-constrained" and, Phillips argues, cannot be represented by a CRN without intrinsic defects. Some of the defects may take the form of an extended mediumrange structure or interfaces in a granular structure.

4.2.2 Crystallographic Order as the Paradigm

Similarity between structural parameters, such as the structure factor S(Q) or the pair correlation function, for glasses and compositionally-equivalent crystals is a common circumstance. This provides support for the notion that glasses can be thought of as assemblies of microcrystals. Strain introduced due to lattice mismatch at grain boundaries, the presence of a disordered interfacial or matrix region, and

4.2 Conceptual Models

a

189

b

Figure 4-3. Schematic two-dimensional representation of the structure of a) SiO2 (only three bonds are shown); b) a sodium silicate glass. The Na atom marked with an asterisk is isolated. Greaves' "Modified random network", Fig. 4-63, does not include such atoms, see Sec. 4.7.5 (Zachariasen, 1932 and Warren et al, 1936).

defects such as dislocations, or stacking faults can be assumed to give rise to departures from periodicity at distances smaller than the average grain size. 4.2.2.1 Simple Microcrystallite Models In an unqualified form, a microcrystallite model for glasses rightly receives no experimental support. Cargill's early work on a possible model for amorphous Ni-P alloys showed that a model based on 2 nm regions with hexagonal close packing of Ni atoms (which make the major contribution to the X-ray scattering data) was inadequate to explain experimental data (Cargill, 1970). Variations in stacking fault density, dilatation and lattice symmetry proved insufficient to reconcile models

with experiment. Similarly, although the clear impression gained from comparisons of the rdfs of amorphous and crystalline Ge is that the structure to second neighbours is similar in both forms, beyond that, there is virtually no recognizable agreement. This is indicated by the almost complete absence of the third peak in a-Ge at about 0.47 nm, Fig. 4-4. Amorphous and crystalline Ge are thus fundamentally different and since the R 3 peak at 0.47 nm is due to correlations across 6-fold rings, its absence in the correlation function for a-Ge might suggest a relative decrease in the proportion of 6-fold rings in favour of 5-fold rings, in which three bond distances are equivalent to those to second neighbours. The structural differences may thus relate to essential topological variations.

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4 Models for the Structure of Amorphous Solids

lation length. Comparison with experiment may be through the reciprocal space

function, F(Q) = Q(S(Q)-1)

and F{Q)

calculated by the modified sine transform:

F ( 0 = ]Gc(r)F(r) sin (Qr)dr

(4-1)

o and Here, Qc(r) is the r-dependent atom number density and QC0 the average atom density for the crystal. Typical values chosen for L are about 1 nm. Although quasi-crystalline models give some agreement with experiment for the structure of the local environment, discrepancies are too large at higher values of r for the method to be considered as anything other than a first approximation. The problems again seem to stem from differences in topology rather than the detailed form of F(r), or the choice of L. 10 Figure 4-4. Experimental radial distribution function, J (r) = 4 n r2 Q (r), for a) crystalline Ge, b) a-Ge for two specimens deposited at substrate temperature of 350 °C (upper) and 150°C (lower). After Temkin et al. (1973).

4.2.2.2 "Quasi-Crystalline" Models Some time before the term "quasicrystalline" acquired its present meaning, models for glasses based on crystalline polymorphs with variable "correlation lengths" were investigated. An example is the early work of Leadbetter and Wright (1972); further, more recent, examples are quoted in Sec. 4-6. The correlation function for the crystal, Gc (r), is multiplied by some function, F(r), running from unity at r = 0 to zero for r>L, where L is the corre-

4.2.2.3 "Paracrystalline" Models Two authors, Hosemann et al. (1986) and Phillips (1982), have employed the term "paracrystalline" to describe their models for amorphous solids. Both use crystalline polymorphs as the basis for simulation and both introduce specific features that are essential ingredients for any degree of success the models achieve. The work of Hosemann and co-workers is the more general and extensive. The model is predicated on the observation that if the disorder is expressed in terms of interplanar distances, dhkU by

1/2

-1

(4-2)

where N is the number of lattice planes, then experimentally, the relation, N1/2 g = a*, with a* = 0.15, holds to a good approx-

4.2 Conceptual Models

imation for a wide range of semi-ordered materials. Relations such as Eq. (4-2) define the statistics of fluctuations in dhkl as a function of distance from an origin atom clearly correlations become more diffuse at longer interatomic distances. This alone is insufficient to provide agreement with experiment and for the case of SiO2 considered in Sec. 4.6.4.1, a "microparacrystal" with edge length of 1.25 nm is assumed, with a relative twist of 22° between adjacent SiO4 tetrahedra introduced to fit experiment. Glasses have also been pictured as an assembly of misoriented microcrystallites in which random relative orientations and the presence of several polymorphic microcrystalline phases represents the essential ingredients inhibiting devitrification. Most recently, this notion has been advanced by Goodman (1983) as a "strained microcrystallite model" - strain arising from the mismatch between the various sublattices thus giving rise to diffuse scattering. Phillips - among others - rejects this notion pointing out that a material such as As 2 Se 3 , which is an excellent glassformer, has only one known crystallographic phase. Phillips' extensive series of papers describe a variety of glasses, such as the chalcogenides and oxides through to amorphous solids such as a-Si and Ge. The underlying rationale for such models follows from the precept that the relation between the number of constraints - imposed by covalent bonds - and the number of degrees of freedom, implies that certain compositions are "ideal" for glass formation, others are not. Both under- and overconstrained structures are poor glass formers and lead to partially broken topological order - to discrete boundaries between amorphous aggregates and to broken chemical order. In the chalcogenides, for

191

example, deviations from chemical ordering lead to chalcogen-chalcogen bonding at the edges of GeS2 "rafts". In SiO 2 , Phillips argues that broken chemical order arises from a tendency of oxygen to form double bonds. In either case granular rather than "continuous" models result. Phillips' descriptions have the almost unique distinction among crystallite models in that both the nature of the crystallites and their intervening surfaces are prescribed in detail. 4.2.3 Non-Crystallographic Order as the Paradigm

The assumption that an ordering principle necessarily leads to periodic structures clearly has exceptions. It is well known that the lowest free energy configuration for clusters containing small numbers of atoms, involve arrangements based on tetrahedral close-packing. Atoms, or larger groups packed in this way contain symmetry elements - five-fold rotation axes for example - that are inconsistent with translational periodicity and therefore with a crystal lattice. Fig. 4-5 shows examples of some pentagonal structures produced by progressively extending the principle of packing tetrahedra. Hoare and Pal (1975) have enumerated several families of noncrystallographic clusters which can be shown to be more stable than crystallographic structures containing the same number of atoms. Icosahedral packing twelve atoms surrounding a central thirteenth, or twelve packed tetrahedra - is particularly stable, so that icosahedral, or incomplete icosahedral packing is a structure likely to be favoured in non-crystallographic packings. Polytetrahedral packing is not space-filling though, so that infinite aperiodic structures are not possible in general. The angu-

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4 Models for the Structure of Amorphous Solids

Figure 4-5. a, b) Non-crystallographic clusters produced by tetrahedral close packing; c) 55-atom "Mackay icosahedron" (Mackay, 1952); d) Thirteen, 13-atom icosahedra bridged by octahedra producing an icosahedron of icosahedra; e) 471-atom triacontahedron produced from 23 interpenetrating 55-atom Mackay icosahedra. After Barker (1977).

lar mismatch when five tetrahedra are packed around a common 5-fold axis is small (7.5°) but strain accumulates as a tetrahedrally-packed cluster grows. Larger structures thus contain considerable strain energy and eventually become unstable with respect to periodic structures and probably with respect to a composite of small aperiodic clusters in a "random" matrix. The "father" of icosahedral packing is often taken to be F. C. Frank (1952) (although he suggests that "countless generations of schoolboys may have proceeded him"). He pointed out the relative energy and volume savings involved. Subsequently, icosahedrality in randomly packed arrays has become a key issue largly through the work of Turnbull (1985), Sadoc and Mosseri (1982), Sachdev and Nelson (1985) and Yonezawa et al. (1987). The fact that tetrahedral packing is relatively stable for small numbers of atoms and the conflict between local and long range ordering suggests that local energy minimisation in the liquid or glassy state will lead to intercon-

nected, partially icosahedral groups. Further, that the barriers to crystallisation topologically imposed by the organisation of atoms at a local level - to form tetrahedra and octahedra, for instance - will lead to extended kinetic stability for the aperiodic structure. Turnbull (1985) has argued that the crystallisation process in glasses is essentially discontinuous. Whereas microcrystallite models might be expected to crystallise by progressive coarsening, through atomic migration at grain boundaries, devitrification generally occurs by a nucleation and growth mechanism. He then extends the argument to suggest that this provides evidence that the short range order in glasses is essentially different from that of the corresponding crystal, and that icosahedral arrangements provide that necessary difference. Yonezawa et al. (1987) have simulated the structure of Lennard-Jones or Stillinger-Weber monoatomic liquids as functions of temperature and time. Calculations of the local symmetry of nearest neighbour shells allow the proportion of icosahedral clusters to be recorded (as a movie) and show the development and clustering of icosahedral regions near the glass transition. 4.2.3.1 "Curved-Space" Models

An alternative to viewing aperiodic packing in terms of the relative energies of small groups of atoms is to consider polytetrahedrality or icosahedrality as a spacefilling tiling of a suitable non-Euclidean "curved-space". A planar triangulated network requires a mean coordination number of 6, local variations giving 5- or 7-fold coordination require curvature of the two-dimensional plane into 3-D. Similarly, perfectly periodic polytetrahedral tilings that are impossible in 3-D can be designed in a suitable space of higher di-

4.2 Conceptual Models

(a)

193

mension. Sadoc and Mosseri (1982) have developed this theme in a number of influential papers. A 4-D "polytope" may be constructed and can then be de-curved to bring the model back into 3-D space. Clearly, mapping back into Euclidean space involves breaks in symmetry comparable with the tears in the skin of an orange mapped from 3-D towards 2-D. Defect regions separating the polytetrahedral structures are thus an intrinsic property of this type of model, Fig. 4-6. 4.2.3.2 Polytetrahedral Models

Models for network glasses based on the above principle can also be constructed. Thus if a tetrahedrally-bonded atom is placed at the centre of each tetrahedron in an icosahedron, the dual - a pentagonal dodecahedron is formed. This is the basis for several models of amorphous materials: for instance, Tilton (1957) and Robinson's (1965) model for oxide glasses and Grigorivici and Manaila's (1967, 1968) "amorphon" model for amorphous tetrahedral semi-conductors. If the tetrahedra are decorated with sections of a diamond cubic lattice, then polytetrahedral structures, which combine amorphous cluster and microcrystallite models can be constructed, Fig. 4-7. To date, only the properties of complete, symmetrical, polytetrahedral structures have been examined although there is clearly a need to model the "connective tissue" which will not be polytetrahedral.

(c)

Figure 4-6. a) View of the central portion of a polytope constructed by Sadoc and Mosseri (1982) showing the first 13 vertices - with an icosahedral arrangement, b) 20 new vertices (shaded) are added, forming a dodecahedron, c) View of the polytope 'mapped' back into 3-D space.

4.2.4 Constrained Disorder as the Paradigm. Stereo-Chemically Defined Models

It is a common experimental fact that many glasses contain structural elements that are also characteristic of compositionally-equivalent crystals. What implications

194

4 Models for the Structure of Amorphous Solids

{110)

Figure 4-7. Decoration of a tetrahedron with a 14atom diamond cubic lattice. Packing of such tetrahedra give large non-crystallographic cluster models for amorphous tetrahedral semiconductors (Gaskell, 1975).

does this have for structural models? The answer is not obvious. The experimental evidence, though, has prompted the development of a diverse and ill-defined family of structural models. In the most general description this family overlaps the territory occupied by the random models yet also extends into the province of the microcrystallite and amorphous cluster models. In many cases models have been generated as essentially ad hoc responses to specific structural data and the underlying general ideas that link them to other similarly isolated models have not been extracted. In other cases the models can be satisfactorily categorised under other headings - microcrystallite or random networks - and broader parallels have not emerged. Here we attempt to replace the specific solutions with a more general category, one that includes most glasses and amorphous solids.

As mentioned above, the limited structural similarities between crystals and the corresponding glasses represents the central unifying theme. Models are based on characteristic signatures of the structural features observed experimentally in each phase. The common feature may correspond to the presence of a local structural unit - a tetrahedron or octahedron - and include the mode of interconnection. Further analysis may then reveal similarities extending into the medium-range of structure and indicating a more spatially extensive structure-forming principle. The principle underlying the notion of constrained disorder as a model for the amorphous phase is that similarities in structure between a glass and a corresponding crystalline phase are the result of a set of, what can be termed, equivalent structure-forming operations. In the case of the glass, the operations are applied without further constraint. For the crystal, additional constraints are needed to generate translational periodicity. Disorder is central to the structure of the glass but now only within limits: the structure-forming operations - at the level of local or medium-range order - limit the extent of disorder. A simple example serves to illustrate the argument. In almost all the crystalline forms of SiO 2 , Si is tetrahedrally coordinated and each SiO4 tetrahedron is vertexlinked to its four neighbours. We take this as an undisputed structure-forming principle for most crystalline polymorphs of silica and are not surprised to find experimental evidence for the same local structural unit in a-SiO2. If there are no further rules governing the structure, then vertex linking with a random choice of oxygen bond angle, complete connectivity (ideally), leads to the familiar Zachariasen random network model. We could go further and

4.2 Conceptual Models

195

Figure 4-8. Formation of a chain by application of a) a structure-forming operation consisting of connecting triangles at two vertices. For the triangle marked with an asterisk, the choice is between A, B, C, or D (viewed from the local coordinates of the pair of triangles). In b) a random choice is made and the result is one of the infinite set of translationally aperiodic chains. Formation of a periodic chain requires additional rules: in c) the choice is constrained to "ABCD-ABCD" etc. (starting from the atom marked with an asterisk and working upwards).

argue that this model for a-SiO2 is the embodiment of the structure-forming principle in its purest or most idealised form since no other rules have been used to generate the structure. In order to generate a crystal, however, the structure-forming principle is further constrained to apply in only a limited sense - in one direction, say, to ensure that atoms lie in straight lines. A

simple illustration, a 2-D packing of triangles, is shown in Fig. 4-8. A descriptive name for models of this type is needed. The term "stereo-chemically defined" (SCD) model has some attractions. "Stereo-chemical" can be regarded as short-hand for the set of "structureforming" operations that are central to the model. The local structure, therefore, has

196

4 Models for the Structure of Amorphous Solids

been stereo-chemically defined and the longer range structure becomes defined as a result of stereo-chemical constraints. 4.2.4.1 Similarity to Random Networks The principle of limited structural equivalence of crystalline and amorphous phases applied at different levels, can lead to structures that are indistinguishable from CRNs on the one hand or to microcrystallite models on the other. In the example above, the only structure-forming principle linking the crystalline to the amorphous phase involves local structural units, with all arrangements of these units equally probable. The general result is a random model: a random network (or random coil for the example of Fig. 4-8). A further example could be the network models for a-Si generated by Wooten and Weaire (1987) (see Sec. 4.5.3) in which the topology of a diamond-cubic crystal was progressively modified by switching bonds until agreement was reached with experimental data for a-Si. Again, the implicit structure-forming operations are retained as constraints - strictly fourfold, approximately tetrahedral bonding, no breaks in connectivity, and these are also characteristic of the crystal. Another example is the "boroxol ring" model for a-B 2 O 3 where a (medium-range) structural unit - the B 3 O 9 ring (Fig. 4-59 a) is connected randomly through the oxygens to form a CRN. 4.2.4.2 Similarity to Paracrystalline Models Variations in the geometry of a crystal without accompanying topological modification lead to structures that are probably best considered as paracrystalline models. For example, Yasui et al. (1983) modelled the structure of amorphous chain and sheet silicates starting from the corre-

sponding crystalline lattices with modification of the geometry of the chains, so that the SiO3 chains were bent regularly in one plane until agreement with experiment was achieved (see Sec. 4.7.7). Clearly, in so doing, none of the structure-forming principles characteristic of the crystal were violated. 4.2.4.3 Local Order as a Consequence of Medium-Range Order If the last two sections, describing the structures of end members of the series represented the entire picture, then there would be no reason to introduce a new category of SCD models. However, there are glasses for which the structure-forming principle relates to medium-range ordering and which are describable in the same language as the CRN and microcrystallite models. Before discussing these, it is necessary to introduce a connection between local and medium range structure. Several types of glasses exhibit local ordering similar to that of a crystalline phase but any explanation of the local order in either relates to medium-range ordering. Two illustrations serve to focus the discussion. Firstly, amorphous transition metal - metalloid (TM-m) alloys appear to be structurally similar to crystals in that the immediate environment of metalloids in the glass and crystal have similar ninefold coordination, trigonal symmetry and narrow bond length distributions. Secondly, the local environments of several alkali and alkaline earth cations in silicate glasses, mimic the local structure of the corresponding crystals. At first sight, these facts may seem unremarkable. Atoms like Si or B have well-defined coordination spheres in amorphous oxides: models incorporating well-defined coordination shells for B in, say, a-Ni4B or Na in a-Na 2 Si 2 O 3

4.2 Conceptual Models

should thus present no additional difficulty and random models for each should work. Indeed, random models for TM-m alloys have been built (Gaskell, 1979), and these can be considered to be CRNs with a trigonal prismatic BNi9 cluster as the local structural unit. Also, Greaves (1985) has proposed a "modified" CRN model in which the alkali network "modifiers" exhibit a preferred coordination, and exist in defined regions of the structure, giving random percolation channels intercalating the silicon-oxygen "network" sub-structure. The problem is to explain the structureforming principle - why do clusters like BNi9 or NaO 5 exist? Well-defined tetrahedral SiO4 units or triangular BO3 groups can be said to "exist" as a result of the strong, directional interatomic bonds. Although it could be argued that B-Ni bonds are strong too, there is no evidence for nine-fold directional bonding. It is difficult to see how this could be achieved as the central B atom has no available d orbitals. The case is even more compelling for alkali and alkaline earth oxide glasses with weak, ionic bonds to oxygen. In neither case can isolated "molecular units" be contemplated. For both types of materials, local geometry and symmetry observed around B in the closed-packed crystalline transition metal borides and around Li, Na and Ca in the close-packed regions of silicate crystals is an essential consequence of an ordered close-packing. In other words, local structural characteristics in these crystals derive from particular medium-range packing schemes in the crystal. There are reasons to believe that this conclusion extends to glasses also. For aTM-m alloys, the experimental evidence is the most clear-cut and details have now emerged - principally from neutron scattering experiments with isotopic substitu-

197

tion (Lamparter et al., 1982) that the local structure is well-defined, with nine-fold coordination of the metalloid by the metal. Evidence for a well-defined local structure implies the presence of a degree of mediumrange ordering, of some sort. We cannot say at the outset what the nature of the medium-range ordering is, but that it exists. Models for amorphous TM-m alloys were therefore constructed by Dubois, Gaskell and Le Caer (1985) (see Sec. 4.2.4.4) which incorporated the mediumrange structural principles observed in the crystal, to produce a SCD domain model that satisfactorily reproduced the partial distribution functions obtained by Lamparter and co-workers. For the "network modifier" cations in oxide glasses, similar arguments apply and experimental evidence for medium-range ordering is now emerging also and will be considered in Sec. 4.7. The point to stress here is that where experimental evidence shows that atoms in close-packed solids - or within closepacked substructures - have a well-defined local structure, then models for these materials could contain a "medium-range structure-forming principle" similar to that responsible for the structure of the corresponding crystal phase. More generally, evidence for well-defined local structures in materials where the local structural unit has a high connectivity, require definitions of the medium-range structure too. These points may be rationalised by accepting that many crystal structures represent a compromise between the space and coordination requirements of atoms in different sublattices. The result is that not all structures that are topologically possible do, in fact, exist as crystals: a point made clearly by Dent-Glasser (1979) for silicates. Constraints imposed by each of the constituent sublattices in a silicate crystal, lim-

198

4 Models for the Structure of Amorphous Solids

it the range of existing crystals. Can we assume that glasses, because they are noncrystalline, avoid similar rules? The answer is - almost certainly, No. Pauling's rules on which the structure of crystals can be classified are essentially arguments based on considerations of local charge balancing, bond counting, valence, coordination numbers, density and overall composition. Clearly, none of these parameters is specific to the translationally-periodic solid: all should relate to the amorphous state too, so that Pauling's rules alone should constrain amorphous structures. The structure for the crystal is one successful solution to the problem - one of the many structures that could, hypothetically, exist, that does. Investigations of structures for an amorphous solid can use this as a sound starting point - especially if a "structureforming" principles can be extracted from the crystal and transferred to the glass. 4.2.4.4 Stereo-Chemically Defined Models for Close-Packed Oxides and Amorphous Metals Involving Medium-Range Structure-Forming Operations

Several authors have produced random models by modifying the topology of the crystal at the level of the medium-range structure. A recent example is the work of Barenwald (1988) et al. who attempt to model the structure of a chain phosphate, Ba(PO 3 ) 2 by a Monte Carlo method. The structure-forming operation preserved in this work is the essentially parallel packing of infinite, linear (PO3)W chains. PO 4 groups remain intact but the bond and torsion angles are varied randomly to produce a fit to experiment. A similar but more constrained SCD model is that reported by Gaskell (1985 b) for chain metasilicates, see Sec. 4.7.8. The starting point was a Na or Li metasilicate

crystal in which oxygen atoms form a distorted hexagonal close-packed (hep) sublattice. Si, Li (or Na) occupy the tetrahedral interstices (highly distorted for Na). Each (SiO3~)n chain is surrounded by six M-0 chains (M = Na, Li). For the glass, the hep oxygen sublattice was preserved and the tetrahedral interstices were populated with Si or M atoms to form randomly-coiled, self-avoiding silicate chains surrounded by M-O chains. The resulting model thus preserves the following structure-forming operations: oxygen close-packing, semi-infinite, nonbranching chains, chemical ordering, "repulsion" between Si atoms in adjacent chains and "attraction" between Si and Mcontaining chains. SiO4 tetrahedra are preserved, of course, with interconnections through "bridging" oxygens. Randomness while essential to the model, is applied only after taking account of the "stereochemical" constraints imposed by the structureforming operations. A final example comes from the work of Dubois, Gaskell and Le Caer (1985) on amorphous TM-m alloys. The apparently complex structures observed in TM-alloys can be considered as close-packed lattices of TM atoms with twinning at the unit cell level. Specifically, the cementite, Fe 3 C, structure used here as a template for the glass, is produced by inserting twinning planes in every three {112} planes of the hep structure. Capped trigonal prisms are thus formed which are linked through edges and vertices to form planes within which boron atoms are accommodated. These structure-forming operations are preserved in a model for the glass in that parallel twinning planes operate over a defineable correlation length (1 to 2 nm). Beyond, lie other domains also generated by twinning, but with planes lying in other orientations. Topological continuity of the

4.3 Experimental Structural Techniques

local structural units (trigonal prisms) and the twinning planes is preserved by the interface atoms too so that the ground state of the model has no primary discontinuity at domain boundaries. These constraints lead to more detailed local restrictions on the arrangement of structural units and to a model that is topologically ordered (but not geometrically ordered) on a length scale of several nearest neighbour distances, but topologically and geometrically disordered beyond.

4.3 Experimental Structural Techniques In this section, a brief account is given of the principal structural techniques used to study amorphous solids. Details are given in other volumes of this series. For completeness and to establish the basic formalism, some repetition is inevitable. Particular emphasis is placed on the methods required to obtain structural data of high information content. Quantitative results are expressed in terms of probability functions or distribution functions. We can define the probability of finding an atom at a position r, in an element of volume dr. This is a one-particle distribution function. Similarly, we can define a more useful quantity - the probability of finding two atoms simultaneously at positions r1 and r 2 , thus defining a two particle or pair distribution function. It is more convenient to place the origin to coincide with one atom and work with interatomic vectors, or for a homogeneous system, interatomic distances. Then the probability of finding an atom in an element of volume dV at a distance r from the origin atom equals Qog(r)dV= Q(r)dV. Here, g (r) is the pair distribution function, Q (r) is the r-dependent atom density and Q0 the

199

average atom (number) density. For amorphous solids, since g(r) = Q(r)/Q0, the function tends to unity at large values of r. Although experimental information on higher order distribution functions is difficult to obtain, we could define a triplet distribution function in terms of the probability of finding atoms simultaneously at r i •> ri j r3 Setting the origin at a given atom position allows a definition of the triplet distribution function in terms of the probability of finding one atom at an interatomic distance rt, a second at r2 with the included angle being 6. Often the terms distribution function and correlation function are used interchangeably. Strictly, the pair correlation function, h(r) = g{r)-\ so that this function tends to zero as r tends to infinity. Cusack (1987) gives an excellent account of the necessary formalism. 4.3.1 Neutron Scattering Techniques Static Structural Methods Neutrons have zero charge and do not interact with charges in the specimen, in contrast to X-rays and electrons. Neutrons interact with the (small) atomic nuclei and this considerably simplifies any description of the scattering equations, since the scattering mechanism is essentially independent of the scattering angle, if inelastic scattering is neglected. For an isotropic liquid or glass, vectorial information characteristic of a crystal is averaged, so that the intensity is Q-dependent but there is no other angular variation. In a typical (elastic) scattering measurement, the intensity of a monochromatic beam of scattered neutrons is measured as a function of the scattering angle - conventionally 2 9. Usually the result is expressed in terms of the modulus of a scattering vector, Q, \Q\ = Q = 4nsinO/A,

200

4 Models for the Structure of Amorphous Solids

where X is the incident neutron wavelength. The experimental scattered intensity oscillates around a background, I*xpi term equal to the scattering from a structureless medium of the same atomic density and composition as the specimen - "self scattering". Neglecting inelasticity effects, 7fxp = Nb2 where b is the neutron (coherent) scattering length for the atoms of a monoatomic solid and TV is the number of atoms in the neutron beam. Generally there is also a degree of incoherent scattering that is subtracted from the total scattering to obtain the coherently-scattered fraction. Oscillations around /fxp are due to constructive and destructive interference from neutron de Broglie waves scattered from nearby nuclei and these oscillations contain the structural signals, I(Q) (Fig. 4-9). Thus,

= Nb2S(Q)

(4-3 a)

where S (Q) is the so-called structure factor and contains all the structural information. Often the same equation is re-expressed in terms of the "interference function"

i(Q)=I(Q)/Nb2-l

=

N

(4-4)

or, more simply, in terms of a "reduced interference function",

ivii

Each distance in the specimen thus exhibits its signature in the form of a sine wave of "period" AQ = 2n/rmn - short distances giving rise to long period fluctuations in Q-space and vice-versa (see Fig. 4-10). The Debye equation, Eq. (4-5), is convenient for simple calculations on molecular groups with discrete interatomic distances. For a solid or a liquid it is preferable to work with the atomic density, Q (r), defined as the number of atoms in a volume d3r, at

(4-3 b)

It is useful to obtain, at the outset, a conceptual grasp of what information S(Q) contains. For an isotopic specimen, Debye showed that the scattering from N particles separated by a constant distance rmn is given by: 1

Figure 4-9. Typical experimental neutron scattering data showing the "self-scattering", Nb2, from a structureless medium containing the same number of atoms per unit volume as the specimen.

(4-5)

Q /nm"

Figure 4-10. The reduced interference function, F(Q\ for a monoatomic specimen. With a gaussian distribution, centered on R, the result is a damped sinusoidal wave of period 2n/R. The full line shows F(Q) for R1 = 0.246 nm,
4.3 Experimental Structural Techniques

distance r; so that the number of atoms in a spherical shell, radius r, thickness dr is: J(r) = 4nr2Qog(r)dr

= 4nr2Q{r)

t (r) — 4 n r Q (r) or (4-6 b)

It may be shown (Warren, 1969) that:

Q

° (4-7) where Q0 is the average atom (number) density. Defining a "reduced" radial correlation function:

\ = 4nr(Q(r)-Q0)

(4-8)

then, 1 S(Q) = l+— fG(r)singrdr (4-9) Qo or, (4-10) F(Q)= fG(r)sinQrdr o The advantage of these forms of the Debye equation is that only deviations from the average atomic density contribute to F(Q). For liquids and glasses, the atomic density, g(r\ approaches Q0 at large r so that integration can be usually truncated at r& 1.5 to 2.0 nm. It is possible - and often desirable - to fit structural data in the form of S (Q) or F (Q) with computer data for a structural model that gives G (r). However, the structural information is easier to visualise in real space using the fourier (strictly sine) transform of S (Q) or F (Q). We thus have two symmetrical transforms: F(Q)= jG(r)sinQrdr 0

and

=

^F(Q)smrQdQ

(4-1 lb)

(4-6 a)

where J(r) is the so-called radial distribution function (rdf). A function t(r) is often used: T(r) = 4 n rb2 Q{T)

201

(4-1 la)

(In other conventions, G (r) is replaced with D (r) - the differential correlation function.) 4.3.2 X-Ray Scattering X-rays interact with atoms of the specimens chiefly through their electrons. (A term involving the nuclei is reduced by the ratios of the masses of electrons and nuclei.) Since electron orbitals - particularly the outer valence shells - have radii that are comparable to interatomic distances, interference terms arise from the "shape" of the orbitals. Assuming spherical shells, the effect is to replace the neutron scattering lengths, b, in the above equations with an atomic scattering factor, f(Q% i.e. atomic scattering factors are now g-dependent, due to interference from waves scattered by electrons within the shells. Such atomic scattering factors (or "form factors") are tabulated in standard works. Thus the scattered intensity is now related to a Q-dependent background, Fig. 4-11. With this modification, the remaining equations in Sec. 4.3.1 hold.

u Figure 4-11. Typical X-ray scattering data, oscillating around a Q-dependent atomic scattering factor, / (k). (Here, k is used instead of Q.)

202

4 Models for the Structure of Amorphous Solids

For electron diffraction, interaction is again with the electrons but the charge on the nucleus now becomes important. If the atomic scattering factors for electron and X-ray scattering are fE(Q) and fx(Q) then:

^=

4n2(Z-fx(Q))/Q2

(4-12)

Electron scattering is much stronger (typically 104 larger) than X-ray scattering which is in turn very much stronger than neutron scattering. Thus very thin films are necessary for electron diffraction compared to specimens of 5 to 10 g for neutron scattering.

and the transform of the gaussian broadening function, which is another gaussian given by the exponential term in Eq. (4-13). Similarly, the transform of a product of two functions is the convolution of the fourier transforms of the two functions. Broadening of the distribution of interatomic distances arises partly from differences in the environment of each atom due to disorder - the static broadening, as. In addition, thermal motion leads to another contribution, ath. For the j t h interatomic distance the total effect is obtained by addition in quadrature: (c^)2 = (asj)2 + 2

4.3.3 Effects of Disorder on Scattering Data

4.3.3.1 "Termination" Smearing

F(Q) for a monoatomic specimen with all atoms at a constant distance, R, will be an infinite sine wave. Non-crystalline solids are characterised by a distribution of local sites rather than a single environment, so that the distributions are broadened. The corresponding F (Q) is a damped sine function, Fig. 4-10. For a peak shape in the form of a gaussian i.e.

Since scattering measurements are limited to a scattering angle, 2 6max = n9 g max is limited to 4 n/ 2, and for typical X-ray and neutron wavelengths of 0.05 to 0.1 nm, Qmax = 250 to 125 nm" 1 . Eq.(4-llb) involved a transform of the scattering function F(Q) over an infinite Q range. The effect of truncating the integral at Qmax is equivalent to multiplying F (Q) with a modification function, M(Q), such that:

G(r)ozQxp(-(R-r)2/2(i2)

M(Q) = M{Q) = \

then, F{Q)K

R

exp(-

(4-13)

For more general r-space distributions with a number of peaks in r-space, the transform of each is multiplied by the corresponding "damping function" exp(— Q2a2/2) and the contributions are then summed. The result is a smearing of F(Q) at high Q. The above is an example of the convolution or folding theorem. G (r) in this case is a convolution of a set of delta functions with a gaussian. The transform, F ( 0 , is a product of the transform of G (r)

Q < e max

From the convolution theorem, if G* (r) is the "true" real space function which would be obtained by transformation of F(Q) with <2max=oo, then truncation of the fourier transform of F (Q) at Qmax implies that G* (r) is convoluted with a peak shape function, P*(r) which is the cosine transform of M(Q): P* (r) = - J M (Q) cos (r Q) &Q 71

(4-14)

0

(See for example Waser and Schomaker (1953).)

203

4.3 Experimental Structural Techniques

For M (Q) in the form of a step function, the peak shape function is a SINC function, Fig. 4-12. Thus if G*(r) is considered to be made up of a set of (5-functions, the effect of multiplying of ^-function by P (r) and then summing to obtain G (r) - which amounts to a convolution of G*(r) with P* (r) - is to broaden the features of G* (r) and to introduce satellite "termination ripples". The ripple may be suppressed, at the expense of further broadening, by using smooth modification functions. A number are quoted in Fig. 4-12.

4,3,4 Polyatomic Solids Scattering in polyatomic solids can be treated using the Debye equation but the terms involving the different atomic species, a, /?, etc. must now be accounted. We must now consider partial structure factors, Sap(Q), and partial pair correlation functions Gap(r). For a solid containing m atomic species, there are m(m + l)/2 independent partial functions. The number of atoms of type /? in a volume d 3 r at a distance r from an origin a is: )=

4nr2Qap(r)

(4-15)

The relative density can also be defined in terms of the mean density of atoms of type P,Q0(p) = npQ0 where np is the atomic fraction of species /?. Thus: 9ap(r) = Qap(r)/npQ0

(4-16)

The partial reduced radial correlation function is:

(4-17) Eqs. (4-11) now become:

= \Gap{r) sin(Qr)dr

(4-18a)

and Gap (r)=-$FaP

(Q) sin (r Q) dQ

(4-18 b)

4.3.4.1 Total Distribution Functions and Structure Factors

-40 Figure 4-12. Peak shape functions corresponding to a fourier transform of reciprocal space data truncated at Qmax by a modification function M (Q). A. M(Q) =

B.

with B = \oge(10/Q Leadbetter (1976)).

2

max).

C. M(fi) = l (Wright and

Partial distribution functions and structure factors give a detailed description of the environment of each atomic species and the information content is equivalent to G (r) or S (Q) obtained for a monoatomic solid. Experimental scattering measure-

204

4 Models for the Structure of Amorphous Solids

ments from polyatomic solids do not directly give the partial functions. The measured total structure factor, S(Q) is a weighted sum of contributions from independent pairs of atom types, a a, /?/?, a/?, etc. Thus for a diatomic solid: 7

aeSaAQ)

(4-19 a)

a fi

where WaP is a weighting factor, nanfibab*

(4-19 b)

and b a , bp (or / a , /^ for X-rays) are the scattering lengths for atomic species a, /? and

The total structure factor is defined as:

S(0 = . ^

N\(by\2

(4-20)

+1

Again, the brackets, < >, refer to a compo2

m

sition average so that = Z (**«&«)• a=1

From iS (<2) the total reduced radial correlation function, G(r) can be obtained as: G(r) = I Z ^ G ^ ( r )

(4-21)

Since the weighting factors differ for X-ray and neutron scattering, S (Q) and G (r) measured by X-rays will not be identical to that measured using neutrons. 4.3.5 Extraction of Partial Structure Factors It will be obvious that averaging over three partials for a diatomic solid leads to a drastic reduction in the information content of a measurement. Peaks in one partial tend to overlap with troughs of another, so that the resulting destructive interference leads to smooth total functions in cases

where the underlying partial functions are strongly oscillatory. Furthermore, partials with small weighting factors are buried beneath the oscillations of strongly-weighted partials. For the most informative structural measurements, it becomes vital to extract partial structure factors from total structure factors and partial correlation functions from total correlation functions. Apart from a few simple solids like SiO2 where this can be done by inspection (see Mozzi and Warren, 1969), it is necessary to employ special techniques. We consider five possibilities. 4.3.5.1 Combination of the Results of X-Ray, Neutron and Electron Scattering For a binary alloy, if three experiments can be performed with three types of radiation thus providing three sets of equations of the form S (Q) = £ £ WaP Safi ( 0 , and if a fi

values of Wafi are sufficiently different for the three measurements, then the three equations can be solved for the three unknown quantities S aa , Safi9 Spp. The atomic scattering factors depend on the character of the probing radiation, as mentioned earlier. Furthermore, although X-ray and electron form factors increase monotonically with atomic number Z, the neutron scattering length, b, is determined by two contributions - "potential scattering" which increases very slowly with Z, and a "resonance scattering" term - that oscillates, apparently haphazardly. It is thus possible to choose systems for which the X-ray and neutron weighting factors, Wap9 are significantly different for the various types of radiation. Form factors for electrons are insufficiently different from those for X-rays for electron diffraction to be of much use as a third experiment (in addition to X-ray and

4.3 Experimental Structural Techniques

205

Figure 4-13. Partial structure factors, Gij{f) for aCo 81 P 19 obtained by Sadoc and Dixmier (1976). 5

6

10

r(A)

neutron scattering). For elements with a magnetic moment, such as Co, the moment may be oriented with a suitable external magnetic field. The atomic scattering length for polarised neutrons depends on whether the atomic moment lies parallel or anti-parallel to the neutron spin, so that for Co-containing alloys, magnetic scattering offers two experiments. A classic investigation of a-Co 4 P was performed in this way by Sadoc and Dixmier (1976) using a combination of X-ray scattering, polarised and unpolarised neutron scattering to obtain the three partial structure factors for the alloy (Fig. 4-13). 43.5.2 Neutron Scattering with Isotopic Substitution

Not only do neutron scattering lengths vary sharply from element to element; they also vary from isotope of the same element. For example, Ni has isotopes in which b (in units l(T 1 5 m) varies from - 8 . 7 (62Ni) to 14,4 (58Ni). Three experiments with three isotopic mixtures of Ni in a binary alloy

thus allow extraction of partials from three sets of neutron scattering data. In another seminal measurement, Lamparter et al. (1982) obtained the partials for a-Ni 81 B 19 using alloys of X1B with nat Ni, 62 Ni, and a mixture of 62 Ni and 60 Ni giving a coherent scattering length of zero. X-ray scattering data was also collected for good measure. The results are shown in Fig. 4-14. 4.3.5.3 "Difference" Methods

For compounds with more than two atomic species, direct extraction of partials would be impractical. For a triatomic material, six independent measurements would be required. However, it is still possible to simplify the problem and to increase the information content of measurements by obtaining information on the environment of a selected atomic species. This is done by taking differences of the neutron intensities scattered by two samples of the same material, identical apart from the isotopic concentrations of one of the species, M, say. Writing the normalised neutron scattering

206

4 Models for the Structure of Amorphous Solids

where bM and b'u are the neutron scattering lengths of the two isotopes. The technique, pioneered by Soper et al. (1977) in studies of molten salts and aqueous solutions has now been applied to many glasses (see Sec. 4.7).

geometrical packing model

4.3.5.4 X-Ray Absorption Spectroscopy

2.0

4.0

6.0

8.0

10.0

12

Figure4-14. Partial structure factors Gtj(r) for aNi 81 B 19 obtained by Lamparter et al. (1982).

intensity per atom:

^'

a

a, B

(4-22)

The first term on the right hand side contains g-independent "self scattering" terms; the second, terms involving M such as: b^ HM(SMM(Q) -1) and terms involving pairs of atoms other than M. Only the terms involving bM are affected by isotopic substitution so that (apart from a difference of background levels) the difference between two intensities for the two measurements, A J ( 0 , contains only terms involving correlations between M and other species (including M) thus: M (Q) = Const + A (SMM (Q) - 1 ) +

where

Each element has a characteristic absorption edge, corresponding to excitation of a bound electron from a core shell to an excited state above the conduction band minimum. The energy involved lies in the X-ray region and is specific for each element. At energies, £, immediately above the threshold, £ 0 , the absorption coefficient exhibits a series of oscillations extending up to 1 keV above the absorption edge. After background subtraction and suitable normalisation, the oscillatory part of the signal, x (E), the X-ray absorption fine structure (XAFS) contains structural information on the environment of the excited atom. Specifically, x (E) represents interference between the photoelectron wave emitted by the excited atom and waves back-scattered from its neighbours. It thus has considerable similarity to the interference function in X-ray, electron and neutron diffraction and provides similar structural information. Similar effects occur after excitation with fast electrons: scattering processes that involve excitations from core states, appear in the electron energy loss spectrum (EELS) as saw-tooth peaks with an associated fine structure at higher energies. Such transitions can be observed in an electron microscope, for example, if the transmitted electron beam is energy-analysed. The fine structure in both types of spectra can be roughly categorised as the relatively sharp oscillations in the immediate

4.3 Experimental Structural Techniques

vicinity of the "edge" and the gentler oscillation of the extended XAFS. The former involves strong scattering of low energy photoelectrons for E — Eo «100 eV and the latter region can be treated by a single scattering approximation (Sayers et al., 1971). Writing the latter approximation in terms of the modulus of the photoelectron wave vector, k2 = 2mQ(E—E0)/h2 then:

• exp ( - 2 o) k2) exp ( - 2 Rj/A (fc)) (4-24) This expression is clearly more complicated than the corresponding expression for X-ray or neutron scattering (Eq. (4-5)). However, the similarities become more obvious on inspection. Rj is the distance from the central atom to a shell of Nj neighbours. Eq. (4-5) contains a term in sin QRj whereas Eq. (4-24) has a similar term in sin 2 kRj. Each, therefore, indicates that a discrete peak in r-space at Rj gives rise to sine wave oscillations in Q-space or kspace, of period 2 n/Rj or n/Rj respectively. (In XAFS, the interfering wave travels from the central particle to its neighbours and back again - a distance of 2 Rj.) Complications inherent in Eq. (4-24) involve a phase shift term Sj(k% a 'Debye-Waller' term exp (— 2 a? fc2) where Oj measures the breadth of the r-space distribution, and a term exp (— 2 Rj/A (k)) representing the decay of the amplitude of the photoelectron wave due to inelastic processes. A is a measure of the mean free path. The back scattering factor, \fn(k)\9 corresponds to the term f(Q) in X-ray scattering (the n indicating 180° scattering). As with X-ray or neutron scattering, it may be preferable to convert Eq. (4-24) from its Debye-like form into a version that includes pair distribution functions,

,(*)_

207

3=n-l

kr2\fn(k)\

•exp(-2rM(fc))

(4-25)

Here, a corresponds to the excited element of species a, and /? to neighbours of other species which includes neighbouring atoms of species a. The important point is that in a triatomic alloy, say Xa involves terms in P aa , Pafi, Pay but excludes other terms not involving a. The structural information is thus analogous to that obtainable from neutron scattering with isotopic substitution of species a in the difference mode, or to X-ray differential anomalous scattering at the absorption edge of element a. The advantages, though, are that this element-specific technique is much more generally applicable since medium atomic number elements can be examined by Xray absorption techniques and light elements by EELS without any requirement for isotopes with contrasting scattering properties. Moreover, a high maximum value of reciprocal space or fc-space data is routinely available - typically kmax = 200 nm x equivalent to g max = 400nm x in neutron scattering. There is a major disadvantage, however, for disordered materials. If a peak in rspace is broad - as they are in glasses for second- and higher-neighbours, then the Debye-Waller term tends to zero except for the region below fc^40nm-1 - which is also the region corresponding to strong multiple scattering of low energy photoelectrons and where single scattering theory does not apply. The extended XAFS spectrum thus offers little information beyond the first peak in r-space and even then is not sensitive to broad features - shoulders or wings - that correspond to higher frequency fourier components in reciprocal space.

208

4 Models for the Structure of Amorphous Solids

One answer to this problem, of course, would be to analyse the low energy region where information on high neighbour correlations is contained. The difficulty with this approach is that there is no method for inverting the data to obtain, directly, the real-space distribution. One must proceed by comparing experimental data with computed low energy XAFS or EELS data computed from trial structures. Although some success has been achieved by this method - for example work on a-Si discussed in section 5 - the accessible information content is limited.

4.3.5.5 X-Ray Anomalous Scattering In the vicinity of an absorption edge in the X-ray spectrum of an element, the atomic scattering factor, / , for that element becomes energy-dependent. Writing / in terms of its real (f±) and imaginary (f2) components: f=f0 +f1 + if2 - Here, f0 represents the contributions to the scattering factor from all processes other than that associated with the absorption. The imaginary (absorptive) part shows a step function change as the energy is increased through the region of the absorption edge, whereas fx is small and negative at energies below the edge, has a deep minimum at the position of the edge and then rises progressively beyond that. By taking scattering measurements at two incident X-ray energies on either side of the absorption edge, preferably using a tunable X-ray Synchrotron source, values of/ x can be sufficiently different that subtraction of the two scattering curves gives elementspecific information - as in the isotopic substitution technique. Thus, A/(g) can be written as a similar equation to Eq. 4-23 with weighting factors given by Ludwig et al. (1987). In principle, further measure-

ments can be taken at the absorption edges of other elements in the material. The magnitude of the changes in ft can be about 20 % but it has proved quite difficult to obtain good separation of the partials in binary alloys due to a combination of random and systematic errors. Moreover, the X-ray wavelength is determined by the position of the absorption edge which increases with atomic number, Z, so that to obtain X-ray scattering with a reasonably large Q range, the element of interest should have a high atomic number. On the other hand, there are none of the problems associated with the low Q cut-off that limit the usefulness of XAFS data. Pioneering measurements on the structure of Ge-Se alloys were performed by Fuoss et al. (1981) and more recent work includes studies of a-Ni2Zr (de Lima et al., 1988).

4.3.6 Vibrational Spectroscopy The static structural properties considered above give one view of the properties of an amorphous solid. Dynamical properties - the response of the solid to an excitation, not only give additional information on the static structure but also add new information. The simplest description of the vibrational properties of a material is given by the vibrational density of states function, g(co); the number of vibrational modes with frequencies between co + Aco. This quantity is not directly measurable but experimental methods provide information that can be related to g(co). However, for amorphous solids - in contrast to crystals - this transformation is by no means without uncertainty. Lack of periodicity in an amorphous solid has the important effect that the (crystal) momentum selection rule

4.3 Experimental Structural Techniques

appropriate to crystals is no longer strictly valid. The infra-red absorption process in a crystal is governed by laws of conservation of energy and momentum, E(ko) = E(q); ko = q, where k0 and q are the wavevectors of the incident photon and the created phonon respectively, and a selection rule restricting the modes to those for which there is a net change in the dipole moment. For isotropic solids, k = \k\ = 2njX so that for the IR effect with 2^10 jim, k is effectively zero on the scale of the Brillouin zone boundary ( ^ l O n m " 1 ) and the IR spectrum therefore picks out the sub-set of modes in g (co) for which £ = 0. In an amorphous solid with no identifiable unit cell, k becomes a poor quantum number so that all modes in g(co) become potentially optically active. Similar statements applies to the Raman effect (although now it is the changes in polarisability rather than the dipole moment that provides one of the selection rules). Thermal neutrons with energies similar to vibrational quanta can also be scattered inelastically that is with the creation or destruction of one or more phonons. The static structure factor, S(Q), discussed above is thus replaced in a complete treatment by S(Q, co) - the dynamical structure factor. Certain nuclei - notably H - possess a spin, /, and since scattering of neutrons involves the properties of a compound nucleus, neutron + nucleus, with spin 7+1/2 or 7—1/2, the two states have different scattering lengths so that scattering from such nuclei is only partially coherent. H has a particularly large incoherent cross section and since incoherent scattering involves addition of intensities of scattered waves - the scattering intensity is given by a sum over essentially independent vibrating atoms. Thus the energy gain (or loss) of neutron scattered by such pro-

209

cesses is directly related to g(co), i.e. S(Q,co) = g(co)fN(Q,co) where, /N iQ, exp ( - 2 Wi (Q)) 1 Mi (4-26) Here, bt and Mt are the incoherent scattering lengths and mass of the ith species; <w? (co)} is the mean square displacement of the ith atom averaged over phonon modes near co and Wt(Q) = Q2 /6 is a Debye-Waller factor. Neutron incoherent scattering data from any materials is useful because of the close resemblance of the experimentally measured spectrum to g (co) with few of the problems associated with the transform from, say, Raman data to g(cn). Experimental data from Raman and IR spectra has great value in structural studies on amorphous solids. The symmetrybased selection rule still operate so that totally symmetric vibrations, for example, that produce no change in dipole moment but a change in polarisability are, to first order, IR-inactive and Raman-active - as in molecules. This is valuable information therefore. Secondly, the high frequency vibrational bands, at least, associated with the motion of atoms in local structural units are only slightly shifted (and broadened) compared to the crystal, that it is trivial (and cheap) to distinguish between tetrahedral and octahedral coordination in, say, a-GeO 2 . The problem for amorphous solids is that in some materials - such as the amorphous semiconductors, the observed IR or Raman spectrum does indeed mimic g (co) whereas for many oxide glasses - notably borates and phosphates - sharp bands are observed that are unlikely to give any direct representation of g(co).

210

4 Models for the Structure of Amorphous Solids

In a glass like SiO 2 , or an amorphous semiconductor such as a-Si, the tetrahedrally-bonded atoms are extensively interconnected but without any simplifying periodicity. The vibrations of the atoms comprising the ensemble now depend on the relative phase of all the other atoms nearest-neighbour atoms being most important. Since there is no unit cell, the concept of a well-defined phase difference between equivalent atoms in adjacent unit cells is inapplicable and the independent, plane wave-like vibrational states no longer exist. Modes are therefore strictly hybrids of all others. We can still require that selection rules operate but now strictly over the total number of atoms in a macroscopic specimen. Progress has been made for example by Shuker and Gammon (1970), Galeener and Sen (1978) and others but the exact quantitative treatment depends on calculations of the properties of relatively large models. 4.3.7 High Resolution Transmission Electron Microscopy

High resolution transmission electron microscopy (HTREM) differs fundamentally from the diffraction techniques discussed earlier. Diffraction of X-rays, neutrons or electrons involves interference between waves scattered from neighbouring atoms as a result of phase and amplitude differences: structural information is conveyed in the angular distribution of the intensity of scattered waves but phase information is absent in the final signal. The information content is significantly degraded therefore. HRTEM images are the result of scattering of electron by atoms of the specimen but amplitude and phase information is preserved - albeit with some significant distortion introduced by the electron optics.

For sufficiently thin specimens, the electron wave incident on the specimen is weakly scattered and the wave function of the emergent beam can be represented in terms of an (almost) unchanged amplitude but with the phase shifted by an amount proportional to the specimen potential projected onto a plane perpendicular to the incident electron wave vector. This is related to the projected electron density of the specimen, so that the emergent wave can be considered as a 2-D mapping of the projected electron density of the specimen. An optically faithful electron microscope could thus give a magnified view of the electron density on the scale of interatomic distances, if this phase difference map were to be translated into- an intensity, or contrast, difference in the image. This is achieved in a "phase-contrast" image which makes use of changes in phase introduced by the imaging electron optics, in an analogous manner to phase microscopy in (light) optics. A microcrystalline specimen can thus be imaged as a series of lattice planes in which a suitably Bragg-oriented microcrystallite generates a periodic fluctuation of the phase of the scattered electron wave of period dhkl in a plane perpendicular to the electron beam direction, z. This phase grating is translated into a magnified periodic fluctuation in the contrast of the final image. One of the major differences between this structural information and that derived from the angular distribution of the scattered intensity is in the degree of averaging involved. In an X-ray measurement, the scattered information is a representation of the sum of interatomic vectors from about 1020 origin atoms. In a TEM image, structural information relating to a local region of the specimen is retained within a corresponding local region of the image. Consequently a cubic microcrystal-

211

4.3 Experimental Structural Techniques

lite of, say, 4 nm edge length involves averaging over about 104 atoms. Moreover the image is a 2-D representation of a 3-D object, rather than a one-dimensioned picture as in electron diffraction. In practice, perfect transmission of structural information is not achievable and current high resolution images are significantly degraded maps of the electron density of the specimen. The problems arise from aberrations in the electron optical imaging system and from the difficulties inherent in unscrambling information from a projection of the atomic density over the thickness ( « 4 nm) of the specimen. Abberations in the objective lens of the microscope limit faithful imaging to waves scattered through angles, 9 to the optic axis that lie within "windows" where phase contrast is effective. Specifically, a so-called "contrast transfer function", T(Q), can be defined in terms of 6 and therefore Q, with the effect of an instrument response function. This function can be positive or negative (implying contrast reversal) and good imaging corresponds to a range in Q for which T(Q) has a relatively large and constant value (see Fig. 4-15). T(Q) for modern high resolution electron microscopes is large at moderate angles, corresponding to Bragg scattering from lattice planes with Q in the range 5 to 30 nm" 1 and interplanar spacings of about 1 to 0.2 nm. For Q values greater than this, the CTF passes through zero (with zero transmission of information, therefore) and then becomes oscillatory and this defines an effective resolution limit. Effects of beam convergence, chromatic aberration, incoherence etc. also limit the resolution to about 0.15 nm. The effects of the above are that a HRTEM image is only a partial representation - and in many cases a "scrambled" representation, at that - of the projected

Specimen periodicity (A) 2010 6 U 3 2 1.5 i

1 1 1

1

i

•

i

1

1 /

•

-

\

/ / /

C3

/

T 0

"

b)

J

L/ v/ J X /

\

/

a) /

V

\

\

f

31-

A

\ V s \ ________ f-A /' J! / \ t<'' 2 --

i \ \ \ — V- —

•,%

to

_

_

_

_

_

' \ / \ /- * / \

_

\

\

>

•

i

1

Figure 4-15. a) Contrast transfer functions, T(Q), for 100 kV microscopes (dashed line) and 500 kV (full line) corresponding to a generalised defocus value of 3 1/2 . b) Structure factors for a-Pd4Si taken from neutron scattering data (full line) and X-ray data for a-Ge (dashed line) (Gaskell et al., 1979).

specimen potential and electron density. In terms of the interference function, i(Q), high resolution images contain information limited to the first peak in i{Q) for amorphous semiconductors and only the best microscopes have resolution extending to the first peak for amorphous metals, which have smaller d-spacings. With modern high resolution microscopes, the problems are no longer severe for the majority of amorphous solids with relatively large d-spacings. However, much of the older work in the literature needs to be treated with caution due to neglect of the effects of the aberrations in 100 keV microscopes operated at or beyond their limits of resolution.

212

4 Models for the Structure of Amorphous Solids

The second problem arises as a result of the effects of projection. Since the electron wave-function immediately after the specimen is a projection of the specimen potential over a column which is the thickness of the specimen, it becomes impossible to distinguish atoms that are, say, nearest neighbours, from those that appear to be at the same projected distance but in fact lie at the upper and lower edge of the foil and are thus separated by about 4 nm in the z direction. Moreover, ordered regions giving coherent Bragg diffraction, are unlikely to be larger than 2 nm in size so that there is at least as much material contributing information to the image which is either ordered but not Bragg orientated, or from a random matrix. The non-Bragg oriented material therefore contributes noise which significantly degrades the image. In practice, there is a third problem due to inelastic scattering which is especially prominent at low scattering angles and can submerge the coherently scattered electron intensity and thus further degrade the image. As a result of these problems, HRTEM has proved to be of only limited use in establishing the short-range structure of amorphous solids. It is important to recognise, though, that when the technique is used to complement diffraction studies, the information gained concerns the medium-range structure in the range 1 to 2 nm where diffraction methods are relatively powerless. Examples of the use of HRTEM will be discussed in Sec. 4.5.

4.3.8 Nuclear Magnetic Resonance In a strong applied magnetic field, Ho, the degeneracy of nuclear spin states is removed (Zeeman interaction). For nuclei with spin, /, the difference between the en-

ergy levels is given by:

E(m) = yhmH0

(4-27)

where, y is the gyromagnetic ratio characteristic of the nucleus and m is the magnetic quantum number. Application of exciting radiation results in a transitions between states with quantum numbers that differ by Am= ± 1, and the frequency at which this transition occurs depends, through y, on the excited nucleus. NMR is thus an element-specific structural technique. Sensitivity to the local environment of the nucleus comes from electrons near the nucleus which, by their motion, create small magnetic fields that add vectorially to // 0 , so modifying the local magnetic field at the nucleus. The nucleus can be said to be partially shielded from the external field by the electron distribution of the atom which, in turn, is determined by bonding interactions with neighbouring atoms. Since the electron distribution is, in general, non-spherical, the interaction is orientation-dependent, represented by a shielding tensor, a; the isotropic component being represented by the "trace" of the tensor: a{ = 1/3Tr(d) = 1/3(tT±1 +
4.3 Experimental Structural Techniques a)

Zeeman

-1/2 -

Chemical shift anisotropy

213

b)

T

Na 2 Si 2 0 5

1/2 < i

.

|

i r i T—y .

,

,

, ,

,

,

, ,

-50 -100 -150 -200 Parts per million from TMS

c)

d) Na2Si205 SSB

Rotation axis

CB

Flutes SSB

Sample rotor

Magic angle R.f. coil

Driving gas 1

I

T

Stator

-50 -100 -150 -200 Parts per million from TMS Figure 4-16. a) Energy levels for a nucleus such as 29Si with spin, 1 = 1/2 in an external magnetic field, HQ. The nuclear Zeeman splitting and the effect of chemical shift anisotropy are shown, b) The broad "powder" line-shape for sodium disilicate due to anisotropic chemical shielding, measured as the shift in parts per million (ppm) from the corresponding line for tetramethyl silane (TMS). c) MASNMR spectrum of Na 2 Si 2 O 5 showing the splitting of the spectrum into the resonance line (CB) at about 97 ppm and spinning side-bands, SSB. d) Magic angle spinning (schematic) (Oldfield and Kirkpatrick, 1985).

quencies (and including other interactions - nuclear dipole-dipole and nuclear quadrupolar interactions, for nuclei with / > 1). The result is therefore a broad spectrum with structural information contained in the shape of the distribution. Interpretation of such broad line spectra has allowed the composition-dependence of the various boron oxygen species to be identified in alkali borate glasses (see Sec. 4.7.4.1). In liquids, where rotational motion occurs on a time-scale faster than the characteristic time-scale of the NMR frequency, the anisotropic interactions are averaged

out leading to very narrow peaks corresponding to the frequency associated with the isotropic part of the chemical shift interaction, G{. For solids, similar effects can be achieved by spinning the specimen at a frequency, co, of the order of the peak breadth (a few kHz) at an angle 6 to Ho. This causes the anisotropic interactions to be multiplied by a term 3 cos2 0 - 1 , which equals zero for 0 = cos" 1 (3~ 1/2 ) = 54.74° the "magic angle". The effect of magic angle spinning is to cause the broad powder resonance, shown for 29Si in Na 2 Si 2 O 5 in Fig. 4-16b to collapse into an underlying frequency related

214

4 Models for the Structure of Amorphous Solids

to (ji? and spinning side-bands associated with time-dependent terms in the various interactions. The true resonance (CB), at about 97 ppm in Fig. 4-16 c is independent of the spinning speed, the side bands are not. In favourable compounds, the lines are sufficiently narrow in relation to the frequency splitting associated with different bonding arrangements around the excited atom, that the species present can be quantitatively analysed (see Sec. 4.7.4.2 and an excellent review by Kirkpatrick et al., 1986).

4.4 Modelling Techniques In this section, a brief account is presented of computational methods for production, refinement and testing of atomic models for amorphous materials. References to the literature will suffice to direct the reader to examples of the major computational "experiments" and further details will emerge in Sees. 4.5 to 4.7. The subject conveniently divides into three sections - construction of the model, refinement and validation. 4.4.1 Construction of Atomic Models for Amorphous Solids

Perhaps the most difficult - certainly the most tedious - part of the modelling process is finished when a structural idea has been translated into a set of atomic coordinates in a computer. Ideally, generation also should be the preserve of the computer but increasingly, as models become more sophisticated, algorithms contain some form of human guidance - either actually through a physical model or implicitly through the construction algorithm. At the outset we should question the need for atomic models. After all, most structural information represents a one-di-

mensional average over 1020 or more atomic centres and, possibly, over the environment of several atomic species. What is to be gained by an approximate fit to these data by a model in the form of a finite cluster of atoms? Several answers to this question occur. Firstly, once a 3-D model has been constructed that is compatible with X-ray diffraction data, for instance, it is then possible to use the coordinates to calculate other properties - elastic moduli, vibrational spectra, optical properties - information that is not contained in the X-ray data and which would be difficult or impossible to calculate otherwise. Secondly, it becomes possible to compare the information contained in the results of two or more different types of experiments by reference to an atomic model that eventually can be adjusted to fit both datasets. In this way the amount of structural information is multiplied. Perhaps the most important factor is that a 3-D atomic model allows a rather complicated series of packing or connectivity constraints to be incorporated into the model - constraints that might be difficult or impossible to formulate otherwise. The fact that atoms cannot occupy the same region of space introduces constraints - involving rules that are not easily expressed analytically. Space-filling random structures encapsulate packing rules expressed through topology rather than geometry, and homotopy groups describe the connectivity rather than space group symmetry, as pointed out be Rivier and Lissowski (1982), Rivier (1983). Similarly, connectivity relationships in directionallybonded systems - especially the provision of particular fractions of ra-membered rings - can be incorporated in atomic models but, except for near neighbour correlations, become too clumsy otherwise.

4.4 Modelling Techniques

Finally, there is a sense that juggling atoms in a computer comes close to the processes that nature adopts to "choose" a particular structure. 4.4.1.1 Physical Models In the early history of the subject, almost every model was hand-built. Notable pioneers were Bernal (1964), Scott (1960) and Finney (1970). For network glasses, probably the most influential random model has been Bell and Dean's (1972) "ball and stick" model for SiO 2 , although Evans and King's (1966) work on the same material has historical precedence. Coordinates were established by metrology and properties then calculated by "digital" computation. Models of a similar kind for amorphous tetrahedral semiconductors were produced - notably by Polk (1971) and for a-Si:H by Mosseri and Dixmier (1981). In later work, computer algorithms enter at an earlier stage - physical models were used to establish the topology in a polytetrahedral model of a-Ge and to ensure close packing in models for amorphous TM-m alloys, the detailed coordinates then being computed from the topology of the physical model. The domain model of Dubois et al. (1985) for these amorphous alloys also started with a physical model. Until recently, there seemed little alternative for structures of some complexity but the advent of molecular graphics packages now offers real prospects of advance. Many hand-built physical models are clusters of no more than a few hundred atoms so that a high proportion lie near the surface. Apart from the problem of excluding underbonded surface atoms in subsequent calculations, near-surface atoms have additional degrees of freedom

215

not possessed by those comprising the interior. The problems of "imbedding" cluster models have been reviewed by Finney (1977). One alternative is to construct models with periodic boundary conditions. A rare example of a hand-built random model with periodic boundary conditions was the 61-atom cell constructed by Henderson in (1974), and more recently by Guttmann and Rahman (1988). Although periodic models are routinely constructed by Monte Carlo and Molecular Dynamics algorithms, physical models with periodic boundaries remain a rarity. 4.4.2 Molecular Dynamics The subject has progressed some way since the pioneering days of Alder and Wainwright (1959). Typically, the procedure involved construction of an initial starting structure - a random collection of atoms or a crystal structure - inside a periodic cubic box. Atoms are allowed to move under the action of an assumed potential energy function and Newtonian equations of motion are solved over time slices of the order 10~ 14 to 10~ 15 s. (See, for example, Soules (1990).) A typical example of a recent investigation is that of Vashishta et al. (1989 b) on a-GeSe2 in which the authors assumed an effective two-body potential involving a Coulomb term, charge-dipole interactions and steric repulsions. The motion of 648 atoms was followed over time steps, Af = 5 x l O ~ 1 5 s in a cubic box of side 2.75 nm, adjusted to provide agreement with the experimental density. The system was equilibrated at 1100 K for about 3 x 104 At and the properties average over a further 3.6 x 103 At to provide structural properties for liquid GeSe 2 . The glass is simulated by progressively reducing the particle velocities over about 3 x 104 steps (corresponding to a

216

4 Models for the Structure of Amorphous Solids

2 0 Ge-Se _

12 10

Figure 4-17. Partial pair correlation functions, ga/?(r), for two simulations of a-GeSe2 at 300 K using a) a two-body potential; b) a potential including three-body terms. Coordination numbers are indicated (Vashishta et al. 1989 b; Vashishta et al., 1989 a).

8 r6 i

4 2 0 2 0 0 a

4

8 r(A)

12

0

quenching rate o f 5 x l 0 1 2 K s 1 )to values corresponding to T
4

8

12

has been reported by Stillinger and Weber (1983, 1985). The configuration generated by MD at any temperature is energy-minimised, using a steepest-descents algorithm and the resultant "mapping" of the initial configuration onto the nearby potential minimum produces a pronounced enhancement of all the structural features, Fig. 4-18 a, b. Apart from the obvious interpretation that the configuration has

9 2

Figure 4-18. a) Pair correlation function, g, for a MD simulation of liquid Si at a reduced temperature, T* = kBT/s = 0.0817 where s is proportional to the cohesive energy, b) The corresponding function obtained by allowing the liquid configuration at T* =0.0677 to settle to an energy minimum giving the "inherent" pair correlation function for liquid Si. The higher temperature structure for a liquid at T* = 0.1492 relaxes to essentially the same configuration. Stillinger and Weber (1985).

217

4.4 Modelling Techniques

been allowed to eliminate high energy unstable local bonding arrangements, Stillinger and Weber point out that mapping of liquid MD configurations at various temperatures leads to a relatively small set of underlying (temperature-independent) "inherent structures". That is, the temperature-dependence of pair correlation functions in simple liquids consists of variations in "vibrational" displacement away from potential minima; not in substantial shifts from region to region of configuration space, corresponding to other groups of potential energy minima. This procedure, involving potential energy mapping and averaging over a number of local configurations belonging to different potential energy minima, has been used to effect in simulations of metallic glasses by Hafner and co-workers (e.g. Hafner, 1988).

of a Coulombic (first term) and a repulsive (hard sphere) term. The BMH potential has been used extensively in MD simulations for covalent solids with the long range Coulomb term summed using Ewald's method. For amorphous semiconductors, a potential proposed by Stillinger and Weber (1985) has proved popular. This consists of a mixture of two- and three-body terms: (4-30)

where i is the index of one of N identical atoms. Neglecting the single particle potential terms, V1(r), the interaction can be expressed in terms of the pair and triplet functions, V2(r) and V3(r). For Si, Stillinger and Weber introduce the functions V2(r) and V3(r) in the form:

4.4.3 Potential Energy Functions Given adequate potential energy functions, molecular dynamics simulations could provide an entirely adequate description of the complexity of structure generation and the transformations involved in quenching from the melt. Many MD calculations - particularly the early ones - necessarily used simplified potentials. Woodcock etal. (1976) employed a Born-Mayer-Huggins potential:

•exp[(r-a) ']

V2(r) = 0

\

J r>a

(4-31)

Where e is an energy unit and a is a cut-off radius and r is a reduced radius. V(ri9rj9rk) = s[h(rij9rik, 6jik) +

^2)

+ h(rji9rjk9 9ijk) + h(rki9rkj9 6ikj)] Here 9jik is the angle at i between r>} and rk and h is given by:

b+ 7(rik-ay1] • exp

L

Q J

(4-29)

where za is the electronic charge on an atom of species a, n is the number of outer shell electrons, a is a distance parameter characteristic of the ionic radius and b and Q are constants. The function thus consists

(cos 0jik +1/3) 2 (4-33)

for rij9rik< a, otherwise h = 0. The effects of introducing three-body terms in simulations of covalent systems are pronounced. Most simulations of amorphous elemental semiconductors, oxides and chalcogenides are unrealistic in

218

4 Models for the Structure of Amorphous Solids

a)

b) i

» Expt. 108AK — MD

2 — ~

1071 K

i

i

Liquic

T = 1070K

A

1 -

"

o^-

w <

a)

' ' I I I 2 -

I

I

I

1

Glass

1

1

T=300K

-

JL

1 _ t

8

12

16

20

U

i

.

i

.

i

.

8

12 Q (A"1) Figure 4-19. Comparison of experimental and computed total neutron structure factors S(Q) for a-GeSe2. Computer data was obtained using a) a two-body potential function and b) a Stillinger-Weber potential including three-body terms (Vashishta et al. 1989 a, b). Q (A"1)

that distortions are significantly greater than experiment: bond angle distributions are generally much broader with a high proportion of atoms with unexpected valence and ring sizes. Figs. 4-17 b and 4-19 b show the improved agreement between computed and experimental static structure factors for a-GeSe2 obtained by Vashishta et al. (1989) using three-body terms of the Stillinger-Weber type compared with pairwise functions of Vashishta etal. (1989). For amorphous metals, the simplest potential energy function is a Lennard-Jones function: >.-=4eiy

'•-Rfj)

(4-34)

where -t is the potential of the ith atom and Rtj is a reduced distance; R(j = 2'1/6Rfj/riJ, where Rfj is the equilibrium internuclear distance and ri-J is the actual distance between atoms i and j . Hafner, in an extended sequence of investigations on metallic alloys has calculated interatomic forces on the basis of

pseudopotentials, see for example Hafner (1980, 1986). Energy minimisation techniques applied to elemental semiconductors and oxides often assume a Keating potential (Keating, 1966) that is computationally simpler than a valence potential. This consists of bond stretching and bending terms:

3a 3($

>rik~r20 cos 90)2

(4-35)

where a and p are stretching and bending force constants, r0 and rtj are the equilibrium and actual internuclear distances between atoms / and j and 90 is the equilibrium angle jik. Lapiccirella et al. (1984) have introduced a more sophisticated version of the valence force-field - the LipsonWarshel PE function, in calculations of the structure and properties of a-Si and a-Ge (Tomassini et al., 1987).

4.4 Modelling Techniques

Molecular dynamics simulations using empirical potential energy functions have the drawbacks noted above. A method for removing this difficulty has been proposed and applied by Car and Parrinello (1985) and coworkers. In this approach, the interatomic potential is derived from the electronic ground state of the system calculated with accurate density-functional techniques. Specifically, the sets of atomic coordinates and electronic wavefunctions of the occupied states are both considered as dynamical variables, governed by equations of motion for electron and nuclei. The minimum energy state is obtained by following the "motion", as the temperature is reduced, by a process described as "Dynamical simulated annealing" to compare with the "simulated annealing" method of Kirkpatrick et al. (1983) (using MC formalism). The method is effectively parameter-free so that such ab-initio calculations can describe the "true" structure of an amorphous material given only the electronic properties of its atoms. Applications to aSi and a-C are considered in Sec. 4.5.

4.4.4 Energy Minimisation Models constructed by hand or by various computer algorithms lack realism in that bonds are strained, broken, or the coordination numbers are unrealistic. By calculating the potential energy - essentially the elastic strain energy of the structure and the gradient, atoms can be moved in directions that minimise the energy. After a relatively small number of iterations the model settles into the potential energy minimum in the local region of configurational space corresponding to the starting structure: the model becomes "relaxed", implying an increase in geometrical order.

219

The extent of topological ordering depends on the detailed algorithm. The method embraces a number of minimisation algorithms. A popular and easy method is the steepest-gradients method which involves calculation of the energy and the force on each atom. Each atom is then moved either a distance proportional to the force or to an estimated position of minimum energy (Steinhardt et al., 1974). Another method is the so-called "conjugate gradient" method which attempts to find the minimum in configuration space by searching in orthogonal directions at each iteration. Like MC calculations, the potential energy functions and derivatives are reasonably simple to compute so that with the Keating potential energy function the method is computationally cheap. Various sophisticated potentials have been devised for silicon, and carbon compounds and are only marginally more difficult to deal with.

4.4.5 Monte Carlo Calculations Models may also be generated and refined using variations of the Metropolis Monte Carlo method. An initial, essentially arbitrary starting structure is chosen usually with periodic boundaries. An atom is selected at random and given a randomly chosen displacement. The state of the system, as characterised by the energy or the fit to an experimental variable such as the structure factor, is then tested. The move is accepted if the goodness of fit is improved, rejected if not. A variant is that the move may be accepted according to a Boltzmann probability, exp(— AE/kBT) where AE is a measure of the goodness of fit - the decrease in energy, say, and kBTis a suitable scaling factor. Thus the algorithm allows the system to explore con-

220

4 Models for the Structure of Amorphous Solids

figurations that initially may be unfavourable, so that the procedure helps to prevent the model becoming trapped in a local minimum of configuration space. The process is repeated until the fit to experiment is judged to have converged. The method has been used extensively in constructing models for amorphous metals, chalcogenides, amorphous semiconductors and oxides. It has the advantage that a relatively large number of configurations can be explored quickly and cheaply in computer time. Moreover, it is generally possible to use more realistic potentials so that difficulties introduced by pairwise potentials have not been so prominent in MC as in MD simulations. McGreevy and Putztai (1988) have revised a method similar to that used by Renninger et al. (1974) in which the criterion for guiding the approach of the MC computation is the quality of the fit to experimental scattering measurements alone. The energy is not considered. The authors point out that the amount of information normally extracted from experimental diffraction data is generally small and that a fitting procedure offers a more detailed idea of the real 3-D geometric structure. The authors are clear that while it appears that a 3-D structure has been extracted from 1-D S(Q) or G(r) information, this is strictly impossible and that the final structure is only one (of many, perhaps) that is consistent with the data. Evans (1990) has commented on the apparent contradiction that higher order functions such as the three-body distribution should be obtainable from structural knowledge that contains no more than pairwise information (see Sec. 4.3). Evans points out that a simulation could succeed for an amorphous solid for which the atomic forces are describeable solely by a pairwise potential. For materials with sig-

nificant three-body terms in the PE function, such as the covalently-bonded amorphous semiconductors, this need not be so. Although the pair distribution function, g(r), depends on three-body terms, this dependence is insufficient to determine, uniquely, any higher order correlations. If two- and three-body terms are present in the PE function then experimental g (r) and triplet correlation functions would be necessary. 4.4.6 Validation of the Model: Calculation of Microscopic and Macroscopic Properties

Given a complete set of atomic coordinates, it is then possible to calculate microscopic properties such as G(r), S(Q), or S(Q), even S(Q, co). With further assumptions, vibrational and electronic densities of states functions can also be computed as described below. Macroscopic physical properties are also accessible - density, enthalpy of crystallisation, free energy, entropy, elastic moduli, gas solubility, diffusivity etc. These are often neglected or deemphasized when checking the validity of a model, which is generally a mistake. It comes as a surprise to find that a simple property like density is sensitive to structural details that appear to evade comparisons with microscopic properties - particularly when the latter are used in a qualitative or semi-quantitative fashion. An accurate fit to the experimental density should be seen as an essential prerequisite for further consideration of the model, and failure to agree should lead to its demise. Density values may be built into a simulation as a constraint. When this is done, it follows from the foregoing that it is a rather strong constraint. The most useful properties are probably G(r) and S{Q\ combined with density and heat of crystallisation data. For reasons

221

4.4 Modelling Techniques

discussed earlier, the information content of partial pair correlation functions and partial structure factors is so much greater than that contained in the total functions, that the former provide the most discriminating test of a structure model. For polyatomic materials, even models that are radically different produce adequate fits to S(Q) or G(r) - especially when experimental data is measured to low values of Q. Only by examination of the detail of these functions can differences be discriminated.

pulsed neutron sources), multiple scattering introduces low Q limitations also. The result of terminating S(Q) at g max leads to convolution of G{r) with a peak shape function so that a ^-function in G(r) is transformed into a broadened peak with side lobes - so-called termination broadening and termination ripple (see Fig. 4-20). Thus a

^ || 2 V y a *

is replaced with: 4.4.6.1 Bond Length Distributions

Successful models must reproduce the details of each of the bond length distributions, that is, not only the interatomic distance corresponding to the peak and the integrated area leading to the coordination number, but the shape of the distribution as expressed through higher moments: standard deviation and (possibly) asymmetry (kurtosis). Such parameters are important structurally and represent valuable diagnostic information. Microscopic parameters computed from models and those derived by experiment must be compared in detail, as indicated above, and using equivalent data. Early models were relatively crude and thus the two data sets were compared only superficially without proper regard for equivalence. However, the efforts of a number of authors such as Wright and Leadbetter (1976) have emphasized the proper treatment. A major problem arises from the fact that experimental data are generally limited in reciprocal space. X-ray and neutron diffraction S(Q) data are often limited to values of Qmax in the region of 200 nm" 1 and whilst EXAFS data can routinely be extended to higher values (as can X-ray and neutron data with synchrotron and

a

p

0

(4-36)

where P*p(r-r') is a peak shape function given by: Pa%(x) = M(Q)cos(Qx)dQ (4-37)

E GO

o

-0.2 1

Figure 4-20. Experimental difference distribution function GCa (r) for a calcium silicate glass (bold line) and a fit to the data to about 0.5 nm (upper dashed line). The latter has been convoluted with a SINC function to compare with experimental data. The underlying (unconvoluted) sum of gaussian functions is shown by the lower dashed line. This function has more information, since the termination smearing is absent but is only one of the possible fits to the experimental data (Eckersley et al., 1988).

222

4 Models for the Structure of Amorphous Solids

Here M(Q) is a modification function (see Sec. 4.3.3). For X-ray and neutron diffraction this could be a step function, M ( 0 = 1, for Q < Q m a x , and M(Q) = 0 thereafter, or some smoother function such as the exponential function. For neutron scattering where the atomic scattering lengths are Q-independent, or for X-ray scattering in those cases where the ratios fa{Q)ffi(Q)/Kf>\2 are essentially g-independent for all a and /?, then: P«%(x) = c*°^2 K\\U/\

TM(Q)cos(Qx)dQ o

(4-38) If M (Q) is a smooth function, it may be possible to replace P*p (x) with a gaussian,

(2nr1/2exp(-x2/2a2)

with a = l.6/Qmax

for approximate work. For accurate comparison, a convolution of the model G (r) is necessary before comparison is made with experimental realspace data. Even analysis of the experimental data to obtain parameters such as the first, second and higher coordination numbers and associated mean bond lengths and G values requires care. Although the coordination number can be obtained approximately from an integral: jG aj3 (r) n

where r1? and r2 represent the "limits" of the peak, such limits cannot be defined accurately - especially if termination ripple is present and peaks overlap. A better method involves fitting the experimental data with a series of gaussian peaks (say) convoluted by P*p (x). Once this has been done, the set of gaussians (unsmeared by the peak shape function) is narrower and may be more representative of the structure. Thus where available, this function should be quoted. An example is shown in Fig. 4-20 from recent investigations of Eckersley et al. (1988) on a-CaSiO 3 . Convolution by a peak shape function and the resulting smearing thus represents

some degradation of the structural information and efforts have been made to minimise the impact. One solution is to compare computed and experimental data in reciprocal space so that problems of termination broadening of the g-space data are circumvented. However, unless the model is large, with a radius greater than about 1.5 nm, truncation of the r-space data leads to a convolution of computed reciprocal space data with another peak-shape function. Ideally comparison of models with experiments should be made in both Q- and r-space since although they both contain the same information, certain features such as the first sharp diffraction peak, may be more evident in one than the other. Konnert, Karle and coworkers and others have attempted to devise methods to reduce the impact of termination at Qmax. Their treatment is based on the fact that if Qmax is reasonably large - say 150 nm" 1 for oxide glasses - then only the first one or two interatomic correlations are sufficiently sharp in r-space to contribute to S(Q) near Qmax. If the contribution from these peaks to S(Q) is removed, then Qmax c a n be set to infinity for the remainder with no loss in accuracy. Since the result is obtainable only by fitting the experimental data for the first few peaks, it represents a nonunique solution and lacks some of the objectivity of the Fourier transform. The choice of the fitting algorithm clearly biases the results and a question arises as to the most appropriate choice of function. Recently, the claims of maximum entropy techniques in this field have been enhanced by several workers. If experimental data is fitted by a procedure that maximises the (information) entropy, then this set of choices represents the least biased (maximally non-committal) choice. Wei (1986) has shown that experimental neutron scat-

4.5 Elemental Tetrahedral Semiconductors

tering data for a-Ni 64 B 36 (Cowlam et al., 1984), analysed using a maximum entropy technique provides more informative data in real space than the fourier transform technique (Fig. 4-21). This would be expected for most fitting algorithms - the advantage of the Maximum Entropy technique is that it allows an objective (unbiased) choice of one of the manifold of possible solutions that could fit experimental data. The use of ME techniques in extraction of partial distribution functions in a ternary Ag-Ge-Se alloy has been demonstrated by Westwood and Georgopoulos

223

(1989). In this case the data was from Xray anomalous scattering measurements at two energies at each of the K-edges of all the elements. 4.4.7 Calculation of Dynamical Properties

From the coordinates of an atomic model and an assumed PE function, the vibrational density of states function can be calculated. Description of the various computational techniques lies beyond the scope of this review and a brief list of references giving an entree into the subject must suffice. Vibrational frequencies are obtainable directly in a MD simulation - see for example Hockney and Eastwood (1981). A popular and efficient method for calculating the phonon states of a cluster is the "recursion method" reviewed in Heine et al. (1980). A similar method is the "equation of motion" method (Beeman and Alben, 1977). Electron states can also be calculated by the use of these techniques (Heine et al., 1980).

4.5 Elemental Tetrahedral Semiconductors

Figure 4-21. Reduced radial distribution function, G (r) for 58 Ni 64 B 36 obtained from the neutron scattering data of Cowlam et al., 1984 by fourier transform (FT) (a, c) and maximum entropy (ME) methods (c? d). Km is the maximum value of 4 n sin djX in the dataset (Wei et al., 1986).

Of all amorphous solids, silicon and germanium are perhaps the most extensively investigated. Recently, interest has mounted in a a third element - carbon - although this is not strictly a tetrahedral material the extent of tetrahedral bonding is variable and as yet, inadequately defined. The three materials have important properties - Si and Ge are semiconductors and, like the crystalline elements, can be doped to provide a range of useful electronic properties. Carbon, in its diamond-like form, can be very hard and has useful properties

224

4 Models for the Structure of Amorphous Solids

as a damage-resistant coating and as a dielectric. Each can be prepared as an alloy with other elements - notably hydrogen. Indeed, some contamination with H is difficult to avoid but, more importantly, deliberate alloying with H decreases the number of energetic defects such as 'dangling bonds' thus improving optical and electronic properties. In this section, we concentrate on the structure of the essentially pure elements, recognising that H may be an almost unavoidable impurity. A recent review by Elliott (1989) extends the subject to alloys of Si containing large amounts of H and other elements. With the exception of amorphous carbon, there is no paucity of good experimental, data for amorphous semiconductors. The most complete data is for a-Ge and, since there are strong qualitative similarities between the results for all the Group IV elements (and their alloys) we concentrate on data for a-Ge and introduce deviant behaviour as appropriate amorphous carbon being the most important case. 4.5.1 Amorphous Ge and Si 4.5.1.1 Local Structure - Diffraction Data X-ray data for several specimens of aGe has been reported by Temkin et al. (1974) (see Fig. 4-4) and Kinney (1976). Neutron scattering data was obtained by Etherington et al. (1982) from the specimen of evaporated Ge used by Kinney. A small amount of H was observed (indirectly). Results of this work are shown in Fig. 4-22 as the experimentally-derived correlation function f (r) and the authors' best estimate of the true correlation functions t(r). The latter function was obtained by subtracting the contribution of the first peak (in r-space) to the reciprocal space data, Q(S(Q) — 1). This gives a reciprocal

Figure 4-22. Experimental correlation function (full line) t'(r) = 4n rg{r) for a-Ge, together with Etherington et al.'s (1962) estimate of the true correlation function t(r) (dashed line) obtained as a fit to the experimental scattering data.

space function that has effectively reached an asymptotic value below Qmax, so that fourier transformation is possible without any truncation effects. The overall tetrahedral nature of the material is confirmed, with = 0.246 3 nm (0.2450 nm for c-Ge) although the first shell coordination number, 3.68, is less than the expected value. Second shell coordination numbers depend on the assumptions made in fitting the second peak around 0.395 nm but a figure below the value of 12 expected for a fully-coordinated network is likely. Deviation from fourfold coordination is ascribed to broken bonds associated with voids etc. A notable feature of the structure of a-Ge and a-Si is the small disorder-induced broadening of the first neighbour distance. For a-Ge, the static broadening parameter o\ amounts to 0.0074 nm. By contrast, the static breadth of the second peak is much larger, as2 = 0.026 nm, indicating that the disorder chiefly introduces variations in the bond angle of about a (6) = 10° from the mean tetrahedral angle. Current data

225

4.5 Elemental Tetrahedral Semiconductors

for a-Si is less accurate but results from X-ray and electron diffraction techniques on a-Si: H alloys suggest values of the first coordination number less than four and that the second coordination number is less than 12. For instance, Schulke (1981) finds = 0.2363 nm,
2.5

~~T~

2.0

a)

1.5

S 1.0 2 0.5

I 2-°

«_ £ i.o 0.5 0

2.34 A

'W

•2 0 £2.5 o

0

7

k 6 Radial coordinate (A)

Figure 4-24. a) Fourier transform of the EXAFS data, k2 x (fc), for a-Ge: H from 30 < k < 140 nm " 1 . b) Similar transform for c-Ge (Bouldin et al., 1984).

10 Figure 4-23. Partial pair correlation function, g (r), for a-Si: H obtained by H/D substitution (Bellissent et al., 1985).

Both a-Si, a-Ge and their hydrogen alloys have been thoroughly studied by EXAFS techniques. An example is the work reported by Bouldin et al. (1984). They measured the EXAFS spectrum for specimens of a-Ge that were nominally free of H and samples with around 5 6 at. % H. The fourier transform of the resulting data for the pure material (Fig. 4-24) shows a sharp peak corresponding to the first neighbour distance which is almost identical to that for c-Ge and the coordination number is 4.0 to within a few percent. In contrast to the data for crystalline germanium, Fig. 4-24 b, information on second- and higher-neighbour peaks is almost indistinguishable from the noise in the transform as Fig. 4-24 a indicates. This is the result of the limitation of

226

4 Models for the Structure of Amorphous Solids

the data analysis procedure to values of the photoelectron wave-vector, k, greater than about 30 nm" 1 , where the effects of multiple scattering are not too large, as discussed in Sec. 4.3.5.5. The Debye-Waller term, Qxp(-2a2k2) in Eq. (4-24) has the values 0.24 at £ = 30 nm" 1 (with o2 = 0.028 nm deduced from Etherington et al., 1982) and only 0.08 at £ = 40 nm" 1 where the contribution of x(k) (weighted by a smooth windowing function) is significantly greater than zero. Information on second and higher-neighbour peaks is thus very difficult to obtain from the extended spectrum. On the other hand, the presence of the second-neighbour peak in the fourier transform can be used as a diagnostic test of partial crystallisation, as shown by Evangelisti et al. (1981) and by Menelle etal. (1986). Nonetheless, a signal due to second neighbours is present in the experimental data and recent work by Mobilio, Filipponi and coworkers has shown some progress in extracting this information. For example, Mobilio and Filipponi (1987) show that a weak higher neighbour signal can be extracted from accurate experimental x(k) data using the regularised least squares fitting procedure proposed by Babanov et al. (1981). In this way they reproduce the first and second peaks in g(r), extending to about 0.5 nm. In more recent work (Filipponi et al., 1989), the contribution to the EXAFS signal of a-Si arising from the first peak in g(r) is subtracted from the experimental data and the residual signal can then be analysed in terms of single and multiple-scattering terms from higher neighbours, Fig. 4-25. In fact, the residual signal cannot be satisfactorily analysed unless multiple scattering is included. The r-space feature corresponding to the difference signal occurs not at the position of the second peak as would be

Figure 4-25. Multiple scattering contribution to the XAFS signal in a-Ge. Each contribution is labelled by the number of atoms involved in the scattering event and the degeneracy. Thus, #3A 12 represents a wave emitted from the origin and scattered by two further atoms. There are 12 such paths in a fully bonded tetrahedral network (Filipponi et al., 1989).

expected, but at the position of a third neighbour in c-Si. Filipponi et al. show that this is the result of destructive interference between single scattering from second neighbours and multiple scattering arising from paths involving two, three, etc. scattering events, Fig. 4-25. An essential contribution to the signal comes, therefore, from paths involving a photoelectron wave emitted from an origin atom, which is then scattered by a neighbour of that atom, to another neighbour and then back to the origin atom, where it interferes with the outgoing wave, resulting in a modulation of the X-ray absorption coefficient. The importance of this type of analysis is that in addition to functions like g(r),

4.5 Elemental Tetrahedral Semiconductors

which represent the distribution of pairs of atoms, an exact fit to the EXAFS data for a-Si seems to require specification of triplet correlation functions g(r1,r2,9). The latter function expresses the probability that an atom lies at a distance rx from an origin atom, another at r 2 , with an angle 9 between the vectors to the two atoms. Clearly, this is data additional to that which can be derived directly from an analysis in terms of g (r), and this represents potentially new and valuable structural information. Another way of looking at this is to recognise that triplet correlation functions also relate to the local site symmetry, which again is not available directly from pair functions.

4.5.1.2 Local Structure - Complementary Techniques. Medium-Range Structure

Infra-red and Raman spectra of a-Si and a-Ge display the behaviour noted in Sec. 4.3.6, namely the broad double humped

227

structure, Fig. 4-26, characteristic of the vibrational density of states function, g (co) and with little resemblance to the sharp features seen in the IR or Raman spectra of crystalline materials. This is the result of the loss of translational symmetry which removes the force of the crystal momentum, k = 0, selection rule so that all modes of g(co) become potentially optically active (Sec. 4.3.6). In fact, the major features of g (co) for amorphous tetrahedral semiconductors are obtained by just broadening the density of states function for the crystal. Experimental g(co) data for a-Ge has been reported by Maley et al. (1986); Maley and Lannin (1987) and for a-Si by Kamitakahara et al. (1987). The former also made detailed comparisons with the Raman spectra of a-Ge, Fig. 4-26, which shows the close relationship between the Raman intensity and g(co) determined from neutron inelastic scattering. Dynamical structure factor data, S(Q,co) also exists for a-Ge (Maley et al. 1986) - Fig. 4-27.

Figure 4-26, Neutron inelastic scattering data (solid lines) and a) depolarised, c) polarised components of the Raman spectra for a "highly-ordered" specimen of a-Ge (substrate temperature =150 °C): b) and d) show similar data for a more disordered specimen prepared at a substrate temperature of 5 °C (Maley and Lannin, 1987). 100

200

300 0 100 Frequency (cm"1)

200

300

228

4 Models for the Structure of Amorphous Solids

Figure 4-27. Two-dimensional plot of the dynamical structure factor, S (Q, E\ of a-Ge (Lannin, 1987). O.O

High resolution electron microscopic examinations of a-Ge and a-Si have a long history. The subject was particularly active in the 1970's as a result of efforts to "see" details of the structure of amorphous semiconductors directly. The presence of microcrystallites in a-Ge was claimed by Rudee and Howie (1972) on the basis of images produced by tilted-illumination dark-field microscopy. The controversy these early results generated lead to a detailed analysis of the power - and limitations - of high resolution electron microscopy as applied to amorphous solids (see for example Cochran, 1973; Howie, 1978). Subsequently, most experimental effort has concentrated on studies using axial bright-field microscopy - as discussed in Sec. 4.3.7. Smith et al. (1981) made a careful study of foils of amorphous C, Si and Ge using a 120 kV microscope. They showed that images of thick films («10 nm) presented no structurally significant features. That is, the image appeared to be qualitatively identical to a secondary image produced by randomising the phase, while maintaining the intensity distribution (Krivanek et al., 1976). For thin foils of thickness « 3 nm, the images did differ from their phase-randomised counterparts - graphitic planes are visible in the images

of a-C, for example. Even thinner foils of a-Ge ( « 2 nm) were examined by Saito (1984). Crossed fringes were observed over an area of about 2 nm 2 with a spacing of 0.3 nm corresponding to the {111} planes of Ge. The image compared well with that simulated for a 2 nm Ge crystal with correction for the aberrations introduced by the microscope. Ourmazd et al. (1985) and Phillips (1987) re-awakened interest in the subject. The former studied relatively thin (10 nm) specimens of a-Si near the interface with a crystalline Si wafer that had been cleaned by ion milling to remove oxide or other contamination before deposition of a-Si. The specimen was examined with the electron beam parallel to the interface, so that a cross-sectional view was obtained. Near the interface, a number of ordered regions resembling microcrystallites were observed - as shown by the presence of crossed lattice fringes with a spacing corresponding to dltl for c-Si. The (photographic) images were then converted into optical diffractograms - a standard technique being to illuminate the photographic negative with a laser beam. Diffraction patterns from regions of about 5 nm in diameter were found to be exhibit sharp Bragg spots. Moreover, it was claimed that the spots

4.5 Elemental Tetrahedral Semiconductors

were orientated and in registry with the lattice planes of the substrate. Such features were observed up to 50 nm from the interface and the effect was termed the Orientational Proximity Effect - reflecting the suggestion that the submicrocrystallites in a-Ge become quasi-epitaxially orientated near the interface. In later work using a microscope with superior resolution, structurally significant features were observed less easily in the image but were nonetheless seen in the optical microdiffraction patterns. In this case, sharp "spotty" optical diffraction patterns were observed almost 8 nm from the substrate (Phillips, 1987). The picture that emerges from this work is that a-Si - which is overconstrained according to Phillips' (1979) criteria - cannot form a continuous network and the strain resulting from disorder is distributed locally as grain boundaries. Within the grain, the material adopts the more stable crystalline structure. The orientational proximity effect allows the intrinsically granular microcrystalline structure of the material to be more easily detected. 4.5.2 Amorphous Carbon 4.5.2.1 Static Properties Amorphous carbon represents a classic example for structural studies of local and medium-range ordering in amorphous materials. As mentioned earlier, carbon is an unusual element in that both trigonal, sp 2 , and tetrahedral, sp 3 , bonding is possible. Moreover, the extent to which sp 2 atoms form in clusters - as chains or "aromatic" rings, either singly or fused to give planar graphite-like sheets, and the extent to which such sheets have a parallel orientation to give laminar structure of graphitic islands - are questions to which there are only partial answers. Since structure and

229

properties are strongly dependent functions of deposition conditions, it is more sensible to talk about a hierarchy of amorphous carbon structures. "Amorphous carbon" is, in fact, a generic term for a whole family of materials with diverse structures and properties. It is usual now to refer to carbon evaporated from a carbon arc, say, at ambient temperatures as (ordinary) amorphous carbon: variations introduced by some form of energetic deposition leading to hard films and increased sp 3 content as "diamond-like" carbon. In addition, hydrogen may be introduced - deliberately or accidentally and this appears to make the films harder and more "diamond-like". A further form of non-crystalline carbon is the so-called "glassy carbon". However, it is clear that this material is extensively graphitized with very obvious parallel lattice fringes seen in electron microscopy the fringes having a spacing corresponding to the {002} planes of graphite. Diffraction data of Mildner and Carpenter (1982) confirms this. Scattering data from a-C are very limited. Kakinoki et al. (1960) measured electron scattering from arc-evaporated carbon to <2max = 27Onm~1 and found a C-C peak at 0.151 nm which lies between distances corresponding to diamond (0.155 nm) and graphite (0.141 nm). The data were interpreted in terms of a mixture model consisting of 55 to 60% of the diamond-like structure. Energy-filtered electron diffraction has been used by McKenzie et al. (1987), (see also Green et al., 1989) to obtain G(r) for a number of specimens of a-C and a-C: H. The specimens were thin foils, and measurements were made in an adapted electron microscope so that very small specimen volumes contributed to the data. McKenzie et al. observed values of the carbon bond angle ranging

230

4 Models for the Structure of Amorphous Solids

from 118 to 120° for glassy carbon and a-C:H, to 115° for evaporated a-C. The bond angle was found to be 110° for a form of amorphous carbon prepared by condensation from a plasma, generated by a carbon arc, with magnetic filtering to minimise contamination by graphite microcrystals produced as a result of the action of the arc. This latter material they refer to as "amorphous diamond". A specimen of "amorphous diamond" has been examined by neutron scattering to 2max = 165 nm" 1 by Gaskell et al. (1991). The specimen was very small (^20-30 mg) so that intensities were difficult to normalise. However, data for G(r) shown in Fig. 4-28 is very informative. The first peak, = 0.153 nm; iV=4.0±0.5; G± = 0.011 nm, indicates predominantly sp 3 bonding. However, the slight shift of the first peak from the position for crystalline diamond (0.1546 nm) could be the result of a small amount of graphitic bonding. The first peak has been modelled as a weighted sum of two gaussian distributions with centres corresponding to the bond lengths of graphite and diamond. The proportion of "graphite-like" material appears to be 10-15 %. The second peak position, 0.2517 nm, corresponds to tetrahedral bonding - the calculated C bond

angle is 110 + 1°. The static breadth of the second peak, a\ = 0.016 nm is much smaller than values for Ge (0.026 nm) - a reflection of the large bond bending force constant in carbon. The major difficulty with this work, apart from the problems introduced by the miniscule sample mass, is the uncertainty surrounding the extent of H contamination. Estimates of the concentration of H from the magnitude of the inelasticity correction, suggest 9 to 11 % H. The amount bonded as C-H must be less than this, otherwise the first coordination number would be significantly less than the value of 4, but estimates of the fraction of bonded H have proved to be difficult. Taken at face value, though, there can be little doubt that this material is largely tetrahedral carbon and is analogous therefore to a a-Si and a-Ge. Honeybone et al. (1991) have also used neutron scattering to examine a specimen of amorphous carbon containing around 30% H. The films were produced from an ion beam source using propane or acetylene. Measurements to Qmax = 500 nm" 1 allowed good real space resolution of the first C-C peak at 0.140.15 nm. This was found to be split into two components, in the ratio 1:4, Fig. 4-29. The C-C coordination number was

So

Figure 4-28. Reduced radial distribution function, G(r) for amorphous diamond-like carbon (Gaskell etal., 1991b).

Figure 4-29. G (r) for an amorphous C: H film prepared from an ion-beam source using propane as a precursor (Honeybone et al., 1991 a).

4.5 Elemental Tetrahedral Semiconductors

4.5.2.2 Excitations Work by Berger et al. (1988) using electron energy loss spectroscopy showed the presence of only a small amount of sp 2 bonded material in "amorphous diamond" thin films. Graphite has a pronounced peak at 6.2 eV (Fig. 4-30) corresponding to transitions from the highest filled valence band state to the lowest empty conduction band state (n*) and it is this feature that is absent in crystalline diamond and only barely detectable in

a)

/ . . • • • '

\

• • • • '

/A \\ \ \ A

!

b)

/ \\\\

u a

o U) >>

: i

DJ1H

2.5 + 1.0 compared to about 3.5 for a fully connected sp 3 network - after making allowance for the proportion of C-H bonds. A second neighbour shell is observed between 0.23 to 0.27 nm with a coordination number of 4.0 + 2.0. Strong C-H and H - H features are seen and inelastic scattering confirms the presence of H 2 molecules in a high pressure state (Honeybone e t a l , 1991a). EXAFS and XANES spectra for a-C: H have been studied by several workers. A recent example is that by Comelli et al. (1988). Near edge data shows a prominent 1 s -> 7i* transition which grows as the film is annealed, indicating an increasing sp 2 content. The EXAFS spectrum has been analysed to give a C-C distance of 0.1445 nm - very close to that for graphite, 0.1421 nm. Moreover, this distance remains constant on annealing. It is suggested that the film consists of a two-phase structure: a disordered graphite-like network of even- and odd-membered C-C rings and a random matrix consisting of different types of C-C bonds but with chain-like units and defects in the form of dangling bonds. The amount of the graphitic material is estimated to be 60% in the as-deposited film and to rise to over 90% on annealing at 1050 °C.

231

j {.....

"

j j >,

in

c

03

c)

:

\ \.\

i

! i

A

/

i i l\

r'l

/

\

/

d)

/

. !

/

j v..

..

/

/

' • • • • • . . . .

20

30 AE(eV)

Figure 4-30. Electron energy loss spectra for several forms of amorphous carbon: a) diamond, b) "amorphous diamond", c) graphitised carbon, d) evaporated a-C (Berger et al, 1988).

"amorphous diamond". Similar features are seen at higher energies due to transition from core state, 1 s levels to the TC* state, and the intensities of the ls->7c* transition in amorphous diamond compared to graphite was used to estimate the proportion of n states in the material. This lead to a value of 85 % sp 3 bonds - a figure with which the neutron data of Gaskell et al. (1991) agrees.

232 E

4 Models for the Structure of Amorphous Solids

OPT

1.1

3.0 eV

"Nvv 300

200

100

0 - 1 0 0

Chemical shift/ppm vs T M S

305 295 285 Electron loss energy (eV)

Energy loss spectroscopy and 13 C magic angle NMR have both been used to by Jarman et al. (1986) to examine specimens a-C: H prepared in a r.f. plasma discharge. Specimens were characterised by the value of the energy of the optical gap, Eg. NMR data and EELS data are shown in Fig. 4-31. Peaks due to the various forms of carbon are shown and the ratios measured by each technique agree to about 10%. Raman spectra for various forms of amorphous carbon give relatively little information on the sp 3 /sp 2 ratio: most specimens exhibit a broad region of scattering which stretches from frequencies below the fundamental mode of c-diamond (1332 cm" 1 ) to about 1800 cm" 1 - that is, above the frequency corresponding to cgraphite, 1550cm""1. The reason is likely to lie in the larger Raman cross-section for graphite: estimates suggest that the intensity of the 1550 cm" 1 mode in graphite is 30 to 60 times larger than that for the 1332 cm" 1 mode of diamond. Since most of the amorphous carbons contain at least 10% sp 2 carbon, the Raman spectrum principally reflects the structure of this component. Raman spectroscopy does give important indications of the extent of medium range ordering, though. Specifically, the extent to which sp 2 carbons cluster can be examined by studying the ratio of the intensities of the peaks at 1550 cm" 1 and at 1350 cm" 1 . These are related to a mode at

Figure 4-31. a) 13 C magic angle NMR spectra for three amorphous carbon films measured with tetramethylsilane (TMS) as standard. The films are characterised by their optical gaps, EOPT. b) EELS spectra for the same amorphous carbon films with the electron beam perpendicular to the substrate. The energy gaps, £ g and the ratio of n/o states derived from these spectra are also shown (Jarman et al., 1986).

4.5 Elemental Tetrahedral Semiconductors

the centre of the Brillouin zone, and a zone edge mode; the latter being inactive in a perfect single crystal with activity induced by the breakdown of ^-conservation due to disorder. The ratio of these two modes has been shown to relate to the size of graphite microcrystallites (Tuistra and Koenig, 1970): k ^(1550)

IT

(4-39)

where La is a characteristic mean intraplanar length of graphite microcrystals and k is a constant. Microcrystallisation of a-C by annealing or irradiation is easily observed by this means, therefore. The extent of clustering of sp 2 carbon is also observable through changes in the optical band gap. Crystalline graphite - an infinite cluster - is an anisotropic metal and as the graphite crystallite size decreases, the band gap increases (Robertson and O'Reilly, 1987) - as discussed in Sec. 4.5.5. 4.5.3 Network Models - Static Properties A number of CRN models for amorphous tetrahedral semiconductors were built by hand using tetrahedral units and plastic connectors. Polk (1971) produced a 519-atom model and calculated the rdf for the unrelaxed coordinates. Energy-minimised versions using a Keating potential were subsequently published by Steinhardt et al. (1974) and by Duffy et al. (1974). Beeman and Bobbs (1975) also produced a number of random models and Connell and Temkin (1974) generated a model with even-membered rings only. Models of other kinds were also produced. Grigorivici and Manaila revived a pentagonal cluster model - known as an "amorphon" - and Gaskell et al. (1977) examined the properties of a multiply-

233

twinned structure with a 14-atom diamond cubic motif. Several of these models were tested against experimental neutron scattering data for a-Ge by Etherington et al. (1982). They used the coordinates of each model and calculated the pair function T(r) = 4nrb2Q(r) with the same procedure to simulate termination smearing etc. as used in the analysis of the experimental data. Their results are reproduced in Fig. 4-32. Although most of the models produce an approximate fit to the experimental data, none is adequate in that agreement in detail is not achieved. The situation has been improved by simulations of the structure of a-Si by Wooten and Weaire (1987) and co-workers. Their approach is to start from a fully-bonded diamond cubic lattice and to arrange for certain types of bonds to be switched as shown in Fig. 4-33. Specifically, bonds that are parallel in the crystal, and almost parallel in the disordered structure, are allowed to switch. The method involves the following steps. After an exchange of a pair of atoms, the (Keating) energy is reduced after a few iterations of an energy minimisation routine. The semi-relaxed energy is calculated and the move accepted or rejected according to the probability given by a Boltzmann factor exp(—Ej kB T\ with kB T typically 1 eV, corresponding to the melting point. After a number of steps at this temperature, sufficient to give at least 0.3 bond switches per atom, the crystal structure has lost the memory of its ordered state and the temperature is then reduced progressively to zero. A large number of models have been produced by this method using variations in the heating/cooling cycles and results are quite impressive. The fit between experimental data for a-Ge and calculated values for T{r) are shown in Fig. 4-34.

234 6

4 Models for the Structure of Amorphous Solids

6

Henderson

1

1

!

1

1

1

1

1

1

Polk (500 atom) -

f

ill

U

I*

2

2

0

r\

1 "

u^

Evans

J,

» Polk (519 atom) ^

U

ro

111

< r 2

~ 2 Connell-Temkin / •

i» Steinhardt ;! (201 atom)

i

t_

r?

A2

2 0

n I

Beeman

6

0

JIJ 1

2

1

1

1

U

I

-6

r(A)

I

1

1

8 10

Figure 4-32. Distribution function, t' (r), for a series of random net- " work models (dashed lines) compared with experimental data (solid lines) for a-Ge. Etherington et al., 1982.

8 10

Somewhat remarkably it is found that, starting from the diamond cubic structure, the final annealed structure either reverts to the crystal (if the initial melting time has been too short) or to a random structure that is in very close agreement with the experimental data. This argues for the validity of the CRN model as a representation of the real structure of amorphous tetrahedral semiconductors. The method has several in-principle advantages. Not only is it simple and easy to programme but the steps are relatively transparent. Periodic boundaries can of course be used. Moreover the number of transitions over the energy barriers represented by bond switches is more than can be contemplated using MD simulations. Note also that the number of constraints on the final model is relatively large: not

Figure 4-33. Bond rearrangements between two almost parallel bonds a) before and b) after switching atoms 1 and 6 and allowing relaxation of the atoms which are embedded in a 216-atom unit cell (Wooten and Weaire, 1987).

4.5 Elemental Tetrahedral Semiconductors

— Calculated — Experiment

Figure 4-34. Comparison of the distribution function, t(r) = 4nr Q (r), for a-Si (scaled to Ge) with experimental data for a-Ge (Wooten and Weaire, 1987).

only does the model preserve tetrahedral bonding, but attempts are made to try to find a global minimum of energy and the comparison with the experimental T{r) function - even if made only at the end of the calculation - also acts as a valid constraint. In this, the method differs from Monte Carlo simulations in which often only one of these constraints is employed. A number of MD simulations of a-Si and a-Ge have been reported. Ding and Andersen (1986) devised a Stillinger-Weber potential for a-Ge: as discussed in Sec. 4.4.3, this contains three-body terms, the detailed parameters being obtained by fits to properties such as the cohesive energy, elastic constants etc. In this case, Ding and Andersen were unable to find a set of parameters that gave an acceptable fit to liquid, crystalline and amorphous Ge. Their parameters fitted the last two phases mentioned only. Calculations were performed on 216- and 512-atom clusters with the box size fixed to agree with the experimental density of a-Ge. A good fit to the experimental rdf was observed (Fig. 4-35). Ding and Andersen discussed the inability of the potential to give an adequate

235

simulation of all three phases and concluded that the cause lay with inadequacies in the potential, rather than any lack of realism in the simulation of the quenching process - due to incommensurate time-scales etc. Biswas et al. (1987) re-examined this question by investigating changes in the strength of the three-body term which constrains the size of bond angle fluctuations. Structural properties were compared with experimental data, principally the vibrational density of states function, with only moderate agreement. Luedke and Landman (1989) also used MD simulations with a S-W potential but with a slower quench rate and found that it was possible to obtain results representative of experiment either by increasing the three-body term during the initial stages of computer quenching, or by using a slower quench rate. They therefore suggest that the S-W potential may be adequate but that care is needed to reproduce the atomic transport and relaxation processes involved in (real) quenching experiments. These authors give a rather detailed comparison of the properties of their simulated model for a-Si with experimental data but agreement is not

Figure 4-35. Comparison of the RDF for a-Ge by MD simulation (solid line) with experimental data (dashed line) with allowance for the modification function used in transforming the experimental data (Ding and Andersen, 1986).

236

4 Models for the Structure of Amorphous Solids

particularly impressive. For example, the bond angle distribution is much broader than that found experimentally. Moreover, the high proportion of 3- and 5bonded atoms is difficult to reconcile with prejudice - if not with experiment. A first-principles MD calculation (see Sec. 4.4.4) of the structure of a-Si has been performed by Car and Parinello (1988). The pair correlation function calculated for a-Si was compared with scaled experimental data for a-Ge and found to be in good agreement. 4.5.4 Models for Amorphous Carbon

With a shortage of hard experimental facts, it is not surprising that the number of structural models for a-C is rather small. Beeman et al. (1984) produced a number of hand-built models for a-C, which were then energy-minimised. One model consisted of four stacked 280-atom warped sheets consisting of purely trigonal carbon atoms. The sheets were rotated with respect to each other. A second (356 atoms) contained approximately equal proportions of tetrahedrally- and trigonally-bonded atoms and was designed to test the model proposed by Kakinoki et al. (1960). A third (340 atoms) contained about 14% sp 3 atoms in the central core. In the latter two models, 5- and 7-membered rings were included and sp 2 and sp 3 atoms were randomly mixed. Computed rdfs and i(Q) data were compared with the limited number of experimental results available at that time. Agreement is poor in all cases - with significant errrors in the density. Robertson (1991) has commented that from energetic considerations, sp 2 atoms would tend to cluster and odd-membered rings should be disadvantaged; whereas Beeman et al.'s model takes no account of this.

Tersoff (1988) has constructed several 216-atom, periodic boundary models for a-C using Monte-Carlo techniques. Models were produced either by quenching from the vapour phase or from the liquid using an empirical potential energy function fitted to the cohesive energies of carbon poly types. C-C bond lengths (0.147 nm) close to graphite were found and with a coordination number of only 3.1 - about 9 % of the atoms being 4-coordinated and the bond angle distribution peaked at 120°. To try to reproduce the properties of hard carbon coatings, a simulation was performed in which liquid carbon was quenched under lOOGPa pressure. The resulting bond length was observed to be = 0.151 nm (diamond is 0.1554 nm) and the coordination number, 3.4, with almost half the atoms 4-coordinated. A broad bond angle distribution was found suggesting an overlap of peaks corresponding to sp2 and sp3 carbon atoms. Galli et al. (1989) have conducted a firstprinciple simulation of the structure of a-C starting from a 54-atom periodic cell, with a macroscopic density of 2000 kgm~ 3 . The resulting model consists of 85% sp2 sites, graphitic in nature with the remaining 15% sp 3 forming a distorted diamond-like structure. At high temperatures, sp-bonded carbons are also present but these disappear on simulated cooling and the proportion of sp 3 bonds increases. Interestingly, this simulation shows that the sp 3 sites tend to cluster and interconnect the essentially planar sp2 regions as shown in Fig. 4-36. The electronic density of states is also calculated and shows the appearance of a sharp n and n * states and broader a features (Fig. 4-37). The notion that a-C consists of an essentially granular two-phase structure with graphitic islands separated by a sp 3 matrix

4.5 Elemental Tetrahedral Semiconductors

237

O'Reilly (1987) calculated the energy of the n states in "monomeric" ethylene, through polyacetylene chains, aromatic rings to condensed aromatic rings and then a graphite layer. Calculations were also performed of the electronic density of states of the models of Beeman et al. (1984). The energy gain produced by the formation of compact fused rings is significant but it is the narrowing of the gap between valence and conduction band states (Fig. 4-38) that is particularly interesting. Robertson and O'Reilly show, Fig. 4-39, how the optical gap varies for linear and compact condensed 6-fold rings and the inset to this diagram indicates that the clusters in a-C and a-C: H are likely to contain 10 to 30 rings, corresponding to islands of about 1.5 nm. The model presented is one in which sp 2 clusters are in-

Figure 4-36. Section through the a-C network generated by Car and Parinello, 1989. a) The entire set of atoms in one MD cell Grey circle show atoms that are four-fold coordinated; black - threefold, b) Ring structures.

phase is a case most elequently made by Robertson (1986, 1991), although the proposal is an old one dating back to Kakinoki et al. (1960). Robertson's arguments are based on the energetics of sp2 bonds and the tendency to form planar ring and sheet structures, with hard experimental evidence coming from calculations of the electronic density of states and the optical band gap. Specifically, Robertson and

-20

-10 0 Energy (eV)

Figure 4-37. Electronic density of states for the model of Car and Parinello, 1989. Positions of experimental peaks are shown by arrows.

238

4 Models for the Structure of Amorphous Solids

-0.1 0.01

1

10 Number of rings (M)

100

Figure 4-39. Minimum energy gap, Eg, for compact (upper) and linear (lower) clusters of fused six-fold rings of C atoms. Inset shows probable number of rings per cluster in a-C and a-C:H (Robertson, 1986; Robertson and O'Reilly, 1987).

2

1

0 - 1 - 2 - 3 Energy (/3)

Figure 4-38. Calculated electronic energy levels for increasingly polymerised carbon atoms (Robertson, 1986; Robertson and O'Reilly, 1987).

terconnected by sp 3 bonds and it is argued that the reason for the granular structure rather than the percolating patterns of sp2 and sp 3 bonds - is related to strain. Rather than the strain being distributed randomly and thus tending to homogeneity, strain is relieved abruptly at the edges of the islands. Planar sheets have parallel n orbitals and this is adduced at the main influence. The electronic properties of a-C - on this model - are not solely determined by nearest neighbour interactions — the local structure. Electronic and optical properties in the low energy range (< 6 eV) are closely correlated with the extent of medi-

um-range structural organisation. This is in contrast to a-tetrahedral semiconductors where the dominant role is associated with the local tetrahedral structure and with defects - such as dangling bonds etc.

4.6 Amorphous Silica 4.6.1 Experimental Situation

Amorphous silicon dioxide is probably the most extensively-studied glass. The early work of Warren and co-workers (1936) established the experimental support for Zachariasen's random network model by a series of X-ray diffraction measurements. Subsequently, Mozzi and Warren (1969) returned to the subject towards the close of Warren's scientific career, to complete a classic investigation by providing data corrected for Compton and multiple scattering that is still almost unequalled. Static neutron structure factors

4.6 Amorphous Silica

have been published from several investigations by Wright and Sinclair (1985), and Price and Carpenter (1987) have recently reported experiments leading to the dynamical structure factor, S(Q,co). Although static diffraction data exists to values of Qmax that are entirely adequate (400 nm" 1 ), the information content is still relatively small compared to, say, amorphous Ni-based binary alloys - due to the absence of suitable isotopes of Si and O and, therefore, accurate partial functions. Complementary structural information is also plentiful; good IR, Raman, and neutron inelastic scattering data have been available for some years for specimens prepared by melting, by sol-gel routes and by chemical vapour deposition. NMR, ESR and vacuum ultraviolet spectroscopy are useful ancillary techniques and, although less obviously interpretable, high resolution transmission electron micrographs have also been published. 4.6.2 Local Structure 4.6.2.1 Diffraction Data Experimental data is adequate to form, directly, a reasonably coherent description of the structure out to second neighbours, Wright (1988) quoted values obtained from fits to the first two peaks of the neutron correlation function and obtained values quoted below: Si-O O-O

/nm cr1/nm TV 13 0.1608 4.7 x l O " 3.85 ±4xl0~4 ±0.16 0.2626 9.1 xlO" 3 5.94 4 ±6xl0" ±0.25

The Si bond angle, assuming no correlation between bond length and bond angle variations is 109.7 ±0.6° with a standard deviation of 4.5°. The value of a (9) ob-

239

tained from the ESR data of Griscom et al. (1977) is much lower than this, around 0.6°. The mean and standard deviation of the oxygen bond angle is open to greater uncertainty: here we quote Mozzi and Warren's values, <e> = 144° and o-(e) = 15°. These data have been questioned by Da Silva et al. (1975) who suggest that Mozzi and Warren's data can be interpreted with a most probable oxygen bond angle of 152°. This result has, in turn, been questioned by Coombs et al. (1985) and by Galeener (1985). The former point out that a complete bond angle distribution calculated by Da Silva et al.'s method does, in fact, peak at 144°. 4.6.2.2 Complementary Techniques Vibrational spectroscopy clearly shows that the symmetry of the local silicon-oxygen unit is tetrahedral as in most of the crystalline polymorphs of SiO2, rather than octahedral as found in the high pressure phase stishovite. Similar results can be obtained from magic angle NMR - with all four oxygens around Si being 'bridging', (i.e. species QA) the chemical shift is observed as — 112ppm compared with an almost identical value for crystalline tridymite, and in contrast with values of around —213 ppm found in high P-content phosphosilicate glasses (Dupree et al., 1987) and c-SiP2O7 in which Si is octahedrally coordinated. Magic angle NMR has also been used to determine the distribution of oxygen bond angles in a-SiO2. Several models exist which relate the 29Si chemical shift to the oxygen bond angle (through the Si-O overlap integral, or alternatively the s-orbital participation in the hybridised O orbitals). Pettifer et al. (1988) have recently reviewed the experimental data and the interpretations based on each model. Results

4 Models for the Structure of Amorphous Solids

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X-ray or neutron scattering data for a-SiO2 contains a prominent feature at about 15 nm" 1 . In the spirit of a crystallite model, this feature could correspond to a prominent interatomic correlation at r = 2n/15 = 0A2 nm which could be due, perhaps, to a preferred interlayer distance or ring size. The interpretation of such "first sharp diffraction peaks" - common features of S(Q) for chalcogenide glasses such as a-GeSe2 (see Fig. 4-34) is a matter for current debate simply because they are not easily reproduced in models. Vibrational spectra for a-SiO2 have added considerable fuel to the recent arguments over the relative merits of crystallite and random network models and the relative populations of various ft-membered Si-O rings. The major peaks in the IR and Raman spectra of a-SiO2 reproduce features seen in the corresponding spectra for

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4.6.3 Medium-Range Structure

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are shown in Fig. 4-40. Significant variations are found in estimates for the mean oxygen bond angle - from 151° to 142° and even more in the breadth of the distribution. All the NMR data suggests a significantly narrower distribution than that obtained from Mozzi and Warren's X-ray data.

i

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Figure 4-40. Various estimates of the oxygen bond angle distribution, V(a), obtained from NMR a)-c), and X-ray data (d) (Pettifer et al., 1988).

c-SiO2. The exceptions are, firstly, the intense Raman continuum below about 500 cm" 1 which can be seen as a manifestation of the breakdown of the crystal momentum selection rule imposed by disorder; secondly, a number of sharp lines are seen in the Raman spectrum at about 495, 605 and 1200 cm" 1 , Fig. 4-41. Since these features can, in some senses, be considered to be "excess" modes and as their intensities change as a result of neutron bom-

il

240

c) Energy loss function

3

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500

1000

1500

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Figure 4-41. Comparison of the reduced Raman spectra a) for a-SiO2 with b) the imaginary component of the dielectric constant, e2 = Im (e) and c) the energy loss function, — Im(l/e) Peaks in e2 and in the loss function mark the frequencies of transverse and longitudinal optic modes, respectively (Galeener et al., 1983).

4.6 Amorphous Silica

bardment, or the degree polymerisation in glasses produced by condensation of monomeric species in sol-gel preparations, they are often considered to be ''defect" modes rather than intrinsic vibrations of a SiO2 "lattice". Galeener, in an extensive series of publications (see Galeener et al., 1983) has adduced arguments for treating these modes as the signature of 3- and 4membered Si-0 rings. Phillips (1982) also views these modes as defect modes - associated with the non-bridging oxygens postulated in his micro paracrystallite model. The arguments for both are presented in Sec. 4.6.4.2. Electron micrographs of SiO2 have been published by a number of authors. Zarzycki and Mezard (1962), Zarzycki (1970) published a series of medium resolution micrographs of SiO2 and other glasses in the form of thin filaments that had been formed by in situ electron beam irradiation. A domain-like structure was observed on a scale of a few nanometres which Phillips (1982) has interpreted in terms of his granular model (see Sec. 4.6.4.1). Gaskell and Mistry (1978) showed examples of bright-field images of particulate SiO2 specimens produced by precipitation from a monomer solution and by the high temperature hydrolysis of SiCl4. There is some evidence for coherently diffracting domains on a scale of about 1 nm in the high temperature material but the low temperature specimens shows more extensive ordering. 4.6.4 Random Network Models

Bell and Dean's is the classic physical model for a-SiO2. The model contained 614 atoms, was hand-built and the coordinates established by optical metrology (Bell and Dean, 1972). In addition to simulating the X-ray and neutron scattering

1

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241

r

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b) Experimental

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Figure 4-42. Computed and experimental radial distribution functions for a-SiO2 after Bell and Dean, 1972.

data, the authors have computed the vibrational spectra and configurational entropy. Fig. 4-42 shows the calculated radial distribution functions. The model has also been used as a basis for computations of the energy-minimised structure. Gaskell and Tarrant (1980) reported a detailed calculation of the static properties of several models relaxed under a Keating potential with variations in oxygen bond angle and with fixed and free boundaries. Calculations included estimates of thermal broadening, and termination ripple was modelled using the prescriptions of Mozzi and Warren (1969). More recently, Robertson and Moss (1988) have made a similar set of calculations. Evans et al. (1983) included Bell and Dean's model in a comparative survey of network models for a-SiO2. Specifically, four existing models for amorphous tetrahedral semiconductors were modified by adding oxygens midway between the silicon sites. A similar modification was made

242

4 Models for the Structure of Amorphous Solids

to Gaskell's (1975) polytetrahedral model. All models were relaxed using the same Keating potential and comparisons with the experimental and neutron scattering data of Wright and Sinclair (1985), Fig. 443. The results of this work are that all the models produce reasonable fits to the experimental data: none produces an ade-

8 Figure 4-43. Computed total correlation functions, T(r), for several models of a-SiO2 compared with experimental data of Wright and Sinclair, 1985 (WS). The models are based on CRN structures for amorphous tetrahedral semiconductors with added oxygens. BD, Bell and Dean; P = Polk; CT=Connell and Temkin (even membered rings); BB = Beeman and Bobbs. PT is a polytetrahedral model for a-Si or a-Ge (see Fig. 4-7) with added oxygen (Evans et al., 1983).

quate fit. All models fail to reproduce the experimental density - they are more than 4% too dense. Moreover, the calculated enthalpy is too small by a factor ranging from 2 to 7. In particular, the shape of the Si-O(2) distribution near 0.4 nm is inadequate in all models. Evans et al. analyse the reasons for this and suggest that it is the narrow distribution of oxygen bond angles - cr(s) - typically half that determined by Mozzi and Warren - and that this, in turn, reflects inadequacies in the topology of the models. Paradoxically, even the random models are too ordered - fluctuations in local structure are too small. The relative success of the polytetrahedral model in this regard reflects the inherent strain accumulated in the model which can increase until the compressed regions in the interior of the model collapse. Apart from the relative merits of this particular granular model, it can be argued that granularity - by introducing large interfacial strains or otherwise - may be an important ingredient in the model-building process. Ching (1982) also produced models for a-SiO2 and a range of suboxides, SiO^, by adding oxygens mid-way between silicon atoms in models for Si with periodic boundaries. Three models, containing about 170 atoms in the unit cell, were constructed and energy-minimised using a modified Keating potential. Good agreement with the measured density was observed, and bond lengths and angles were close to those determined by Mozzi and Warren (1969). Unfortunately, comparison with experimental X-ray data was only qualitative, so that the accuracy of the models cannot be adequately judged. Recently, Gladden (1990) has taken up the challenge of producing an acceptable model for a-SiO2 that remedies the defects of the models described above. She has produced models containing 1-2000

4.6 Amorphous Silica

243

Figure 4-45. Comparison of the detailed shape of T(r) from 2 to 4 A with three models for a-SiO2. Experimental results are shown by the crosses and computed data for a model with a minimum ring size of five units and oxygen bond angles of 140° (dashed line); 143° (dotted line) and 150° (full line) (Gladden, 1990).

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r(A) Figure 4-44. Computed (full line) and experimental (dashed line) data for a-SiO2. a) T(r); the computed curve being corrected for termination effects, thermal broadening and the finite size of the model, b) Q i (Q), after correction for finite model size, c) The total function (full line) and the component pair distribution functions calculated from the model. Finite model size and thermal broadening corrections are included but convolution with the termination smearing function is omitted (Gladden, 1990).

atoms by translating the operations involved in handbuilding a "ball and stick" model into a computer algorithm that allows the automatic generation of CRN models subject to constraints such as the smallest ring size, mean O bond angle, connectivity, relative magnitude of terms in the PE function etc. This has allowed a thorough search of the parameter space and delineation of the parameters which correspond to the best fit to experimental data. Results are impressive - as shown in Figs. 4-44 and 4-45. Particular features of the experimental data to be given attention were the shape of the Si-O (2) distribution near 0.4 nm and the intensity of the first sharp diffraction peak in Qi(Q) that had not been adequately modelled hitherto. Gladden has shown that the best fit corresponds to a choice of a mean oxygen angle of 150° and a minimum ring size of five SiO2 units. Arguably this work should now be taken as one of the most authoritative interpretations of the scattering data for a-SiO2.

244

4 Models for the Structure of Amorphous Solids

4.6.5 Ordered Models 4.6.5.1 Quasi-Crystalline Models Quasicrystalline models, described by Wright and Leadbetter (1976), were mentioned earlier in Sec. 4.2.2.2. Two other models, explicitly based on the network topology of crystalline polymorphs of SiO2 have been proposed by Konnert, Karle and co-workers, and more recently, by Phillips. Konnert, Karle and co-workers base their models on X-ray data refined as described in Sec. 4.4.6.1, so that details, presented as r2 G(r), are obvious out to distances of the order 2.0 nm. Computed data were produced by broadening the Bragg peaks in the powder patterns for the crystalline polymorphs so that detail was not apparent beyond 1.4 nm. Comparison with experimental data suggested that the topology of the tridymite lattice was more closely associated with the structure of amorphous silica than any other form. It is not entirely clear what these crystal-based models represent; Wright and Leadbetter (1976) suggest that misunderstanding of the nature of the model may have lead to the controversy that subsequently surrounded it. Konnert and Karle (1973) suggest "a structure composed nearly entirely of ordered regions similar to tridymite, . . . having dimensions up to at least 20 A and bonded efficiently together in configurations analogous to twinned crystals. In such a model the ordered regions have the same bonding topology as the crystalline polymorphs and are distorted slightly owing to the junctions between the ordered regions. However, microcrystalline boundaries are not implied. The junctions may not vary significantly in energy and density from the ordered regions". Konnert et al. (1974) quote data for the RDF calculated from broadened Bragg peaks corresponding to tridymite crystals with a particle size

8

r(A)

12

Figure 4-46. Comparison of models for a-SiO2, based on the crystal structures of tridymite, cristobalite and quartz, with experimentally-derived data (Konnert and Karle, 1973). Also shown (MODEL) data for a 1412-atom structure based on a model for a-Si by adding oxygen, and experimental data (SILICA) (Konnert et al., 1982).

between 1.1 and 2.0 nm. Konnert et al. (1982) also present data (Fig. 4-46) for a random network model of a-SiO2. Duffy et al. (1974) model for a-Si formed the basis, with oxygen added. The authors also list correlation coefficients, thus providing a quantitative estimate of the goodness of fit and quote values of 0.91 for the random model compared to 0.83 for tridymite, and 0.68 for one based on cristobalite. 4.6.5.2 Microparacrystalline Models Phillips (1982) produced a model for a-SiO2 based on cristobalite. The details again are subject to some re-interpretation although, in this case, this arises from modifications resulting from critical comments rather than any lack of precision. As mentioned earlier, Phillips argues that constraints imposed by bonding or connectivity can lead to broken "chemical order" if the number of degrees of freedom proves inadequate for that structure. In the case of SiO 2 , departures from chemical order-

4.6 Amorphous Silica

ing are considered to take the form of nonbridging oxygens, Os*, that form surfaces separating chemically-ordered regions. Specifically, "large surface areas (corresponding to low index crystal faces) are covered by Os* atoms which are nearly equivalent and are bonded to the cluster interior as siliconyl units, namely, Os* = Si-(O 1/2 ) 2 •" "In the present model the internal surfaces are intrinsic features of the glass structure . . . " In its original form, Phillips assumes a topology based on paracrystallites of (3-cristobalite with diameters up to 6 nm and with 20 to 25 % of the Si atoms double-bonded (see Fig. 447). The arguments for this model are principally based on vibrational spectra, rather than diffraction data and are considered in detail below. In response to criticism by Galeener and Wright (1986), that quasicrystalline models based on (3-cristobalite provide inadequate fits to X-ray or neutron data, even for correlation lengths as small as 2 nm, Phillips (1986) pointed out that such a literal view is inappropriate. Specifically, internal lattice defects - stacking faults or microtwins on a scale of 1 to 1.5 nm are postulated in an attempt to remove the difficulties. The suggestion of > Si = O groups is also dropped in favour of = S i - O - O - S i = groups. Hosemann et al. (1984, 1986) have produced a remarkable but little-understood model for a-SiO2. A pair of SiO4 tetrahedra, Fig. 4-48 a, form the basis for a f.c.c. lattice with a lattice constant of 0.715 nm, Fig. 4-48 b. In order to fit the density, tetrahedra are given correlated twists of + 22° parallel to the cell axes. The spacing of the {111} planes of this lattice are allowed to vary according to Eq. (4-2). A good fit to experimental X-ray data is found with the interplanar variation constant, g = 0.12, corresponding to an octa-

245

Figure 4-47. Phillips' (1982) sketch of the {100} interface in cristobalite formed by removing a "molecular plane" of thickness 0.37 nm and allowing the interface to relax.

hedral microparacrystal comprising 3 or 4 {111} planes, with an edge length of 1.25 nm. The glass is pictured as being composed of microparacrystals with "parallel oriented twists of SiO 4/2 tetrahedra" separated by grain boundaries where the distortions are larger due to different orientations of the rotation axes in adjoining domains. The fit to experimental data is impressive, Fig. 4-48 c - the authors claim that their model fits experimental data to "within the thickness of the drawn line". The domain structure is compared with several of the crystalline modifications of SiO2 but is identical to none of them with cristobalite being the closest approximant. 4.6.6 Simulation of Dynamical Properties As mentioned earlier, a number of features of the vibrational spectra of silica particularly the polarised Raman Spectrum - have no obvious counterparts in spectra for crystalline forms of SiO 2 . Two of the Raman bands at 495 and 605 cm" 1 are sharp (see Fig. 4-41) and, since they are sensitive to preparation conditions and to radiation damage, they have been termed "defect" bands.

246

4 Models for the Structure of Amorphous Solids

Figure 4-48. a) The building block, consisting of two silicon-oxygen tetrahedra, proposed by Hosemann et al. (1984, 1986) which is then connected to form the structure shown in b). Circles are oxygens and squares, silicons. The fit to experimental data (Mozzi and Warren, 1969) is shown in c) with component partials indicated. The agreement with experimental data is "within the thickness of the drawn line". The insert shows the peak shape function with a full width at half height of 0.19 A compared to the computed width of the first peak of 0.21 A.

4.6 Amorphous Silica

Interpretation of the defect bands by Galeener (see for example Galeener, 1983), Galeener et al. (1983) and by Phillips (1982) starts from the assumption that calculated vibrational spectra, based on coupled SiO4 tetrahedra and for random network models such as Bell and Dean's, do not agree either with the number or the frequency of those modes observed experimentally. Phillips (1982) then proposes that the two defect bands are assigned to localised vibrations of point defects or surface oxygens associated with the postulated 'broken chemical order' at the bonding surface of (3-cristobalite microparacrystallites and involving a double Si = O bond. Galeener (1983) takes the view that the additional features in the spectrum reflect the presence of three-membered rings (Si3O9) by analogy with vibrations near 600 cm" 1 in hexa methylcyclotrisiloxane, and four-membered rings corresponding to octamethyl cyclotetrasiloxane which has a Raman active mode at about 480 cm" 1 . These explanations fit uncomfortably with the findings of Bell (1983) and Evans et al. (1983). These authors calculated the vibrational densities of states, g(co), for several cluster models of a-SiO2, none of which contain 3-membered rings but give results that are in reasonable agreement with the experimental data of Leadbetter and Stringfellow (1974). Bell (1982) also calculated the IR, polarised and unpolarised Raman spectrum and observed Raman and IR-active modes near 600 cm" 1 . Evans et al. (1983) also found IR activity in the energy-minimised Bell-Dean structures at 600 cm" 1 and peaks in g((o) for all models considered in the region near 600 cm" 1 . The problem therefore, as Bell says, is not what type of network defect could be responsible for the vibrations but to understand why, in conflict with experi-

247

ment, the cluster-based calculations predict a measure of IR and depolarised Raman activity at 600 cm" 1 . The matter is still controversial, therefore. 4.6.7 Molecular Dynamics Models Similation of the static structural properties of a-SiO2 using molecular dynamics was pioneered by Woodcock et al. (1976). A modified Born-Mayer-Huggins potential was used and the resulting distribution functions are shown in Fig. 4-49. Soules (1979, 1982) and Mitra et al. (1982) have also produced fits to experimental X-ray data for SiO2 using larger models than that used by Woodcock et al. (54 molecular units in the periodic box). Mitra, for example, used 375 ions in a

Figure 4-49. Pair correlation functions, G(r), for aSiO2 obtained from the MD simulations of Woodcock et al., 1976 (full line). Experimental data of Mozzi and Warren (1969) is also shown (dashed line). N (r) is the running coordination number centred on Si.

248

4 Models for the Structure of Amorphous Solids

cubic box with dimensions adjusted to provide agreement with the experimental room temperature density. The results of the MD simulation were compared with experimental data without any attempt to reproduce termination broadening or to match thermal broadening. Good agreement with experiment is reported, although there are discrepancies in the detail. For instance, the authors draw attention to the spread of ±7° in the Si bond angle compared with a = 0.6° from ESR data and (7 = 4.5° from neutron and X-ray data. The oxygen bond angle distribution agrees with that proposed by Da Silva with a peak value of 151°. A few of the atoms are abnormally coordinated as 3- or 5-coordinated Si or singly- or triply-bonded oxygens. Kubicki and Lasaga (1988) have simulated a-SiO2 using ionic and covalent potentials parameterised by fitting ab initio quantum mechanical potential energy surfaces for H 4 SiO 4 and H 6 Si 2 O 7 molecules. Again the authors claim a good fit to experimental X-ray data but the secondneighbour coordination numbers are in error by factors of 2 in some cases, and there are also significant errors in nearest neighbour bond lengths and in the breadth of bond angle distributions (apart from questionable values of the mean oxygen angle). A recent MD simulation of Feuston and Garofalini (1988) has used Stillinger-Weber three body potentials adapted for aSiO 2 . The results, Fig. 4-50, are a great improvement on earlier calculations based on two- body terms - the bond angle distributions and the numbers of over- and under-coordinated atoms are more realistic. MD simulations of a-SiO2 have thus far failed to match the potential of the technique (or the claims of their adherents) - at least in so far as realism is concerned. None of the simulations matches experi-

Figure 4-50. Structure factor, S (Q\ for a-SiO2 calculated by Feuston and Garofalini (1988) using Stillinger-Weber potentials including three-body interactions, compared with experimental data (Misawa et al., 1980).

mental data to the accuracy of that data few authors have even tried to make meaningful comparisons. Unphysical potential energy functions are probably the cause of the mismatch in early work, but the recent efforts of Feuston and Garofalini using Stillinger-Weber type three-body interactions shows that the challenge of matching experimental data to within statistical error still exists (see Fig. 4-50). 4.6.8 Monte Carlo Simulations Guttman and Rahman (1988) have produced a number of models for a-SiO2 by methods in which the central step involves randomly-chosen exchanges of neighbours followed by energy minimisation and acceptance or rejection of the move based on an assessment of the changes in energy. Variations in the number of n-membered rings in the starting structures were tried, as well as changes in the relative magnitude of the terms in the modified Keating PE function. Once the energy had ef-

4.6 Amorphous Silica

fectively converged, the reality of the models was tested by the fit to experimental values of the density, elastic moduli and Q(S(Q) — 1) data - particular attention being paid to the position and intensity of the first sharp diffraction peak at about 15 nm" 1 . The most successful models (324 atoms) were generated and energy-minimised in the form of models for a-Si (with the density fixed at values appropriate to a-Si) and oxygens only inserted at the final stage. (Models based on SiO2 throughout were less successful.) Agreement with g-space data is (again) said to be "excellent", but the best models fail to reproduce experimental data to within experimental statistics. Models with 3-membered Si-O rings were observed to reproduce inadequately the low Q features in the experimental results and with more than one 4-membered ring per 10 Si atoms, errors are again noticeable at low Q. Keen and McGreevy (1990) have presented a simulation of the structure of aSiO2 using a "Reverse Monte-Carlo" algorithm. The procedure, outlined in Sec. 4.4.5, takes an arbitrary starting structure - in this case 2596 atoms in a periodic cubic box of length 3.4 nm. Atoms are randomly chosen and moved to minimise the weighted difference between the structure factors for the model and those obtained from X-ray and neutron scattering measurements for the same sample. At no stage are energetic terms involved. Results are shown in Fig. 4-51 and are clearly impressive. The structural parameters derived from the model are similar to those derived "directly". However, the authors draw attention to the low value of the Si-0 coordination number of 3.7. The average oxygen bond angle is 141° in good agreement with Mozzi and Warren's (1969) value, although the distribution is found to

249

0.2-

,0.0:

-0.2:

0.2:

,0.0:

-0.2tt.O

Figure 4-51. Calculated neutron and X-ray structure factors for a-SiO2 (solid line) using the Reverse Monte Carlo method. The dashed line shows experimental neutron and X-ray data (Keen and McGreevy, 1990),

be significantly broader, as is the Si bond angle distribution. The Si-Si-Si angle distribution shows a significant peak at 60° corresponding to three-membered rings, which are also observed in projections of the structure. Such rings are thus not inconsistent with the diffraction data and it remains to be seen just how the additional constraints employed in many other construction algorithms - particularly that of Gladden (1990) - have lead to radically different models. This work certainly concentrates the mind on the limited amount of information available in diffraction data for amorphous solids and the extent to which other prior knowledge - or prejudice - has been incorporated in less objective constructs.

250

4 Models for the Structure of Amorphous Solids

4.7 Binary Alkali and Alkaline Earth Silicates, Borates and Phosphates 4.7.1 Apologia These glasses may not be the most popular materials with academic scientists. Their compositional complexity leads to structural investigations that are necessarily difficult and inconclusive. But it would be artificial to exclude them from this chapter. Silicates, borosilicates, aluminosilicates and (less usually) phosphates, form the basis of the modern glass industry. Moreover, the class of ionic oxide glasses represented here is of central importance in the earth sciences. There is every reason, therefore, to establish what we now know about these materials - since it is far from insubstantial - and how it may be incorporated into our understanding of structure of glasses in general. Section 4.1.4 outlined the various ways in which the structure of glasses can be discussed - positional and compositional ordering, local symmetry and coordination, network topology, speciation etc. Each aspect merits attention in the case of the binary oxide glasses. But in this section we focus on two interwoven aspects - firstly, the local structure around an alkali (or alkaline earth) element and especially on the consequences this may have at the level of medium-range structure. The reasons for emphasising this topic were set out in Sec. 4.2.3. If local order is observed in close-packed regions, so that local structural units are highly interconnected and if the bonds to nearest-neighbours are not strongly directional, then the arguments of Sec. 4.2.3 suggest that the perceived local order is a consequence of medium-range ordering. Local ordering around cationic "network modifiers" like Li, Na, Mg, Ca,

and (possibly) the trivalent elements thus gives very important clues to the degree of ordering over distance scales much larger than nearest-neighbour bond lengths. Secondly, we consider several determinations, chiefly by NMR, of the distribution of anionic species present in a glass speciation. These questions focus attention on the extent to which randomness inherent in the Warren-Zachariasen model, actually represents the structure of real amorphous materials. I am not aware of a modern restatement of the Warren-Zachariasen model for oxide glasses but the consensus view seems to be the following. Elements such as Si, B, P etc., bonded to oxygen, constitute an extended network: such elements are thus the "network-formers". Alkali, alkaline earth and similar elements denoted here by M - "modify" the connectivity and thus determine the dimensionality of the network. The B-, P- and Si-0 bonds are regarded as the strongest and most directional interactions - largely covalent, perhaps - whereas network modifier, M-O links are considered to be weak mostly ionic and with isotropic, pairwise forces. The Si environment should thus be well-defined in contrast to M-0 correlations, where variable coordination is possible (or probable). Moreover, the M-M distribution in the Warren-Zachariasen picture is viewed as being random - determined largely by composition; although it is a common over-simplification to regard the M ions as fitting into suitable cavities in a silicate framework "formed" to satisfy the coordination and bonding requirements of Si and O, as Zachariasen pointed out in his original paper (1932).

4.7 Binary Alkali and Alkaline Earth Silicates, Borates and Phosphates

4.7.2 Local Structure Around "Network Modifiers" in Oxide Glasses 4.7.2.1 Diffraction and EXAFS Data A major difficulty in establishing the structure around atoms such as Li, Na, Mg, Ca in oxide glasses stems from the fact that M-O, M-Si and particularly M-M correlations generally give only weak contributions to the total scattered X-ray or neutron intensity. This follows from the dependence of the weighting factors in Eq. (4-19) on the concentration and atomic scattering factors, so that for light elements, M-M correlations can be virtually invisible in X-ray scattering. Moreover, M-0 first- and higher-neighbour peaks often lie at similar distances to the more intense 0 - 0 correlations. Some insight was gained in early work by taking differences between scattering data for specimens containing ions of two chemically similar species which are assumed to substitute isomorphously. Urnes and coworkers (see for example, Hanssen and Urnes, 1978) have used Si/Ge replacement to identify features in K 2 O-SiO 2 and Cs2O-SiO2 glasses and differences between X-ray and neutron atomic scattering factors to identify features in silicates (Urnes et al, 1978). An exceptionally thorough survey of the structure of silicate glasses and melts was conducted by Waseda and Suito (1976, 1977) - work that probably did not receive due attention until the results were later republished (Waseda, 1980). X-ray and neutron scattering data were collected to Qmax = 170 nm" 1 from about eight compositions in each series of Li, Na, and K silicate glasses both as the room temperature glass and the melt. In addition, melts in the CaO-, MgO- and FeO-SiO2 series were also examined by X-ray scattering (Waseda, 1980). Structural parameters were estimat-

251

ed by fitting the reciprocal space data with a modified Debye equation. Coordination numbers were found to vary slightly with concentration - at the metasilicate composition approximate values are Li-O 4, NaO 6, K-0 8, Mg-O 5 and Ca-O 7 (see also Table 4-1). Misawa et al. (1980) used pulsed neutron scattering techniques to study SiO 2 , Li 2 O-2SiO 2 and Na 2 O-2SiO 2 and a mixed Li/Na glass to Qmax = 4$Q nm" 1 . No real attempts were made, however, to analyse the M-O contributions in detail apart from indicating peak positions, 0.20 and 0.24 nm for Li-O and Na-O, respectively. A further paper by Ueno and Suzuki (1981) ona-Na 2 Si 2 O 5 to 0 max = 3OO nm" 1 , reported the position of the Na-O peak at 0.241 nm with a coordination number of 5, in good agreement with values for cNa 2 Si 2 0 5 (0.241 nm and 5.0). Also in 1981, Greaves et al. reported studies on a-Na 2 Si 2 O 5 and other Na-containing glasses using EXAFS. This represented the first use of a soft X-ray monochromator on a synchrotron to obtain "element-specific" local structural information for a light-element in oxide glasses, Fig. 4-52. The Na-O mean bond length was established to be 0.23 nm with a = 0.004 nm and a coordination number of 5 + 0.5. This paper marked the beginning of an impressive series of measurements by Greaves and coworkers on the local structure around modifying elements in oxide glasses of scientific, commercial and geological importance (see also Greaves (1990)). Similar EXAFS investigations by Brown and coworkers relate principally to glasses relevant to the earth sciences. A number of EXAFS results are collected in Table 4-1. There are some clear discrepancies between the results of Greaves and coworkers and Brown et al. (1986), over the local

N> Ol I\D

Table 4-1. Local structural parameters for silicate and phosphate glasses. Bond

M-O/nm

cr/nm

Li-O Li-O Li-O Na-O Na-O Na-O Na-O Na-O Na-O Na-O Na-O Na-O Na-O Na-O Na-O K-O K-O K-O K-O K-O K-O K-O Cs-O Cs-O Cs-O Ca-O Ca-O Ca-O Ca-O

0.207 ±0.001 0.20 0.212 0.240 0.235 + 0.001 0.24 0.23(0) ±0.003 0.24(3) ±0.003 0.241 0.240 0.247 0.261 0.262 0.257 0.260 0.25(6) 0.300 ±0.002 0.303 ±0.002 0.306 ±0.002 0.302 ±0.002 0.278 0.288 0.308 0.318 0.30(0) 0.243 ±0.001 0.241 ±0.001 0.241 0.237

0.010 0.009 0.012 0.010 0.007 0.012 0.02 0.004 0.015 0.010 0.015 0.019 0.015 0.013 0.015 0.015 0.013 0.0035 0.023 0.015 0.028 0.016 0.013 0.01 0.012

3.9 ±0.3 4 5 6.0 5 ±0.5 2 ±0.5 5.0 4.0 5 6.4 5.1 5.5 7.6 5 8.9 ±0.9 9.6 + 1.0 10.4 ±1.0 9.5 ±1.0 5 6 5 6 5 6.8 ±0.3 6.9 ±0.3 6 6.15 + 0.17

Ca-O Ca-O Ca-O Mg-O

0.237 0.264 0.263 0.214 ±0.001

0.022 0.023 0.011

5.40 ±0.18 7 8 4.5

CN

Composition

Reference

Tech

Comments

Li2SiO5 Li 2 Si 2 O 5 Li2SiO3 a-Na 2 Si 2 O 5 Na 2 Si 2 O 5 Na 2 Si 2 O 5 Na 2 Si 2 O 5 Na 2 CaSi 5 O 12 Na 2 Si 2 O 5 Na 2 SiO 3

Wasedaetal.(1977) Misawa et al. (1980) Yasui et al. (1983) Waseda et al. (1977) Misawa et al. (1980) Greaves et al. (1981) Greaves et al. (1981) Ueno etal.(1981) Yasui et al. (1983) Yasui et al. (1983) McKeown et al. (1985) McKeown et al. (1985) McKeown et al. (1985) McKeown et al. (1985) Greaves (1989) Jackson et al. Jackson et al. Jackson et al. Jackson et al. Yasui et al. (1983) Yasui et al. (1983) Yasui etal.(1983) Yasui et al. (1983) Greaves (1989) Waseda (1980) Waseda (1980) Yin et al. (1983, 1986) Eckersley et al. (1988)

X,N N X X X,N N E E N X

6 other glasses and melts e max = 480nm- 1 Fitted data Crystal data 6 other glasses and melts

E X N X N

Fitting with a crystal model Isotope substitution

Matsubara et al. (1988) Binsted et al. (1985) Binsted et al. (1985) Waseda (1980)

X E E X

Other compositions reported Asymmetric peak Asymmetric peak - mean value quoted Data for melt also

Na 2 Si 2 O 5 KNa3(AlSiO4)4 KNa3(AlSiO4)4 Na 2 Si 3 O 7 KCsSi2O5 KAlSi3O8 Na 0 . 3 K 0 . 7 AlSi 3 O 8 Na 0 . 5 K 0 . 5 AlSi 3 O 8 Na 0 . 3 K 0-7 AlSi 3 O 8 K 2 SiO 3 K 2 SiO 3 Cs2SiO3 Cs2SiO3 KCsSi2O5 (CaO)0.45(SiO2)0.55 (CaO)0-45(SiO2)0.55 CaSiO3 (CaO)0.48(SiO2)0.49 (Al2O3)0.03 Ca(PO 3 ) 2 CaAl2Si2O8 CaMgSi 2 O 6 MgSiO3

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4.7 Binary Alkali and Alkaline Earth Silicates, Borates and Phosphates

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Figure 4-52. Atomic distribution centred on Na obtained by fourier transforming normalised Na-edge EXAFS spectra for a) vitreous sodium disilicate and b) a soda-lime-silica glass (Greaves et al., 1981).

structure around Na and K particularly. In part of this may be due to the different choice of specimen composition, but data for Na 2 Si 2 0 5 do not allow this interpretation. Differences are more likely to be the result of either adventitious composition changes or differences in experimental techniques (transmission and total yield) or even to systematic variations in data analysis procedures. Many of the X-ray and neutron scattering studies of network modifiers in oxide glasses have relied on some form of modelling to extract the weak M-O, M-Si correlations from total scattering data that is dominated by Si-O and O-O correlations. Consequently many of the results are relatively imprecise: coordination number and o values, particularly, are subject to large

254

4 Models for the Structure of Amorphous Solids

uncertainties especially for the X-ray scattering measurements involving M elements of low atomic number. The situation is much more favourable, however, in phosphates of the heavier divalent elements, such as Zn, Cu, which provide a relatively large contribution to X-ray scattering. Moreover, the M-O peak lies in the gap between P-O correlations at 0.15 nm and the first 0 - 0 peak at 0.25 nm. Neutron data, to Qmax = l%0 nm" 1 , has been reported by Matz et al. (1988), for Zn, Ca,' Sr, Ba metaphosphates and X-ray data (emax^lSOnm- 1 ) for Mg, Zn and Ca metaphosphates by Matsubara et al. (1988). Musinu et al. (1989) have also studied Zn metaphosphate by X-ray scattering (Q max =150 nm" 1 ) together with a mixed CuZn metaphosphate. Results are given in Table 4-1. As with some of the EXAFS data, the last three measurements are revealing in that well-defined M-O first coordination shells are observed. Typically, o values for the Zn- or Mg-O distances are about 0.011 nm - a value that is larger than that for the P-O peak by a factor of 2.5, but the M-O distribution in the crystal is almost equally broad (a = 0.012 in Zn(PO 3 ) 2 ). There are, however, significant variations in the coordination numbers outside the estimated errors of the measurements. Thus three values for the Zn-O coordination numbers are 3.75 (Matz et al., 1988), 3.90 (Matsubara et al., 1988), and 5.0 (Musinu et al., 1989). In c-Zn(PO3)2 the Zn coordination number is 6. There are also unexpected differences in the Mg-O distance in a-Mg(PO3)2 between the two datasets and, more understandably, in the Ca-O distances: since this peak is not resolved in either the neutron or X-ray data. EXAFS data for Ca in silicate glasses has been reported by Geere et al. (1983), and Binsted et al. (1985). The latter is the

more comprehensive and results (Fig. 453) show that the pair distribution functions for a-CaAl2Si2O8 and a-CaMgSi2O6 are very asymmetric and can be synthesized by 7 to 8 gaussian components stretching from 0.235 to 0.31 nm, with a standard deviation of 0.021 nm for CaAl 2 Si 2 O 8 and 0.019 nm for CaMgSi 2 O 6 . Eckersley et al. (1988) have used isotopic substitution of Ca in neutron scatter-

20-

Figure 4-53. Pair distribution functions for C a - O in amorphous silicates and aluminosilicates obtained by curve-fitting the Ca K-shell EXAFS data. Each C a - O distance has been broadened by a thermal factor cr = O.OO85 nm. Spectra are shown for glasses of the composition of the minerals, anorthite CaAl2Si2O8 (upper diagram) and diopside, CaMgSi2O6 (lower). Dotted lines are the pair distribution functions for crystalline anorthite and diopside (Binsted et al., 1985).

4.7 Binary Alkali and Alkaline Earth Silicates, Borates and Phosphates

255

Figure 4-54. Pair distribution function, GCa (r), centred on the Ca atom (full line). The dashed line represents data for c-CaSiO3 calculated with gaussian broadening parameters a = 0.01 nm for the first (CaO) peak and a = 0.02 nm for the remaining peaks. The data for the crystal has been convoluted with a SINC function to reproduce the termination ripple introduced into the experimental data by a truncated fourier transform (Eckersley etal, 1988).

-0.2

r/nm

ing studies of a calcium metasilicate glass, lightly doped with A12O3 to minimise the risk of crystallisation on cooling from the melt. Results shown in Fig. 4-54 indicate a well-defined first neighbour shell of 6.15 oxygens around Ca, with a mean bond length of 0.237 nm - almost identical to the value found in c-CaSiO3. The distribution is also narrow: fitting the data with gaussian peaks suggests a well-ordered environment around Ca for about 85% of the oxygens which lie in a peak centred at 0.237 nm with a standard deviation of 0.012 nm. The remaining oxygens lie in a broad tail stretching from 0.25 to 0.285 nm. There is a suggestion, therefore, that the coordination polyhedron around Ca in this glass is octahedral as in cCaSiO 3 . Space does not permit a discussion of the environment of transition metals and other polyvalent elements that, within the Warren-Zachariasen framework, could be classed as network modifiers. Studies have a long history - particularly by optical spectroscopy. Generally, first peaks occur at similar positions to those in the corre-

sponding crystals but EXAFS data indicates some shortening. For an excellent review see Calas and Petiau (1983). One recent result, combining neutron scattering with isotopic substitution and XAS gives the flavour of the results in this area. Yarker et al. (1986) have measured the scattered intensities (g max = 300 nm" 1 ) for a K 2 O • TiO 2 • 2SiO 2 glass with substitution of 46 Ti and 48 Ti. The Ti-O peak is split with two components at 0.165 and 0.196 nm (similar to distances observed in crystalline Na2TiSiO5) with a a value (corrected for termination broadening) of effectively zero (6 x 1 0 " 4 ± 2 x 10" 3 nm) for the first peak and 0.01 ±0.001 nm for the second. The environment of the Ti ion in this glass is extremely well-defined. Summarising the results on the local structure around "modifer" ions in oxide glasses: there is no doubt that experimental data suggests that even weakly-bonded elements like Na have a reasonably well-defined oxygen first shell. Representation of the extent of disorder around a given atom site is probably best achieved by comparison with the crystal. Thus if as is the static

256

4 Models for the Structure of Amorphous Solids

broadening parameter - after correction of the experimentally measured a value for termination and thermal broadening (see Sec. 4.3.3) - and if ac is the standard deviation of the corresponding distribution in the crystal, then: a A =
(4-40)

Here
The environment of alkali and alkaline earth ions has been probed indirectly by studies of defects associated with elements like Tl + that are considered to be representative of the structure of alkali ions. Thus Kawazoe (1985), Kawazoe and Takagi (1983) report ESR measurements on Tl2 + , generated from Tl + by y-irradiation, in K 2 O- and Na 2 O-SiO 2 glasses. Two sites for the precursor Tl + atom were detected one with a highly distorted ligand field, the other being symmetrical. The former appears in glasses where both bridging and non-bridging oxygens co-exist and the latter in glasses where all bridging or all nonbridging oxygens are present - such as mixed nitrate glasses. The concentration of the two types of site are composition-dependent. The possibility of two types of sites in alkali silicates is raised by Dupree et al.

(1986) in connection with the compositiondependence of the 133 Cs MASNMR signal in caesium silicate glasses. Their data is interpreted in terms of a "wide range of (Cs) sites which are based on two main types and the range of these sites narrows with increased Cs 2 O". Similar conclusions emerge from optical spectroscopy - particularly of dopant ions. A recent discussion by Belliveau and Simkin (1989) of the fluorescence line-narrowed spectra of Eu 3 + doped into silicate glasses, suggests that the environment of the dopant may be relatively constant, with perhaps a small number of configurations, rather than a continuous distribution as advocated by others (e.g. Weber, 1981). This conclusion is based both on the authors' own results and similarities observed in the Eu 3 + spectra in wide range of glass compositions, and on the absence of any dependence on the concentration of Eu 3 + spectra in these glasses. Vibrational spectroscopy provides ambivalent conclusions. Vibrations associated with ionically-bonded elements appear in the low-frequency IR spectrum rather than the Raman spectrum. The contributions of these modes to the total integrated absorption - and therefore to the low frequency dielectric constant is approximately half the contribution from all other mechanisms combined - over the entire spectrum from the high energy ultraviolet to radio-frequencies as pointed out by Birch et al. (1975) and Ellis et al. (1977). The breadth of the "alkali" band - stretching from below 10cm" 1 to 103 cm" 1 according to Ellis et al. suggests a multiplicity of sites for Ca + + and Na + . The subject has been treated more recently by Exarhos (1983) and by Gervais et al. (1987). The latter paper is particularly interesting as the data is presented for the imaginary part, e 2 , of the complex dielectric constant,

4.7 Binary Alkali and Alkaline Earth Silicates, Borates and Phosphates

500 WAVENUMBER

1000 (cm-1)

1500

Figure 4-55. Imaginary component of the dielectric function for silica and silicate glasses containing Na and K. Note the low frequency band assigned to the stretching vibrations of alkali cations (Gervais et al., 1987).

c, thus giving a direct, quantitative measure of the "oscillator strengths". (Moreover it gives an excellent overview of the subject). Fig. 4-55 shows the low frequency IR "continuum", compared to silica. 4.7.3 Medium Range Structure Centred on "Network Modifiers" in Oxide Glasses 4.7.3.1 Diffraction Data As mentioned in Sec. 4.3.5.5, the effective range of EXAFS data in amorphous solids is limited by the breadth of second and higher neighbour real-space correlation functions. In practice it is difficult to obtain quantitative information beyond the first neighbours of atoms such as Na or Ca which are of interest here. Diffraction data thus proves to be most useful. We focus on determinations of the M-M distance in oxide glasses in order to gain some impression of the spatial distribution of network modifier atoms. One method for identifying peaks due to network-modifying elements in total diffraction data is to use a heavy element, so that M-centred correlations are prominent

257

in X-ray scattering due to atomic number, Z, contrast. In early work, a number of authors used this technique in attempts to prove that preferred M-M distances occurred near 0.7 nm - a value predicted by a structural theory of liquid-liquid immiscibility (Levin and Block, 1957). Results overall were not conclusive. Although peaks in real-space distributions near 0.4 nm in Ba- and Cs-silicates and borates were "ascribed" to M-M distances by Brosset (1963), the contribution from MM correlations calculated (by this author) using Eq. (4-21) is small in all the compositions and almost negligible in some of the compositions where a peak is observed. Similar comments apply to data for a barium borosilicate studied by Piermarini and Block (1963). On the other hand, the Ba-O peak is dominant and it is likely that the feature ascribed to Ba-Ba, Cs-Cs is the signature of M-O(2) distances as Krogh-Moe (1962) argues. Some of the most impressive work is that by Krogh-Moe and Jurine (1965) and by Milberg and Peters (1969) on thallium borates and silicates, respectively. Tl has a high atomic number (Z= 81), so that Tl-0 and Tl-Tl pairs dominate the total distribution functions. In fact, Tl-Tl contributes 51 % of the total scattering for the Tl-rich silicate studied by Milberg and Peters. Fig. 4-56 shows these data which were interpreted as mainly Tl-O for the 0.5 nm peak and Tl-Tl (Cs-Cs) for the peak at 0.7 nm by Krogh-Moe and Jurine, and "probably" as Tl-Tl peaks at 0.4, 0.7 and 1.0 nm by Milberg and Peters. Note the apparent composition-independence of peak positions. Note also that all the authors argued that their data indicates a non-random distribution of network modifier atoms. More recently Hanson and Egami (1986) investigated Cs-containing silicate glasses (ZCs = 55). Their results are

258

4 Models for the Structure of Amorphous Solids

12

in qualitative agreement with the X-ray work of Yasui et al. (1983) and Guaker et al. (1974). Hanson and Egami assigned the main peak at 0.41 nm to Cs-Cs pairs and further peaks at 0.69 and 0.8 nm to higher Cs neighbours in random close-packing. Yarker et al. (1986) have also obtained a M-M distribution by taking second differences of their neutron scattering data for three different isotopic ratios of Ti. There is considerable scatter in their data shown in Fig. 4-57 as a composite curve however the first Ti-Ti peak at 0.34 nm is

2

o (r)

Figure 4-56. a) "Electronic" radial distribution function, a(r) = rG (r), for Tl2O-SiO2 glasses containing 1) 34.5, 2) 22.8, 3) 16.1 mol% T12O (Milberg and Peters, 1969). b) Similar data for thallium and caesium borate glasses measured by Krogh-Moe and Jurine (1965). Upper curve (full line) shows data for a glass containing 4.7 mol% T12O and the lower curve, 9.6 mol% T12O. Dotted curves show o (r) for borate glasses with similar quantities of Cs2O.

4

6

r/A

Figure 4-57. Three estimates of the Ti-Ti distribution, T(r), for vitreous K 2 O TiO 2 -2SiO 2 (after Yarker et al., 1986). A first peak is seen at about 0.34 nm suggesting Ti-Ti clustering at a smaller distance than the mean value 0.61 nm (arrow), calculated for a spatially random distribution of Ti atoms (Gaskell, 1985 b).

observable in all the component curves. As pointed out by Gaskell (1985 b), the position of this peak directly indicates a preferred Ti-Ti distance - corresponding to clusters, perhaps - rather than a random distribution of Ti throughout the glass. The latter model would give a peak at 0.61 nm, close to the second peak in the double difference data. Double difference measurements for Ca in a silicate glass have recently been reported by Gaskell et al. (1991 a). Neutron scattering from glasses consisting essentially of calcium metasilicate with 3mol% A12O3 added to reduce the risk of devitrification,

4.7 Binary Alkali and Alkaline Earth Silicates, Borates and Phosphates

259

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V

; -0.010

i

,

i

, ,

Figure 4-58, Distribution of Ca-Ca neighbours for r > 0.25 nm inferred from the fourier transform of the double difference data obtained in a calcium silicate glass. There is some "contamination" of the data by a peak at 0.23 nm associated with inadequate subtraction of the C a - O distances (Gaskell et al., 1990 a).

10

-(A)

were measured with three isotopic concentrations of Ca and the resulting distribution is shown in Fig. 4-58. Assuming perfect composition matching and ideal data reduction procedures, the resultant second difference should represent Ca-Ca correlations only. As shown in Fig. 4-57 there is some "contamination" of Ca-O correlations giving a peak at about 0.23 nm. The prominent peak at 0.37 nm corresponds closely to distances observed in c-CaSiO3 (0.36, 0.375 nm). For this composition, the Ca-Ca distance in a "randomly-stuffed" glass would correspond to 0.44 nm. The experimental data has been fitted with a series of gaussian peaks allowing the coordination number to be estimated. The total of 4.8 atoms are located in the two peaks at 0.35 and 0.4 nm, with a further 0.95 atoms at 0.45 nm. In the crystal, 4.67 CaCa pairs are observed near 0.4 nm. A further pronounced peak is observed at 0.64 nm and a smaller one at 0.9 nm. Interestingly, the first corresponds closely to ^/3R1 where R1 is the first Ca-Ca distance of 0.37 nm. For a DRP cluster, similar to that proposed by Hanson and Egami (1986) for Cs-silicates? the second peak would lie between 0.63 to 0.73 nm, and the third peak near 0.94 nm.

4.7.3.2 Complementary Techniques Relatively little conclusive information on the M-M correlations has been obtained from techniques other than diffraction. An exception is the work of Panek and Bray (1977) who used 2O5T1 NMR to show Tl-Tl pairing, even in Tl-dilute glasses. 4.7.4 Speciation 4.7.4.1 Borates Borates differ from silicates in that while Si is normally tetrahedrally bonded, boron can exist in tetrahedral and trigonal coordination. Experimental methods (chiefly NMR and vibrational spectroscopy) allow the B 4 ratio to be examined as a function of composition, for instance. Crystalline borates exhibit a wide range of anionic groupings, combining B-O triangles and tetrahedra linked through bridging oxygens, Fig. 4-59. Vibrational spectroscopy and X-ray diffraction have provided evidence that such anionic groups persist in glasses too, a review of this work being given by Krogh-Moe (1965). NMR has also figured prominently in attempts to understand the medium-range structure,

260

4 Models for the Structure of Amorphous Solids

Computer fitting of similar wide-band B NMR data, allows the medium-range structure to be examined. Features in the 10 B NMR signal are sensitive to changes in the local structure around the atom, and these are reflected in variations in the quadrupole coupling constant and the asymmetry of the electric field gradient. Fig. 4-61 shows computer fits to experimental spectra using parameters derived from the borate groups shown in Fig. 4-59. Constraints include bond number and charge conservation, together with detailed rules relating the fraction of B 4 , B 3 and concentrations of the anionic groups of which they form components. Additional constraints preclude participation of a given anionic group in composition regions far from that appropriate to its composition. Effectively this follows the suggestion of Krogh-Moe (1965) that glasses contain structural groups appropriate to compositionally-equivalent crystals. 10

J> Figure 4-59. Anionic units in borates after Bray and Liu (1983). a) Boroxol, b) pentaborate, c) triborate, d) diborate, e) metaborate, f) pyroborate, g) orthoborate, h) "loose" BO 4 unit.

chiefly through the research of Bray and coworkers - for recent reviews see Bray and Lui (1983), Bray (1987). 1XB NMR has been used to determine the fraction of 4coordinated boron atoms in alkali silicate glasses as a function of composition. Physical properties of alkali borates such as density, coefficient of thermal expansion and refractive index, show sharp changes in the region 15-20 mol%. This had been attributed to structural changes in which BO 4 groups with bridging oxygens become progressively replaced by trigonal groups with at least one non-bridging oxygen. Data shown in Fig. 4-60 indicates that the fraction of tetrahedral B continues to increase to about 40 mol%, however.

4.7.4.2 Silicates Relatively few conclusive results emerged on the anionic species present in silicates until the mid 1980's. Raman investigations - essentially qualitative - suggest a broad species distribution. Since the advent of 29Si NMR applied to silicates, with N4 0.50.40.30.20.10.0 0.0

0.4

0.8

1.2

1.6

2.0

Figure 4-60. The fraction of 4-coordinated boron atoms in lithium borate glasses determined by Bray and Liu (1983) by X1B NMR spectroscopy. (R is the ratio of molar concentrations of Li2O and B2O3.)

4.7 Binary Alkali and Alkaline Earth Silicates, Borates and Phosphates

261

100 KHz

Figure 4-61. Experimental 10B NMR data for lithium borate glasses as a function of composition expressed as the ratio, R, of the molar concentrations of LiO 2 and B 2 O 3 . The smooth lines represent computed fits to the data based on variations in the fraction of anionic units shown in Sec. 4.7.8 (Bray and Liu, 1983).

or without magic angle spinning, the situation has been transformed (Grimmer et al., 1984; Dupree et a l , 1984, 1986 and Schramm et al., 1986). The narrow peaks obtained for the alkali silicates can be analysed by fitting, using comparisons with crystalline compounds, to give the relative fractions of silicons of species

Qn(0
For a glass of composition, say, Na 2 Si 2 O 5 , a chemically-ordered model would suggest that the glass contains Q3 species alone, whereas a random model favours a distribution with all species present

to some extent. For a composition corresponding to the trisilicate, Na 2 Si 3 O 7 , a mixture of Q3 and Q4 species is the minimum binary combination according to an ordered model but, again, all species are possible in a random model. Although the results differ in detail, all the investigations conclude that alkali silicates are more chemically-ordered than random models predict. Analysis of the data of Grimmer et al. (1986) and Dupree et al. (1984) for lithium and sodium silicates leads the authors to propose significant ordering. Thus at "stoichiometric"

262

4 Models for the Structure of Amorphous Solids

compositions, corresponding to the disilicates and metasilicates, the magic angle NMR data indicates a dominant contribution from g 3 and Q2 respectively. Intermediate compositions were analysed in terms

of binary weighted mixtures. Other workers have fitted spectra with multiple peaks. Thus Schramm et al. (1986), Selvaraj et al. (1985), Murdoch et al. (1985), Hater et al. (1989), interpret their data in terms of 3 to 5 species. Stebbins (1987, 1988) has pointed out that MASNMR alone, may not be the most sensitive method for establishing the proportions of silicate species and that a combinatioin of spinning and static NMR techniques improves the data. The reason lies in the variation of the chemical shift for 29Si with the symmetry of the site. Variations in local symmetry produce shifts of the order of 150 ppm - depending on the relative orientations of the anisotropy and the external magnetic field. This is typically the breadth of the spectrum. This chemical shift anisotropy is averaged out in MASNMR leading to improvements in resolution. Stebbins points out that for highly disordered solids, resolution may be better in static spectra, taking advantage of differences in chemical shift anisotropy, which will be small for a highly symmetrical site such as a Q4 Si, and therefore the contribution is less broadened. Thus Q4 sites can be detected much more easily in the static spectra than in the spinning spectra, Fig. 4-62 a. The MASNMR spectra do, however, allow detection of the Q2 species, Fig. 4-62 b. The extent of any departure from a single species, Qn, can be represented by an equilibrium: 2Qn = Qm+1 + Qm~1

0<m<4

and an associated "equilibrium constant": -60

-80

-100 ppm

Figure 4-62. 29Si NMR spectra of sodium silicate glasses as a function of composition (the molar fraction of Na 2 O is shown), a) Without sample spinning - cross hatching shows the areas of the Q 4 peaks, b) With magic angle spinning (Stebbins, 1987).

K =

C2(n)

(4-41)

where C(n) is the concentration of species Qn-

4.7 Binary Alkali and Alkaline Earth Silicates, Borates and Phosphates

Thus, Kn = 0 implies a chemicallyordered distribution with: C(n + 1) = C(n — l) = 0;C(n) = l. For a non-stoichiometric composition lying between §iO and Na 2 Si 2 O 5 , say, only a binary distribution of components Q3 and Q4 need be considered. This was the result observed by Grimmer et al. and Dupree et al. Kn > 0 implies the presence of at least three species and therefore a contribution to the configurational entropy. Stebbins (1988) presents values for the fraction of Q4 species in Li- and Na-disilicates (6.4 and 11.5%) leading to K3 values of 0.005 and 0.022. For a random distribution, K3 would be much larger, 0.375, (Lacy, 1965) corresponding to C(4) = 32%. The extent of disorder is greater as the field strength of the ion M increases - that is for small polyvalent ions. Thus K3 for Li + is greater than for Na + , and K 3 for C a + + greater than for N a + . Even in the latter case, however, the distribution is far from the limit suggested by a random model. Gurman (1991) has produced a thermodynamic model which describes the silicate anion species present in alkali silicates as a function of composition. Specifically, the equilibrium constant given by Eq. (4-41), is expressed in terms of a Boltzmann factor, exp( —2A£/£: B r), where AE = EBB + + ENN — 2 EBN. In this expression, EBB represents the energy of interaction between two bridging atoms, B; ENN and £ B N , are similar terms involving non-bridging and bridging atoms. T is identified with Tg. Gurman's expression is compared with experimental Raman and NMR data and gives a pleasing explanation. NMR, either static or spinning, is much less useful for silicates with divalent cations; spectra are broad and relatively featureless (Kirkpatrick et al., 1986;

263

Schneider et al., 1987), and deconvolution into the spectra of component species is not possible. Schneider et al. suggest that this is due to a combination of factors such as the smaller differences between bridging and non-bridging oxygens as the electronegativity of the modifier ion increases, rather than the signature of a broad, continuous distribution of species. Structural variables other than populations of Qn species, variations in bond angles and lengths, for example, are also important. Stebbins and coworkers have also studied the temperature-dependence of silicate speciation: directly, by measurements at temperatures above Tg (Liu et al., 1987, 1988), and by variation of the fictive temperature by quenching or annealing schedules (Brandriss and Stebbins, 1988; Stebbins, 1988). Disproportionation was found to increase for a sodium disilicate glass, rapidly quenched so that its fictive temperature was about 80 °C higher than that for annealed glass. The Q4 population increased from 0.06 to 0.08. This disproportionation is still smaller than that estimated either from Raman spectroscopy or from the statistics of random models. As the temperature is increased, not only does the average species population change but also life-times decrease. NMR studies show that silicon atoms exchange rapidly among sites in the liquid at temperatures greater than 100 to 200 K above Tg. At temperatures around 300 K above Tg9 the broad NMR signal shrinks to a narrow line due to the rearrangements occurring on a time-scale less than the experimental time-scale (inverse of the static line width). The atomistic picture is of a rapid reorientation of the local symmetry axis for a Si atom, involving interconversion of bridging and non-bridging oxygens on time scales of a few microseconds for temperatures above the liquidus, to nanoseconds at

264

4 Models for the Structure of Amorphous Solids

2000 K. Such structural rearrangements are, of course, on time-scales much longer than vibration frequencies of around 10~ 1 3 s. 4.7.5 Network Models Compared with the effort devoted to modelling all other families of glasses surveyed in this chapter, simple metal oxide glasses have been almost neglected. Apart from a few simulations by MD techniques, the essentially qualitative notions advanced as the random network model almost 60 years ago at the time of writing - have hardly been given any thorough quantitative examination. Difficulties in producing physical models is a significant factor of course, physical and computergenerated models (apart from MD studies) are virtually non-existent. The classical picture of alkali silicate glasses due to Warren and Zachariasen is shown in Fig. 4-3 b. It can be considered as being derived from the random network of the glass-forming oxide - SiO 2 , say - by addition of the network-modifying oxide which breaks Si-O-Si bonds so that for every oxygen atom of the modifier, two bonds are broken to form negatively charged non-bridging oxygens. The charges are balanced by the M + cations in the vicinity. The environment of the M + cations is unspecified as the diagram indicates. One of the simplest physical properties that appears to be quantitatively inconsistent with this model for alkali silicate glasses is the density. Clearly, this is not a structural property but, as in many other systems, density data is sensitive to the details of proposed structure - see Sec. 4.4.6. Gaskell (1982) pointed out that differences in density between alkali silicate crystals and glasses is so small that an understand-

ing of the former leads to a model for the latter. Specifically, lithium silicate glasses are based on a close-packed oxygen sublattice with Si and Li occupying the interstices. The lattice is dilated mainly due to the cations expanding the lattice in directions normal to the planes containing sheets or chains. Also, the directional S i - 0 bonding introduces an expansion corresponding to the difference between the tetrahedral oxygen bond angle (in close-packing) and that observed (125 to 135°). This acts in the plane of the sheets or chains. Simple geometrical arguments based on these principles lead to good agreement with experimental data for the crystals. It then becomes difficult to see why similar explanations should not apertain in glasses too and leads to the conclusion of dense packing around the alkali cations, "probably within well-defined channels" and that the silicate sheets, for example, extend over distances of 2 to 3 nm in each direction. This follows from the need for co-operative atomic motion to achieve the necessary degree of close packing of oxygens around Li. Later simulations described in Sec. 4.7.8 further illuminate this point as (more) random models disagree with density data. In order to explain the well-defined coordination around network modifier atoms as observed by EXAFS, Greaves (1985) proposed that such elements are incorporated into the structures in a manner complementary to that of the network formers like SiO2 so that "the overall structure will necessarily comprise two interlacing sublattices: network regions constructed from network formers and inter-network regions made up of modifiers". Fig. 4-63 shows Greaves' pictorial representation of an archipelago structure " . . . peninsulas and islands of network interspersed by channels and lakes of modifier.

4.7 Binary Alkali and Alkaline Earth Silicates, Borates and Phosphates

265

Figure 4-63. Schematic representation of the "modified random network" structure proposed by Greaves (1985). Strong covalent bonds between the "networkforming" atoms are shown by double solid lines and ionic M - O bonds by the dashed lines. The shaded region delineates the network regions and highlights the percolation paths linking the M cations.

Whether the modifier regions . . . extend to precolation channels will depend on the composition . . .". Greaves refers to this model as a modified random network. The chief difference between this model and earlier CRN models for silicates is the presence of modifier cations within an anionic sublattice composed principally (or entirely) of non-bridging oxygen ions. An atom such as that marked in Fig. 4-3 b in the Warren-Zachariasen picture would appear to be disallowed in Greaves' model. Thus far, the modified CRN has been used as a conceptual tool only, with no attempt to build a model and test its structural properties. 4.7.6 Molecular Dynamics Much of the early work on alkali silicates was carried out by Soules and coworkers using a modified Born-MayerHuggins potential. Soules (1989) has recently reviewed MD simulations on oxide glasses but more detailed treatments are given in Soules (1979, 1985). Soules shows that M + ions are associated with nonbridging oxygens, but no discernable coor-

dination shell is found. The number of atoms increases continously with distance - in contrast to the behaviour of B which is a network former with a first coordination shell of 4. Tesar and Varshneya (1987), have used a similar potential to study alkali silicate glasses over the composition range that is subject to sub-liquidus immiscibility in the real glasses, in an effort to identify composition fluctuations associated with phaseseparation. Although unsuccessful in this aim - more definite evidence of a first coordination shell of oxygens was observed. Coordination numbers of 3 to 4 for Li, and 2 to 3 for Na and K are lower than experimental values, however. M-M clustering was not observed - the calculated M-M pair correlation functions are essentially featureless. A far-reaching survey of the properties of sodium silicate glasses (5 to 33 mol%) has been reported by Mitra and Hockney (1983 a, b). Total radial distribution functions and interference functions were calculated and compared with experimental X-ray and neutron data and the fit is found to be reasonably good. Unfortunately Mi-

266

4 Models for the Structure of Amorphous Solids

tra and Hockney did not compare their computations with the high Qmax neutron scattering data of Misawa et al. (1980) (which in fact provides a good fit). The partial distribution functions are particularly revealing. A pronounced Na-O peak is seen at 0.23 nm corresponding to about 4.8 to 5.0 oxygens is in good agreement with experimental data of Greaves et al. (1981). Moreover, a broad Na-Na peak is seen (Fig. 4-64) around 0.32 nm for all compositions - even those dilute in Na, and there are indications from the models of clustering on a scale of 1.0 nm diameter. These are most obvious in the silica-rich glasses. At 33mol% Na 2 O, the distribu-

Na-Na Na2O/SiO2 33%

20%

tion of Na + is more liquid-like. Mitra and Hockney conclude that in the silica-rich glasses (5 and 10 mol%), Na + ions occupy holes in the silica network but as the Na concentration rises, this influence on the surrounding structure becomes more prominent and a simple geometric model of sodium occupancy of holes is inappropriate. An interesting MD simulation of a sodium trisilicate glass, Na 2 O • 3 SiO 2 , is that by Newell et al. (1988), who introduced a Stillinger-Weber three-body interaction in addition to the Born-Mayer-Huggins pair potential (see Sees. 4.4.4 and 4.7.6) in a simulation. A sharp O bond angle distribution was obtained, a = 6° with very few overcoordinated Si atoms. A broad oxygen bond angle distribution (a = 12°) with a mean of 149° was found. A broad Na-Na peak at ^0.30 to 0.31 nm was observed and a Na-O distance of 0.242 nm, with a coordination number of 5.0 in good agreement with the experimental value of Greaves et al. (1981) and Misawa et al. (1980). The proportions of Q4 and Q3 (and other) silicate species were calculated - the Q4 and Q3 concentrations being about 48 and 43% respectively with 8% Q2. Although the authors did not attempt a detailed comparison with experimental correlation functions, the work indicates the possibility of future progress.

10%

4.7.7 Microcrystallite Models

r(A) Figure 4-64. Distribution of N a - N a pairs in several sodium silicate glasses simulated by molecular dynamics. The first peak position is not dependent on the Na concentration indicating N a - N a clustering (Mitra and Hockney, 1983 a, b).

The intensity and position of Raman bands of alkali silicate glasses is interpreted by Phillips in terms of vibrations internal to grains and to the "surface" modes of disilicate and metasilicate clusters. The interested reader is referred to Phillips (1982) for details. Several workers have used clusters comprising a number of unit cells of the corre-

4.7 Binary Alkali and Alkaline Earth Silicates, Borates and Phosphates

267

2 600 _xlO

S 400

500

200

1 2

3

4

5

(a)

1

2

3

4

5

(b)

1000

4000 ^

500 2000

0 (c)

1 2

3 4 Radius (A)

5

0

sponding crystalline phase as bases for models of the corresponding glasses. Thus Yasui et al. (1983) and Imaoka et al. (1983) have modelled alkali metasilicates and disilicates by distorting the geometry of the silicate chain - specifically varying the corrugation - with alkali positions altered to maintain ionic radii. Variations in the network topology were excluded so that no attempt was made to introduce Q3 or Q1 species into models for metasilicates, say. Agreement with experimental radial distribution functions to 0.5 nm is quite impressive (Fig. 4-65). Surprisingly, most of the chains are almost straight in the models only for the sodium glass does the corrugation (represented by 9) approach values for the crystals. Results of a similar quality were obtained for Na 2 Si 2 O 5 .

1 2

3 4 5 6 Radius (A)

7

Figure 4-65. Calculated RDFS (full lines) for models of several alkali metasilicates containing, a) Li; b) Na; c) K; d) Cs, compared with experimental data (dashed lines) from X-ray scattering measurements (Yasui et al., 1983).

4.7.8 Stereo-Chemically Defined Models Barenwald et al. (1988) proposed a model for barium metaphosphate, Ba(PO3)2 in which the chain structure of the crystal forms the basis. This is then varied by a Monte-Carlo process in which arbitrary PO 4 tetrahedra comprising the chain are rotated through a randomly-chosen angle. Randomly chosen Ba atoms are given random translations. Moves are accepted or rejected according to the degree of improvement between experiment and model data, although the authors do not make clear what criteria are used. Results are good to about 0.4 nm but somewhat haphazard thereafter. Gaskell (1985 b) constructed a model for amorphous alkali chain metasilicates,

4 Models for the Structure of Amorphous Solids

268

starting from idealised structures of the crystalline phases. Crystalline Li 2 Si0 3 can be considered to be derived from a hexagonally close-packed (hep) oxygen sub-lattice with Li atoms occupying part of the tetrahedral interstices and Si atoms occupying the remainder. Each cation has a nearest

neighbour shell of 4 oxygens, therefore. Ordered insertion of Li and Si into a set of interstices running parallel to the hexad axis provides a structure that is topologically identical to c-Li2SiO3, as shown in Fig. 4-66 a. If connections to nearest neighbours are introduced, the structure

b) 20

.

.

.

.

1

1

I

15 :

. .

I

si-o

-

10

T

5

e? 0

•

-5

-10

i

.

.

.

. t

,

,

,

,

i

i

.

,

,

i

,

,

,

,

1

r/A

r/A

Figure 4-66. a) The hexagonally close-packed oxygen sub-lattice corresponding to an idealised (crystalline) lithium metasilicate structure. Si atoms are shown by small circles and occupy tetrahedral interstices (at two levels) forming chains running parallel to the hexad axis (out of the plane of the diagram). Each Si-O chain is surrounded by six parallel Li-O chains (medium-sized circles), b) Computed partial pair distribution functions, Gap(r), for random chain models of a-Li2SiO3 (Gaskell, 1985b).

4.8 Concluding Remarks

can be seen to be a series of parallel chains of interconnected silicon-oxygen tetrahedra, each (SiO3)n chain being surrounded by a sheath of six (LiO3)n chains. The actual structure of the crystal involves geometrical distortions to allow the atoms to fit together but the only significant result of this is that the pair correlation functions become somewhat broader and the Li atom aquires a fifth long Li-O bond. Crystalline Na 2 Si0 3 is almost identical in structure - the distortions are larger, reflecting the larger size of the Na ion and the distances to all five near oxygens are almost equal, so that Na can be regarded as having a coordination number of five. It is known that the density of lithium silicate and other alkali silicate glasses is only slightly less ( « 5 % ) than that of the corresponding crystals suggesting that the close-packed oxygen sublattice is common to both phases. A model for the glass was thus constructed by inserting Li (or Na) into tetrahedral interstices but with a more random choice. Specifically, the constraint that Si-containing tetrahedra are surrounded by Li-O chains was retained and two-fold connectivity was preserved by rejecting Q4 or Q3 species - although chain ends (Q1) were unavoidable. The sites were chosen randomly subject to an overall check on the Li/Si ratio. The result was a set of random, self-avoiding Si-0 chains surrounded by connected Li-O tetrahedra. The model was then relaxed using a modified Keating potential with parameters chosen so that a close-packed structure which, as stated above, is topologically identical to the crystal, relaxed to give the geometrical structure of the crystal too. Partial distribution functions were then calculated (Fig. 4-65 b) and give a reasonable representation of the major features observed from inspection of the total rdf. In particular, the environment of the Li

269

atom which can be extracted from neutron scattering measurements with isotopic substitution, agrees quite well with the predictions of the model. There are similarities too with the distribution functions proposed by Mitra and Hockney (1983 a, b). Nonetheless, this simulation was judged to be less than adequate. The values of the density for the amorphous model proved to be about 12% larger than values for the crystal whereas the experimental value is about 5% less. The discrepancy was thought to be the result of incorrect topology. Specifically, the disordered chain model - despite the extensive constraints on randomness - was thought to be still too disordered. It was suggested that a more successful model might be a domain model in which small ( « 1 nm) bundles of chains and therefore the local hexad axis of the hep oxygen sublattice, ran parallel over distances of 1 to 2 nm. Beyond, the structure is postulated to be statistically identical apart from a change of direction. The underlying philosophy is thus identical to Dubois et al.'s (1985) model for transition metal-metalloid glasses (Sec. 4.2.4.4).

4.8 Concluding Remarks It is perhaps only when one is confronted with the mass of literature on the structure of glasses and amorphous solids, and faces the task of distilling the essential features into an article of this length, that the magnitude of the human effort involved becomes fully apparent. The reasons are clear enough. As outlined at the start, amorphous solids are socially and commercially important. Moreover, they present one of the more interesting challenges in condensed matter science, and glasses represent an entree into an even less

270

4 Models for the Structure of Amorphous Solids

tractable subject - the liquid state. In this section, it might be worth summarising just what has been achieved as a result of all this effort, what is still needed and how this might be done. What follows is necessarily an even more personal judgement than the foregoing. 4.8.1 Information Content

Firstly, a theme that runs throughout this chapter, is the need to press for experimental structural information of the highest precision and information content, and to interpret such data in terms of models that fully represent the detail disclosed by experiment. The reasons will be clear from reading any of the last three sections. Certain types of experimental data are information-dilute - total scattering functions for polyatomic solids, vibrational density of states functions, high resolution micrographs of thick specimens. Such data can be shown to be almost equally consistent with several models based on radically different precepts. It is also clear that where experimental information does have high information content - a high resolution pair correlation function for an elemental amorphous tetrahedral semiconductor for example then, again, a variety of models gives an approximate fit to experiment. But until recently, it was not clear that any model had achieved a fit approaching the accuracy of experiment (and this point may still be considered contentious by some). It is only with the combination of fast, cheap computing - and patient research work - that enough options have been explored and tested to allow models to "home in" on the subtleties of experimental results. How should the situation be improved? Experimental techniques are already very sophisticated and it might be consid-

ered unrealistic to hope for major breakthroughs as a result of the application of "new wonder" techniques. It is difficult to see how elastic scattering measurements for say, a-Ge could advance sufficiently to allow any sort of quantum leap, although the increasing use of high Qmax X-ray and neutron scattering measurements will lead to continued evolutionary developments. For polyatomic solids, improvements are clearly possible by making more use of those techniques that allow investigations of partials or weighted sums of subsets of partials. Thus the application of neutron scattering with isotopic substitution, XAFS and the increasingly powerful Xray anomalous scattering techniques become areas for further concentration of effort. Developments in XAFS have already allowed great strides to be made and with the increasing possibility of successful analysis of the low energy region dominated by multiple scattering, it is possible to hope that information can routinely be extended beyond nearest neighbours. Furthermore the possibility of combining techniques like X-ray anomalous scattering with XAFS, so that each complements the other's weaknesses, continues to be an exciting prospect. With recent developments in high voltage high resolution electron microscopes, there is now every prospect that this technique - with immense potential (in both senses) - can reach something like that promise, with unambiguous information on just the scale, 0.5 to 1.5 nm that other techniques are currently finding difficult or impossible to handle. Structural techniques based on excitations of the solid probably justify more optimism for further growth in the near future. In part this is because techniques like neutron inelastic scattering have been relatively used until recently. The extent of

4.8 Concluding Remarks

new information in the dynamical structure factor remains to be seen: analysis of the data that does exist in terms of structural models has hardly been tackled. The possibilities raised by partial dynamical structure factors are clearly immense but the experimental difficulties and the cost in terms of neutron beam time remain severe drawbacks. Another reason for emphasising the progress possible in vibrational studies comes from the fact that so much remains to be done. I believe that it is still correct to say that there is no convincing comprehensive explanation of the vibrational spectra of a single oxide glass. The brief account of recent applications of NMR to silicates should be sufficient to convince the reader that the potential of this technique too is immense. Improved knowledge of anionic speciation as a function of preparation variables, composition, temperature, etc. should answer several outstanding structural questions. Computational power has now reached the point where some of the limitations imposed on structural simulations are no longer insurmountable. The problem of choosing the correct potential function remains but constraints on computer time should no longer force the unhappy compromise that was common previously. The attractions of ab initio calculations for even quite complex polyatomic amorphous systems is, clearly, a reason for great optimism. Apart from the confidence conferred on results calculated with realistic potentials, increased computing power has lead to advances in the use of more humble simulation techniques. The drudgery involved in constructing models can now be removed, in principle at least, through the use of molecular graphics programmes similar to those used by molecular biologists. More thorough surveys of parameter space are possible to establish the best set

271

of atomic coordinates to represent the experimental data. An example is the recent work (Sec. 4.6.4.1) on vitreous silica by Gladden (1990), whose patience and computer budget extended to a search of over 30 models. Automatic, blind, objective, searches through parameter space using maximum entropy or Monte Carlo fits to experimental diffraction data are also appealing - and, again, there are recent examples to prove this, It certainly should be possible now to leave the computer to produce a fit that agrees with experimental data within statistical errors - and given the precision of modern experimental neutron scattering data this is a powerful constraint on any resulting model. But this type of work has also raised the difficult question of just how much structural information is contained in such data and how many additional constraints may be necessary to specify the structure. There is mounting evidence that even the most accurate scattering data will be inadequate to specify the structure of covalent amorphous solids to the degree necessary to make progress in understanding the relationships between microscopic structure and macroscopic properties. Indeed, the spectre has been raised: all our accessible information may be inadequate to "solve" the structure in any real sense. Put another way, the set of possible structures that adequately fits all experimental data within statistical errors may still be so broad that subjective judgements alone distinguish the final choice.

4.8.2 Microscopic and Macroscopic Properties A neglected area in this chapter has been any attempt to relate any of the above to macroscopic physical or chemical proper-

272

4 Models for the Structure of Amorphous Solids

ties of glasses. What use can any of this esoteric investigation be to those who deal with the production of these "socially and commercially useful" materials or those who have to live with their acknowledged limitations? The answer must be that applications of microstructural knowledge exist but that they are infrequent. Partly this must be because microstructural knowledge is so limited - certainly inadequate to sustain a large industry in the 20th century - still less in the 21st. To conclude this review, a brief account of some of the areas where application has been made and others where progress seems likely soon. Firstly, it can be argued that several of the experimental techniques have been involved in investigations of phenomena that are central to the glassy state. Examples are electron microscopy, small angle X-ray or neutron scattering that have been central techniques in investigations of crystal nucleation or catalysed crystallisation on which glass ceramics depend, or with microstructural studies on a larger scale involving phase separation, void formation in amorphous semiconductors, sintering of sol-gel glasses, studies of the fundamental transport processes involved in the glass transition by quasielastic neutron scattering etc. On a more rarified level, techniques that probe the low frequency vibrational characteristics illuminate details of the low temperature thermal properties - heat capacity, thermal conductivity and thermal expansion. Secondly, the potential exists now - even if it has not often been expressed in the past - to compute properties ranging from the transport properties such as viscosity, gas permeability, ionic mobility, to electronic densities of states and by extension, optical and electronic properties. The extent to which first-principles calculations

will be involved remains to be seen but the prospects appear promising. Revision of models for the alkali silicates have also allowed a qualitative appreciation of the changes in certain physical properties with composition. For example, Greaves has pointed out that the percolation network of cations in the modified random network model will act as conduction channels for ion transport and that the regions where the modifying cations lie represent regions of easy shear, thus providing visualisation of the processes involved in viscous flow. Perhaps the most potentially far-reaching development has come from the exploration of the constraint hypothesis, associated with the work of Phillips and Thorpe. As mentioned in Sec. 4.2.1.2, Phillips (1979) introduced the notion that the relation between the number of mechanical degrees of freedom and the number of constraints acting on an atom holds the key to an understanding of the glass transition and the composition-dependence of glass formation. Specifically, Phillips related the constraints to the forces acting on an atom in a simple valence force field and arrived at a specification of properties in terms of the average atomic coordination number. Compositions appropriate for easy glass formation correspond to a mean coordination number of 2.4. Subsequently, Thorpe (1983) examined the connection between average coordination number and the rigidity of a network, a subject that as Phillips and Thorpe (1985) point out, dates back to Maxwell. Thorpe showed that a network would become floppy at a critical value, 2.4, of the mean coordination number. This would then become apparent in the elastic moduli and in the low frequency vibrational spectrum. These propositions have been confirmed (Thorpe and Cai, 1989) and the subject of rigidity percola-

4.8 Concluding Remarks

tion and glass formation integrated through the concepts of vector and scalar percolation by Phillips and Thorpe (1985), Robertson (1986, 1991) has used these notions to describe the hardness of a-C films: specifically to relate the mechanical properties to the ratio of sp 3 and sp 2 atoms and the extent of medium range clustering - to form graphitic islands, for instance. 4.8.3 Structural Models Present and Future

It is difficult to summarise the current understanding of how the structure of glasses may best be expressed. This depends so much on the type of glass or amorphous solid, the viewpoint - experimentalist or theorist - personal taste even. It is probably safe to say that the extreme models - microcrystallite, random network - are now recognised as being extreme models, and that the truth probably lies somewhere between them for most materials. Setting up the random network or dense random packed hard sphere models as the paradigm was certainly the most rational choice in early work - an expression of Occam's razor. But more recent work has shifted the balance of evidence towards structures that are more complicated, more diverse and more ordered - at least in the sense that there may be an underlying ordering or structure-forming principle. Even the idea that a material is homogeneous on the scale of the medium range structure - that a continuous random network really is continuous - cannot now go unquestioned and structures that are essentially granular have gained in credibility. We can no longer assume, I believe, that we can think in the seductive simplicity of the language of randomness alone. What should replace it is not clear. The very diversity of the properties of the dif-

273

ferent families of glasses suggests that we should not allow our concepts to be shackled with the entrancing notions of some kind of universal explanation - a grand unified theory of everything amorphous. Not yet, at least. For amorphous monoatomic metallic glasses, amorphous tetrahedral semiconductors (probably), oxides like a-SiO2, random models represent the safest assumption. Despite recent evidence in favour of microcrystallite models for a-Si and the charm of curved-space structures, the experimental evidence is not, I believe, enough to overturn the presumption in favour of a random model. For many other glasses, especially those that have close-packed regions - like the amorphous transition metal-metalloid alloys, alkali and alkaline earth silicates, phosphates and borates - randomness as a central concept may have lost its usefulness. Experimental facts - local chemical ordering, correlated domains in TM-m glasses, M-M ordering in silicates, preferred ionic species in silicates - are inconsistent with the central tenet of randomness, that all possible structures are each equally probable. Successful models for these materials expressing the experimental facts above involve a considerable degree of preference - bond lengths and angles constrained to values close to those of the crystal, compositional ordering, medium-range "domains" as in models for a-C, TM-m glasses and possibly in silicates, preferred ionic species in borates. Should we view such models as essentially disordered but with impressed ordering reflecting a quenching rate in the real system that is inadequate to prevent it? Or are the models essentially ordered but with a degree of disorder reflecting some kinetic or topological constraint? The distinction, is partly philosophical and semantic.

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Which is the more ideal glass - the most rapidly quenched solid that can be envisaged or the slowly annealed material representing the region in configurational space close to a local energy minimum? By analogy with the idealised single crystal, clearly the latter. But should the distinction be drawn on operational considerations which concept is the more useful, for a particular composition made under practical preparation conditions? Again, there is considerable appeal in the argument that the structure of glasses is a reflection of a structure-forming principle, of its inherent stereochemistry - albeit inadequately expressed, due to compositional, kinetic, or topological constraints. What that structure-forming principle may be varies from material to material. If the only structure-forming principle involves tetrahedral bonding and vertex connection, as in SiO 2 , then the model is clearly operationally disordered with constraints on randomness limited to the local structure. In the alkali silicates, recognition that ionic cations have a local order is expressed in the modified random network model of Greaves (1985). But does this go far enough to prescribe the extent of ordering? For certain glasses were the cations show a tendency to cluster, especially at concentrations where a percolation model would suggest otherwise, or where the distance between atoms cannot easily be reconciled with the limited constraints on randomness implied by the modified random network model - the answer is probably no. In these cases and that of the TM-m alloys the question raised in the last paragraph is less easily answered. The relative success of the crystal-based models for silicates, borates, phosphates and the TM-m alloys suggests that defective order rather than constrained disorder may represent the better guide to the underlying struc-

ture-forming principle. Operationally, therefore, it makes sound sense to consider models based on a defective ordering principle as well as those that are more truly based on random applications of a structure-forming principle. Whether either of these will prove to be generally applicable must be left for the future.

4.9 Acknowledgements In addition to the generous financial support of Pilkington pic, I am indebted to several individuals who have helped with the preparation of this paper. Mrs. Pat Perrett typed the script and Mr. Keith Papworth photographed many of the figures. Discussions with Dr. Steve Gurman and Mr. Mark Eckersley on the subject matter of Sec. 4.7 have proved valuable and various sections have benefitted from discussions with Paul Fallon, Kai Gilkes, Dr. Azmat Saeed and Jianguo Zhao. Apart from plenteous moral support, Catherine Gaskell has ironed out many of my English infelicities.

4.10 References Alben, R., Weaire, D., Smith, I E., Brodsky, M. H. (1975), Phys. Rev. B 11,2271. Alder, B. X, Wainwright, T. E. (1959), J. Chem. Physics 31, 459. Babanov, Y. A., Vasin, V. V., Ageen, A. C , Ershov, N. V. (1981), Phys. Stat. Sol. 105, 747. Barenwald, U., Dubiel, M., Matz, W., Ehrt, D., Vogel, W. (1988), J. Non-Cryst. Solids 103, 311. Barker, J. A. (1977), J. de Physique 38C-2, 37. Beeman, D., Alben, R. (1977), Advances in Physics 26, 339. Beeman, D., Bobbs, B. L. (1975), Phys. Rev. B 12, 1399. Beeman, D., Silverman, X, Lynds, R., Anderson, M. R. (1984), Phys. Rev. B 30, 870. Bell, R. X (1983), in: The Structure of Non-Crystalline Materials 1982: Gaskell, P. H., Parker, J. M., Davis, E. A. (Eds.) London, New York: Taylor & Francis Limited, p. 417.

4.9 References

Bell, R. J., Dean, P. (1972), Phil. Mag. 25, 1381. Bellissent, R., Menelle, A., Chenevas-Paule, A., Chieux, P. (1985), J. de Physique 12 Coll. C 8, 93. Belliveau, T. E, Simkin, D. J. (1989), /. Non-Cryst. Solids 110, 127. Berger, S. D., McKenzie, D. R., Martin, P. J. (1988), Phil Mag. Lett. 57, 285. Bernal, J. D. (1960), Nature 185, 68. Bernal, J. D. (1964), Proc. Roy. Soc. A 280, 299. Binsted, N., Greaves, G. N., Henderson, C. M. B. (1985), Contrib. Min. Pet. 89, 103. Birch, J. R., Cook, R. X, Harding, A. K, Jones, R. G., Price, G. D. (1975), /. Physics D: Appl. Phys., 8, 1353. Biswas, R., Grest, G. S., Soukoulis, C. M. (1987), Phys. Rev. B 36, 7437. Bouldin, C. E., Stern, E. A., von Roedern, B, Azoulay, J. (1984), Phys. Rev. B 30, 4462. Brandriss, M. E., Stebbins, J. F. (1988), Geochimica et Cosmochimica Acta, 52, 2659. Bray, P. J. (1987), J. Non-Cryst. Solids 95 u. 96, 45. Bray, P. I, Liu, M. L. (1983), in: Structure and Bonding in Non-Crystalline Solids: Walrafen, G. E., Revesz, A. G. (Eds.). New York, London: Plenum, p. 285. Brown, G. S., Waychunas, G. A., Ponader, C. W, Jackson, W. E., McKeown, D. A. (1986), J. de Physique 47 Coll. C 8, 665. Calas, G., Petiau, J. (1983), Bull. Miner, 106, 33. Car, R., Parrinello, M. (1985), Phys. Rev. Lett. 55, 2471. Car, R., Parrinello, M. (1988), Phys. Rev. Lett. 60, 204. Cargill, G. S. (1970), J. Appl. Physics 41, 12. Ching, W. Y. (1982), Phys. Rev. B 26, 6610. Cochran, W. (1973), Phys. Rev. B 8, 623. Comelli, G., Stohr, X, Robinson, C. X, Jark, W. (1988), Phys. Rev. B 38, 7511. Connell, G. A. N., Temkin, R. X (1974), Phys. Rev. B 9, 5323. Coombs, P. G., De Natale, X E, Hood, P. X, McElfresh, D. K., Wortman, R. S., Shackleford, X F. (1985), Phil. Mag. 51, L39. Cowlam, N., Guoan, W, Garner, P. P., Davies, H. A. (1984), / Non-Cryst. Solids 61/62, 337. Cusack, N. E. (1987), The physics of structurally disordered matter: Bristol: Adam Hilger Da Silva, X R. G., Pinatti, D. G., Anderson, C. E., Rudee, M. L. (1975), Phil. Mag. 31, 713. Dent-Glasser, L. S. (1979), Zeit.fur Kristallogr, 149, 291. Ding, K., Andersen, H. C. (1986), Phys. Rev. B 34, 6987. Dubois, J.-M., Gaskell, P. H., Le Caer, G. (1985), Proc. Roy. Soc, A 402, 323. Duffy, M. G., Boudreaux, D. S., Polk, D. E. (1974), /. Non-Cryst. Solids 15, 435. Dupree, R., Holland, D., McMillan, P. W, Pettifer, R. F. (1984), J. Non-Cryst. Solids 68, 399.

275

Dupree, R., Holland, D., Williams, D. S. (1986), J. Non-Cryst. Solids 81, 185. Dupree, R., Holland, D., Mortuza, R. (1987), Nature 328, 416. Eckersley, M. C , Gaskell, P. H., Barnes, A. C , Chieux, P. (1988), Nature 335, 525. Elliot, S. R. (1989), Adv. Physics 38, 1. Ellis, E., Gaskell, P. H., Johnson, D. W. (1977), in: Physics of Non-Crystalline Solids: Frischat, G. (Ed.). Aedermannsdorf: Trans Tech. SA, p. 312. Etherington, G., Wright, A. C , Wenzel, X X, Dore, X C , Clarke, X H., Sinclair, R. N. (1982), J. NonCryst. Solids 48, 265. Evangelisti, E, Proietti, M. G., Balzarotti, A., Comin, E, Incoccia, L., Mobilio, S. (1981), Solid State Commun, 37, 413. Evans, R. (1990), Molecular Simulation 4, 409. Evans, D. L., King, S. V. (1966), Nature 212, 1353. Evans, K. M., Gaskell, P. H., Nex, C. M. M. (1983), in: The Structure of Non-Crystalline Materials 1982: Gaskell, P. H., Parker, X M., Davis, E. A. (Eds.). London, New York: Taylor & Francis Ltd., p. 426. Exharos, G. X (1983), in: Structure and Bonding in Non-Crystalline Solids: Walrafen, G. E., Revesz, A. G. (Eds.). New York, London: Plenum Press, p. 203. Feuston, B. P., Garofalini, S. H. (1988), J. Chem. Phys. 89, 5818. Filipponi, A., Evangelisti, F , Benfatto, M., Mobilio, S., Natoli, C. R. (1989), Phys. Rev. B 40, 9636. Finney, X L. (1970), Proc. Roy. Soc. A 319, 479. Finney, X L. (1977), Nature 266, 309. Finney, X L., Wallace, X (1981), /. Non-Cryst. Solids 43, 165. Frank, F. C. (1952), Proc. Roy. Soc. A 215, 43. Fuoss, P. H., Eisenberger, P., Warburton, W. K., Bienenstock, A. (1981), Phys. Rev. Lett. 46, 1537. Galeener, F L. (1983) in: The Structure of Non-Crystalline Materials 1982: Gaskell, P. H., Parker, X M., Davis, E. A. (Eds.). London, New York: Taylor & Francis Ltd., p. 337. Galeener, F. L. (1985), Phil. Mag. Lett. 51, LI. Galeener, F. L., Sen, P. N. (1978), Phys. Rev. B 17, 1928. Galeener, E L., Wright, A. C. (1986), Solid State Commun. 57, 677. Galeener, F. L., Leadbetter, A. X, Stringfellow, M. W. (1983), Phys. Rev B 27, 1052. Galli, G., Martin, R. M., Car, R., Parrinello, M. (1989), Phys. Rev. Lett. 62, 555. Gaskell, P. H. (1975), Phil. Mag. 32, 211. Gaskell, P. H. (1979), /. Non-Cryst. Solids 32, 207. Gaskell, P. H. (1982), J. de Physique 43, C 9-101. Gaskell, P. H. (1983), in: Topics in Applied Physics Glassy Metals II: Berlin: Springer-Verlag 53, 5. Gaskell, P. H. (1985 a), /. Non-Cryst. Solids 75, 329. Gaskell, P. H. (1985 b), /. de Physique 46, C 8-3. Gaskell, P. H., Mistry, A. B. (1978), Phil. Mag. 39, 249.

276

4 Models for the Structure of Amorphous Solids

Gaskell, P. H., Saeed, A. (1988), J. Non-Cryst. Solids 106, 250. Gaskell, P. H., Tarrant, I. D. (1980), Phil Mag. B 42, 265. Gaskell, P. H., Gibson, J. M., Howie, A. (1977), in: The Structure of Non-Crystalline Materials: Gaskell, P. H. (Ed.). London: Taylor & Francis Ltd., p. 181. Gaskell, P. H., Smith, D. I , Catto, C. J. D., Cleaver, X R. A. (1979), Nature 281, 465. Gaskell, P. H., Eckersley, M. C , Barnes, A. C , Chieux, P. (1991 a), Nature 350, 675. Gaskell, P. H., Saeed, A., Chieux, P., McKenzie, D. R. (1991b), in press. Geere, R. G., Gaskell, P. H., Greaves, G. N., Greengrass, I , Binsted, N. (1983), in: "EXAFS and NearEdge Structure", Springer Series in Chemical Physics 27, 256. Gervais, R, Blin, A., Massiot, D., Coutures, J. P., Chopinet, M. H., Naudin, F. (1987), /. Non-Cryst. Solids 89, 384. Gladden, L. F. (1990), /. Non-Cryst. Solids 119, 318. Goodmann, C. H. L. (1983), in: The Structure of Non-Crystalline Materials 1982: Gaskell, P. H., Parker, J. M., Davis, E. A. (Eds.). London, New York: Taylor & Francis Ltd., p. 151. Greaves, G. N. (1985), J. Non-Cryst. Solids 71, 203. Greaves, G. N. (1990), in: Glass Science and Technology, Vol. 4B: Uhlmann, D. R., Kreidl, N. J. (Eds.), p.l. Greaves, G. N., Fontaine, A., Lagarde, P., Raoux, D., Gurman, S. J. (1981), Nature 293, 611. Greaves, G. N., Gurman, S. J., Gladden, L. R, Spence, C. A., Cox, P., Sales, B. C , Boatner, L. A., Jenkins, R. N. (1988), Phil. Mag. 58, 271. Greaves, G. N., Barrett, N. T, Antonini, G. M., Thornley, F. R., Willis, B. T. M., Steel, A. (1989), / Am. Chem. Soc. Ill, 4313. Green, D. C , McKenzie, D. R., Lukins, P. B. (1989), Mat. Sci. Forum 52 & 53, 103. Grimmer, A. R., Magi, M., Hahnert, M., Stade, H., Samosau, A., Wieker, W., Lipmaa, E. (1984), Physics Chem. Glasses 25, 105. Griscom, D. L., Friebele, E. T, Sigel, G. H., Ginther, R. J. (1977), Structure of Non-Crystalline Solids: Gaskell, P. H. (Ed.). London: Taylor & Francis, p. 113. Guaker, R., Rafu, I., Urnes, S. (1974), /. Non-Cryst. Solids 16, All. Gurman, S. J. (1990), J. Non-Cryst. Solids (in press). Gurman, S. X (1992), Structure of Amorphous Materials, Cambridge: University Press (To be published). Guttman, L., Rahman, S. M. (1988), Phys. Rev. B 37, 2657. Hafner, X (1980), Phys. Rev. B 21, 406. Hafner, X (1981), in: Topics in Applied Physics, Glassy Metals I. Berlin: Springer-Verlag, p. 46, 79. Hafner, X, Tegze, M. (1989), J. Phys. Condens. Matter 1, 8277.

Hanson, C. D., Egami, T. (1986), /. Non-Cryst. Solids 87, 111. Hanssen, K. O., Urnes, S. (1978), Physics Chem. Glasses 19, 34. Hater, W, Muller-Warmuth, W, Meier, M., Frischat, G. H. (1989), /. Non-Cryst. Solids 113, 210. Heine, V., Bullett, D. W, Haydock, R., Kelly, M. X (1980), Solid State Physics: Ehrenreich, H., Seitz, F , Turnbull, D. (Eds.). New York: Academic Press, Vol35. Henderson, D. (1974), /. Non-Cryst. Solids 16, 317. Hockney, R, W, Eastwood, X W. (1981), Computer simulation using particles: New York: Me Graw Hill. Honeybone, P. X R., Newport, R. X, Howells, W. S., Franks, X (1991a), NATO ASI, Pisa 1990: C. McHargue (Ed.). New York, London: Plenum Press. Honeybone, P. X R., Newport, R. X, Howells, W. S., Tomkinson, X, Bennington, S. B., Reven, P. X (1991b), Chem. Phys. Lett., in press. Hosemann, R., Hentschel, M. P., Lange, A., Uther, B., Bruckner, R. (1984), Zeits.fur Kristallogr. 169, 13. Hosemann, R., Hentschel, M. P. Schmeisser, U., Bruckner, R. (1986), /. Non-Cryst. Solids 83, 223. Howie, A. (1978), J. Non-Cryst. Solids 31, 41. Imaoka, M., Hasegawa, H., Yasui, I. (1983), Physics Chem. Glasses 24, 72. Jackson, W. E., Brown, G. E., Ponader, C. W. (1987), /. Non-Cryst. Solids 93,311. Jarman, R. H., Ray, G. X, Standley, R. W, Zajac, G. W. (1986), Appl. Phys. Lett. 49, 1065. Kakinoki, X, Katada, K., Hanawa, T, Ino, T. (1960), Ada. Cryst. 13, 111. Kamitakahara, W. A., Soukoulis, C. M., Buchenau, U., Grest, G. S. (1987), Phys. Rev. B 36, 6539. Kawazoe, H. (1985), J. Non-Cryst. Solids 71, 231. Kawazoe, H., Takagi, M. (1983), in: The Structure of Non-Crystalline Materials 1982: Gaskell, P. H., Parker, J. M., Davis, E. A. (Eds.). London, New York: Taylor & Francis Ltd., p. 81. Keating, P. N. (1966), Phys. Rev. 145, 637. Keen, D. A., McGreevy, R. L. (1990), Nature344,423. Kinney, W. I. (1976), J. Non-Cryst. Solids 21, 275. Kirkpatrick, S., Gelatt, C. D., Vecchi, M. P. (1983), Science 220, 671. Kirkpatrick, R. X, Dunn, T, Schramm, S., Smith, K. A., Oestrike, R., Turner, G. (1986), in: Structure and Bonding in Non-Crystalline Solids: Walrafen, G. E., Revesz, A. G. (Eds.). New York and London: Plenum Press, p. 303. Konnert, X H., Karle, X (1973), Acta Cryst. 429, 702. Konnert, X H., Ferguson, G. A., Karle, X (1974), Science 184, 93. Konnert, X H., D'Antonio, P., Karle, X (1982), /. Non-Cryst. Solids 53, 135. Krivanek, O. L., Gaskell, P. H., Howie, A. (1976), Nature 262, 254.

4.9 References

Krogh-Moe, J. (1962), Physics Chem. Glasses 3, 208. Krogh-Moe, J. (1965), Physics Chem. Glasses 6, 46. Krogh-Moe, J., Jurine, H. (1965), Physics Chem. Glasses 6, 30. Kubicki, J. D., Lasaga, A. C. (1988), Am. Miner. 73, 941. Lacy, E. D. (1965), Physics Chem. Glasses 6, 171. Lamparter, P., Sped, W, Steeb, S., Bletry, J. (1982), Z. Naturforsch 37a, 1223. Lannin, J. S. (1987), J. Non-Cryst. Solids 97 & 98, 39. Lapiccirella, A., Tomassini, N., Lodge, K. W., Altmann, S. L. (1984), J. Non-Cryst. Solids 63, 301. Leadbetter, A. I, Stringfellow, M. W. (1974), in: Neutron Inelastic Scattering, Proceedings of International Conference, Grenoble 1972. Vienna: IAEA, p. 501. Leadbetter, A. I, Wright, A. C. (1972), /. Non-Cryst. Solids 7, 23. Levin, E. M., Block, S. (1957), J. Am. Cer. Soc. 40, 95. de Lima, J. C , Tonnerre, J. M., Raoux, D. (1988), / Non-Cryst. Solids 106, 38. Liu, S. B., Pines, A., Brandriss, M., Stebbins, J. F. (1987), Phys. Chem. Minerals 15, 155. Liu, S. B., Stebbins, J. R, Schneider, E., Pines, A. (1988), Geochimica et Cosmochimica Acta 52, 527. Ludwig, K. R, Warburton, W. K., Wilson, L., Bienenstock, A. (1987), /. Chem. Phys. 87, 604. Luedtke, W. D., Landman, V. (1989), Phys. Rev. B40, 1164. McGreevy, R. L., Putztai, L. (1988), Molecular Simulation 1, 359. McKenzie, D. R., Martin, P. X, White, S. B., Liu, Z., Sainty, W. G., Cockayne, D. J. H., Dwarte, D. M. (1987), Euro - MRS meeting June 1987, Les Editions de Physique 17, 203. McKeown, D. A., Waychunas, G. A, Brown, G. E. (1985), J. Non-Cryst. Solids 74, 349 Maley, N., Lannin, J. (1987), Phys. Rev. B. 35, 2456. Maley, N., Lannin, X, Price, D. L. (1986), Phys. Rev. Lett. 56, 1720. Matsubara, E., Waseda, Y, Ashizuka, M., Ishida, E. (1988), J. Non-Cryst. Solids 103, 111. Matz, W, Stachel, D., Goremychkin, E. A. (1988), /. Non-Cryst. Solids 101, 80. Menelle, A., Plank, A. M., Lagarde, P., Bellissent, R. (1986),/ Phys. 47 C 8, 375. Milberg, M. E., Peters, C. R. (1969), Physics Chem. Glasses 10, 46. Misawa, M., Price, D. L, Suzuki, K. (1980), /. NonCryst. Solids 37, 85. Mitra, S. K. (1982), Phil. Mag. B 45, 529. Mitra, S. K., Hockney, R. W. (1983 a), in: The Structure of Non-Crystalline Materials 1982: Gaskell, P. H., Parker, J. M., Davis, E. A. (Eds.). London, New York: Taylor & Francis Ltd., p. 316. Mitra, S. K., Hockney, R. W. (1983 b), Phil. Mag. B 48, 151. Mobilio, R, Filipponi, A. (1987), /. Non-Cryst. Solids 97 & 98, 365.

277

Mosseri, R., Dixmier, X (1981), J. Non-Cryst. Solids 44, 383. Mozzi, R. L., Warren, B. E. (1969), / Appl. Crystallogr. 2, 164. Murdoch, X B., Stebbins, X R, Carmichael, I. S. E. (1985), Am. Miner. 70, 322. Musino, A., Piccaluga, G., Pinna, G., Narducci, D., Pizzini, S. (1989), J. Non-Cryst. Solids 111, 221. Newell, R. G., Reuston, B. P., Garofalini, S. H. (1988), J. Mater. Res. 4, 434. Oldfield, E., Kirkpatrick, R. X (1985), Science 227, 1537. Panek, L. W, Bray, P. X (1977), /. Chem. Phys. 66, 3822. Pettifer, R. R, Dupree, R., Farnan, I., Sternberg, U. (1988), /. Non-Cryst. Solids 106, 408. Phillips, X C. (1979), J. Non-Cryst. Solids 34, 153. Phillips, X C. (1982), Solid State Physics: Ehrenreich, H., Seitz, R, Turnbull, D. (Eds.). New York: Academic Press, 37, 93. Phillips, X C. (1986), Solid State Commun. 60, 209. Phillips, J. C , Thorpe, M. R (1985), Solid State Commun. 53, 699. Phillips, X C , Bean, X C , Wilson, B. A., Ourmazd, A. (1987), Nature 325, 121. Piermarini, G. X, Block, S. (1963), /. Res. Nat. Bur. Stand, 67A, 37. Polk, D. E. (1971), J. Non-Cryst. Solids 5, 365. Polk, D. E. (1972), Acta Met. 20, 485. Postol, T. A., Palco, C. M., Kampwirth, R. T, Schuller, I. K., Yelon, W. B. (1980), Physics Rev. Lett. 45, 648. Price, D. L., Carpenter, X M. (1987), J. Non-Cryst. Solids 92, 153. Renninger, A. L., Rechtin, M. D., Averbach, B. L. (1974), J. Non-Cryst. Solids 16, 1. Rivier, N. (1983), in: The Structure of Non-Crystalline Materials 1982: Gaskell, P. H., Parker, X M., Davis, E. A. (Eds.). London, New York: Taylor & Prancis Ltd., p. 517. Rivier, N., Lissowski, A. (1982), J. Physics A 15, L143. Robertson, X (1986), Adv. Physics 35, 317. Robertson, X (1991), in: NATO Advanced Study Institute. Pisa 1990: McHargue, C. (Ed.). London: Plenum Press (to be published). Robertson, X L., Moss, S. C. (1988), J. Non-Cryst. Solids 106, 330. Robertson, X, O'Reilly, E. P. (1987), Phys. Rev. B 35, 2946. Rudee, M. L., Howie, A. (1972), Phil. Mag. 25, 1001. Sadoc, X R, Dixmier, X (1976), Mat. Sci. Eng. 23,187. Sadoc, X R, Mosseri, R. (1982), Phil Mag. B 45, 467. Sachdev, S., Nelson, D. R. (1985), Phys. Rev. B 32, 4592. Saito, Y (1984), J. Phys. Soc. Japan 53, 4230. Sayer, D. E., Stern, E. A., Lytte, R-W (1971), Phys. Rev. Lett. 27, 1204. Scott, G. D. (1960), Nature 188, 908.

278

4 Models for the Structure of Amorphous Solids

Schneider, E., Stebbins, J. R, Pines, A. (1987), J. NonCryst. Solids 89, 371. Schramm, C. M., de Jong, B. H. W. S., Parziale, B. E. (1986), J. Am. Chem. Soc. 106, 4391. Schulke, W. (1981), Phil. Mag. B 43, 451. Selvaraj, V., Rao, K. L., Rao, C. N. R., Klinowski, X, Thomas, J. M. (1985), Chem. Phys. Lett. 114, 24. Shuker, R., Gammon, R. W. (1970), Phys. Rev. Lett. 25, 222. Smith, D. J., Stobbs, W. M., Saxton, W. O. (1981), Phil. Mag. 43, 907. Soper, A. K., Neilson, G. W., Enderby, J. E., Howe, R. A. (1977), /. Physics C 10, 1793. Soules, T. F. (1979), J. Chem. Physics 71, 4570. Soules, T. F. (1982), /. Non-Cryst. Solids 49, 29. Soules, T. F. (1985), /. Non-Cryst. Solids 73, 315. Soules, T. F. (1989), in: "Glass 89" Survey papers of XVth International Congress on Glass, Leningrad, p. 84. Soules, T. F. (1990), in: Glass Science and Technology, Vol. 4 A: Uhlmann, D. R., Kreidl, N. J. (Eds.), p. 268. Stebbins, J. F. (1987), Nature 330, 465. Stebbins, J. F. (1988), / Non-Cryst. Solids 106, 359. Steinhardt, P., Alben, R., Weaire, D. (1974), /. NonCryst. Solids 15, 199. Stillinger, F. H., Weber, T. A. (1983), Phys. Rev. A 28, 2408. Stillinger, F. H., Weber, T. A. (1985), Phys. Rev. B 31, 5262. Temkin, R. X, Paul, W, Connell, G. A. N. (1973), Adv. Physics 22, 581. Tersoff, X (1988), Phys. Rev. Lett. 61, 2879. Tesar, A. A., Varshneya, A. K. (1987), J. Chem. Physics 87, 2986. Thorpe, M. F. (1983), /. Non-Cryst. Solids 57, 355. Thorpe, M. R, Cai, Y. (1989), J. Non-Cryst. Solids 114, 19. Tomassini, N., Amore Bonapasta, A., Lapiccirella, A., Lodge, K. W, Altmann, S. L. (1987), /. NonCryst. Solids 93, 241. Tuistra, R, Koenig, X L. (1970), J. Chem. Phys. 53, 1126. Turnbull, D. (1969), Contemp. Physics 10, 473. Turnbull, D. (1985), /. Non-Cryst. Solids 75, 197. Ueno, M., Suzuki, K. (1981), Res. Rep. Lab. Nucl. Sci. Tohuku Univ. 14, 162. Urnes, S., Anderson, A. R, Herstad, O. (1978), /. Non-Cryst. Solids 29, 1. Vashishta, P., Kalia, R. K., Antonio, G. A., Ebbsjo, I. (1989a), Phys. Rev. Lett. 62, 1651. Vashishta, P., Kalia, R. K., Ebbsjo, I. (1989b), Phys. Rev. B 39, 6034. Warren, B. E. (1969), X-Ray Diffraction. Reading (Mass): Addison-Wesley. Warren, B. E., Krutter, H., Morningstar, O. (1936), J. Am. Cer. Soc. 19, 202. Waseda, Y. (1980), The Structure of Non-Crystalline Materials: New York: Me Graw Hill, Ch. 5.

Waseda, Y, Suito, H. (1976), Tetsu-to-Hagane 62, 1493. Waseda, Y, Suito, H. (1977), Trans. Iron Steel Inst. Jap. 18, 783. Waser, X, Schomaker, V. (1953), Rev. Mod. Physics. 25, 671. Westwood, X D., Georgopoulous, P. (1989), J. NonCryst. Solids 108, 169. Weber, M. J. (1981), in: Laser Spectroscopy of Solids: Yen, W. M., Selzer, P. M. (Eds.). Berlin: Springer, p. 227. Wei, W (1986), /. Non-Cryst. Solids 81, 239. Woodcock, L. V, Angell, C. A., Cheeseman, P. (1976), J. Chem. Phys. 65, 1565. Wooten, R, Weaire, D. (1987), in: Solid State Physics. Ehrenreich, H., Turnbull, D. (Eds.). Orlando: Academic Press 40, 2. Wright, A. C. (1988), /. Non-Cryst. Solids 106, 1. Wright, A. C, Leadbetter, A. X (1976), Physics Chem. Glasses 17, 122. Wright, A. C , Sinclair, R. N. (1985), J. Non-Cryst. Solids 76,351. Yarker, C. A., Johnson, P. A. V, Wright, A. C , Wong, X, Greegor, R. B., Lytle, F. W, Sinclair, R. N. (1986), /. Non-Cryst. Solids 79, 117. Yasui, I., Hasegawa, H., Imaoka, M. (1983), Physics Chem. Glasses 24, 65. Yin, C. D., Okuno, M., Morikawa, H., Marumo, R, Yamanaka, T. (1983), J. Non-Cryst. Solids 55, 131. Yin, C. D., Okuno, M., Morikawa, H., Marumo, R, Yamanaka, T. (1986), J. Non-Cryst. Solids 80, 167. Yonezawa, R, Nose, S., Sakamoto, S. (1987), /. NonCryst. Solids 95 & 96, 83. Zachariasen, W. H. (1932), J. Am. Soc. 54, 3841. Zarzycki, X (1970), Compt. Rend. Acad. Sci. B 271, 242. Zarzycki, X, Mezard, R. (1982), Physics, Chem. Glasses 3, 163.

General Reading Cusack, N. E. (1987), The Physics of Structurally disordered Materials. Bristol: Adam Hilger. Elliott, S. R. (1990), Physics of Amorphous Materials. London and New York: Longmans. Hosemann, R., Bagchi, S. N. (1962), Direct Analysis of Diffraction by Matter. Amsterdam: North Holland. Wright, A. C. (1974), "The structure of amorphous solids by X-ray and neutron diffraction" in Advances in Structure Research and Diffraction Methods, Vol. 5, Pergamon, Oxford. Zallen, R. (1983), The Physics of Amorphous Solids. New York: Wiley. Zarzycki, X (1991), Glasses and the Vitreous State. Cambridge: Cambridge Univ. Press.

5 Oxide Glasses Harold Rawson Emeritus Professor of Glass Technology, University of Sheffield, Sheffield, U.K.

List of 5.1 5.1.1 5.1.2 5.1.3 5.1.4 5.1.5 5.1.6 5.2 5.3 5.3.1 5.3.2 5.3.3 5.3.4 5.3.5 5.3.6 5.4 5.4.1 5.4.2 5.4.3 5.4.4 5.4.5 5.4.6 5.4.7 5.5 5.6 5.6.1 5.6.2 5.6.3 5.6.4 5.6.5 5.7 5.7.1 5.7.2 5.7.3

Symbols and Abbreviations Glass Formation in Oxides Systems The Zachariasen Random Network Hypothesis Early Experimental Studies of Oxide Glass Structures Some Factors Affecting Glass Formation Bond Type and Glass Formation Bond Strength and Glass Formation Immiscibility in Oxide Systems Commercial Oxide Glasses Vitreous Silica Manufacturing Processes and Impurity Contents Devitrification Kinetics Viscosity Refractive Index Structure Defects in Silica Alkali Silicate Glasses Glass Formation and Devitrification Kinetics Other Binary Silicate Systems Physical Properties Immiscibility and Properties Chemistry of Alkali Silicate Glasses Oxygen Ion Activity; Basicity Structure Boric Oxide Glass Borate Glasses Glass Formation in Binary Systems Sub-Liquidus Immiscibility in Binary Borate Glasses Structures of Binary Borate Glasses Properties Technological Applications of Borate Glasses Borosilicate Glasses Thermal Expansion Coefficient Viscosity Structure

Materials Science and Technology Copyright © WILEY-VCH Verlag GmbH & Co KGaA. All rights reserved.

281 282 283 284 285 285 286 288 289 290 290 291 292 292 293 293 294 294 295 296 296 296 297 299 301 302 302 302 303 304 305 305 306 306 306

280

5.7.4 5.8 5.8.1 5.8.2 5.9 5.9.1 5.9.2 5.9.3 5.9.4 5.9.5 5.10 5.10.1 5.10.2 5.10.3 5.10.4 5.11 5.12 5.12.1 5.12.2 5.13 5.13.1 5.13.2 5.13.3 5.14 5.14.1 5.14.2 5.15 5.15.1 5.15.2 5.15.3 5.15.4 5.16

5 Oxide Glasses

Sub-Liquidus Immiscibility Aluminosilicate Glasses The Alumina-Silica System Sodium Aluminosilicate Glasses Phosphate Glasses Phosphorus Pentoxide Regions of Glass Formation in Binary Phosphate Systems Properties of Binary Phosphate Glasses Multi-Component Phosphate Glasses Structure Germanate Glasses Germanium Dioxide Glass Regions of Glass Formation in Germanate Systems Structure Properties Aluminate Glasses Tellurite Glasses Glass Formation in Tellurite Systems Structure Vanadate Glasses Glass Formation Properties Structure Mixed Anion Glasses Oxynitride Glasses Oxyhalide Glasses Ionic Salts and Solution Glasses Nitrate Glasses Acetate Glasses Sulfate Glasses Hydrates and Aqueous Solutions References

307 308 308 309 311 311 312 312 313 314 315 315 315 316 316 317 317 318 319 319 320 320 321 321 321 322 323 323 324 324 324 324

List of Symbols and Abbreviations

List of Symbols and Abbreviations A B G K M n n* Q Qn R r R t

symbol for chemical elements symbol for chemical elements reciprocal of the maximum growth rate in mm/min ratio of mol% SiO 2 and mol% B 2 O 3 symbol for chemical elements count number number average chain length quality of extracted material SiO 4 tetrahedron containing n bridging oxygens ratio of mol% N a 2 O and m o l % B 2 O 3 radius (of an ion) symbol for chemical elements time

Tg Um x x x y z

transformation temperature maximum rate of crystal growth Pauling electronegativity value mole fraction of R 2 O in glass number of atoms in an entity number of atoms in an entity charge number of an ion

y Y \ (^m) A v_ Oi v_ fi v _ gi

cation factor, basicity moderating power temperature of maximum growth rate optical basicity absorption frequency of probe ion absorption frequency of the free ion measured absorption frequency of the ion in glass

A.U. Angstrom unit CVD chemical vapor deposition DC direct current ESCA electron spectroscopy for chemical analysis ESR electron spin resonance EXAFS extended X-ray absorption fine structure MAS N M R magic angle spinning nuclear magnetic resonance NBO non-bridging oxygen PES photo-electron spectroscopy r.m.s. root mean square UV ultra violet XAFS X-ray absorption fine structure XANES X-ray absorption near edge structure XRD X-ray diffraction

281

282

5 Oxide Glasses

5.1 Glass Formation in Oxide Systems Oxide glasses have been known and used for more than 4000 years. During that period an industry has grown up, developed initially by exploiting various ways of using the glass-makers blowing iron, introduced by the Romans. Techniques were also developed for the cold working of glass, e.g. by cutting and engraving. These developments took place with no scientific understanding of the nature of the material or of the physical principles of the various manufacturing processes. Yet generations of craftsmen were able to produce articles of the highest quality, some of a type which is difficult to reproduce today. Until the present century, the composition of the material has remained practically unchanged - most glasses have been of the soda-lime-silica type, silica being the major component (see Sec. 5.2). Small additions of colouring materials were added as required. One new composition was introduced by Ravenscroft in 1674 - a silicate glass containing approximately 30 wt.% of PbO, this component significantly increasing the refractive index and giving a brilliant appearance to the glass when cut. The new glass was an essential component in making the first achromatic doublet lens in about 1750 by Hall and Dolland. However the development which can be regarded as being the beginning of glass science was the work of Schott, Abbe and Zeiss in the latter part of the nineteenth century. Schott made a systematic study of the effects of the composition of oxide glasses on their optical properties in order to develop glasses that would make it possible to produce lens designs of greatly reduced secondary aberrations. Several oxides, e.g. BaO, were incorporated which had not been used pre-

viously as glass constituents. The collaboration led in 1886 to the foundation of Jena Glass Works to manufacture and market the new glasses. There was no possibility at the time of interpreting the property - composition relationships in terms of glass structure and very little progress was made in that direction until the early 1930's. Early papers on the structure of oxide glasses were purely speculative and much influenced by the thinking of chemists, trained in the physical chemistry of solutions. It was known by the early 1930's that a few oxides would form glasses when melted alone, namely SiO 2 , B 2 O 3 , GeO 2 , P 2 O 5 and As 2 O 3 and that extensive regions of glass-formation existed in many binary and more complex systems containing these oxides together with a number of basic oxides, especially the alkali and alkaline earth oxides. Some of the nineteenth century work, which subsequently turned out to be important, had been forgotten. Thus Roscoe (1868) had shown that stable glasses could be made in the BaO-V 2 O 5 system and Berzelius (1834) had studied several tellurite glass systems. It is now known that glass formation occurs in many oxide systems which differ considerably from one another chemically and in other ways. In addition to the systems just listed, glass formation occurs in several aluminate, gallate, tungstate, molybdate, selenite, titanate, niobate and tantalate systems. Although of little technological interest, there is also an interesting group of glasses based on simple ionic salts e.g. nitrates, sulfates, acetates, and thiocyanates - some made from the fused anhydrous salts, others from aqueous solutions of these materials. By very rapid cooling, more substances can be added to the list of glass-formers or the extent of the region of glass formation

5.1 Glass Formation in Oxide Systems

in a particular system can be increased (Scherer and Schultz, 1983). Most of the compositions in the above list can be made as glasses without using particularly high cooling rates. 5.1.1 The Zachariasen Random Network Hypothesis

In 1932 the first significant step was made by W. H. Zachariasen towards answering two fundamental questions which are still not fully resolved today: what can we say about the structure of oxide glasses and why do some oxide compositions form glasses whilst others do not? Zachariasen's paper (1932) is remarkable for the impact it had on thinking about the structure and properties of oxide glasses. The paper is also remarkable in that it is entirely speculative and qualitative - no new observations were reported. The author was a crystallographer, very familiar with the early X-ray diffraction studies of the structure of crystalline silicates. The central hypothesis of his paper is that the vitreous form of an oxide should

283

not have a significantly higher internal energy than the crystalline form. This requires, he suggested, that both forms must contain the same kind of oxygen polyhedra and these must be joined together in a similar way, except that in the glassy form there is a range of bond angles and bond lengths. Only substances in which the polyhedra are joined by their corners have structures which are sufficiently flexible to incorporate the disorder which is characteristic of the glassy state without the lattice energy of the structure being greatly increased. (The emphasis on lattice energy was subsequently criticized by Morey (1934) who pointed out a number of examples of substances which appear to show that such energy differences are not important.) Fig. 5-1 is a schematic diagram showing the structure of a hypothetical oxide A 2 O 3 in both the crystalline and glassy forms. In this material the basic 'polyhedron' is the AO3 triangle. In both forms, the triangles are joined only at their corners by 'bridging' oxygens. In silica glass, the basic polyhedron is the SiO4 tetrahedron. Again each

Figure 5-1. Schematic twodimensional representation of the structure of (a) a hypothetical crystalline compond A 2 O 3 and (b) the glassy form of the same compound (from Zachariasen, 1932; reprinted with permission from Journal of the American Chemical Society, Copyright 1932 American Chemical Society).

284

5 Oxide Glasses

tetrahedron is linked through each corner to neighbouring tetrahedra. The appropriates of the term 'random network' is obvious from Fig. 5-1. Zachariasen argued that the requirement that disorder should not increase the internal energy led to certain rules which must be obeyed if an oxide is to form a glass: 1. No oxygen atom may be linked to more than two A atoms. 2. The number of oxygen atoms surrounding atoms A must be small. 3. The oxygen polyhedra share corners with each other but not edges or faces. 4. If it is required that the network be threedimensional, at least three corners in each polyhedron must be shared. All the then known glass-forming oxides obey the Zachariasen rules, as does the glass-former BeF2, which has a silica-like structure.

5.1.2 Early Experimental Studies of Oxide Glass Structures Shortly after the publication of Zachariasen's paper (1932), Warren and his colleagues began a series of structural studies of simple silicate glasses using X-ray diffraction. The results were summarized by Warren (1941). They were interpreted in terms of the random network model and important information was obtained concerning the way in which the alkali and alkaline earth ions are incorporated in the structure. This is illustrated in Fig. 5-2. The significant features are: 1. The cations are situated in the relatively large voids in the structure. 2. For each additional oxygen anion introduced, one A - O - A bridge is broken so that two non-bridging oxygens are formed. The positive charge on the cations intro-

•

Si

O

0

Figure 5-2. Two-dimensional representation of the structure of a sodium silicate glass (from Warren, 1941).

duced is locally neutralized by the negative charge on the non-bridging oxygens. Oxides which have a similar structural effect to that shown are referred to as network modifiers or simply modifiers. Many structural studies have been carried out on silicate glasses since then by various techniques. Some workers have contested particular aspects of Warren's interpretation. Others have added a great deal of detail, especially for those systems in which a network-forming cation undergoes a change in coordination number as the glass composition is changed. Few would question however that the WarrenZachariasen random network model has provided a valuable basis for the discussion of the structure and properties of oxide glasses. It is worth noting that Cooper (1982) in particular has considered it worthwhile returning to Zachariasen's paper, offering a re-interpretation in terms of its topological implications. However if one focuses on what Zachariasen has to say about the conditions for glass formation in particular, rather than

5.1 Glass Formation in Oxide Systems

about the structure, the value of his contribution is more open to question. 5.1.3 Some Factors Affecting Glass Formation The reason why a melt may form a glass is that within a limited temperature range below the liquidus temperature, the rate of crystal growth and/or the rate of nucleation is sufficiently low on a time scale determined by the rate of cooling. It must be possible to cool the melt to a temperature below the transformation range without crystallization occurring. That merely moves the question of understanding glass formation further back to a consideration of the factors that determine the nucleation and crystal growth rates for a particular substance. Uhlmann and his colleagues in particular have made many experimental and theoretical studies of crystallization and nucleation kinetics in supercooled oxide melts (Uhlmann 1977, 1985; Uhlmann and Yinnon, 1983). Their work has been of great value in many areas of glass science. However it has limited ability to provide pointers to new glass-forming compositions or to give a general understanding of why some compositions form glasses more readily than others. The equations of classical nucleation and crystal growth theory, which describe the temperature dependence of nucleation rate and crystal growth rate, contain many thermodynamic and kinetic parameters, which are not easy to measure or to relate in a simple way to what may be known about the composition and structure of the material under consideration. Given this situation, it is not surprising that many individuals have looked for simple criteria, preferably with some theoretical basis, which can direct attention to potential glass-forming compositions.

285

5.1.4 Bond Type and Glass Formation Several authors have proposed criteria for glass formation based on the nature of the interatomic bonds rather than on the structure of the material. The intention was to find criteria that would cover a wide range of materials including for example the glass-forming elements such as selenium as well as the oxides. Thus Winter (1955) concluded that the ability of a material to form a glass could be related to the number of outer shell p electrons per atom. The most favorable number was four but glasses could be made from substances containing between two and four p electrons per atom. The reasoning behind this correlation was not made clear and no explanation was offered for the fact that there is a considerable variation in glass-forming ability amongst the substances which meet the criterion. Stanworth's electronegativity criterion is more interesting in that it led him to the rediscovery of tellurite glasses. In a series of papers Stanworth (1946, 1948 a, b, 1952) drew attention to the significance of the degree of covalency of the interatomic bonds, as measured by the electronegativity difference between the constituent atoms. Using Pauling's electronegativity values for silicon and oxygen (1.8 and 3.5 respectively) and Pauling's curve relating the degree of covalency to the electronegativity difference, one finds that the siliconoxygen bond is 50% covalent. For the well-kown glass-forming oxides (or network formers) the cation electronegativity lies between 1.8 and 2.1. For the intermediate oxides which under suitable circumstances can behave as network-formers, the range is 1.5 to 1.8 and for the modifiers, i.e. the alkali and alkaline earth oxides, the range is 0.7 to 1.2. Stanworth noted that the electronegativity of Te is the same as

286

5 Oxide Glasses

that of P i.e. 2.1, suggesting that TeO2 might be a glass former, like P 2 O 5 - an observation which led him to investigate glass-formation in the tellurite systems (Sec. 5.12). In a later paper, reviewing more recent information on glass-forming oxides, Stanworth (1979) recognizes that the bond type alone is not a sufficient criterion. Thus he states: 'the most general conclusion is that the compounds Ax By can form glass from their melts when they have sufficiently open, sufficiently covalent network structures. Splat cooling is necessary unless the structures are based on the very open extended three dimensional networks when glass formation with slow cooling from the melt is possible'. This seems to echo much of the thinking behind the Zachariasen rules. A general comment one may fairly make about these simple bond type criteria is that they can hardly have any general fundamental significance, although they may be of some value within a particular group of compounds. Very many quite different types of inorganic substances are known to form glasses including simple fused salts in which the relevant bonds are largely ionic (e.g. fused nitrates, see Sec. 5.15) and a large number of metallic systems. 5.1.5 Bond Strength and Glass Formation

Sun (1947) recognized that the processes of melting and crystallization will often involve the breaking of interatomic bonds. The stronger the bonds, the more sluggish will be the processes of structural rearrangement and hence the more likely will a glass form on cooling. Using calculated values of single-bond strengths, he noted that these were particularly high in the glass-forming oxides: SiO 2 , B 2 O 3 etc. He was clearly aware of the limitations of such

a simple correlation, since he drew attention to the importance of structural factors. In anisodesmic structures (Evans, 1946) some bonds are very strong whilst others are weak, and it is then not clear which bond strength is relevant. An extreme example of such a substance is CO 2 . Rawson (1956) pointed out that if one is to use a bond strength criterion, one should also take into account the thermal energy available at the melting point for breaking the bonds. Thus glass formation would be more likely the higher the ratio of single bond strength to the melting point in K. This may explain why a boric oxide melt is almost impossible to crystallize. The B - O bonds are very strong, yet the melting point of the material is relatively low (450 °C). Rawson (1956,1967) extended this argument to binary and multicomponent systems, noting that one frequently finds regions of glass formation or regions of particularly low devitrification rates in regions where the liquidus temperature is low. Examples of the liquidus temperature effect are shown in the next two figures. Fig. 5-3 is based on the results of Dietzel and Wickert (1956) for the Na 2 O-SiO 2 system. G is the reciprocal of the maximum growth rate in mm/min. The highest value of G, i.e. the lowest crystallization rate, is for a composition very close to the eutectic in the phase diagram between silica and sodium disilicate. Fig. 5-4 shows the liquidus temperature effect in the CaO-Al 2 O 3 system where neither oxide component is a glass former (Rawson, 1967). In the related CaO-Ga 2 O 3 system, Wichard and Day (1984) have shown by critical cooling rate determinations that the most stable glass is the eutectic composition at 37.5 mol% Ga 2 O 3 . Commercial glass compositions are in general quite complex - for a number of

5.1 Glass Formation in Oxide Systems

v

2.8-

A

2.42.0-

f

/ /

1.6-

/

1.2-

/

0.8-

u0-

\\

X>o—O^ 5

C

10

15

25 20 Mol % N Q 2 0

30

35

LQ Li

Figure 5-3. Variation of log G with Na 2 O content in the system Na 2 O-SiO 2 (from Dietzel and Wickert, 1956).

2500-

\\

\ \

2300-

\

\

\\

\ \

\

2100-

\ \\ \ \ \

1900-

!

!

Glass-

\ 1 forming \ \ ^ region j \ \

1700-

\ \

13000 CaO

/

V

1500-

/ / /

/I

J

i

i

i

i

20

40

60

80

Wt.°/o

Al 2 0 3

1

100 Al 2 0 3

Figure 5-4. The glass-forming region in relation to the phase diagram for the CaO-Al 2 O 3 system (from Rawson, 1967).

reasons (see Sec. 5.2). One reason is that adding further oxide components often reduces the liquidus temperature and so makes the glass less prone to devitrification.

287

One has to admit that the simple relationship between glass stability and a low liquidus temperature appears to break down in some oxide systems. That is not surprising. Structural factors must also play an important role. The kinetic and thermodynamic energy terms associated with these factors must change as one traverses the system. One should also recognize that some melts may contain appreciable unknown percentages of components such as CO 2 and combined water, which affect the liquidus temperature and introduce a complicating factor which has rarely been taken into account in studies of glass formation. This emphasis on liquidus temperature is clearly based on the qualitative ideas behind the classical theory of nucleation and crystal growth (a point clearly brought out by Cohen and Turnbull (1961)). In spite of the exceptions, the liquidus temperature criterion has a wide range of applicability and appears to work equally well for a number of quite different types of material e.g. for metallic glasses as well as for oxide glasses. However the approach has limitations as a simple predictive tool since there is no simple way of predicting melting points of elements and compounds or the variation of liquidus temperature with composition in binary and multicomponent systems. In an interesting recent contribution, Chechetkina (1990) shows that there is a relationship between bonding, melting point and glass formation. For most elements and within particular classes of compounds, a plot of melting point against the averaged atomization energy shows points tightly clustered about a straight line. The glass-forming compounds however fall well below the line in each class. She postulates that the abnormally low melting point of the glass-forming substances is re-

288

5 Oxide Glasses

lated to a reversible and temperature-dependent formation of 'three centre bonds' which alternate with normal covalent bonds at various points in the structure. Although the relationship between melting point and structure had been discussed previously by Ubbelohde (1965), this work appears to be the first to discuss the relationship in the context of glass formation.

1700-

S 1600-

1500-

5.1.6 Immiscibility in Oxide Systems In many binary silicate and borate systems, the melt separates into two phases over a wide range of compositions. This is illustrated in Fig. 5-5 for a number of silicate systems. Immiscibility is a feature of systems containing cations of relatively high field strength. Note that although the BaO- and Li 2 O-SiO 2 systems form single phase melts, the liquidus curve in the silicarich region of each system shows a marked deviation from ideality. Although each component of a phaseseparated melt may form a glass on cooling, the resulting material will also be phase-separated on a relatively coarse scale and will be of no practical value. However phase separated melts can usually be made single phase by adding a few percent of a third component, especially one of the alkali oxides (Shartsis et al., 1958). It is of much greater scientific and technological interest that in many binary and ternary systems, immiscibility occurs below the liquidus temperature. Regions of sub-liquidus immiscibility in the R 2 O-SiO 2 systems are shown in Fig. 5-6. The separation in the glass is usually on a very fine scale, detectable only by electron microscopy or by sensitive light scattering measurements. The separation morphology depends on the glass composition and on the heat treatment which the glass has experi-

70

60

80 Si0 2 (mol7o)

90

Figure 5-5. The extent of immiscibility in binary silicate systems (from Levin and Block, 1957). 1100

1000

900

Xf / Na2O

Li20 \ \ \

/

\

\ \

i// / \

700

600

r

K20

/ / / /

\

i / / /

\ \

\ * \ 1 I

[

500 30

20 Mol.% R20

10

Figure 5-6. Regions of sub-liquidus immiscibility and corresponding liquidus curves for the Li2O-, Na 2 Oand K 2 O-SiO 2 systems (from Scholze, 1988).

enced above the transformation range. The physical and chemical properties of some glasses are markedly affected by sub-liquidus immiscibility, hence these properties may be affected in unexpected ways by heat treatment.

5.2 Commercial Oxide Glasses

Early interpretations of immiscibility were in terms of competition for the available oxygen anions between cations of differing ionic potential (see for example Levin and Block (1957)). The current approach introduced, in the discussion of sub-liquidus immiscibility by Cahn and Charles (1965), is based on the effects of temperature on the free energy-composition curves of the various phases (as for example in the interpretation of metallurgical phase diagrams - see Raynor (1970)).

5.2 Commercial Oxide Glasses Table 5-1 gives the compositions of a number of commercially important glasses. The intention here is merely to indicate the general features of each. For any particular type, glass compositions vary somewhat from one manufacturer to another. Note that most glasses contain many oxide components. This is largely due to the fact that any commercial glass has to meet a number of requirements, some imposed by its applications and others by the manufacturing process. (See also Chapter 1 of this volume.)

289

The first group of three glasses (1 to 3) are respectively float glass, container glass, and the glass used to make incandescent lamp bulbs. They are very similar in composition. They have suitable viscosity-temperature characteristics for the fabrication (shaping) processes which are used to make the glassware required. They have adequate chemical durability and the raw material costs are relatively low. Apart from meeting these main requirements, there are no other important property requirements to be met, except that for glass 3 the thermal expansion coefficient has to be carefully controlled. Glass 4 is a traditional lead crystal composition, in which the high PbO content gives a high refractive index and a brilliant appearance to the glass when it is cut. A similar composition is used to make the high electrical resistivity glass for the 'stem' in incandescent lamps. Glasses 5 to 7 represent the large and important group of borosilicate glasses. Composition 5 is widely used to make chemical apparatus and domestic ovenware. It has good resistance to thermal shock on account of its low thermal expan-

Table 5-1. Compositions of some commercial glasses (wt.%). SiO2 A12O3 B 2 O 3 MgO CaO PbO Na 2 O K 2 O BaO 1 2 3 4 5 6 7 8 9 10 11 12 13 14

72.8 72.0 71.5 56.0 80.8 67.5 75.5 52.9 67.0 68.3 26.9 5.5 5.0

0.7 1.3 2.0

3.6 3.5 2.8

8.8 8.2 6.5 29.0

2.2 2.5 2.6 14.5 5.0 0.2 0.5 17.5

12.0 21.7 16.0 9.2

0.3

0.3

4.4

17.4

2.2

4.6

20.0 16.0 17.0

2.9 71.3

13.8 14.3 15.5 2.0 4.2 3.2 3.7 1.0 7.0 14.4 1.0

1.0 13.0 0.6 4.2 1.7 1.0 8.3 7.0

11.7

Li2O La 2 O 3 Ta 2 O 5 ThO 2

0.6

36.0 9.5

ZnO

28.0

16.0

52.0 64.0

14.0

290

5 Oxide Glasses

sion coefficient and also has excellent resistance to chemical attack, especially by acids. Compositions 6 and 7 are sealing glasses with expansion coefficients matched to those of particular metals. Glass 6 seals to the iron-nickel-cobalt alloys Kovar, Nilo K or Fernico and is widely used both in large seals of tubular design and also in small terminal seals. Glass 7 has a somewhat lower expansion coefficient and seals to tungsten. Glass 8 is one of a group of high melting point, low alkali, aluminosilicate glasses. It is commonly known as E glass and is made as continuous fibre for glass fibre reinforced composite materials and for weaving into glass textiles used in electrical insulation. Glass 9 is a TV tube glass composition. Glasses 10 and 11 are optical glasses, 10 having a refractive index of 1.518 and 11 of 1.805. The unusual composition 12 is also an optical glass (refractive index 1.85), the use of which makes it possible to design more highly corrected lens systems than is possible with the high lead glasses. Glass 13 is resistant to attack by sodium vapour at elevated temperatures and is used as a coating on the inner wall of the glass arc tube in low pressure sodium vapour street lamps. Glass 14 is a 'solder' glass. It is quite fluid at about 550 °C and is used to seal together, without distortion, components made from soda-lime glasses such as composition 3. It is necessary, of course, that the expansion coefficient of the solder glass should match that of the components to be joined together. A detailed account of the properties of technical glasses has been given by Volf (1961). Scholze (1988) and Rawson (1980) summarize information on the propertycomposition relationships in simpler systems.

Other glasses of technological importance will be referred to in later sections.

5.3 Vitreous Silica 5.3.1 Manufacturing Processes and Impurity Contents

Vitreous silica or silica glass is the only one-component oxide glass to have any practical applications. These are of considerable technological importance. Uses include envelopes for high-intensity arc lamps and tungsten-halogen lamps, components for chemical ware, in both laboratory and chemical plant applications, and, more recently, optical communication fibres (Beales and Day, 1980; Gambling, 1980, 1986). There are several methods of manufacture (Dumbaugh and Schultz, 1969; Danielson, 1982) and the properties of the various grades of material available differ according to their impurity contents, 'water' content and their stoichiometry (Table 5-2). _ Initially the material was made exclusively by the fusion of a pure sand or crushed Brazilian quartz at a temperature of about 2000 °C. In some early processes, a boule of fused material was built up by flame-spraying ground quartz onto a target. Now the material is melted either in vacuo or a reducing atmosphere in a refractory metal or graphite crucible. The glass contains impurities from the raw material and crucible and is oxygen-deficient as a result of the reducing conditions under which it has been melted. According to Bell et al. (1962), the composition of this type of material should be written SiO 2 _ x where x lies between 10" 4 and 10" 5 . Much purer material, initially made to meet the requirements of the semi-conductor industry, is produced by the hydrolysis

291

5.3 Vitreous Silica Table 5-2. Impurity contents of various grades of fused silica (Rawson, 1967). Method of manufacture

Major metallic impurities ppm.

Water content

Ref.

Thermal Syndicate grades OG & OH

Flame fusion of rock crystal

0.04 wt.% as OH

a

Thermal Syndicate grade IR

Electric fusion of rock crystal

0.003 wt.% as OH

a

Thermal Syndicate 'Spectrosil'

Vapour phase hydrolysis of SiCl4 in a flame

0.12 wt.%

a

Thermal Syndicate 'Spectrosil WF'

Vapour phase oxidation of SiCl4

Al 10 B<0.5 Ca 0.35 Fe 0.51 Na 0.06 Al 50 Sb 0.23 B<0.5 Ca 0.4 Fe 0.74 Na 4 Al<0.02 Ca<0.1 Fe<0.1 Na<0.04 As 'Spectrosil'

Manufacturer and type no.

AsIR. plus 0.05 wt.% Cl

b

GE (USA) 201

Fusion of rock crystal

Total impurity content = 240 ppm Al 2 O 3 = 180ppm

'Water free'

c

GE (USA) 204 A

Fusion of rock crystal

Total impurity content =110 ppm A12O3= 52 ppm CaO= 23 ppm

'Water free'

c

Corning 7943

Flame hydrolysis of SiCl4 Then fired on graphite mandrel in hydrogen

'Negligible' Similar to 'Spectrosil'

0.001 wt.% as OH

c

Corning 7940

Flame hydrolysis of SiCl4

'Negligible'

c

Cab-O-SilO

Vacuum fusion of powder made by hydrolysis of SiCl4 vapour

Al 2 O 3 = 100ppm Na 2 O<200ppm

0.1 wt.% as OH 0.02 wt.% as OH

d

a. Hetherington and Jack (1962), b. Hetherington et al. (1964), c. Wagstaff et al. (1964), d. Brown and Kistler (1959).

or oxidation of SiCl4 in a flame. The hydrolyzed material has a high content of 'water', present as - O H groups. Various modifications of the vapour phase process are now used to make the very high purity material required for optical communication fibres (Schultz and Smyth, 1972; Nassau and Shiever, 1975; Gossink, 1977). (See also Chapter 2 for sol-gel processing.)

5.3.2 Devitrification Kinetics

The results of measurements on various grades of material and in various atmospheres have been summarized by Rawson (1967). At atmospheric pressure, the silica melt crystallizes at temperatures below 1723 °C to form the high temperature modification

292

5 Oxide Glasses

of cristobalite. Crystallization occurs from the surface, eventually forming an opaque coating which can only be removed by etching with hydrofluoric acid. Even trace quantities of impurities on the surface greatly increase the crystallization rate. According to Dietzel and Wickert (1956), as little as 0.32% Na 2 O added to silica glass increases the maximum devitrification rate by twenty to thirty times. Detailed studies of devitrification kinetics have been carried out by Ainslie et al. (1962), Brown and Kistler (1959) and Wagstaff et al. (1964). The surrounding atmosphere was found to have a large effect, the rates being much lower when the material was heated under reducing conditions. For the less pure grades, containing oxide impurities, the crystal layer thickness increased as t 1/2 whilst for the higher purity grades the growth rate was constant. Not all aspects of the results could be explained. However they clearly demonstrate the importance of impurities (including combined -OH) and atmosphere on the crystallization kinetics. The devitrification kinetics of multi-component silicate glasses are not so sensitive to atmosphere. Fratello et al. (1980) have studied the devitrification kinetics of the material under pressure, when the crystalline phase is quartz rather than cristobalite.

an equilibrium value, characteristic of the temperature of measurement. The rate of change is too low to be interpreted as a stabilization effect. It is more likely that it signifies a chemical change either in - O H content or in stoichiometry. 5.3.4 Refractive Index

Silica glass doped with small percentages of oxides or fluorides is easily made by the Chemical Vapor Deposition (CVD) process. These additions affect the physical properties, including the refractive index as shown in Fig. 5-8. Such doping is a normal feature of the manufacture of material to be made into optical communication fibre,

5.3.3 Viscosity

The viscosity data show considerable scatter. At the highest temperatures (> 1600°C) a large part of the variability is probably due to experimental error, which is difficult to eliminate in measurements at such high temperatures. Data for the lower temperature range is shown in Fig. 5-7. Here the viscosity is markedly affected by the - O H content of the material. Hetherington et al. (1964) noted that the viscosity changes slowly with the time to

1050

1150

1250

Temperature (°C)

1350

U50

Figure 5-7. Viscosity-temperature results for fused silica obtained by various workers (from Bruckner, 1964).

5.3 Vitreous Silica

1.50U98 U8

o

I U6B203(fibre)

U51.U 2

4

6 8 10 12 U Dopant concentration (mol°/o)

16

Figure 5-8. The effect of dopants on the refractive index of vitreous silica (from Beales and Day, 1980).

the radial distribution of refractive index being an important factor determining the propagation of light pulses along the fibre. 5.3.5 Structure

Many studies of the structure of silica glass have been made during the past ten years, which have refined but not greatly modified the picture based, on the early Xray diffraction work of Warren and the repetition of that work by Mozzi and Warren (1969) (Wright and Leadbetter, 1976; Wright, 1989; Elliott, 1989). The X-ray results provide information primarily about the short range order. Some information about medium-range order has been obtained from attempts to fit together the results of the experimental investigations with those obtained from computer-based models. Wright (1988, 1989) points out the uncertainties in this approach, since it may be possible for more than one computer model to fit the experimental data equally well. (See Chapter 4 of this volume.) Disregarding the effect of the low concentration of structural defects, each silicon is surrounded tetrahedrally by four nearly equidistant oxygens and each of these is bonded to two silicons. According

293

to Wright, the mean Si-O distance is 1.608 + 0.004 A.U. the O-O peak distance is 2.626 A.U. and the mean bond angle is 109.7 + 0.6° with an r.m.s. bond angle variation of 4.5°. Direct information about medium-range order in silicate glasses has been obtained by Magic Angle Spinning Nuclear Magnetic Resonance (MAS NMR). Fig. 5-9 (Elliott, 1989) shows results for the Si-O-Si angle distribution obtained in this way. The X-ray diffraction results of Mozzi and Warren (1969) are included for comparison. 5.3.6 Defects in Silica The extensive literature on defects in silica has been reviewed by Griscom (1978 a, 1985). The subject is of practical importance in a number of contexts, e. g. radiation induced changes in the optical absorption of silica glass used in lamp envelopes and in communication fibres. The study of defects has also made an important contri-

120 130 UO 150 160 170 180 Intertetrahedral angle (degrees)

Figure 5-9. Si-O-Si bond angle distribution for glassy SiO2 evaluated from 29Si NMR data compared with distribution obtained by Mozzi and Warren from X-ray diffraction (points) (from Elliott, 1989).

294

5 Oxide Glasses

bution to the general understanding of electron energy levels in amorphous silica, a subject of practical importance to the semiconductor industry. The number and nature of defects is changed by irradiation of the material with UV or more energetic radiation and, as was discovered relatively recently, by drawing the material into fibre. Temperature also has an important effect, especially on the rate at which defects are annealed out, either during or after irradiation. Most studies have been based on Electron Spin Resonance, ESR, and, to a lesser extent, on optical absorption measurements. With low energy radiation, the formation of a detectable defect may involve no more than the capture of an electron or hole by a defect already present in the glass structure. With more energetic ionising radiations, defects may be formed by the displacement of an oxygen ion from its normal position in the glass network. (See Chapter 6.) The formation of defects by irradiation depends on the wavelength of the radiation, the impurities present in the material, including the - O H content, and the stoichiometry. The variety of behaviour of the material in this particular area is very large and has been extensively studied.

5.4 Alkali Silicate Glasses 5.4.1 Glass Formation and Devitrification Kinetics Glasses can be made in all the alkali silicate systems over ranges of composition which are continuous from silica itself up to a limit which may lie on the alkali-rich side of the metasilicate composition. Thus Imaoka (1962) made on a scale of 1-2 g, melting in platinum, glasses containing up

to 33.5 mol% Li 2 O, 57.9 mol% Na 2 O and 54.5 mol% K 2 O. On a similar scale, Marinov and Dimitriev (1964) made glasses containing up to 59.4 mol% Rb 2 O and 61.0 mol% Cs 2 O. The glass-forming regions are more limited at larger scales of melting. The glasses of low alkali content ( < 5 mol%) are difficult to prepare on account of the high viscosity of the melt and the high rate of volatilization of the alkali at the melting temperature. Those of high alkali content are water-soluble. The solutions are of considerable industrial importance and their properties have been extensively studied (Her, 1979; Vail, 1952). Phase diagrams of the systems have been determined and are readily available in the collections of Levin et al. (1956,1964, 1969) and Levin and McMurdie (1959, 1975). Fig. 5-6 shows the variation of liquidus temperature with composition in the R 2 O-SiO 2 systems. In all of them, there is a large fall in liquidus temperature as the first few percent of alkali is added. The relationship between glass stability and liquidus temperature in the Na 2 O-SiO 2 system has been discussed in Sec. 5.1.5. Havermans et al. (1970) have determined the critical cooling rates for glass formation of alkali silicate melts in the region 20-60 mol% R 2 O. They show that the ease of glass formation greatly increases in the order Li 2 O, Na 2 O, K 2 O, i.e. in the order of decreasing liquidus temperature. The ease of glass formation is increased still further in the K 2 O-SiO 2 system by replacing half the K 2 O by Na 2 O and, in more complex systems still, the region of glass-formation can be further extended to compositions in which the average number of bridging oxygens per SiO4 tetrahedron is as low as one (Trap and Stevels, 1959, 1960 a, b). Such compositions clearly do not obey Zachariasen's rule 4 (Sec. 5.1.1).

5.4 Alkali Silicate Glasses

Detailed studies of nucleation and crystallization in alkali silicate systems have been carried out especially by Uhlmann and his co-workers (Uhlmann, 1983). Scherer and Uhlmann (1977) observed that in potassium silicate glasses the size of the crystals increases linearly with time, as is observed in many other silicate melts. They show that this behaviour, unexpected for a diffusion-controlled growth process, is predictable, provided that the growing crystals are dendritic, as in fact they are. Good agreement was obtained between the measured growth rates and values calculated using previously determined interdiffusion coefficients. Scherer and Uhlmann (1976) have investigated the effects of sub-liquidus immiscibility on crystal growth in three Na 2 O-SiO 2 glasses, pointing out that since immiscibility may greatly affect several properties, especially viscosity, it might be expected to affect crystal growth rates also (Tomozawa (1972,1973) had previously observed effects of immiscibility on crystal growth rates in lithia-silica glasses). However for glasses containing 10 and 15 mole% Na 2 O, no effect of phase separation on crystallization kinetics was found. They suggest that this may because the scale of the phase separation texture is much smaller than the size of the growing crystals. The interpretation of nucleation and growth kinetics using the classical theory depends on reliable kinetic and thermodynamic data being available. James (1985) has investigated nucleation and growth in a number of congruently melting silicate compositions. He notes that the nucleation results for a number of such compositions, especially Li 2 O • 2SiO 2 , do not appear to fit the theory and require abnormally high values of the pre-exponential factor. Hishinuma and Uhlmann (1987) suggest that the

295

problem may arise from the unsuspected crystallization of a metastable crystalline phase and that the discrepancy will be resolved once the correct value for the bulk free energy of crystallization of this phase can be determined. 5.4.2 Other Binary Silicate Systems The regions of glass formation in most other binary silicate systems are limited by immiscibility in the melt. In some, the liquidus temperatures are also high. Thus in the MgO-, CaO-, and SrO-SiO 2 systems, the silica-rich melts separate into two phases and have liquidus temperatures of the order of 1700°C (Fig. 5-5). However Imaoka (1962) was able to make glasses in the BaO-SiO 2 system containing up to 40 mol% BaO (1/80 mol scale, melted in platinum, cooled in air). Very high melting point glasses can also be made in the A12O3 SiO2 system, but only when the melt is rapidly quenched. By flame spherulization, Takamori and Roy (1973) were able to obtain glasses containing up to 80mol% A12O3. Addition of only a few percent of an alkali oxide to immiscible binary melts nearly always results in a single phase melt. Many of these ternary compositions are simplified versions of commercially important glasses (Shartsis et al, 1958). Binary silicate glasses can also be made with other important glass-forming oxides, especially B 2 O 3 and GeO 2 . According to Imaoka (1962), glasses can be made throughout the whole composition range in the systems B 2 O 3 -SiO 2 and GeO 2 -SiO 2 . At high SiO2 contents, volatilization of B 2 O 3 makes composition control difficult. (See also Sec. 2.7.6.) The PbO-SiO 2 system is of particular interest, partly for scientific and partly for technological reasons. Stable glasses can

296

5 Oxide Glasses

be made on a scale of several grams containing up to 70 mol% PbO. The melting temperatures of the high PbO glasses are relatively low. They form the basis of many high refractive index optical glass compositions. 5.4.3 Physical Properties

It is not possible to give here more than a very brief and highly selective account of the effects of composition and temperature on properties. A very large amount of information is available, much of which is summarized in the handbooks of Mazurin etal. (1983, 1985, 1987). The books by Rawson (1980) and Scholze (1988) are less comprehensive but provide a certain amount of interpretation of the information. The breakdown of the silica network and the increasing number of non-bridging oxygens which results from the introduction of alkali oxides has two important effects: - an increase in thermal expansion coefficient, - a decrease in viscosity at any specified temperature. For example, in the Na 2 O-SiO 2 system, the thermal expansion coefficient increases almost linearly with mol% Na 2 O from 5

.

1 0

-

7

o

C

-i

for

s i l i c a

g l a s s

t Q

2 0 0

increasing temperature. Thus a flat glass composition has a room temperature resistivity of l O ^ f l m , falling to 0.03fim at 1400°C. Those silicate glasses containing two alkali oxides e.g. Na 2 O and K 2 O, show a pronounced maximum in resistivity as one alkali is substituted for the other at constant total alkali content (mixed alkali effect). Various interpretations have been proposed (Isard, 1968/69; Hendrikson and Bray, 1972 a, b; Moynihan and Lesikar, 1981) but none appears to be universally accepted (Ingram, 1987). 5.4.4 Immiscibility and Properties

Several examples are given in this Chapter of the effect of sub-liquidus immiscibility on properties. In any systematic study of the properties or the structure of a series of glasses, it is necessary to know whether the glass is single phase or not. The subject has been discussed by Uhlmann and Kohlbeck (1976), Uhlmann (1982) and Tomozawa (1989). Tomozawa has discussed in detail the dielectric relaxation properties in alkali silicate glasses across the immiscibility region, showing that they can be interpreted only by taking the immiscibility and nonideality of the system into account.

.

1

l O - ^ C T at 45mol% Na 2 O. For the same composition range the transformation temperature Tg (temperature at which the viscosity is 10 12 Pa s) decreases from 1200 to 350 °C. For comparison a typical commercial container glass composition has a thermal expansion coefficient of 90 - l O ^ C r 1 and a Tg of 520°C. The DC conductivity and dielectric properties are primarily determined by the number and mobility of the alkali ions. The electrical resistivity falls rapidly with

5.4.5 Chemistry of Alkali Silicate Glasses

Flat glass and container glass compositions having adequate resistance to chemical attack by moist atmospheres and neutral aqueous solutions had been developed empirically well before the beginning of the present century. Any problems encountered could usually be attributed to inadequate control of the glass composition. On the other hand, the chemical durability of binary alkali silicate glasses is too

5.4 Alkali Silicate Glasses

poor for them to be of any practical use. Nevertheless the reactions between these glasses and aqueous solutions have been studied in considerable detail, the information obtained being of value in understanding the reactions involving the more complex silicate glasses. The main variables studied have been glass composition, temperature and the pH of the aqueous phase. Resistance to attack at a given R 2 O content increases in the order R = K, Na, Li. At low values of pH (<9), the reaction is primarily one in which alkali ions in the surface layers of the glass are exchanged with H + or H 3 O + ions from the solution. This involves diffusion through the surface reaction layer and the amount of alkali extracted increases as (time)1/2. At higher values of pH, the silica network itself is attacked and passes into solution. In this regime, the weight of material extracted is linearly proportional to time. As material is extracted from the glass, the composition of the aqueous phase and its pH changes. This complicates the interpretation of the results. Reactions involving substantially pure water of constant composition have been studied using apparatus in which the water condenses on glass granules suspended inside a distillation column. As the condensed water runs off, it is collected for analysis. In this type of experiment, the quantity of material extracted, Q, at first increases as (time)1/2, but at long times, the rate of reaction becomes constant. It is suggested that at long times, the siliceous surface film on the particles is dissolved at the same rate as that at which it is formed i.e. it attains a constant thickness, at which point a constant rate of extraction is to be expected. The chemical durability is greatly increased by the addition of oxides of divalent and trivalent elements (e.g. CaO and

297

A12O3) leading to the commercial sodalime-silica compositions (Sec. 5.2). There is a considerable literature dealing with the mechanisms of the reactions between simple and more complex glasses with aqueous solutions and with the testing of glasses of technological interest to meet specific durability requirements. The importance of this subject both to the traditional glass industry and for new applications of glass (e.g. for nuclear waste storage, for controlled release of trace elements and for prosthetic applications) cannot be overestimated (Hench, 1977, 1985 a; Paul, 1982; Hench and Spilman, 1985; Knott, 1989). Other ion-exchange reactions at the glass surface are also of technological importance. They are usually carried out at elevated temperatures so that the entering ions may penetrate one or two hundred microns into the glass. Reactions of this kind include: - ion-exchange strengthening in which sodium ions in the glass surface are replaced by larger ions e.g. K + , thus developing a comprehensive layer in the glass surface (Garfinkel, 1969). (See Chapter 13.) - manufacture of optical waveguides in which the exchange reaction can be controlled to produce a strip in the surface having a higher refractive index than the unmodified glass (Ramaswamy and Srivastava, 1988). (See Chapter 15.) 5.4.6 Oxygen Ion Activity; Basicity Oxidation-reduction reactions in glass play an important role in the high temperature chemistry of glass melting reactions. Also changes in the state of oxidation of transitional metal ions dissolved in glass are of considerable scientific interest and of technological importance because of their effects on the spectral transmission. These

298

5 Oxide Glasses

reactions are markedly affected by the glass composition. Changes which affect the state of oxidation of ions of elements such as Fe, Cr and Mn are of particular interest. For example, in a glass containing iron oxide which has been brought into equilibrium with an atmosphere of controlled oxygen partial pressure, the oxidation-reduction equilibrium of F e 2 + / F e 3 + can be written as follows: 4FeO + O ? + 2 O 2

4FeO 7

(5-1)

If the reaction proceeds to the right, ferrous iron is oxidized to ferric with a consequent change in colour. The equation written in this form is in accordance with the dependence on oxygen partial pressure of the experimentally determined (Fe 3 + / Fe 2 + ) ratio in the glass, it being assumed that each chemical symbol in the equation represents the activity of that constituent in the system. There has been considerable discussion arising from work of this kind as to whether the term 'free oxygen ion activity' or simply 'oxygen ion activity' (represented by the term O2~ in Eq. (5-1)) has any real meaning, whether it can be measured and whether the discussion of the equilibria in this way can be justified (Wagner, 1975; Schreiber 1986). It does however seem to represent a helpful way of discussing the equilibria and has been widely used in other contexts e.g. in work on metallurgical slags. Increasing the alkali content of the glass produces more singly bonded oxygens, which has the effect of shifting the equilibria to the right giving a higher proportion of the oxidized form. This, it is said, is due to an increased oxygen ion activity in the glass. In an equilibrium such as that above, for a given R 2 O content in the

R 2 O-SiO 2 glasses, the proportion of the higher valent form increases in the order R = Li, Na, K. Thus the K 2 O glasses apparently have the highest oxygen ion activity at a given R 2 O/SiO 2 ratio. Alternatively they are said to have the highest basicity - the concepts are closely related. Oxygen ion electrodes using CaO-stabilized zirconia electrolytes have been used to measure the oxygen potential or oxygen ion activity of glass melts as a function of glass composition, temperature and the composition of the gas in contact with the melt (Tran and Brungs, 1980; Schaeffer et al, 1982). Oxygen potentials were determined on a number of samples of sodium disilicate glass containing iron oxide and the F e 2 + / F e 3 + ratios in these glasses were determined chemically. Results were compared with earlier melt-equilibration studies on the same glass in which the F e 2 + / Fe 3 + ratio was varied by equilibrating the melts with CO/CO 2 gas mixtures. The results were self-consistent, supporting the above equation for the interpretation of the redox reaction and giving one of several examples of the value of high temperature oxygen electrodes in the study of the high temperature chemistry of glass melts. High temperature equilibration measurements are difficult and time-consuming. It is therefore of considerable interest that a much simpler method exists which is capable of providing similar information. In this method, developed by Duffy and Ingram (1976) and by Duffy et al. (1978), ions such as Pb 2 + , Tl + and Bi 3+ are dissolved in the glass. They cause an intense UV absorption band, usually having a sharp maximum due to a 6 s -• 6 p transition. The frequency of the band is greatly reduced as the basicity of the glass is increased due to orbital expansion effects within the probe ion, bought about by electron donation from the oxygens.

5,4 Alkali Silicate Glasses

An 'optical basicity' A of the glass is defined by the equation: = (%-v gi )/( v fi- v oi)

(5-2)

where vn = the absorption frequency of the free ion. This is determined by extrapolation, the value being 60 700 cm"* for Pb 2 + . voi = the absorption frequency of the probe ion in an ionic oxide e.g. CaO. For Pb 2 + this is 29 700 cm" 1 . vgi = the measured absorption frequency of the ion in the glass. It has been shown that the optical basicity of any oxide glass can be calculated from its composition using a table of cation factors, termed the basicity moderating power, y. These factors are related in a simple way to the corresponding Pauling electronegativity value, x ' = 1.36(x-0.26)

(5-3)

The papers by Duffy and Ingram (1976) and Duffy et al. (1978) referred to above give a number of examples illustrating the value of this approach in interpreting redox phenomena in oxide glasses and in metallurgical slags.

5.4.7 Structure

Several new techniques have been applied to the study of oxide glass structure in recent years. Some provide selective probes for determining short-range order i.e. they give information about the oxygen co-ordination number around some particular ions or about some aspect of bonding between nearest neighbours. Other techniques are beginning to provide longawaited information about medium-range order. The combination of results from the experimental techniques with those obtained from the construction of computerbased models is beginning to make it possi-

299

ble to determine whether or not particular conjectures concerning medium-range order are likely to be correct. As described in Sec. 5.1.2, each 'R 2 O molecule' introduced produces two nonbridging oxygens, the R cations being incorporated in the voids in the silica network. The formation of non-bridging oxygens can now be followed quantitatively by ESCA (Bruckner, 1978), a technique which is particularly informative when applied to borosilicate and aluminosilicate glasses. The cations are accommodated close to the negatively charged nonbridging oxygens so as to maintain local electroneutrality in the structure. There has been a conflict of evidence, reviewed by Kreidl (1983), as to whether the non-bridging oxygens are produced entirely randomly or whether there is a tendency to form alkali-rich clusters. Recent work using Magic Angle Spinning NMR (MAS NMR) suggests that the degree of clustering varies within a given system as the alkali content is increased and also varies from one system to another. The technique can distinguish between Si-O tetrahedra containing between one and four non-bridging oxygens. Dupree et al. (1984) report that Na 2 O-SiO 2 glasses containing 33.3 mol% of Na 2 O contain only Q 3 groups i.e. groups containing only one non-bridging oxygen per SiO4 tetrahedron. With further addition of Na 2 O, the Q 3 groups are progressively converted to Q 2 (two non-bridging oxygens per tetrahedron) and at 50 mol% Na 2 O only Q 2 groups are present. Thus there is no evidence of clustering in this particular system. Dupree et al. (1986) have extended their use of the technique to other alkali-silicate systems. No evidence of clustering was found in the Cs 2 O- and Rb2O-containing systems but in the lithia glasses, containing

300

5 Oxide Glasses

less than 30 mol% Li 2 O, clustering of the lithium ions does occur. Molecular dynamic modelling of the structure of soda-silica glasses supports the generally held ideas about the structure of silicate glasses (Varshneya, 1987; Soules, 1989). The oxygen co-ordination number around the sodium ions varies between 3 and 8, with a most probable value of 5. At low soda contents, two Na ions are found around each NBO and three at higher Na contents. Concerning the anionic structure, Yasui etal. (1983 a, b) interpret their X-ray diffraction results as indicating that infinite chains of SiO4 tetrahedra exist in alkali metasilicate glasses and that the disilicate glass structures consist of infinite sheets. A molecular dynamics study of the metasilicate glass structure by Inoue and Yasui (1987) supports the conclusions of the Xray work. Dorfield (1988) has used thermodynamic data for the Na 2 O-SiO 2 system to calculate the effect of composition on the relative proportions of various anionic species assumed to be present. This is the most recent of many studies of this kind. Although the results are sensitive to small errors in the thermodynamic data used and depend on initial assumptions which have to be made, it is interesting that he arrives at similar conclusions about the constitution of metasilicate and disilicate glasses to those inferred from the most recent X-ray and MAS NMR investigations i.e. that the disilicate glasses contain predominantly Q 3 groups and the metasilicate melts predominantly Q 2 groups. The variation in the physical and chemical properties of simple silicate glasses with composition shows little evidence of changes in trend at the disilicate and metasilicate compositions. However the recent results on the systematic changes in

the anionic structures remind one of the work done many years ago by Huggins and Sun (1943) and Huggins and Stevels (1954) which involved very careful analysis of the refractive index and density data. This showed changes in slope at particular alkali-silica ratios. The changes are small, but the recent structural work suggests that there are reasons for expecting them to be real. Results of recent structural studies of PbO-SiO 2 glasses show features which differ from those found in the alkali silicate systems. This is not surprising in view of the differences between the R - O and P b - O bonds. The stability to devitrification of glasses of particularly high PbO content has often in the past been attributed to directional characteristics of the P b - O bond and to the supposed ability of that oxide to act as a 'network former'. The structural role of PbO in glasses has been reviewed by Rabinovitch (1976). An MAS NMR investigation has been carried out by Dupree et al. (1987) on several PbO-SiO 2 glasses containing up to 70 mol% PbO. The latter glass appears to contain isolated SiO4 groups 'in a leadoxygen matrix'. The X-ray PES work of Smets and Lommen (1982) also indicates that some form of lead-oxygen network exists at the high PbO contents. Below 30 mol% PbO, the oxide acts as a conventional modifier, but at intermediate compositions there is no indication of the presence of mixtures of Q n species as found in the alkali silicate systems. As the PbO content increased, the P b - O bonds were found to become more covalent indicating that the PbO was changing its role from that of a modifier to that of an intermediate. Another technique which can give information about the anionic constitution of silicate glasses is gas-liquid chromatogra-

5.5 Boric Oxide Glass

301

phy pioneered by Masson (1977). Recent results by this method on PbO-SiO 2 glasses have been reported by Smart and Glasser (1978). The method can be applied only to glasses containing more than 50 mol% PbO. In this region, most of the 51 was found to be present as SiO4 groups - in agreement with the results of the NMR work. However, significant proportions of di-, tri- and tetramers were also detected.

5.5 Boric Oxide Glass The properties of the oxide melt and the glass are markedly affected by their - O H contents. Bruckner (1964) found that as the water content is decreased from 0.248 to 0.025%, the temperature at which the viscosity is 103 Pa s rises from 537 to 550 °C. An anhydrous melt is difficult to prepare starting from orthoboric acid, but a substantially water-free material was obtained by Poch (1964) by melting the material for several hours at a pressure of 1 mm Hg. Fig. 5-10 shows that the viscosity of the oxide at its melting point is much less than that of silica yet crystallization is extremely slow, except at high pressures (Uhlmann

•«5a-

T fS'°2 / Fc;n

C/5

O

r.

<J

3~

T m =1115°C

/

/

A\ m

= 550°C

°c

/

f

^GeO2



V

J

j3BeF2

'•>

3

i-

if

5

7

10

11

i

i

12

13

U

Figure 5-10. The relationship between log viscosity and 1/T K for some network liquids (from Mackenzie, 1960).

Figure 5-11. The structure of B 2 O 3 glass with (B3O6)3~ boroxol groups (from Krogh-Moe, 1969).

et al, 1967). Recent structural studies (e.g. Johnson et al., 1982) suggest that the crystallization of the B 2 O 3 melt involves greater structural changes than is the case for SiO2. That, together with the much lower melting point of B 2 O 3 , makes the difference between the crystallization rates of the two materials understandable. The structure of the crystalline oxide consists of infinite chains of BO 3 triangles. Nearly all investigations of the glass structure, using various techniques, support the model proposed by Krogh-Moe (1969) (Mozzi and Warren, 1970; Griscom, 1978 b; Johnson et al., 1982). This is illustrated in Fig. 5-11. The main feature is the preponderance of boroxol groups which constitute 60-80% of the structure.

302

5 Oxide Glasses

5.6 Borate Glasses

Table 5-4. Crystallization rates of binary borate melts (Bergeron, 1978).

5.6.1 Glass Formation in Binary Systems

Compound

Imaoka (1962) has determined the regions of glass formation in many binary systems with the results given in Table 5-3. The melts were prepared on a scale of 1 to 3 g in a platinum crucible and were allowed to cool freely in the crucible. As in the silicate systems, the regions of glass formation in the alkaline earth borate systems (and in some others) are limited by immiscibility in the compositions of high B 2 O 3 content. It is interesting that two separate regions of glass formation exist in the Na 2 O-B 2 O 3 system. Sakka et al. (1978) and Martin and Angell (1984) have shown that the gap between the two can be closed by adding a small percentage of alumina. A more important point brought out by Martin and Angell (1984) and by Lim et al. (1987) is that considerable percentages of CO 2 are retained in the high alkali borate melts if a carbonate is used as the source of alkali. This affects the stability of the glasses and their properties. Such materials should be

Table 5-3. Regions of glass-formation in binary borate systems (Imaoka, 1962). System

Na 2 O Li2O BaO SrO MgO

ZnO CdO PbO Bi2O3

100.0-62.3 100.0-62.0 33.5-28.5 100.0-57.3 83.0-60.2 75.8-57.0 57.0-55.8 81.0-71.8 100.0-55.5 56.0-36.4 60.9-45.0 80.0-23.5 78.0-34.7

PbO-2B 2 O 3 SrO-2B 2 O 3 BaO-2B 2 O 3 Li 2 O-2B 2 O 3 Na 2 O-2B 2 O 3 Cs2O 3B 2 O 3 Na 2 O 4B 2 O 3 K 2 O-4B 2 O 3 BaO-4B 2 O 3

M.Pt. °C

cm/sxlO" 4

775 997 910 917 742 837 816 857 889

2 154 35 3000 33 140 7 12 15

n(um) Pas 6 5 32.2

0.3 25 23 23 15 55

regarded as mixed anion glasses and not as binary borates. In the alkali borate systems, the liquidus temperature increases rapidly with the first addition of alkali. These glasses are much easier to crystallize than B 2 O 3 itself. Baeten et al. (1972) have shown that in the N a 2 O - B 2 O 3 system, there is no simple relationship between the stability of the glass and its liquidus temperature, such as one finds in the corresponding silicate and other systems. Table 5-4 (Bergeron, 1978) gives for a number of congruently melting borate compositions, the maximum rate of crystal growth t/m, the melting point and the viscosity of the melt at the temperature of maximum growth rate (rj (Um)). The maximum growth rate is not inversely proportional to q(Um) i.e. glass formation does not depend simply on the melt having a high viscosity at or just below the melting point, nor is there a simple relationship between glass stability and melting point. 5.6.2 Sub-Liquidus Immiscibility in Binary Borate Glasses

Information on immiscibility in borate systems has been reviewed by Macedo and Simmons (1974). Shaw and Uhlmann

303

5.6 Borate Glasses

(1968) have shown that sub-liquidus immiscibility occurs in all alkali borate systems, as is shown for the Na 2 O-B 2 O 3 system in Fig. 5-12. Uhlmann and Shaw (1969) and Shaw and Uhlmann (1969) have discussed whether the presence of immiscibility in these glasses may have led to misinterpretation of property-composition relationships in earlier work. For such properties as density, refractive index and thermal expansivity, this is unlikely. However viscosity may be markedly affected by phase separation and by the nature of the separation microstructure.

900 Liquidus^.

~ 700-

| 60 °"

8 ~ 8 ^ ^Region of sub-

•500-

" U)0-

Approximate glass transition temperature

3006

L

8

12

16 20 U Mol.% Na20

28

32

36

Figure 5-12. Region of sub-liquidus immiscibility and liquidus curve for the system Na 2 O-B 2 O 3 (from Shaw and Uhlmann, 1968).

5.6.3 Structures of Binary Borate Glasses

The structures of alkali borate glasses have been investigated by a number of techniques and the results summarized by Griscom (1978 b). Nearly all the results are in agreement with a model first proposed by Krogh-Moe (1969). Fig. 5-13 shows the four groups which have been shown to be present in the borate network, depending on the glass composition. They are also found in anhydrous crystalline borates of similar composition. Note that all contain both three- and four-co-ordinated borons. The lines in Fig. 5-14 are derived by application of the lever rule, giving the relative proportions of each group as a function of glass composition. The NMR results in particular support this simple model very well. Recent molecular dynamics calculations (Inoue et al., 1987) also confirm the existence of boroxol groups in vitreous B 2 O 3 and of diborate groups in borate glasses. Although a large body of results has supported the Krogh-Moe structural model and the interpretation of data on which it is based, Button et al. (1982) doubt if NMR, in particular, is capable of identify-

(a)

(b)

(0 Figure 5-13. The borate groups postulated as existing in alkali borate glasses containing less than 34 mol% R 2 O. (a) The boroxol group, (b) the pentaborate group, (c) the triborate group, (d) the diborate group (from Krogh-Moe, 1969).

ing specific polyborate groups in a glass. They found that the technique failed to detect structural differences between lithium chloroborate and simple lithium borate glasses even though the physical properties of the glasses are significantly different.

304

5 Oxide Glasses

1.0-

Figure 5-15. The fraction N 4 of boron atoms in fourcoordination in alkali borate glasses, o K 2 O; • Na 2 O; A Li 2 O; +Rb 2 O; x Cs2O (from Bray and O'Keefe, 1963).

0

0.1

0.2

0.3

0.4

0.5

0.6

Figure 5-14. The results of 10B NMR measurements of the fraction of borons in five distinguishable sites plotted as a function of R = x/(1 — x), where x is the molar fraction of Na 2 O in the sodium borate glasses. A Three-coordinated borons in boroxol groups and 'loose' BO3 triangles (B3), o three-coordinated borons in tetraborate groups (T3), + four-coordinated borons in tetraborate groups (T4), • three and four-coordinated borons in diborate groups (D 3 and D 4 ). The straight lines and the symbols with suffixes correspond to predictions from Krogh-Moe's theory (1969) (from Jellison and Bray, 1978 a).

Fig. 5-15 shows some early NMR results in which the fraction of four coordinated boron atoms is plotted as a function of alkali content. Recent X-ray diffraction studies (Herms et al., 1986) appear to be in agreement with this interpretation. 5.6.4 Properties

It is not surprising, considering the different structural effects of R2O additions in silicate and borate melts that their proper-

ties should vary so differently with composition. Fig. 5-16 shows high temperature viscosity data for several R 2 O-B 2 O 3 systems (Shartsis et al., 1953; Kaiura and Toguri, 1976). In the corresponding silicate glasses the viscosity decreases monotonically with increasing R2O content. Clearly the effect of the alkali addition depends markedly on temperature, suggesting that temperature may also have a marked effect on the melt structure. This view is supported by the theoretical considerations of Araujo (1979, 1983) and by high temperature measurements of optical basicity (Duffy and Grant, 1975). It seems very likely that the value of N 4 , the fraction of boron atoms in four-fold coordination decreases with increasing temperature. Fig. 5-17 shows the effect of composition on thermal expansion for the alkali borate glasses. The shape and position of the minimum depends on the temperature range over which the expansion coefficient is determined (Ahmed et al., 1985; Mader and Loretz, 1978). It is suggested that the initial reduction in expansion coefficient in the 0-20 mol% alkali region is due to the re-

5.7 Borosilicate Glasses

305

placement of BO3 triangles by BO4 tetrahedra, increasing the degree of three-dimensional bonding in the structure. The increase in expansivity above 35 mol% alkali is due to the formation of non-bridging oxygens. 5.6.5 Technological Applications of Borate Glasses

30

U)

Mol.7o R20

Figure 5-16. Isothermal viscosity curves for alkali borate glasses - all systems show similar trends (from Shartsis et al., 1953).

These are very limited. Borate optical glasses containing high percentages of rare earth oxides are used to manufacture lens systems with high numerical aperture and low spherical aberration (Meinecke, 1959). Other applications are as solder glasses, for making vacuum-tight seals between silicate glass components without risking their distortion during sealing. Solder glasses based on the PbO-SiO 2 system are suitable for joining glass and/or metals having an expansivity of about 90 10" 7 o C" 1 . Materials with an expansivity of approximately 5 0 - 1 0 " 7 o C " 1 may be joined using solder glasses based on the ZnO-B 2 O 3 system (Frieser, 1975).

5.7 Borosilicate Glasses

0

5

10

15

20 25 30 Mol.%, R20

35 /.0

Figure 5-17. Thermal expansion coefficients of alkali borate glasses as a function of composition (from Uhlmann and Shaw, 1969).

The ternary system Na 2 O-B 2 O 3 -SiO 2 forms the basis of a number of glasses of considerable technological importance. They include the glass commonly known as Tyrex', used for chemical apparatus and ovenware, a series of glasses used in the electronics industry to make seals to metals and other materials (Volf, 1961; Kohl, 1967; Espe, 1968) and glasses used for the vitrification of nuclear fission product wastes (Hench, 1958 b). At a given alkali content, the addition of boric oxide to a silicate glass markedly reduces the thermal expansion coefficient and enhances the chemical durability, especially to attack by acids.

306

5 Oxide Glasses

5.7.1 Thermal Expansion Coefficient

5.7.2 Viscosity

Fig. 5-18 shows the effect of B 2 O 3 content at various levels of Na 2 O content on the expansion coefficient (Streltsina, 1967; Mazurin et al., 1969). These are mean values over the range 20-300°C It is clear that variation in the alkali content has less effect on the expansion coefficient the higher the B 2 O 3 content. The borosilicate glasses of technical importance have expansion coefficients in the range 30-80 • 10" 7 .

Tait et al. (1984) have determined the viscosity-temperature curves of 16 ternary compositions in the system over the temperature range 900 to 1500°C. The compositions were in the range 5-35 Na 2 O, 5-35 B 2 O 3 , 45-80 SiO2 mol%. Polynomials were fitted to the viscosity-temperature data and these were used to plot viscosity contours on the triangular composition diagram. Fig. 5-19 shows the viscosity contours at two temperatures.

5.7.3 Structure

50 Mol.% B203

Figure 5-18. Effect of B 2 O 3 content on the thermal expansion coefficient of Na 2 O-B 2 O 3 -SiO2 glasses at various Na 2 O contents (data from Streltsina, 1967, and Mazurin et al., 1969).

The results of several NMR investigations agree that when R ( = mol% Na 2 O/ mol% B 2 O 3 ) is less than 0.5, the additional oxygen atoms introduced with the Na 2 O are used entirely to convert BO3 units to BO 4 units i.e. the glasses behave as if they were sodium borate glasses with the silica acting as an inert diluent. Fig. 5-20 shows that above R = 0.5, the value of N 4 , the fraction of boron atoms in BO4 units, varies with R in a way which depends on composition and in particular on the value of the ratio K = mol% SiO 2 / mol% B 2 O 3 . Yun and Bray (1978) postulate that for 0.5
5.7 Borosilicate Glasses

307

1200°C 0.8 0.7 %

0.2

0.8-

0.6-

0.4-

0.2-

0.5

1.0 1.5 2.0 2.5 3.0 R (mol%Na 2 0/mol% B203)

Figure 5-20. The fraction N 4 of boron atoms in BO4 units versus K=mol% Na 2 O/mol% B 2 O 3 for various values of K = mol% SiO 2 /mol% B 2 O 3 . A K = 0; A K = 0.5; o K = 1; • K = 2; n K = 3 (from Bray, 1978).

5.7.4 Sub-Liquidus Immiscibility

Fig. 5-21 due to Haller et al. (1970) shows the regions of sub-liquidus immiscibility in the Na 2 O-B 2 O 3 -SiO 2 ternary system. The region of greater importance is

0.3 B203

0.4

0.5 0.6

Figure 5-19. Viscosity contours at 1050 °C and 1200°C for melts in the system Na 2 O-B 2 O 3 -SiO 2 (from Tait et al., 1984).

that running almost parallel to the silicaboric oxide side of the diagram. Heat treatment below the miscibility temperature results in a separation texture which depends on the temperature and time of heat treatment. The properties of the resulting material are greatly affected by the separation, especially when the high-silica phase is continuous (Mahoney et al., 1974). Fig. 5-22 shows the large increase in viscosity with time which results as phase separation takes place. Heat treatment of glasses with compositions in the immiscibility region produces a texture consisting of two interconnecting phases, one consisting largely of a sodium borate glass (Na 2 O • 2.4B 2 O 3 • 0.16 SiO2) and the other almost pure silica. The sodium borate phase can be leached out completely by immersing the material in acid. After drying and heat treatment at 900-1200 °C, the silica skeleton densifies to a transparent glass containing about 96 wt.% silica and with properties very similar to those of silica glass itself. This material, 'Vycor', a product of Corning Glass Works, was patented by Hood and Nordberg (1938), many years before subliquidus immiscibility had been studied in detail and its nature appreciated. Detailed accounts have been given by Kreidl (1983)

308

5 Oxide Glasses

Figure 5-21. Region of subliquidus immiscibility in theNa 2 O-B 2 O 3 -SiO 2 system. In the shaded region three amorphous phases co-exist (from Haller et al., 1970).

\

10

BO

60 Mol.% SiO2

and Volf (1961) of the various stages in the manufacture of this material. There are also interesting and important applications for the porous silica skeleton material produced by acid leaching the phase-separated glass. These include uses as carriers for enzymes and other catalysts, desalination membranes etc. (Phillips etal., 1974; Janowski and Heyer, 1982; Schnabel and Langer, 1989).

100

5.8 Aluminosilicate Glasses Table 5-5 gives the compositions of a number of commercial aluminosilicate glasses. They are used in situations where a high softening point, a high electrical resistivity and/or good resistance to chemical attack by aqueous solutions are required. Many fibreglass compositions belong to this group of glasses. Glasses in the systems Li 2 O-Al 2 O 3 SiO2 and MgO-Al 2 O 3 -SiO 2 are made for subsequent conversion into important classes of glass ceramics (Strnad, 1986). Aluminosilicate melts are also of interest to geochemists and metallurgists (volcanic glasses and some metallurgical slags). 5.8.1 The Alumina-Silica System

10

10* Time (min)

Figure 5-22. Effect of time of heat treatment on the viscosity at 560 °C and 600 °C for a glass of composition 70mol% SiO2, 23mol% B 2 O 3 , 7 mol% Na 2 O (from Mahoney et al., 1974).

Much information exists on the region of stable and metastable immiscibility in alkali- and alkaline earth silicate systems. It has proved more difficult to investigate metastable immiscibility in the aluminasilica system. Liquidus temperatures across the system are high and, in the region above 30mol% alumina, glasses can be made only by very rapid quenching. The phase diagram is shown in Fig. 5-23 together with the region of metastable immiscibility as determined by McDowell and Beall (1969). Takamori and Roy (1973) have expressed doubts as to whether the immiscibility region has been determined with suf-

5.8 Aluminosilicate Glasses

Table 5-5. Compositions of commercial aluminosilicate glasses.

SiO2 A12O3 B2O3 P2O5 MgO CaO BaO R2O ZrO 2 TiO 2

1

2

51.2 22.6 1.5 4.5 5.4 9.0 5.3

52.0-56.0 12.0-16.0 8.0-13.0

60.0-70.0 59.0-64.0 0.0- 5.0 3.5- 5.5 6.5- 7.0

0.0- 6.0 16.0-25.0

2.5- 3.5 0.0-10.0 13.5-14.5

3

4

0.4- 0.7

1.0 15.0-20.0 0.0- 5.0

1 High softening point glass for mercury arc discharge lamps. 2 Glasses 2, 3 and 4 are fiberglass compositions. 2 is E glass, resistant to neutral and acidic solutions and used in making glass-reinforced plastics. 3 is a composition resistant to attack by highly alkaline solutions. It is used in making glass fiber reinforced cement (Proctor, 1985).

2000* / 1800^

/corundum* liquid

Si02+liquic mullite* liquid

16002/ /

uoo*

/ /

/

/

• • :

\

• • '• •

j

•

\

\

corundum* mullite SS

\ \ \ \ \ \ \ \ \

-mullite SS

\

1200^ : -l

\ : : : •

\

30

\ \ \

I \

50 Mol.% Al 2 0 3

70

90

Figure 5-23. The Al 2 O 3 -SiO 2 phase diagram showing regions of metastable immiscibility (from McDowell and Beall, 1969).

309

ficient accuracy. On the other hand Risbud and Pask (1977) were able to show, by thermodynamic methods, that one should expect an immiscibility region in the position observed by McDowell and Beall and possibly also a second region at higher alumina contents. Jantzen et al. (1981) have used small angle neutron scattering to study the kinetics of phase separation in rapidly quenched glasses in the system. They confirmed the existence of a metastable immiscibility region in the position reported by McDowell and Beall (1969) but with a much lower critical temperature. 5.8.2 Sodium Aluminosilicate Glasses

Glasses in this ternary system have attracted considerable interest, not because they have any great technological importance but on account of the marked changes in the dependence of properties on composition which are observed on passing across the line in the ternary composition diagram defining a Na 2 O/Al 2 O 3 ratio of 1. Two well known examples are shown in Figs. 5-24 and 5-25. Fig. 5-24 shows the lines of equal refractive index (isofracts) in the system and Fig. 5-25 shows the effect of composition on the activation energy for d.c. conduction. These and similar results suggest that they might have a simple explanation in terms of glass structure. There is general agreement that when the Al/Na ratio is significantly less than 1, each Al 3+ ion added substitutes for a Si 4+ ion in the network and two non-bridging ions are eliminated. The Al 3+ ion and a nearby Na + ion are together electrostatically equivalent to one Si 4+ ion. Thus local charge balance in the network is maintained. It is possible to envisage this process continuing with increasing alumina content up to Al/Na = 1 at which point the

310

100

50

0 NQ 2 O

NQ 2 0 Al 2 0 3

weight %> A 2 0 3

Figure 5-24. Lines of equal refractive index of glasses in the system Na 2 O-Al 2 O 3 -SiO 2 (from Schairer and Bowen (1956); reprinted by permission of Americal Journal of Science).

glass would contain no non-bridging oxygens. Day and Rindone (1962) proposed that beyond this point any further Al 3+ ions introduced will be six-coordinated by oxygen and behave as network modifiers. It has been proposed that such a change in behaviour, or something like it, could

0.5

Figure 5-25. Effect of composition on the activation energy for DC conductivity in the system Na 2 O • • x A12O3 • 2 (4-x) SiO2 (from Isard, 1959).

account for the property-composition relationships described above. However Lacy (1963) argued that the formation of (A1O6)3" groups was unlikely on grounds of their large packing requirements. He proposed instead the formation of 'triclusters' consisting of, for example, one A1O4 and two SiO4 tetrahedra sharing a common corner i.e. with one three-coordinated oxygen ion. Such groups exist in some crystalline silicates, but as yet no direct structural investigation has shown conclusively that they exist in glasses. Note that such an arrangement breaks Zachariasen's rule 3. Recent results have tended to cast doubts on the Day and Rindone model (1962). Smets and Lommen (1981b) have used X-ray photoelectron spectroscopy to investigate glasses in the system 0.2 Na 2 O, x A12O3, (0.8-x) SiO2. Their results show that the signal due to non-bridging oxygens disappears at x = 0.15 i.e. at Al/Na = 0.75. They suggest that even below the equivalence point of Al/Na = 1, some Al3 + ions are probably incorporated into the structure as (A1O6)3~ octahedra. They recognize that their results make it difficult to account for the abrupt changes in physical properties described above but make a comment which reflects our limited understanding of the relationship between glass properties and structure: "It should be pointed out that there is often no distinct relation between the physical properties of a glass and its short range structure. A notorious example of this is found with borate glasses." McKeown (1987) studied by the energy dispersive X-ray technique, Raman scattering, EXAFS and XANES a series of glasses containing 75 mol% SiO2 with Al/Na ranging from 0.02 to 1.61. He concludes that all the Al3 + ions are tetrahedrally coordinated throughout the series and sug-

5.9 Phosphate Glasses

gests therefore that since the local co-ordination environments do not change, longer range structural changes must be responsible for the property changes. For example, some tetrahedra may link across rings and three-coordinated oxygens may form at these links (as proposed by Lacy (1963)). On the other hand Klonowski (1983), on the basis of refractive index and ESR measurements, appears to favour the original Day and Rindone model (1962). Thus although there are reasons to doubt the Day and Rindone model, as yet there is no generally accepted alternative. An example of a change in long range order in the structure (though not necessarily of the type envisaged by McKeown (1987)) arises in the melting of the compounds NaAlSi3O8 and KAlSi 3 O 8 . In the crystalline materials, the SiO4 tetrahedra are joined to form four-membered rings. Taylor and Brown (1979) showed by X-ray diffraction that six-membered rings are present in the glass, indicating that a considerable structural rearrangement must take place on melting and on crystallization. This fact together with the relatively low melting points of the compounds and their high viscosity at the melting point may explain why they are so difficult to crystallize (Schairer, 1951; Cranmer and Uhlmann, 1981).

5.9 Phosphate Glasses Small quantities of phosphate glasses and P2O5-containing glasses are used in a number of applications: 1. Aluminophosphate laser glasses containing Nd 3 + in high power laser fusion facilities (Jiang et al., 1986; Toratoni et al., 1987). 2. Phosphate glasses containing transition metal oxides (controlled release

311

glasses). These are used for the treatment of crops and animals suffering from trace element deficiences (Knott, 1989). 3. Phosphate glasses doped with halides have high ionic conductivities and are being studied for battery applications (Ravaine, 1985). 4. A small percentage (6%) of P 2 O 5 is an essential component of 'Bioglass™', a material being used in prosthetic applications (Hench and Spilman, 1985). 5. Some glass-ceramics use the oxide as a nucleating agent (Strnad, 1986). 6. Some low melting phosphate compositions have been studied with the intention of producing articles from them using standard polymer-processing equipment (Ray, 1978). Some of these applications are referred to again later. 5.9.1 Phosphorus Pentoxide

All forms of the oxide, both crystalline and vitreous, react readily with water. Consequently the oxide glass is of no practical value. There are three crystalline forms, all having structures based on the PO 4 tetrahedron. In all of them one oxygen is nonbridging. Crystals of the hexagonal form melt at 422 + 6 °C, the liquid formed polymerizing rapidly. The tetragonal form melts at 580 + 5 °C to form a very viscous liquid which can readily be superheated to temperatures well above the melting point. The melts made from all three crystalline forms can easily be supercooled to form a glass, the properties of which depend on the crystalline form from which it was made. This suggests that the attainment of equilibrium in the melt is sluggish. Cormia et al. (1963) have studied the rates of melting and crystallization of the tetragonal form.

312

5 Oxide Glasses

5.9.2 Regions of Glass Formation in Binary Phosphate Systems Information on regions of glass formation quoted in the literature should be treated with reserve because of uncertainty with regard to the amount of water retained in the melt. The same applies to property values, which are also markedly affected by the amount of water retained. However it is clear that the regions of glass formation in many binary phosphate systems are very extensive and regions of immiscibility, which are common in alkaline earth borate and silicate systems, are rarely found in the corresponding phosphate systems. Table 5-6 gives Imaoka's results (1962) for the maximum percentage of the second oxide in glasses in a number of binary systems (melted on a 3 g scale in platinum). Extensive regions of glass formation also exist in the binary systems with the oxides V2O5, TeO2, WO 3 and MoO 3 .

Table 5-6. Regions of glass formation in binary phosphate systems (Imaoka, 1962). Maximum percentage of second oxide 47.0 60.0 60.0 66.0 60.0 56.0 56.0 58.0 66.0 50.0 64.0 57.0 62.0

Na 2 O Li2O BeO MgO CaO SrO BaO Ag2O T12O

ZnO CdO PbO

5.9.3 Properties of Binary Phosphate Glasses Fig. 5-26 shows the variation with composition of the thermal expansion coefficient of glasses in the systems R 2 O-P 2 O 5 (Takahashi, 1962) and RO-P 2 O 5 (Elyard and Rawson, 1962). Fig. 5-27 shows Ray's data (1974) for the Tg values of alkali- and alkaline earth metaphosphate glasses. Other properties are given in Mazurin etal. (1985). Physical property data for phosphate glasses is of little value without detailed information about the melting schedule and the raw materials used. It is now well known that phosphate glasses retain appreciable percentages of water, to an extent which depends on the composition and on the time and temperature of melting.

6-

0

20

&0 Mol.7o (R2O.RO)

60

Figure 5-26. Effect of composition on thermal expansion coefficient of some binary phosphate glasses. (Data for R 2 O-P 2 O 5 glasses from Takahashi (1962); data for RO-B 2 O 3 glasses; from Elyard and Rawson (1962)).

313

5.9 Phosphate Glasses

600-

Mg ~- 5005 "^

DQ

1" 60011011

Li

1 300K

cr C3

20050

i

60 70 80 Oxygen density g-atom litre" 1

Figure 5-27. Effect of composition on the Tg values of alkali and alkaline earth metaphosphate glasses (from Ray, 1974).

By melting for long periods of time the water content can be reduced with a marked effect on glass properties. Thus for a multicomponent glass containing 70mol% P 2 O 5 , initially melted at 400 °C, Ray and Lewis (1972) found the water content to be 4.5% and the transformation temperature 119°C. Samples taken during a subsequent 'refining' at 700 °C showed the water content decreasing to 0.3% and the Tg rising to 256 °C over a period of 96 h. Fig. 5-28 shows the transformation temperature plotted against the cross-link density, as calculated from the composition (taking into account the water content). The glass as initially melted at 400 °C dissolved in water to form a clear highly viscous solution. The material heated at 700 °C, however, was no longer soluble in cold water and dissolved only partly in boiling water. The changes in both the physical and chemical properties are clearly related and reflect the effect of prolonged melting in increasing the cross-linking by the elimination of water. Some phosphate glasses have been shown to contain much higher percentages

of water, 10% being not uncommon and values as high as 30% having been reported. It is worth noting that very high water contents can also be obtained in silicate glasses, but only by melting under high pressures of water vapour. As in the phosphate systems, the presence of combined water has a large effect on glass properties. A number of investigations have shown that the degree of cross-linking in watercontaining phosphate glasses and its effect on glass properties can be calculated or interpreted using theories developed in the field of organic polymers (Eisenberg and Sasada, 1965; Ray et al, 1973a, b, 1976; Ray, 1978; Furdanowicz and Klein, 1983; Gray and Klein, 1983). 5.9.4 Multi-Component Phosphate Glasses

Ray et al. (1973 a, b, 1976) have carried out a wide-ranging program to develop

240-

/ 220-

/ "^200-

/

s 180~ 160=> *-* a

I5 uo-

r

r

/

So

" 120<

3

i

0.1

I

i

I

0.2 0.3 U Cross-link density

I

0.5

Figure 5-28. Change in Tg with increasing cross-linking density (from Ray and Lewis, 1972).

314

5 Oxide Glasses

low-softening glasses of good chemical durability which can be fabricated into shapes by standard equipment used in the plastics industry. The most promising compositions had a Tg of about 170°C. The incorporation of 5 mol% B 2 O 3 significantly increased the durability without increasing Tg. Spierings et al. (1981) have shown that one of Ray's compositions, made from ultra-high purity materials, may be suitable for use as an optical communication fibre material. Controlled-release glasses dissolve at a controlled rate to release transition metal additives and other active materials which they contain. Knott (1989) has made wide use of multi-component phosphate glasses for this purpose. An important application of aluminophosphate glasses is in making the large laser amplifier discs which have been used in several high power laser fusion facilities. They are suitable for this application because of their large stimulated emission

•5

10-

T" 5 k 3 Number average chain length, n

cross section, low non-linear refractive index and satisfactory mechanical and chemical properties. Additions of B 2 O 3 and A12O3 increase the degree of cross-linking in the glasses and some borophosphate and aluminophosphate glasses have physical and chemical properties similar to those of commercial silicate glasses. 5.9.5 Structure

In the limited region of glass formation on the modifier-rich side of the metaphosphate composition, interesting structural information can be obtained by paper chromatography. Summaries of this work have been published by Van Wazer (1958) and Westman (1960). Fig. 5-29 shows the results for Na 2 O-P 2 O 5 glasses (Westman and Crowther, 1954; Westman and Gartaganis, 1957). The curves give the percentage of the total phosphorus present in chain molecules of various lengths i.e. with n values ranging from 2 to 9. The curve HP

Figure 5-29. Constitution of sodium phosphate glasses as determined by paper chromatography (from Westman, 1960).

5.10 Germanate Glasses

gives the percentage present in linear molecules for which n is greater than 9 and that labelled C gives the percentage present in cyclic molecules. The number average chain length, n*9 is given approximately by: :

= 2/(Na/P-l)

(5-4)

Thus at the metaphosphate composition (Na = P), ?2* is infinite and is 1 at the orthophosphate composition (Na = 4 P). As the Na 2 O content is reduced towards the metaphosphate composition, the proportion of long chain phosphates gradually increases at the expense of the short chain anions. Westman (1960) suggests that the presence of short chain molecules in compositions just on the high-Na2O side of the metaphosphate composition indicates that a dynamic equilibrium exists in the melt between the various anion species. Unless the time of melting is very short, the equilibrium should be independent of the nature of the starting materials. Results are also available for other binary and more complex alkali phosphate systems. It is interesting that in the mixed alkali systems, glasses can be made with remarkably high alkali contents e.g. 72mol% R 2 O (ft* = 1.25). Such glasses consist predominantly of small anionic groups i.e. of mixtures of orthophosphate and pyrophosphate anions. A limited amount of work by paper chromatography has also been carried out on calcium and zinc phosphate glasses (Meadowcroft and Richardson, 1965) with similar results. In borophosphate glasses, Scagliotti et al. (1987) have shown by Raman spectroscopy how the BO4 groups act as links between the phosphate chains with a consequent increase in Tg. Villa et al. (1987) have reported MAS NMR results on the same series of glasses.

315

5.10 Germanate Glasses Glasses containing high percentages of germania are rarely, if ever, used. The oxide is expensive and the glasses have little to offer in the way of properties that cannot be obtained in other ways. The oxide has, however, been used instead of silica as a minor constituent to improve the stability against devitrification of calcium aluminate infrared transmitting glasses (Sec. 5.11). The benefit is a slight shift of the long wavelength transmission cut-off further into the infrared. The oxide is also used as a minor constituent to increase the refractive index in silica-based material for communication fibres. 5.10.1 Germanium Dioxide Glass The melt is very viscous (Fig. 5-10) and readily forms a glass on a scale of many grams. The melting and crystallization kinetics have been studied in detail by Vergano and Uhlmann (1970 a, b) who observed that the rate of crystallization was affected by the stoichiometry of the material. Oxygen deficient material crystallizes more rapidly than the stoichiometric, the opposite trend to that observed for silica. This behaviour of GeO2 may be related to the fact that the oxygen deficient melt has a lower viscosity. 5.10.2 Regions of Glass Formation in Germanate Systems Imaoka (1962) has determined the regions of glass formation in a number of binary systems, melting on a scale of 1 - 3 g and allowing the melt to cool in the crucible (Table 5-7). Nassau and Chadwick (1982) studied glass formation in 21 binary melts of the composition MOX • 9 GeO2 (melted in a platinum crucible and water quenched).

316

5 Oxide Glasses

Table 5-7. Regions of glass-formation in binary germanate systems (Imaoka, 1962). Second oxide

Region of glass formation (mol%)

Li2O Na 2 O K2O CaO SrO BaO T12O ZnO PbO Bi2O3

0-23.8 0-38.0 0-59.5 15.5-35.5 14.0-39.0 0-10.0 0-47.5 0-48.0 0-57.0 0-34.0

and

17.5-29.6

Only a few systems gave clear glasses with no sign of phase separation (M = Rb, Cs, Tl, Pb, Bi, Sb, Ti). Some partly crystallized (M = Sr, Ba, Zn, Ga, Mo, W) whilst others showed excessive vaporization or could not be melted. Three- and four-component glasses were found to be much more stable. Murthy and Scroggie (1965) have shown that there are extensive regions of glass formation in the alkali-aluminogermanate glasses, especially those containing Na 2 O and K 2 O and that the glass-forming region is bounded on one side by the R2O/A12O3 tie line. This observation is at variance with that of Trojer and Geyer (1972) who were able to study the effects of composition on melt viscosities and glass refractive indices for compositions on both sides of the line. 5.10.3 Structure

Investigations have been carried out, using various techniques, to study the coordination number of germanium in germanate glasses and melts. All the germanium ions are four-coordinated in GeO 2 glass (Desa et al, 1988), but the addition of alkali converts some to sixfold co-ordination. The higher co-ordination number is also found in some crystalline alkali ger-

manates e.g. Na 4 Ge 9 O 2 0 and in the tetragonal form of the crystalline oxide. The change of Ge co-ordination with composition is shown by the XAFS and XRD work of Sakka and Kamiya (1982) on alkali germanate glasses, by XRD on Na 2 O-GeO 2 melts (Kamiya et al., 1986), and by X-ray chemical shift measurements on N a 2 O GeO 2 glasses (Yin et al., 1984). Smets and Lommen (1981 a) used photoelectron spectroscopy, a technique sensitive to the presence of non-bridging oxygens, to study alkali germanate and alkali silico-germanate glasses. They concluded that up to 20 mol% alkali, the co-ordination number of some of the Ge ions is changed from 4 to 6. Only beyond that composition are non-bridging atoms formed. Their conclusions are similar to those obtained earlier by Raman spectroscopy (Verweij and Buster, 1979) and may be summarized as follows: x = 0-0.18 GeO 6 groups are formed with no non-bridging oxygens, x = 0.18-0.33 addition of alkali results in the breakdown of some GeO 6 , octahedra with one NBO being formed per octahedron, x = 0.33-0.5 germanate and silicate glasses are isostructural in this region. (In the above, x represents the mole fraction of R 2 O in the glass.) In these simple glasses, the maximum value of N 6 , the fraction of Ge atoms in 6-coordination, is about 0.25. 5.10.4 Properties

Structural changes of the kind described in the previous section were earlier inferred from studies of the effects of composition on the properties of germanate melts and

5.12 Tellurite Glasses

glasses (Ivanov and Epstropiev, 1962; Riebling, 1963 a, b). Thus in the R 2 O GeO 2 systems, there are maxima at between 10 and 20 mol% R 2 O in the curves relating density or refractive index to composition (Murthy and Ip, 1964). More recent property studies which include structural interpretation of the results are those of Riebling (1972) of (Ag,Tl) aluminogermanates, Riebling and Kotian (1973) of thallium germanosilicates, Riebling (1973) of (Na, K, Ag, Tl) germanates and Osaka et al. (1986) of alkali germanates. Trojer and Geyer (1972) determined the activation energy for viscous flow of melts and the refractive indices of glasses in the R 2 O aluminogermanate systems with a constant GeO 2 content of 60 mol% and with the R2O/A12O3 ratio increasing and crossing the R2O/A12O3 = 1 line. The effects observed were very similar to those in the corresponding aluminosilicate systems, which have been interpreted in terms of a change in the co-ordination number of the Al (Sec. 5.8.2). There was no indication in these compositions of any change in the co-ordination number of germanium. Other property-composition studies include Topping et al. (1974a) on PbO-GeO 2 glasses, Topping et al. (1974 b) on P b O GeO 2 SiO2 glasses and Nassau and Chadwick (1983) on (PbO, T12O, Bi 2 O 3 )-GeO 2 glasses.

5.11 Aluminate Glasses Glasses in the CaO-Al 2 O 3 system were discovered in the course of phase diagram studies of that system and of the ternary MgO-CaO-Al 2 O 3 system (Sheperd et al., 1909). Glass formation is possible in small melts (a few mg) when rapidly cooled. The region of glass formation shown in Fig. 5-3

317

is for a 20 mg scale of melting, the melt cooling freely in air. The addition of ca. 5% of silica or germania greatly increases the stability so that glass formation becomes possible on a scale of many grams (Stanworth, 1948 a; Sun, 1946, 1949). The aluminate glasses transmit to somewhat longer wavelengths in the infra-red than do the silicates and, when vacuum melted to remove the IR absorbing - O H impurity, they have important applications in various IR detection systems, provided that the emitter is at a relatively high temperature. The commercial glasses can be made on a scale of kilograms (Worrall, 1968). The development of the manufacturing technology has been described by Davy (1978). The stability of the glasses is also improved by making the composition more complex and in this way Florence et al. (1955) and Hafner et al. (1958) were able to produce silica-free glasses on a commercially useful scale. Elimination of the silica results in a useful improvement in the long wavelength IR transmission. The glasses require high melting temperatures (ca. 1400°C) and have high Tg temperatures (ca. 800 °C). Their thermal expansion coefficients are similar to those of commercial soda-lime-silica glasses. Glass formation also occurs in the related CaO-Ga 2 O 3 system (Baynton et al., 1957 b; Wichard and Day, 1984). A number of investigations have been made on this system and especially on the gallosilicate glasses with interesting results. However there are no indications that these glasses are of technological interest.

5.12 Tellurite Glasses Tellurite glasses were first studied in detail by Stanworth (1952, 1954). They are

318

5 Oxide Glasses

easily prepared by melting at low temperature - usually below 1100 °C. The melts are very fluid and are easily homogenized. For many compositions, specimens ranging up to tens of grams can be made simply by casting the melt into a metal mould. The colour of the glass depends on the purity of the raw materials used but it is usually pale yellow. Their most notable properties are the high refractive index (up to 2.3) and high thermal expansion coefficient (up to 250 • 10~7 C" 1 ). Transformation temperatures are low. Resistance to atmospheric attack is generally good. Technological applications have been limited and only two or three glasses of high TeO2 content are commercially available as optical glasses. Although Te forms two oxides, TeO2 and TeO3, and corresponding oxysalts, the glasses are based on the lower oxide. The structures of several crystalline tellurites have been determined and the results used to guide the interpretation of structural studies of the glasses. 5.12.1 Glass Formation in Tellurite Systems It is uncertain whether or not pure TeO2 forms a glass. Stanworth (1954) originally believed it did, but the glass in question had been melted in an alumina crucible and was found to contain several percent of dissolved alumina which stabilizes the glass. When the experiment was repeated using a gold crucible, the melt devitrified. However Bridge et al. (1986) report that a TeO2 glass can be prepared, melted in alumina but containing as little as 1.5% of the oxide. They discount the significance of the alumina contamination but stress the importance of the temperature at which the melt is cast. To obtain a "pure" TeO2 glass, the melt should be cast at as low a temperature as possible, when it is relatively viscous.

The chemistry of TeO2 indicates that it is an acidic oxide. It forms a number of crystalline compounds with basic RO and R 2 O oxides but does not form compounds or low melting point melts with SiO2. However it does form glasses with the other glass-forming oxides B 2 O 3 , P2O5 and GeO 2 . For these three systems, the ranges of glass formation are (Vogel et al., 1974 d): 10-100 mol% GeO 2 , 2-100mol% P 2 O 5 , 12-100mol% B 2 O 3 . The useful range of glass formation is limited by immiscibility in the GeO 2 - and B2O3-systems. In the former, immiscibility is observed in glasses above 30 mol% GeO2 and in the latter above 26.4 mol% B 2 O 3 . Immiscibility in the TeO 2 -B 2 O 3 system has been studied in detail by Burger et al. (1984). Extensive studies to determine the regions of glass formation have been carried out by Imaoka (1962) and more recently by Vogel et al. (1974, a, b, c, d) and Kozhukarov. et al. (1983). Glass formation has been reported in a very large number of binary and ternary oxide systems with glasses being made on such a scale as to make possible their practical application, should the need arise. The systems studied include binaries of TeO2 with: 1. Alkali and alkaline earth oxides (Vogel etal., 1974 a). 2. The group: ZnO, A12O3, T12O, PbO, Nb 2 O 3 , Ta 3 O 3 , WO 3 , La 2 O 3 , TiO 2 , ThO 2 (Vogel etal., 1974b). 3. Transition metal oxides (Kozhukarov etal., 1978). Amongst the more stable glasses are those studied earlier by Stanworth i.e. those in the systems: BaO-TeO 2 (8-35.7 mol% BaO), PbO-TeO 2 (12.8-22.6 mol% PbO), WO 3 -TeO 2 (8.5-44.0 mol% WO3) and V 2 O 5 -TeO 2 (7.5-58.0 mol% V2O5). Regions of glass formation are limited in

5.13 Vanadate Glasses

systems containing the alkaline earth oxides (other than BaO) and no glasses could be made in the system containing CaO. Glass formation was also absent from binary systems containing Cr 2 O 3 , Fe 3 O 4 , NiO andNi 2 O 3 . It is remarkable that amongst the forty or so binary systems investigated, only six showed no sign of glass formation. The glasses of Vogel, Kozhukarov et al. were melted in gold or platinum crucibles on a scale of 20-100 g and cooled relatively slowly (8-10°C s"1) through the transformation range. Glass formation has been reported in many binary systems containing halides and sulphates (Vogel et al., 1974 c). The use of chlorides or bromides made glass-formation easier than when the corresponding oxides were used. Vogel (1985) gives a useful summary of the regions of glass formation in the binary systems. From this account of glass formation in binary systems, it is not surprising that there should be extensive regions of glass formation in many ternary and quaternary systems. Work on these more complex systems have been described by Marinov et al. (1983). 5.12.2 Structure

Johnson et al. (1986) have summarized the results of earlier structural studies of tellurite glasses and related crystalline compounds when reporting their own neutron diffraction results for a V 2 O 5 -TeO 2 glass. This material contained 90 mol% of TeO2 and would be expected to show the structural features of a tellurite rather than those of a vanadate glass. They conclude that the glass structure contains units having some similarity to those found in one of the crystalline polymorphs of TeO2, /?-

319

o

o 6

6

Figure 5-30. (a) TeO4 and (b) Te2O6 structural units (from Johnson et al., 1986).

TeO2. This unit, it is suggested, should be considered to be a distorted trigonal bipyramid. How the units are joined together is not clear. Their summary of structural studies of a variety of binary tellurite glasses shows that many kinds of structural unit have been proposed, all with the tellurium atom asymmetrically placed relative to the adjacent oxygens (Fig. 5-30). In the V 2 O 5 -TeO 2 system, there is a change in the co-ordination number of the Te atoms from 4 to 3 at high V2O5 contents (Dimitriev et al., 1977; Dimitriev and Dimitrov, 1978).

5.13 Vanadate Glasses Most of the interest in vanadate glasses has arisen from the fact that they are semiconductors with room temperature resistivities which can be as low as l Q m , depending on the V2O5 content and the melting conditions. In general the melts are very fluid. Also additions of V2O5 to borate and phosphate melts, for example, greatly reduce their viscosities. Use has been made of this fact to develop low softening point glasses.

320

5 Oxide Glasses

5.13.1 Glass Formation Vanadium pentoxide melts at ca. 660 °C and forms a glass only when very rapidly cooled (Wright, 1984; Rivoalen et al., 1976). In a number of binary systems, glasses are readily formed on a scale of several grams simply by casting the melt into a cold steel mould. The regions of glass formation in several binary systems are given in Table 5-8. Although the glass-forming regions are narrow in the barium and lead vanadate systems, glasses in these systems can easily be made on a scale of some tens of grams by the addition of small percentages of P 2 O 5 , TeO2 or GeO 2 . The addition of B 2 O 3 has a similar effect on the zinc vanadate glasses. Thus there is a wide range of vanadate glass compositions available for study and application. Even without the addition of glass-forming oxides, many stable glasses can be made containing between 30 and 70 mol% V2O5 simply by adding further components i.e. making the composition more complex. Thus stable glasses have been made by Kawamoto et al. (1979) in the system V 2 O 5 -BaO-K 2 O-ZnO. They also studied the glass properties and some aspects of the phase diagram. Table 5-8. Regions of glass formation in binary vanadate systems (Denton et al., 1954; Denton and Rawson, 1956). System

Mol%

Crucible used

v2o5 P2O5-V2O5

GeO 2 -V 2 O 5 TeO 2 -V 2 O 5 As 2 O 3 -V 2 O 5 BaO-V 2 O 5 PbO-Y 2 O 5 ZnO-V 2 O 5 a

<94 6-64 9-57 >52 58-69 51-67 46-72

Platinum Platinum Silica and alumina Silica and aluminaa Platinum Silica and alumina Platinum (20 mg)

Maximum content of As 2 O 3 limited by volatilization.

By very rapid cooling (i.e. roller quenching), Dimitriev et al. (1981) were able to show that glasses could also be made in binary systems containing Li 2 O, Cu 2 O, CuO, Ag2O, MgO, CaO, SrO, CdO, B 2 O 3 , A12O3, Ga 2 O 3 , Nd 2 O 3 , CeO 2 , WO 3 , Fe 2 O 3 , TiO 2 , Nb 2 O 3 , MnO, CoO, Cr 2 O 3 , MoO 3 , NiO, SnO 2 , ZrO 2 , SiO2. The lower melting compositions were melted in glazed porcelain crucibles. Those with melting temperatures above 1100°C were melted in alumina. These simple binary glasses are unlikely to be of any practical interest, though some could be if stabilizing oxides were added. Another system in which glasses form only by rapid quenching is the Bi 2 O 3 V2O5 system. Glass foils 0.5-1.0 mm thick can be made by pressing the melt between metal blocks. Ghosh et al. (1987) have studied the properties of these glasses in detail. Small percentage additions of V2O5 have been used in the development of low softening point borate and phosphate glasses (Denton and Rawson, 1956; Ray et al., 1973 a, b; Wozniak and James, 1984). 5.13.2 Properties Most of the vanadate glasses, except those with a high P2O5 content, have a good resistance to attack by normal ambient conditions. They can be enamelled onto substrates of matched expansion coefficient without difficulty. Thermal expansion coefficients are high (typically >100-10~ 7 o C" 1 ) and the expansion curves are typified by an unusually large increase in slope above Tg. The melts and glasses are far from stoichiometric. For example, Szorenyi et al. (1982) show that the V 4+ /V total ratio increases with the P 2 O 5 content in V 2 O 5 P 2 O 5 glasses to more than 0.5 at 45 mol%

5.14 Mixed Anion Glasses

P 2 O 5 . The stoichiometry is also affected by the melting atmosphere and the melting temperature. The glasses are green or brown when blown into thin films, but thicker sections appear black. That they are semiconductors was first shown by Baynton et al. (1957 a), the first occasion on which semiconductivity had been observed in an oxide glass system. Studies on other semi-conducting oxide glasses soon followed, as part of a very large research effort on the physics of conduction in amorphous solids. Electrical properties have been reviewed by Owen (1970, 1977). Structural studies have probably not given sufficient attention to the effects of melting conditions on the degree of stoichiometry or have followed up indications in the literature that some compositions may be phase separated (Szorenyi et al., 1980, 1982; Janakarama-Rao, 1966). 5.13.3 Structure

The available structural information on vanadate glasses has been summarized by Wright et al. (1985). On the basis of their neutron diffraction study of P2O5-, BaOand PbO-V 2 O 5 glasses, they note that there are no close similarities between the structures of the glasses and those of related crystalline compounds. In all three glass systems there is a vanadate network 'composed of interconnected, distorted trigonal bipyramids'. The vanadium-oxygen co-ordination polyhedra and the linkage between them appears to be less regular than in corresponding phosphate glasses and crystals.

5,14 Mixed Anion Glasses A very wide range of compositions can be made and properties obtained within

321

the range of oxide glasses. This can be extended even further by the partial substitution of the oxygen anions by nitrogen or halogen anions. This type of substitution affects the cross-linking within the network and greatly modifies the properties. 5.14.1 Oxynitride Glasses

The preparation and properties of these materials has been summarized by Loehmann (1985). They first became of interest when it was noted that the intergranular phase in silicon nitride and oxynitride ceramics is partly vitreous. Subsequently many oxynitride glasses were prepared and their properties studied. The most effective method for making nitrogen-containing silicate glasses is to melt together mixtures of oxide and nitride powders in a protective atmosphere of nitrogen or argon. In this way nitrogen contents of ca. 10at.% can be attained. Another method is to heat a silicate gel composition containing a high concentration of - O H groups in an atmosphere of ammonia (Brinker, 1982). If the composition contains alumina, the nitrogen solubility is increased and the melt more readily forms a glass. It has been suggested that the beneficial effect of alumina is related to the fact that the A1O4 and Si (O, N) 4 tetrahedra are of similar size (Jack, 1977). Also the aluminium and oxygen ions readily substitute into the lattice of crystalline Si 3 N 4 to form phases such as jg-SiAlON. Substitution of divalent oxygen by trivalent nitrogen increases the degree of crosslinking in the network. Presumably each nitrogen anion is shared between three tetrahedra - another violation of the Zachariasen rules. The properties change with increasing nitrogen content in a way to be

322

5 Oxide Glasses

1000{= 7-

it= 6"~

900-

/

800i

L 6 Atomic percent nitrogen

expected from increased cross-linking. Thus Fig. 5-31 shows the effect of increasing nitrogen content on properties of glasses in the system Y - S i - A l - O - N . Their compositions are given in Table 5-9. The marked decrease in expansion coefficient and increase in glass transformation temperature both indicate an increase in the degree of cross-linking. Oxynitride glasses based on phosphate glasses have been studied by Marchand (1983) and on borate glasses by Wilder (1980), and Wilder et al. (1983).

Table 5-9. Compositions of Y - S i - A l - O - N glasses (Loehmann, 1985).

SG6 SG7 SG8 SG10 SG11 SG12 SG13 SG14 SG15

i

I

i

i

2 L 6 Atomic percent nitrogen

2

Glass composition (at.%)

Sample number

i

Figure 5-31. Effect of nitrogen content on Tg and expansion coefficients of glasses in the system Y - S i - A l - O - N (from Loehmann, 1985).

Y

Si

Al

O

N

10.3 6.4 5.6 8.9 16.6 12.7 15.2 9.6 16.6

17.6 19.0 20.3 20.9 15.0 18.6 14.3 18.8 15.0

11.7 9.9 8.1 2.8 3.2 6.7 7.9 7.5 3.2

54.0 57.6 60.3 65.8 63.6 57.6 57.5 57.8 65.1

6.5 7.0 5.7 1.6 1.5 4.4 5.1 6.3 0.

5.14.2 Oxyhalide Glasses Substitution of oxygen anions by halogen anions has the opposite effect to that produced by the nitrogen substitution. The degree of cross-linking within the network is reduced. Large percentages of halides can be introduced into most low-melting point oxide glass, especially into phosphate and borate compositions. In silicate melts, similar to commercial soda-lime-silica compositions, the addition of more than 2 - 3 % of a halide results in the crystallization of a halide phase on cooling. This is the basis for the manufacture of the well-known fluoride opal glass (Rothwell, 1956). Extensive development work has been carried out on fluorophosphate glasses, initially for use as optical glasses but more recently for use in high power lasers. It is interesting that stable glasses can be made with P2O5 contents as low as 2%. Thus Heidenreich (1983) made a wide-ranging study of glasses containing 3.4 mol% Ba(PO 3 ) 2 , the rest of the composition being made up of mixtures of the fluorides of Mg, Ca, Sr, Ba and Al. Some compositions of high halide content have very high ionic conductivities

5.15 Ionic Salts and Solution Glasses

and are being studied for possible use as battery electrolytes (Ravaine, 1985; Minami, 1985). Examples of some of these unusual compositions are the following: 0.7 LiPO 3 • 0.3 (LiCl, LiBr, Lil); 0.85 Agl • 0.15 Ag 4 P 2 O 7 ; 0.60 Agl • 0.30 Ag2O • 10B 2 O 3 .

5.15 Ionic Salts and Solution Glasses This section deals with groups of oxide glasses which are quite different from those described earlier. They consist of simple salts such as nitrates, sulphates or acetates, the structures of which contain discrete anions. Often glass formation is confined to certain ranges of composition in binary or more complex mixtures of these salts or in aqueous solutions containing them. However there is no anionic network as in the glasses considered earlier and hence the concepts of network former and network modifier are not relevant, nor are the Zachariasen rules. There may therefore be some difficulty in understanding why such materials form glasses. In a valuable summary of this group of materials, Angell (1983) implies that an important factor is the 'geometrical asymmetry of the anion and the packing problems that follow, particularly in unbalanced cation force fields'. This view is also expressed by Thilo et al. (1964) and van Uitert et al. (1971) who have made extensive studies of glass-formation in nitrate and acetate systems respectively. They note that glass formation is most probable in those systems in which the electrical field strength, z/r2, of the two cations differ by 0.7 or more. It is suggested that the higher field strength cations tend to form clusters with the anions and that

323

these inhibit the nucleation of crystalline phases with different structures. No doubt structural factors have important effects on the kinetics of nucleation and crystal growth but one should also note that in these systems, the regions of glass formation usually coincide with regions of low liquidus temperature. It may be sensible to enquire to what extent the shape of the liquidus curve is determined by the cation field strength difference. Structure, melting and glass formation are clearly interrelated. One needs to examine all the interrelationships before one can form a view as to which is the most important. The opportunities for doing so are probably greater in the ionic salt systems than in the technologically more important but structurally more complex glassforming systems. Some of the pure salts themselves have low melting points. Thus the alkali metal nitrates melt at much lower temperatures than the corresponding chlorides. This is discussed further by Rawson (1967). 5.15.1 Nitrate Glasses Dietzel and Poegel (1954) made the first detailed study of a binary nitrate glassforming system -KNO 3 -Ca(NO 3 ) 2 . The region of glass formation was found to be 54-67 mol% KNO 3 , the most stable glass having the composition 60mol% KNO 3 , 40 mol% Ca(NO 3 ) 2 with a Tg as low as 60 °C. This glass is very stable indeed with a maximum crystallization rate as low as the most stable of the sodium silicate glasses. The eutectic temperature is 146 °C, much lower than the melting points of the constituent nitrates (KNO 3 337 °C, Ca(NO 3 ) 2 561 °C). Thilo et al. (1964) and van Uitert et al. (1971) have investigated many other nitrate systems containing both univalent

324

5 Oxide Glasses

and divalent cations. Although the liquidus effect is evident, it is interesting that the glass-forming region does not always contain the eutectic composition. Angell (1983) draws attention to the difficulty of dehydrating some compositions. It is possible therefore that some of the glass-forming regions reported are for poorly defined compositions. Angell and Helphrey (1971) have shown that stable glasses can be made in nitrate systems containing only monovalent ions (e.g. LiNO 3 -AgNO 3 -NH 4 NO 3 ). 5.15.2 Acetate Glasses Although carbonate glasses can be made, usually by melting under pressure, considerably more work has been carried out on the acetates. From the viewpoint of anion shape, the acetate ion can be thought of as a carbonate ion with one of its oxygens substituted by a methyl group, thus reducing its symmetry and favouring glass formation. The acetate glasses have been studied by Bartholomew and Holland (1969), Duffy and Ingram (1969) and van Uitert et al. (1971). Glass transition temperatures are approximately 30 °C higher than for the corresponding nitrate glasses and they are more resistant to atmospheric weathering. 5.15.3 Sulfate Glasses The first mixed cation sulfate glass to be studied was KHSO 4 (Forland and Weyl, 1950). An equimolar KHSO 4 -NaHSO 4 glass was subsequently found to be extremely resistant to crystallization. Several studies have been made of glasses and glass formation in the ZnSO 4 -K 2 SO 4 system (Ishii and Akawa, 1965; Angell, 1965; Kolesova, 1975; Narasimhan and Rao, 1978), in the Tl 2 SO 4 -ZnSO 4 system (Ishii

and Akawa, 1965) and in the NH 4 SO 4 ZnSO 4 system (Wong, 1970). 5.15.4 Hydrates and Aqueous Solutions Many crystalline hydrates melt at temperatures lower than the corresponding anhydrous salts. In some e.g. Ca(NO 3 ) 2 • 4 H 2 O the water molecules co-ordinate the cation. In others, e.g. K 2 S 2 O 3 • 5H 2 O, they co-ordinate the anion. Glass formation and glass properties have been investigated in many binary mixtures of hydrates of both types (Angell and Helphrey, 1971; Moynihan, 1966; Moynihan et al., 1969; Jain, 1978). Vuillard (1954, 1955, 1957) has shown that many concentrated aqueous solutions of inorganic acids, bases and salts readily form glasses. Shepley and Bestul (1963) and Angell and Sare (1970) have investigated some systems in detail and have determined the phase diagrams. Although none of the glasses listed in this section is likely to be of any technological importance, they are all of considerable scientific interest and importance. Experimentation with such low melting point materials is in general easier than with the higher melting oxide systems and their study gives a broader perspective to the study of oxide glasses in general. It may indeed throw light on many unsolved questions relating to the more conventional glasses.

5.16 References Ahmed, A. A., Abbas, A.R, Solman, S. M. (1985), Phys. Chem. Glasses 26, 17-23. Ainslie, N. G., Morelock, C. R., Turnbull, D. (1962), in: Symposium on Nucleation and Crystallization and Melts: Reser, M.K., Smith, G., Insley, H. (Eds.). Columbus, OH: American Ceramic Society, pp. 97-107. Angell, C.A. (1965), J. Am. Ceram. Soc. 48, 540.

5.16 References

Angell, C.A., Sare, E. (1970), J. Chem. Phys 52, 1058-1068. Angell, C. A., Helphrey, D. B. (1971), J. Phys. Chem. 75, 2306-2312. Angell, C.A. (1983), in: Glass Science and Technology, Vol.1: Glass-Forming Systems: Uhlmann, D.R., Kreidl, N . I (Eds.). London: Academic Press, pp. 209-223. Araujo, R. J. (1979), Phys. Chem. Glasses 20, 115, Araujo, R. J. (1983), /. Non-Cryst. Solids 58, 201-208. Baeten, M.H.C., Stein, H.N., Stevels, XM. (1972), Silicates Ind. 37, 33-36. Bartholomew, R., Holland, H. (1969), /. Am. Ceram. Soc. 52, 402-403. Baynton, P. L., Rawson, H., Stanworth, J. E. (1957 a), J. Electrochem. Soc. 104, 237-240. Baynton, P. L., Rawson, H., Stanworth, J. E. (1957b), Nature 179, 434-435. Beales, K.J., Day, C.R. (1980), Phys. Chem. Glasses 21, 5-21. Bell, T., Hetherington, G., Jack, K.H. (1962), Phys. Chem. Glasses 3, 141-146. Bergeron, C, G. (1978), in: Borate Glasses: Pye, L.D., Frechette, V.D., Kreidl, N . I (Eds.). New York: Plenum Press, pp. 445-461. Berzelius, XI (1834), Ann. Phys. Chem. 32, 511. Bray, P.X (1978), in: Borate Glasses: Pye, L.D., Frechette, V.D., Kreidl, N.X (Eds.). New York: Plenum Press, pp. 321-351. Bray, P. X, O'Keefe, X G. (1963), Phys. Chem. Glasses 4, 37-46. Bridge, B., Bavins, T. E., Woods, D., Woolven, T. (1986), J. Non-Cryst. Solids 88, 262-270. Brinker, C.X (1982), /. Am. Ceram. Soc. 65, C 4 - 5 . Brown, S. D., Kistler, S. S. (1959), J. Am. Ceram. Soc. 42, 263-270. Bruckner, R. (1964), Glastech. Ber. 37, 413-425. Bruckner, R. (1978), Glastech. Ber. 51, 1-7. Burger, H., Vogel, W, Kozhukharov, V., Marinov, M. (1984), J. Mater. Sci. 19, 403-412. Button, D.P., Tandon, R., King, C , Velez, M.H., Tuller, H. L., Uhlmann, D. R. (1982), /. Non-Cryst. Solids 49, 129-142. Cahn, X W, Charles, R. X (1965), Phys. Chem. Glasses 6, 181-191. Chechetkina, E. A. (1990), to be published in /. NonCryst. Solids. Cohen, H. M., Turnbull, D. (1961), Nature 189, 131132. Cooper, A.R. (1982), J. Non-Cryst. Solids 49, 1-18. Cormia, R. L., Mackenzie, X D., Turnbull, D. (1963), J. Appl. Phys. 34, 2239-248. Cranmer, D., Uhlmann, D. R. (1981), J. Non-Cryst. Solids 45, 283-288. Danielson, P. (1982), in: Kirk-Othmer Encyclopaedia of Chemical Technology, 3rd ed., Vol. 20. New York: Wiley, pp. 782-817. Davy, XR. (1978), Glass TechnoL 19, 32-36. Day, D.E., Rindone, G. E. (1962), J. Am. Ceram. Soc. 45, 489-496.

325

Denton, E. P., Rawson, H. (1956), / Soc. Glass TechnoL 40, 252-259. Desa, X A. E., Wright, A. C , Sinclair, R. N. (1988), /. Non-Cryst. Solids 99, 276-288. Dietzel, A., Poegel, H. (1954), Int. Congr. Glass, 3rd., Venice. Rome: Stabilimento Grafica di Roma, pp. 219-243. Dietzel, A., Wickert, H. (1956), Glastech. Ber. 29, 1-4. Dimitriev, Y, Gateff, E., Kashchieva, E., Dimitrov, V (1977), Int. Congr. Glass, 11th, Prague, Vol. 1, Prague: CVTS-DUM TECHNIKY, pp. 159-172. Dimitriev, Y, Dimitrov, V. (1978), Mat. Res. Bull. 13, 1071-1075. Dimitriev, Y, Ivanova, I., Gatev, E. (1981), J. NonCryst. Solids 45, 297-300. Dorfield, W. G. (1988), Phys. Chem. Glasses 29, 179186. Duffy, X A., Ingram, M. (1969). /. Am. Ceram. Soc. 52, 224-225. Duffy, J.A., Grant, R.X (1975), J. Phys. Chem. 79, 2780-2784. Duffy, J.A., Ingram, M.D. (1976), J. Non-Cryst. Solids 21, 373-410. Duffy, X A., Ingram, M.D., Somerville, I.D. (1978), /. Chem. Soc. Farad. Trans. I. 74, 1410-1419. Dumbaugh, W, Schultz, P. (1969), in: Kirk-Othmer Encyclopaedia of Chemical Technology, 2nd. ed., Vol. 18. New York: Wiley, p. 73-105. Dupree, R., Holland, D., McMillan, P.W, Pettifer, R.F. (1984), J. Non-Cryst. Solids 68, 399-410. Dupree, R., Holland, D., Williams D. S. (1986), /. Non-Cryst. Solids 81, 185-200. Dupree, R., Ford, N., Holland, D. (1987), Phys. Chem. Glasses 28, 78-84. Eisenberg, A., Sasada, T. (1965), in: Physics of NonCrystalline Solids: Prins, XA. (Ed.). Delft: North Holland, pp. 99-115. Elliott, S.R. (1989), in: Glass '99, Int. Congr. Glass, XVth, Leningrad. Leningrad: 'NAUK', pp. 65-83. Elyard, C. A., Rawson, H. (1962), in: Advances in Glass Technology. New York: Plenum Press, pp. 270-286. Espe, W. (1968), Materials of High Vacuum Technology, Vol. 2: Silicates. New York: Pergamon Press; p. 660. Evans, R. C. (1946), An Introduction to Crystal Chemistry. Cambridge: Cambridge University Press, p. 388. Florence, J.M., Glaze, F.W., Black, M.H. (1955), J. Res. Natn. Bur. Stand. 55, 231-237. Forland, X, Weyl, WA. (1950), /. Am. Ceram. Soc. 33, 186-187. Fratello, V X, Hays, X F , Turnbull, D. (1980), J. Appl Phys. 51, 4718-4728. Frieser, R. G. (1975), Electrocomm. Sci. TechnoL 2, 162-199. Furdanowicz, W, Klein, L. C. (1983), Glass TechnoL 24, 198-201. Gambling, W A. (1980), Phys. Chem. Glasses 21,1-4.

326

5 Oxide Glasses

Gambling, W. A. (1986), Glass Technol. 27, 179-187. Garfmkel, H. M. (1969), Glass Industry 50, 28-31, 74-76. Ghosh, A., Chaudhuri, B. K. (1987), /. Mater. Sci. 22, 2369-2376. Gossink, R. G. (1977), /. Non-Cryst. Solids 26, 112157. Gotz, J., Hoebel, D., Wieker, W. (1976), J. Non-Cryst. Solids 20,413-425. Gray, P.E., Klein, L.C. (1983), Glass Technol. 24, 202-206. Griscom, D. L. (1978 a), in: The Physics of SiO2 and Its Interfaces: Pantelides, S.P. (Ed.). New York, Oxford: Pergamon, pp. 232-252. Griscom, D. L. (1978 b), in: Borate Glasses: Pye, L.D., Frechette, V.D., Kreidl, N.J. (Eds.). New York: Plenum Press, pp. 11-149. Griscom, D.L. (1985), J. Non-Cryst. Solids 73, 5 1 77. Hafner, H.C., Kreidl, N.J., Weidel, R.A. (1958), /. Am. Ceram. Soc. 41, 315-325. Haller, W., Blackburn, D. H., Wagstaff, F. E., Charles, R. J. (1970), /. Am. Ceram. Soc. 53, 34-39. Havermans, A. C.J., Stein, H.N., Stevels, J. M. (1970), J. Non-Cryst. Solids 5, 66-69. Heidenreich, E. (1983), Wiss. Zeit. Fried. Schill. Univ., Math. Natur. Reihe (2nd International Otto Schott Colloquium) 32, 527-540. Hench, L. L. (1977), J. Non-Cryst. Solids 25, 343-369. Hench, L.L. (1985a), in: Glass... Current Issues: Wright, A.F., Dupuy, J. (Eds.). Dordrecht: MartinusNijhoff, pp. 551-554. Hench, L.L. (1985b), in: Glass... Current Issues: Wright, A. F., Dupuy, J. (Eds.). Dordrecht: Martinus Nijhoff, pp. 631-637. Hench, L. L., Spilman, D. B. (1985), in: Glass... Current Issues: Wright, A. F., Dupuy, J. (Eds.). Dordrecht: Martinus Nijhoff, pp. 656-661. Hendrickson, J.R., Bray, P. J. (1972 a), Phys. Chem. Glasses 13, 43-49. Hendrickson, J.R., Bray, P.X (1972 b), Phys. Chem. Glasses 13, 107-115. Herms, G., Derno, M., Steil, H. (1986), J. Non-Cryst. Solids 88, 381-387. Hetherington, G., Jack, K.H. (1962), Phys. Chem. Glasses 3, 129-133. Hetherington, G., Jack, K. H., Kennedy, J. C. (1964), Phys. Chem. Glasses 5, 130-136. Hishinuma, H., Uhlmann, D. R. (1987), /. Non-Cryst. Solids 95/96, 449-456. Hood, H. P., Nordberg, M.E. (1938), US Patent 2106 744. Huggins, M. L., Sun, K.H. (1943), J. Am. Ceram. Soc. 22, 4-11. Huggins, M.L., Stevels, J. M. (1954), /. Am. Ceram. Soc. 37, 474-479. Her, R. K. (1979), The Chemistry of Silica. New York: Wiley, p. 866. Imaoka, M. (1962), in: Advances in Glass Technology: New York: Plenum Press, pp. 149-164.

Ingram, M.D. (1987), Phys. Chem. Glasses 28, 215234. Inoue, H., Yasui, I. (1987), Phys. Chem. Glasses 28, 63-69. Inoue, H., Aoki, N., Yasui, I. (1987), J. Am. Ceram. Soc. 70, 622-627. Isard, J. O. (1959), /. Soc. Glass Technol. 43,113-123. Isard, J.O. (1968/1969), /. Non-Cryst. Solids 1, 235261. Ishii, A., Akawa, K. (1965), Rep. Res. Lab. Asahi Glass Co. 15, 1-7. Ivanov, A.O., Epstropiev, K. S. (1962), Dokl. Akad. Nauk. SSSR. 145, 797-800. Jack, K.H. (1977), in: Nitrogen Ceramics: Riley, F.L. (Ed.). Leyden: Noordhoff, pp. 109-128. Jain, S.K. (1978), J. Phys. Chem. 82, 1272-1276. James, P. F. (1985), J. Non-Cryst. Solids 73, 517-540. Janakarama-Rao, Bh.V. (1966), J. Am. Ceram. Soc. 49, 605-609. Janowski, X, Heyer, W. (1982), Porose Glaser: Herstellung, Eigenschaften und Anwendung. Leipzig: VEB Deutscher Verlag fur Grundstoffindustrie, p. 274. Jantzen, C M . , Schwahn, D., Schelten, J., Herman, H. (1981), Phys. Chem. Glasses 22, 122-137. Jellison, G. E., Bray, P. J. (1978 a), in: Borate Glasses: Pye, L.D., Frechette, V.D., Kreidl, N.J. (Eds.). New York: Plenum Press, pp. 353-367. Jellison, G.E., Bray, P.J. (1978 b), /. Non-Cryst. Solids 29, 187-206. Jiang, Yasi, Zhang, Junzhou, Xu, Wenjiun et al. (1986), J. Non-Cryst. Solids 80, 623-629. Johnson, P.A.V., Wright, A.C., Sinclair, R.N. (1982), /. Non-Cryst. Solids 50, 281-311. Johnson, P.A.V., Wright, A.C., Yarker, C.A., Sinclair, R.N. (1986), J. Non-Cryst. Solids 81, 163171. Kaiura, G. H., Toguri, J. M. (1976), Phys. Chem. Glasses 17, 62-29. Kamiya, K., Yoko, T., Itoh, Y, Sakka, S. (1986), /. Non-Cryst. Solids 79, 285-294. Kawamoto, Y, Fukuzawa, M., Ohta, Y, Imai, M. (1979), Phys. Chem. Glasses 20, 54-59. Klonowski, A. (1983), Phys. Chem. Glasses 24, 166171. Knott, P. (1989), Glastech. Ber. 62, 29-34. Kohl, W. H. (1967), Handbook of Materials and Techniques for Vacuum Devices. New York: Reinhold, p. 450. Kolesova, V. (1975), Fiz. Khim. Stekla 1, 290. Kozhukharov, V., Marinov, M., Grigorova, G. (1978), J. Non-Cryst. Solids 28, 429-430. Kozhukharov, V., Marinov, M., Gugov, I., Burger, H., Vogel, W. (1983), J. Mater. Sci. 18, 1557-1563. Kreidl, N.J. (1983), in: Glass, Science and Technology, Vol.1: Glass-Forming Systems: Uhlmann, D.R., Kreidl, N.J. (Eds.). London: Academic Press, pp. 105-229. Krogh-Moe, J. (1969), J. Non-Cryst. Solids 1, 269284.

5.16 References

Lacy, E.D. (1963), Phys. Chem. Glasses 4, 234-238. Levin, E. M., Block, S. (1957), J. Am. Ceram. Soc. 40, 95-106. Levin, E. M., McMurdie, H. E, Hall, E P . (1956), Phase Diagrams for Ceramists. Columbus, OH: Am. Ceram. Soc, p. 286. Levin, E. M., McMurdie, H.R (1959), Phase Diagrams for Ceramists. Columbus, OH: Am. Ceram. Soc, p. 153. Levin, E.M., Robbins, C.R,, McMurdie, H.E (1964), Phase Diagrams for Ceramists. Columbus, OH: Am. Ceram. Soc, p. 601. Levin, E.M., Robbins, C.R., McMurdie, H.E (1969), Phase Diagrams for Ceramists. Columbus, OH: Am. Ceram. Soc, p. 625. Levin, E.M., McMurdie, H. E (1975), Phase Diagrams for Ceramists. Columbus, OH: Am. Ceram. Soc, p. 513. Lim, H.P., Karki, A., Feller, S., Kasper, J.E., Sumcad, G. (1987), /. Non-Cryst. Solids 91, 324-332. Loehmann, R. E. (1985), in: Treatise on Materials Science and Technology, Vol. 26: Glass IV: Tomozawa, M., Doremus, R. H. (Eds.). Orlando, San Diego: Academic Press, p. 119-149. Macedo, P.B., Simmons, J.H. (1974), J. Res. Nat. Bur. Stands. 78 A, 53-59. Mackenzie, J. D. (I960), in: Modern Aspects of Vitreous State, Vol. 1: Mackenzie, J.D. (Ed.). London: Butterworths, pp. 188-218. MacDowell, I E , Beall, G.H. (1969), /. Am. Ceram. Soc. 52, 17-25. McKeown, D.A. (1987), Phys. Chem. Glasses 28, 156-163. Mader, K. H., Loretz, T. J. (1978), in: Borate Glasses: Pye, L.D., Frechette, V.D., Kreidl, N . I (Eds.). New York: Plenum Press, pp. 549-566. Mahoney, R., Srinivasan, G. R., Macedo, P. B., Napolitano, A., Simmons, J.H. (1974), Phys. Chem. Glasses 15, 24-31. Marchand, R. (1983), J. Non-Cryst. Solids 56, 173178. Marinov, M., Kozhukharov, V, Vogel, W, Burger, H. (1983), Wiss. Zeit. Fried. Schill Univ., Math. Nat. Reihe (2nd International Otto Schott Colloquium) 32, 253-261. Marinov, M., Dimitriev, J. (1964), Dokl. Bulg. Akad. Nauk. 17 (No. 8), 717-720. Martin, S.W., Angell, C.A. (1984), /. Non-Cryst. Solids 66, 429-442. Masson, C.A. (1977), /. Non-Cryst. Solids 25, 3-41. Mazurin, O.V., Streltsina, M.V., Shvaiko-Shvaikovskaya, T.P. (1983), Handbook of Glass Data, Part A: Silica Glass and Binary Silicate Glasses. New York: Elsevier, p. 443. Mazurin, O.V., Streltsina, M.V., Shvaiko-Shvaikovskaya, T.P. (1985), Handbook of Glass Data, Part B: Single Component and Binary Non-Silicate Oxide Glasses. New York: Elsevier, p. 805. Mazurin, O.V., Streltsina, M.V., Shvaiko-Shvaikovskaya, T.P. (1987), Handbook of Glass Data,

327

PartC: Ternary Silicate Glasses. New York: Elsevier, p. 586. Mazurin, O.V., Streltsina, M.V., Totesh, A. S. (1969), Phys. Chem. Glasses 10, 63-68. Meadowcroft, T. R., Richardson, E D. (1965), Trans. Farad. Soc. 61, 54-70. Meinecke, G. (1959), Glas-Email-Keramo-Technik 10, 209-212. Minami, T. (1985), J. Non-Cryst. Solids 73, 273-284. Morey, G. W. (1934), /. Am. Ceram. Soc. 17, 315-328. Moynihan, C.T. (1966), J. Phys. Chem. 70, 33993403. Moynihan, C.T, Smalley, C.R., Angell, C. A., Sare, E.I (1969), J. Phys. Chem. 73, 2287-2293. Moynihan, C. T, Lesikar, A, V (1981), J. Am. Ceram. Soc. 64, 40-46. Mozzi, R.L., Warren, B.E. (1969), /. Appl. Crystallogr. 2, 164-172. Mozzi, R.L., Warren, B.E. (1970), /. Appl. Crystallogr. 3, 251-257. Murthy, K. M., Ip, I (1964), J. Am. Ceram. Soc. 47, 328-331. Murthy, K.M., Scroggie, B. (1965), Phys. Chem. Glasses 6, 162-167. Narasimhan, P., Rao, K . I (1978), J. Non-Cryst. Solids 27, 225-246. Nassau, K., Shiever, J.W. (1975), Am. Ceram. Bull. 54, 1001-1004. Nassau, K., Chadwick, D. L. (1982), Mater. Res. Bull. 17, 715-719. Nassau, K., Chadwick, D. L. (1983), /. Am. Ceram. Soc. 66, 332-337. Osaka, A., Ariyoshi, K., Takahashi, K. (1986), /. Non-Cryst. Solids 83, 335-343. Owen, A.E. (1970), Contemp. Phys. 11, 227-286. Owen, A. E. (1977), J. Non-Cryst. Solids 25, 370-423. Paul, A. (1982), Chemistry of Glasses. New York: Chapman and Hall, p. 293. Phillips, S.V., Crozier, D.S., McMillan, P.W., Taylor, I McC (1974), Desalination 14, 209-216. Poch, W. (1964), Glastech. Ber. 37, 533-535. Proctor, B.A. (1985), in: Glass... Current Issues: Wright, A. E, Dupuy, I (Eds.). Dordrecht: Martinus Nijhoff, pp. 524-550. Rabinovich, E. M. (1976), J. Mater. Sci. 11, 925-948. Ramaswamy, R.V, Srivastava, R. (1988), /. Lightwave Technol. 6, 984-1000. Ravaine, D. (1985), in: Glass... Current Issues. Wright, A. E, Dupuy, I (Eds.). Dordrecht: Martinus Nijhoff, pp. 435-455. Rawson, H. (1956), Int. Cong. Glass, IVth, Paris. 6269. Rawson, H. (1967), Inorganic Glass-Forming Systems. London: Academic Press, p. 317. Rawson, H. (1980), Properties and Applications of Glass. New York: Elsevier, p. 318. Ray, N. H. (1974), /. Non-Cryst. Solids 15, 423-434. Ray, N.H., Lewis, C.I (1972), /. Mater. Sci. 7, 4 7 51.

328

5 Oxide Glasses

Ray, N. H., Lewis, C. I, Laycock, I N . C , Robinson, W.D. (1973 a), Glass Technol. 14, 50-54. Ray, N.H., Laycock, I N . C , Robinson, W.D. (1973 b), Glass Technol. 14, 55-59. Ray, N.H., Plaisted, R . I , Robinson, W.D. (1976), Glass Technol. 17, 66-71. Ray, N. H. (1978), Inorganic Polymers. London: Academic Press; p. 174. Raynor, G.V. (1970), in: Physical Metallurgy, 2nd ed.: Cahn, R.W (Ed.). Amsterdam: North Holland, pp. 309-381. Riebling, E. F. (1963 a), J. Chem. Phys. 39,1889-1895. Riebling, E. F. (1963 b), J. Chem. Phys. 39, 3022-3030. Riebling, E.F. (1972), /. Mater. Sci. 7, 40-46. Riebling, E.F., Kotian, V. (1973), J. Mater. Sci. 8, 1145-1153. Riebling, E. F. (1973), /. Am. Ceram. Soc. 56, 25-30. Risbud, S.H., Pask, J. A. (1977), J. Am. Ceram. Soc. 60, 418-429. Rivoalen, L., Revcolevischi, A., Livage, I, Collongues, R. (1976), /. Non-Cryst. Solids 21, 171 — 179. Roscoe, H.E. (1868), Phil. Trans. R. Soc. 158, 1-27. Rothwell, G. (1956), J. Am. Ceram. Soc. 39, 407-414. Sakka, S., Kamiya, K., Yoshikawa, H. (1978), /. NonCryst. Solids 27, 289-293. Sakka, S., Kamiya, K. (1982), J. Non-Cryst. Solids49, 103-116. Scagliotti, M., Villa, M., Chiodelli, G. (1987), J. NonCryst. Solids 93, 350-360. Schaeffer, H.A., Frey, T., Loh, I., Baucke, F.G.K. (1982), J. Non-Cryst. Solids 49, 179-188. Schairer, I F . (1951), in: Phase Transformations in Solids: Smolochowski, R., Mayer, I E . , Weyl, W A. (Eds.). New York: John Wiley, pp. 278-295. Schairer, I E , Bowen (1956), Am. J. Sci. 254, 158. Scherer, G. W, Uhlmann, D. R. (1976), J. Non-Cryst. Solids 21, 199-213. Scherer, G. W, Uhlmann, D. R. (1977), J. Non-Cryst. Solids 23, 59-80. Scherer, G. W, Schultz, P.C. (1983), in: Glass: Science and Technology, Vol. I: Glass-Forming Systems: Uhlmann, D.R., Kreidl, N.J. (Eds.). London: Academic Press, pp. 49-106. Schnabel, H., Langer, P. (1989), Glastech. Ber. 62, 56-62. Scholze, H. (1988), Glas - Natur, Struktur und Eigenschaften, 3rd ed. Heidelberg: Springer Verlag, p. 407. Schreiber, H. D. (1986), /. Non-Cryst. Solids 84, 129141. Schultz, P . C , Smyth, H. T. (1972), in: Amorphous Materials: Douglas, R. W, Ellis, B. E. (Eds.). New York: Wiley-Interscience, pp. 435-461. Shartsis, L., Capps, W, Spinner, S. (1953), J. Am. Ceram. Soc. 36, 319-326. Shartsis, L., Shermer, H.F., Bestul, A.G. (1958), /. Am. Ceram. Soc. 41, 507-516. Shaw, R.R., Uhlmann, D. R. (1968), / Am. Ceram. Soc. 37, 377-382.

Shaw, R.R., Uhlmann, D.R. (1969), /. Non-Cryst. Solids 1, 474-498. Sheperd, E.S., Rankin, G.A., Wright, F.E. (1909), Am. J. Sci. 28, 293-333. Shepley, L. C , Bestul, A. B. (1963), /. Chem. Phys. 39, 680-687. Smart, R.M., Glasser, F.P. (1978), Phys. Chem. Glasses 19, 95-102. Smets, B.M.J., Lommen, T.P.A. (1979), /. NonCryst. Solids 34, 81. Smets, B.M.J., Lommen, T.P.A. (1981a), J. NonCryst. Solids 46, 21-32. Smets, B.M.J., Lommen, T.P.A. (1981b), Phys. Chem. Glasses 2, 158-162. Smets, B.M.J., Lommen, T.P.A. (1982), /. NonCryst. Solids 48, 423. Soules, T.F. (1989), Int. Congr. Glass XVth, Leningrad. Leningrad: 'NAUK', pp. 84-102. Spierings, G. A. C. M., Jochem, C. M. G., Meeuwsen, T.P.M. (1981), Glass Technol. 22, 247-250. Stanworth, J. E. (1946), J. Soc. Glass Technol. 30, 5464 T. Stanworth, I E . (1948a), /. Soc. Glass Technol. 32, 154-172 T. Stanworth, I E . (1948b), /. Soc. Glass Technol. 32, 366-372 T. Stanworth, I E . (1952), J. Soc. Glass Technol. 36, 217-241. Stanworth, I E . (1954), /. Soc. Glass Technol. 38, 425-435. Stanworth, J. E. (1979), Phys. Chem. Glasses 20, 116— 118. Streltsina, M.V. (1967), Steklo 1, 82-85. Strnad, Z. (1986), Glass-Ceramic Materials. New York: Elsevier, p. 268. Sun, K.H. (1946), Glass Ind. 27, 552-554, 590, 581. Sun, K.H. (1947), /. Am. Ceram. Soc. 30, 277-281. Sun, K.H. (1949), Glass Ind. 30, 199-200, 232. Szorenyi, T, Wojnarovits, I., Hevesi, I. (1980), /. NonCryst. Solids 42, 393. Szorenyi, T., Bali, K., Hevesi, I. (1982), Phys. Chem. Glasses 23, 42-44. Tait, J.C., Mandolesi, D.L., Rummens, H.E.C. (1984), Phys. Chem. Glasses 25, 100-104. Takahashi, K. (1962), in: Advances in Glass Technology, Vol. I. New York: Plenum Press, pp. 366-376. Takamori, T, Roy, R. (1973), /. Am. Ceram. Soc. 53, 639-644. Taylor, M., Brown, G. E. (1979), Geochim. Cosmochim. Ada 43, 61-75. Thilo, E., Wiecker, C , Wieker, W. (1964), Silikat Technik 15, 109-111. Tomozawa, M. (1972), Phys. Chem. Glasses 13, 161166. Tomozawa, M. (1973), Phys. Chem. Glasses 14, 112113. Tomozawa, M. (1989), Int. Congr. Glass, XVth, Leningrad. Leningrad: 'NAUK', pp. 187-208. Topping, J. A., Harrower, I. T, Murthy, M.K. (1974 a), J. Am. Ceram. Soc. 57, 209-212.

5.16 References

Topping, J. A., Fuchs, P., Murthy, M.K. (1974 b), /. Am. Ceram. Soc. 57, 205-208. Toratani, H., Meissner, H. E., Izumitani, T., Stokowski, S.E. (1987), J. Non-Cryst. Solids 95/96, 701-708. Tran, X, Brungs, M. P. (1980), Phys. Chem. Glasses 21, 178-183. Trap, H.L., Stevels, J.M. (1959), Glastech. Ber. 32 K (No. 4), 51-52. Trap, H. L., Stevels, X M. (1960 a), Phys. Chem. Glasses 1, 107-118. Trap, H.L., Stevels, J.M. (1960b), Phys. Chem. Glasses 1, 181-188. Trojer, R, Geyer, D. (1972), Glastechn. Ber. 45, 545581. Ubbelohde, A. R. (1965), Melting and Crystal Structure. Oxford: Clarendon Press, p. 325. Uhlmann, D. R., Kolbeck, A. G. (1976), Phys. Chem. Glasses 17, 146-158. Uhlmann, D. R. (1977), J. Non-Cryst. Solids 25, 4 2 85. Uhlmann, D. R. (1982), /. Non-Cryst. Solids 49, 439560. Uhlmann, D. R. (1983), /. Am. Ceram. Soc. 66, 9 5 100. Uhlmann, D. R., Yinnon, H. (1983), in: Glass Science and Technology, Vol. I: Glass-Forming Systems: Uhlmann, D.R., Kreidl, N.J. (Eds.). London: Academic Press, pp. 1-48. Uhlmann, D. R. (1985), in: Glass... Current Issues: Wright, A.F., Dupuy, J. (Eds.). Dordrecht: Martinus Nijhoff, pp. 1-20. Uhlmann, D.R., Hays, J.F., Turnbull, D. (1967), Phys. Chem. Glasses 8, 1-10. Uhlmann, D. R., Shaw, R.R. (1969), J. Non-Cryst. Solids 1, 347-360. Uhlmann, D.R., Yinnon, H. (1983), in: Glass Science and Technology, Vol. 1: Glass-Forming Systems. Uhlmann, D. R., Kreidl, N. J. (Eds.). London: Academic Press, pp. 1-45. Vail, J. G. (1952), Soluble Silicates, Vol. 1 and Vol. 2, ACS Monograph Series. New York: Reinhold. Van Uitert, L., Bonner, W, Grodkiewicz, W. (1971), Mat. Res. Bull. 6, 283-291, 513-517. Van Wazer, J. R. (1958), Phosphorus and Its Compounds, Vol. I. New York: Interscience, p. 954. Varshneya, A.K. (1987), /. Chem. Phys. 87, 29862989. Vergano, P. I, Uhlmann, D. R. (1970 a), Phys. Chem. Glasses 11, 30-38. Vergano, P. J., Uhlmann, D. R. (1970 b), Phys. Chem. Glasses 11, 39-45. Verweij, H., Buster, J.H.J. (1979), J. Non-Cryst. Solids 34, 81-99. Villa, M., Scagliotti, M., Chiodelli, G. (1987), J. NonCryst. Solids 94, 101-121. Vogel, W, Burger, H., Miiller, B., Zerge, G., Miiller, W., Forkel, K. (1974a), Silikattechn. 25, 205. Vogel, W, Burger, H., Folger, R, Ochrling, R., Winterstein, G., Ratzenberger, H.-G. (1974 b), Silikattechn. 25, 206-207.

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Vogel, W, Burger, H., Miiller, B., Zerge, G., Forkel, K., Winterstein, W, Boxberger, A. (1974c), Silikattechn. 25, 207-208. Vogel, W., Burger, H., Miiller, B., Winterstein, G., Jackel, W (1974d), Silikattechn. 25, 209. Vogel, W (1985), Chemistry of Glasses. Columbus, OH: Am. Ceram. Soc, p. 325. Volf, M.B. (1961), Technical Glasses. London: Pitman, p. 465. Vuillard, G. E. (1954), Bull. Soc. Chim. Fr., 802-807. Vuillard, G. E. (1955), C. R. Hebd. Seanc. Acad. Sci. Paris 241, 1126-1128. Vuillard, G. E. (1957), Ann. Chim. (Paris) 2, 233297. Wagner, C. (1975), Metall. Trans. 6B, 405-409. Wagstaff, F.E., Brown, S.E., Cutler, I. B. (1964), Phys. Chem. Glasses 5, 76-81. Warren, B. E. (1941), J. Am. Ceram. Soc. 24, 256261. Westman, A. E.R., Crowther, J. (1954), J. Am. Ceram. Soc. 37, 420-427. Westman, A.E.R., Gartaganis, P. A. (1957), /. Am. Ceram. Soc. 40, 293-299. Westman, A. E. R. (1960), in: Modern Aspects of the Vitreous State, Vol. I: Mackenzie, I D . (Ed.). London: Butterworths, 63-91. Wichard, G., Day, D. E. (1984), J. Non-Cryst. Solids 66, All-mi. Wilder, J. A. (1980), /. Non-Cryst. Solids 38-39, 879849. ? Wilder, X A., Day, D., Bunker, B. C. (1983), Glastech. Ber. 56K (No. 2), 845-849. Winter, A. (1955), Verres Refract. 9, 147-156. Wong, X (1970), Ph. D. Thesis, Purdue University. Worrall, A.X (1968), Infrared Phys. 8, 49-58. Wozniak, I., James, P.R (1984), Glass Technol. 25, 98-104. Wright, A . C , Yarker, C.A., Johnson, P.A.V, Sinclair, R.N. (1985), J. Non-Cryst. Solids 76, 333350. Wright, A.C. (1988), J. Non-Cryst. Solids 106, 1-16. Wright, A.C. (1984), Phil. Mag. B.50, L23-L28. Wright, A . C , Leadbetter, A.X (1976), Phys. Chem. Glasses 17, 122-145. Wright, A.C. (1989), Int. Congr. Glass, XVth, Leningrad, p. 30-64. Yasui, I., Hasegawa, H., Imaoka, M. (1983 a), Phys. Chem. Glasses 24, 65-71. Yasui, I., Hasegawa, H., Imaoka, M. (1983 b), Phys. Chem. Glasses 24, 72-78. Yin, C D . , Morikawa, H., Marumo, R, Gohshi, Y, Bai, Y.Z., Pukushima, S. (1984), J. Non-Cryst. Solids 69, 97-103. Yun, Y. H., Bray, P. X (1978), /. Non-Cryst. Solids 27, 363-380. Zachariasen, WH. (1932), J. Am. Ceram. Soc. 54, 3841-3851.

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General Reading Elliott, S. R. (1983), Physics of Amorphous Materials. London: Longman. Kreidl, N. J. (1983), "Inorganic Glass-Forming Systems", in: Glass Science and Technology Vol. 1: Glass-Forming Systems: Uhlmann, F. R., Kreidl, N. J. (Eds.). New York: Academic Press, pp. 105299. Pye, L. D., Frechette, V. D., Kreidl, N. J. (Eds.) (1970), Borate Glasses. New York: Plenum. Rawson, H. (1967), Inorganic Glass-Forming Systems, New York: Academic Press.

Scholze, H. (1988), Glas - Natur, Struktur undEigenschaften. 3rd ed. Heidelberg: Springer. Sosman, R. B. (1955), Phases of Silica. New Brunswick: Rutgers Univ. Press. Wong, X, Angell, C. A. (1976), Glass Structure by Spectroscopy. New York: Marcel Dekker. Zallen, R. (1983), The Physics of Amorphous Solids. New York: Wiley-Interscience. Zarzycki, J. (1982), Les verres et Vetat vitreux. Paris: Masson Zarzycki, J. (1991), Glasses and the Vitreous State. Cambridge: Cambridge Univ. Press.

6 Optical and Magnetic Properties of Ion Implanted Glasses Robert A. Weeks Department of Materials Science and Engineering, Vanderbilt University, Nashville, TN, U.S.A.

List of 6.1 6.2 6.2.1 6.2.2 6.3 6.3.1 6.3.1.1 6.3.1.2 6.3.1.3 6.3.1.4 6.3.2 6.3.2.1 6.3.3 6.3.3.1 6.3.3.2 6.4 6.5 6.5.1 6.5.2 6.5.2.1 6.5.2.2 6.6 6.7 6.8

Symbols and Abbreviations 332 Introduction 334 Distribution of Implanted Ions in Wide Band-Gap Materials 336 Atomic Collisions and Ionization Processes 336 Distributions of Implanted Ions 338 First-Order Optical Properties of Implanted Wide Band-Gap Glasses 340 Optical Absorption Spectra, and the Imaginary Part of the Refractive Index 341 Optical Absorption Spectra of Glasses Implanted with H, He, Ne, Ar, Kr, Xe . 341 Ions from the First Transition Series of Elements 343 Refractive Index, Real Part 349 Infrared Spectra 351 Alkali Silicate Glasses 351 Noble Gas Ions 351 Multi-Component Glasses 352 Noble Metals 352 Halide Glasses 353 Non-Linear Optical Properties 353 Magnetic States 355 Paramagnetic Defect States of Silica Substrates 355 Magnetic Properties of Implanted Ions 359 Magnetic States of Implanted Oxygen in Silica 359 Elements of the First Transition Series 360 Glasses Produced by Implantation of Crystalline Substrates 368 Conclusions and Prognosis 370 References 371

Materials Science and Technology Copyright © WILEY-VCH Verlag GmbH & Co KGaA. All rights reserved.

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6 Optical and Magnetic Properties of Ion Implanted Glasses

List of Symbols and Abbreviations A B2 c C E, E' Et F / g h H I k K Kahs kB Kscat m M n n n0 n2 Nt R S T V

absorptivity coefficient energy band speed of light contamination factor energy center electric field of the photons local field correction volume fraction of particles g-tensor Planck's constant magnetic field intensity absorptivity extinction coefficient extinction coefficient for absorption Boltzmann constant extinction coefficient for scattering integer smaller than 5 magnetization complex refractive index neutron real part of the refractive index non-linear index number density of f th constituent ion particle radius spin absolute temperature volume per particle

a e 80 X \x v X X(l) Xt CD

absorption coefficient electronic interaction processes dielectric constant of the vacuum photon wavelength nuclear interaction processes spectrometer frequency susceptibility i'th term of the expansion of the susceptibility polarizability of fth constituent ion photon frequency

CEMS EMR EPR

conversion electron Mossbauer spectroscopy electron magnetic resonance electron paramagnetic resonance

List of Symbols and Abbreviations

FMR FWHM NBOH POR TEM

ferromagnetic resonance full width at half maximum amplitude non-bridging oxygen peroxy radical transition electron microscopy

333

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6 Optical and Magnetic Properties of Ion Implanted Glasses

6.1 Introduction Optical properties of oxide glasses have been of interest since the first papers on glass were published. These first "papers" were clay tablets and the language was cuneiform and they were published about 4000 years ago (Oppenheim et al., 1970). The efforts of these glass scientists were to prepare glasses with particular colors. Following their instructions Robert H. Brill (1986) reports that the glasses produced in his laboratory do have the colors described in the original reports. The properties of oxide glasses continued to be a primary interest of glass makers and scientists until approximately 1900 A.D. Since then oxide glasses have become a subset of the universe of solid materials which can be formed into a non-crystalline form. Some of the materials which are now part of this universe are metals, semi-conductors, other chalcogenides, halides, and organic compounds. With the development of communication technologies in which oxide glasses form a critical part research into the interaction between photons with energies in the range of ~0.1 to ~ 10 eV and wide band-gap glasses has become important to the development of these technologies. The properties of wide band-gap glasses which are of primary importance for optical technologies are electric and magnetic susceptibilities. In many materials magnetic susceptibilities are small relative to electric susceptibilities. Resolution of these properties by measurement techniques are possible. Most wide band-gap glasses have electric susceptibilities in which first order terms are many orders of magnitude greater than higher order terms. In the past photon sources did not have sufficient intensity for the measurement of higher order terms. With the development of lasers

and the increase in intensities of these sources higher order terms in electric susceptibilities could be measured. Development of glasses with greatly increased values of second and third order terms became of interest. The development of glasses with higher values of the first order term or their magnetic susceptibilities and small values of the first order term in their electric susceptibilities is also of importance to the applications of glasses in optical technologies. Some techniques by which these susceptibilities are measured are optical (Raman, infrared, visible, and vacuum UV) and magnetic (electron paramagnetic resonance, and nuclear magnetic resonance) spectroscopies. These techniques may be used to also measure the time-dependence of the electronic excitations induced by irradiation with the probing photons. Pulsed lasers with pulse duration times of the order of femto-seconds (fs) provide the means for investigating processes which may occur in times of the order of a few atomic vibrations. The processes, by which energy deposited into a glass by incident photons is redistributed from the locale in which the deposition occurs, affects the deposition process. For example the deposited energy may be redistributed by emission of another photon, by increasing the vibration energy of the atoms in the material, or by both processes. Other processes may be involved such as disruption of local atomic structure. The electro-magnetic susceptibilities are a function of the electronic states of a glass. These states are determined by the atoms and their structure comprising the glass. First order terms of the susceptibilities contain information about these states. A major fraction of the literature on the electronic states of wide band-gap glasses is derived from measurements of these terms.

6.1 Introduction

One of the most important reviews of these states in many glasses is found in the book Glass: Structure by Spectroscopy (Wong and Angell, 1976). Since that time there have been a number of reviews of some of the topics included in the Wong and Angell book. An excellent review of electron paramagnetic resonance spectroscopy of oxide glasses has been published recently (Griscom, 1990). In the past several years optical properties of glasses have been modified by diffusion of ions into surface regions (Vogel et al., 1989) and by exchanging ions through diffusion (Brow et al., 1990). Another technique for modification is ion implantation. There are many reasons for implanting glasses. They range from the wish to study the fundamental physics and chemistry of the effects, via the development of practical devices such as optical waveguides and lasers, to increasing the fracture resistance and decreasing rates of corrosion. Implantation into glasses cannot disrupt crystalline order, hence ordering effects of the substrate on the implanted ions are minimal. The ion implantation induced transition from the crystalline state to the amorphous state does not occur in the case of glasses. Interactions between implanted ions and substrate ions are not those which occur for interactions in thermal or chemical equilibrium. Thus, the atomic and chemical structure of implanted materials produced under conditions far from equilibrium are of fundamental interest. The implantation process provides control over concentrations of ions, the depths to which ions are implanted inside the substrate, their distribution through implantation at various energies, mixtures of ions by subsequent implantations, geometries of implantation, chemical interactions between substrate ions and implanted ions

335

and between implanted ions through control of substrate temperatures, and an influence over most of these parameters by the imposition of external electric and magnetic fields and thermal gradients. Substrate composition is another variable which has profound influence on the consequences of implantation. Because the compositions of glasses are extremely varied, implantations have frequently been made into relatively simple glasses in an effort to reduce the varieties of implanted ion-substrate ion interactions. The enormous variety of glass forming materials and compositions and the possibility of implanting almost the entire periodic table provide a range of experiments that cannot be encompassed within any theoretical framework at the moment. Thus much of the research is dictated by potential applications and guided by empirical experiments. Ion implantation into wide band-gap crystalline materials will, in some materials, produce an amorphous layer in the implanted region. For example, an amorphous layer can be produced on single crystal A12O3 (sapphire) (McHargue et al., 1989). These amorphous layers are also of interest since they may have optical or magnetic properties that have applications in electronic and optical devices. In some materials the mechanical and chemical properties of surfaces can be changed to improve their usefulness. Sapphire is also a material for which such improvements have been demonstrated (White et al., 1989). We expect that there are a number of materials used in optical devices for which improved optical properties (e.g., decreases in reflectivity of lenses), increase in resistance to corrosive gases (e.g., windows in excimer lasers), increases in mechanical hardness (e.g., windows of chalcogenide glasses for use in infrared devices), may be

336

6 Optical and Magnetic Properties of Ion Implanted Glasses

achieved through ion implantation of surface regions of many materials. We expect that there are many materials which can be implanted to form optical waveguides in integrated circuits (Townsend, 1987 a), to form second harmonic generators (Osterberg, 1989), lasers (Townsend, 1987 b; Friborg and Smith, 1987), optical switches with switching times determined by the mobilities of electrons in noble and other metals (Hache et al., 1986) or graded-index optical devices. This is only a partial list of the potential applications for ion-implanted glasses and for amorphous layers formed on crystalline substrates. Materials that can be prepared in the glassy state with current techniques are metal alloys (see Vol. 15, Chapter 6), semiconductors, and an enormous range of inorganic and organic compounds. The variety of glasses on which implantation experiments have been performed is quite limited. Those glassy materials which have wide band-gaps, > 2 eV, which are inorganic and on which ion implantation experiments have been performed are a subset and consequently, much smaller in number. It is this subset which will be discussed in this review. The purview of this review will be: i. Optical properties of ion-implanted glasses, including first, second and third order terms in the susceptibility of the glass to electromagnetic radiation within the band-gap of the material and ranging from band-gap energies to the infrared vibrational bands. ii. Magnetic properties of implanted ions and of the substrate modified by implantation. iii. Optical and magnetic properties of amorphous materials produced by implanting insulating crystalline substrates. iv. Structures in the implanted materials.

v. Most of the glasses with which this review will be concerned will be wide bandgap materials. The review will not be comprehensive, that is, it will not note, neither in the citations nor in the text, all papers published on these topics. The selection of papers is idiosyncratic and, of course, biased to the author's interests. The selection has also been guided by our perception of good experiments and those which may have technical applications at some time in the future. A review of the literature clearly shows that this topic of research is being diligently pursued in only a few laboratories. These laboratories are best identified by reference to the names of a few individuals in these laboratories whose names appear, almost consistently, with many coauthors. The research of these individuals, M. Antonini, G. W. Arnold, P. Mazzoldi, A. Perez, P. D. Townsend and their collaborators, will be frequently cited in this review.

6.2 Distributions of Implanted Ions in Wide Band-Gap Materials 6.2.1 Atomic Collisions and Ionization Processes

Implanting ions (+1 or + 2 charges) into metals (see Vol.15, Chapter 6) or semiconductors does not have the problem of substrate charging which occurs in insulating materials, i.e., wide band-gap materials. In the case of metals and semiconductors attaching ground to a substrate provides a route through which a charge to compensate the charge introduced by implantation can move into the implanted material. In the case of wide band-gap materials which may have resistivities >10 1 8 Qcm at room temperature, the

6.2 Distributions of Implanted Ions in Wide Band-Gap Materials

source of compensating charge and the process of compensation is not evident. Before briefly reviewing the process of implantation we will discuss briefly some aspects of the charging phenomenon when implanting wide band-gap materials. Charging of insulating materials when irradiated with charged particles frequently results in electrostatic discharges within the material. Another consequence is the growth of an electric field which repels subsequent charges. Irradiation of some insulating materials with a y-ray beam also will produce catastrophic discharges if there are trapping sites for the Compton electrons, predominantly scattered in the direction of the y-ray photons, which are stable at the ambient temperature of the material (Gross, 1964; Hilczer and Malecki, 1986; Weeks et al., 1977). These effects may be ameliorated if there are ions in the material with sufficient mobility to redistribute in the electric field produced by the added charge. This redistribution reduces the field generated by the additional charge. The field due to the irradiating particles may be compensated by injection of charge of the opposite sign. In the case of irradiating with positively charged particles the injected charge would be electrons. If the material is in contact with an electron source, if the potential barrier to injection is small and if the mobility of the injected charge is not too small then the charge added by irradiation may be compensated. Both of these processes appear to be active, depending upon the material, when insulating materials are implanted with positively charged ions. It is possible to implant insulating glasses with a range of compositions without catastrophic electrostatic discharges. Some of the compositions which have been implanted are silica, alkali silicates (Arnold and Mazzoldi, 1987) and fluoro-zirconates

337

(ZBLAN) (cf. Chapter 8; Mazzoldi, 1990). All of these glasses have resistivities at room temperature, the usual temperature of implantation, >10 1 2 ficm. Samples used for these investigations have usually been either discs with a thickness of ~ 1 mm or parallelpipeds with one dimension of the order of 1 mm. During implantation, samples have been mounted on grounded metal supports. Thus the support has provided a source of electrons to compensate the positive implanted charge. Zuhr and Weeks (1988) observed that a discharge could be induced in silica disc samples of 0.2 cm thickness mounted on a grounded metal sample support when the current was >20jiAcm~ 2 . The discharge was between the planar faces of the sample. The current in this case was more than an order of magnitude greater than that used to implant SiO2 in the experiments of Whichard (1989). Beam currents used in experiments are often not reported in published papers. In view of the potential for charging effects during implantation of insulting materials, it is essential that experimentalists report the conditions, average (ions c m ~ 2 s - 1 ) and instantaneous currents, sample mounting geometries, and grounding circuits for their experiments. For ions with energies greater than a few keV, the initial loss of energy after impinging on a target is primarily through excitation of substrate electrons (Biersack, 1987). An implanted particle slows with this loss of energy, elastic collisions with substrate ions absorb the remainder of energy of the implanted particle (Biersack, 1987). These elastic collisions displace substrate ions creating disorder in the substrate, or in the case of glass substrates changing the already disordered structure to a different type of disorder (Wittels and Sherill, 1954). In the last part of the loss of energy by an implanted ion, in the case of wide band-

338

6 Optical and Magnetic Properties of Ion Implanted Glasses

gap materials, the implanted ion changes its charge state and reacts with substrate ions to form an implanted phase (Perez etal., 1987). 6.2.2 Distributions of Implanted Ions

The experimental and theoretical bases for calculating the distribution of ions implanted in a solid material through the use of a probe ion elastically scattered from the substrate and implanted ion is thoroughly described in many papers and books (see also Vol. 15, Chapter 6). Only one reference will be given here. It cites many of the most pertinent references and it also provides a table of ion ranges in many materials. It is the first chapter in "Ion Beam Modification of Insulators", written by Biersack (1987). Calculations based on the TRIM model (Biersack and Eckstein, 1984) give a distribution of the implanted ion that is approximately Gaussian about the mean range projected on the velocity vector of the ion beam. Implanting a planar surface then results in a distribution of ions which is shown in Figure 6-1 (Whichard, 1989). In the case of a material in the glass phase there is no channeling effect (Kelly, 1987). Implanting ions with large mass, greater than the mass of substrate ions, and with energies of the order of a few keV, sputters ions and atoms from the substrate (Kelly, 1987; Wang et al., 1987). Hence, there is a loss of substrate material and implanted ions. In some cases the loss of material by sputtering has a significant effect on the distribution as a function of distance from the surface into which ions are implanted. The range of an implanted ion is a function of ion energy and density of the substrate. For low-density substrates the range is larger than for high-density substrates for identical ion energies. Implanting an ion with an atomic mass greater

than that of substrate ions produces a back scattering spectrum shown in Figure 6-1 (Whichard, 1989). The distribution of ions as a function of distance from a surface on which the implanted ions were incident can be calculated. An example of such is the TRIM 17 calculation. The distribution shown in Figure 6-2 (Whichard, 1989) is typical of the profile observed for many ions with atomic masses >Si when implanted in a silicate glass at a single energy. The partition of energy of implanted + H , He + , O + , Ar + , Kr + , and Xe + between electronic and nuclear interactions is given in Table 6-1 (Arnold, 1973). This table shows that, for an energy of 250 keV, the fraction of energy dissipated in nuclear interactions increases with increasing atom mass. Although the relative fractions of energy will change with changing implant energies, these partitions will be representative for most of the ion energies used in experiments which will be reviewed here. There are two reports, to our knowledge, that describe implantations at a single energy for which distributions do not have Gaussian shapes. Arnold and Borders (1977) observed a bimodal distribution of Ag ions implanted in alkali silicate glasses. In the other case (Whichard, 1989), a bimodal distribution is observed for Cu-implanted samples of SiO2 glass in as-implanted samples when the implanted dose Table 6-1. Partition of 250 keV accelerating energy into electronic (s) and nuclear (u) interaction processes for various ions. Ions

ji(keV)

e (keV)

H+ He + O+ A+ Kr + Xe +

0.6 6.5

249.4 243.5 182.4 91.6 41.7 28.3

67.6 158.4 208.3 221.7

6.2 Distributions of Implanted Ions in Wide Band-Gap Materials

339

Mn implantation profile in SiO2 a Weeks C 0.014 A Weeks C 0.015 ° Weeks C 0.016

6***www«rt^Don^

0.4

0.6

0.8

1.0 1.2 Energy in MeV

1.4

1.6

Figure 6-1. Energy spectrum of He + ions back-scattered from SiO2 glass implanted with Mn + .

Fe implantation profiles in SiO2 + -0.95 E16 Fe-cm" 2 Weeks I 0.035 A -2.77 E16 Fe-cm" 2 Weeks I 0.036 x -5.43 E16 Fe-cm" 2 Weeks I 0,040

Figure 6-2. Depth profiles of Fe implanted in SiO2 glass samples. Energy of the ions was 160 keV, at a current of 4 uA cm" 2 . Ion backscattering data were used to calculate the implanted ion distributions. 0.00

0.05 0.10 0.15 Depth in pm

0.20

0.25

Cu implanted in SiO2

#68 #67 #66

-

E16/cm2 E16/cm2 E16/cm2

5.4 2.8 1.0

)

o

o °0

o

o

o OgA

A

A

*

°o <

>v

o<

0.00

0.10 Depth in |j

> ooo w. °°O0 >§

«*$ ftA4 222f

0.20

Figure 6-3. Depth profiles of Cu ions implanted in SiO2 glass samples. The energy of the ions was 160 keV at a current of 4 uA cm" 2 . The TRIM calculation was used to calculate the distribution.

340

6 Optical and Magnetic Properties of Ion Implanted Glasses

was 10 16 ions/cm 2 and the ion energy was 160 keV. The distribution for three doses is shown in Figure 6-3 (Magruder et al., 1989). The bimodal distribution was observed for substrate temperatures during implantation which ranged from 100 to 673 K (Magruder et al., 1989). Implantation of an ion at a single energy, with the exceptions noted above, produces a Gaussian distribution, the peak of the distribution being determined by the projected range of the ion in the material implanted. By implanting ions at two or more energies, distributions approaching a step function can be produced. By choosing energies with a sufficient difference, two well resolved Gaussian distributions can be produced. Accelerators which can produce ions with energies > 1 MeV can implant, in many materials, ions to depths of several microns. After one ion has been implanted, another ion or ions can be implanted with the same energy to produce a layer in which the ions may interact with each other and the substrate ions. Thus the number of possible combinations of substrate/ions/energies is quite large.

6.3 First-Order Optical Properties of Implanted Wide Band-Gap Glasses Optical properties of wide band-gap glasses have usually been described in terms of the first order approximation of the electric susceptibility of glass materials. With the development of coherent and intense light sources it is now necessary to consider higher order terms in the susceptibility of a material to interaction with photons (see Chapter 12). In wide band-gap materials it is usually assumed that interaction with photons whose energies fall within the band-gap can be described in

terms of a linear function of refractive index and absorptivity. It has been demonstrated that for very high fluxes of photons this linear relation is insufficient to describe the interaction (Taylor et al., 1988). The higher order terms are usually small when compared with the first order terms. Consequently, before laser sources were available, the higher order terms were of little consequence. The polarization due to photon-material interaction can be expressed in terms of the susceptibility of the material, a property of the elements comprising the material and their structure. The susceptibility can be written as an expansion (Bloembergen, 1965): + X(3)E1-E2-E3...)

(6-1)

in which e0 is the dielectric constant of vacuum, x(l) is the fth term in the expansion, and Et is the electric field of the photons. Each of the x are complex and experiments have been developed to measure the first 3 terms (Milonni and Elerly, 1988). The first order term can be written, using the Lorentz-Lorenz model: w X

=FZNiXi(co)

(6-2)

i

in which F is the local field correction, Nt is the number density of the fth constituent ion, and Xi *s the polarizability of this ion. (The hypothesis that the ion polarizabilities are independent of each other and their surroundings and that the total polarizability of a material is a linear sum of these ion polarizabilities has been questioned (Lines, 1990). Then (Joos, 1934): n2-l = 4nZNixi(co)

(6-3)

i

where n is the complex refractive index, and n=

(6-4)

6.3 First-Order Optical Properties of Implanted Wide Band-Gap Glasses

341

2U

I20 o 16

Figure 6-4. Optical density (arbitrary units) vs. wavelength in nm for Corning silica 7940 which has first been implanted with 5 • 1015 400 keV Xe+ ions cm" 2 and then with 6 • 1014 400 keV H + ions cm""2. Bottom curve is for a similar sample with 1 • 1014 400 keV H + ions cm" 2 only.

5x1015 400 keV XeVcm 2 Xenon implant plus 1x 10 u 400 keV HVcm 2 1x10 u 400 keV HVcm 2

150

200

350

where n0 is the refractive index and k is the absorptivity. The absorption coefficient, A, of a material is (Frohlich, 1958):

A = 2kco/c

(6-5)

where co is the photon frequency and c is the speed of light. In Section 6.3.1 we will review the effects of ion implantation on n and k for some glasses. In the following section (Sec. 6.4) the effects on # (2) and %(3) will be reviewed.

the E' center (Weeks and Nelson, 1960). Also evident in the spectrum of the Heimplanted sample is a band emerging at 250 nm. With increasing mass of the implanted ion this band becomes well resolved. It has been labeled the B 2 band (Arnold, 1973) and attributed to the E" center (Arnold, 1973; Weeks and Nelson, 1960).

Xe\

i1

6.3.1.1 Optical Absorption Spectra of Glasses Implanted with H, He, Ne, Ar, Kr, Xe

The absorption of silica implanted with H, with Xe, and with H and Xe sequentially, as a function of photon wavelengths, in the range 350 to 190 nm, is shown in Figure 6-4 (Arnold, 1973). The absorption in silica samples each implanted with one of the following ions: H, He, A, Kr, and Xe, at various energies and integrated fluxes, is shown in Figure 6-5 (Arnold, 1973). The most intense band produced by implanting H or He is at 210 nm. This band is due to

JQ

O C

Absorpition

6.3.1 Optical Absorption Spectra and the Imaginary Part of the Refractive Index

trar>' units

\

\

A\\

\X \ \ He \ \ \ \ ^

B2

-A

\\

\

\

H—'""Y

i

200

250 A in nm

i

300

350

Figure 6-5. Optical density (arbitrary units) vs. wavelength in nm for Corning silica 7940 implanted with H, He, Ar, Kr, and Xe ions at various energies and fluences. Individual curves have been displaced vertically for clarity. Relative values of absorption can be obtained by normalizing all curves to zero optical density at 350 nm.

342

6 Optical and Magnetic Properties of Ion Implanted Glasses

The assignment of this band to the E" center is based on deductions based on the relative intensities of the band in the spectra of samples irradiated with energetic ions of differing elements. This model for this band is placed into question by the absorption spectrum of samples implanted with O + . The optical absorption spectrum of a sample, so implanted, is shown in Figure 6-6 (Arnold, 1973). In this spectrum the intensity of the 250 nm band is much greater relative to the intensities of the 210 nm bands shown in Figure 6-5. It has been suggested that the peroxy molecule ion has an absorption band at ~ 250 nm (Friebele et al., 1987; Hosono and Weeks, 1990 a). In a sample implanted with O + it would be expected that the oxygen molecule ion would be produced. The EPR spectra of Derryberry et al. (1990) clearly show that there is a relatively high concentration of such molecule ions and very small concentrations of E' centers compared with concentrations in silica samples implanted with other ions. We suggest that in the spectra of oxygen-implanted samples the absorption at ~ 245 nm is due to oxygen molecule ions. The paper by Derryberry et al. is discussed below in Section 6.5.1. Antonini et al. (1982) have also implanted silica with these ions and others. Figure 6-7 (Antonini et al., 1982) shows the spectra of one of their samples. The range of wavelength over which these measurements were made extends into the vacuum ultra-violet, to 120 nm. These data show that well-resolved bands are produced near the band edge at ~120 nm. It is evident from these data that the variety of bands and their production rate is dependent upon the element implanted. That there should be such a dependence on a particular noble gas ion may be indicative of chemical reactions between the noble

18 16

Corning 79£0 1 x 1016 250 keV OVcm 2

"12 •e 10

a

o. 6 o in

•9

4

200

250

300

350

A in nm

Figure 6-6. Optical density (arbitrary units) vs. wavelength in nm for Corning silica 7940 implanted with 1 -1016250keVOionscnr2.

gas ions and the substrate ions. Even though these data may be interpreted as showing noble gas ion-substrate interactions, such interactions are very small when compared with implanted cationsubstrate ion interactions. This disparity of effect is demonstrated in Figure 6-8 (Ar-

E-Band A

5 ooo Experimental points Computer fitted components in vacuum UV

A \i\ 1!

3 -

2 -

10.5 eV ft

/

B2

E-

Al

6 Energy in eV

7

v

J i

Figure 6-7. Absorption spectrum of v-SiO2 after R.T. irradiation with 46.5 MeV Ni + 6 ions (~ 1014 particles cm" 2 ). Solid line, bestfit spectrum; dotted lines, computer resolved structures in the vacuum u. v. (low energy details omitted).

343

6.3 First-Order Optical Properties of Implanted Wide Band-Gap Glasses 1017 B, Si and N/Ar implants in Si 0 2 0.500 0.400 .2 0.300 ! 0.200 0.100 0.000

200

220 240 260 Wavelength in nm

280

300

Figure 6-8. Optical absorbance vs. wavelength (nm) for samples implanted with 50 keV B, 95 keV Si and 50 keV N. The 50 keV N implant yield somewhat less absorbance than a 250 keV Ar implant, but on this scale the differences are not visible. All implants were at the 1 10 17 fluence level. The B 2 absorbance is at 245 nm.

nold etal, 1990). The absorption bands due to E', B 2 and a background absorption which increases with decreasing wavelength are more than an order of magnitude greater for implants of B and Si than for N or Ar. We suggest, as did Arnold (1978) in a comparison of the optical absorption spectra of Al (200 keV, 1016 ions cm" 2 ) and Ne (180 keV, 1.1-10" 16 ions cm" 2 ), that this difference is, in large part, due to chemical reactions between B, Al, Si and other cations with substrate Si and O. The noble metal cations and Cu are an exception which will be discussed below. 6.3.1.2 Ions from the First Transition Series of Elements

The group in the Departement de Physique des Materiaux, Universite Claude Bernard has been investigating the properties of ion-implanted glasses for several years. This group has implanted the iron ion in a variety of materials (Perez, 1984). High purity silica was their choice of a glass for implantations of iron. Their beam energies were 100 and 200 keV at a beam

current of ~ 1 JIA cm 2. Conversion electron Mossbauer, optical absorption and electron magnetic resonance spectroscopies, among other techniques, were used to determine some of the properties of the implanted glass (Perez et al., 1983 a, b, 1985, 1987; Griscom et al., 1988). On the basis of their Mossbauer and TEM (transmission electron microscopy) data, they identify several chemical states for Fe after implantation, and a major fraction of the implanted ions are found in separate phases. The relative fractions of Fe in differing charge states and sites are given in Table 6-2 in as-implanted samples as a function of dose and in Table 6-3 as a function of annealing temperature for one Table 6-2. An abstract of Table 1 in the paper of Perez et al. (1987). The numbers are relative areas of Mossbauer components in the conversion electron Mossbauer spectra of implanted silica samples. Doses (ions cm 2)

Components

Fe° Fe 3 O 4 single line Fe + 2 Fe + 2 Fe° (sextet)

4-10 1 6

6-10 1 6

14 10 16

13 29 35 23

20 40 21 19

2 12 8 13 65

Table 6-3. An abstract from Table 2 in the paper of Perez et al. (1987) implanted with a dose of 1.4 * 10 17 250 keV Fe ions cm ~ 2 and subsequently annealed in air at 600 and 800 °C. The values are percentages of each species of Fe ion. Components

Single line Fe 3 O 4 Doublet Fe + 2 Doublet Fe 2 O 3 Sextet Fe° Sextet Fe 2 O 3

Annealing temperature (°C) 600

800

10 10 37 33 10

13 21 66

344

6 Optical and Magnetic Properties of Ion Implanted Glasses

dose. The various types of Fe in the as implanted samples are Fe° in colloid particles, and Fe + 2 in two distinct environments one of which is Fe 3 O 4 particles. The fraction of ions in these various states was a function of the dose in the range 4 • 1016 to 14 • 1016 ions cm" 2 for 25°C substrate temperature during implantations. The precipitates were crystalline and ranged from 2 to 50 nm in size. a) Cr, Mn, and Fe The optical absorption of the implanted samples, shown in Figure 6-9 (Perez, 1987) as a function of dose, was reasonably explained by the Mie theory (Mie, 1908) for absorption and scattering by small particles (dimensions ^ the wavelength of the incident light) suspended in a material whose refractive index differs from that of the particles. The optical absorption was due primarily to absorption by the precipitated particles of iron and iron oxides. The absorption spectrum of samples implanted to a dose of 12 • 10 16 cm ~ 2 and annealed at 800 °C in air contained three peaks at 220, 400 and 550 nm (curve e in Figure 6-9, indicated by arrows), which were attributed to Fe + 3 charge transfer bands. Stark et al. (1987) have described the optical absorption spectra of high-purity silica implanted with Cr, Mn and Fe to doses ranging from 10 16 to 6 10 16 cm~ 2 at a substrate temperature of ~ 25 °C during implantation. Beam currents were ~ 4 JIA cm" 2 and beam energy was 160 keV. The spectra observed, shown in Figure 6-10 (Stark et al., 1987) for the three ions after implanting a dose of 1016 cm" 2 consisted of two bands with peaks at ~ 5 and 5.8 eV and the tail of a band with a peak at higher energy. Their measurements were limited to energies less than or equal to 6 eV. They attributed these bands to defects of the sil-

300

400 500 600 Wavelength in nm

700

Figure 6-9. Optical absorption of Fe-implanted SiO2 glass samples, a) 1016 ions cm" 2 , b) 3 • 1016 ions 20- 1016 ions cm" 2 , cm 2, c) 6 16 ions cm" 2 heated for 20 h at d) sample with 20 • 10 ^ 800 K in air.

ica substrate produced by the implanted ions. The defects were the B 2 band (Antonini et al., 1982) and the E' center (Weeks and Sonder, 1963). In this regime of doses, and for the same dose, the absorptivity was a function of the ion implanted, as shown in Figure 6-10 b. Iron was the most absorbing and Mn the least. This ion-dependent absorptivity is attributed to the differing absorptivities, i.e., differing complex refractive indices, of particles of Cr, Mn and Fe oxides. The absorption spectra in samples implanted with 0.5 • 1016, 2 • 1016, and 6 • 1016 160 keV Fe ions cm" 2 have been measured in the range from 5.5 to ~ 8 eV (Hosono et al., 1990). The spectra of the three samples have a single very intense peak at ~ 7.6 eV whose peak absorption increases with increasing dose. The peak is attributed to a transition from the ground state

6.3 First-Order Optical Properties of Implanted Wide Band-Gap Glasses

1 x 1016 ions/cm 2 3x 1016 ions/cm 2 6x 1016 ions/cm 2

15 10 -

Cr

5 -

(/) 0

4.0 5.0 Energy in eV

3.0

(a)

6.0

15

Cr* 3x1016 ions/cm2/side Mn+ 3 x 1016 ions/cmVside Fe+ 3 x 1016 ions/cmVside £ 10

o 5

2.5

(b)

3.0

3.5

4.0 Lb 5.0 Energy in eV

5.5

6.0

6.5

Figure 6-10. Optical absorption of SiO2 glass samples implanted with ions from the first transition series of elements, Cr, Mn, Fe ions each implanted to three doses, (b) comparison of optical absorption of samples implanted with Cr, Mn, Fe with the same dose of 3-10 1 6 ions c m ' 2 (160 keV, 4uAcm~ 2 , substrate temperature ~30°C).

345

of a neutrally charged Si-Si bond, labeled homo-bond (Imai et al., 1988). The model proposed for the homo-bond is indistinguishable from that of the E" center. For doses < 3 • 1016 ions c m ' 2 the amplitude of the absorption peak is the same for either Cr, Mn, or Fe. It is much larger for Ti. For larger doses the amplitude for Cr and Mn are almost the same and larger than for the Fe-implanted sample. The amplitude in the case of the Ti implanted sample is almost twice larger. Assuming an implantation layer thickness =140 nm and an absorption cross-section for the transition of 8 • 10~~17 cm" 2 , the calculated concentration of the homo-bond as a function of dose is approximately equal to the dose in the case of the Cr-, Mn-, and Fe-implanted samples. The concentration of homo-bonds in the sample with the largest dose of Ti ions is approximately 1.5 times larger than the dose. At higher doses, spectra for Cr, Mn, Fe implanted samples in the range 2 eV (700 nm) to 6 eV (190 nm) were similar in that the absorptivity increased approximately linearly with increasing photon energy from ~ 2 to 6 eV. This linear increase with increasing energy is similar to that reported by Perez et al. (1987) and attributed to absorption by particles with diameters much less than the wavelength of the light, i.e., Mie absorption. For particles with radii smaller than the incident photon wavelength the extinction coefficient, for both absorption and scattering, is given approximately by (Arnold and Borders, 1977): (6-6) where Kahs is the absorption by small particles and Kscat is the scattering by small particles. These two terms are given by: Kabs = - (6 TI/A) / Im ((n2 - n20)/(n2 + 2 n2) (6-7)

346

and Kscai

6 Optical and Magnetic Properties of Ion Implanted Glasses

(6-8) 3 2 2 2 = (24 7i VN/X*) ((n - n 0)/(n + 2 n2))

where n is the complex refractive index of the particles, n0 is the real part of the refractive index of the material in which the particles are imbedded, V is the volume per particle, / is the volume fraction of the particles, X is the wavelength of the incident photons, and N is the particle concentration. The spectrum will be approximately a linear function of photon energy for particles with R < X and with small conductivities. For metallic particles of Ag, Cu, and Au and for J^ < 20 nm, an absorption maximum will be observed at photon energies < 5 eV (Arnold and Borders, 1977). In the case of Cr, Mn, and Fe ions implanted at energies of the order of 200 keV, the distribution, as typically in Figure 6-2, has a width at half maximum amplitude of ~ 140 nm. Hence most (~ 80%) of the particles which form will have radii < 70 nm. For wavelengths > 200 nm both the absorption and scattering equations will be applicable. Absorption-plus-scattering spectra would be expexted to have a dependence on photon energy which falls somewhere between being proportional to photon energy and photon energy to the fourth power. Since the absorption spectra of Cr- and Mn-implanted samples are similar to those of the Fe-implanted samples and this Fe spectrum is similar to that reported by Perez et al. (1987), it is reasonable to attribute a major fraction of the absorption spectra of the Cr- and Mn-implanted samples to Mie absorption of precipitates containing Cr and Mn and with sizes that are small compared to the wavelength of the incident photons. It is interesting to note that the absorption spectra shown in Figure 6-5, although

containing well resolved components due to the E' center and the B 2 band, have a background component which is approximately linear with photon energy. The rather featureless spectra, without well resolved bands, are surprising since Perez et al. (1987) have identified several charge states for implanted Fe, given in Table 6-2, from conversion electron Mossbauer spectra. Although for a dose of 6 • 1016 ions cm" 2 the fraction of ions in the + 3 state is ~ 27% no bands attributable to charge transfer bands are resolved. Given the similar oxygen activities of Fe, Cr, and Mn (Table 6-4) we expect that the fraction of ions in the 0, + 2 and + 3 charge states of implanted Cr and Mn to be similar to those of Fe. After an anneal at 800 °C, bands are resolved in Fe-implanted samples which are attributed to charge-transfer bonds of Fe 3 + (see Figure 6-9). The absorption spectra of Cu implanted SiO2 glass differ from the spectra observed for ions of the other transition series of elements. Only at doses <10 1 6 cm~ 2 do the spectra of Cu implanted samples resemble the spectra of samples implanted with other ions. For these doses optical bands in the 4 to 6 eV range due to silica defect states are more intense than those due to implanted ions. Thus, for these doses the spectra of Cr-, Mn-, Fe- and Cuimplanted samples are similar. b) Copper The spectra of Cu-implanted silica samples for several doses is shown in Figure 6-11 (Magruder et al., 1989). These spectra show that several bands are resolved and that one of these, with a peak at 2.2 eV, increases with increasing dose. The refractive index, measured at 633 nm, also increases with the increasing intensity of this band, as shown in Figure 6-12 (Weeks

6.3 First-Order Optical Properties of Implanted Wide Band-Gap Glasses

et al., 1989). For doses > 1016 ions cm~ 2 and for several substrate temperatures the refractive index as a function of the optical absorption at 2.2 eV is well fitted by a linear function. Weeks et al. (1989) attribute 2000

1.00

3.00 5.00 Energy in eV

zoo

Figure 6-11. Optical absorption of SiO2 glass samples implanted with Cu ions, (a) 6-10 16 ionscm~ 2 , (b) 3 • 1016 ions cm" 2 , (c) 1016 ions cm" 2 , (d) 0,5 • 1016 ions cm' 2 , (e) 0.3 • 1016 ions cm" 2 (160 keV, 4 A cm" 2 , ~30°C).

1.5

1.6 Refractive index

Figure 6-12. The optical density measured at 2.2 eV (the peak of the first resolved band in the spectra shown in Figure 6.6) is plotted as a function of the refractive index, measured at 1.9 eV (633 nm) by an ellipsometric technique. The numbers and symbols have the following meanings: A, dose = 1016 ions cm" 2 ; n, dose = 3 • 1016 ions cm" 2 ; o, dose = 6 • 1016 ions cm" 2 : 1, substrate temperature ~ 100 K; 2, substrate temperature — 300 K; 3, substrate temperature ~ 700 K.

347

this linear relation to the case in which the imaginary part of the refractive index is much larger than the real part. Magruder et al. (1989,1991) have attributed the absorption band in the region of 4.2 and 2.2 eV to spherical particles of Cu° and oblate or prolate colloidal spheroids of Cu with an axial ratio of ~ 2, respectively. The 4.2 eV band is attributed to spheroidal colloids of Cu with diameters ranging from a few nm to ~ 10 nm. Calculations have shown (Arnold and Borders, 1977) that for Ag particles with radii > 10 nm the peak absorption shifts to lower energies. In the spectra of samples implanted with doses > 3 • 1016 Cu ions cm" 2 there is a shift to lower energies of the shoulder at ~ 4.2 eV observed in the spectra of samples implanted with smaller doses (1016 Cu ions cm ). Spectra calculated for Ag particles shows that for particle radii > 25 nm the absorption splits into two maxima, one at the wavelength of the absorption for particles with radii < 14 nm and one with a wavelength that shifts to longer wavelengths with increasing particle radii and whose width at half maximum amplitude also increases. With the bimodal distribution of Cu shown in Figure 6-3 for doses > 1 • 10 16 ions cm" 2 the fraction of Cu particles with radii > 200 nm must be very small. Most of the spheroidal Cu particles have radii < 50 nm, assessed on the basis of the shift of the 4.2 eV shoulder. Another property of colloidal particles which produces a splitting of the absorption is deviation of particle shape from spherical (Trotter et al., 1982). Thus, an absorption band at 2.2 eV, observed by Magruder et al. (1989) was attributed to oblate or prolate spheroids with a major-to-minor axis ratio of ~ 2 . Optical absorption of Cu + 1 in silicate glasses has been observed at ~ 5.2 eV (Parke and Webb, 1972). The absorption

348

6 Optical and Magnetic Properties of Ion Implanted Glasses

spectra of implanted silica samples have a shoulder at ~ 5.2 eV which may be due to Cu + 1. Weeks et al. (1989) report that no spectral component attributable to Cu + 2 was detected in the EPR spectra of implanted samples. Thus it appears that in the case of Cu implanted into silica a major fraction, perhaps as high as 99%, is in the Cu° and C u + 1 states. Weeks et al. (1989) did not detect any EPR spectral component attributable to Cu + 2 in Cu implanted borosilicate and aluminosilicate commercial glasses. They also note that neither is an optical absorption band detected at 2.2 eV nor at ~ 4 eV. They tentatively conclude that most of the Cu in these glasses is in the + 1 state. They comment that optical absorption measurements could not be made at energies > 4 eV because of very intense absorption at these energies in their samples. We noted above that the chemical reactivity between implant ions and substrate ions will, in part, determine the optical absorption spectra directly attributable to implanted ions and also, as we will discuss below, the paramagnetic states of defect states in the substrate structure. Magruder etal. (1989) have discussed these reactivities in terms of the relative oxygen activities of some implant cations and the substrate cation, Si. These relative activities are given in Table 6-4. From this table we note that Ti has a higher free energy of Table 6-4. Gibbs free energy, G*, of formation at 298 K (Kcal/mol) (per mol oxygen). Reduced oxide a-SiO2 TiO MnO Cr 2 O 3 FeO Cu 2 O

G*

Oxidized oxide

G*

-189.9 -233.8 -173.5 -168.8 -117.3 - 35.5

TiO 2 Fe 2 O 3 MnO 2 CrO 3 CuO

-212.4 -118.3 -111.3 - 80.6 - 61.7

formation with oxygen than does Si. Hence we expect that displaced oxygen ions will react with implanted Ti ions to form oxides and that these reactions will result in higher concentrations of E' centers, E" centers, and smaller concentrations of oxygen related paramagnetic centers such as peroxy molecule ions. The lowest free energy of formation is between Cu and O. In this case the reactions between Si and O will dominate. The result will be smaller numbers of E' and E" centers, higher numbers of oxygen related centers as compared with those for Ti implanted samples. We expect that the numbers of these centers in Cr, Mn, and Fe implanted samples will be intermediate between those for Ti and Cu. The optical absorption spectra of lithiaalumina-silica glasses implanted with Ag and Au will be described below in Section 6.3.3.1. Colloidal particles also form in these glasses during implantation and in some glasses after thermal treatments. c) Titanium There is little to report on the absorption of Ti-implanted silica. For doses < 5 - 1 0 1 5 Cu ions the optical spectra shown in Figure 6-13 is due primarily to the bands of B 2 and E' centers. With increase in dose the absorption at energies > 5.5 eV increases three-fold while there is little change at energies < 5 eV. Becker et al. (1990) note that the absorption of Ti implanted samples increase by a factor of two with an increase in dose from 1 • 10 16 to 6 • 1016 ions cm" 2 . Their measurements of the absorptivities of samples implanted with Ti have values of a ~ 5 • 103 cm" 1 for a dose of 1016 ions cm" 2 , assuming that the thickness of the absorbing layer is equal to the width at half maximum amplitude of the distribution as a function of depth, i.e., 2-130 nm = 260 nm, since both

6.3 First-Order Optical Properties of Implanted Wide Band-Gap Glasses

0 4.00

5.00 6.00 Energy in eV

7.00

Figure 6-13. Optical absorption as a function of photon energy of Ti implanted samples with (a) 1 • 1015 ions cm" 2 and (b) 3 • 1015 ions cm" 2 .

sides of their samples were implanted with the same dose. The non-linear properties of the absorption spectra of Cu and Ti implanted samples will be discussed below.

349

ellipsometric technique. The variation in the index near the implant surface of the as-received sample may be due to surface contaminants and polishing defects. The heat treatment appears to have removed these. In the treated sample there does appear to be a small maximum in the index at a depth of ~200nm and at a depth of ~ 600 nm the effects of implantation disappear. The increase in index over the entire range in the heat treated sample is An/n -0.005. The refractive index changes produced by various ions are shown in Figure 6-15 (Webb and Townsend, 1976). The data in this figure illustrates, in our opinion, the effects of chemical reactions between substrate ions and implanted ions. For example a dose of 1015 20keVH + or B + ions cm" 2 increases the index of the implant surface as much as 10 16 20 keV He + ions cm" 2 . The much greater range of the H + ions produces an increase in the index

63.1.3 Refractive Index, Real Part Neutron irradiation of silica increases the density by 2.5% (Wittels and Sherill, 1954). Implantation of noble gas ions, for which chemical reactions with substrate ions would be expected to be negligible, produce increases in refractive index An/n ~ 1.5% (Bayly and Townsend, 1973). The refractive index as a function of distance from the implant surface is shown in Figure 6-14 (Boyly and Townsend, 1973) after implanting 1016 Ar ions cm" 2 at 300 keV. Although no information about substrate temperature is given, the lack of information is probably indicative of nominal room temperature. Shown in the figure are profiles for two samples, one as received and one thermally treated for 90 min at 425 °C. Samples were sectioned by three techniques and the index measured by an

After"! 90minat425°C 0.010 An n

0.005

=n LJ

0.010 nK 0.005 0

—>

L..J

i i

r

J 1

•—I

j—'

b n_

1 r__.j

2

3

4

1

5

H

Range in nm

Figure 6-14. Refractive index profiles of samples implanted with 300 kV Ar, 1016 ions cm" 2 , with and without prior annealing for 90 min at 425 °C in air.

350

6 Optical and Magnetic Properties of Ion Implanted Glasses

800

Figure 6-15. Refractive index profiles for implantations of silica with (a) 20 keV B + to a dose of 1 • 1015 ions cm" 2 , (b) 20keV He + to 1 • 1016 ions cm" 2 , (c) 20 keV H + for 1 • 1015 ions cm" 2 , and (d) 2000 keV Bi + for 1 -10 ionscm~ 2 .

that extends to a depth > 400 nm. The maximum change in the index in the three cases is An/n ~ 0.017. A high energy (2000 keV) implant of Bi increased the index to a depth of ~ 800 nm, with the maximum at a depth of ~ 600 nm. The increase was slightly larger than in the case of the H ions. Reactions between Bi and substrate ions may be a factor in this increase, also. Some data on the effects of Cr, Mn, and Fe implanted in silica on refractive index have been reported (Whichard et al, 1988). These data show that the index, measured by an ellipsometric technique at ~ 633 nm, increases with in-

creasing dose when the dose is 1016 ions cm" 2 or greater and the increases are similar for the three ions. The values for the refractive indices were calculated for a "single layer" model. In this model it was assumed that the change in index was uniform throughout the implanted layer. For the highest dose, 6 • 1016 ions cm" 2 , the indices increased ~ 5%, with the largest increase in the Fe implanted sample (Whichard and Weeks, 1989). One of the interesting features of the changes in refractive index produced by heavy ions is that the variation in the index with depth from the implanted surface is not large until the end of the range of the implanted ions. A comparison of the index change, together with vacancy and implanted ion distributions calculated with the TRIM program, are shown in Figure 6-16 (Faik et al., 1986). Before annealing the index is almost constant to a depth at which the distribution of the implanted ion is a maximum. After annealing it varies in the same way as the calculated vacancy concentration and not as the implant ion distribution. The temperature of the anneal (450 °C) was sufficient to remove most of the electronic states which were paramagnetic

- U6 0.3 Depth in jjm

Figure 6-16. A comparison of the experimentally determined refractive index profiles (a) before and (b) after annealing at 450 °C with TRIM calculations of (c) vacancy and (d) impurity distributions. The N + ion energy was 0.18 MeV for a

6.3 First-Order Optical Properties of Implanted Wide Band-Gap Glasses

states of intrinsic defects (Perez et al., 1983 b). It was not sufficient to remove the chemical disorder introduced by the implantation. At the dose used for these measurements and calculations, 1016 180keV N + ions cm = 2, all of the substrate ions will have been displaced a least once. Weeks and Sonder (1963) and Stevens et al. (1958) showed that for a neutron dose sufficient to displace all silica ions at least once the concentration of intrinsic paramagnetic states begins to decrease. At neutron doses much higher (1021 n cm" 2 ) than this dose (3 • 1019 n cm" 2 ) the decrease is almost a factor of two. For implant doses >10 1 4 ions cm" 2 most substrate ions have been displaced at least once. Thus for all of the implant doses, discussed thus far, we expect that the vacancy concentration as measured by intrinsic paramagnetic states is less than the maximum concentration observed in the case of neutron irradiation. It is difficult to interpret the TRIM calculation of vacancies per ion when the vacancies per ion exceeds the concentration of ions. It may be that the agreement between the index after thermal treatment and the number of vacancies per ion is fortuitous. In Section 6.5.1 we review the data of Hosono and Weeks (1990 b) in which it is shown that E' centers, i.e., singly charged vacancies, have a higher concentration near the implant surface and peroxy radical centers, i.e., interstitial oxygen, has a higher concentration at the peak of the implanted ion distribution. Thus the distribution of defects is a function of the type of defect and is not uniform. 6.3.1.4 Infrared Spectra One of the problems in measuring the effects of ion implantation on the vibrational bands of silica is the measurement of a very thin layer on a thick substrate, both

351

of which are principally SiO 2 . The usual technique is to measure the reflectivity of implanted samples. This technique, for wavelengths > 5 jim, samples a layer that is less than ten times thicker than the implanted layer (Magruder et al., 1990 a) if that layer is < 300 nm thick. Quantitative measurement of relative amplitudes of bands is difficult whereas relative measurement of peak positions of bands is more accurate by this method. In our review of the literature reports of bands due to implanted ion-substrate ion vibration bands have not been detected. The effects reported are due to changes in the bands observed in silica before implantation (Arnold and Borders, 1977; Arnold, 1978,1980,1981). These changes are attributed to changes in the SiO2 structure. 6.3.2 Alkali Silicate Glasses Glasses with alkali silicate compositions are an extensive group with many uses. For most applications, additional elements are added to design a glass with particular properties. In most of the research on effects of ion implantation on properties, three-component (alkali, silicon, oxygen) glass compositions have been chosen for investigation. The vast literature on properties of these glasses provides an excellent basis for interpreting effects produced by ion implantation. 6.3.2.1 Noble Gas Ions During implantation of Xe a depletion of Li and Na in Li 2 O:SiO 2 (Arnold and Peercy, 1980) and Na 2 O:nSiO 2 (Bach, 1975) glasses, respectively, in the implanted layers has been observed. In the case of the Li 2 O:SiO 2 glass samples, Arnold and Peercy (1980) observed that H, already present in their samples, diffused into the Li-depleted region. In the case of the

352

6 Optical and Magnetic Properties of Ion Implanted Glasses

Na 2 O: n SiO2 glass samples, this effect was not reported (Arnold, 1978). In either case the optical absorption spectra produced by the implantation of Xe ions would be affected. In the paper of Bach (1975) the absorption spectra of the Xe implanted Li 2 O:SiO 2 glass samples are only given after the samples have been annealed at 500 °C. In these spectra an intense band with a peak at 470 nm is present. The spectra of samples of silica implanted with Li have a band with a peak at ~ 500 nm (Arnold and Peercy, 1980). The peak position shifts to smaller wavelengths after annealing. In both cases the band in annealed samples is attributed to colloidal Li. We note that bands in the region of 500 nm in silica and in alkali silicate glasses have been attributed to non-bridging oxygen hole centers (Friebele and Griscom, 1986). The band, produced by radiation with energetic photons, electrons, protons, or noble gas particles in either glass system, disappears after an anneal at temperatures above 300 °C. The absence of a decrease and the presence of an increase with annealing at temperatures above 500 °C is strong evidence that the ~ 500 nm band in both systems implanted with Xe or Li is not due to non-bridging oxygen hole centers. The stability and increase in intensities is certainly consistent with the formation and growth of colloidal Li particles. The specular reflectances of samples of a soda-lime glass implanted with Ar ions has been reported (Geotti-Bianchini et al., 1984). The samples had a composition 73.4 wt.% SiO2,13.6 wt.% Na 2 O, 6.8 wt.% CaO, 3.8 wt.% MgO and 2.4wt.% of other oxides. Measurements were made over a range of wavelengths from 300 to ~ 2000 nm. The reflectance decreased with increasing doses of Ar (2 JIA cm~ 2 , 50 keV) with a minima in the range of 700 nm and

with no measurable change at ~ 380 nm for doses less than or equal to 5 • 1016 ions cm" 2 . At higher ion energies the wavelength dependence of the reflectivity was more complex. The maxima and minima shifted to longer wavelengths with increasing ion energy. 6.3.3 Multi-Component Glasses Four-component glasses such as alkalialkaline earth-silica compositions have many applications and, consequently, there is considerable research on the modification of the properties of these glasses by ion implantation. The alkali aluminosilicate compositions are used in many applications and glasses with these elements have been frequently chosen for ion implantation experiments. 6.3.3.1 Noble Metals In Section 6.2 we noted that Ag implanted in samples with those compositions have a distribution similar to that of Cu in silica. This ion also forms colloids as implanted and after implantation and subsequent thermal treatments. Figure 6-17 (Arnold and Border, 1977) shows the absorption spectra of samples implanted with 1016 Ag ions cm" 2 at an energy of 275 keV. Arnold (1975) and Arnold and Borders (1977) attribute this spectrum to colloidal Ag particles with radii of the order of 2 nm. The spectrum has only one well resolved peak at a wavelength of ~410nm. The spectrum for Cu in silica is much more complex (see Section 6.3.1.2, above). The peak, in the spectrum of samples given isochromal (30min) anneals, shifts to longer wavelengths until a 400 °C anneal. After an anneal at 500 °C the peak shifts to a shorter wavelength. These shifts are due to an increase in particle radii from 15 to

6.4 Non-Linear Optical Properties 1016 275 keV Ag+ ions/cm 2

6.3.3.2 Halide Glasses

(no annealing) this experiment MIE theory. R = fl = 1.75nm ) Kreibic and /9 = 2.75nml v - Fragstein data

340

380

420

460 500 A in nm

540

353

580

620

Figure 6-17. Measured optical extinction K (arbitrary units) as a function of wavelength A (nm) for 1 • 1016 275 keV Ag ions cm ~ 2 as implanted into a lithia-alumina-silica glass compared with Equation (6-1) evaluated for R ~ 20 A, contamination factor C ~ 1, and d = 2.2.

~ 40 nm and then a decrease to 10 nm after the 500 °C anneal. The formation of colloidal particles in as implanted samples is attributed to beam heating by Arnold and Borders (1977). In the Cu implanted silica colloids formed at substrate temperatures ~100K. We suggest that colloid formation may be due to other processes. In the case of Au implantation into the lithia-alumina-silica glass samples, colloids did not form until samples were annealed (Arnold and Borders, 1976). Implanting Ag into crystalline LiNbO 3 , A12O3, and a-quartz caused colloids to form upon implantation (Rahmani and Townsend, 1989). At implant doses > 5 • 1016 ions cm" 2 , the implanted layers were amorphous in the three crystals.

Halide glasses composed of Zr, Ba, Al, and other cations have been considered as potential fiber optic glasses for applications in the 2 to 10 jim wavelength range (cf. Chapters 8 and 15). They have the potential for attenuations that are one to two orders of magnitude lower than silica fibers. The effects of implanting samples of various compositions have not been extensively reported. Most of the research has been in the laboratories of P. Mazzoldi (1990). One of the effects of implanting Ar is an increase in the relative amounts of Zr and Ba in the implanted layer. The reflectance of the surface increased in the range 350 to 2500 nm. The absorptivity of the samples also increased in the range from 250 to 2000 nm. The wavelength dependence of the absorptivity was observed to be a function of the implanted ion species, e.g., N produced the largest increases compared with H and Ar. The data reported were for differing doses of these ions and hence a comparison for the same dose is not possible.

6.4 Non-Linear Optical Properties It was noted above that the polarization of a wide band-gap material can be expressed as a power series of electric fields interacting with the material. The third order term, expressed as the refractive index, is n = no + n2E3

(6-9)

in which n0 is the first order term of the refractive index, n2 is the non-linear index, and E is the electric field. In the case of photons, E is the field of the photons. Thus to measure the value of n7 the E-field of

6 Optical and Magnetic Properties of Ion Implanted Glasses

500 1000 Laser power in mW

Figure 6-18. Absorption of Ti implanted samples as a function of incident photon power, X = 532 nm. Doses (1015 ions cm" 2 ): o = 60, A = 60, + =10, x = 3, * =1.

550

600

650 700 750 Wavelength in nm

800

Figure 6-19. Laser induced fluorescence of Ti implanted fused silica. The structure in the region of 5500 nm is stray light from the laser.

1 uni

en

Cu h

i arbit

(JDJ

incident photons must be varied. One technique for this measurement is called the z-scan method (Sheik-Behae et al., 1989). Becker et al. (1990) have made such measurements on Ti and Cu implanted silica. They used a frequency-doubled Nd-YAG laser (532 nm, 100 ps FWHM pulse width, 76 MHz pulse repetition rate, and 1.8 W average power). Both samples absorbed strongly at this wavelength. Absorption at 532 nm in samples implanted with Ti to doses of 1015, 3 • 1015, 10 • 1015, 60 • 1015 and 60 • 10 15 ions cm~ 2 is shown in Figure 6-18 (Beeker et al., 1990) as a function of photon power in mW. Interesting features of this absorption are: the similar absorptivity of samples with 1 to 10 • 1015 ions cm" 2 and the two samples with a dose of 60 • 1015 ions cm" 2 , absorptivity in the low dose samples saturates and absorption decreases from 17% to 12% with increase of power from 100 to 1300 mW, absorptivity in the high dose samples was independent of power in the same range, and the increase in absorptivity with increase of dose from 10 to 60 • 10 16 ions cm" 2 is from 17% to 30%. A 17% decrease in transmission represents a very large change in absorption coefficient since the thickness of the absorbing layer is only 120 nm. The absorption coefficient is of the order of H^cm" 1 . Luminescence stimulated by the 532 nm photons is shown for one Ti-implanted sample in Figure 6-19 (Beeker et al., 1990). Luminescence in Cu-implanted sample was similar, with the peak occurring at a wavelength ~ 30 nm greater than that for the Ti samples. The z-scan data are shown in Figure 6-20 (Beeker et al., 1990) for Ti- and Cuimplanted samples. The z-scan spectrum for an unimplanted silica sample is also shown in both parts of the figure. The shape and amplitude of the two spectra are

(NJ

\ pure FS l_Lirm

*

•tLIULJiTl-lWW.-MiP'*

->>

Q

detector

354

c o >^

pure FS

U)


Distance from focus in arbitrary units

Figure 6-20. Results of z-scan for pure silica Ti- and Cu-implanted fused silica.

6.5 Magnetic States

similar. However, structure is resolved in the Cu spectrum on both sides of the focus. Becker et al. (1990) do not have an explanation for the structure. These data clearly show that the ion implanted samples have n2 that are very large (~ 10" 8 M2/W) compared with unimplanted silica. These data are tantalizing. The values of n2 are large. For such values there is the possibility of optical switching with switching times that are a function of the transit times of conduction electrons in colloidal particles, if the colloidal particles are the source of the non-linear index. These non-linear effects may be due to properties other than those of the implanted ions. Tsai et al. (1989) have shown a correlation between second harmonic generation and defects in an optical fiber. The defects are those usually observed in silica, i.e., E' centers. The differences between the z-scan data for Ti- and Cu-implanted samples does indicate that some part of the effect is related to implanted ions. Although not produced by ion implantation, non-linear optical properties of glasses have been noted by a number of investigations. These may be of interest to readers who wish to consider glass systems in which non-linear optical properties are observed (Friberg and Smith, 1987; Ross, 1989; Taylor et al., 1988; Vogel et al., 1989; cf. Chapter 12).

6.5 Magnetic States Magnetic states of implanted materials have two sources (see also Volume 3 of this series). One is unpaired electronic states of substrate ions. These states are usually due to defects of crystal structure or, in the case of wide band-gap glasses, chemical disorder. The lowest energy states of these de-

355

fects usually have energies between the valence and conduction bands. In the case of silica, the E' and peroxy radical centers, discussed above, are examples. - The second source is the implanted ion. Ions are usually implanted either in the + 1 or + 2 states. For some ions these states will have unpaired electrons and hence lead to magnetic states. An example is the Fe ion, which will be discussed below. Some fraction of ions implanted in the + 1 or + 2 states will have a final state that ranges from 0 to + 4 (the + 4 state has been detected in A12O3 implanted with Fe and will be discussed in Section 6.6). The intrinsic defect states of implanted samples will be reviewed first, followed by a review of magnetic states of implanted ions. 6.5.1 Paramagnetic Defect States of Silica Substrates Energetic ions implanted in a material displace ions of the substrate creating interstitial ions and vacancies. In a simple compound such as SiO2 or elemental material such as Si in the glass state interstitials and vacancies are usually labeled "chemical disorder" or "defects". Another consequence of the deposition of energy by the implanted ions is excitation of electrons. The excited electrons may be trapped in states that are between the valence and conduction bands. In some case these states are paramagnetic. Thus implanted glasses can have paramagnetic states associated with implanted ions and defects in the glass produced by displacement and ionization processes. The paramagnetic states of defects in the substrate will be discussed followed by a discussion of magnetic states of implanted ions. Magnetic states of implanted ions can be detected by various techniques, one of

356

6 Optical and Magnetic Properties of Ion Implanted Glasses

which, conversion electron Mossbauer spectroscopy, was discussed above (Perez et al., 1987); another is a vibrating magnetometer (Perez, 1984). Electron paramagnetic (or ferromagnetic) resonance spectroscopy is a technique particularly useful for detecting small (of the order of 1012 spins with S = 1/2 and a line width ~ 0.1 mT) numbers of paramagnetic states or ferrimagnetic particles. The reader is referred to standard texts for detailed descriptions of these techniques (Orton, 1970; McMillan, 1968). Models for paramagnetic defect states are usually deduced from a fit of observed spectra to a "spin Hamiltonian" (Orton, 1970). In the case of wide band-gap glasses, the spin states of most defects are either 1/2 or 1. The effects of the Coulomb field of nearest neighbor ions on the spin state of defects is a second order effect. Consequently, the magnitude of the external spin-aligning magnetic field for a resonance transition between spin states differs only slightly from that field required for transitions between the spin states of a free electron. In a solid these Coulombic field effects are incorporated into the Hamiltonian in the "g-tensor". The eigenvalues of this ^-tensor are observed in the spectrum of a defect in a glass as singularities of the "powder pattern" (McMillan, 1968). These singularities provide one means for identifying defects in a glass. Thus defects produced in glasses by ion implantation can be identified in most case by these singularities. It will be noted in the following discussion that one type of defect has several variants in ion-implanted silica. Many of the electronic states due to chemical disorder (defects) in SiO2 have been described (Weeks, 1956, 1967; Griscom, 1980; Griscom etal., 1988). The three defects for which detailed atomic structures have been developed are the singly charged oxygen

vacancy (E' center) (Weeks and Nelson, 1990; Griscom, 1980; Weeks, 1967; Arnold, 1978; Arnold etal., 1990; Antonini et al., 1982), neutral non-bridging oxygen (NBOH center) (Griscom, 1980), and singly charged oxygen molecule ion (POR) bonded to a Si (Friebele et al., 1979; Purcell and Weeks, 1969). These paramagnetic states are not detected in well annealed samples of the purest silica. Implanting ions in silica produces these defects since in most cases ion energies are sufficient to produce many displacements. In Section 6.3 we described the optical bands produced by implanting a variety of ions into silica. Although EPR spectra were not reported in the papers referenced in Section 6.3, the three paramagnetic defect states discussed above were produced. Whichard (1989) measured the concentration of E' centers as a function of type of implanted ion and dose. Figure 6-21 (Whichard, 1989) shows E' center concentration in the implanted layer as a function of dose and of ion type for doses >10 1 6 cm" 2 . The highest concentrations are found for a dose of 1016 cm~ 2 Cr or Fe ions. The concentrations decrease with in-

E1 type signal

a. 60 .£ 40 -

•£ 20 -

• Mn

A

O Cr

o Ti

I

o

O

A

D

A

8

• I Q.

Fe

I

l

1

!

i

1 2 3 4 5 6 Implantation dose in 1016 ions/cm 2

Figure 6-21. The concentrations of E' centers in the implanted layer as a function of dose. The thickness of the implanted layer was assumed to be 200 nm (see Figure 6-1).

6.5 Magnetic States

creasing dose. In the case of Ti and Mn the concentration is, within the errors of measurement, invariant with dose and less than for Cr and Fe. Whichard notes that for a dose of 1015 cm" 2 every substrate ion in the implanted layer is displaced at least once. He then notes that in the case of the production of defects by neutron irradiation, concentrations of E' centers in silica or in a-quartz decrease with increasing dose when the dose is sufficient to displace every ion at least once (Stevens, 1955; Stevens et al, 1958; Weeks, 1965). The decrease in the case of ion implantation is due to the same factors that cause a decrease in the case of neutron irradiation (Weeks, 1965). The differences between types of implanted ions is attributed to differing reactions between substrate defects and ion types. Magruder et al. (1990 b) have attributed the differing reactions between implanted ion types and substrate ions to differences in the reactivity of the implanted ions with oxygen (see Table 6-4). Hosono et al. (1990) have investigated paramagnetic defects in silica samples implanted with ions of the first transition series of elements. The EPR spectra of samples implanted with Ti, Fe and Cu, to a nominal dose of 6 • 1016 cm" 2 , have relatively intense components due to the POR and E' centers. In the spectrum of a sample implanted with Cr to a nominal dose of 6-10 1 6 cm~ 2 only E' centers were observed. Measurements at room temperature as a function of power show that there are two distinct E' components. Neither is the one observed in y-ray irradiated silica. One of these centers saturates at the highest power (~ 200 mW) while the other is not saturated. On the basis of the temperature dependence, shapes of the first derivative of the absorption, and gf-values, one of these components is attributed to

357

sites in which the Si, on which the paramagnetic state is localized, is bonded to two oxygen ions and one Si ion. They (Hosono et al., 1990) show that an optical absorption band with a peak at ~ 7.5 eV due to a transition of the E" center, i.e., the neutral oxygen vacancy, has an intensity that increases approximately linearly with dose in the Cr, Mn, and Fe implanted samples. Hosono and Weeks (1990 b) have measured the dose dependence and depth dependence of the E' centers and POR concentrations in Cr-implanted samples. Figure 6-22 (Hosono and Weeks, 1990 b) shows the spectra as a function of dose for three doses. The spectrum of the sample with the lowest dose (0.5 • 1016 cm" 2 ) has components due to POR's, E' centers, and to Cr + 3 . With increasing dose all the resolved components decrease. The POR and Cr + 3 components are not detected at a dose of 6 • 1016 cm" 2 . Two types of E' centers, shown on the right side of the figure, are detected. By etching the implanted surfaces with dilute HF solutions, material was removed to increasing depths. The depths of material removed were determined by measuring, by means of the backscattering technique, the distribution of Cr ions remaining after each etching treatment. The concentrations of POR and E' centers were measured as a function of distance from the implanted surface of the sample. Figure 6-23 (Hosono and Weeks, 1990 a) shows the changes in intensities of these two defects with distance from the implanted surfaces. The E' center concentrations are highest at the surface and decrease with distance from the surface. The POR concentration increases with distance from the surface and is a maximum at the depth at which the implanted ion concentration is a maximum. On the basis

358

6 Optical and Magnetic Properties of Ion Implanted Glasses

2.0072

2.069

336

346

Magnetic field in mT

2U2

Figure 6-22. The EPR spectra of SiO2 samples implant-ed with Cr. On the left of the figure the spectra at three doses, (a) 0.5 • 1016 ions cm" 2 , (b) 3 • 1016 ions cm" 2 , (c) 6 • 1016 ions cm~2, measured at a temperature of 110 K and attenuation of the microwave power of 0 db. On the right the spectra in the region of the E' center measured at 300 K and the two power levels indicated on the figure. The thin arrows on the left side indicate the g-values of the peroxy radical center and the fat arrow indicates the X component. The X component is the one shown in the lower part of the right side of the figure.

(b)

E' type

E"' type |

1

0.1 0.2 Depth in pm

0.3

i

0.1 0.2 Depth in pm

0.3

POR

0.1 0.2 Depth in pm

0.3

Figure 6-23. Concentrations of E' and peroxy radical (POR) centers as a function of distance from the implanted surface. AN, number of centers removed by an etch; Ad, the thickness of material removed in an etch, (a) Sample implanted with 0.5 • 1016 ions cm" 2 , (b) sample implanted with 6 • 1016 ions cm" 2 . The measurements for the POR spectra were made at 0 dB attenuation and 110 K and the E' center measurements were made at 40 dB and 300 K.

6.5 Magnetic States

of their data they concluded that oxygen ions were predominantly displaced in the direction of the implanted ion velocity vectors. This preferential displacement of oxygen ions provides a reservoir of oxygen at the peak of the implanted ion concentration with which the implanted ions can react. 6.5.2 Magnetic Properties of Implanted Ions In many implanting experiments the ion is implanted in the + 1 charge state. In this state some ions are paramagnetic and if they retained this charge state after coming to rest their magnetic properties may be detected. As noted above in Section 6.1, the final charge states are a consequence of reactions between the implanted and substrate ions. The ion may have several possible charge states, ranging from 0 to ± m, where m is some integer, usually < 5 (Perez et al, 1987). In the case of noble gas and metal ions the final state may well be 0. These charge states and reaction with substrate ions determine the magnetic properties of the implanted ions. The properties are also a function of dose, dose rate and substrate temperature during implantation. 6.5.2.1 Magnetic States of Implanted Oxygen in Silica There are few reports (Arnold, 1973) on the states of oxygen implanted in glasses. The only paper, to our knowledge, on magnetic states of implanted oxygen is one by Derryberry et al. (1990). They report that the most intense paramagnetic state is the POR. Beginning with a dose of 0.8 • 10 16 cm" 2 the number of POR's decreases with the next increase in dose and then increases with further increases in dose. The E' center numbers decrease to a constant number

359

with increasing dose. The dose dependence of these two centers are shown in Figure 6-24. The number of E' centers is three order of magnitude less than the number of POR's as shown in Fig. 6-24 a. The intensities of the E' center component increase with decreasing temperature, in good agreement with a Boltzmann function, i.e. for hv <^feB7^I ~hv/kBT, where / is the intensity of the component, h is Planck's constant, v is spectrometer frequency, /cB is Boltzmann's constant and T is absolute temperature. The intensity of Dose dependence EPR signals

4.0 8.0 Dose in 1016 ions/cm 2

(a)

12.0

POR temperature dependence 15

8 10

O 8 -10 15 o 1.6-1016 16 A u • 10 16 a 8- 10

a

I 5

0 0.002

0.004

0.006

0.008

1/7 in K"1 (b) Figure 6-24. (a) Dose dependence of the EPR components (POR and E') in the spectra of oxygen-implanted SiO2 glass samples, (b) temperature dependence of the POR component.

360

6 Optical and Magnetic Properties of Ion Implanted Glasses

the POR component deviates markedly from a Boltzmann function. With decreasing temperature, the increase of intensity of the POR component is much greater than expected for a Boltzmann dependence, for the highest dose, 6 • 10 16 cm" 2 , as shown in Figure 6-24 b (Derryberry et al., 1990). This temperature dependence may have two possible sources. One of these may be a wide distribution of relaxation times for the POR spin-lattice relaxation. With decrease in temperature the line width for these spins decreases and contributes to the observed component. The second may be exchange interactions between POR's in clusters with the result that the clusters are super-paramagnetic. With decrease in temperature the relaxation times for the magnetization of the clusters increase. With decrease in temperature increasing number of clusters contribute to the component. In this case the shape of the component should change with decreasing temperature. The singularities would disappear into an almost symmetrical line shape. Derryberry et al. (1990) do not report such a change in line shape. 6.5.2.2 Elements of the First Transition Series

The paramagnetic resonance spectra of elements of the first transition series introduced into many glassy solids by thermal processes have been described in several thousand papers since Sands' publication (1955) describing the spectra of F e + 3 in an oxide glass. An excellent review of the paramagnetic resonance spectra of the 3 d, 4d and 5d elements in a few oxide glasses has recently been published (Griscom, 1990). When concentrations of these ions exceed approximately 1 mol%, magnetic interactions change the EMR spectral prop-

erties. The magnetic properties of such glasses have been labeled "spin glasses". A major fraction of the published research on these materials concerns metallic glasses (Moorjani and Coey, 1984). One chapter in Moorjani and Coey's book, chapter V, discusses the properties of insulating spin glasses. Spin glasses are materials in which the concentrations of magnetic ions or states are sufficient for spin-spin interactions, such as St'Sj, to be the largest energy term in the spin Hamiltonian and in which the spin states do not have translational symmetry. This lack of symmetry and a coupling of spins in which the summation pathway determines the net magnetic moment produces spero- and sperimagnetic materials (Moorjani and Coey, 1984). Implanting magnetic ions in a substrate insures the absence of translational symmetry. Although the ions may form separate phases, ion doses for which the concentrations of implanted ions in the implanted layer are greater than a few percent of the substrate ions in the layer occur for doses ^ 1016 ions cm" 2 when implanted at one ion energy. Even with the formation of separate phases particle-particle magnetic interactions may be expected to lead to the properties of spin glasses. We note that implanting ions at one energy into a substrate material such as SiO2 will result in a concentration of ions at the maximum of the distribution of the order of 1 mol% for a dose of 1015 cm" 2 . In the case of transition elements, magnetic interactions between ions with a random distribution in a substrate is a significant determinant of the electron magnetic resonance (EMR) spectra of the implanted ions. Another factor affecting the EMR spectra of ions, implanted at one energy in most oxide glasses is the distribution of ions. This distribution has a width at half maximum amplitude ~120nm for 160 keV

6.5 Magnetic States

ions. When implanted into a flat surface these ions form a thin film in which two dimensions of the film are several orders of magnitude greater than the thickness of the film. Weeks et al. (1985, 1986), Whichard and Weeks (1989) and Whichard (1989) have measured the EMR spectra of silica implanted with Ti, Cr, Mn, Fe, and Cu. In addition to spectral components due to paramagnetic defect states of silica produced by the implantations, they attribute other components to magnetic states of the implanted ions in the case of Ti, Mn, and Fe. In the case of Cr a spectral component attributed to Cr was observed at doses ^ 3 • 1016 cm" 2 (Hosono et al., 1990). At a dose of 6 • 1016 ions cm~ 2 it was not resolved. In the case of Cu ions no component due to Cu + 2 was detected (Magruder etal, 1991). The magnetic properties of each of these ions implanted in various glasses will be considered in turn. The order in which they will be discussed will be the order of the intensities of the magnetic resonance spectral component attributable to the implanted ion. We will begin with the most intense component. a) Fe Ions The spectrum of a silica sample implanted with 6 • 1016 ions cm" 2 is shown in Figure 6-25 (Whichard, 1989; Weeks et al., 1985) for two orientations of the implanted surface of the sample with respect to the laboratory magnetic field (Arnold, 1975). The shift of the peak of the component to a higher field when the field is perpendicular to the implanted surface is due to an internal field within the implanted layer. This field, produced by exchange interactions between the Fe ions, is oriented in the implanted plane. This internal field

361

3000 £000 Magnetic field in G

Figure 6-25. The EPR spectra of a SiO2 glass sample implanted with 6 • 1016 Fe ions cm" 2 with a current of 4 JJA cm" 2 and substrate temperature of 300 K. (1) implanted surface parallel to the laboratory magnetic field; (2) implanted surface perpendicular to laboratory field.

decreases with decreasing dose and is not resolved for doses < 3 • 1016 ions cm" 2 (Whichard, 1989). In the case of a dose 6 • 1016 cm" 2 , this internal field increases, the line width of the component increases, and the intensity increases to ~ 200 K and then decreases, below 200 K, with decreasing temperature. Whichard (1989) concludes that these magnetic properties are due to a spin glass being formed in the implanted layer. These properties are illustrated in Figure 6-26 (Whichard, 1989). Whichard (1989) showed the transition to a magnetically ordered state occurred over a range of doses. This transition is illustrated in Table 6-5. The intensity of the component increased from 1 to 33 (relative units) when the dose increased from 2 to 3 in units of 1016 ions cm" 2 . Since this increase in intensity is much greater than the increase in dose, Whichard attributed the excess to an ordering of the Fe ions into a ferrimagnetic state. Even the state for doses

362

6 Optical and Magnetic Properties of Ion Implanted Glasses Temperature dependence of Fe EPR signal Resonance field line width and intensity

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Figure 6-26. The temperature dependence of the resonance field, line width, and intensity of the Fe EPR component in the spectrum of a SiO2 glass sample implanted with 6 • 1016 ions cm" 2 . The implanted surface of the sample is parallel to the laboratory field for the angle 180°, and perpendicular for the angle 90°. The error in the each data is represented by the size of the symbol for the data.

< 1 • 10 16 ions cm 2 was not a paramagnetic state. The reason for this assertion is that if it is assumed that the component is a paramagnetic component then it would be expected that because of the Boltzmann dependence of paramagnetic states only 0.1% of the total number of ions would be

observed at ~ 300 K instead of the 7% fraction observed and given in Table 6-5. At a dose of 6 • 1016 ions cm~ 2 the ordering effect increases, since the table shows that the intensity increases by a factor of 5 with an increase of dose of only a factor of 2. Weeks et al. (1986) heat-treated a sample implanted with 3 • 1016 Fe ions cm" 2 for 20 h in air at 800 °C. The intense component due to the iron ions remained but its temperature dependent properties changed. The magnitude of the internal field decreased from ~ 50 mT to ~ 10 mT at 300 K and then increased only to ~ 30 mT at ~ 5 K. The intensity decreased - 1 5 % from 200 to 5 K as compared to the 75% decrease in an as implanted sample. These data are consistent with the relative fractions of Fe charge states given in Table 6-3. Griscom et al. (1988) also observed an intense electron magnetic resonance spectral component in samples implanted with (0.8, 1.3 and 2.8) • 1017 Fe ions cm" 2 . The spectra shown in Figure 6-27 show that with an increase in dose above that used by Whichard the internal magnetic field increases, and for a dose of 2.8 • 10 17 ions cm" 2 it has a value of ~ 0.7 T. Using KitteFs conditions for resonance for ferromagnetic material with a planar geometry and assuming that the implanted samples are ideal continuous films (Kittel, 1948), Griscom calculates the magnetization, M, of the implanted layer based on the fields for resonance with the applied laboratory field in the plane and out of the plane of his samples. He finds that there is reasonable agreement between the parameters of the spectra, #-value and magnetization, M, at room temperature measured at - 9 and - 35 GHz. The temperature dependence of the intensity of a sample implanted with 8 • 1016

363

6.5 Magnetic States

Table 6-5. The g-value, line width, and relative intensity of the Fe EPR signal for three implantation doses. Nominal dose (1016 ions/cm2) Fe 6 1 6 II 31 3 11 21 2||

9

Relative intensity (arbitrary units)

AH (G)

Fractiona

1.897 + 0.003 2.130 + 0.004 2.014 ±0.002 2.082 + 0.003 2.070 + 0.003 2.079 + 0.003

171 168 31 33 1 1

497 ± 8 358 + 6 321 ± 9 295 ± 5 315 + 11 264 ± 30

340 + 5 350 + 5 120 ± 5 125 ± 5 7+5

1 = perpendicular, || = parallel,

a

= fraction of implanted ions assuming a paramagnetic system.

ions cm 2 is shown in Figure 6-28 over the temperature range of ~100 to ~58OK. The temperature dependence has the appearance of a Curie transition with T/C - 5 0 0 K . Griscom (1988) also plots the value of A = Hres(out of plane)— Ho = (a)

A

g=2.0

/— /-/out of plane

(b)

r-H

in plane

AL

H out of plane

OC

Ir

105K"

/-105K

290 K-U 0.0

0.1

0.2

0.3

7±5

(U 0.5 0.6 0.7 Magnetic field in T

0.8

0.9

4 7i M and finds, as expected, that it has the same temperature dependence as the intensity. Whichard (1989) showed that the onset of the ordered magnetic phase occurs for doses < 1016 cm" 2 . Based on his data and using the equation given above we find that the magnetization, M, of Whichards samples implanted with 6 • 1016 ions cm" 2 is M = 0.0002 T. The Griscom et al.'s sample (1988) with 8 • 1016 ions cm" 2 has M ~ 0.02 T. An increase in dose by a factor of 1.4 increases the magnetization by a factor of ~ 100. The dose dependence of the magnetization is given in Table 6-6. The Griscom et al. samples were implanted with ions whose energy was ~ 100 keV and for the Whichard samples it was 160 keV. The concentration of implanted ions at sample surfaces in Griscom et al.'s samples was much higher than in the Whichard et al.'s samples. The magnetic layers in Whichard samples were

1.0

Figure 6-27. X-band (9.2 GHz) FMR spectra of two planar Fe-implanted silica samples for various angles between the applied magnetic field and the sample plane: (a) sample implanted with 8 • 1016 ions cm" 2 : (b) sample implanted with 1.3 • 1016 ions cm" 2 . Spectra of (a) were obtained at 290 K; those of (b) were recorded at the indicated temperatures. (The dimensions of the implanted dose are given on the original figure as ions/cm3. We believe these dimensions to be in error and should be ions/cm2).

Table 6-6. Dose dependence of magnetization of Fe implanted silica. Dose in (1017 ions cm 2) 0.58 0.8 1.3 2.8

M in (T) 0.0002 0.02 0.04 0.10

364

6 Optical and Magnetic Properties of Ion Implanted Glasses

Figure 6-28. Integrated FMR intensity (•) and parameter A (O) VS. temperature (of Fe implanted sample, dose 8 • 1016 ions cm" 2 ). 200 300 400 Temperature in K

100

Fe

/

Mn x20

/

Ml .II. ' - * — < * < ^

./

V

dH

Ti *50

500

600

completely buried. It would be interesting to determine whether the exposure of the samples examined by Griscom et al. to normal atmosphere after implantation changed the relative fractions of the chemical states of Fe. The diffusivity of oxygen at room temperature in silica implanted with Fe is unknown. In silica it is very small (Schaefer, 1974). It is known (Webb et al., 1976) that ion implanted silica has a much higher etching rate in dilute HF than does silica. This higher etching rate may be indicative of a porosity of the surface of implanted samples that enhances the etching rate. If such is the case, then it might be expected that the diffusivity of oxygen would be enhanced and the oxidation of implanted ions near the implanted surface would occur. b) Mn Ions

Cr.Cu *50

i

i

2000

3000

i

4000 G 5000

Figure 6-29. EPR spectra of silica samples implanted with 6-10 1 6 ions cm" 2 at 300 K, 4|aAcm~ 2 , and 160 keV.

Figure 6-29 (Whichard, 1989) shows the relative amplitudes of the first derivative of the absorption of the ion related component in the EMR spectra of Fe, Mn, Ti, Cr and Cu ions implanted to the same dose 6 • 1016 ions cm" 2 . The very narrow component in the spectra of the Ti, Cr and Cu implanted samples is due to the E' center. The receiver gain for the spectrum of the Fe implanted sample was too small to de-

365

6.5 Magnetic States

tect the E' center. At higher gain it is detected as shown in Figure 6-21. The temperature dependence of the line width, relative intensity and resonance field of the component due to the Mn ions are shown in Figure 6-30 (Whichard, 1989). No long-range ordering of Mn spins was detected. The resonance field decreased and the line width increased to the lowest temperature at which measurements were made, ~ 5 K. The relative intensity increased to ~ 80 K and then decreased with decreasing temperature. This temperature dependence of these magnetic parameters are similar to those of the Fe component in the Fe implanted samples. Thus it is reasonable to assume that the magnetic properties of that fraction of Mn ions contributing to the resonance component are in a spin glass state. It is evident from Figure 6-29 that the fraction of Mn ions contributing to the resonance component is approximately a factor of 50 less than the fraction of Fe ions contributing to the Fe component. Given the chemical similarities of Mn and Fe implanted into the same substrate composition, it is reasonable to assume that the chemical states of Mn ions after implantation are similar to those of Fe. On the basis of estimates by Perez et al. (1987) of the fraction of Fe ions in the 0, + 2, and 4- 3 states, there should be approximately the same fraction of Mn ions in these states for the same dose as there are Fe ions in this

state. No hyperfine components (Mn) (Whichard, 1989) were resolved in the spectra of the Mn implanted samples. Thus Temperature dependence of Fe EPR signal resonance field, line width and intensity 3550

100

200 300 Temperature in K

£00

500

Figure 6-30. The temperature dependence of the resonance field, line width, and signal intensity of the Mn spectral component in the spectrum of a sample implanted to a dose of 6 • 1016 ions cm~2 (at 4 uA cm" 2 , 160 keV, and substrate temperature 300 K).

Table 6-7. The g-value, line width, and relative intensity of the Mn EPR signal for three implantation doses.

Nominal dose (1016 ions/cm 2) Mn 6 3 1

9

Relative intensity (arbitrary units)

AH (G)

Fractiona

1.995 ±0.004 1.996 ±0.002 1.998 + 0.003

3.3 2.4 1.0

196 ±12 208 ±11 235 ±23

6.0 ± 0.5 7.5 ± 0.5 9.2 ± 0.5

Fraction of implanted ions assuming a paramagnetic system.

366

6 Optical and Magnetic Properties of Ion Implanted Glasses

the magnetic interactions between the Mn ions apparently suppressed the hyperfine structure of any Mn + 2 ions. We note that Whichard did not report detection of a g = 4.3 component in Mn implanted samples. It appears that Mn ions, randomly distributed in the silica structure, at least in sites which have crystal fields which produce the g = 4.3 component, have not been detected. Table 6-7, taken from Whichard's dissertation (1989), shows that the relative intensity and fraction of ions detected based on the "paramagnetic assumption" as a function of dose differ markedly from the dependence shown in Table 6-7. Whichard attributes this dose dependence to an antiferromagnetic or speromagnetic ordering of the Mn spins. He notes that MnO has a Neel transition at 118 K and MnO 2 one at 90 K and ascribes the maximum in relative intensity which occurs at ~100 K, shown in Figure 6-30, to the onset of such transitions. c) Cr Ions Hosono et al. (1990) have detected a component in the spectra of samples implanted with doses between 0.5 and 3 • 1016 ions cm" 2 . The #-value (1.97) and line shape are those expected for Cr + 3 in oxide glasses (Landry et al., 1967). The absence of a component due to Cr ions when the dose of implanted ions > 3 • 1016 ions cm ~2 is evident in Figure 6-22. The intensity of this component (# = 1.97) decreases with increasing dose and is not detected in the spectrum of the sample implanted with 6 • 10 16 ions cm" 2 . The argument which we proposed above that the fractional distribution of chemical states in the Mn case is similar to that of the Fe case can also be made for the Cr case. The paramagnetic resonance spectra

of Cr + 3 has most often been observed in silicate glasses (Arnold, 1978). If, as in the case of Fe, Cr forms oxide precipitates the various chromium oxide phases, CrO, Cr 2 O 3 and CrO 2 , would determine the magnetic properties and the EMR spectra. The Neel transition of Cr 2 O 3 is - 307 K (Gray, 1957). Thus we suggest that in the case of Cr the tendency to anti-ferromagnetic or speri-magnetic ordering is well established at 300 K and no EMR component due to Cr precipitates would be expected. The Neel transition of Cr colloids would be - 4 7 5 K (Arnold, 1980). As discussed in Section 6.3 the optical absorption properties of the Cr, Mn and Fe implanted samples are consistent with absorption expected for particles whose sizes are small compared to the wavelength of the absorbed light. d) Ti Ions A component due to Ti 3 + is well resolved in the spectrum shown for a Ti implanted sample in Figure 6-31 (Whichard and Weeks, 1990). The temperature depen-

3000

3500 Magnetic field in G

4000

Figure 6-31. The EPR spectrum of a sample implanted with titanium to a dose of 6 • 1016 ions cm" 2 (at 4 uA cm ~ 2, 160 keV and substrate temperature 300 K).

367

6.5 Magnetic States

dence of the intensity of the component is well fitted by a Boltzmann function down to ~ 5 K. Within experimental error the line width and field for resonance are invariant with temperature from 300 to 10 K for doses from 1 to 6 • 1016 ions cm" 2 . Hence the Ti + 3 ions which contribute are paramagnetic from 300 to 5 K. Table 6-8 shows that the number of Ti + 3 ions detected is not a linear function of the dose and that the fraction of ions contributing to the component decreases between < 1 and > 3 • 1016 ions cm" 2 . A major fraction, - 9 0 % for a dose of 6 • 1016 ions cm" 2 , is not detected in the EPR spectrum. Whichard et al. (1990) have found that the magnitude of the exchange integral for the paramagnetic fraction of the Ti 3 + ions ranges from 10 to 1.6 • 10 ~6 eV. They assume that the paramagnetic fraction is that fraction in the tails of the ion distribution measured by ion back scattering, as shown in Figure 6-32 (Whichard et al., 1990) by the triangles. The temperature dependence from 5 to 300 K of line width, resonance field and intensity for all doses was that expected for a paramagnetic state. The chemical states of the large fraction of Ti ions not detected in the EPR spectra were not identified. It is plausible to assume that some fraction of those undetected Ti ions are in + 2 and + 3 states. On the basis of this assumption we then suggest that these Ti ions have large exchange Table 6-8. The g-value, line width, and relative intensity of the Ti EPR signal for three implantation doses. g

AH (G)

Relative intensitiy (arbitrary units)

1.936 + 0.007 1.931 ±0.007 1.941 ± 0.005

145 + 15 180 ± 15 205 + 15

6 3 4

Nominal dose (1016 ions/cm2 )

Ti 6 3 1

RBS of Ti ion implanted silica Ti dose in ions/cm2 A

1 x10,16

0.15 E

° 3 0.10 -2

0.05 £ a

1°o A.2 °A

^ '

0.0

0.1 0.2 Depth in |jm

0.3

0.00

Figure 6-32. The backscattering depth profiles for titanium implanted samples. The outlined regions in the tails at depths > 150 nm account for half of the implanted ions detected by EPR in that sample. The other half of the detected ions are assumed to be located in the tail near the sample surface.

interactions which are either anti-ferrimagnetic or speri-magnetic. Whichard (1989) reports some experiments in which he detected transient signals that were at least two orders of magnitude more intense than the paramagnetic component. He does not describe an experimental procedure which ensured reproducible data. He did note that the transient signal was detected again when a sample was removed from the EPR spectrometer and magnetic field for more than three days. e) Cu Ions The only EMR or EPR components detected in Cu implanted samples were those due to silica defects. Weeks et al. (1989) implanted silica and two other types of glass samples. The other two samples were a standard Corning borosilicate and alumino-silicate glasses. In none of these glasses did they detect any compoent attributable to Cu + 2. They suggest that implanted Cu is either in a colloidal state, i.e. Cu°, or Cu + 1 . They note that in the case of silica implanted with Cu, the optical absorption spectra of samples, with a range of doses

368

6 Optical and Magnetic Properties of Ion Implanted Glasses

>10 1 6 ions cm 2, contained no resolved band at 5.2 eV, the energy of a band attributed to Cu + 1 in silicate glasses. They note that in the case of the samples of the other glasses the optical absorption at energies > 4 e V were too intense to observe this band. By comparison with the absorption spectra of Cu in silica samples in which the absorption bands in the 2 to 4 eV range are attributed to Cu colloids, the absence of these bands in implanted samples of the other glasses leads to the conclusion that in these glasses a major fraction of the Cu is in the + 1 state.

6.6 Glasses Produced by Implantation of Crystalline Substrates Irradiation of one of the crystalline forms of silica, a-quartz, with neutrons transforms the crystal to a glass with a density that is ~ 2 . 5 % greater than the density of a silica glass formed by thermal processing (Lines and Arndt, 1960; Primak et al, 1955). The increase in the refractive index of silica implanted with noble gas ions is ~ 2%. This is the increase expected from the increase in density which results from the modification of the structure of thermally processed silica by atomic displacements. In addition to the changes in structure which produce the increase in density, optical absorption bands and paramagnetic states due to defects are introduced by the irradiation. Among other wide band-gap crystals which have been observed to transform to the amorphous state under some conditions of ion implantation are A12O3 (McHargue et al., 1990a, b), SiC (McHargue et al., 1990 c), Si^N* (Arnold and Borders, 1976), CaTiO 3 (White et al.,

1989), KTaO 3 (Arnold and Borders, 1976), and many naturally occurring silicates (Wangetal., 1990). Townsend et al. (1990) have fabricated optical waveguides in A12O3 by implanting group IV elements. The amorphous state is produced by elements of the group IV column at doses and substrate temperatures during implantation, less than for the elements in other columns of the periodic table. The dose is < 10% of the dose and the substrate temperature during implantation may be 300 K compared with a temperature of ~ 80 K required for other elements (McHargue et al., 1985). Figure 6-33 (Townsend et al., 1990) shows the refractive index of A12O3 implanted with 5 • 1016 carbon ions cm" 2 . The data show that larger decreases in the refractive index are produced when the implanted face of an A12O3 crystal is the Z face. The damage profile and the carbon ion profile have substantial differences as shown in Figure 6-34 (Antonini et al., 1982; Arnold, 1980). The chemical state of the C ion has not yet been investigated. Townsend et al. (1990) suggest that the column IV ions act as catalysts in the process of forming a glass network: "The distortions associated I./D

Z

Y

/77 = 2

m=1 1.77

n

h

Z

1.76

-

m-\

\ 1.78

i

i

1

Depth in nm

Figure 6-33. Waveguide refractive index profiles (for an implanted dose of 5 • 1016 carbon ions cm" 2 ): 6MeV.

6.6 Glasses Produced by Implantation of Crystalline Substrates

Figure 6-34. Comparison of ion range and damage distributions (for 6 MeV carbon implants in A12O3).

with the tetravalent bonding are not localized at a single site but influence some tens of neighboring lattice atoms." This quotation clearly indicates that Townsend et al. have assumed that the C ions are multivalent. The chemical reactions between implanted ions and substrate ions affect the structure of substrate ions far beyond the nearest neighbor range. The mechanism for such a long range interaction is not obvious, as is indicated by the use of the term "catalyst". In this case C ions cannot react directly with each of the "tens of neighboring ions" as is the case for those chemical reactions usually labeled "catalytic". Conversion electron Mossbauer spectroscopy (CEMS) has been used to determine the chemical states of Fe and Sn implanted in A12O3 (McHargue et al., 1987, 1990 b). The chemical states of Fe, as a function of dose implanted at ~ 300 K, are shown in Figure 6-35 (Perez, 1984). The implanted layers for these doses implanted at ~ 300 K are still crystalline. A substrate temperature ~ 80 K is necessary for the formation of an amorphous layer. The chemical states of Fe in this case are shown in Figure 6-35 (Perez, 1984). The data show that there are differences in the chemical states which form at the two temperatures.

369

The major differences are the production of Fe + 4 which increases with increasing dose in two different sites and the absence of Fe + 3 in samples implanted at 77 K. A decrease in Fe + 2 in two differing sites with increasing dose occurs in both cases. The fraction of Fe in the Fe° state is invariant with dose for implantation at 77 K but increases with dose for implantation at 300 K. The optical absorption of the implanted layer, implanted at ~ 300 K, has a dependence on photon energy that is similar to that of Fe implanted silica (Stark et al., 1987). Optical absorption of A12O3 implanted at 77 K has not yet been reported. Based on this similarity, the explantation proposed by Perez et al. (1987) for the photon energy dependence of the absorption in Fe: SiO2 is also applicable to the Fe: A12O3 case. In the case of implanted C ions in A12O3, Townsend et al. (1990) suggested that column IV elements were much more effective in producing an amorphous state in A12O3 than were other elements. McHargue et al. (1990) have determined the chemical states and their fractions of implanted Sn ions in the amorphous layer of A12O3 produced by implantation at - 3 0 0 K of 4 • 1016 ions cm" 2 . The final charge states of the Sn ions were + 2 and + 4. The possibility that some small (< 2%) fraction of the Sn was in the 0 state could not be resolved. Neither refractive index nor optical absorption of Sn implanted samples have been reported, to our knowledge. If the Sn ions interact with the substrate ions to form the amorphous state does this interaction also affect the defect states of the substrate? McHargue et al. (1990 b) have used CEMS to determine the chemical states of Fe implanted in single crystal SiC. Their samples were implanted with doses ranging from 1 to 6 • 1016 ions c m ' 2 at - 3 0 0 K .

370

6 Optical and Magnetic Properties of Ion Implanted Glasses (b)

(a) 16

Ion fluence in 10

) 20 -

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0

Ion fluence in 1016 ions cm" 2 2 4 6 8 10

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0

1

1 I

1

40 -

40

20

20

Feu 0

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'.

Fe°

n- a-—°~~ r

Figure 6-35. (a) Fluence (integrated flux) dependence of the different components present in the Mossbauer spectra (A12O3 single crystals implanted with 160 keV 57 Fe at 77 K). (b) Fluence (integrated flux) dependence of the components present in the Mossbauer spectra of iron-implanted crystalline A12O3 (300 K).

10 20 30 Concentration Fe/AI in %

The implanted layers were amorphous for all doses. The CEMS spectra were attributed to a single charge state in sites with small differences in local symmetries. Refractive indices, optical absorptions and magnetic properties have not been reported.

6.7 Conclusions and Prognosis This review has been primarily about ion implanted silica. The reason for the absence of other glass systems is that little research has been reported on substrates other than silica. In our opinion, there are many fascinating, scientifically interesting, and useful possibilities in the unknown

phenomena which will appear upon ion implanting samples chosen from the enormously wide range of glass systems. The final charge state of ions from the first transition series of elements implanted into silica, range from 0 to + 3 . Implanted Cu has, apparently, only one charge state, i.e. 0. Implanted into a boro- or alumino-silicate glass the charge state is only + 1 . Thus it was possible, in this case, to control the charge state of the implanted ion by changing the composition of the substrate. It may be possible to control the charge states of the transition elements and other elements by substrate composition. Successive implantation of two or more ions from the first transition series in silica is still to be done. To our knowledge, co-

6.8 References

implantation into substrates of other compositions has not been performed either. The revolution in communication technology which has taken place over the past two decades with the introduction of glass fibers may continue with the development of optical circuit elements by implantation technologies.

6.8 References Antonini, M., Camagni, P., Gibson, P. N., Manara, A (1982), Rad. Eff 65, 41. Arnold, G. W. (1973), Nucl. Sci. NS-20, 220-223. This table is taken from: Johnson, W. S., Gibbson, J. R, Projected Range Statistics in Semiconductors. Dowden, Ross, and Hutchinson: Stroudberg, PA. Arnold, G. W. (1978), in: The Physics ofSiO2 audits Interfaces: Pantelides, S. T. (Ed.). New York: Pergamon. Arnold, G. W. (1980), Rad. Eff. 47, 15-20. Arnold, G. W. (1981), in: The Physics of MOSInsulators: Lucovsky, G., Pantelides, S. T., Galeener, E L. (Eds.). New York: Pergamon, pp. 112-116. Arnold, G. W, Borders, J. A. (1976), Inst. Phys. Conf Ser. No. 28, Chapter 3. Arnold, G. W, Borders, I A. (1977), J. Appl Phys. 48, 1488. Arnold, G. W, Brow, R. K., Carr, M. J., Barbour, J. C. (1990), Mater. Res. Soc. Proc, Vol. 157, 569574. Arnold, G. W, Mazzoldi, P. (1987), in: Ion Beam Modification of Insulators: Mazzoldi, P., Arnold, G. W. (Eds.). Amsterdam: Elsevier, p. 222. Arnold, G. W, Peercy, P. S. (1980), /. Non-Cryst. Solids 41, 350-379. Bach, H. (1975), Rad. Eff. 25, 209-212. Bayly, A. P., Townsend, P. D. (1973), J. Phys. D (London), Appl. Phys. <J, 1115-1128. Becker, K., Yang, L., Haglund, Jr., R. R, Magruder, R. H., Weeks, R. A., Zuhr, R. A. (1990), Nucl. Instrum. Methods B, Proc. Intl. Conf. Ion Beam Modification of Materials, 5-9 Sept. 1990, Knoxville, Tennessee, accepted for publication. Biersack, J. P. (1987), in: Ion Beam Modification of Insulators: Mazzoldi, P., Arnold, G. W. (Eds.). Amsterdam: Elsevier, pp. 1-55. Biersack, J. P., Eckstein, W. G. (1984), Appl. Phys. 34, 73. Bloembergen, N., Gibson, R. B., Roberts, J. P. (1988), in: Non-Linear Optics. New York: W. A. Benjamin, Chapter 1. Brill, R. H. (1986), private communication. Brow, R. K., Zhu, Y, Day, D. E., Arnold, G. W. (1990), J. Non-Cryst. Solids 120, 172-177.

371

Derryberry, S., Weeks, R. A., Weller, R., Mendenhall, M. (1990), Nucl. Instrum. Methods Phys. Res., Proc. Intl. Conf. Ion Beam Modification of Materials, Knoxville, Tennessee, 5-9 Sept. 1990; to be published. Faik, A. B., Chandler, P. X, Townsend, P. D., Webb, R. (1986), Rad. Eff 98, 399-407. Friborg, S. R., Smith, P.W. (1987b), IEEE J. Quantum Electron. QE-23, 2089-2094. Friebele, E. X, Griscom, D. L. (1986), in: Defects in Glasses, Vol61: Galeener, R, Griscom, D., Weber, M. (Eds.). Pittsburgh, PA: Materials Research Society, pp. 319-332. Friebele, E. I, Griscom, D. L., Staplebroek, M., Weeks, R. A. (1979), Phys. Rev. Lett. 42, 1346. Friebele, E. X, Higby, P. L., Tsai, T. E. (1987), Diffusion and Defect Data 53154, 203-212. Frohlich, H. (1958), Theory of Dielectrics, 2nd. ed. Oxford, UK: Oxford University Press, p. 163. Geotti-Bianchini, R, Polato, P., Lo Russo, S., Mazzoldi, P. (1984), J. Amer. Ceram. Soc. 67, 39-42. Gray, D. W (Ed.) (1957), American Institute of Physics Handbook. New York: McGraw-Hill, pp. 5-226. Griscom, D. L. (1980), J. Non-Cryst. Solids 40, 211. Griscom, D. L. (1990), "Electron Spin Resonance", in: Glass Science and Technology, Vol. 4b: Uhlmann, D., Kreidl, N. (Eds.). New York: Academic Press, pp. 151-251. Griscom, D. L., Krebs, X X, Perez, A., Treilleux, M. (1988), Nucl. Instrum. Methods Phys. Res. B32, 272-278. Gross, B. (1964), Charge Storage in Solid Dielectrics, Amsterdam: Elsevier. Hache, R, Ricard, D., Flytzanis, C. (1986), J. Opt. Soc. Am. B3, 1647-1655. Hilczer, B., Malecki, X (1986), Electrets. Amsterdam: Elsevier. Hosono, H., Weeks, R. A. (1990a), /. Non-Cryst. Solids, 116. Hosono, H.? Weeks, R. A. (1990b), Phys. Rev. B40, 10543. Hosono, H., Weeks, R. A., Imagawa, H., Zuhr, R. A. (1990), J. Non-Cryst. Solids 120, 250-255. Imai, H., Arai, K., Imagawa, H., Hosono, H., Abe, Y (1988), Phys. Rev. B38, 1272. Joos, G. (1934), Theoretical Physics. London: Blackie, p. 432. Kelly, R. (1987), in: Ion Beam Modification of Insulators: Mazzoldi, P., Arnold, G. W. (Eds.). Amsterdam: Elsevier, pp. 57-110. Kittel, C. (1948), Phys. Rev. 73, 155. Landry, R. X, Fournier, X T., Young, C. G. (1967), / Chem. Phys. 46, 1285. Lines, M. E. (1990), Phys. Rev. B41, 3372, and 3383. Lines, R. L., Arndt, R. (1960), Phys. Rev. 119 (2), 623. Magruder, R. H., Kinser, D. L., Weeks, R. A., Zuhr, R. A. (1989), Mater. Res. Soc. Symp., accepted for publication.

372

6 Optical and Magnetic Properties of Ion Implanted Glasses

Magruder, R. H., Morgan, S. H., Weeks, R. A., Zuhr, R. A. (1990a), /. Non-Cryst. Solids 120, 241 249. Magruder, R. H., Weeks, R. A., Zuhr, R. A. (1990b), Mater. Res. Soc. Symp. 157, Pittsburgh, PA: Material Research Society, p. 210. Magruder, R. H., Weeks, R. A., Zuhr, R. A. (1991), J. Non-Cry st. Solids, accepted for publication. Mazzoldi, P. (1990), J. Non-Cryst. Solids 120, 223233. McHargue, C. I, Farlow, G. C , Sklad, P. S., White, C. W, Perez, A., Kornilios, N., Marest, G. (1987), Nucl. Instrum. Methods B19/20, 813. McHargue, C.I, Farlow, G. C, White, C. W, Williams, J. M., Appleton, B. R., Naramoto, H. (1985), Mater. Sci. Eng. 69, 123-127. McHargue, C. X, Perez, A., McCallum, J. C. (1990c), Nucl. Instrum. Methods Phys. Res., Proc. Intl. Conf. Ion Beam Modulation of Materials 1990, to be published. McHargue, C.I, Sklad, P. S., McCallum, J. C , White, C.W. (1990 a), Nucl. Instrum. Methods Phys. Res. B46, 144-148. McHargue, C. X, Sklad, P. S., McCallum, J.C., White, C.W, Perez, A., Abonneau, E., Marest, G. (1990 b), Nucl. Instrum. Methods Phys. Res. B46, 74-78. McHargue, C. X, Sklad, P. S., Angelini, P., White, C.W, McCallum, X C. (1990), Mater. Res. Soc. Symp., Vol. 157. Pittsburgh, PA: Materials Research Society, pp. 505-512. McMillan, X A. (1968), Electron Paramagnetism. New York: Reinhold, Chapter 9. Mie, G. (1908), Ann. Phys. 25, 371. Milonni, P.W., Elerly, X H. (1988), Lasers. New York: John Wiley. Moorjani, K., Coey, X M. D. (1984), Magnetic Glasses. Amsterdam: Elsevier. Oppenheim, A. L., Brill, R. H., Dorag, D., von Saldern, A. (1970), Glass and Glassmaking in Ancient Mesopotamia. Corning, NY: Museum of Glass. Orton, XW. (1968), Electron Paramagnetic Resonance. London: ILIFFE Books LTD. Osterberg, U. (1989), Mater. Res. Soc. Symp. Vol. 152. Pittsburgh, PA: Materials Research Society, pp. 235-243. Parke, S., Webb., R. S. (1972), Phys. Chem. Glasses 13, 157. Perez, A. (1984), Nucl. Instrum. Methods Phys. Res. Bl, 621. Perez, A., Bert, X, Marest, G., Sawika, B., Sawiki, X (1983), Nucl. Instrum. Methods 209/210, 281. Perez, A., Marest, G., Sawiki, B., Tyliszczak, P. (1983b), Phys. Rev. B28, 1227. Perez, A., Meaudre, R., Thevanard, P., Sibut, P. (1985), in: Induced Defects in Insulators: Mazzoldi, P. (Ed.). Cedex, France: Les Editions des Physique, p. 171.

Perez, A., Treilleux, M., Capra, T., Griscom, D. L. (1987), /. Mater. Res. 2, 910. Primak, W, Fuchs, L. H., Day, P. (1955), J. Amer. Ceram. Soc. 38, 135. Purcell, T., Weeks, R. A. (1969), Phys. Chem. Glasses 10, 198. Rahmani, M., Townsend, P. D. (1989), Vacuum 39, 1157-1162. Roos, L. (1989), Glastech. Ber. 62, 285-297. Sands, R. H. (1955), Phys. Rev. 99, 1222. Schaefer, H. (1974), in: Material Science Research: Cooper, A. R., Heuer, A.X (Eds.). New York: Plenum, pp. 311-326. Sheik-Behae, M., Said, A. A., Van Stryland, E.W. (1989), Opt. Lett. 14, 955. Stark, X D., Weeks, R. A., Whichard, G., Kinser, D. L., Zuhr, R. (1987), /. Non-Cryst. Solids 95/96, 685. Stevens, D. K. (1955), Phys. Rev. 98, 1541. Stevens, D. K., Sturm, W.X, Silsbee, R. H. (1958), /. Appl. Phys. 29, 66. Taylor, A. X, Gibson, R. B., Roberts, X P. (1988), Opt. Lett. 13, 814-816. Townsend, P. D. (1987 a), "Optical Effects of Ion Implantation", Rep. Prog. Phys. 50, 501-558. Townsend, P. D. (1987b), private communication. Townsend, P. D., Chandler, P. X, Wood, R. A., Zhang, L., McCallum, X, McHargue, C. X (1990), Electron. Lett. 26, 1193. Trotter Jr., D. M., Schreurs, I W . H , Tick, P. A. (1982), / Appl. Phys. 53, 4652. Tsai, T. E., Saifl, M. A., Friebele, E. X, Griscom, D. L., Osterberg, U. (1989), Opt. Lett. 14, 10231025. Vogel, E. M., Chase, E. W, Jackel, X L., Wilkes, B. X (1989), Appl. Opt. 28, 649-650. Vogel, E. M., Kosinski, S. G., Krol, D. M., Jackel, X L., Friborg, S. R., Oliver, M. K., Powers, X D. (1989), J. Non-Cryst. Solids 107, 244-250. Vogel, E. M., Krol, D. M., Jackel, X L., Aitchison, X S. (1989), Mater. Res. Soc. Symp. Proc. Vol. 152. Pittsburgh, PA: Materials Research Society, pp. 83-87. Wang, L. M., Eby, R. K., Janeczek, X, Ewing, R. C. (1990), "Proc. Intl. Conf. Ion Beam Modification of Materials, 9-14 Sept., 1990", Nucl. Instrum. Methods Phys. Res., to be published. Wang, P., Hagland, R. F , Kinser, D. L., Mogul, H. C , Tolk, N. H., Weeks, R. A. (1987), Diffusion and Defect Data 53/54, 463-468. Webb, A. P., Townsend, P. D. (1976), /. Phys. D (London). Appl. Phys. 9, 1343-1354. Webb, P. A., Houghton, A. X, Townsend, P. D. (1976), Rad. Eff 30, 177-182. Weeks, R. A. (1956), /. Appl. Phys. 27, 1376. Weeks, R. A. (1965), Proc. VII Intl. Glass Congr., Brussels, 1965. New York: Gordon and Breach, p. 42.

6.8 References

Weeks, R. A. (1967), in: Interactions of Radiation with Solids: Bishay, A. (Ed.)- New York: Plenum, pp. 55-94. Weeks, R. A., Hosono, H., Zuhr, R. A., Magruder, R. H., Mogul, H. (1989), Mater. Res. Soc. Symp. Proc. Vol. 152. Pittsburgh, PA: Materials Research Society, p. 115. Weeks, R. A., Kinser, D. L., Lee, J. M. (1977), NonCrystalline Solids: Frischat, G. H. (Ed.). Aedermannsdorf, CH: Trans.-Tech. S.A., pp. 266-271. Weeks, R. A., Nelson, C. M. (1960), J. Amer. Ceram. Soc. 1/3, 399. Weeks, R. A., Silva, M. C , Kordas, G., Kinser, D. L., Appleton, B. R. (1985), Mater. Res. Soc. Symp. Proc. Vol. 85. Pittsburgh, PA: Materials Research Society, p. 59. Weeks, R. A., Sonder, E. (1963), in: Paramagnetic Resonance: Low, W. (Ed.). New York: Academic, pp. 869-879. Weeks, R. A., Whichard, G., Kordas, G., Appleton, B. R. (1986), XIV Intl. Glass Congr., Coll Papers Vol. 3. New Delhi: Indian Ceramic Society, p. 236. Whichard, G. (1989), "Electron Paramagnetic Resonance Spectroscopy of a Silica Surface Modified by Transition Metal Ion Implantation", Ph.D. Thesis, submitted to Vanderbilt University. Whichard, G., Mogul, H. C , Weeks, R. A., Stark, J. D., Zuhr, R. A. (1988), Mater. Res. Soc. Symp. Proc. Vol. 126. Pittsburgh, PA: Materials Research Society, p. 105.

373

Whichard, G., Weeks, R. A. (1989), /. Non-Cryst. Solids 112, 1-6. Whichard, G., Hosono, H., Weeks, R. A., Zuhr, R. A., Magruder, R. H. Ill (1990), J. Appl. Phys. 67, 7526-7530. White, C. W, McHargue, C. X, Sklad, P. S., Boatner, L.A., Farlow, G. C. (1989), Mater. Sci. Rep. 4, 123-133. Wittels, M. C , Sherill, F. (1954), Phys. Rev. 93,1117. Wong, I , Angell, C. A. (1976), Glass: Structure by Spectroscopy. New York: Marcel Dekker. Zuhr, R. A., Weeks, R. A. (1988), unpublished data.

General Reading Feldmann, L. C , Mayer, J. M. (1986), Fundamentals of Surface and Thin Film Analysis. Amsterdam: North-Holland. Galeener, F. L., Griscom, D. L., Weber, M. J. (1986), Defects in Glasses. MRS Symp. Vol. 61. Griscom, D. L. (1976), Defects and Their Structure in Nonmetallic Solids: Henderson, B., Hughes, A. E. (Eds.). New York: Plenum, p. 323. Shen, Y. R. (1984), The Principles of Non-Linear Optics. New York: John Wiley. Wong, X, Angell, C. A. (1976), Glass Structure by Spectroscopy. New York: Dekker.

7 Chalcogenide Glasses Stephen R. Elliott Department of Chemistry, University of Cambridge, Cambridge, U.K.

List of 7.1 7.1.1 7.2 7.2.1 7.2.2 7.2.3 7.3 7.3.1 7.3.1.1 7.3.1.2 7.3.1.3 7.3.2 7.3.2.1 7.3.2.2 7.3.3 7.3.3.1 7.3.3.2 7.3.3.3 7.3.3.4 7.3.3.5 7.3.3.6 7.4 7.4.1 7.4.2 7.4.3 7.4.4 7.4.4.1 7.4.4.2 7.5 7.5.1 7.5.2 7.5.3 7.5.4

Symbols and Abbreviations Introduction Classification of Amorphous Chalcogenide Materials Preparation of Amorphous Chalcogenide Materials Melt Quenching Vapour Deposition Other Preparation Methods Structure Definitions Short-Range Order Medium-Range Order Long-Range Structure General Aspects of the Structure of Amorphous Chalcogenide Materials . . SRO in Chalcogenides MRO in Chalcogenides Structure of Specific Amorphous Chalcogenide Materials Structure of Pure Chalcogens Structure of V-VI Materials Structure of IV-VI Materials Structure of III-VI Materials Metal Chalcogenide Materials Structure of Halogen Chalcogenides Defects Introduction Wrong Bonds Coordination Defects Experimental Probes for Defects Electron Spin Resonance Photoluminescence Opto-Electronic Properties Electronic Structure Optical Properties Electrical Properties Photo-Induced Changes

Materials Science and Technology Copyright © WILEY-VCH Verlag GmbH & Co KGaA. Allrightsreserved.

377 380 380 381 381 389 391 391 391 391 393 395 395 395 396 401 401 403 409 414 414 416 416 416 417 420 423 423 425 427 427 428 432 438

376

7.6 7.6.1 7.6.2 7.6.3 7.6.4 7.6.5 7.7

7 Chalcogenide Glasses

Applications Infrared-Transmitting Optical Components Xerography Lithography Solid Electrolytes Threshold and Memory Switching References

441 441 442 444 445 446 448

List of Symbols and Abbreviations

377

List of Symbols and Abbreviations D

DJQ) d EA EF Eg E« Es Ea E" e /»(Q) G{E) g g(E) i k m N Nd n pNL

Q Qn r

s S(Q) S(Q,co) T T% U

vB vth w X

characteristic coherence length molecular-packing structure factor spatial repeat distance valence band edge Fermi energy (level) bandgap viscosity activation energy thermopower activation energy conductivity activation energy configuration of edge-sharing tetrahedra (ft = 0-2) electronic charge molecular form factor vibrational density of states (eV"1) Lande ^-factor electronic density of states (eV" 1 cm" 3 ) current Boltzmann constant average coordination number number of valence electrons per atom number of mechanical constraints number of degrees of freedom refractive index coordination number non-linear electronic polarizability scattering vector configuration of coordination polyhedron in terms of number n of bridging ligands load resistor bond length thermopower structure factor dynamic structure factor temperature glass-transition temperature quench temperature effective correlation energy strain potential energy voltage applied by a bias battery holding voltage threshold voltage electronic hopping energy mole fraction

378

7 Chalcogenide Glasses

a a~* as P y F s r\ rja 9 ju n Q a•a-* X co

optical absorption coefficient electron localization length bond-stretching force constant bond-bending force constant temperature coefficient of b a n d g a p Urbaeh-edge parameter dielectric constant viscosity asymmetry parameter of electric-field gradient tensor b o n d angle electronic drift mobility Peltier coefficient electrical resistivity bonding orbital antibonding orbital d.c. electrical conductivity pre-factor for d.c. conductivity a.c. conductivity dihedral angle electronegativity radial frequency

aC CBH COCRN CON CRN CVD CW DOS EPR ESR EXAFS FSDP gIR IRMRO IVAP LP LRMRO LRS MAS MD MHC

amorphous chalcogen correlated barrier hopping chemically ordered continuous random network chemically ordered network continuous random network chemical vapour deposition continuous wave density of states electron paramagnetic resonance electron spin resonance extended X-ray absorption fine structure first sharp diffraction peak glassy infra-red intermediate-range medium-range order intimate valence-alternation pair lone pair (non-bonding) orbital long-range medium-range order long-range structure magic-angle spinning molecular dynamics minimum holding current

List of Symbols and Abbreviations

MRO NB NBO NMR NQR ODMR P PECVD PL PLE RCN RDF RI SRMRO SRO STAG STE T TPC UV UPS VAP VB VDOS XPS 1D 2D 3D

medium-range order non-bridging non-bridging oxygen nuclear magnetic resonance nuclear quadrupole resonance optically-detected magnetic resonance pnictogen plasma-enhanced chemical vapour deposition photoluminescence photoluminescence excitation random covalent network radial distribution function refractive index short-range medium-range order short-range order Si~Te-As-Ge alloy self-trapped exciton tetragen transient photoconductivity ultra-violet ultra-violet photoemission spectroscopy valence-alternation pair valence band vibrational density of states X-ray photoemission spectroscopy one-dimensional two-dimensional three-dimensional

379

380

7 Chalcogenide Glasses

7.1 Introduction Chalcogenide materials are compounds containing elements from Group VI (B) of the Periodic Table, viz. S, Se, Te. Strictly speaking, oxides should also be included in this category, but they are often considered separately. There are two reasons for this division, one historic and one scientific. Oxide materials, particularly those based on silica, are the oldest-known glass-forming systems, and it has become traditional to treat them separately from the more recently discovered chalcogenide materials. Furthermore, although oxygen is also a Group VI element, the physical behaviour of oxides is often rather different from that of chalcogenides, principally because the former have a much more significant ionic contribution to the chemical bonding than the latter, which are essentially completely covalent materials (in the absence of network-modifying cations). For example, oxides are generally insulators, with large values of the bandgap (~ 10 eV in the case of SiO2), whereas for chalcogenides the gap is generally considerably smaller (1-3 eV), and hence these materials are semiconductors. Chalcogenide materials are of interest for a variety of reasons: they can be prepared in amorphous form in a variety of ways, either as vapour-deposited thin films or as melt-quenched glasses; they mostly form glasses continuously over wide composition ranges, the physical properties of which also vary in a continuous fashion; they exhibit behaviour which is often unique; finally, there are a number of actual and potential technological applications of such materials. In spite of the undoubted importance of chalcogenides as a major category amongst amorphous materials, there have been few previous reviews devoted entirely

to general properties of these materials, with the exception of the book by Borisova (1981); glass-formation aspects have been emphasized in the book by Rawson (1967) and the review by Kreidl (1983), and the physics of chalcogenide materials (as well as that of other amorphous solids) has been discussed by Elliott (1984, 1990) and Zallen (1983). In this review, we will follow the nomenclature proposed by Elliott (1984, 1990), namely that the term amorphous (or equivalently, non-crystalline) applies generally to those materials lacking the long-range translational periodicity characteristic of crystals, whereas the term glassy (or equivalently, vitreous) is reserved only for those amorphous materials (not necessarily produced by melt-quenching) which exhibit a glass transition, i.e. a discontinuity in heat capacity, or a change in slope of the density, at the glass-transition temperature, Tg. 7.1.1 Classification of Amorphous Chalcogenide Materials

A number of families of chalcogen-containing amorphous systems can be distinguished (see Table 7-1). Simplest amongst these are materials consisting either of a single chalcogen (C) element (e.g. S, Se, Table 7-1. Categories of amorphous chalcogenide systems. Class 1. Pure chalcogen 2. Pnictogen-chalcogen (V-VI) 3. Tetragen-chalcogen (IV -VI) 4. Ill-VI 5. Metal chalcogenide 6. Halogen-chalcogenide

Examples S, Se, Te, SxSe1_x As 2 S 3 , P2Se SiSe2, GeS2 B2S3, I n ^ e ! _ x MoS 3 , WS 3 , Ag 2 S-GeS 2 As-Se-I, Ge-S-Br, Te-Cl

7.2 Preparation of Amorphous Chalcogenide Materials

Te) or alloys or compounds of two such chalcogens. (The conditional glass-former, TeO2 - viz. a material which by itself does not form a glass, but which does when alloyed with another material - could also be considered to be a member of this family.) Two common chalcogenide systems consist of V-VI materials, i.e. compounds with pnictogen (P) atoms from Gp VB (e.g. P, As, Sb), where the glass-forming regions are mostly centred around the stoichiometric composition P 2 C 3 , and compounds with Gp IVB elements, i.e. Si, Ge (denoted tetragens, T, in view of the prevalent tetrahedral coordination associated with such elements), where binary glass-forming I V VI compositions are centred around the composition TC 2 , i.e. analogues of silica, SiO 2 . In addition, amorphous binary III— VI compounds can be formed with elements from Gp III B . Of course ternary (or higher) compounds within each of the above categories can also be made amorphous (e.g. As-S-Se), as well as ternary (or higher) compounds between categories (e.g. Ge-As-Se). Binary metal chalcogenide systems are rather rare, exceptions being the compounds with the Gp VIA metals molybdenum and tungsten, viz. MoS 3 , WS 3 or the selenium analogues, which are unusual in that they can only be prepared in amorphous form (see Sec. 7.2.3). More frequently, monovalent metals such as the alkalis (Gp IA) or the Gp IB elements, Cu and Ag, can be incorporated as a ternary component to form amorphous chalcogenide compounds. Finally, halogens (e.g. Cl, Br or I) from Gp VIIB can also be incorporated in chalcogenide materials, e.g. in the binary system Te-Cl, or its ternary derivatives (Zhang et al, 1988) or as ternary components in Ge- or As-chalcogenide systems (Sanghera et al, 1988).

381

It can be seen from the discussion above that the range of possible chalcogenide materials forming amorphous solids is essentially infinite in extent, taking into account the fact that, in general, the composition of materials within a particular class of chalcogenide can be varied over a wide range whilst still retaining an amorphous structure, and also the possibility of forming multicomponent systems, i.e. involving combinations of the classes shown in Table 7-1, allows very many other permutations of composition to be achieved.

7.2 Preparation of Amorphous Chalcogenide Materials Very many methods can be used to produce chalcogenide materials in an amorphous form, some of which lead to bulk materials, whilst others yield thin films deposited upon a substrate. The compositional range for which chalcogenide materials can be rendered amorphous depends on the preparation method used, the more rapid vapour-quenching (thin film) techniques in general permitting a wider composition range to be produced in non-crystalline form than is the case for those methods producing bulk material, notably melt-quenching. 7.2.1 Melt Quenching

The technique of preparing bulk glasses by means of rapid quenching of a melt is historically the most established and is still the most widely used in the preparation of amorphous chalcogenide materials. Very many chalcogenide materials are, in fact, good glass formers and the melts of such materials, held in sealed evacuated (silica) ampoules, will often vitrify when cooled relatively slowly ( ^ l - l O O K s ^ 1 ) by quenching in either air or water. More

382

7 Chalcogenide Glasses

rapid quenching techniques have also been used, e.g. roller-quenching for Sb 2 S 3 (Cervinka and Hruby, 1982) and melt-spinning for Te-Se, Ge-Se, and Te-Ge alloys (Dembovsky et al., 1987) (see also Chap. 2). Glass formation, however, is a poorlyunderstood phenomenon, and many factors appear to be important in determining whether or not a particular material readily vitrifies. The overwhelming consideration, of course, is the avoidance of crystallization in the quenching process; thermodynamic, kinetic and structural factors can influence this process. Thermodynamic aspects relating to the melt can sometimes be important; for instance, Rawson (1967) has emphasized the fact that the sharp decrease in the liquidus temperature associated with eutectic formation in alloys facilitates glass formation for compositions straddling the eutectic composition due to the relatively low amount of thermal energy present in such melts which is available for atomic migration and which could lead to the formation of crystalline nuclei. However, in chalcogenide materials, such behaviour does not seem to be prevalent; instead, compound formation and the resulting atomic structure seem to be the dominant controlling influences. For example, Fig. 7-1 shows the phase diagram for the As^Se^,, system, whence it can be seen that the liquidus temperature exhibits a pronounced maximum at the stoichiometric composition x = 0.4, corresponding to the compound As2Se3, in which the structure can be completely chemically ordered, viz. each type of atom exerts its normal valence (As = 3, Se = 2) with unlike atoms as nearest neighbours (see Sec. 7.3). This composition also corresponds to that at which the glass-forming ability is optimum, as evidenced by the maximum in the glass-transition temperature, Tg, at the same composition (Fig. 7-1).

100 -

at% As

Figure 7-1. Phase diagram for the As-Se system (Kadoun et al., 1983). The dashed zone is the range of measurements. The compositional dependence of the glass-transition temperature is given by the open and filled circles.

Another important quantity which affects glass-forming ability is the viscosity of the melt. Generally speaking, the more viscous the melt at a given temperature above the melting point, the greater is the propensity for glass formation. On cooling (and ultimately supercooling) the melt, the viscosity rj invariably increases even fur-

383

7.2 Preparation of Amorphous Chalcogenide Materials

ther since it is usually thermally activated, viz. i, = i/oexp(£lf/fcr)

(7-1)

Consequently crystal formation is kinetically constrained, since the necessary atomic mobility in the liquid to form crystallites becomes increasingly difficult. In this regard, the compositional dependence of the isothermal viscosity of the system As x S 1 _ x is of interest (Fig. 7-2a), for which three regions can be distinguished: a pronounced maximum of r\ occurs at x = 0.4 (II), with Y\ rapidly decreasing to a very low value at an As content of JC^O.5 (region I), whilst on the S-rich side of the stoichiometric composition, the viscosity decreases more slowly (region III) (Chaussemy et al., 1983). This behaviour for rj is due to a similar compositional dependence of the viscosity activation energy (Fig. 7-2 b). Similar, but smaller, anomalies in the viscosity at the stoichiometric composition are also observed in the chemically similar system As^Se^^ (Kadoun et al., 1983). The compositional dependence of the isothermal viscosity can be understood in terms of the dominant structural moieties present in the liquids of these binary arsenic chalcogenides at a given composition (Fig. 7-3). The addition of As atoms to the pure chalcogen (sulfur or selenium) structure causes the chains therein to become increasingly cross-linked by the threefold coordinated As atoms (Fig. 7-3 a); as a result, the viscosity steadily increases with increasing As content (region III of Fig. 7-2 a). This process continues until the stoichiometric composition (x = 0.4) is attained, for which (ideally) the structure is completely chemically ordered (Fig. 7-3 b) and the viscosity is a maximum (region II of Fig. 7-2 a). At still higher As contents, discrete molecular species, e.g. As 4 S 4 for

0.001

Figure 7-2 a). Compositional dependence of the isothermal viscosity of As^S^^ liquids at 900 K, calculated (dashed line) and experimental values (vertical bars) (Chaussemy et al., 1983).

En(eV)

,

,

_

r

1 1.0

0.5

0

[ -

*

AsxS1_x

|

v=v o exp(E n /kT)

-4 , 0.5

0.6

i

i

0.7

0.8

.. ..

1-x

Figure 7-2 b). Compositional dependence of the viscosity activation energy, E^, for liquid As x S!_ x (Chaussemy et al., 1983).

the As^Sj _x system (Fig. 7-3 c) increasingly are formed which, being almost spherical and therefore contributing little to the viscosity, cause the precipitate drop in rj at x^0.45 (region I of Fig. 7-2 a). (Since the As 4 S 4 molecule is thermodynamically more stable than the As4Se4 entity, this accounts for the fact that in the As^Se^^ system a pronounced drop in rj for x > 0.45 is not observed, but only a small dip at x^0.5 - the structure of the melt in this case is still extensively cross-linked with

384

7 Chalcogenide Glasses

©As OX a high proportion of wrong As-As bonds (Kadoun et al., 1983).) This behaviour of the viscosity of the melt, and its microscopic cause in terms of the structure of the liquid, is consequently responsible for the glass-forming region in the As^S^^ (0<x<0.43) system being appreciably smaller than that for the AsxSe1 _x system (0<x <0.57). The spherical nature of the As 4 S 4 molecules means that there are insufficient steric constraints present to prevent As-rich As-S melts solidifying into a crystalline (realgar) structural arrangement on cooling. Similar considerations apply also to the ^xSex _x system, in which the quasi-spherical P 4 Se 3 molecule is also very stable thermodynamically. As a result, melts with this composition (x = 0.57) cannot be vitrified, and this composition in fact divides two glass-forming regions, viz. 0 < x < 0 . 5 and 0.63 < x < 0.85, the latter being centred around the composition P2Se (Borisova, 1981). Another factor that can influence the glass-forming ability of chalcogenide materials concerns the kinetics of the quenching process: in general, the faster the rate of quenching of a melt, the greater is the likelihood of forming a glassy and not a crystalline product. Thus, some materials can only be produced as bulk glasses with

Figure 7-3. Structural configurations in the As x X 1 _ x (X = S, Se) system (Kadoun etal, 1983). a) As crosslinks in chalcogen-rich material; b) stoichiometric, chemically ordered structure (x = 0.4); c) As4X4 quasi-spherical molecule.

extreme difficulty, and then only using very high quenching rates; an example is As2Te3 which, unlike its chemical analogues As 2 S 3 and As2Se3, is very difficult to vitrify. A further factor controlling glass-forming ability can be regarded in terms of a process of frustration; that is crystallisation in a multicomponent melt is prevented from occurring readily, either by a competition between the formation of several different types of crystal (with different compositions) or simply due to the (entropic) difficulty of rearranging many different types of atoms to form a multicomponent crystal. Thus, whilst in some cases glass formation is difficult, in the case of say binary compositions (e.g. As2Te3), the addition of a third (or additional) element usually leads to an appreciable improvement in glass-forming ability (e.g. Si-As-Te alloys readily form glasses over rather a wide range of compositions). In the case of ternary compositions, the glass-forming region (for a given quenching rate) can be represented in a triangular, two-dimensional plot. Fig. 7-4 shows the glass-forming regions of the Ge-Aschalcogenide (S, Se, Te) system; it can be seen clearly that, whilst the sulphide and selenide materials are both good glassforming materials (i.e. the areas enclosed by the glass-formation boundaries are ex-

385

7.2 Preparation of Amorphous Chalcogenide Materials

S(SeJe)

20

40

60

80

complicated. For instance, for the case of a quaternary compound, a three-dimensional figure (tetrahedron) is required; an example is shown in Fig. 7-6 for the case of the Hg-Ge-Se-Te system (Feltz and Burkhardt, 1980). Chemical factors can also determine the ease of glass formation for chalcogenide materials. Thus, it is generally found that glass formation becomes progressively more difficult as an element in a given group of the periodic table is substituted by heavier elements in the same group. This trend has already been seen in the case of chalcogen substitution (S-»Se->Te), but it is also true, for example, for the case of pnictogens. In general, only a few atomic percent of Bi can be incorporated in a multicomponent chalcogenide material before devitrification occurs, whereas a few tens of percent of Sb can be so introduced (see Fig. 7-7); in contrast, As-containing glasses are generally relatively much better glass formers (see Fig. 7-4). One possible reason for this decrease in glass-forming tendency with increasing metallicity (or equivalently atomic number in a given group of the periodic table) stems from the fact that, in general, heavy

As

Figure 7-4 Glass-formation regions in the systems 1) Ge-As-S; 2) Ge-As-Se; 3) Ge-As-Te (Borisova, 1981).

tensive and comparable), the glass-forming ability of the ternary telluride system is somewhat worse than that of the S- or Seanalogues (and limited to two glass-forming regions), but nevertheless glass formation is easier than for the binary As-Te system. Fig. 7-5 shows further examples of glass-forming regions in ternary I V - V - VI systems. In the case of materials with more than three components, representation of the glass-forming regions becomes much more

Si,Ge

80, 20

40

60

80

P

Te

20

40

60

80

As,P

Figure 7-5. Glass-formation regions in the systems 1) Ge-P-S; 2) Ge-P-Se; 3) Ge-P-Te; 4) Si-As-Te; 5) Si-P-Te; 6) Ge-As-Te (Borisova, 1981).

386

7 Chalcogenide Glasses

HgSi

Figure 7-6. Glass-formation region in the quaternary system Hg-Ge-Se-Te between the Hg-Ge-Se front plane and the Ge-Se-Te basal plane of the tetrahedron (Feltz and Burckhardt, 1980). E^^ and E 2 are eutectics. Glass-formation regions in the sub-system (A) HgSe-GeSe-GeSe 2 , (B) HgTe-GeSe-GeSe 2 , and (C) HgTe-GeTe-GeSe 2 are also indicated.

Figure 7-7. Glass formation region in the systems (1) Bi-Ge-S and (2) Sb-Ge-S (Borisova, 1981).

elements such as Sn or Pb, Bi and Te tend to adopt structures (in the crystalline state) with high coordination numbers, e.g. (quasi-) octahedral rather than trigonal or tetrahedral, as a result of the delocalization of the bonding charge associated with the

increased metallicity. The empirical rules for glass formation proposed by Zachariasen (1932) asserted that glass formation was favourable only for those materials whose structure consists of cation-centred polyhedra having a small number (three or four) of anionic ligands (in this case chalcogen atoms) surrounding a cation such as Ge or As etc. Cooper (1978) has shown that these rules in fact arise from topological considerations; topological disorder can readily be introduced into structures consisting of corner-sharing triangular or tetrahedral polyhedra, and even also into one consisting of such polyhedra connected together in an edge-sharing fashion (thereby forming chains), but not if connection between such small polyhedra is by means of sharing of faces, or if large (e.g. octahedral) polyhedra constitute the structural units (even with corner-sharing connections). In the latter cases, insufficient degrees of geometrical freedom remain after the connections between units (polyhedra) are all satisfied for disorder to be introduced and consequently only crystalline structures are possible. (Structural aspects of chalcogenide materials are dealt with in more detail in Sec. 7-3.) Finally, the glass-forming ability of chalcogenide materials can be discussed in terms of constraint theory (Phillips, 1979). Most inorganic, covalently-bonded glassforming systems have relatively low values of (average) coordination number-chalcogenides are a canonical example. The propensity for glass formation can then be understood in terms of the mechanical constraints, i.e. the degrees of freedom associated with bond-stretching and bondbending interactions, in a perfectly connected structure. An atom having all covalent bonds satisfied obeys the so-called 8 —JV rule (Mott, 1967), where N is the number of valence

7.2 Preparation of Amorphous Chalcogenide Materials

387

electrons and the coordination number nc is given by the relation

a sum of contributions from bond-stretching and bond-bending forces:

nc = 8 - N

C/s = ia 8 Ar 2 + ±j8rgA02

(7-2)

Strictly speaking, this relation is only valid for elements from Groups IV-VII of the periodic table, although Liu and Taylor (1989) have generalised this expression taking account of (formal) charge-transfer effects. Thus, a chalcogen (from Group VI) will have a coordination number nc = 2. For a binary alloy AXB1_X, the average coordination number, m, is given by

(l-x)nc(B)

(7-3)

In general, of course, m is non-integral; for example, for GeSe2 m = 2.67 and for As 2 S 3 m = 2.4. Thus, m can be regarded as being the coordination number of a hypothetical pseudoatom forming a structure whose topology is identical to that of the real material. Phillips (1979) proposed that glass-forming tendency is maximised when Nc = Nd

(7-4)

where Nc is the number of (mechanical) constraints, Nc, experienced by each atom (due to the interatomic forces acting on it), and Nd is the number of available degrees of freedom. The number of constraints per atom depends on the coordination number, and the number of degrees of freedom is related to the spatial dimensionality of the system. A material is said to be overconstrained if Nc> Nd, and cannot then easily form a glass (by quenching from a melt), although an amorphous structure may still be obtained by employing very rapid (vapour) quenching techniques. The mechanical constraints experienced by an atom can be considered in terms of the interatomic forces acting on an atom in the valence-force-field model, in which the (strain) potential energy Us is expressed as

(7-5)

where as and f} are the bond-stretching and bond-bending force constants, respectively, and Ar and A6 represent small deviations in bond length and bond angle from the equilibrium values for the bond length, r 0 , and bond angle, 0O. For a binary alloy, AXB±-X9 there is only one bond-stretching interaction (as), but there are two bond-bending force constants, ft (BAB) and p (ABA), for bending motions centred on atoms A and B, respectively. For simplicity it is assumed at the outset that p(BAB) = p(ABA)9 and that all three force constants act as rigid mechanical constraints. Then, the number of constraints per pseudoatom is given by (Phillips, 1979): ATC = m/2 + m(m-l)/2 = m2/2

m^Nd-l

where the first term is associated with as interactions (the factor of \ arises because a bond-stretching mode involves two atoms) and the second term arises from P interactions. Eq. (7-6) is only valid for m ^ JV d -l (Dohler et al., 1980). Otherwise, the fact that Nd + 1 bond angles (in JVd-dimensional space) are not linearly independent must be taken into account (Dohler et al., 1980). For a two-fold coordinated atom (such as a chalcogen), there is one angular constraint associated with the second term in Eq. (7-5), whereas adding each additional bond gives two more constraints because the angles with two existing bonds must be specified (Thorpe, 1983). This yields

Nc = m/2 + (Nd-l)(2rn-Nd)/2

m^Nd-l

For ideal glass formation, iVc = Nd (Eq. (7-4)), and so from Eq. (7-7) the optimum

388

7 Chalcogenide Glasses

average coordination number is given by -1 (7-8) For a system in 3D space, Nd = 3, and so from Eq. (7-8) mc = 2.4. Thus, the stoichiometric composition for V-VI materials, e.g. As 2 S 3 , corresponds, in this picture, to the optimum glass-forming condition itself; experimentally, this appears to be the case (Fig. 7-1). For IV-VI materials, such as Ge^Se! _ x , use of Eq. (7-3) together with Eq. (7-8) yields for the optimum glassforming composition xc = 0.2, i.e. GeSe 4 . The tendency for glass formation in this system has been investigated experimentally by finding for each composition the minimum quenching rate needed to avoid crystallization, and this is shown in Fig. 7-8 for three quenching methods, viz. waterquenching, air-quenching and slow-cooling. It does appear that the optimal glassforming composition corresponds to a state of mechanical stability rather than chemical stability (i.e. at the compound composition GeSe2). Chemical stability

Mechanical stability

Glass-forming difficulty

I

Water quenching Air quenching

Slow cooling 30 GeSe2

20 A t %

10 Ge

0 Se

Figure 7-8. Glass-forming ability (tendency) in the Ge^Se^^ system (Elliott, 1990). Experimental data are indicated by solid horizontal bars for various rates of cooling (water, air and slow quenching). The solid line is drawn through the data to guide the eye; the prediction of Phillips' mechanical constraint theory is shown by the dotted line.

Table 7-2. Glass-transition and melting temperatures for some chalcogenide materials. Material

Tg(K) Reference

S Se As 2 S 3 As2Se3 As2Te3 GeSe2 GeS2

246 318 478 468 379 695 765

1 2 2 2 3 2 4

rm(K)

Reference

392 490 573 633 633 980 1073

1 1 5 5 6 5 6

References: 1) Van Uitert, L. G. (1979), I Appl. Phys. 50, 8052; 2) de Neufville, I P . and Rockstad, H.K. (1974), in: Proc. 5 th Int. Conf. on Amorphous and Liquid Semiconductors: Stuke, J. and Brenig, W. (Eds.). Taylor and Francis, p. 419; 3) Seeger, C.H. and Quinn, R.K. (1975), J. Non-Cryst. Sol. 17, 386; 4) Wright, A.C., Etherington, G., Erwin Desa, J.R., Sinclair, R.N., Connell, G.A.N., and Mikkelson, J.C. (1982), /. Non-Cryst. Sol. 49, 63; 5) Weast, R.C. and Astle, M. J. (Eds.) (1980), Handbook of Chemistry and Physics (61st edn). CRC; 6) Trotman-Dickensen, A.F. (Ed.) (1973), Comprehensive Inorganic Chemistry, Vol. 2. Pergamon.

However, this simple model has to be treated with some caution, for it predicts that glass formation in the Si^C^ _x system should also be favoured at x = 0.2, instead of the stoichiometric composition x = 0.33 (viz. SiO2) as is found experimentally. This contradiction can be circumvented by noting that the distribution of Si-O-Si bond angles is rather wide, and so the constraints associated with these bond angles should be relatively weak; if these are neglected, Eq. (7-8), suitably modified, then yields xc = 0.33 (Thorpe, 1983). Tanaka (1989 b) has also modified the constraint model to take account of the presence of 2D-like MRO, and obtains the value mc = 2.61.

Finally, in this section dealing with glass formation of chalcogenide materials, values for the glass-transition temperature Tg for various representative materials are given in Table 7-2.

7.2 Preparation of Amorphous Chalcogenide Materials

7.2.2 Vapour Deposition

Although the technique of melt quenching is much used to prepare chalcogenide materials in bulk glassy form, there are also several techniques based on vapourdeposition methods which can yield amorphous thin films deposited onto substrates (see Chap. 2). These techniques can be regarded as having extremely fast quenching rates and therefore can be used to produce chalcogenide materials in amorphous form which are difficult to vitrify (e.g. As2Te3) or to extend the compositional range for which a given system can be made amorphous compared with that attainable using conventional melt-quenching techniques. Such vapour-deposition techniques can be divided into two categories, depending on whether the process involved is physical in nature, i.e. atomic or molecular species are converted into the vapour phase from either solid or liquid sources with no chemical modification, or alternatively reactive, in which either the vapour species are chemically modified with respect to the source material or a solid-vapour reaction occurs in the condensation process of the vapour on the substrate. Thus, three different vapour-deposition techniques can be identified which can fall into either or both of the above categories: these are evaporation, sputtering and chemical vapour deposition. Thermal evaporation is perhaps the simplest vapour-deposition technique, and involves resistive or electron-beam heating in vacuo of a boat containing the material to be evaporated; the melt so produced then evaporates and the vapour is condensed onto a substrate, forming a thin amorphous film if the adatom mobility is sufficiently restricted to preclude atomic reconstruction leading to crystallization. Chalcogenides are particularly suitable mate-

389

rials for use in evaporation deposition because of their relatively low melting points (see Table 7-2); the technique is widely used, as for example in the deposition of the selenium-rich alloys onto cylindrical drums used until recently as the photosensitive component in the xerographic process. However, a number of complications can arise in the use of this technique. One such concerns differential evaporation, in which the various elements in a (non-compound) multicomponent melt can evaporate at substantially different rates due to the differing melting temperatures and hence vapour pressures of the constituents. As a result, the chemical composition of the deposited thin film can differ appreciably from that of the melt and also vary significantly through the thickness of the film. This problem is obviously exacerbated for the case of those materials containing both high and low melting point elements, e.g. the so-called STAG (Si-Te-AsGe) alloys showing electrical switching behaviour. In order to obviate this problem, the variant, termed flash evaporation, may be used, in which powder of the material to be evaporated is dropped from a hopper onto a very hot filament, and the material is thereby volatilized almost instantaneously; since a melt-vapour equilibrium is not established in this process, differential evaporation effects can be minimised. A further complication can arise in the case of thin evaporated films deposited at oblique angles of incidence which, in certain cases (particularly where adatom mobility on the surface of the substrate is minimised), can be structurally inhomogeneous. A shadowing effect of material on the substrate for incoming evaporant atoms incident at an oblique angle of incidence leads to the formation of a columnar-growth morphology (see Fig. 7-9). In

390

7 Chalcogenide Glasses

Evaporation source

\

I

Film

Figure 7-9. Schematic illustration of the formation of a columnar growth morphology for thin films evaporated at oblique angles of incidence. Note that the columns do not lie parallel to the evaporation beam direction.

general, the direction of the columns in the films (at an angle /? to the film normal) and the evaporant beam direction (at an angle a) do not lie parallel to each other; instead they are found to obey the empirical relation (Leamy et al., 1980) tana = 2 tan/?

(7-9)

This effect is observed for many different types of evaporated materials (see Leamy et al., 1980 for a review). In chalcogenide materials, it is particularly prevalent for the Ge chalcogenides (Rajagopalan et al., 1982; Spence and Elliott, 1989), but curiously seems to be much less pronounced for the case of, say, the As chalcogenides. Consequently, the film porosity increases and the density decreases as the angle of incidence of the evaporant beam (a) increases (Rajagopalan et al., 1982; Spence and Elliott, 1989). Such obliquely-evaporated chalcogenide films possessing a columnar microstructure exhibit enhanced photostructural effects (see Sec. 7.5.4). A final complication which can arise in thermal (but not flash) evaporation concerns the possible formation of stable molecular vapour species, and the possible effect this has on the final composition and structure of the evaporated film. As an example, the equilibrium vapour above a melt of As 2 S 3 consists primarily of As 4 S 4

(and S2) molecules; the relative stability of the quasi-spherical As 4 S 4 molecules has been commented upon already in Sec. 7.2.1. Thus, the structure of as-evaporated films of amorphous "As 2 S 3 " in fact consists of an aggregate of such As 4 S 4 molecules (Apling etal, 1977; Daniel et al., 1979, 1980), and the composition of the films can differ from that of the starting material (e.g. As2S3) if the lighter molecular species (e.g. S2) are pumped away before they can condense onto the substrate. Such as-evaporated chalcogenide films are also unstable with respect to thermal annealing or optical illumination (see Sec. 7.5.4), such treatment causing the rupture of bonds within the cage-like As 4 S 4 molecules and subsequent reformation to form a more nearly cross-linked structure (Nemanich et al., 1979). The technique of sputtering is also widely used to prepare amorphous thin films of chalcogenides. In this, an r.f. electric field (in the case of non-metallic materials such as chalcogenides) is applied between the target material and the substrate in a vacuum chamber in which a low pressure of an inert gas (e.g. Ar) is present at a pressure of ~10mTorr. After a plasma is struck, ions are accelerated by the field onto the target, material from which is then (physically) sputtered away and condenses onto the substrate. The advantage of this technique is that differential deposition rates for multicomponent systems are much lower than for the case of evaporation because sputtering rates are comparable for most elements; thus, r.f. sputtering has been used to deposit STAG and similar component chalcogenide films. Furthermore, this technique is advantageous in that reactive sputtering can take place when a reactive gas, e.g. hydrogen, is introduced into the sputtering chamber, and which then can react chemically with the material sput-

7,3 Structure

tered from the target, and be incorporated into the growing film. Finally, another technique which can be used to deposit thin films from the vapour phase is chemical vapour deposition (CVD). In its simplest form, precursor materials in the vapour phase either decompose or react together in a heated reactor tube or on a heated substrate; the reactions involved can be homogeneous (nucleated in the gas phase) or heterogeneous (occurring at the surface of the substrate). A variant uses plasma enhancement (PECVD), or equivalently glow discharge decomposition, in which plasma excitation rather than thermal energy provides the driving force for the reaction. There have been a few reports of chalcogenide materials prepared using PECVD, namely films of As 2 S 3 : H and As 2 Se 3 : H prepared by the glow-discharge decomposition of mixtures of AsH 3 with H 2 S or H2Se, respectively (Smid and Fritzsche, 1980), and Ge-Se films prepared from GeCl 4 and Se2Cl2 (Blanc and Wilson, 1985). 7.2.3 Other Preparation Methods A number of other techniques can be used to prepare chalcogenide materials in amorphous form, many of which are only of academic interest. The simple act of grinding a powder can introduce such a degree of shear-induced strain that crystals are transformed into an amorphous phase; this effect occurs for the case of GeSe 2 , for example. The solid precipitated products of reactions occurring in solution can also be amorphous. Thus, a-As2S3 is formed by passing H 2 S gas through a solution of As 2 O 3 in dilute hydrochloric acid. Similarly, powdered a-WS3 and a-MoS 3 can be produced by the thermal decomposition of ammonium tetrathiotungstate (Deroide et al, 1986) or tetrathiomolybdate (Bhat-

391

tacharya et al., 1987) or the acid-catalysed decomposition of solutions of these compounds. Finally, thin films of chalcogenides have been prepared by spin-coating, i.e. by placing on a substrate a solution of a chalcogenide material dissolved in a suitable solvent, rapidly spinning the substrate to produce a thin uniform film of the liquid and then finally evaporating the solvent to leave a solid chalcogenide layer. This technique has been used by Hajto et al. (1987) to prepare thin films of a-As2S3 using anhydrous n-propylamine as a solvent.

7.3 Structure 7.3.1 Definitions In order properly to discuss the structure of amorphous chalcogenide materials, it is necessary at the outset to outline a framework within which the structural features can be described. With this in mind, it is convenient to consider the structure on three different ascending length scales according to the scheme proposed by Elliott (1990) (see also Chap. 4 and Vol. 1 of this series). 7.3.1.1 Short-Range Order In covalently-bonded amorphous materials with strongly directed bonding, such as chalcogenides, short-range order (SRO) can be defined in terms of rather welldefined coordination polyhedra (see Fig. 7-10). Thus the parameters which are sufficient to describe topological SRO are the type and number Nj of nearest neighbours j around an origin atom of type i, the nearest-neighbour bond length rtj, the bond angle subtended at atom i, 6t, and the corresponding quantities when atom j is regarded as the origin, viz. Nt and 9j. Thus, this description involves both two and

392

j

7 Chalcogenide Glasses

J

Figure 7-10. Short-range order of covalent materials in terms of coordination polyhedra.

three-body correlation functions associated with rtj and 6j9 respectively. Note that in this description of SRO, nothing is said about the connectivity of the coordination polyhedra (e.g. corner-, edge- or facesharing); the form of connection of the polyhedra essentially determines the type and extent of the medium-range order (see Sec. 7.3.1.2). An additional parameter is required if the degree of chemical SRO also needs to be described, e.g. when different types of atoms constitute the coordination polyhedron centred on a given origin atom. Thus, for non-stoichiometric compositions, for example, excess atoms must be accommodated by the introduction of wrong, i.e. homopolar, bonds (in the absence of coordination or valence changes), breaking thereby the chemical order (i.e. heteropolar bonding) which might otherwise occur at the stoichiometric composition; the parameter of relevance here would then be the proportion of wrong bonds. A related type of chemical SRO is when the different types of atomic species in the coordination shell around a given origin atom are in fact the same element, but such atoms may have a different charge state, bonding connectivity, etc. An example of this are the non-bridging ligands introduced into an otherwise fully-bonded structure by the introduction of charged

modifier atoms, e.g. alkali ions or Ag + . Chalcogen (or oxygen) atoms can act as such non-bridging sites, in which case they are singly coordinated and (formally) carry one unit of negative charge (see Fig. 7-11); such sites can be regarded as defects in an otherwise perfectly connected amorphous structure (see Sec. 7.4). Such species can be described by the symbol Qn (first introduced for the case of non-bridging oxygen sites in modified silicate glasses), where n is the number of bridging ligands around a central cation, e.g. 0 < n < 4 for I V - VI materials, and 0 < n < 3 for V-VI materials. NQ2S NQ+S-

-G/'

-A

S

-NQ+

Ge e

\

Figure 7-11. Schematic illustration of the formation of non-bridging chalcogen sites in the Na 2 S-GeS 2 system.

The question of chemical ordering in covalent systems is most simply discussed for the case of binary alloy systems such as A_xB1_:c where, if the elements A and B are in columns a and b of the periodic table, they will have coordination numbers na = & — a and nb = & — b by the 8 —AT rule (neglecting the effect of any coordination defects such as dangling bonds). In general, A-A, A-B, and B-B bonds can coexist in an alloy with an arbitrary composition, and two extreme models can describe the distribution of such bond types (Lucovsky etal, 1977). One model is the random covalent network (RCN) model which treats the distribution of bond types in purely statistical terms, determined only by the local coordinations na and nb and the concentration variable x, and which neglects any preferential ordering effects (e.g. arising from

7.3 Structure

differences in bond energies). The RCN model, therefore, admits A-A, A-B, and B-B bonds at all compositions except at x = 0 and 1. Thus, for a 4 : 2 alloy (e.g. A = Ge, £ = Se), the RCN model predicts the following relations for the numbers of the different types of bond (Lucovsky et al, 1977): = 4(l-x)2/(2-x) NBB=x2/(2-x)

(7-10 a) (7-10 b) (7-10 c)

These bond-counting statistics are shown in Fig. 7-12, together with those for a 3 : 2 system (e.g. AsJCSe1_x). The other model is the chemically-ordered network (CON) model, in which heteropolar A-B bonds are favoured; a completely chemically-ordered phase thus occurs at the stoichiometric composition

A,_,BA

393

3:2

o

Random covalent network Chemically ordered covalent network

*5s c

o

1.4 1.2 1.0 0.8 0.6 0.4 0.2

°°1

0.8

(a)

0.6 0.4 0.2 0.0 <— JT. Atomic fraction B

A.-.B, 4:2 Random covalent network Chemically ordered covalent network 2.0 : 1.8 AB

1.6 1.4 1.2

;

= nj(na •

(7-11)

(e.g. as in As 2 Se 3 , GeS2). In contrast to the RCN model, only A-A and A-B bonds are allowed for ,4-rich compositions (1 > x > x c ) and only B-B and A-B bonds for 0<x<xc. Thus, the bond statistics for the CON model for a 4 : 2 alloy are, for the ,4-rich region = 2-3x N.AB = 2x NBB=0

(7-12 a) (7-12b) (7-12 c)

and for the B-rich region

=

3x-2

(7-13 a) (7-13 b) (7-13 c)

These bond-counting statistics are also shown in Fig. 7-12, together with those for a 3 : 2 network.

1.0 0.8 0.6 0.4 0.2

O.CJ (b)

0.8

0.6 0.4 0.2 * - x. Atomic fraction B

Figure 7-12. Bond-counting statistics (Elliott, 1990) for (a) 3:2 networks (e.g. As 2 Se 3 ) and (b) 4 : 2 networks (e.g. SiO 2 ).

7.3.1.2 Medium-Range Order The question of medium-range order (MRO), or equivalently intermediate-range order, in amorphous materials is currently extremely contentious; even a definition of MRO is subject to much debate (Elliott, 1987; Galeener, 1988; Cervinka, 1987, Lucovsky, 1987) and it is very difficult experimentally to investigate MRO. In this article we will use the definition of MRO

394

7 Chalcogenide Glasses

proposed previously (Elliott, 1987, 1990), which is simply that it is the next highest level of structural organization beyond SRO (see Sec. 7.3.1.1), extending over a length scale of say 5-20 A. In practice, and particularly for covalently-bonded materials, it is convenient to divide MRO into three categories, corresponding to progressively increasing length scales. At the shortest length scale (say 3 - 5 A), short-range MRO (SRMRO) is concerned with the type of connection between, and relative orientation of, pairs of the coordination polyhedra which form the basic structural units in the SRO description given above; SRMRO will be pronounced if the degrees of freedom associated with the relative orientation of pairs of neighbouring polyhedra are restricted in some way, e.g. by the occurrence of edge- (or face-)sharing connections. However, even where polyhedral units are interconnected by corner-sharing, for which free rotation about the common bonds could occur in principle, nevertheless certain orientations may be more favourable than others (e.g. due to steric effects). A structural parameter which is a measure of such orientational correlations for covalent systems with well-defined bonds is the dihedral (or torsion) angle, , defined as in Fig. 7-13 a. This is the angle of rotation about a common bond required to bring into coincidence the projections, onto the plane perpendicular to this bond, of the two bonds either side of the common bond forming parts of the two connected polyhedral units; obviously this is a four-body correlation function (see Fig. 7-13). At the next largest length scale, say 5 10 A, in an hierarchical sense intermediaterange order is determined by the type and extent of SRMRO present. Such intermediate-range MRO (IRMRO) is therefore associated with correlations (i.e. phase rela-

(a)

(b) Figure 7-13. Dihedral angles in covalent networks, (a) Definition of dihedral angle 0 characterising the relative angle of rotation between two neighbouring polyhedra. (b) Correlations between neighbouring dihedral angles.

tionships) between pairs of dihedral angles for neighbouring bonds, i.e. it accounts for triplet correlations between connected polyhedra, or equivalently five-atom correlations (see Fig. 7-13 b). A simple measure of such correlations between dihedral angles involves the two order parameters given by the average sum (Ps) and difference (Pd) of the two dihedral angles for adjacent bonds (Luedtke and Landman, 1989), viz. (7-14a)

7.3 Structure

and (744 b) Thus, a pronounced degree of IRMRO is associated with triplets of coordination polyhedra lying in well-defined relative orientations; this circumstance naturally leads to the presence of super structural units (Elliott, 1987 b) consisting of several basic polyhedra connected together, e.g. forming rings or clusters of atoms, and which exist in a significantly higher proportion than would be expected on a purely statistical (random) basis. Finally, on a yet larger length scale, say greater than 10 A, long-range MRO (LRMRO) can be associated with the local dimensionality of a covalently-bonded amorphous network; this can be ascertained by finding the dimension traced out locally (over distances ~10 A) by bond percolation among the covalent bonds of the structure, neglecting the much weaker Van der Waals bonds (Zallen, 1983). A local dimensionality different from 3 (corresponding to isotropy) can arise from two causes: either the type of connection between coordination polyhedra may impose such a reduced dimensionality (e.g. in the ID chain-like structures resulting from edge-sharing of tetrahedra), or it may result from network depolymerization due to the introduction of network-modifying atoms into the structure. As will be seen later, all three variants of MRO are observable in amorphous chalcogenide materials; MRO is prevalent in such systems primarily because of the structural flexibility associated with the low coordination of the chalcogen atoms. 7.3.13 Long-Range Structure

Although there is no long-range (translational) order in amorphous materials, by

395

definition, nevertheless not all such materials are isotropic on a macroscopic scale, at length scales of say 50-1000 A. An example of such inhomogeneous long-range structure (LRS) is the columnar microstructure associated with obliquely-evaporated films (see Sec. 7.2.2). 7.3.2 General Aspects of the Structure of Amorphous Chalcogenide Materials

Before discussing the structure of individual chalcogenide materials in detail, it is perhaps useful to mention some general features of the structure of such materials and it is convenient to divide such a discussion into three parts as above, dealing with SRO, MRO, and LRS, respectively. 7.3.2.1 SRO in Chalcogenides

In the case of pure amorphous chalcogen (C) elements or alloys (class 1 in Table 7-1), the fundamental structural unit is based on a single atom and as such the SRO is rather straightforward. In the case of binary (or more complex) compositions, the situation is more complicated, and coordination polyhedra centred on the nonchalcogen component can be identified. Thus, in the case of the III-VI glass, B 2 S 3 , the structural unit is a planar BS 3/2 triangular unit, as confirmed from B 1 1 NMR studies (Rubinstein, 1976; Hiirter et al., 1985). The structural unit in the case of V-VI glasses, e.g. As 2 S 3 , is also trigonal (e.g. AsS3/2), but pyramidal, with the pnictogen atom raised above the plane defined by the three chalcogens. This geometry is confirmed by X-ray diffraction results (e.g. Cervinka and Hruby, 1982). For the case of materials in the I V - VI system, e.g. GeSe2, the polyhedral unit is a tetrahedron centred on the tetragen, e.g. GeSe 4/2 . This geometry is consistent with the vibrational characteristics found from inelastic neu-

396

7 Chalcogenide Glasses

tron scattering measurements (Walter et al., 1988), which can be understood in terms of essentially vibrationally decoupled (molecular-like) excitations of GeSe 4/2 tetrahedra, with a vibrational frequency comparable to that of GeBr4 molecules. It has been assumed in the above that the materials are completely chemically ordered, and hence each apex of the polyhedral units is occupied by a chalcogen atom, which acts as a bridging link between two units. In the case of more complicated (e.g. ternary) systems, or those containing wrong bonds, often the type of the polyhedral unit remains unchanged but the chalcogen atoms at the apices are substituted by other elements, thereby changing the local connectivity of the units. In some cases, however, the addition of networkmodifying cations causes a change in the geometry of the structural unit. An example is glassy B 2 S 3 ; the addition of either Li + or Tl + ions causes the coordination of the B to change from planar trigonal to tetrahedral (Eckert, 1989), exactly as in the corresponding borate systems. 7.3.2.2 MRO in Chalcogenides As mentioned in Sec. 7.3.1.2, MRO is generally prevalent in amorphous chalcogenide materials due to the low (two-fold) coordination associated with the chalcogen atoms; as a result, the degree of crosslinking is sufficiently low so that a threedimensionally isotropic structure does not necessarily result, and superstructural units may form. However, it is difficult to probe quantitatively the type and extent of MRO in glasses: in general, those techniques, such as diffraction and EXAFS, which are sensitive to pair correlations of atoms are rather insensitive to MRO, and instead it is techniques such as vibrational spectroscopy (e.g. Raman scattering), which

probe the collective behaviour of several atoms, which are more useful in this regard. Nevertheless, one aspect of the diffraction results on chalcogenide materials has been ascribed to the influence of MRO, and this is the so-called first sharp diffraction peak (FSDP) or pre-peak in the structure factor, S ( 0 . This peak almost invariably occurs at a value of scattering vector Q ~ 1 A" 1 in amorphous compound chalcogenides. This feature is referred to as a pre-peak because Fourier transformation of S ( 0 , both including and omitting this peak, produces essentially indistinguishable real-space correlation functions, indicating that the peak does not contain structural information about SRO, being associated instead with subtle MRO structural arrangements. The FSDP is anomalous in a number of ways. It is observed in a wide variety of mixed chalcogenide amorphous materials, e.g. As 2 S 3 , As 2 Se 3 , GeS 2 , GeSe2, as well as the corresponding oxide materials (e.g. SiO 2 , B 2 O 3 ) and also a-P and a-As, but it is not present for the case of the pure chalcogen a-Se, or Ge or Si. Although the position of the FSDP is at Q±«1 A" 1 for the case of the chalcogenides (and As and P), it is somewhat larger (Qx«1.5 A"1) for oxide materials. Nevertheless, if the structure factor is plotted against the reduced variable Qr l9 where rx is the nearest-neighbour bond length, the FSDP's of chalcogenides and oxides alike fall at approximately the same value, viz. Q1r1^ 2.5 (Wright et al., 1985) (see Fig. 7-14), perhaps indicative of a common origin. The FSDP alone of all the peaks in S (Q) shows anomalous behaviour as a function of temperature and pressure. The intensity of the FSDP increases with increasing temperature in for example a-As2S3 (Busse, 1984), As2Se3 (Busse and Nagel, 1981) and GeS 2 (Lin et al., 1984), as well as in SiO 2

7.3 Structure

Figure 7-14. Experimental structure factors, S (Q), for oxide and chalcogenide glasses plotted versus the reduced variable where rA_x is the nearest neighbour bond length between A and X atoms (Wright et al, 1985).

397

(Soklakov and Nechaeva, 1967). (All other peaks in S(Q) decrease in intensity with increasing temperature, in accordance with the normal behaviour of the Debye-Waller factor.) Indeed, the FSDP is still pronounced even in the liquid state of chalcogenide materials, e.g. GeSe2 (see Fig. 7-15) (Uemura et al., 1978; Susman et al., 1988). The application of pressure also produces an anomalous behaviour of the FSDP in amorphous chalcogenide materials (Tanaka, 1987, 1989 a); its intensity decreases and the position of the peak shifts to higher values of Q with increasing pressure (see Fig. 746). The intensity of the FSDP increases as the atomic number of the chalcogen C decreases for a particular type of chalcogenide glass, e.g. GeC 2 , As 2 C 3 (Susman etal., 1988). Furthermore, it appears that cation-cation correlations are primarily responsible for the FSDP; anomalous X-ray scattering results for a-GeSe2 indicate that Ge-centred correlations (Ge-Ge, Ge-Se) contribute predominantly to the FSDP intensity (Fuoss et al., 1981). There has been, and remains, much controversy over the structural origin of the FSDP in covalent glasses, and a number of

2.5 rg-GeSe2 10 K Glass

2.0-

1.5 a i/)

1.0 Figure 7-15. Structure factor, S(Q), for GeSe 2 in both glassy and liquid states (Susman et al., 1988).

0.5

0.0 0.0

8.0

12.0

16.0

20.0

398

7 Chalcogenide Glasses

Figure 7-16. Pressure-dependent X-ray diffraction patterns for amorphous As2S3 in (a) bulk glass and (a') thin-film forms, and amorphous GeSe2 in (b) bulk glass and (V) thin-film forms (Tanaka, 1989 a).

explanations have been proposed. These can be effectively divided into two categories, depending on how the peak in S (Q) is assumed to originate. One model assumes that the FSDP is separate from the rest of S(Q), i.e. it is regarded as a single Fourier component in reciprocal space arising, therefore, from a (quasi-)periodic correlation function in real space characteristic of the MRO. The width of the pre-peak in S (Q) then arises from the damping in the amplitude of the real-space oscillations, and the DebyeScherer equation relating diffraction line broadening to crystallite size can be used to provide a relationship between the FSDP peak width AQ and D, a characteristic coherence length over which the periodicity in real space is maintained: (7-15 a)

Using this relation, correlation lengths in the range D& 20-30 A are inferred from the width of the FSDP. In addition, the position of the FSDP in this picture is determined by the periodicity in real space via :2n/Q±

(7-15 b)

where d is the spatial repeat distance. For Q± ~ 1 A" 1 , this implies a repeat distance of d - 5 - 6 A. This model, essentially based on a micro- or quasi-crystalline approach in which regions of the structure have a more- or less-ordered structural arrangement, has some appeal since many crystalline chalcogenides are layer materials, and the repeating element is then taken to be the interlayer separation which is assumed to persist into the amorphous phase (e.g. Vaipolin and Porai-Koshits, 1963; Leadbetter

7.3 Structure

and Apling, 1974; Busse, 1984). Various variants of this picture involving interlayer correlations have also been proposed, e.g. that involving crumpled layers (Tanaka, 1988), and that of Cervinka (1988) in which a parallel ordering in a particular orientation of pairs of configurations of between two and five connected coordination polyhedra (effectively forming layers) is assumed to occur. The second interpretation of the FSDP is in terms of a cluster picture which is, in Fourier terms, the converse of the above model. In the simplest case, there is a single (broad) peak in real space at rm characterising the MRO, which produces a strongly damped sinusoidal function in reciprocal space of which the observed FSDP is simply the first, most intense peak. Thus in this picture, the FSDP in itself has no structural significance (c.f. Eq. (7-15)). This approach is therefore similar to that used in the interpretation of the scattering from molecular liquids such as CC14. In this case, the total measured structure factor can be written as the sum of two terms S(Q) = fm(Q) + Dm(Q)

(7-16)

where Dm(Q) is the molecular-packing structure factor describing the inter-molecular interference arising from the scattering of neutrons or X-rays from structural (molecular) entities separated by an average distance rm, and fm(Q) is the molecular form factor describing the mtra-molecular scattering. Dm(Q) is dominant at low Q values and is highly damped because of the large fluctuations in rm, whereas fm(Q) is much less damped (because fluctuations in intra-molecular covalent bond lengths are considerably smaller than those for rm), and it therefore dominates at high values ofQ. The cluster picture has been proposed for the case of amorphous chalcogenides in

399

general by Moss and Price (1985) and Fowler and Elliott (1987), perhaps associated with the packing of coordination polyhedra (although the precise clusters were not identified). Veprek and Beyeler (1981) have further proposed that, whilst the FSDP may result from many Fourier components of the real-space correlation function, nevertheless it may be associated with regions of low atomic occupancy characterised by the minimum in the radial distribution function (RDF) beyond the SRO correlations (related to the packing of coordination polyhedra and the interstitial voids between them). However, one incontrovertible example of a cluster origin for the FSDP is provided by thin evaporated films of As-S materials. These contain quasi-spherical As 4 S 4 molecules (see Sec. 7.2.2) and the very intense FSDP in the diffraction pattern of such films has been convincingly explained in terms of scattering from such clusters (Wright et al., 1985). Whilst the explanation of the FSDP in terms of scattering from a quasi-ordered stacking of layers is appealing, it is unlikely to be a general solution for several reasons: an FSDP is observed at approximately the same value of reduced coordinate (Qr±) even for those cases (e.g. SiO2) where there is no evidence whatsoever for layering in either crystalline or amorphous phases; furthermore, a quasi-regular stack of layers extending over a correlation length D « 20 A would not be expected to survive in the liquid state; and finally, if such a quasi-microcrystalline stacking of layers were to occur in the glassy phase, many more peaks would be expected to be observed in the structure factor, S(Q) (Wright et al., 1987). Conversely, in the absence of well-defined molecular species such as As 4 S 4 in the structure, it is difficult to associate particular structural features with clusters. For instance, such clusters

400

7 Chalcogenide Glasses

cannot be related to just the coordination polyhedra themselves, but instead may be defined by the excluded volume, i.e. the interstitial space, surrounding a particular coordination polyhedron and which results from steric effects (see e.g. Galeener, 1985). Finally in this section on general aspects of MRO in amorphous chalcogenides, mention should be made of experimental data relating to the local dimensionality of the structure. In the case of IV-VI materials, where the coordination polyhedron is a tetrahedron centred on the tetragen, both corner- and edge-sharing of these units is possible whilst maintaining the normal two-fold coordination of the chalcogen (Fig. 7-17), and both types of connection are found in varying proportions in the crystalline compounds of this system. Thus, for silica (SiO2) and germania (GeO2), only corner-sharing of tetrahedra occurs; as a result, a three-dimensional covalently-bonded structure results. In the case of crystalline GeSe2 and GeS 2 , however, a proportion of edge-sharing connections also occur; as a consequence, a twodimensional (2D), layer-like structure results (see Fig. 7-17 a). Finally, for the case of crystalline SiSe2 and SiS2, only edgesharing connections occur, with the result

b)

that the structure becomes chain-like or one-dimensional (ID) (see Fig. 7-17b). The structures of the corresponding glassy phases of these materials are believed also to contain similar structural elements. Consequently, the bonding in amorphous Si and Ge chalcogenides with ID or 2D structures has a weak Van der Waals component between the chains or layers, respectively, in the structure as do the As chalcogenides which, because of the trigonal pyramidal coordination, also can be regarded as being layer-like (see Fig. 7-3 b). This is in contrast to the case of threedimensionally bonded materials (e.g. Ge or SiO2) in which covalent bonding is dominant. Such weak Van der Waals interactions, characteristic of low-dimensional solids, can be investigated using pressure as a probe. Extensive measurements of the pressure dependence of the optical absorption edge have been performed for chalcogenide materials (see e.g. Besson et al, 1981), and some results due to Tanaka (1989 a) are shown in Fig. 7-18. It can be seen that indeed chalcogens, As and Ge chalcogenides, in both amorphous and crystalline forms, exhibit marked red shifts in the optical gap with increasing pressure, due to the preferential compression of the

Figure 7-17. (a) Crystal structure of GeSe2, showing a layer-structure formed from edge- and corner-sharing tetrahedra, termed a raft, (b) Crystal structure of SiSe2, showing one-dimensional chains formed from edge-sharing tetrahedra.

7.3 Structure i

i

i

i k

-GeS..(2D

—^c-Gei7(3l7

*•>

3

"c-ZnSe

hAs2S3(g) \ G e S 2 (g) ^>As2S3(f) Si:H(50%) 2 = = U. Si: H (10%) ^ ^ o ^ . Oi m i_

Ban<

Q) (2 0)

-n

GeSe 2

^ t r a n s ^ 1

^—iGe

[

ir

H> i

i

i

- — c-Se

i

100 50 Pressure (kbar) Figure 7-18. Pressure dependence of the optical bandgap for glasses (g) and amorphous thin films (f) and crystalline (c) semiconductors (Tanaka, 1989 a). GeS2 crystals have both two-dimensional (2D) and three-dimensional (3D) forms. (Polyacetylene is abbreviated as PA).

space between chains or layers; the decrease in the gap arises because of an increase in the broadening of the top of the valence and the bottom of the conduction band due to an increase in repulsive interactions (overlap) between filled lone-pair p-orbitals associated with the chalcogen atoms. In contrast, crystalline Ge or a-Si: H exhibit essentially zero pressure coefficients of the optical gap, reflecting the lower compressibility of these 3D materials. 7.3.3 Structure of Specific Amorphous Chalcogenide Materials

In this section, we will discuss the structures of specific chalcogenide materials, classified according to the categories given in Sec. 7.1.1 (see Table 7-1). 7.3.3.1 Structure of Pure Chalcogens

Since chalcogen elements are normally two-fold coordinated, the structural con-

401

figurations which can be formed are limited essentially to rings or chains, these configurations being held together in the structure by Van der Waals interactions. The determination of the proportion of rings to chains in the structure of amorphous chalcogens has long been a contentious issue. For the case of sulfur, several crystalline allotropic forms are known, each based on a packing of S 8 (cyclooctasulfur) rings (Rawson, 1967). The high-temperature form melts at 388 K to a low viscosity liquid, consisting of monomeric S8 rings; at the so-called ^-transition point (433 K), the rings start to break and a high viscosity liquid forms, consisting of long (10 5 106 atoms) polymeric chains (Myers and Felty, 1967). Glassy sulfur can be quenched from melts above the X point; however, the low value of Tg (=246 K) has precluded extensive work on this material. Three structural modelling studies have been performed for glassy sulfur: an early simulation by Malaurent and Dixmier (1977) was based on a freely rotating chain model (in which the dihedral angle is not constrained). More recently, Popescu (1987) has modelled the structure of liquid and glassy S in terms of two models, one a relaxed packing of chains and the other with a stacking of S 8 rings, assuming a nearestneighbour bond length of r1 = 2.07 A and a bond angle of 0 = 108°; the structure of the glassy phase was inferred to comprise a mixture of these two structural configurations, although the experimental data compared with were very old (Tompson and Gingrich, 1959). Furthermore, Stillinger etal. (1986) have performed a molecular dynamics simulation of cyclooctasulfur in the liquid state and produced a quenched amorphous solid structure from the liquid starting state. More recently, Winter et al. (1990) have performed a high-resolution

402

7 Chalcogenide Glasses

figurations possible, depending on the phase relationship between two neighbouring dihedral angles: if the sense of sequential 0's is fixed (+ + +, or ), the trans configuration results, which has a c/iam-like symmetry with either right- or left-handed helicity; on the other hand, if the phase of cj) alternates (H h — etc.), the cis configuration results, which has a ring-like symmetry. Misawa and Suzuki (1978) have estimated that the cis configuration is energetically more stable than the trans configuration by only « 0.03 eV/ atom, implying that in the glassy phase both configurations may coexist. This prediction is supported by the assignment of a weak feature in the Raman spectrum in terms of monomeric Se8 rings in a proportion of 5-10% (Lucovsky et al., 1967; Gorman and Solin, 1976), as well as from dissolution studies in CS 2 (Briegleb, 1929). A modelling study of a-Se by Corb et al. (1982), based on X-ray diffraction results by Wei et al. (1982), has indicated that whilst a model with (f) = lO2° and mostly trans configurations gives a reasonable fit to the data, a better fit was achieved by allowing both the distribution of <j> to broaden about an average value of 4> ~ 105° and to allow some randomness in the phase relationship between neighbouring dihedral angles. The fit of this model to the X-ray data is shown in Fig. 7-20, for which 60% of configurations were trans-like and 40% cis-like. A model of freely-rotating chains does not seem to give as good a fit. TRANS With increasing temperature, above the melting point (493 K) in the liquid domain, it is expected that the ring-chain equilibrium should shift in favour of chain-like molecules, the average chain length decreasing rapidly with increasing temperaCIS Figure 7-19. Definition of dihedral angle <j> for the ture. This picture has been supported by neutron diffraction measurements (Edeling case of a Se chain, and the atomic configurations of the cis and trans conformers. and Freyland, 1981; Bellisent and Tourand,

neutron-scattering study of glassy sulfur, prepared by quenching the melt in liquid nitrogen. They find that the structure of the melt and of the quenched glass are rather similar with a bond length of 2.06 A, although the experimental RDF of the glass differs in significant details from that of the molecular dynamics S 8 model of Stillinger et al. (1986), indicating that, as expected, the structure of the glass comprises an appreciable fraction of chains. The structure of amorphous (and liquid) Se has been much more extensively studied than is the case for S, and reviews have been given by Andonov (1982) and Corb et al. (1982). Four crystalline forms exist: the most stable trigonal (or hexagonal) form consists of helical chains packed in a parallel fashion, whereas the a- and /?-monoclinic forms are composed of S8 rings but packed differently; in all cases the bond length is ^2.32 A and the bond angle is 0^105°. What distinguishes the various polymorphs is the dihedral angle, or more specifically the correlation between neighbouring dihedral angles. Fig. 7-19 shows how «102° for the crystalline forms. Fig. 7-19 also shows the two distinct five-atom con-

7.3 Structure 1

2 _-

1

1

1 i 1

1

1

1

° 1

1

5

6

1

1

1

Experimental Model n 1

1

r(A)

Figure 7-20. Comparison of the RDFs predicted by the quasi-random coil model and measured experimentally for a-Se (Corb et al, 1982).

1980) as well as by NMR studies (Warren and Dupree, 1980). Glassy Se is more easy to prepare by melt quenching than is the case for S (Rawson, 1967), probably because Se8 rings are more unstable; however, the glass-transition temperature for Se is also low (Tg = 303 K). Te, unlike S and Se, has only one crystalline form; this trigonal modification comprises infinite spiral chains packed in a parallel arrangement (as in trigonal Se) with a bond length of 2.86 A and a bond angle of 9 = 102°. Above the melting point, at 726 K, the chain structure starts to break up, with the shortened chains becoming entangled and cross-linked by three-fold coordinated Te sites with the melt ultimately becoming metallic; recent neutron scattering measurements by Menelle et al. (1987, 1989) indicate that the nearest-neighbour coordination number increases from a value of N± «2.5 just above the melting point to Nt^3 at T = 1100K. A very recent molecular dynamics simulation of the structure of liquid Te has confirmed this picture (Hafner, 1990). It is not possible to quench the hightemperature low-viscosity (metallic) melt into a glassy form (Moffat et al., 1964); a possible reason for this is that at high tem-

403

peratures the average nearest-neighbour coordination number (Nx«3) is much larger than the optimum coordination number mc = 2.4 for glass formation (Eq. 7-8) resulting from the application of constraint theory (see Sec. 7.2.1). Perhaps Te could be prepared as a glass by very rapid quenching from the high-viscosity liquid state just above the melting point, where JVi « 2.5. However, amorphous thin films of Te can be prepared by vapour deposition, in which a chain-like structure also seems to exist (Ichikawa, 1972). Some structural investigations have been carried out on alloys of chalcogen elements, e.g. on Se^Te^^ using neutron diffraction (Bellisent and Tourand, 1980). It was found that the structure of amorphous alloys (l>x>0.6) and liquid alloys (l>x>0.3) could be well fitted by a chain-like model, in which Te substitutes for Se atoms whilst maintaining two-fold coordination. In the more Te-rich liquid alloys, however, the influence of three-fold coordinated Te atoms could not be neglected. Finally, an interesting feature of Se-Te alloys is that if the metallic crystalline phase (of Se67Te33), produced by the application of high pressure to the amorphous form, is quenched to atmospheric pressure and 223 K, the semiconducting trigonal form results but, when heated up to 300 K, the material becomes amorphous again (Mushiage et al., 1983). 7.3,3.2 Structure of V-VI Materials The most commonly studied materials in this system are the As chalcogenides, based on the stoichiometric compositions As 2 S 3 , As2Se3 and As2Te3. The structure of amorphous As 2 S 3 , in both bulk glassy and amorphous thin-film forms has been studied by Daniel et al. (1979), and the experimental data are

7 Chalcogenide Glasses

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2000 0

-1200

V

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10

r(A)

2.4 0.8 o <

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0.4 0.0

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f

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0.8

0.0

-0.8

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0.4

a

f\ k Vn 4

6

8

Figure 7-21. X-ray (X) and neutron (n) diffraction data for samples of amorphous As 2 S 3 : - bulk glass, film, annealed film (Daniel et al, 1979).

shown in Fig. 7-21. Although superficially similar, in fact there are a number of significant differences in the structure between film and glass. The structure of the glass is both chemically and topologically more ordered than that of the evaporated film: the asymmetry on the high-r side of the first peak in the real-space correlation function for the films (due mainly to As-S bonds, with a length of 2.26 A) can be accounted for by the presence of a significant proportion of As-As wrong bonds with a bond length of ~2.5 A. The structure of the stoichiometric glass is thus consistent with that expected from the 8-N rule (see Fig. 7-3 b) where chemical order is dominant, with an As-S bond length of 2.28 A and bond angles at the As and S atoms inferred to be 102° and 99.5°, respectively (Cervinka and Hruby, 1982), whereas the

10

r(A) thin

structure of the film is well described by a packing of quasi-spherical As 4 S 4 molecules which contain As-As homopolar bonds (Wright et al., 1985) (see Fig. 7-3 c). Yang et al. (1987) have also studied the occurrence of like-atom bonds in glassy As^Si-* using EXAFS. The question of broken chemical order in stoichiometric glassy As 2 S 3 , i.e. the existence of homopolar As-As and S-S bonds, has been much discussed. There now appears to be incontrovertible evidence for the existence of a small concentration (~1%) of such homopolar bonds in stoichiometric material; evidence comes from Raman scattering measurements (Ewen and Owen, 1980; Tanaka et al., 1985) where the stretching frequency for As-As bonds (at ^220 cm" 1 ) is readily distinguishable from that corresponding to As-S bonds in

405

7.3 Structure

AsS 3/2 units (344 cm 1), as well as from Mossbauer spectroscopy (Boolchand et al., 1986), and it appears that the concentration of wrong bonds increases markedly with increasing temperature from which the melt is quenched (Tanaka et al., 1985). As K-edge EXAFS measurements have also revealed an increase in the static disorder of the nearest-neighbour (As-S) bond length with increasing quench temperature (Yangetal., 1987). A number of models have been constructed to simulate the structure of glassy As x S 1 _ x alloys. The stoichiometric material has been simulated using computer-relaxed ball-and-stick models with perfect chemical order and connectivity (Pfeiffer et al., 1989), a model generated by a threestep process involving packing atoms randomly in a box with subsequent structural relaxation and reformation of bonds to give a low-energy structure (Fujiwara et al., 1981), and various models generated by bond-breaking and reformation or atomic decoration of existing continuous random network models (Fowler and Elliott, 1987). Models for the non-stoichiometric alloys have been constructed by the three-step procedure (Itoh et al., 1982) and by a Monte Carlo repositioning of atoms in order to give the best fit to the experimental scattering data (Rechtin et al., 1974; Renninger et al., 1974). Although none of these models give perfect agreement with experimental data, nevertheless, they do indicate that a restricted local layer-like structure persists, reminiscent of the layer structure of the crystal orpiment; however, a microcrystallite-like stacking involving orpimentlike layers is not necessary to give rise to the FSDP at Qx~1.2 A" 1 (N.b. the orpiment 020 reflection lies close to this value), since many of these models, which do not have such a quasi-periodic structural repeat, also reproduce the FSDP.

Finally, Pfeiffer et al. (1989) have analysed the MRO in their models in terms of the correlation between dihedral angles subtended by the S atoms. In the orpiment structure there are two distinguishable S sites: one occurs in a helical (H) arrangement of alternating As and S atoms and is associated with two different dihedral angles (68°, 146°); the other is in a bridging (B) site between two different helices, for which the two dihedral angles are identical (163°, 163°). Pfeiffer et al. (1989) found in their models a slight preponderance for B and H sites (see Fig. 7-22), indicating that perhaps the structure of glassy As 2 S 3 retains vestiges of the helical arrangement found in the crystal, which would be one manifestation of the MRO. However, there are two distinct (distorted) As sites in the orpiment structure as well, and these can be identi-

'B .'

160 • Type U0

of atom B-Bridging H-Helical Ill-defined

V.

Fraction of total 0.124 0.245 0.632

• ••

i.

..•

*

•

:

,120 100

*

•

• •

*

80-•

60 60

80

100

120 0.1 (deg)

160

Figure 7-22. Correlation diagram for the two dihedral angles subtended at the sulphur atoms in a CRN model for a-As2S3 (Pfeiffer et al., 1989). The dihedral angle is here defined as the angle between the As-centred vector along the symmetry axis of an AsS3/2 unit and the S-centred vector along the bisector and in the plane of an SAs2/3 unit. The values denoted by B and H refer to bridging and helical S sites, respectively, in the orpiment structure.

406

7 Chalcogenide Glasses

fied using 75As nuclear quadrupole resonance (NQR) spectroscopy in terms of two distinct asymmetry parameters rja of the electric field gradient tensor (Rubinstein and Taylor, 1974). However, in glassy As 2 S 3 (and As2Se3), similar measurements have revealed that in fact 70% of the sites are symmetric, with only 30% which could have an environment similar to that in crystalline orpiment (Szeftel and Alloul, 1979). The interpretation here is that a significant part of the structure can be described in terms of a CRN, with only a relatively minor proportion having a MRO in the form of cross-linked helical chains. Phillips et al. (1980) (see also Phillips, 1981) have also proposed that MRO in the form of orpiment-like structural elements exists in the glass. They proposed that the structure consists of the twelve-membered rings, found in orpiment, linked together in a chain-like fashion by bridging chalcogen atoms, with two extra chalcogens (outriggers) bordering each raft on the other sides of the ring from the chain connections. The structure of glassy As2Se3 appears to be more-or-less isomorphous with that of g-As2S3, as found from NQR studies (Szeftel and Alloul, 1979) and X-ray diffraction data (Cervinka and Hruby, 1982), except that the As-Se bond length (2.43 A) is correspondingly larger than for As-S, and the bond angles subtended at As and Se atoms are inferred to be smaller, viz. 100° and 95°, respectively (Cervinka and Hruby, 1982). Chen et al. (1984) have reported a large-scale domain structure in evaporated thin films of a-As2Se3, in the form of polygonal domains with diameters up to 1000 A. 75 As NQR measurements have also been carried out on the mixed chalcogenide glass system, As 2 S x Se 3 _ x (Treacy et al., 1983). These studies found that S substituted for Se, so that the basic structural units comprised AsS x/2 S (3 _ x)/2 pyramids, with no

evidence being apparent for anionic subsite segregation. In contrast to the case of the S- and Se-based As chalcogenides, where the SRO of glass and crystal appear to be very similar, the structure of the glassy and crystalline forms of As2Te3 appear to be very different: crystalline As2Te3 contains As sites which are octahedrally coordinated by Te, whereas the glass contains mainly AsTe3/2 pyramidal units with an As-Te bond length of 2.65 A, an As bond angle of 98° and Te bond angles in the range 9 5 98°, as found from X-ray diffraction studies (Cornet and Rossier, 1973; Cervinka and Hruby, 1982), from 75As NQR (Szeftel and Alloul, 1979), and from 125Te absorption (Faigel et al., 1983) and 129 I emission Mossbauer experiments (Boolchand et al., 1982 a, b). However, there is also evidence that some of the Te atoms in glassy As2Te3 are three-fold coordinated (Cornet and Rossier, 1973; Boolchand et al., 1982a, b). 125 Te and 129 I Mossbauer measurements have also been performed on the binary (As2Se3)JC(As2Te3)1_JC glass system (Wells and Boolchand, 1987) in which evidence is adduced for broken chemical order, i.e. the presence of chalcogen-chalcogen wrong bonds. Vazquez et al. (1986) have undertaken an X-ray diffraction study on the binary system As0 2Se0.5Te0 3 , and have simulated the structure using a Monte Carlo approach in which As atoms were assumed to be either three-fold or four-fold coordinated. The structure of the Sb chalcogenides has been relatively little studied. Cervinka and Hruby (1982) performed an X-ray diffraction study of two forms of bulk amorphous Sb 2 S 3 , one formed by very rapid (roller) quenching, and the other formed by a chemical reaction technique (precipitation of Sb 2 S 3 by passing H 2 S through a solution of SbCl3). In both cases, trigonal

7.3 Structure

pyramidal coordination of Sb atoms by S was found (with an Sb-S bond length of 2.50 A), S atoms being coordinated by two Sb atoms, with an Sb bond angle of 90° and an S bond angle of 100.7°. The structures of the two amorphous forms were rather similar, and could be understood in terms of a CRN arrangement of SbS 3/2 pyramidal units. More recently Dalba et al. (1989) have also studied amorphous Sb 2 S 3 (in both bulk glassy and thin-film forms), by X-ray diffraction and EXAFS. Their findings for the glass agree with those of Cervinka and Hruby (1982), and more particularly they find, unlike in some earlier studies (Zacharova and Gerasimenko, 1972; Tatarinova, 1972), that the structure of the glassy and thin-film forms are very similar. Watanabe et al. (1983) have studied amorphous thin films of Sb x S 1 0 0 _ x by Raman scattering. The stoichiometric film (x = 0.4) exhibits a narrow band at 170 cm" l and a broad band at 290 cm" 1 , the latter band increasing in intensity and the former band decreasing in intensity with increasing S content (decreasing x). The band at 290 cm" 1 was ascribed to Sb-S vibrations (in say SbS 3/2 units), and the band at 170cm" 1 was ascribed to Sb-Sb vibrations; thus, even at the stoichiometric composition, the chemical order in the films appears to be broken. Finally, we discuss the structure of amorphous phosphorus chalcogenide materials. In a sense, these exhibit perhaps the most interesting structural features of all the members of the V-VI family because of the propensity to form P4Xn (n = 3-10; X = S, Se) cage-like molecules (see Fig. 723). As mentioned in Sec. 7.2.1, the PxSe1 _x system exhibits two glass-forming regions, I (0<x<0.52) and II (0.63<x<0.85), separated by the stoichiometric composition P4Se3 (x = 0.57). Neutron diffraction, EXAFS and Raman measurements have been

407

performed by Price et al. (1984) on glasses in region I, including Se isotopic substitution diffraction measurements for x = 0.4 and 0.5 (Arai et al., 1986), and neutron diffraction and EXAFS measurements have also been performed by Verrall and Elliott (1988,1989,1990) and Verrall et al. (1988 a) for glasses in both composition region I (where the results agreed with those of Price et al., 1984) and in II, the latter centred around the composition P2Se. Price et al. (1984) inferred from their neutron diffraction results on the Se-rich glasses that there was some evidence for the existence of P4Se5 and P4Se3 molecules in the structure, depending on the composition, these presumably being embedded in a Se-rich matrix. The Raman spectrum for glassy P 50 Se 50 has many features in common with that of the molecular species P 4 Se 3 , supporting the supposition that a reasonable proportion of such molecules exists in the structure of this glass. Furthermore, magic-angle spinning (MAS) NMR experi-

Figure 7-23. Schematic illustration of the structural arrangement of the cage-like molecular species P4Xn (X = S, Se;tt= 0-10). Chalcogens tend to be inserted preferentially at edge (E) positions, rather than the double-bonded apical (A) positions.

408

7 Chalcogenide Glasses

0 15 i

50

100

1

r

150 1

200

250

1

>

V

10 -

5

V

6

300

350

1

1

V

1

V

7

400 (cm'1)

V

8

9

'

V

10

> LJLJ

o

v 10 v 9

ti t 10 a)

20

u

tltt Uti ,

30 E(meV)

300 400 500 Raman shift/cm"1 b) Figure 7-24. (a) Vibrational density of states (VDOS) for glassy P2Se measured by inelastic neutron scattering (Verrall and Elliott, 1988). (b) Raman spectra of a-PxSe1_x alloys (0.67 < x < 1.0) (Phillips et al., 1989). In both cases, the cage-like vibrational modes of the P4Se3 molecule are indicated, together with an assignment of features in the VDOS and Raman spectrum in terms of these modes.

I

,

,

,

tl , I

50

60

ments on P-Se glasses also provide evidence for the existence of P4Sen clusters in the structure (Lathrop and Eckert, 1988; Eckert, 1989). In particular, the proportion of tetrahedral P sites (with a doubly-bonded Se terminator atom, viz. Se = PSe3/2) progressively increases with decreasing P content (see Fig. 7-25); this is evidence for the existence of say P 4 Se 10 clusters (see Fig. 7-23) at low P contents. In the case of glassy P2Se, evidence that the structure consists almost entirely of P4Se3 molecules (with a small excess of P) is overwhelming. The static structure factor S(Q) for g-P2Se can be fitted almost exactly for Q 2> 6 A" 1 by the form factor calculated for the P4Se3 molecule (Verrall and Elliott, 1989). Inelastic neutron scattering studies of the vibrational excitations of g-P2Se reveal a highly structured density of states (see Fig. 7-24 a), the peaks in which can be assigned to the vibrational excitations of a P4Se3 molecule (Verrall and Elliott, 1988 a, 1989); Raman measurements by Phillips et al. (1989) support this finding, and the higher resolution of this technique allows more of the vibrational modes to be distinguished (Fig. 7-24 b). Finally, quasi-elastic neutron scattering mea-

409

7.3 Structure

surements have been performed on g-P2Se, and a quasi-elastic broadening of the elastic line was observed at elevated temperatures (300-450 K), indicative of the presence of atomic motion (Verrall and Elliott, 1989). These findings have been interpreted in terms of a rotational diffusion of P4Se3 molecules in the glassy structure, similar to that which occurs in the plastic phase (T > 355 K) of crystalline P 4 Se 3 .

Se=PSe3/2

PSe3/2

5.0

7.3.3.3 Structure of I V - V I Materials

The Ge and Si chalcogenides also exhibit a rich variety of structural features, particularly related to MRO, as a result of the propensity for the formation of edgesharing tetrahedra compared with their oxide counterparts. A survey of the structural features of amorphous IV-VI materials determined by diffraction methods has been given by Wright et al. (1982). It is significant that in the AX2 materials (A = Si, Ge; X = O, S, Se), oxides have an A-X-A bond angle greater than the tetrahedral angle of 109.47°, where the corresponding chalcogenide materials have an angle 6 (A-X-A) which is smaller than this. The structure of amorphous GeS 2 has been relatively little studied, perhaps because of the difficulty of preparing exactly stoichiometric material in a glassy form (Voigt etal, 1978). Feltz et al. (1985) and Cervinka etal. (1987) have performed X-ray diffraction studies on glassy GeS 2 , finding the Ge-S bond length to be 2.23 A or 2.26 A, respectively and the Ge-S-Ge bond-angle distribution to be centred at 115°. From a ball-and-stick structural modelling study, Feltz etal. (1985) infer that the structure consists mainly of corner-sharing GeS 4/2 tetrahedra, but that about 25% of the tetrahedra form edgesharing connections. The structure of (the

400

300

200

100

0 ppm

-100

-200

-300

Figure 7-25. 31 P magic-angle spinning NMR spectra of various P^Se^^ glasses (Eckert, 1989). Assignments of the two principal features in the spectra in terms of trigonal PSe3/2 and tetrahedrally-coordinated Se = PSe 3/2 units are indicated.

high-temperature form of) crystalline GeS 2 (and GeSe2) consists of two types of structural configuration, one which contains corner-sharing tetrahedra in a chain-like configuration, and the other containing edge-sharing units bridging two chains (see Fig. 7-26). Cervinka (1988) has discussed the MRO in glassy GeS 2 , particularly as-

410

7 Chalcogenide Glasses

C-Configuration

E-Configuration Figure 7-26. Chain (C) and edge (E) sharing configurations in GeX2 (X = S, Se) (Cervinka, 1988).

sociated with the FSDP at Qx«1 A \ in terms of correlations between such structural configurations; a reasonable fit to the first two peaks in the X-ray scattering pattern was achieved in terms of a parallel packing of chain-like clusters separated by about 7-8 A. The structure of glassy Ge 2 S 3 has been studied by X-ray diffraction by Pohle et al. (1985); the structure could be well described in terms of the structural unit being the ethane-like grouping [Ge2S6], with all chalcogens being two-fold coordinated in corner-sharing links. 4: 2 coordination of Ge and S, respectively, was found for the case of a-GeS by Drahokoupil et al. (1986) using X-ray emission and EXAFS, despite the fact that in the structure of crystalline GeS the Ge (and S) atoms have a 3 : 3 coordination. Drchal and Malek (1988) have constructed two structural models for a-GeS, one a 3D structure containing Ge(Ge 4 _ n SJ tetrahedra of all types, and the other a layered model in which Ge(Ge 2 S 2 ) units were predominant, the former giving the best fit with experimental scattering data.

There have been many more structural investigations of glassy GeSe 2 . An X-ray diffraction study has been performed by Feltz et al. (1985), an anomalous X-ray scattering study by Fuoss et al. (1981) and neutron scattering measurements made by Uemura et al. (1978), Nemanich et al. (1983), Wright et al. (1987), and Susman et al. (1988); a Ge-Se bond length of 2.37 A is found. As for the case of g-GeS2, the presence of a significant proportion (—15%, c.f. 25% for the crystal) of edge-sharing connections between GeSe 4/2 tetrahedra in the structure of g-GeSe2 has been suggested on the basis of diffraction data (Nemanich etal., 1983), Raman scattering (Bridenbaugh et al, 1979; Sugai, 1987) and a molecular dynamics (MD) structure simulation involving two-body interaction potentials only (Vashishta et al, 1989). MRO in glassy GeSe2 has been the subject of much controversy, and two experimental features have been the centre of discussion, namely the FSDP at Q ^ l A " 1 and the so-called companion line to the main Ge-Se stretch mode in the Raman spectrum. From neutron scattering measurements the FSDP found in the glassy phase remains with the same intensity (Susman etal, 1988), or even enhanced (Uemura et al, 1978) in the liquid state see Fig. 7-15. (This behaviour is also reproduced by the MD simulation of Vashishta et al, 1989). This observation makes it unlikely that any microcrystalline-like structural ordering is responsible for the FSDP. The anomalous X-ray scattering results of Fuoss et al. (1981) indicate that Ge-centred (Ge-Ge, Ge-Se) correlations contribute primarily to the FSDP; this conclusion is supported by X-ray diffraction measurements on GeSe 2 -GeTe 2 glassy alloys, in which the FSDP grows in intensity as Te is replaced by Se, thereby enhancing the Ge contribution (Moss, 1974). The MD simu-

7.3 Structure

lation study by Vashishta et al. (1989) also found that Ge-based correlations were mainly responsible (although for the simulated structure the FSDP appears at a larger value, Q 1 ^1.35A"" 1 , than observed experimentally), and they ascribed this to Ge-Ge correlations at separations of 9-10 A (since the FSDP disappeared if only atomic correlations less than 8.8 A were included in the calculation of S (Q)). The companion line at ^220 cm" 1 (26.5 meV) to the main At symmetricstretch breathing mode of GeSe 4/2 tetrahedra at ^200 cm" 1 (25 meV) observed in the Raman spectrum of g-GeSe2 has also been taken to be a signature of MRO in this material. The band is unusally narrow and strongly polarized; moreover it exhibits an unusually strong compositional dependence (Nemanich et al., 1977), varying as ~x5 in the alloys Ge^Se^,,, whereas the intensity of the Ax mode varies linearly with x as expected from a progressive break-up of GeSe 4/2 tetrahedra with increasingly off-stoichiometric composition (see Fig. 7-27). Nemanich et al. (1983) and Sugai (1987) have ascribed the anomalous companion line to the vibration of the four-membered (Ge2Se2) rings associated with edge-sharing tetrahedra (Fig. 7-26), whereas Bridenbaugh et al. (1979) have ascribed it to the vibrations of Se-Se bonds (dimers) bordering what they have termed a raft, namely a 2D section of the crystalline structure containing edge-sharing units cross-linking parallel chains of cornersharing tetrahedra (see Fig. 7-17 a). (Wright et al. (1987), however, have indicated that the structural correlations associated with such rafts are incompatible with the measured RDF; in particular, the third peak at ~4.7A is much too pronounced in raftlike structures). However, matrix-element enhancement of Raman bands can occur in the case of symmetric vibrational modes

300

411

200 100 0 Raman shift Icrrf1)

Figure 7-27. Raman (solid line) and depolarization (dashed line) spectra of a-GexSe1 _x. Note the anomalous composition dependence of the companion line at ^220 c m ' 1 compared with the symmetric-stretch At breathing modes of GeSe4/2 tetrahedra at %;200 cncT1 (Nemanich et al., 1977).

(Elliott, 1990), and thus it is not clear whether the anomalous compositional changes in the Raman intensity of the 220 cm" 1 band are due entirely to a systematic change in the structure (e.g. in the proportion of edge-sharing tetrahedra), or from a change in the Raman matrix element. An experiment probing the vibrational density of states which is less sensitive to matrix-element effects is inelastic neutron scattering, and two such experiments have been reported for g-GeSe2 (Gladden et al., 1988; Walter et al., 1988). The dynamic structure factor S (Q, co) is shown in Fig. 7-28 a and the vibrational density of states (VDOS) G(E) in Fig. 7-28 b (Walter et al., 1988). The four modes labelled v1-vA, in

412

7 Chalcogenide Glasses

6O

a)

O.O

GeSe 2 DOS13K

Figure 7-28. (a) Dynamical neutron structure factor, S(Q, w), of glassy GeSe2 with the elastic contribution removed (Walter et al., 1988). (b) Vibrational density of states of glassy GeSe2 obtained from inelastic neutron scattering (Walter et al., 1988).

10 b)

20 25 E(meV)

Fig. 7-28 b correspond to the vibrational modes of GeSe 4/2 tetrahedra which, in the central-force-field model of Sen and Thorpe (1977) where bond-bending forces are neglected, are vibrationally decoupled as long as the chalcogen bond angle is near 90°. The origin of the other features in the VDOS is less clear, although Bridenbaugh et al. (1979) and Kumagai et al. (1977) have

assigned a (Raman) peak at 265 cm 1 (and 175 cm""1) to vibrations of Ge-Ge bonds in ethane-like (Ge2Se6/2) structural groupings. Unfortunately, even the highest-resolution inelastic neutron scattering spectrometers available have a considerably worse energy resolution than is routinely attained in Raman scattering experiments; as a result, the companion line has not yet

7.3 Structure

been unambiguously resolved from the A± mode in inelastic neutron scattering measurements (Gladden et al., 1988). There has been some controversy concerning the atomic coordination in the material a-GeSe (see Fowler and Elliott, 1982, for a review), although the anomalous X-ray scattering data of Fuoss et al. (1981) seem to favour 3 : 3 coordination, with a Ge-Se bond length of 2.4 A and an average bond angle of ^106° (Uemura et al., 1974). A modelling study by Fowler and Elliott (1982), in which 3 : 3 coordination was assumed, gave good agreement with the neutron scattering results of Uemura et al. (1974) and also the anomalous X-ray scattering results of Fuoss et al. (1981). Pohle et al. (1985) have investigated the structure of amorphous Ge 2 Se 3 using X-ray diffraction, and found that the structure can be understood in terms of cornersharing (Ge2Se6/2) structural units, i.e. containing a Ge-Ge homopolar bond. The macrostructure of obliquely-evaporated a-GeSe2 (and GeS 2 and GeSe3) films exhibiting a columnar microstructure has been investigated by Rayment and Elliott (1983), Spence and Elliott (1987) and Verrall etal. (1988 b) using small-angle neutron and X-ray scattering. The Si chalcogenide glasses SiS2 and SiSe2 also exhibit extremely interesting structural features. The crystalline modifications of these materials are chain-like structures consisting entirely of edgeshared SiX4/2 tetrahedra (X = S, Se), and there is much experimental evidence that this form of MRO persists in the glassy phase as well. Neutron diffraction measurements have been carried out on the glassy Si x Se!_ x system (Johnson etal., 1986; Johnson, 1986), and many Raman scattering studies have been performed on both SiS2 and SiSe2 glasses (Tenhover etal., 1983a, 1983b; Griffiths etal., 1984;

413

Malyj etal. 1985; Tenhover etal., 1984, 1985; Susman et al, 1986; Sugai, 1987). In addition, 29Si MASNMR experiments have been performed on these materials (Tenhover et al, 1988; Eckert, 1989) as well as inelastic neutron scattering measurements (Arai et al, 1988). Although there is no consensus concerning the detailed assignment in terms of vibrational modes of the various bands observed in the Raman spectra of these glasses (Arai etal, 1988), nevertheless it is generally agreed that the structure of the glasses cannot be understood in terms of either being completely chain-like (i.e. 100% edge-shared units) or completely corner-sharing (as in SiO2), but that both types of connection are present with edge-sharing being dominant. 29Si MASNMR results (Tenhover etal, 1988; Eckert, 1989) provide evidence for three distinct types of Si environment in the glass compared with the single site in the crystal (Fig. 7-29); these have been ascribed to SiX4/2 units (X = S, Se) having zero, one and two edge-sharing connections (labelled E°, E 1 , E 2 , respectively). Tenhover et al. (1988) find that in glassy SiS2 and SiSe2 the proportions of these sites are approximately 25% E°, 50% E \ and 25% E2. An extensive structural modelling study of glassy SiSe2 (SiS2) has been undertaken by Gladden and Elliott (1987, 1989) in which the neutron diffraction data of Johnson et al. (1986) is best fitted by a mixture of structural groupings, including about 15% of the cross-linked chain cluster (essentially a 12-membered ring consisting of four E 1 and two E° units) proposed by Griffiths etal. (1984) (see also Griffiths, 1986) with the rest of the structure in the form of random chains containing an average of seven E 2 units, of which approximately 15% show some degree of local parallelism between two chains extending for two or three E 2 units. Fig. 7-30 shows

414

7 Chalcogenide Glasses

+50

-150 29

Si (ppm)

Figure 7-29. 29Si magic-angle spinning NMR of glassy and crystalline SiS2 (Tenhover et al., 1988). The assignment of the peaks in the spectrum of the glass in terms of En (n = 0-2) configurations, where n is the number of edge-sharing connections per SiS4/2 tetrahedron, is shown.

the fit of the model to the experimental structure factor and RDF with, in the latter case, an indication of which MRO features contribute to particular regions of the RDF. 7.3.3.4 Structure of III-VI Materials

Relatively little structural work has been undertaken on the boron chalcogenide glasses, mainly because of their great sensitivity to hydrolysis; moreover, neutron scattering measurements are not possible

with the naturally occurring isotopic mixture of boron due to the very high absorption cross-section of the 10B nucleus. Nevertheless, there have been a number of X1 B c.w. (broad-line) NMR studies of the structure of boron chalcogenides (Hendrickson and Bishop, 1975; Rubinstein, 1976; Hintenlang and Bray, 1985; Hiirter et al., 1985). For the case of the stoichiometric B 2 X 3 materials (X = S, Se), the NMR spectra exhibit clear evidence for second-order quadrupolar splitting due to the presence of an appreciable quadrupole coupling constant associated with trigonal planar BX 3/2 units. These triangular units are presumably connected by corner-sharing at the apical chalcogen atoms, as in the corresponding oxide glass, B 2 O 3 . The addition of the modifiers Li2S (Hintenlang and Bray, 1985) and T12S (Eckert et al., 1984) to B 2 S 3 converts the coordination of the B from trigonal to tetrahedral; the proportion of tetrahedrally-coordinated B is a maximum at about 40mol.% modifier, as for the analogous behaviour found in the alkali borates, and at higher modifier contents trigonal B units are created with non-bridging (singly-coordinated) sulfur atoms. 7.3.3.5 Metal Chalcogenide Materials

In many cases, metals are present in amorphous chalcogenide materials as ternary (or higher) constituents, acting as network modifiers. In such cases, a major structural influence of the modifier is to alter in some way the structure of the network-forming matrix, either by a change in coordination of the network-forming cation (e.g. from 3 to 4 for B as evidenced by NMR studies (Eckert et al., 1984) - see Sec. 7.3.3.4) or of the network-forming anion, usually a reduction in coordination, resulting in a network depolymerisation

7.3 Structure

b) Figure 7-30. (a) Experimental neutron scattering intensity function, i(Q) (dashed line) for glassy SiSe2 (Johnson et al., 1986) compared with that calculated for the model of Gladden and Elliott (1987, 1989) (solid line), (b) Experimental RDF for glassy SiSe2 (points) (Johnson et al., 1986) compared with that calculated for the model of Gladden and Elliott (1987, 1989) (solid line). The contributions of various structural groupings to the RDF are also indicated.

415

and the creation of non-bridging chalcogen atoms (e.g. in Tl 2 S-As 2 S 3 studied by XPS by Heo et al. (1988)). However, the structural environment of the metal (modifier) atom is often difficult to investigate in such multicomponent materials and atomspecific structural probes must be used. Thus, as examples, the technique of EXAFS has been applied to the Ag-As-S system (Steel etal, 1989), anomalous X-ray scattering to the Ag-Ge-Se system (Westwood and Georgopoulos, 1989) and isotopic substitution neutron scattering to the Ag-As-S system (Penfold and Salmon, 1989). From such studies, it is found that the Ag atoms are generally coordinated by ~ 3 chalcogen atoms. Less common are (binary) metal chalcogenide systems in which the metal atoms play a significant structural role. The structure of a-MoS 3 has been extensively studied by X-ray diffraction and EXAFS measurements (Liang etal., 1980a, 1980b; Chien etal., 1984) and Raman scattering (Bhattacharya et al., 1987). Octahedral coordination of Mo atoms by S atoms was found with a bond length of 2.47 A, and evidence was also found for Mo-Mo dimers with a bond length of ~ 2.9 A, considerably shorter than the normal Mo-Mo

416

7 Chalcogenide Glasses

bond length of 3.4 A (Chien et al., 1984). The structure proposed by Chien et al. (1984), based on modelling studies, is of a chain-like structure built from Mo atoms with an alternating sequence of long and short bonds and with disulphide (S-S) bonds between two S atoms in alternate octahedra. It is interesting that the X-ray scattering intensity shows a sharp intense FSDP at Q i - l A " 1 (Chien et al., 1984) which, because of the relative weightings of the scattering factors involved, must be due almost entirely to Mo-Mo correlations. Chien et al. (1984) account for this feature in terms of a local parallel coupling of chains, much as in the case of g-SiSe2 or SiS2 (Gladden and Elliott, 1989). 7.3.3.6 Structure of Halogen Chalcogenides

The structural and other properties of a wide range of halogen-containing chalcogenide glasses have recently been extensively reviewed by Sanghera et al. (1988). In general, the structural effect of the inclusion of halogens is for the atoms to act as network terminators, i.e. singly-coordinated halogen atoms substitute for two-fold coordinated chalcogens, and as a result the structure is depolymerised and the viscosity is concomitantly dramatically lowered (Rawson, 1967). Although direct structural techniques (e.g. diffraction) appear to have been seldom used for these materials, with the exception of the (GeS2)JCBr1__x and (GeS^Ji _x systems (Wagner et al., 1988), Raman spectroscopy has been widely applied, e.g. for the As-S-I system (Koudelka and Pisarcik, 1982, 1984), As-S-Br (Koudelka et al., 1979; Koudelka and Pisarcik, 1983), Ge-S-Br (Koudelka et al., 1984), and G e - S - I (Sanghera et al., 1988). In all cases it appears that the halogens (H) replace the chalcogens (C) in the structure, i.e. As-H or, Ge-H bonds form preferen-

tially with respect to C-H bonds. As a result, in some cases there appears to be evidence, from the Raman spectra, for a type of microphase separation in which discrete molecular species, e.g. AsBr3 (Koudelka et al., 1979) and S8 rings (presumably formed from the chalcogens displaced by the halogens) are dissolved in the remaining glassy matrix. In the case of the binary halogenchalcogen Te-X (X = Cl, Br) materials discovered recently (Zhang et al., 1988; Lucas and Zhang, 1990), bonds between halogens and chalcogens must occur. Zhang et al. (1988) suggest that the structure of glassy Te3Cl2 or Te3Br2 is similar to that of the corresponding crystal (Kniep et al., 1973), which is based on helical Te chains, in which every third Te atom is bonded axially to two additional halogen atoms, making such Te atoms tetrahedrally coordinated (see Fig. 7-31 a), and the structure of glassy Te2Cl and Te2Br is also proposed to be similar to that of the crystalline modification (see Fig. 7-31 b), which consists of a ladder-like structure of two interconnected Te chains, with bridging halogen atoms. However, there does not yet appear to be any direct structural evidence for these proposed structures.

7.4 Defects 7.4.1 Introduction

Defects can only be discussed sensibly in the context of some reference structure which is non-defective. In the case of crystalline materials, this requirement is readily satisfied, in terms of a perfect single crystal, but in the case of amorphous materials the situation is not as clear-cut: what is to be taken as the reference, non-defective (i.e. ideal), non-crystalline structure?

7.4 Defects

417

Figure 7-31. Structure of crystalline Te3Cl2 (a) and Te2Cl (b) (Kniep et al, 1973), b)

In the case of covalently-bonded systems, at stoichiometric compositions, the ideal reference structure may be taken to be a chemically-ordered continuous random network (COCRN) (Elliott, 1984, 1990). Thus, defects in such a structure can be wrong (homopolar) bonds and coordination defects, e.g. over-coordinated atoms or under-coordinated atoms (dangling bonds). However, in certain cases for amorphous materials it is difficult to decide whether or not a particular structural feature is a defect under the above definition. For instance, should the negativelycharged non-bridging (NB) chalcogen sites, denoted by the symbol C^~ (where C stands for chalcogen, and the superscript and subscript are the charge state and atomic coordination, respectively), resulting from the introduction into chalcogenide glasses of network-modifier cations (e.g. alkalis, Ag + , Tl + ) and which compensate the positively charged cations (see e.g.

Heo etal., 1988), be regarded as defects? We will take the viewpoint that if the structure intentionally and necessarily contains say modifier cations, the concomitant changes in the structure (e.g. over-coordinated boron atoms - Sec. 7.3.3.4) or NB chalcogens (see Sec. 7.3.3.6) should not be regarded as constituting defects, but instead they are a natural feature of the (modified) structure. However, any such structural entities which are present with a concentration in excess of that otherwise normally expected should be regarded as defects. 7.4.2 Wrong Bonds

If the COCRN is taken as the ideal structure for a compound chalcogenide material with stoichiometric composition, wrong or homopolar bonds occurring in a real material are obviously defects in the structure since they represent broken

418

7 Chalcogenide Glasses

chemical order. However, for the case of off-stoichiometric compositions, wrong bonds can naturally occur as the response of the structure in accommodating the element in excess. In this case, such wrong bonds should not be regarded as defects. (Wrong bonds also obviously have no meaning in the case of elemental chalcogen materials.) It is often difficult to detect the presence of wrong bonds, and there are several reasons for this. Often, they are present in very low concentrations (<1%), and conventional direct structural probes, such as diffraction, are often not sufficiently sensitive; furthermore, in the electronic ground state, such defects are diamagnetic and therefore electron spin resonance cannot be used. However, both Raman and Mossbauer spectroscopies have been used successfully to detect wrong bonds in chalcogenide glasses. Wrong bonds in glassy As 2 S 3 have already been discussed in Sec. 7.3.3.2. In the Raman spectrum, in addition to the dominant band at 344 c m - 1 due to As-S vibrations in AsS 3/2 pyramidal units, small peaks at 220-230 cm" 1 and 450-500 cm" 1 are also observed (see Fig. 7-32 a), ascribed to vibrations of homopolar As-As and S-S bonds, respectively (Ewen and Owen, 1980; Tanaka et al., 1985; Kawazoe et al., 1988). The ratio of Raman intensities I (As-As)/ I (As-S) markedly increases with increasing quenching temperature (see Fig. 7-32 b) (Tanaka et al., 1985), indicating that homopolar bonds are more prevalent in glasses quenched from high melt temperatures, as expected. Mossbauer spectroscopy results also support the idea of broken chemical order at the 1% level in glassy As 2 S 3 (Boolchand et al., 1986). Similar experiments have been performed for glassy Ge x Se 1 _ x where again wrong bonds are found in a proportion of ~ 1 %

a)

200 400 Raman shift (cm"1)

TqCC) 500

b) Figure 7-32. (a) Raman spectrum of as-quenched and annealed glassy As2S3 (Tanaka et al., 1985). The dominant peak at 344 cm" 1 is ascribed to the symmetric stretching mode of AsS3/2 units, and the small feature at 220 cm" 1 is ascribed to homopolar As-As bonds, (b) Ratio of the Raman intensities of the 220 cm" 1 (As-As) and the 344 cm" 1 (As-S) modes as a function of glass quench temperature.

419

7.4 Defects

600 0.28

91 0

a)

032

036

b)

VELOC!TY(mm/s) 119

Figure 7-33. (a) Sn Mossbauer spectra of glassy (Ge0 99Sn0 01)xSe1_JC alloys near the stoichiometric composition (x = 0.333) showing evidence for two chemically inequivalent sites (Boolchand, 1986). Site A is a singlet centred near v = 0 mm s ~1 and site B is a doublet displaced to about 2 mm s ~1. (b) The intensity ratio IB/(IA + IB) as a function of composition for the B site in Sn-doped GexSe! _x alloys. The compositional dependence of the glass-transition temperature, Tg, is also shown (Boolchand, 1986).

for the stoichiometric composition (see Boolchand, 1986, for a review). Raman spectra have revealed the presence of a small peak at 180 cm" 1 which appears as a shoulder to the main peak at —200 cm" 1 which is the Ax breathing mode of GeSe 4/2 tetrahedra (Murase et al., 1983 a, 1983 b); the feature at 180cm" 1 is ascribed to the vibrations of Ge-Ge homopolar bonds in ethane-like Ge 2 Se 6/2 units. Boolchand and coworkers have used Mossbauer spectroscopy to probe chemical ordering at both the cation and anion sites in glassy Ge^Se!^ (see Boolchand, 1986, for a review). The cation (Ge) sites have been

probed using 119 Sn absorption Mossbauer experiments in Sn-doped material (Boolchand et al., 1982) and even at the stoichiometric composition (x = 0.333) evidence was found for two chemically inequivalent sites (see Fig. 7-33), the dominant one (A) ascribed to Sn substituting for Ge in a chemically-ordered environment (viz. a GeSe 4/2 tetrahedron) and the other minor site (B) ascribed to Sn substitution in Ge 2 Se 6/2 units, i.e. in homopolar bonds. The anion (Se) sites have been probed using both 125 Te absorption (Boolchand etal, 1982b) and 129 I emission (Bresser et al., 1981) Mossbauer experiments in Te-

420

7 Chalcogenide Glasses

doped Ge^Se^^ glasses. In the emission experiments, unstable 129 Te m atoms are used as the dopant and the local structure is studied by monitoring the nuclear hyperfine structure of the daughter 129 I atoms formed by p-decay from the 129 Te m parent atoms. As for the cation sites, two chemically-inequivalent sites are discernible, which are ascribed to Te substitution in chemically ordered Se(Ge2) and disordered, i.e. homopolar Se (SeGe), sites. It has been suggested by Halpern (1976) that wrong bonds are the dominant type of defect in chalcogenide glasses because of their low formation energy. In the case of As 2 S 3 , the difference AE in bond energies D can be estimated from the As-S electronegativity difference A/ (Halpern, 1976; Vanderbilt and Joannopoulos, 1981; Tanaka et al., 1985): AE - D(As-S) - i[D(As-As) + D(S-S)] « ^(Ax) 2 = 0.3eV (7-17) Thus, the fraction of wrong bonds frozenin on quenching from temperatures in the range 625 < Tq < 1370 K, given by the Boltzmann expression exp(— AE/kTq), is expected to be 0.4-8%. It is significant that the activation energy for homopolar bond formation derived from the quenchtemperature dependence of the Raman intensity ratio for homopolar and heteropolar bonds (see Fig. 7-32) is 0.32 eV for Tq > 1070 K (Tanaka et al, 1985). Vanderbilt and Joannopoulos (1981) have calculated the electronic properties of wrong bonds in the case of glassy As 2 Se 3 , and find that such defects give rise to electron states lying in the bandgap between valence and conduction bands (see Fig. 7-34). The Se—Se wrong bond, denoted by C 2 (CXP) where the symbols in parentheses refer to the type of nearest neighbours (C = chalcogen, P = pnictogen), gives rise to a deep-lying gap state due to an anti-

As 2 Se 3

C 2 (C.P)

P 3 (P.2C)

Figure 7-34. Electronic density of states for arsenic chalcogenides with heteropolar (a) and homopolar bonds (b, chalcogen-chalcogen; c, pnictogen-pnictogen) (Vanderbilt and Joannopoulos, 1981).

bonding a| e state associated with the abonded pair of p Se orbitals of the Se-Se bond; the defect is neutral when the afe state is unoccupied. Similarly the As-As bond also gives rise to a deep gap state, now due to the TI* combination resulting from a ^-interaction between the aAs bond orbital of the homopolar bond and two neighbouring pSe orbitals; the defect is neutral when this gap state is fully occupied. 7.4.3 Coordination Defects Much discussion has also been devoted to coordination defects in chalcogenide glasses, i.e. those defects arising from broken bonds where, if atomic reconstruction does not subsequently take place, the defects will be under-coordinated, and if local reconstructions can occur, the defects may be over-coordinated with respect to the normal bonding configurations in a chemically-ordered network. Such reconstructions are favourable in chalcogenide mate-

7.4 Defects

rials owing to the presence of the nonbonding p-like lone-pair orbitals of the chaleogens, forming the top of the valence band in the electronic density of states (Kastner, 1972; see Sec. 7.5.1), and which can take part in dative-bonding reactions. In Fig. 7-35 is shown the hypothetical transformation of two neutrally-charged chain-end dangling bonds (C?) to a negatively-charged under-coordinated defect (Cf) and a positively-charged overcoordinated (Cj) site, viz.

2c?^c 3 + + e r

(7-i8)

The transfer of an electron from one Cj centre to another in Fig. 7-35 involves a change in energy U, the effective correlation (or Hubbard) energy, with C/R

(7-19)

where Uc is the positive coulombic energy cost involved in placing a second electron at a site (i.e. in forming a Cj~), and UR are the energy changes involved in any subsequent reconstructions at the defects, e.g. in the formation of the dative bond between the empty p-orbital of a Ct+ centre (after the removal of an electron from Cf) and the occupied lone-pair p-orbital of a neighbouring normally-bonded chalcogen, viz.

421

Anderson (1975), in a general discussion of defects in chalcogenide materials, argued that the effective correlation energy U should be negative, i.e. reaction (7-18) should be exothermic, essentially because the structure of an amorphous material will minimise its energy by ensuring that electron pairing always occurs, either in covalent bonds or lone-pair (non-bonding) orbitals. Subsequently, Mott et al. (1975) and Kastner et al. (1976) applied the general spin-pairing picture of Anderson (1975) to the specific case of point (dangling-bond) defects in chalcogenide glasses, as in Fig. 7-35, where it was assumed from simple chemical-bonding arguments that U was negative, so that the spin-paired, oppositely charged valence-alternation pairs (VAPs; Kastner et al., 1976) would be energetically favourable. Realistic total-energy calculations for aSe by Vanderbilt and Joannopoulos (1980) have indicated that the neutral undercoordinated C° centre is lower in energy, i.e. more stable, than the overcoordinated C° centre and that the C° defect produces a deep-lying gap state due to a 71-bonding interaction between the unpaired spin and a lone-pair orbital on the neighbouring chalcogen atom. However, subsequent calculations by Vanderbilt and Joannopoulos

Figure 7-35. Schematic illustration of the formation of valence alternation pair coordination defects (D + , D~) from neutral dangling bonds in a-Se (Elliott, 1990).

422

7 Chalcogenide Glasses

(1983 a, 1983 b) have shown that for the case of a-Se, in fact the effective correlation energy is positive, U«0.4 eV, since although the relaxation UR in Eq. (7-19) associated with the process C^ -»C J is negative (^ — 0.5 eV), the intra-site couloumb repulsion energy for the process C?->C^ is much larger in magnitude {Uc~ +0.9eV). Hence, diamagnetic spin pairing in a-Se is predicted to be energetically unfavourable. The situation is considerably more complicated for compound chalcogenide materials, e.g. V-VI materials, where both pnictogen- and chalcogen-based defects could occur in principle (e.g. C j , C^, P 2 , P4, PJ, and the neutral centres C°, P 2 and possibly P^); furthermore the type of atoms (P or C) which are nearest neighbours of the coordination defect should also be specified since they affect the energy levels of the associated gap states. In summary, the theoretical calculations of Vanderbilt and Joannopoulos (1981) indicate that for V-VI materials, deep gap states associated with neutral paramagnetic defect centres only occur when homopolar bonds are immediately adjacent to the defect (e.g. C° (C), P°(2P),P°(P,C)). Dangling-bond defects at which the local bonding is chemically ordered (viz. CX(P) and P2(2C)) give rise to electron states which prefer to be charged and diamagnetic, i.e. Cj~, P j ; the empty nonbonding orbital (NBO) associated with the P^ centre can, in principle, take part in further dative-bonding reactions with a nearby Se p-like NBO, thereby forming a C3 centre, or even with the s-like NBO of a nearby As atom, thereby resulting in an overcoordinated P4 centre at which sp 3 hybridization has occurred. Although realistic total-energy calculations have not been performed for amorphous compound chalcogenides, e.g. As2Se3, nevertheless it is likely that the

effective correlation energy U for such systems would be negative (Vanderbilt and Joannopoulos, 1981). The concentration of such coordination defects will be determined by the VAP creation energy EVAP associated with the defect creation reaction 2C°2

(7-20)

£y AP might be expected to be relatively low (^0.5 eV) since reaction (7-20) involves essentially just a bond flip. The concentration of randomly-distributed VAP centres frozen-in on quenching through Tg will then be given by (Vanderbilt and Joannopoulos, 1981): nR « n0 exp(-£ VAP /2/e T)

(7-21)

where n0 is the total atomic density. Experimental evidence for the existence of such thermally-generated defects in As2Se3 has come from transient photoconductivity (TPC) measurements in the glassy state below Tg and in the liquid state above Tg (Thio et al., 1984). If neutral defects (C?) are the dominant recombination centres, measurement of the recombination time from TPC measurements yields an estimate for the concentration n of such defects. Thio et al. (1984) found that n was thermally activated, with an activation energy 0.35 eV and a pre-exponential factor of ^ 4 x 1017 cm" 3 for T < Tg, whereas for T > Tg, the activation energy was 0.8 eV and the pre-factor ^ 6 x 1022 cm" 3 . Above Tg, defects are created thermally from normally-bonded atoms (C2) with a number density of —1022 cm" 3 ; the activation energy involved in the creation of (C°) recombination centres from C^ or C^~ centres will be therefore (\U\ + EyAP)/2, which is identified with the value of 0.8 eV found experimentally. However, for temperatures below Tg, the total defect concentration is frozen-in, but the conversion of C? centres

7.4 Defects

from C^ or Cx centres (the reverse of reaction (7-18)) continues to be thermally activated with an activation energy \U\/2; experimentally this value is 0.35 eV. Thus, these results indicate that for a-As2Se3, £ VAP ^0.9eV and E/«-0.7eV. 7.4.4 Experimental Probes for Defects

In this section we will review some experimental techniques which are sensitive to the presence of small concentrations of defects, particularly coordination defects, utilising their opto-electronic properties. Those techniques which are sensitive to homopolar bond defects, i.e. Raman and Mossbauer spectroscopies, have been discussed in Sec. 7.4.2 (see also Chap. 6). 7.4.4.1 Electron Spin Resonance

Electron spin resonance (ESR), or equivalently paramagnetic resonance (EPR), is a probe for unpaired electron spins associated, say, with neutral (paramagnetic) dangling-bond defects, e.g. C° or P°; the method has the advantage of having a high sensitivity (^10 1 5 spins cm" 3 ). ESR signals in pure chalcogenide glasses are generally observed only after optical excitation (see Bishop et al.91977), the materials being diamagnetic in cold, dark conditions (Agarwal, 1973). (It was this observation that prompted Anderson (1975) to propose the negative effective correlation model.) An exception to this rule concerns glassy G e ^ S i ^ materials which, exceptionally, do exhibit an ESR signal in the absence of optical excitation (Cerny and Frumar, 1979; Kordas et al., 1985; T. Shimizu, 1985; Watanabe et al., 1988). The nature of the spin centres in a-Ge^S^^ has been the subject of some disagreement: Cerny and Frumar (1979), Gaczi (1982), and T. Shimizu (1985) have ascribed them to Ge or S dangling bonds depending on

423

the stoichiometry (x>0.33 and x<0.33, respectively), whilst Kordas et al. (1985) have suggested that the ESR line consists of two components, one being associated with paramagnetic electron hopping between sites and the other to conduction electrons in Ge-rich regions. It is likely, however, that dangling bonds with a distribution of correlation energies, U, are responsible: indeed T. Shimizu (1985) finds that the ESR intensity decreases with temperature up to T « 200 K (due to a sub-set of defects with a negative U) and increases at higher temperatures (due to a sub-set of defects with a positive U). In general, however, chalcogenide glasses are normally diamagnetic and exhibit an ESR signal only after illumination with bandgap light. Two types of behaviour can be distinguished, depending on the intensity of the light used to induce the signal. Low intensity (~lmWcm~ 2 ) irradiation of chalcogenides, with photons of energy comparable to the bandgap, at low temperatures (~ 10 K) produces an ESR intensity which saturates with illumination time (Bishop et al., 1977), indicating that preexisting diamagnetic defects are being transformed by optical excitation into paramagnetic centres. Freitas et al. (1985) have also shown that irradiation with lowintensity sub-bandgap light produces similar effects. In the case of the As chalcogenides, both chalcogen-based and pnictogen-based paramagnetic centres have been identified (Bishop et al., 1977; Hautala et al., 1988), viz. C? or P° centres, respectively, presumably resulting from the trapping of photo-created holes and electrons by the diamagnetic defects C^ or P^. The photo-induced ESR signals for a series of a-AsJCS1_x alloys are shown in Fig. 7-36 (Hautala et al., 1988): the S-related signal, seen in the S-rich samples, is rather narrow, and has an anisotropic g-tensor with

424

7 Chalcogenide Glasses

3.5

Magnetic Field (kG)

tics of the s-p hybridized centre P° do not agree with experiment (Gaczi, 1982). With high-intensity (^100mWcm~ 2 ) illumination at low temperatures, on the other hand, the photo-induced ESR signal does not saturate (Benoit a la Guillaume etal, 1977; Biegelsen and Street, 1980; Hautala et al., 1988); furthermore, if such an irradiated glass is thermally annealed (at ~ 300 K) and then reilluminated at low temperature, a very rapid re-inducing of the ESR signal up to the previous level occurs, followed by a further much slower non-saturating growth (Fig. 7-37). The slow non-saturating growth of the ESR signal is ascribed to the creation of new defects (by bond-breaking), and it is assumed that on annealing these photo-generated paramagnetic defects convert to a diamagnetic form but do not disappear; subsequent illumination causes a rapid transformation of these defects back to a paramagnetic state by charge trapping, followed by further (slower) bond-breaking defect creation. In fact, Hautala et al. (1988) have shown that four different metastable light-induced ESR centres can be induced in a-As^Si-^ by prolonged illumination. Type-I defects, consisting of an As and a S centre, anneal out at a low temperature (180 K) and their

Figure 7-36. Photo-induced electron-spin resonance spectra measured at 20 K for As x S 1 _ x glasses (Hautala et al, 1988).

gi = 2.00, g2 = 2.02, and g3 = 2.07 (Bishop et al., 1977), whilst the As-related signal, which is dominant in As-rich samples, exhibits a characteristic hyperfine splitting resulting from the interaction of the unpaired electron spin with the 75As nucleus. From an analysis of the hyperfine splitting, it is concluded that the wavefunction of the As-related unpaired electron is almost completely p-like in character (Bishop et al., 1977); the predicted ESR characteris-

50

100 150 200 Exposure time (s)

250

300

Figure 7-37. Kinetics of photo-induced ESR spin density and that reinduced after annealing for glassy As2S3 measured at 20 K (Hautala et al., 1988).

425

7.4 Defects

concentration is independent of x; type-II defects, also consisting of an As and a S centre, anneal out at a higher temperature (300 K), and Asn defects dominate in Asrich material and S n in S-rich glasses, with the Asn centres being more purely p-like than the Asj centres. Elliott and Shimakawa (1990) have discussed in detail the bond-breaking mechanisms leading to such defects, and ascribe the type-I centres to As^(2S) and S?(As) defects, and the type-II centres are ascribed to As^As, S) and S? (S) defects; such an interpretation is in accord with the theoretical description of the electronic states of such defects by Vanderbilt and Joannopoulos (1981).

a-As2Se3

10

/a-As 2 S 3

PL

- /A\ - /--

10 -

, a \~ \

PLET

-// i

/

\ i

10 7.4.4.2 Photoluminescence

The technique of photoluminescence (PL) probes the radiative recombination of optically-created electron-hole pairs in a material. Coordination defects can act either as radiative or non-radiative recombination centres. Steady-state (c.w.) optical excitation of chalcogenide materials (both amorphous and crystalline) produces a single, rather broad luminescence band, which is significantly Stokes-shifted from the peak in the photoluminescence excitation (PLE) spectrum (see Fig. 7-38); note that a-SiO2 behaves in a qualitatively similar fashion. Reviews of the subject have been given by Street (1976) and Kastner (1985). The model first proposed for (c.w.) PL in chalcogenide glasses involved the trapping of one member of the photo-generated electron-hole pair by an isolated charged defect, say Cj~ +h->C?; the remaining carrier was then supposed to recombine radiatively with the trapped carrier, viz. C? -+- e -»C[" -h h vPL. The luminescence and excitation photon energies differ (by a Stokes shift) if a structural relaxation occurs upon charge trapping.

5 10 Photon energy (eV) Figure 7-38. Comparison of spectra for steady-state (c.w.) photoluminescence (PL), photoluminescence excitation (PLE), optical absorption (a) and photo-induced absorption (dashed line) for two chalcogenide and an oxide glass (Elliott, 1990).

However, this simple model for the PL process has had to be revised in the light of time-resolved (transient) PL studies (e.g. Murayama, 1983; Higashi and Kastner, 1983; Robins and Kastner, 1984). For both amorphous and crystalline chalcogenides, the PL decay exhibits a knee in a doublelogarithmic plot (see Fig. 7-39). Thus the PL decay behaviour can be divided into two regimes, one being dominated by processes characterised by short times (t^ 10" 6 s) and the other by longer times (t^lO~ 4 s); the long-time processes account for most of the PL quantum efficiency and therefore they dominate the steady-state (c.w.) behaviour. The origin of these two decay processes is still not entirely clear but probably is as follows.

426

7 Chalcogenide Glasses

J Ditrar>f uni

if)

105 2.15 eV

104

bio- 7 a

103 intensit

= 2.56eV

To 10"6 c

1.78 eV

^ icr

2

10

£ 10" c

i

10 1

_L 10"

6

_L

I

10' 10"* Time delay (s)

10" 10-2

10-6

10"*

10-2

Time (s)

ta)

(b)

Figure 7-39. Photoluminescence time decays in chalcogenide materials: (a) amorphous As2Se3 (Higashi and Kastner, 1983), (b) crystalline As2Se3 (Robins and Kastner, 1984).

The short-time behaviour seems to be consistent with a mechanism of donoracceptor pair recombination (Higashi and Kastner, 1981; Depinna et al., 1983), in which radiative recombination occurs when an electron of a neutralized donor is transferred to a neutralized acceptor; the centres are equally and oppositely charged in the ground state (e.g. CJ, C^ pairs) and neutral in the excited state. There is an extra coulombic contribution Ec to the PL recombination energy, resulting from the interaction between ionized donor and acceptor, given by = e2/4nss0R"

(7-22)

with the PL energy therefore being Ep = E» + Ec

(7-23)

where E™ is the energy corresponding to infinite separation. Since the rate of radiative recombination is governed by the rate at which the electron tunnels between sites, given by v = v0 exp(—2aJR)

(7-24)

where a describes the spatial extent of the wavefunction, varying the distances R between the donor and acceptor sites produces a correlation between the PL energy and the time at which the PL is measured. From Eqs. (7-23) and (7-24), the mean PL energy is predicted to shift to lower photon energies with increasing delay time according to (Higashi and Kastner, 1981) <£„(*)> = £» +

2cce2

47tee0 ln(vot)

(7-25)

and the width A(t) of the PL peak is also predicted to narrow with increasing time delay. I" 2 a e2 1 (7-26) 2 L47i££ o ln (i? o 0j where a is the width of an assumed Gaussian homogeneous line shape. The time dependence embodied in Eqs. (7-25) and (7-26) appears to have been observed experimentally (Higashi and Kastner, 1981). For the case of PL decays at long times, Higashi and Kastner (1983) have suggested

7.5 Opto-Electronic Properties

that such slow rates (long times) are determined by a forbidden quantum-mechanical selection rule involving spin, in particular resulting from the (formally forbidden) transition between a spin triplet excitedstate configuration and a singlet (i.e. spinpaired) ground state. Further evidence in support of the triplet excited state has come from optically-detected magnetic resonance (ODMR) measurements (see e.g. Cavenett, 1981). Two possible candidates for PL centres involving triplet excited states are a self-trapped exciton (STE), where the initially free photo-created exciton can subsequently lower its energy by forming self-trapped (localised) states in which the lattice is locally distorted (see Fig. 7-40) (Emin, 1980; Murayama et al., 1980); Street (1977) has suggested that a metastable version of such an STE state could arise from a photo-induced bond switch, resulting in an intimate valence al-

Energy Configuration coordinate

Figure 7-40. Schematic illustration of the model for self-trapping of excitons in chalcogenide glasses. Optical excitation (I) to an exciton state can be followed by two non-radiative decay channels (Street, 1977), either directly back to the ground state (III) or to the metastable self-trapped exciton (STE) state (IV), which can be regarded as a D + - D ~ pair (IVAP). Alternatively, STE states can form where the lattice distortion is less severe, and may then act as the (triplet) radiative recombination PL centre (II) (Elliott, 1990).

427

ternation pair (IVAP) (see Fig. 7-40). Alternatively, previously existing IVAP defects could act as sites for triplet excitation (Higashi and Kastner, 1981).

7.5 Opto-Electronic Properties 7.5.1 Electronic Structure The electronic density of states (DOS) in chalcogenide materials comprises a valence band, composed principally of p-like bonding (a) orbitals, and a conduction band formed from antibonding (a*) orbitals, with the top of the valence band being composed of chalcogen-derived plike non-bonding orbitals and the nonbonding s-states lying at the bottom of the band (see Fig. 7-41 for a schematic representation for the case of As2Se3 and Fig. 7-34 a for a calculated DOS (Vanderbilt and Joannopoulos, 1981)). Numerous calculations of the DOS for various chalcogenides have confirmed this general picture, although it appears that the lone-pair band is less distinct, i.e. there is more mixing of p - a and p-7i states, in the As chalcogenides (Bullett, 1976; Althaus et al., 1978) than for either the pure chalcogens (Joannopoulos et al., 1975) or the Ge chalcogenides (Louie, 1982). The electronic DOS can be probed experimentally using photoemission techniques and this has been done, for example, for the case of Se (Takahashi, 1982), As 2 X 3 (X = S, Se, Te) (Bishop and Shevchik, 1975) and GeX2 (X = S, Se) (Takahashi and Harada, 1980; Hindo et al., 1980); the lone-pair band at the top of the valence band can be seen clearly (see Fig. 7-42). The changes in XPS and UPS spectra have also been used to demonstrate that a-GeSe films deposited onto cooled substrates have 3 : 3 coordination, but this changes to 4 : 2 after thermal annealing (Takahashi and Sagawa, 1982).

428

7 Chalcogenide Glasses

BULK \

AS

\ / \

/ /

•

v

v

V

>

2.

O cc 0 ui z UJ

c* Se

/

p

/

/

|

\

.1...

/

/\ \ / /

/

Y

/ \ y

, ' '

Pc Se

.N

/

^

\

t 5 i.

\


>''

\ N

/

v

/

/

Amorphous chalcogenide materials are invariably semiconductors, with the size of the bandgap varying in the range ~ 1 3 eV. Several factors influence the magnitude of the gap: the gap generally increases as chalcogen atoms are substituted at fixed composition by other chalcogens in the series Te-*Se->S; furthermore, the gap for chalcogenide alloys varies with composition and often exhibits extrema at stoichiometric compositions, for example, minima in the case of A s ^ S ^ (Fisher et al., 1976) and As^Se^^ (Kosek et al., 1976), and a maximum in the case of GexSe1_JC (Tronc etal, 1973). Shimakawa (1981) has accounted for such compositional variations in terms of a simple alloying model in which the energy gap, Eg of a chalcogenide alloy AXC±_X (e.g. ,4 = Ge, As; C - S , Se) can be represented as the sum of two contributions, one associated with the gap of aji ordered (stoichiometric) composition, and the other associated with the element in excess, both weighted by the appropriate atomic fractions, e.g.

Eg = yEg(A) + (l-y)Eg(AmC^m)

Q 2

\

/

b

b

\

\ V

a

i a.

/

.

V

ft. Se

p *s

, \

i -2

'

/ N

a.1

\

a

/

V

BAI

cr# BAND

r—"i

DEFECTS

BASIS

(7-27)

Se

b

Figure 7-41. Schematic origin of the electronic density of states in As2Se3 in terms of atomic and molecular orbital states (Vanderbilt and Joannopoulos, 1981). The positions of various defect states are also marked.

where AmC1_m is the stoichiometric composition. 7.5.2 Optical Properties

In this section, we will consider only those optical properties of amorphous chalcogenide materials resulting from optical transitions across the bandgap, between electron states at the top of the valence band (i.e. the p-n lone-pair band) and the bottom of the conduction band, neglecting, therefore, the transitions occurring at higher energies (in the UV and Xray regions) from states deeper in the valence band or from the core states. In the case of the semiconducting amorphous chalcogenides, the optical absorption coefficient, a, changes rapidly for photon energies comparable to that of the bandgap, Eg9 giving rise to an absorption edge. Three regions can be distinguished: I - at the largest photon energies where a is concomitantly also the highest (^10 4 cm" 1 ), and tends to a saturated value, interband transitions occur between valence and conduction bands; II - in the

7.5 Opto-Electronic Properties

429

region I exhibits a power-law dependence on photon energy hco if the densities of states in the valence and conduction bands also have a power-law energy dependence in the vicinity of the gap, viz. 0 c (E-E o )ocE«

(7-28 a) (7-28 b)

whence (DOL{(D) GC (hco — Eo)

5

and where Eo is some measure of the bandgap. In the special case, where both valence and conduction band edges have a parabolic shape (p = q = \\ Eq. (7-29) becomes

20

10 15 Binding energy (eV)

a)

cooc(co) oc (hco — E 0 ) 2

uni

larb. ;ity V) C CD

XPS ii

a

Monochromatized XPS (hv = U86.6eV)

s.

V)

\

\r\

J

J\

n\ \

As2S3 glass (bulk)

\

^ ^

\

>v \ J

/

f

**—""* * \ III

>v

As2S3 crystal

\ I ! 5 10 Binding energy (eV)

^V

(orpirnent)

(7-29)

^

i 15

b)

Figure 7-42. (a) X-ray photoemission spectra (XPS) of amorphous, trigonal (t) and monoclinic (m) Se taken using Mg Ka radiation (Takahashi, 1982). The upper and lower 4 p bonding bands are indicated by bars in the spectra of t- and m-Se, and the approximate 4 s bandwidths are indicated by dashed lines, (b) XPS of glassy and crystalline As2S3 (Bishop and Shevchick, 1975).

region of the edge itself (10 < a < 104 cm 1); and III - at the lowest photon energies and at low values of a ^ 10 cm" 1 where transitions between (defect) states in the gap and the bands take place. Under certain conditions (in the random-phase model, where the k-selection rule breaks down - see Elliott, 1990), the absorption coefficient in

(7-30)

Thus, Tauc plots of (ahco)112 versus hco should be linear and extrapolate to values of the (optical) gap, Eo. Fig. 7-43 shows this quadratic dependence for chalcogenide glasses (and a-Si). However, not all chalcogenide materials exhibit this behaviour for coa(co): a-Se exhibits a linear energy dependence, and multicomponent chalcogenide alloys (e.g. Ge-As-Te-Si) show a cubic energy dependence. It should be noted that Eo, obtained in this way, is not necessarily exactly equal to the true gap £ g between mobility edges in the valence and conduction bands. Part of the uncertainty arises from a breakdown of the random-phase approximation for photon energies hco& Eg (Dersch et al., 1987; Abe and Toyozawa, 1981); as a result, the optical absorption is not just determined by the joint density of states, as in Eq. (7-29), but also depends on energy-dependent matrix-element terms. The optical absorption edge in amorphous semiconductors is not as sharp as predicted from Eqs. (7-29) or (7-30), but exhibits a long tail into the gap region, and which almost invariably depends exponen-

430

7 Chalcogenide Glasses

Figure 7-43. Tauc plots of optical absorption coefficient ([ahco]112 vs. hco) for

various chalcogenide glasses (Mott and Davis, 1979). 1.0

U

1.8

2.2

2.6

3.0

Photon energy (eV)

tially on the photon energy: a((o) = oc0 exp[— r(Ef0 — hco)]

(7-31)

where E'o is an energy comparable to the threshold energy Eo involved in interband transitions (see Eq. (7-30)), and F is a temperature-dependent constant, typically having values in the range 10-25 eV" 1 . This Urbach-edge behaviour is also exhibited by chalcogenide materials (Fig. 7-44). The origin of the Urbach edge is still unclear, but two general mechanisms may be responsible: either the exponential en-

ergy dependence of a arises from an exponential energy dependence of the valence and conduction band densities of states at the band edges (neglecting matrix-element effects), or a particular universal absorption mechanism exists which gives rise to the exponential behaviour of a, e.g. the field-broadened exciton model of Dow and Redfield (1970). In the former case, Abe and Toyozawa (1981) and Soukoulis et al. (1984) have shown theoretically that exponential band tails can result from potential fluctuations associated with structural dis-

10-

0)

S 103

_Q <

GeTe

Figure 7-44. Urbach edges for chalcogenide glasses (Mott and Davis, 1979).

CdGeAsJ 0.8

1.2 1.6 2.0 Photon energy (eV)

2.L

2.8

7.5 Opto-Electronic Properties

order, where the inverse of the slope parameter in Eq. (7-31), T" 1 , is related directly to the extent of disorder. Experimental evidence for the existence of exponential band tails (at least for the valence band) in a-As2Se3 has come from the transient hole photoconductivity measurements of Orenstein and Kastner (1981) and Monroe (1985) - see Kastner (1985) for a review. The observed power-law time dependence of the photocurrent decay requires an accurately exponential density of states in the multi-trapping model (Orenstein and Kastner, 1981). Although there is experimental evidence in the case of a-Si: H that the magnitude of F " 1 is determined by the degree of disorder (Cody, 1984), the position for chalcogenides is not as clear-cut. For example, Tanaka et al. (1985) have reported that the slope of the Urbach absorption edge (viz. F) for glassy As 2 S 3 does not change as a function of the quench temperature Tq, even though the EXAFS measurements of Yang etal. (1987) have indicated that the structural disorder (in the As-S bond length) does increase with increasing Tq. However, the optical gap (in particular, the photon energy at which a = 2x 10 3 cm~ 1 ) does decrease slightly with increasing Tq, perhaps due to the influence of the introduction of homopolar bonds (Tanaka et al., 1985). These rather contradictory results could be explicable, however, in terms of the lone-pair (LP) nature of the top of the valence band (VB) in chalcogenides. If the tailing of the VB is mainly responsible for the Urbach edge, intra-molecular (bond-length and bond-angle) fluctuations should have relatively little effect on the width of the LP band and hence on F. However, the application of pressure would be expected to change the width of the LP band due to an increase in L P - L P repulsive interactions with increasing pres-

431

sure in those materials with a local dimensionality less than 3 (see Sec. 7.3.2.2). This effect would lead to a pressure-induced decrease in the gap (see Fig. 7-17), as well as to an increase in the degree of tailing at the band edge; a decrease in F (increase in F ~x) with pressure is indeed observed in amorphous chalcogenide materials (see Fig. 7-45) (Tanaka, 1989 a). Finally, we discuss the low-energy region of the optical absorption profile in amorphous chalcogenides. The exponential decrease in a with decreasing photon energy characteristic of the Urbach edge implies great transparency in the IR region for such pure (i.e. impurity- and defect-free) materials. This characteristic, of course, makes chalcogenides attractive materials for low-loss optical transmission (Savage, 1985) in the window region, corresponding to the minimum in a, between the optical absorption edge and the multiphonon edge, i.e. the high-energy side of the vibrational density of states (see Fig. 7-46 (Strom et al., 1974)). However, in this low-a, low-frequency region, oxide and other prevalent impurities can give rise to unwanted extrinsic absorption bands (see Fig. 7-47). In addition, intrinsic defects, such as coordination defects, in chalcogenide glasses can

100 50 Pressure (kbar) Figure 7-45. Pressure dependence of the slope parameter, F, of the Urbach edges of amorphous chalcogenide materials (g = glass, f=film) (Tanaka, 1989 a).

432

7 Chalcogenide Glasses

also give rise to optical absorption in midgap. This is particularly so when samples are illuminated at low temperatures under conditions where a metastable ESR signal is induced (see Sec. 7.4.4.1); a mid-gap absorption in excess of the Urbach edge is induced thereby (see Fig. 7-48), the precise shape of the absorption band depending on the intensity and wavelength of the inducing light (Biegelsen and Street, 1980). These mid-gap absorption bands have been ascribed to electron or hole transitions to the conduction band or valence band, respectively, from optically-induced neutral paramagnetic defect centres, e.g. C? (Bishop etal., 1977; Biegelsen and Street, 1980). A collection of optical properties for various amorphous chalcogenide materials is given in Table 7-3.

80 I I I 11

r

i

~i—r

i—r—r

tinl

(a)

-

40-

I

_LLL

1 I I I I 11

I

\

1

(b)

£

-

I M i l l I i ,' \ I A I 1

0

40

id) . 40

01 I I 11 I 0.5 1.0

I

I

1 I I I1 I

5 Wavelength (pm)

10

50

Figure 7-47. Transmittance spectra of chalcogenide glasses, with (dashed curve) and without (solid curve) extrinsic impurities: a) Ge 30 As 20 S 50 ; b) Ge 34 As 8 Se 58 ; c) Ge 30 As 13 Se 27 Te 30 ; d) Ge 10 As 50 Te 40 (Savage, 1985).

7.5.3 Electrical Properties

10-3 10*

103

102

10

10"

1

Wavelength (cm" )

Figure 7-46. Vee-shaped optical profile for glassy As2S3 showing the window region of optical transparency between the optical absorption and multiphonon edges (Strom et al., 1974).

As mentioned in the previous section, amorphous chalcogenides typically have bandgaps in the range l-2.5eV and are therefore semiconductors. As a consequence, the temperature dependence of the dx. conductivity
(7-32)

where the pre-exponential factor takes values typically in the range K ^ - K ^ f l T 1

433

7.5 Opto-Electronic Properties TO4

Table 7-3. Optical properties of chalcogenide glasses. As 2 S 3

Material

Eo (eV)

Reference

Se As 2 S 3 As2Se3 As2Te3 SiSe2 SiTe3 GeS2 GeSe2 Sb2Se3

2.05 2.32 1.76 0.83 3.35 1.33 3.07 2.18 0.70

1 2 2 3 4 5 6 7 7

30K

3

10 -

o = 2.41 eV / INITIAL 102

8 o

101 EY = 2.41 eV

1.4

1.6

1.8

2.0

2.2

2.4

2.6

PHOTON ENERGY (eV)

Figure 7-48. Mid-gap optical absorption in glassy As2S3 at 30 K induced by 2.4 eV light with intensities of 10 (dashed line) and 100 mWcm~ 2 (solid line). The optical absorption spectrum before illumination is shown by the dotted line (Biegelsen and Street, 1980).

cm * and the activation energy Ea is usually approximately half the optical gap, £ g , indicating that the Fermi level lies near mid-gap (Elliott, 1984,1990). For the most part, the d.c. electrical behaviour in such systems can be understood in terms of a picture involving transport in extended states in the valence or conduction band, beyond a mobility edge separating extended and localized gap states (Mott and Davis, 1979; Elliott, 1984). Some data relating to the d.c. conductivity of amorphous chalcogenides is given in Table 7-4, and an extensive collection is given in Borisova (1981). It is noteworthy that in chalcogenides £ o w £ g / 2 and that plots of lna dc vs. 1/T are generally linear except at the lowest temperatures; both these features are indicative of the Fermi level at E F being pinned

References: 1) Davis, E. A. (1970), J. Non-Cryst. Sol. 4, 107; 2) Mott, N.F. and Davis, E.A. (1979), Electronic Processes in Non-Crystalline Materials. OUP; 3) Weiser, K. and Brodsky, M.H. (1970), Phys. Rev. El, 791; 4) Harris, XH. and Tenhover, M. A. (1986), /. Non-Cryst. Sol. 83, 272; 5) Madhusoodanan, K.N., Philip, X, Asokan, S., Parathasarathy, G., and Gopal, E.S.R. (1989), /. Non-Cryst. Sol. 109, 255; 6) Ticha, H., Tichy, L., and Cernoskova, E. (1983), Phys. Stat. Sol. B119, K135; 7) Shimakawa, K, (1981), /. NonCryst. Sol. 43, 229.

Table 7-4. Electrical properties of chalcogenide glasses. (eV)

Material

r

Se As 2 S 3 As2Se3 As2Te3 GeS2 GeSe2

1.10 1.14 0.91 0.42 0.72 0.95

a (300 K)

Reference

References: 1) Hartke, XL. (1962), Phys. Rev. 125, 1111; 2) Seager, C.H. and Quinn, R.K. (1975), 1 Non-Cryst. Sol. 17, 386; 3) Ticha, H., Tichy, L., Rysava, N. and Triska, A. (1985), /. Non-Cryst. Sol. 74, 37; 4) Narasimhan, P.S.L., Giridhar, A., and Mahadevan, S. (1981), /. Non-Cryst. Sol. 43, 365.

near mid-gap. It appears that E¥ does not itself lie in a band of states (e.g. in the absence of illumination there are no mid-gap states apparent from optical absorption measurements), but rather is pinned between two bands of states lying near the valence and conduction bands, correspond-

434

7 Chalcogenide Glasses

ing to negative-U VAP defects (e.g. CJ, Cx - see Sec. 7.4.3) (Adler and Yoffa, 1976). As a result of this pinning of the Fermi level by native defects, it is extremely difficult to dope chalcogenides so as controllably to vary their electrical characteristics. Nevertheless, it appears that under certain circumstances, amorphous chalcogenides can be electrically doped. For example, the addition of more than ~10at.% Bi to chalcogenide glasses causes them to become n-type (Schottmiller et al., 1968; Tohge et al., 1979) - for a review see Elliott and Steel (1987). (Such a phenomenon is perhaps better described as one of chemical modification rather than conventional doping, since the concentration of impurity required to effect the change is so large.) The d.c. conductivity increases by about seven orders of magnitude with the incorporation of about 10 at.% Bi in the case of Ge-S (Tichy et al., 1985) and Ge-Se glasses (Tohge et al., 1980) (see Fig. 7-49 a), and the sharp change in adc at the p - n doping transition is accompanied by an equally precipitate drop in the conductivity activation energy, E a , at the same Bi content. On the other hand, the optical gap, E g , decreases continuously with increasing Bi content until a plateau is reached (see Fig. 7-49 b). The change in Eg with Bi content is much more marked than is the case for incorporation of Sb, which obeys approximately the alloying model of Shimakawa (1981) (see Eq. (7-27)). Two different explanations have been advanced to account for the effect of Bi: one ascribes the change in electrical properties to an inhomogeneous (percolation) transport mechanism in which microphase separation into (microcrystalline) clusters of n-type Bi 2 X 3 (X = S, Se) occurs (Tichy et al., 1985); the other supposes that the Bi impurities are distributed homogeneously in the glass structure in a charged state,

•

£ o

> 8

10

•

106 6 8 x(at.% Bi)

a)

10

12

3.0

Sb-Ge-Se \~ I Bi-Ge-Se Sb-Ge-Se 1.5

~--j-

-i—jBi-Ge-S

Bi-Ge-Se

1.0 b)

x (at. %)

10

15

Figure 7-49. Chemical modification of electrical and optical properties of chalcogenide glasses by the incorporation of Bi (Elliott and Steel, 1987); a) electrical resistivity, Q (circles Bi-Ge-Se, crosses Bi-Ge-S), b) optical gap, Eg (solid curves, calculated from Eq. (7-27)), dashed curves, guides for the eye).

7.5 Opto-Electronic Properties

causing the relative proportion of charged coordination defects to change and thereby unpinning the Fermi level (Nagels et al., 1983; Saiter et al, 1985; Elliott and Steel, 1987). The Bi Lm-edge EXAFS results of Elliott and Steel (1986,1987) for Bi-Ge-S glasses indicate that Bi is always 3-fold coordinated by chalcogen atoms, but that a marked change in Debye-Waller factor occurs at —5 at.% Bi; this change has been ascribed to an increase in the static disorder at the Bi sites associated with the formation of positively-charged Bi^. In the case of sputtered thin films of amorphous Bi-Ge-Se, however, Sotiropoulos and Fuhs (1989) found no abrupt change in £ a , and therefore ascribed the change in oAc to an alloying-induced decrease in the bandgap. Modification of the electrical properties of amorphous chalcogenides has also been found for other impurities, e.g. Pb in P b Ge-Se glasses (Tohge et al, 1987), Ni in co-sputtered As2Se3 films (Barclay et al, 1985) and K and Rb in a-Se thin films (Abkowitz et al, 1985). Holes are the dominant current charge carriers in amorphous chalcogenide materials, i.e. they are p-type semiconductors in general. The sign of the charge carriers cannot be determined from measurements of the Hall effect, which is invariably anomalous (see e.g. Elliott, 1990), but can be obtained from the thermoelectric power (thermopower), S, where

= n/T

(7-33)

and where 17 is the Peltier coefficient. In the model of conduction in extended states beyond the mobility edge, the thermopower can be written as (Mott and Davis, 1979)

435

where Es = £ c , y is the (linear) coefficient of the temperature dependence of the band edge (where conduction takes place) with respect to EF and A k T is the average energy of the transported electrons with respect to the mobility edge. Thus, in this model both
436

7 Chalcogenide Glasses

d.c. conductivity mobility; such a weakly temperature-dependent //H has been found for chalcogenide glasses (see Fig. 7-50 (Nagels, 1979)). Furthermore, for certain geometries of hopping sites for small-polaron motion, an anomalous sign of the Hall coefficient is also predicted (see Elliott, 1984, 1990). More recent theoretical work on conduction processes in amorphous semiconductors has tended to lead to a sort of harmonization of these opposing points of view. Since the work by Abrahams et al. (1979) on a scaling theory of localization concluded that a sharp mobility edge most likely does not exist in three-dimensional materials, the two-channel model has become less tenable. A theoretical consideration of electron-phonon interactions has led Miiller and Thomas (1984), Fenz et al. (1985) and Dersch and Thomas (1987) to propose that a phonon-induced delocalization occurs, whereby at finite temperature, electron states in the band tails become delocalized, essentially by allowing electrical transport to occur by phonon-assisted hopping processes. At very low temperatures, and particularly in highly-disordered chalcogenide materials prepared by vapour deposition, variable-range hopping conduction has been found, as characterised by the Mott law for the d.c. conductivity (see Mott and Davis, 1979): adc = G'oexp(-A/TV4)

(7-35)

in, for example, a-As2Te3 films deposited using r.f. sputtering onto substrates held at 77 K (Hauser and Hutton, 1976). In such Figure 7-50. Electrical transport data for five AsTe! 5Six glasses (the values of x are indicated in the figures) and an As0 3 Te 0>48 Si 0 . 12 Ge 0A glass for a) d.c. electrical conductivity; b) thermopower; c) Hall mobility (Nagels, 1979).

(

K"1 )

7.5 Opto-Electronic Properties

cases, conduction takes place by variablerange hopping between (paramagnetic) defect states lying at EF in mid-gap. In chalcogenide bulk glasses, or well-annealed thin films, variable-range hopping conduction is not normally observed because the negative effective correlation energy associated with the coordination defects in chalcogenides results in the formation of spin-paired, charged defects lying away from EF (see Sec. 7.4.3), and for which the electron-phonon coupling is so large that the hopping rates become unobservably slow (Phillips, 1976). In common with other amorphous semiconductors, chalcogenides also exhibit a frequency-dependent (a.c.) conductivity which, in the frequency range 10< 1 0 9 s ~ \ exhibits a power-law frequency dependence, viz. a(co) = Acos

(7-36)

where s < l and both A and s can be (weakly) temperature dependent. At high temperatures and/or low frequencies, the d.c. conductivity becomes dominant since it has a much larger temperature dependence than that of o{co\ so that the total measured conductivity can be written formally as: ^totM = crdc + ^ M

(7-37)

(Eq. (7-37), as written, implies that the d.c. and a.c. conductivities arise from different mechanisms; if they arise from the same mechanism, adc is just the co-+0 limit of a{co).) Elliott (1987 a) has given an extensive review of the a.c. conductivity behaviour of amorphous chalcogenide materials. The mechanism which seems best able to account for the experimentally observed a.c. behaviour is the correlated barrier hopping (CBH) model proposed by Elliott (1977, 1987 a). In this, two electrons (a bipolaron) are assumed to hop under the

Se-

-Se

Se

-Se

Se-

:Sei

D+) Se

a)

Se

437

Se

Se

Se

-Se

Se

Se

Se

Conduction band

Figure 7-51. The correlated barrier hopping (CBH) model for a.c. conductivity in chalcogenide glasses (Elliott, 1987). a) Schematic illustration of two-electron transport in a-Se causing the interconversion of D + , D~ (C3, Cf) defect centres, b) Schematic illustration of the lowering of the activation energy barrier from WM to W for two-electron hopping for two oppositely charged defect centres separated by a distance R due to a coulomb interaction. A site disorder energy A is also shown.

influence of the applied a.c. field between oppositely-charged coordination defect sites (e.g. C^, C^ - see Fig. 7-51 a), or possibly single polarons are assumed to hop between C^, C? or Cf, C° pairs of sites. The hopping rate involved in such processes involves an activation energy W which is correlated with the intersite separation R through a coulombic interaction between charge carrier and defect (see Fig. 7-51 b); for the case of a bipolaron W=WM-2e2/n880R

(7-38)

where WM is the maximum barrier height (for R = 00) and which has a value comparable to the (optical) bandgap (Elliott,

438

7 Chalcogenide Glasses

1987 a). The a.c. conductivity can then be calculated to be (Elliott, 1977, 1987 a) a(co)=7^N28sowRi

(7-39)

where N is the concentration of defects and the hopping distance R^ at a frequency co is given by

100

200

300

400

500 600

(a)

(7-41)

The success of this model in accounting for the experimental a.c. data for, say, amorphous As2Se3 (Hirata et al., 1983; Giuntini etal., 1981) is demonstrated in Fig. 7-52. However, in certain cases, the temperature dependence of a(co) at elevated temperatures (^300K) in chalcogenides, particularly those with smaller bandgaps, is considerably stronger than is predicted for bipolaron CBH (Eqs. (7-39), (7-40)). Shimakawa (1982) has explained this behaviour in terms of the thermal creation of neutral, paramagnetic centres (C?) from pre-existing charged spin-paired centres (the reverse reaction of (7-18)), which is an activated process; single polaron transport involving such defects is then assumed to be dominant. It can be seen from Fig. 7-53 that, with this modification, the CBH model can account for the a.c. conductivity of amorphous chalcogenides over a wide range of temperatures and frequencies. 7.5.4 Photo-Induced Changes

A wide variety of changes can be induced in amorphous chalcogenide materials by the absorption of photons of energy

h nduc t i v i t y

6kT [W M -fcrin(l/eoT o )]

'E 100 kHz

^A in

10

10

v.

id" o o

A.c.

where T0 is a characteristic relaxation time. The frequency exponent s of the a.c. conductivity can then be evaluated to be

10 kHz *•—*

N ^

•

1 kHz

10 12 (by

6 8 10 1000/T (K"1)

Figure 7-52. Application of the CBH model to experimental data for glassy As2Se3 (Elliott, 1987). a) Temperature dependence of the frequency exponent s. b) Temperature dependence of the a.c. conductivity at three frequencies.

comparable to the optical bandgap (or by irradiation by electrons or ions). Such changes may conveniently be divided into two categories, namely transient and metastable changes. Transient changes occur only whilst the sample is illuminated: examples include photoluminescence (see Sec. 7.4.4.2) and photoconductivity (see Sec. 7.4.3), and these will not be considered further here. By contrast, metastable changes remain after being induced, and these can be sub-divided into two further categories, namely irreversible and reversible, i.e. the latter of which can be annealed out by heating the samples to the glass-transition temperature, T . Some reversible changes

7.5 Opto-Electronic Properties

Figure 7-53. Prediction of the CBH model for glassy Se with both single (S) and bipolaron (B) hopping contributions (Shimakawa, 1982).

are associated with the photo-excitation of pre-existing (coordination) defects, e.g. light-induced ESR (see Sec. 7.4.4.1) and optically-induced mid-gap absorption (see Sec. 7.5.2), and these also will not be discussed further. Reviews of photo-induced phenomena have been given by Ka. Tanaka (1982), Owen et al. (1985), Elliott (1986), and Ke. Tanaka (1990). Amongst the class of irreversible photoinduced changes are a variety of chemical changes, including the phenomena of metal photo-dissolution, photo-crystallization and giant photo-densification of films. In the photo-dissolution process, a layer of metal (e.g. Ag, Cu or Zn) in contact

439

with an amorphous chalcogenide film dissolves into the chalcogenide upon irradiation with light having an energy comparable to the bandgap of the chalcogenide (Kostyshin et al., 1966; Ka, Tanaka, 1982; Doane and Heller, 1982; Owen et al., 1985; Lyubin, 1987). The actinic radiation appears to be absorbed at the interface between the metal-doped and undoped chalcogenide (Owen et al., 1985; Rennie and Elliott, 1985, 1987), and the speed of the reaction, as well as the formation of a sharp boundary between doped and undoped layers, appears to be a consequence of the fact that the doped chalcogenide material acts as a superionic conducting matrix for the dissolving metal ions. Another irreversible photo-induced chemical change observed in chalcogenides is photo-vaporization (Janai, 1981), in which an amorphous thin film (e.g. As2S3) is first photooxidised (Kolobov et al., 1989), and the resulting volatile surface oxide subsequently evaporates. Many amorphous chalcogenide materials, particularly those with low values of Tg, crystallize upon optical irradiation (e.g. Se (Dresner and Stringfellow, 1968) and As-Te-Ge (Weiser et al., 1973)). Finally, obliquely evaporated thin films of amorphous Ge chalcogenides, exhibiting a columnar morphology, undergo giant (~20%) changes in thickness (density) after optical excitation (Singh et al., 1980); this effect has been found to be due to a photo-induced collapse of the void structure comprising the columnar microstructure (Spence and Elliott, 1989). Another type of irreversible photo-structural change involves the photo-polymerization of As 4 S 4 molecules in as-deposited amorphous As-S films (Nemanich et al., 1978; Treacy et al., 1980; Lowe et al., 1986) to form a more nearly continuously bonded random network; the same process occurs in the photo-decomposition of realgar (c-

440

7 Chalcogenide Glasses

As4S4) to give orpiment (c-As2S3) (Porter and Sheldrick, 1972). Reversible photo-induced charges in chalcogenides are less well understood than their irreversible counterparts; reviews of the subject have been given by Elliott (1986) and Ke. Tanaka (1990). Perhaps the most studied reversible change is photo-darkening, whereby an increase in the optical absorption at a particular wavelength, resulting from a parallel shift of the Urbach edge to lower energies, occurs on illumination (see Fig. 7-54 a). The

magnitude of the shift A£ in the optical edge is largest for illumination at low temperatures (see Fig. 7-54 b), and A£ decreases to zero at Tg, where the change is annealed as fast as it is induced. It is interesting to note that A£ in chalcogenide alloys appears to exhibit a maximum at an average atomic coordination m^2.67 (see Fig. 7-54 c), the optimum value for satisfaction of mechanical constraints if a 2D-like MRO exists in the glass (Tanaka, 1989 b) (see Sec. 7.2.1). A very interesting variant of this is the photo-induced anisotropy (e.g.

104

I

0.15 -

•

I

i

A

c

a Ge-Se

0.10 -

i

i

o Q

w w

* As-S

o

1

oo

Ge-As-S Ge-S

o

0)

1

<

o

o As-Se

•

•

o "Q.

LU <

C—

o

•

0.05--

annealed

•

o

A

g

•

* * *

o

10'

2.2

2.U fioofeV)

a)

2.6

HhD

c)

i

i

i

1

1

1

i

—i

L-«-

2.5 Z

0.2

o

* \

3. 0.1 LU

As 2 S 3 , S GeS2 As 2 Se 3

A Se

• GeSe2

D\

As2Te3

i

i

i

i

i

0.5

b)

i

i

—J—rt_oJ

Figure 7-54. Photodarkening in chalcogenide glasses (Tanaka, 1990). a) Reversible change in optical absorption coefficient for glassy As 2 S 3 showing the energy shift AE. b) Photodarkening shift AE for various chalcogenide glasses as a function of temperature, normalized to the glass-transition temperature, Tg. c) Photodarkening shift AE for various chalcogenide glasses as a function of effective coordination number Z.

7.6 Applications

dichroism and birefringence) induced in the optical properties of amorphous chalcogenides by illumination with linearlypolarized light (Grigorovici et al., 1983; Janossy et al., 1984; Kimura et al., 1985; Lee and Paesler, 1987). A number of theoretical models for the reversible photodarkening effect have been proposed involving local heating effects (Malinovsky and Zhdanov, 1982), subtle photo-induced structural configurational changes (Kolobov et al., 1981), involving bond-twisting (Tanaka, 1986, 1990), and intra- and intermolecular bond-breaking (Elliott, 1986), but unambiguous experimental structural evidence for these mechanisms is still lacking.

and although a theoretical loss of ^10~ 2 dB/km at 4.5 jim has been predicted for glassy GeSe3 by Shibata et al. (1981), actual losses for chalcogenide fibres are considerably higher (10-10 3 dB/km at « 3 jim) than the predicted intrinsic losses (Andriesh, 1985; Kanamori et al., 1985; Savage, 1987). Three factors can limit the transmission in the IR window, namely impurity absorption, Rayleigh scattering and defect absorption. Oxygen, hydrogen and carbon are prevalent impurities and it is necessary to reduce the concentration of these below the ppm level (see Fig. 7-47). Rayleigh scattering from microscopic density and compositional fluctuations in the glass has a characteristic XA wavelength dependence (Shibata et al., 1981): l

-\)2xkTJX4

7.6 Applications A number of actual and potential technological applications for amorphous chalcogenide materials exist, exploiting their ease of fabrication in either bulk-glass or thinfilm forms and the ability selectively to vary their physical properties by alloying over rather wide composition ranges. Some of these applications are outlined in the following. 7.6.1 Infrared-Transmitting Optical Components

Chalcogenide glasses are of considerable interest for use as optical elements in IRtransmitting applications because of their transparency over a wide wavelength range in the IR region (see Fig. 7-47), and a variety of possible applications can be envisaged depending on the wavelength of the light involved (see also Chap. 12 and 15). Long-distance telecommunication transmission along optic fibres involves lasergenerated radiation in the 1-4 jim range,

441

(7-42)

where n is the refractive index, x is the isothermal compressibility and it is assumed that fluctuations are quenched-in on cooling through Tg. Eq. (7-42) would therefore indicate that chalcogenide glasses, with rather low values of Tg ( ^ 1 5 0 250 °C), would have correspondingly low levels of Rayleigh scattering. Instead, it appears that defect-related mid-gap absorption limits the transmission loss in chalcogenide glasses (Nishii et al., 1987), and the relatively low values of Tg for these materials is a distinct disadvantage, since this leads to high defect concentrations (c.f. Eq. (7-21)). Thus, it appears that chalcogenides will not be suitable for long-distance trunk communication applications. However, for smaller scale applications, the relatively high losses are less important. One such requirement is for highpower transmission of the 10.6 jim radiation from a CO 2 laser for surgery, cutting or welding applications. Bornstein and Croitoru (1985) and Bornstein et al. (1985) have reported on the use of As-Se glass

442

7 Chalcogenide Glasses

fibres up to 500 jim in diameter, both solid (multimode) and hollow, for this application, where attenuations of less than 0.5 dB/cm have been achieved. Savage (1985, 1987) has reported on the use of chalcogenide glasses as IR-transmitting optical elements for the 3-5 jim and 8-14 jim windows in the atmospheric transmission spectrum in thermal surveillance devices detecting hot and room-temperature objects, respectively. Cimpl and Kosek (1987) have described the use of amorphous chalcogenide thin films as antireflection coatings for IR optics (e.g. filters), taking advantage of the fact that the refractive index (RI) may be varied over quite a wide range (2-3.5 for A-s-S and Te-based systems, respectively) by varying the composition so that good matching of the RI of the film (n^ to that of the optical element itself (n) may be achieved - for zero reflectivity (7-43)

Thus, for optical elements made from crystalline Ge (n = 4), relatively good RI matching can be achieved using S-rich As-S films (Cimpl and Kosek, 1987). Finally, Andriesh (1985) has reviewed the possible application of amorphous chalcogenide films as both passive and active elements (wave-guides) for integrated optics. The acousto-optical coefficient of chalcogenide glasses is rather large (about two orders of magnitude larger than that of vitreous SiO2), making it possible to use acoustical modulation of transmitted laser radiation in active elements; such waveguides have been estimated to have losses of 3-5 dB/cm at 0.63 jim and less than 1 dB/cm at 1.15 \xm (Andriesh, 1985). Non-linear optical properties of materials are becoming increasingly important in high-power laser applications (see Chap. 12). One such non-linear quantity is the

refractive index (7-44)

where n0 is the intensity-independent term and <£2> is the mean-square electric field associated with the light incident on the material. The non-linear term, n 2 , can be due to electrostrictive, thermal, electronic polarizability or resonant-absorption effects. Of these, only the latter two mechanisms lead to fast (picosecond) non-linear responses. Large non-linear effects have been found in semiconductor-doped glasses (e.g. CdSdoped silicate glasses), although in these cases the non-linearity is due to the resonant absorption effect, corresponding to the imaginary part of the third-order nonlinearity term in the expression for the non-linear electronic polarizability (7-45) where x(2) and #(3) are the second- and third-order electronic susceptibilities, respectively. However, materials having high refractive indices such as chalcogenide glasses are also candidates for exhibiting large third-order non-linearities (Nasu and Mackenzie, 1987). Recently, Nasu et al. (1989) have found that chalcogenide glasses such as As 2 S 3 and GeS 3 have values of x(3) = 10~ 12 e.s.u., which are about an order of magnitude larger than that of semiconductor-doped glasses (in the optically transparent region) and two orders of magnitude larger than that of vitreous silica. Thus, such chalcogenide materials hold considerable promise in applications involving high-speed non-linear elements for use with highly transmitted light. 7.6.2 Xerography

Until very recently the most widespread use of amorphous chalcogenides was in

7.6 Applications Corona wire R

<

• • + • + • • + Se film

(a)

(b)

(c)

Toner

©00© • +••

0

00

• • 4-

Paper Heater

(e)

Figure 7-55. Schematic illustration of the Xerox process utilising a-Se as the photoreceptor (Elliott, 1984, 1990). a) Positive charging of the surface by a corona discharge, b) Exposure of the photo-receptor by photons reflected from the document to be copied, c) Discharge of the surface potential locally by the photo-generated electrons, the holes drifting across the thickness of the film, d) Development of the latent

443

xerography or electrophotography (see Mort, 1973; Pfister, 1979; and Madan and Shaw, 1988, for reviews of the subject). The active photo-receptor used was evaporated a-Se in thin-film form, with perhaps a small amount of As or other elements added to inhibit crystallization. The essential feature of electrophotography is the conversion of an optical image into an electrostatic one; this process is illustrated in Fig. 7-55. The surface of the photo-conducting Se film is first charged positively to a surface potential of « 700 V by moving the film under a corona charging device. The charged photo-receptor is now exposed to light reflected from the page to be copied; light is reflected preferentially from the white areas of the page and these photons, on striking the film, are strongly absorbed near the surface and create electron-hole pairs. The photo-electrons neutralize the positive charges locally at the surface, while the holes drift across the thickness of the film under the action of the field resulting from the surface potential and neutralize the negative charge induced on the Al substrate. A negative image is therefore formed in the surface charge distribution. The latent image is developed by means of negatively, triboelectrically charged toner particles (each being a carbon black particle ^10 jim in diameter surrounded by a low-melting plastic carrier bead ^100 jim in diameter); these are attracted to the remaining positively charged areas on the photo-receptor film.

image by means of negatively charged toner particles which are attracted to the remaining areas of positive surface charge, e) Transfer of the image to paper by means of a second corona discharge and subsequent fixing by heating the paper to melt the toner particles into place.

444

7 Chalcogenide Glasses

Finally, the developed image is transferred by attracting the toner particles to a sheet of paper, corona-charged to the opposite polarity of that of the toner, whereupon the paper is heated, thereby melting the toner particles and fixing them in position. Certain conditions are required for a material to be a suitable photo-receptor. It must be highly resistive in the dark (Q ^ 1012 Q cm) so that the surface potential Vo does not decrease appreciably after light exposure and so that image contrast is not lost by lateral charge flow on the surface of the film. (See Madan and Shaw (1988), for a fuller discussion of the conditions necessary.) The material must be highly photoconductive, with a quantum efficiency for carrier generation near unity at the output wavelengths of suitable lamps. Furthermore, defect-free large-area films must be produceable, and the material must be both mechanically robust and chemically inert under conditions of exposure to intense light and high electric fields. Although a-Se satisfies these requirements, its relative softness, toxicity and propensity to crystallization have led to it being superceded by a-Si:H as the photo-receptor (Kawamura and Yamamoto, 1982; I. Shimizu, 1985). 7.6.3 Lithography

Chalcogenide materials have been used as resists in a variety of lithographic (printing) applications, all of which utilize photo-structural changes (see Sec. 7.5.4) as the basis of the imaging process. For instance, illumination of chalcogenide glasses or thin films, sufficient to cause photo-darkening, leads to concomitant changes in the chemical properties, notably the etching characteristics in alkaline solutions. For instance, Petkov et al. (1988) have found that irradiation of evaporated As-S films

chalcogenideoxide- ' substratephoto-doped—I

Ag deposition

exposure

Ag etch

vq chalcogenide etch oxide etch photo-doped chalcogenide etch Figure 7-56. Lithographic process based on the photodissolution of Ag into chalcogenide glasses (Elliott, 1985).

can lead to a ten-fold increase in dissolution rate; this behaviour can be used as the basis of a positive lithographic process (see Fig. 7-56 a), resulting in line-widths below 1 jim. Although the precise mechanism responsible for this behaviour is not known, most likely it involves photo-induced bond breaking. Another lithographic process, based on photo-induced effects in chalcogenides, utilises the phenomenon of metal photodissolution (see Sec. 7.5.4). In this, irradiation with light with energy comparable to that of the bandgap of the chalcogenide (or with electrons or ions) causes metal ions (usually Ag + ) to diffuse into an amorphous chalcogenide material from a metal-rich reservoir in contact with it; the reservoir can be in the form either of an evaporated metal film or as a dipped layer consisting of Ag2X (X = S, Se) formed by immersing the chalcogenide material in a solution of AgNO 3 . The Ag + ions diffuse through the thickness of the chalcogenide film (up to

7.6 Applications

distances of - 2 0 jim (Kokado et al, 1976)) with negligible lateral diffusion under the action of the incident radiation until either the chalcogenide film becomes saturated throughout its thickness with metal or the reservoir becomes exhausted (Doane and Heller, 1982). This behaviour results in a negative lithographic process, since the exposed (photo-dissolved) regions become alkali-resistant in development by wet etching; alternatively the unexposed regions of the resist can also be etched preferentially in a dry process, using plasmaetching with CF 4 or SF 6 . A schematic illustration of this lithographic process is shown in Fig. 7-56 b. The dissolution of metal and subsequent transport of the ions is greatly facilitated by the fact that the metal-doped chalcogenide acts as a highly-conducting (superionic) medium for the metal ions, as found from diffusion studies (Kawamoto and Nishida, 1977). Sub-micron (0.3-0.5 \xm) resolution using Ag-Ge chalcogenide resists is possible, in particular using dipped films and UV irradiation (Huggett and Lehmann, 1985). This exceptional performance results partly from an edge-sharpening effect for dipped films (Tai et al, 1982), wherein fast lateral Ag + diffusion occurs in the superionic Ag2Se reservoir layer from unexposed Ag-rich areas into exposed Agdepleted regions; this lateral diffusion occurs predominantly at the edges of patterns where the concentration gradient is the greatest, and the effect therefore counteracts the usual diffraction-related exposure profile. Extremely high resolution patterns can also be achieved using focussed electron-beam irradiation of Ag-Ge chalcogenide resists (Yoshikawa et al., 1977); sub-micron (0.3 ^im) resolution is readily achievable and the ultimate resolving width may in fact only be several hundred angstroms.

445

7.6.4 Solid Electrolytes In general, oxide glasses are only rather poor ionic conductors (aion ~ 10~6 Q" 1 cm" 1 ). However, replacement of the oxygen anions by sulfur leads to a marked enhancement of the ionic conductivity; for example, Li 2 S-GeS 2 ~LiI (Carette et al., 1983), Li 2 S-B 2 S 3 -LiI (Burckhardt et al, 1984), Li 2 S-SiS 2 -LiI (Kennedy and Yang, 1987), and Li 2 S-P 2 S 5 -LiI (Mercier et al, 1981) are superionic materials with cxion 3 ] 10 £ T cm at room temperature (Souquet, 1981; Pradel and Ribes, 1989) (see Chap. 14). The conductivity in these materials is almost entirely due to ionic transport, with an ionic transport number of unity; for instance, the electronic component to the conductivity for an Ag 2 SGeS 2 -AgI glass is about eight orders of magnitude smaller than the ionic part (Robinel et al, 1983). The increase in ionic conductivity caused by the substitution of S can be understood as a result of the concomitant increase in dielectric constant of the conducting glassy matrix, either in terms of the Anderson-Stuart (1954) model affecting the energetics of the microscopic ion jumps or in terms of the weak-electrolyte model (Ravaine and Souquet, 1977) where the conducting ions M + are presumed to arise from the equilibrium M 2 O ^ M + + O M " . Primary cells (batteries) utilizing ionically-conducting sulphide bulk glasses as the electrolytes are now being manufactured (Akridge and Voulis, 1986) (e.g. the Li/Li 2 S-P 2 S 5 -LiI/ TiS2 cell of Eveready), and have the advantage that the leakage problems associated with liquid electrolytes are avoided. Furthermore, these materials can be made in thin-film form and so the prospect arises of being able to manufacture thin-film batteries integrated into microelectronic circuits (Creus et al, 1989).

446

7 Chalcogenide Glasses

Finally, Owen (1980) and Tohge and Tanaka (1986) have demonstrated that chalcogenide glasses (e.g. As2Se3) doped with the appropriate metal can be used as the basis of ion-selective electrodes (electrochemical sensors) for Cu2 + , Pb 2 + , Hg 2 + , and Cd 2 + ions in solution. 7.6.5 Threshold and Memory Switching

The discovery of electrical switching phenomena in (multicomponent) amorphous chalcogenide materials by Ovshinsky (1968) marked the start of a 10-year period of intense investigation of such materials with the prospect that they would find use in high-speed switching applications. Although it has turned out that the new technology involving so-called "Ovonic" switches has not supplanted that based on crystalline semiconductors (e.g. Si), nevertheless these switching phenomena were found to involve some interesting physics. Electrical switching behaviour is not confined to chalcogenide glasses, however, but has been observed in a variety of materials, both crystalline and amorphous (see e.g. Madan and Shaw (1988) for a review). Amongst these non-chalcogenide amorphous materials which have been shown to exhibit switching are the alloy Cd 23 Ge 12 As 65 (Homma etal., 1980) and a-Si:H (Le Comber etal., 1985), but the latter only shows switching behaviour after the application of an initial, irreversible "forming" voltage pulse. Chalcogenide STAG, Te-based alloys within the quaternary Si Te-As-Ge glassforming region are normally used as (reversible) threshold switching materials: the composition Se 18 Te 40 As 35 Ge 7 is typical (Homma etal., 1980). Normally, a sandwich sample geometry is employed, with a sputtered or evaporated film of the chalcogenide a few microns thick between elec-

trodes of graphite or metals such as Mo. Reviews of switching behaviour in amorphous chalcogenide materials have been given by Adler et al. (1978, 1980), Henisch et al. (1985), and Madan and Shaw (1988). A schematic illustration of the type of threshold switching (current-voltage) characteristics observed in amorphous chalcogenide materials is shown in Fig. 7-57. In the OFF-state, the chalcogenide material has a high resistivity (typically Q = 107 Q cm at room temperature) with linear I—V characteristics at low electric fields (<10 3 Vcm" 1 ). At higher fields in the OFF-state, a pronounced non-linearity is evident. In the field range 10 3 -10 5 Vein" 1 , this non-linear response arises from a contact-limiting of the current by the Schottky barriers at the contacts; at still higher fields, the conduction becomes bulk-limited and exponentially dependent on the

Figure 7-57. Schematic illustration of the threshold switching characteristics exhibited by amorphous chalcogenide materials under continuous a.c. excitation; a load resistor in series with the device determines the load line. Switching from a high-resistance (OFF) state to a low-resistance (ON) state occurs when the applied voltage exceeds the threshold voltage VTH. A minimum holding current (MHC), or equivalently a minimum holding voltage, FTH, needs to be maintained for the material to remain in the ON state.

7.6 Applications

applied field (Adler et al., 1980). The current in the OFF-state is proportional to the electrode area (in sandwich geometry). At a critical ("threshold") voltage, FTH (typically 10 V for a 10 \xm thick film), the material switches extremely quickly (in a time <10~ 10 s)(Ovshinsky, 1968) to a lowresistance (ON) state along the "load line" - see Fig. 7-57. The form of the load line is determined by a load resistor RL in series with the switching device through the relation = IRL+V

(7-46)

where VB is the applied voltage provided by a bias battery, / is the current flowing through the switch and V is the voltage dropped across it; the slope of the load line is then given by — 1/RL. Once in the ONstate, the dynamic resistivity is as low as 0.08 Q cm (Adler et al., 1978), and this state is maintained as long as a minimum holding current JH flows through the switch or, equivalently, as long as a minimum holding voltage, FH, is applied. FH is comparable to the (optical) band gap of the material (Adler et al., 1978); for STAG materials this is of the order of 1 V. The ON-voltages are only very weakly dependent on the chalcogenide thickness, implying that in the ONstate most of the potential difference across the switch is dropped near one or both of the electrodes (Henisch et al., 1985). Furthermore, the ON-currents are independent of electrode area, except for samples with diameters of the order of 10 jam, indicating that conducting channels (filaments) of this size carry the current in the ON-state (Petersen and Adler, 1976). In addition, there is convincing experimental evidence that, in the ON-state, the conducting-channel area increases in proportion to the current, indicating that the ON-state current density is more-or-less constant over a wide range of operating conditions.

447

Two types of switching behaviour may be distinguished. Threshold switching is as described above when the OFF-state may be recovered from the ON-state by reducing the applied voltage below VH. Memory switching occurs when the ON-state, and hence the conducting filament, is metastable; this can arise when the conducting channel is caused to crystallize through prolonged application of voltages higher than Vn and is prevalent in less stable chalcogenide glass compositions (i.e. those more prone to crystallization, such as Terich alloys). The OFF-state in such devices can only be recovered following the application of a large voltage pulse, sufficient to cause local melting and subsequent revitrification of the conducting channel. There was considerable controversy at first as to whether the switching mechanism was of a thermal or electronic nature (Adler et al., 1978; Madan and Shaw, 1988). The thermal model (Madan and Shaw, 1988) assumes that the high current density in a conducting channel is sufficient to cause appreciably local heating (say several hundred degrees centigrade) so that eventually a region having a negative differential conductivity appears (as in a thermistor). However, it is now accepted that thermal effects do not play a dominant role in threshold switching in chalcogenide alloys (Adler et al., 1978, 1980): direct and indirect estimates for the temperature of the conducting channel indicate that it is only 1-10 K above ambient; furthermore, the ON-state switches to the OFF-state when the applied voltage is reduced below VH in a sharp, discontinuous fashion, rather than with a gradual decay expected if thermal effects were dominant. Additional evidence for the switching mechanism being primarily electronic in nature comes from experiments in which the switching behaviour is monitored as a

448

7 Chalcogenide Glasses

function of light intensity, the chalcogenide film being illuminated through a semitransparent electrode (Kroll, 1974); no change in FTH is observed, despite the fact that the threshold current in such circumstances increases by at least a factor of 10 as a result of the photoconductivity, indicating that the threshold switching is associated with a critical electrical field, independent of the carrier density. A picture for the electronic behaviour associated with threshold switching is as follows. As the electric field in a chalcogenide sample is increased, the current increases non-linearly, perhaps as the result of impact-ionization processes (Adler et al., 1980; Henisch et al., 1985). This field-induced carrier generation causes the filling by electrons and holes, respectively, of C^ and C^ gap-state defect centres (see Sec. 7.4.3), and a critical field is reached when all traps are filled. At this point, switching occurs to a high-conductivity (ON) state where the conductivity is no longer trap-limited, as it is in the OFFstate (where the dominant hole drift mobility is jih ^ 10 ~5 cm2 V " l s " *), and instead the carrier mobility becomes equal to that characteristic of the bands, viz. \i = 10 cm2 V ^ s " 1 (Adler et al., 1978, 1980). In the ON-state, the current is maintained by double injection into the chalcogenide at the electrodes, electrons tunnelling through an energy barrier at one electrode and holes through a barrier at the other (Mott, 1969; Henisch, 1969).

7.7 References Abe, S., Toyozawa, Y. (1981), J. Phys. Soc. Jap. 50, 2185. Abkowitz, M., Jansen, R, Melnyk, A. R. (1985), Phil. Mag. B51, 405. Abrahams, E., Anderson, P.W., Licciardello, D.C., Ramakrishnan, T.V. (1979), Phys. Rev. Lett. 42, 673.

Adler, D., Yoffa, E.J. (1976), Phys. Rev. Lett. 36, 1197. Adler, D., Henisch, H.K., Mott, N.F. (1978), Rev. Mod. Phys. 50, 209. Adler, D., Shur, M.S., Silver, M., Ovshinsky, S.R. (1980), J. Appl. Phys. 51, 3289. Agarwal, S.C. (1973), Phys. Rev. B7, 685. Akridge, J., Voulis, H. (1986), Sol. St. Ionics 18-19, 351. Althaus, H.L., Weiser, G., Nogel, S. (1978), Phys. Stat. Sol. (b) 87, 117. Anderson, O.L., Stuart, D.A. (1954), /. Am. Ceram. Soc. 37, 573. Anderson, P.W. (1975), Phys. Rev. Lett. 34, 953. Andonov, P. (1982), J. Non-Cryst. Sol. 47, 297. Andriesh, A.M. (1985), /. Non-Cryst. Sol. 77-78, 1219. Apling, A. X, Leadbetter, A. X, Wright, A. C. (1977), J. Non-Cryst. Sol. 23, 369. Arai, M., Price, D.L., Susman, S., Volin, K.X, Walter, U. (1988), Phys. Rev. B37, 4240. Arai, M., Johnson, R.W., Price, D.L., Susman, S., Gay, M., Enderby, J.E. (1986), J. Non-Cryst. Sol. 83, 80. Barclay, R.P., Marshall, J.M., Main, C. (1985), J. Non-Cryst. Sol. 77-78, 1269. Bellisent, R., Tourand, G. (1980), J. Non-Cryst. Sol. 35-36, 1221. Benoit a la Guillaume, C , Mollot, R, Cernogora, X (1977), in: Proc. 7th Int. Conf. Amorphous and Liquid Semiconductors: Spear, W. E. (Ed.). Edinburgh: CICL, p. 612. Besson, J.M., Cernogora, X, Slade, M.L., Weinstein, B.A., Zallen, R. (1981), Physica 105B, 319. Bhattacharya, R.N., Lee, C.Y., Pollak, R.H., Schleich, D.M. (1987), J. Non-Cryst. Sol. 91, 235. Biegelsen, D. K., Street, R. A. (1980), Phys. Rev. Lett. 44, 803. Bishop, S.G., Shevchik, N.X (1975), Phys. Rev. B12, 1567. Bishop, S.G., Strom, U., Taylor, P.C. (1977), Phys. Rev. B15, 2278. Blanc, D., Wilson, XI.B. (1985), J. Non-Cryst. Sol. 77-78, 1129. Boolchand, P. (1986), in: Defects in Glasses, Vol. 61: Galeener, P.L., Griscom, D.L., Weber, M.X (Eds.). Boston: MRS, p. 57. Boolchand, P., Bresser, W X, Suranyi, P. (1986), Hyperfine Int. 27, 385. Boolchand, P., Bresser, W.X, Tenhover, M. (1982a), Phys. Rev. B25, 2971. Boolchand, P., Bresser, W.X, Suranyi, P., de Neufville, XP. (1982b), Nucl. Instr. Meth. 199, 295. Boolchand, P., Grothaus, X, Bresser, W.X, Suranyi, P. (1982a), Phys. Rev. B25, 2975. Borisova, Z.U. (1981), Glassy Semiconductors. New York: Plenum Press. Bornstein, A., Croitoru, N. (1985), J. Non-Cryst. Sol. 77-78, 1277.

7.7 References

Bornstein, A., Croitoru, N., Marom, E. (1985), J. Non-Cryst. Sol. 74, 57. Bresser, W.J., Boolchand, P., Suranyi, P., de Neufville, I P . (1981), Phys. Rev. Lett. 46, 1689. Bridenbaugh, P.M., Espinosa, G.P., Griffiths, IE., Phillips, J.C., Remeika, J.P. (1979), Phys. Rev. B20, 4140. Briegleb, G. (1929), Z. Phys. Chem. A 144, 321. Bullett, D.W. (1976), Phys. Rev. B14, 1683. Burckhardt, W., Makyta, M., Levasseur, A., Hagenmuller, P. (1984), Mat. Res. Bull. 19, 1083. Busse, L.E. (1984), Phys. Rev. B29, 3639. Busse, L.E., Nagel, S.R. (1981), Phys. Rev. Lett. 47, 1848. Carette, B., Maurin, M., Ribes, M., Duclot, M.J. (1983), Sol. St. Ionics 9-10, 655. Cavenett, B.C. (1981), Adv. Phys. 30, 475. Cerny, V., Frumar, M. (1979), / Non-Cryst. Sol. 33, 23. Cervinka, L. (1987), /. Non-Cryst. Sol. 97-98, 207. Cervinka, L. (1988), J. Non-Cryst. Sol. 106, 291. Cervinka, L., Hruby, A. (1982), J. Non-Cryst. Sol. 48, 231. Cervinka, L., Smotlacha, O., Tichy, L. (1987), / NonCryst. Sol 97-98, 183. Chaussemy, G., Fornazero, I, Mackowski, XM. (1983), J. Non-Cryst. Sol 58, 219. Chen, C.H., Phillips, J.C., Bridenbaugh, P.M., Aboav, D.A. (1984), /. Non-Cryst. Sol 65, 1. Chien, F. Z., Moss, S. C , Liang, K. S., Chianelli, P. R. (1984), Phys. Rev. B29, 4606. Cimpl, Z., Kosek, F. (1987), /. Non-Cryst. Sol 90, 577. Cody, G.D. (1984), in: Semiconductors and Semimetals, Vol. 21B: Pankove, J. (Ed.). New York: Academic, p. 9. Cooper, A.R. (1978), Phys. Chem. Glasses 19, 60. Corb, B.W., Wei, W.D., Averbach, B.L. (1982), /. Non-Cryst. Sol 53, 29. Cornet, J., Rossier, D. (1973), /. Non-Cryst. Sol 12, 85. Creus, R., Sarradin, L, Astier, R., Pradel, A., Ribes, M. (1989), Mat. Sci. Eng. B3, 109. Dalba, G., Fornasini, P., Giunta, G., Burattini, E. (1989), J. Non-Cryst. Sol 107, 261. Daniel, M.F., Leadbetter, A.X (1980), /. Non-Cryst. Sol 41, 127. Daniel, M.F., Leadbetter, A.X, Wright, A.C., Sinclair, R.N. (1979), /. Non-Cryst. Sol. 32, 271. Dembovsky, S.A., Ilizarov, L. M., Chechetkina, E.A. (1987), J. Non-Cryst. Sol 97-98, 427. Depinna, S.P., Cavenett, B.C., Lamb, WE. (1983), Phil Mag. B47, 99. Deroide, B., Belougne, P., Giuntini, J.C., Zanchetta, XV. (1986), J. Non-Cryst. Sol 85, 79. Dersch, U., Thomas, P. (1987), in: Disordered Semiconductors: Kastner, M.A., Thomas, G.A., Ovshinsky, S. R. (Ed.). New York: Plenum: p. 697. Dersch, U., Grunewald, M., Overhof, H., Thomas, P. (1987), J. Phys. C20, 121.

449

Doane, D.A., Heller, A. (1982) (Eds.), Proc. Symp. Inorganic Resist Systems. Pennington: Electrochemical Society. Dohler, G.H., Dandoloff, R., Bilz, H. (1980), /. NonCryst. Sol. 42, 87. Dow, I D . , Redfield, D. (1970), Phys. Rev. Bl, 3358. Drahokoupil, X, Smotlacha, O., Fendrych, F., Klokocnikova, H., Kozlov, M.A. (1986), /. NonCryst. Sol. 88, 43. Drchal, V., Malek, X (1988), Phil Mag. B58, 303. Dresner, X, Stringfellow, G.B. (1968), /. Phys. Chem. Solids 29, 303. Eckert, H. (1989), Angew. Chem. Int. Ed. Engl. Adv. Mater. 28, 1723. Eckert, H., Muller-Warmuth, W, Hamann, W, Krebs, B. (1984), /. Non-Cryst. Sol 65, 53. Edeling, M., Freyland, W. (1981), Ber. Bunsenges. Phys. Chem. 85, 1049. Elliott, S.R. (1977), Phil. Mag. 36, 1291. Elliott, S.R. (1984,1990), Physics of Amorphous Materials. London: Longman. Elliott, S.R. (1986), /. Non-Cryst. Sol. 81, 71. Elliott, S.R. (1987a), Adv. Phys. 36, 135. Elliott, S.R. (1987b), /. Non-Cryst. Sol 97-98, 159. Elliott, S.R., Shimakawa, K. (1990), Phys. Rev. B42, 9766. Elliott, S.R., Steel, A.T. (1986), Phys. Rev. Lett. 57, 1316. Elliott, S.R., Steel, A.T. (1987), /. Phys. C20, 4335. Emin, D. (1973), in: Electronic and Structural Properties of Amorphous Semiconductors: Le Comber, P. G., Mort, X (Eds.). New York: Academic, p. 261. Emin, D. (1976), in: Physics of Structurally Disordered Solids: Mitra, S.S. (Ed.). New York: Plenum. Emin, D. (1980), J. Non-Cryst. Sol. 35-36, 969. Ewen, P.IS., Owen, A.E. (1980), /. Non-Cryst. Sol 35^36, 1191. Faigel, G., Granasy, L., Vincze, I., deWaard, H. (1983), J. Non-Cryst. Sol. 57, 411. Feltz, A., Burckhardt, W. (1980), J. Non-Cryst. Sol. 41, 301. Feltz, A., Pohle, M., Steil, H., Herms, G. (1985), /. Non-Cryst. Sol 69,271. Fenz, P., Muller, H., Overhof, H., Thomas, P. (1985), J.Phys. C18, 3191. Fisher, F.D., Marshall, XM., Owen, A.E. (1976), Phil. Mag. 33,261. Fowler, T.G., Elliott, S.R. (1982), J. Non-Cryst. Sol. 53, 43. Fowler, T.G., Elliott, S.R. (1987), J. Non-Cryst. Sol 92, 31. Freitas, I A., Strom, U., Bishop, S.G. (1985), in: Physics of Disordered Materials: Adler, D., Fritzsche, H., Ovshinsky, S.R. (Eds.). New York: Plenum, p. 685. Fujiwara, T, Itoh, S., Okazaki, M. (1981), J. NonCryst. Sol 45f 371.

Fuoss, P.H., Eisenberger, P., Warburton, W.K., Bienenstock, A. (1981), Phys. Rev. Lett. 46, 1537. Gaczi, P.I (1982), Phil. Mag. B45, 241.

450

7 Chalcogenide Glasses

Galeener, F.L. (1985), Phil. Mag. B51, LI. Galeener, E L. (1988), in: The Physics and Technology of Amorphous SiO2: Devine, R.A.B. (Ed.). New York: Plenum, p. 1. Giuntini, I C , Zanchetta, J. V., Jullien, D., Eholie, R., Houenos, P. (1981), J. Non-Cryst. Sol 45, 51. Gladden, L.R, Elliott, S.R. (1987), Phys. Rev. Lett. 59, 908. Gladden, L. E, Elliott, S. R. (1989), J. Non-Cryst. Sol. 109, 211; (1989) ibid. 109, 223. Gladden, L.F., Elliott, S.R., Sinclair, R.N., Wright, A.C. (1988), J Non-Cryst. Sol. 106, 120. Gorman, M., Solin, S.A. (1976), Sol. St. Comm. 18, 1401. Griffiths, J.E. (1986), in: Defects in Glasses, Vol. 61: Galeener, F.L., Griscom, D.L., Weber, M.J. (Eds.). Boston: MRS, p. 75. Griffiths, I E . , Malyj, M., Espinosa, G.P., Remeika, J.P. (1984), Phys. Rev. B30, 6978. Grigorovici, R., Vancu, A., Ghita, L. (1983), /. NonCryst. Sol 59-60, 909. Hafner, J. (1980), J. Phys. Condens. Matter 2, 1271. Hajto, E., Ewen, P.J. S., Belford, R., Hajto, X, Owen, A.E. (1987), /. Non-Cryst. Sol. 97-98, 1191. Halpern, V. (1976), Phil. Mag. 34, 331. Hauser, XI, Hutton, R. S. (1976), Phys. Rev. Lett. 37, 868. Hautala, X, Ohlsen, W.D., Taylor, P.C. (1988), Phys. Rev. B38, 11048. Hendrickson, J.R., Bishop, S.G. (1975), Sol St. Comm. 17, 301. Henisch, H.K. (1969), Sci. Am. 221, 30. Henisch, H.K., Manifacier, LC, Callarotti, R.C., Schmidt, P.E. (1985), in: Physics of Disordered Materials: Adler, D., Fritzsche, H., Ovshinsky, S.R. (Eds.). New York: Plenum, p. 779. Heo, I , Sanghera, I S . , Mackenzie, I D . (1988), /. Non-Cryst. Sol 101, 23. Higashi, G.S., Kastner, M.A. (1981), Phys. Rev. B24, 2295. Higashi, G.S., Kastner, M.A. (1983), Phil Mag. B47, 83. Hindo, S., Takahashi, T., Harada, Y (1980), Sol St. Comm. 35, 379. Hintenlang, D.E., Bray, P.J. (1985), J. Non-Cryst. Sol 69, 243. Hirata, K., Kitao, M., Yamada, S. (1983), J. Phys. Soc. Jap. 52, 1317. Homma, K., Henisch, H. K., Ovshinsky, S. R. (1980), /. Non-Cryst. Sol. 35-36, 1105. Huggett, P.G., Lehmann, H.W. (1985), / Electron. Mat. 14, 205. Hiirter, H.U., Krebs, B., Eckert, H., Muller-Warmuth, W. (1985), Inorg. Chem. 24, 1288. Ichikawa, T. (1972), /. Phys. Soc. Jap. 33, 179. Itoh, S., Fujiwara, T., Okazaki, M. (1982), J. NonCryst. Sol. 50, 49. Janai, M. (1981), J. Phys. Paris 42, 1105. Janossy, I., Jakli, A., Hajto, I (1984), Sol. St. Comm. 51, 761.

Joannopoulos, I D . , Schliiter, M., Cohen, M.L. (1975), Phys. Rev. Bll, 2186. Johnson, R.W. (1986), J. Non-Cryst. Sol 88, 366. Johnson, R.W, Price, D.L., Susman, S., Arai, M., Morrison, T. I., Shenoy, G. K. (1986), /. Non-Cryst. Sol 83, 251. Kadoun, A., Chaussemy, G., Fornazero, I, Mackowski, J.M. (1983), J. Non-Cryst. Sol. 57, 101. Kanamori, T., Terunuma, Y, Takahashi, S., Miyashita, T. (1985), /. Non-Cryst. Sol 69, 231. Kastner, M.A. (1972), Phys. Rev. Lett. 28, 355. Kastner, M.A. (1985), J Non-Cryst. Sol 77-78, 1173. Kastner, M. A., Adler, D., Fritzsche, H. (1976), Phys. Rev. Lett. 37, 1504. Kawamoto, Y, Nishida, M. (1977), Phys. Chem. Glasses 18, 19. Kawamura, T, Yamamoto, N. (1982), in: Amorphous Semiconductors: Technology and Devices: Hamakawa, Y (Ed.). Amsterdam: North Holland, p. 311. Kawazoe, H., Yanagita, H., Watanabe, Y, Yamane, M. (1988), Phys. Rev. B38, 5661. Kennedy, J.H., Yang, Y (1987), J. Solid State Chem. 69, 252. Kimura, K., Murayama, K., Nimomiya, T. (1985), J. Non-Cryst. Sol. 77-78, 1203. Kniep, R., Mootz, D., Rabenau, A. (1973), Angew. Chem. Int. Ed. 12, 499. Kokado, H., Shimizu, L, Inoue, E. (1976), /. NonCryst. Sol. 20, 131. Kolobov, A.V., Badyal, J.P.S., Lambert, R.M. (1989), Surf Sci. 222, LI 89. Kolobov, A. V., Kolomiets, B. T, Konstantinov, O. V., Lyubin, V.M. (1981), /. Non-Cryst. Sol. 45, 335. Kordas, G., Weeks, R.A., Kinser, D.L. (1985), /. Non-Cryst. Sol. 71, 157. Kosek, E, Cimpl, Z., Tulka, I, Matyas, M. (1976), in: Structure and Properties of Non-Crystalline Solids: Kolomiets, B.T. (Ed.). Leningrad: Academy of Science, USSR, p. 331. Kostyshin, M.T., Mikhailovskaya, E.V., Romanenko, P.E (1966), Sov. Phys. Sol State 8, 451. Koudelka, L., Pisarcik, M. (1982), Sol St. Comm. 41, 15. Koudelka, L., Pisarcik, M. (1983), Mat. Chem. Phys. 9, 571. Koudelka, L., Pisarcik, M. (1984), J. Non-Cryst. Sol 64, 87. Koudelka, L., Horak, I, Pisarcik, M., Sakal, L. (1979), J. Non-Cryst. Sol 31, 339. Koudelka, L., Pisarcik, M., Ananichev, V.A. (1984), J. Mat. Sci. Lett. 3, 825. Kreidl, N . I (1983), in: Glass Science and Technology, Vol. 1: Uhlmann, D.R., Kreidl, N . I (Eds.). New York: Academic Press, pp. 231-259. Kroll, D.M. (1974), Phys. Rev. B9, 1669. Kumagai, N., Shirafuji, I, Inuishi, Y. (1977), J. Phys. Soc. Jap. 42, 1262. Lathrop, D., Eckert, H. (1988), J. Non-Cryst. Sol. 106, All.

7.7 References

Leadbetter, A.I, Apling, A.J. (1974), J. Non-Cryst. Sol. 15, 250. Leamy, H.L, Gilmer, G.H., Dirks, A.G. (1980), in: Current Topics in Materials Science, Vol. 6: Kaldis, E. (Ed.). Amsterdam: North Holland, p. 309. Le Comber, P.G., Owen, A.E., Spear, WE., Hajto, I , Snell, A. I, Choi, W. K., Rose, M. I, Reynolds, S. (1985), J. Non-Cryst. Sol. 77-78, 1373. Lee, J.M., Paesler, M.A. (1987), J. Non-Cryst. Sol. 97-98, 1235. Liang, K.S., Cramer, S.P., Johnston, D.C., Chang, C.H., Jacobson, A.X, deNeufville, IP., Chianelli, P.R. (1980a), /. Non-Cryst. Sol. 42, 345. Liang, K.S., deNeufville, J.P., Jacobson, A.I, Chianelli, P.R., Betts, F. (1980 b), / Non-Cryst. Sol. 35-36, 1249. Lin, C , Busse, L.E., Nagel, S.R., Faber, J. (1984), Phys. Rev. B29, 5060. Liu, J.Z., Taylor, P.C. (1989), Sol. State Comm. 70, 81. Louie, S.G. (1982), Phys. Rev. B26, 5993. Lowe, A. I, Greaves, G.N., Elliott, S.R. (1986), Phil. Mag. B54, 483. Lucas, X, Zhang, X.H. (1990), /. Non-Cryst. Sol. 125, 1. Lucovsky, G. (1987), /. Non-Cryst. Sol. 97-98, 155. Lucovsky, G., Galeener, F.L., Geils, R. H., Keezer, R. C. (1977), in: Structure of Non-Crystalline Materials: Gaskell, P. H. (Ed.). London: Taylor and Francis, p. 127. Lucovsky, G., Mooradian, A., Taylor, W., Wright, G.B., Keezer, R.C. (1967), Sol. St. Comm. 5, 113. Luedtke, W.D., Landman, U. (1989), Phys. Rev. B40, 1164. Lyubin, V.M. (1987), J. Non-Cryst. Sol. 97-98, 47. Madan, A., Shaw, M.P. (1988), The Physics and Applications of Amorphous Semiconductors. New York: Academic. Malaurent, J.C., Dixmier, X (1977), Phys. Stat. Sol. 43A, K61. Malinovsky, V.K., Zhdanov, V.G. (1982), J. NonCryst. Sol. 51, 31. Malyj, M., Espinosa, G.P., Griffiths, XE. (1985), Phys. Rev. B31, 3672. Menelle, A., Bellisent, R., Flank, A.M. (1987), Europhys. Lett. 4, 705. Menelle, A., Bellisent, R., Flank, A.M. (1989), Physica 156-157, 174. Mercier, R., Malugani, I P . , Fahys, B., Robert, G. (1981), Sol. St. Ionics 5, 663. Misawa, M., Suzuki, K. (1978), /. Phys. Soc. Jap. 44, 1612. Moffat, T, Pearsall, G., Wulff, X (1964), Structure. New York: Wiley. Monroe, D. (1985), Phys. Rev. Lett. 54, 146. Mort, X (1973), in: Electronic and Structural Properties of Amorphous Semiconductors: Le Comber, P. G., Mort, X (Eds.). New York: Academic, p. 589. Moss, S.C. (1974), in: Proc. 4th Int. Conf. on Amorphous and Liquid Semiconductors. London: Taylor and Francis, p. 17.

451

Moss, S.C, Price, D.L. (1985), in: Physics of Disordered Materials: Adler, D., Fritsche, H., Ovskinsky, S.R. (Eds.). New York: Plenum, p. 77. Mott, N.F. (1967), Adv. Phys. 16, 49. Mott, N.F. (1969), Contemp. Phys. 10, 125. Mott, N.F., Davis, E. A. (1979), Electronic Processes in Non-Crystalline Materials. Oxford: Oxford University Press. Mott, N . F , Davis, E.A., Street, R.A. (1975), Phil. Mag. 32,961. Miiller, H., Thomas, P. (1984), J. Phys. C17, 5337. Murase, K., Fukunaga, T, Yakushiji, K. (1983 a), /. Non-Cryst. Sol. 59-60, 855. Murase, K., Fukunaga, T, Tanaka, Y, Yakushiji, K., Yunoki, I. (1983 b), Physica 118 B, 962. Murayama, K. (1983), /. Non-Cryst. Sol. 59-60, 983, Murayama, K., Suzuki, H., Ninomiya, T. (1980), /. Non-Cryst. Sol. 35-36, 915. Mushiage, M., Tamura, K., Endo, H. (1983), J. NonCryst. Sol. 59-60, 887. Myers, M.B., Felty, E.X (1967), Mat. Res. Bull. 2, 715. Nagels, P. (1979), in: Amorphous Semiconductors: Brodsky, M.H. (Ed.). Topics in Applied Physics, Vol. 36. Berlin: Springer-Verlag, p. 113. Nagels, P., Tichy, L., Triska, A., Ticha, H. (1983), J. Non-Cryst. Sol. 59-60, 1015. Nasu, H., Ibara, Y, Kubodera, K. (1989), J. NonCryst. Sol. 110, 229. Nasu, H., Mackenzie, I D . (1987), Opt. Eng. 26,102. Nemanich, R.X, Connell, G.A.N., Hayes, T.M., Street, R.A. (1978), Phys. Rev. B18, 6900. Nemanich, R.X, Connell, G.A.N., Hayes, T.M., Street, R.A. (1979), Phys. Rev. B18, 6900. Nemanich, R.X, Galeener, F.L., Mikkelsen, J.C., Connell, G.A.N., Etherington, G., Wright, A.C., Sinclair, R.N. (1983), Physica 117-118B, 959. Nemanich, R.X, Solin, S.A., Lucovsky, G. (1977), Sol. St. Comm. 21, 273. Nishii, X, Morimoto, S., Yokota, R., Yamagishi, T. (1987), J. Non-Cryst. Sol. 95-96, 641. Orenstein, X, Kastner, M.A. (1981), Phys. Rev. Lett. 46, 1421. Ovshinsky, S.R. (1968), Phys. Rev. Lett. 21, 1450. Owen, A.E. (1980), /. Non-Cryst. Sol. 35-36, 999. Owen, A.E., Firth, A. P., Ewen, P.XS. (1985), Phil. Mag. B52, 347. Penfold, I.T., Salmon, P.S. (1989), / Non-Cryst. Sol. 114, 82. Petersen, K.E., Adler, D. (1976), /. Appl. Phys. 47, 256. Petkov, K., Sachatchieva, M., Dikova, X (1988), /. Non-Cryst. Sol. 101, 37. Pfeiffer, G, Brabec, C.X, Jefferys, S.R., Paesler, M.A. (1989), Phys. Rev. B39, 12861. Pfister, G. (1979), Contemp. Phys. 20, 449. Phillips, XC. (1979), /. Non-Cryst. Sol. 34, 153. Phillips, XC. (1981), J. Non-Cryst. Sol. 43, 37. Phillips, XC, Beevers, C.A., Gould, S.E.B. (1980), Phys. Rev. B21, 5724.

452

7 Chalcogenide Glasses

Phillips, R. T., Wolverson, D., Burdis, M. S., Fang, Y. (1989), Phys. Rev. Lett. 63, 251 A. Phillips, W.A. (1976), Phil. Mag. 34, 983. Pohle, M., Feltz, A., Steil, H., Herms, G. (1985), J. Non-Cryst. Sol. 69, 283. Popescu, M. (1987), J. Non-Cryst. Sol. 97-98, 187. Porter, EX, Sheldrick, G.M. (1972), J. Chem. Soc. Dalton,p. 1347. Pradel, A., Ribes, M. (1989), Mat. Sci. Eng. B3, 45. Price, D. L., Misawa, M., Susman, S., Morrison, T. I., Shenoy, G.K., Grimsditch, M. (1984), / NonCryst. Sol. 66, 443. Rajagopalan, S., Harshavardhan, K.S., Malhotra, L.K., Chopra, K.L. (1982), /. Non-Cryst. Sol. 50, 29. Ravaine, D., Souquet, XL. (1977), Phys. Chem. Glasses 18, 27. Rawson, H. (1967), Inorganic Glass-forming Systems. London: New York: Academic Press. Rayment, T., Elliott, S.R. (1983), Phys. Rev. B28, 1174. Rechtin, M.D., Renninger, A.L., Averbach, B.L. (1974), /. Non-Cryst. Sol. 15, 74. Rennie, J.H.S., Elliott, S.R. (1985), / Non-Cryst. Sol. 77-78, 1161; (1987), J. Non-Cryst. Sol. 97-98, 1239. Renninger, A.L., Rechtin, M.D., Averbach, B.L. (1974), J. Non-Cryst. Sol. 16, 1. Robinel, E., Kone, A., Duclot, M.X, Souquet, XL. (1983), J. Non-Cryst. Sol. 57, 59. Robins, L. H., Kastner, M. A. (1984), Phil. Mag. B50, 29. Rubinstein, M. (1976), Phys. Rev. B14, 2778. Rubinstein, M., Taylor, P.C. (1974), Phys. Rev. B9, 4258. Saiter, J.M., Derrey, T., Vautier, C. (1985), /. NonCryst. Sol. 77-78, 1169. Sanghera, J.S., Heo, X, Mackenzie, XD. (1988), J. Non-Cryst. Sol. 103, 155. Savage, XA. (1985), /. Non-Cryst. Sol. 47, 101. Savage, XA. (1987), Infrared optical materials and their antireflection coatings. Bristol: Adam Hilger. Schottmiller, XC, Bowman, D.L., Wood, C. (1968), /. Appl. Phys. 39, 1663. Sen, P.N., Thorpe, M.F. (1977), Phys. Rev. B15, 4030. Shibata, S., Horiguchi, M., Jinguji, K., Mitachi, S., Kanamori, T, Manabe, T. (1981), Electronics Lett. 17, 775. Shimakawa, K. (1981), /. Non-Cryst. Sol. 43, 229. Shimakawa, K. (1982), Phil Mag. B46, 123. Shimizu, I. (1985), J. Non-Cryst. Sol. 77-78, 1363. Shimizu, T. (1985), J. Non-Cryst. Sol. 71, 145. Singh, B., Rajagopalan, S., Chopra, K.L. (1980), /. Appl. Phys. 51, 1768. Smid, V., Fritzsche, H. (1980), Sol. State Comm. 33, 735. Soklakov, A. I., Nechaeva, V.V. (1967), Sov. Phys. Sol. St. 9, 715.

Sotiropoulos, X, Fuhs, W. (1989), /. Non-Cryst. Sol. 114, 97. Soukoulis, C M . , Cohen, M.H., Economou, E.N. (1984), Phys. Rev. Lett. 53, 616. Souquet, XL. (1981), Sol. St. Ionics 28-30, 693. Spence, C. A., Elliott, S.R. (1987), Diffusion and Defect Data 53-54, 227. Spence, C.A., Elliott, S.R. (1989), Phys. Rev. B39, 5452. Steel, A.T., Greaves, G.N., Firth, A. P., Owen, A.E. (1989), J. Non-Cryst. Sol. 107, 155. Stillinger, F.H., Weber, T.A., LaViolette, R.A. (1986), J. Chem. Phys. 85, 6460. Street, R.A. (1976), Adv. Phys. 25, 397. Street, R.A. (1977), Sol. St. Comm. 24, 363. Strom, U., Hendrickson, J.R., Wagner, R.X, Taylor, P.C. (1974), Sol. St. Comm. 15, 1871. Sugai, S. (1987), Phys. Rev. B35, 1345. Susman, S., Johnson, R.W., Price, D.L., Volin, K.X (1986), in: Defects in Glasses, Vol. 61: Galeener, F. L., Griscom, D. L., Weber, M. L. (Eds.). Boston: MRS, p. 91. Susman, S., Price, D.L., Volin, K.X, Dejus, R.X, Montague, D. G. (1988), J. Non-Cryst. Sol. 106, 26. Szeftel, X, Alloul, H. (1979), Phys. Rev. Lett. 42,1691. Tai, K.L., Ong, E., Vadimsky, R.G., Kemmerer, C.T., Bridenbaugh, P.M. (1982), in: Proc. Symp. Inorganic Resist Systems: Doane, D. A., Heller, A. (Eds.). Pennington: Electrochemical Society, p. 49. Takahashi, T. (1982), Phys. Rev. B26, 5963. Takahashi, T, Harada, Y. (1980), J. Non-Cryst. Sol. 35-36, 1041. Takahashi, T, Sagawa, T. (1982), /. Non-Cryst. Sol. 53, 195. Tanaka, Ke. (1986), Jap. J. Appl. Phys. 25, 779. Tanaka, Ke. (1987), / Non-Cryst. Sol. 90, 363. Tanaka, Ke. (1989 a), in: Disordered Systems and New Materials: Borissov, M., Kirov, N., Vavrek, A. (Eds.). Singapore: World Scientific, p. 290. Tanaka, Ke. (1989 b), Phys. Rev. B39, 1270. Tanaka, Ke. (1990), Rev. Solid State Sci. 4, 641. Tanaka, K., Gohda, S., Odajima, A. (1985), Solid St. Comm. 56, 899. Tanaka, Ka. (1982), in: Amorphous Semiconductors: Hamakawa, Y. (Ed.). Amsterdam: North-Holland, p. 227. Tatarinova, L.I. (1972), Electronography of amorphous materials. Moscow: Izd. Naukova, p. 61. Tenhover, M., Hazle, M. A., Grasselli, R.K. (1983 a), Phys. Rev. Lett. 51, 404. Tenhover, M., Hazle, M.A., Grasselli, R. K., Tompson, C.W (1983 b), Phys. Rev. B28, 4608. Tenhover, M., Henderson, R.S., Lukco, D., Hazle, M.A., Grasselli, R.K. (1984), Sol. St. Comm. 51, 455; (1985), ibid. 53, 7. Tenhover, M., Boyer, R. D., Henderson, R. S., Hammond, T.E.? Shreve, G.A. (1988), Sol. St. Comm. 65, 1517. Thio, T, Monro, D., Kastner, M.A. (1984), Phys. Rev. Lett. 52, 667.

7.7 References

Thorpe, M.F. (1983), /. Non-Cryst. Sol. 57, 355. Tichy, L., Ticha, H., Triska, A., Nagels, P. (1985), Sol. St. Comm. 53, 399. Tohge, N., Tanaka, M. (1986), /. Non-Cryst. Sol. 80, 550. Tohge, N., Matsuo, H., Minami, T. (1987), J. NonCryst. Sol 95-96, 809. Tohge, N., Minami, T., Yamamoto, Y., Tanaka, M. (1980), J. Appl. Phys. 51, 1048. Tohge, N., Yamamoto, Y, Minami, T, Tanaka, M. (1979), Appl. Phys. Lett. 346, 640. Tompson, C.W., Gingrich, N.S. (1959), J. Chem. Phys. 31, 1598. Treacy, D.J., Greenbaum, S.G., Strom, U., Taylor, P.C. (1983), J. Non-Cryst. Sol. 59-60, 847. Treacy, D.X, Strom, U., Klein, P.B., Taylor, P . C , Martin, T.P. (1980), J. Non-Cryst. Sol. 35-36, 1035. Tronc, P., Bensoussan, M., Brenac, A., Sebenne, C. , (1973), Phys. Rev. B8, 5947. Uemura, O., Sagara, Y, Satow, T. (1974), Phys. Stat. Sol. a 26, 99. Uemura, O., Sagara, Y, Muno, D., Satow, T. (1978), /. Non-Cryst. Sol. 30, 155. Vaipolin, A. A., Porai-Koshits, E.A. (1963), Sov. Phys. Sol. St. 5, 497. Vanderbilt, D., Joannopoulos, J.D. (1980), Phys. Rev. B22, 2927. Vanderbilt, D., Joannopoulos, J.D. (1981), Phys. Rev. B23, 2596. Vanderbilt, D., Joannopoulos, J.D. (1983a), Phys. Rev. B27, 6311; (1983b), /. Non-Cryst. Sol. 59-60, 937. Vashishta, P., Kalia, R.K., Ebbsjo, I. (1989), Phys. Rev. B39, 6034. Vazquez, X, Villares, P., Jimenez-Garay, R. (1986), /. Non-Cryst. Sol. 86, 251. Veprek, S., Beyeler, H.U. (1981), Phil. Mag. B44, 557. Verrall, D. J., Elliott, S. R. (1988), Phys. Rev. Lett. 61, 974. Verrall, D.J., Elliott, S.R. (1989), J. Non-Cryst. Sol. 114, 34. Verrall, D.J., Elliott, S.R. (1990), in: Neutron and X-ray scattering: complementary techniques: Fairbanks, M.C., North, A.N., Newport, R.J. (Eds.). Bristol: Institute of Physics, p. 87. Verrall, D.J., Gladden, L.F., Elliott, S.R. (1988a), /. Non-Cryst. Sol. 106, 47. Verrall, D.X, Spence, C.A., Elliott, S.R. (1988b), Phil. Mag. B57, 445. Voigt, B., Feltz, A., Schorder, B. (1978), Z. Chem. 18, 11. Wagner, C.N.J., Boldrick, M.S., Lee, D., Heo, X, Mackenzie, XD. (1988), /. Non-Cryst. Sol. 106, 50. Walter, U., Price, D.L., Susman, S., Volin, K.X (1988), Phys. Rev. B37, 4232. Warren, W.W., Dupree, R. (1980), Phys. Rev. B22, 2257.

453

Watanabe, L, Noguchi, S., Shimizu, T. (1983), J. NonCryst. Sol. 58, 35. Watanabe, Y, Kawazoe, H., Yamane, M. (1988), Phys. Rev. B38, 5668. Wei, W, Corb, B.W., Averbach, B.L. (1982), /. NonCryst. Sol. 53, 19. Weiser, K., Gambino, R.X, Reinhold, XA. (1973), Appl. Phys. Lett. 22, 48. Wells, X, Boolchand, P. (1987), /. Non-Cryst. Sol. 89, 31. Westwood, J.D., Georgopoulos, P. (1989), J. NonCryst. Sol 108, 169. Winter, R., Pilgrim, W.C., Egelstaff, P. A., Chieux, P., Anlauf, S., Hensel, F. (1990), Europhys. Lett. 11, 225. Wright, A.C., Etherington, G., Desa, J.A.E., Sinclair, R.N., Connell, G.A.N., Mikkelsen, XC. (1982), J. Non-Cryst. Sol. 49, 63. Wright, A.C., Price, D.L., Clare, A.G., Etherington, G., Sinclair, R.N. (1987), Defect and Diffusion Data 53-54, 255. Wright, A. C , Sinclair, R. N., Leadbetter, A. X (1985), /. Non-Cryst. Sol. 71, 295. Yang, C.Y, Sayers, D.E., Paesler, M.A. (1987), Phys. Rev. B36, 8122. Yoshikawa, A., Ochi, O., Nagai, H., Mizushima, Y (1977), Appl. Phys. Lett. 31, 161. Zachariasen, W.H. (1932), J. Am. Chem. Soc. 54, 3841. Zacharov, V.P., Gerasimenko, VS. (1972), in: Structural Properties of Semiconductors in the Amorphous State. Kiev: Izd. Naukova Dumka, p. 124. Zallen, R. (1983), The Physics of Amorphous Solids. New York: John Wiley. Zhang, X. H., Fonteneau, G., Lucas, X (1988), /. NonCryst. Sol. 104, 38.

General Reading Adler, D., Fritzsche, H., Ovshinsky, S. R. (Eds.) (1985), Physics of Disordered Materials. New York: Plenum, pp. 850. Borisova, Z. U. (1981), Glassy Semiconductors. New York: Plenum. Cohen, M. H., Lucovsky, G. (Eds.) (1972), Amorphous and Liquid Semiconductors, /. Non-Cryst. Sol. 8 (10), 1-1050. Elliott, S. R. (1990), Physics of Amorphous Materials, 2nd ed. London: Longman. Evangelisti, F , Stuke, X (Eds.) (1985), "Proc. 11th Intl. Conf. on Amorphous and Liquid Semiconductors Rome, 2-6 Sept. 1985" /. Non Cryst. Sol. 77/78, 1540. Fritzsche, H., Kastner, M. A. (Eds.) (1984), "Proc. Intl. Conf. on Transport and Defects in Amorphous Semiconductors, Bloomfield Hills, Mich., 22-24 March 1984", J. Non Cryst. Sol. 66, 1-392.

454

7 Chalcogenide Glasses

Matyas, M., Kocka, I , Velicky, B. (Eds.) (1987), "Proc. 12th Intl. Conf. on Amorphous and Liquid Semiconductors, Prague, Czechoslovakia, 4-28 Aug. 1987", J. Non Cryst. Sol. 97/98, 1-1524. Mott, N. R, Davis, E. A. (1979), Electronic Processes in Non-Crystalline Materials, 2nd ed. Oxford: Oxford University Press. Mott, N. (Ed.) (1970), "Amorphous and Liquid Semiconductors", J. Non Cryst. Sol. 4. Paesler, M., Agarwal, S. C , Zallen, R. (Eds.) (1989), "Proc. 13th Int. Conf. on Amorphous and Liquid Semiconductors", J. Non-Cryst. Sol. 114, 1-855. Paul, W, Kastner, M. (Eds.) (1980), "Amorphous and Liquid Semiconductors, Proc. 8th Intl. Conf.

on Amorphous and Liquid Semiconductors, Cambridge, Mass., 27-31 Aug. 1979". /. Non Cryst. Sol 35136, 1-1328. Somogyi, I. Kosa (Ed.) (1987), "Proc. 8th Intl. Conf. on Non-Crystalline Semiconductors", /. Non Cryst. Sol. 90, 688. Tanaka, K., Shimizu, M. A. (Eds.) (1983), Proc. 10th Intl. Conf. on Amorphous and Liquid Semiconductors, Tokyo, Japan, 22-26 Aug. 1983", J. Non Cryst. Sol 59/60, 1-1326. Zallen, R. (1983). The Physics of Amorphous Solid. New York: Wiley.

8 Halide Glasses Jacques Lucas Universite de Rennes-Beaulieu, Laboratoire de Chimie Minerale, Rennes, France

List of 8.1 8.2 8.2.1 8.2.1.1 8.2.1.2 8.2.1.3 8.2.1.4 8.2.2 8.2.2.1 8.2.2.2 8.2.2.3 8.2.2.4 8.3 8.3.1 8.3.1.1 8.3.1.2 8.3.1.3 8.3.1.4 8.3.2 8.3.2.1 8.3.2.2 8.3.2.3 8.4 8.4.1 8.4.2 8.4.2.1 8.4.2.2 8.4.3 8.4.3.1 8.4.3.2 8.4.3.3 8.4.3.4 8.4.4 8.4.4.1

Symbols and Abbreviations Introduction Glass Formation in Halide Systems The Fluoride Glasses The MF2-Based Glasses The MF3-Based Glasses The ZrF4-Based Glasses Multicomponent Zr-Free Heavy Metals Glasses Based on Heavy Metals Glasses Based on Divalent Metal Halides Glasses Based on Trivalent and Quatrivalent Metal Halides Miscellaneous Non-Conventional Vitreous Halides The Tellurium Halide Glasses Halide Glasses as Optical Materials Optical Properties of Bulk Glasses The Bandgap Absorption The Multiphonon Absorption Edges Refractive Index of Halide Glasses Origin of Scattering Losses in Fluoride Glasses Fluoride Glass Fibers Introduction The Optical Losses in Fluoride Glass Fibers Fluoride Glass Fiber Presentation Fluoride Glasses: A new Host for Rare-Earth and Transition Metals Active Optical Properties Absorption Spectra of Rare-Earth and Transition Metal Ions Rare-Earth Ions Transition Metal Ions Fluorescence Spectra of Rare-Earth and Transition Metal Ions Radiative Emission of Rare-Earth Ions Non-Radiative Processes in Rare-Earth Doped Glasses Multidoped Fluoride Glasses Up-Conversion or Photon Addition in Fluoride Glasses Interest of Rare-Earth Spectroscopy in Fluoride Glasses Analysis of Impurities by Photoluminescence

Materials Science and Technology Copyright © WILEY-VCH Verlag GmbH & Co KGaA. Allrightsreserved.

457 458 459 459 459 460 460 461 462 462 463 463 464 465 465 465 466 470 471 472 472 472 474 475 475 476 476 476 477 477 479 480 481 481 481

456

8.4.4.2 8.4.4.3 8.4.4.4 8.5 8.5.1 8.5.2 8.6 8.6.1 8.6.2 8.7 8.7.1 8.7.2 8.7.3 8.8

8 Halide Glasses

Crystallization and Structure Investigations Temperature Measurements by Optical Means Lasers and Fiber Lasers Tellurium Halide Glasses (TeX Glasses): New Materials for Low Loss Infrared Fibers Optical Characterization Optical Fibers Operating Between 3 and 14 jim Stability of Halide Glasses against Chemical Attack and Devitrification . . . Chemical Durability Devitrification of Fluoride Glasses Preparation of Fluoride Glasses and some Physical Properties Preparation of Fluoride Glasses Magnetic Properties of Fluoride Glasses Electrical Properties of Fluoride Glasses References

482 482 482 483 483 483 484 484 485 486 486 487 488 488

List of Symbols and Abbreviations

List of Symbols and Abbreviations A, a aext at B B C D Dq E AE / m n n2 n o nd> nF T Tf T

wR

material parameters extrinsic scattering total intrinsic attenuation coefficient Rayleigh factor Racah parameter constant dependent on source of scattering A independent scattering crystal field parameter band gap energy gap force constant mass refractive index non-linear refractive index indices at X\ d = 0.589 mm, F = 0.486 mm, c = 0.656 mm glass softening point freezing temperature glass transition temperature energy transfer rate multiphonon emission rate radiative rate

Qt

attenuation coefficient quantum efficiency Curie-Weiss temperature wavelength reduced mass vibrational frequency indicator of the covalent character bonding phenomenological parameters with t — 2, 4, 6

CN F.L.N. RAP R.E.-R.E. T.M.-R.E.

coordination number fluorescence line narrowing reactive atmosphere processing rare earth-rare earth transition metal-rare earth

n

9 X Vv0 Q2

Composition of glasses BATY 20BaF 2 , 29A1F3, 22ThF 4 , 29YF 3 BiGaZYT Ba 3 0 In 1 8 Ga 1 2 Zn 2 0 Y 1 0 Th 1 0 BIZYT Ba 3 0 In 3 0 Zn 2 0 Y 1 0 Th 1 0 BTYbZ 16 BaF 2 , 28 ThF 4 , 28 YbF 3 , 28 ZnF 2 ZBL 60ZrF 4 , 33BaF 2 , 7LaF 3 ZBLA 55ZrF 4 , 35BaF 2 , 6LaF 3 , 4A1F3 ZBLAN Zr 5 3 Ba 2 0 La 4 Al 3 Na 2 0

457

458

8 Halide Glasses

8.1 Introduction Halide materials are usually reputed to exist in the crystalline state when cooling down from a molten halide salt; they also form easily volatile molecular species when the halogen is associated with small, highly charged cations. Only a limited number of halide systems lead to glass formation and usually the glass to crystal or glass to molecule competition is very severe. Considerable progress has been made during the last two decades both in the discovery of new halide glass-forming compositions based on the anions F, Cl, Br, I, the elements of group VII of the periodic chart, and in knowledge of the optical properties of these exotic glasses. The main justification for research in this field is the possibility of extending the infrared transparency domain towards long wavelengths and of consequently achieving mid-infrared ultratransparency. There are at least three intrinsic factors which limit the technological and scientific development of such vitreous materials and in which they are inferior to oxide based glasses, especially silicates. The first factor, typical of almost all halide compounds, vitreous or otherwise, is their susceptibility to corrosion by water or moisture, which can strongly affect their optical properties. This poor chemical durability can be explained by the fact that the M - O H 2 , M - O H , or M O bonds are usually stronger than the M - X bond (M = metal; X = F, Cl, Br, I). The second factor is also associated with the weakness of the M - X bond compared with the M - O bond: halide-based materials have low characteristic temperatures. For example, glass transition temperatures, Tg, are low and range from room temperature to a maximum of 400 °C. As a direct consequence, the thermal expansion

coefficients of halide glasses are usually high, and these materials are sensitive to thermal shock. Their mechanical strength is also poor compared with traditional oxide glasses. The last factor impeding the development of these glasses is that they are formed from the most electronegative elements of the periodic chart, especially in the case of fluorine F, which has a strong tendency to form ionic crystalline materials. A direct consequence is that the glasscrystal competition in halide systems when crossing the strategic liquidus-solidus line often favors microcrystallite formations. Hence, the optical properties, especially the scattering losses, suffer from the tendency to devitrify. Thus it is not surprising that only a limited number of halide glasses among the numerous compositions which have been described in the literature may be suitable for practical applications. The study of optical properties requires the samples to be of reasonable size and optical quality and to have a strong resistance to corrosion from atmospheric moisture. This explains why only a few halide glasses have been thoroughly investigated. This chapter will briefly review the halide compositions which have been proven to be glass formers, even if the glasses have little chance of becoming optical materials because of their poor stability. Particular attention will be paid to the limited number of stable glasses and to their specific optical properties. Among them, the fluoride glasses occupy a dominant position, especially those based on ZrF4 or other multicomponent compositions. These are usually termed heavy metal fluoride glasses. Most of the investigations on fluoride glasses have been motivated by the potential to develop ultralow-loss optical fibers operating in the mid I.R. Several general

8.2 Glass Formation in Halide Systems

articles reviewing the optical properties of these materials have been published (Baldwin etal., 1981; Tran et al., 1984; Drexhage, 1985; France etal., 1987; Lucas, 1986) as well as four international conference proceedings (Almeida, 1987; Lucas and Moynihan, 1985; Drexhage etal., 1987). This fast growing field of glass science has a short history, only about twelve years, since the only halide materials previously known to give glasses were beryllium fluoride, BeF2, and zinc chloride, ZnCl 2 . Because of the toxicity of the former and the hygroscopicity of both, investigations of their optical properties have been very limited, despite the interest expected in them (Weber, 1986; Van Uitert and Wemple, 1978). The goal of this review is to try to set up for these special glasses relations between the chemical composition, which determines the structure and nature of the bonds, and their optical properties. In addition to the development of very large optics often difficult to realize with crystalline materials, an important property of vitreous materials is the potential to develop very transparent optical waveguides or optical fibers. The formation of fibers from crystalline materials is a very difficult operation, while the glassy state, with its unique viscosity-temperature dependence, represents the ideal situation for transforming a bulk material into a very long waveguide. Among the different objectives for developing these optical waveguides are the possibility of repeaterless long distance telecommunication links and analytical applications such as remote I. R. spectrometry, pyrometry and thermal imaging, and energy transfer of the output of powerful lasers for welding, cutting, and surgical operations (see Chap. 15).

459

8.2 Glass Formation in Halide Systems As indicated already, the term halide glass refers to any vitreous material in which the anions come from the group VIIA elements of the periodic table, namely F, Cl, Br, and I. Because of its size and electronegativity, fluorine is often considered a special halogen which has to be treated separately. In this article, we shall also discuss the fluoride glasses as a special family owing to the very large research effort devoted to this group during the last ten years, and we shall examine the socalled "heavy halide glasses", namely chlorides, bromides, and iodides, together as a separate family. 8.2.1 The Fluoride Glasses

Fluoride glasses can be classified according to structural considerations, and, although glass formation has been observed in many fluoride systems, the vitreous materials obtained cannot be considered of equal interest because of the high tendency for most of them to devitrify. 8.2.1.1 The MF 2 -Based Glasses

The MF2-based glasses are represented only by the BeF2 glass family which shows a strong resistance to devitrification. According to Baldwin et al. (1981) it is generally agreed that these vitreous materials are isotypic with SiO2-based glasses. X-ray and molecular dynamics studies clearly indicate that the aperiodic framework is based on the BeF4 tetrahedron. BeF2 is the only fluoride giving a viscous melt which easily vitrifies on cooling. BeF2-based glasses are of special interest for some optical applications for high power lasers owing to their low linear and non-linear refractive indices (see Chap. 12). However,

460

8 Halide Glasses

because of their toxicity, they have received only limited attention. 8.2.1.2 The MF3-Based Glasses These glasses are represented by the A1F3 or transition metal fluoride groups and result from the formation of an aperiodic 3-D framework based on MF6 octahedra. The MF 3 materials, which have been proven to give glasses when combined appropriately with other fluorides, are A1F3, FeF 3 , CrF 3 , and GaF 3 (Sun, 1947; Jacoboni et al., 1983). The other fluoride components are usually ZnF2 or MnF2 and PbF2 which seems to play the important role of modifier. In the typical glass forming ternary system, FeF 3 -MnF 2 -PbF 2 , the glass composition PbFeMnF 7 , which falls in the vitreous domain, corresponds to a glassy material extremely rich in magnetic cations which exhibits interesting spinglass properties at low temperatures (Renard et al., 1981). The glass-crystal competition is also very severe in this family, and the aperiodicity introduced in the ReO 3 structure by rotating or tilting the octahedra can be easily destroyed, with the formation of ordered crystalline materials. A significant improvement in the stability of A1F3-based glasses has been obtained by incorporating ZrF4 to this glass.

tions. As indicated in Fig. 8-1 the stability of the glasses towards devitrification is strongly improved by using a third fluoride such as ThF4 or LaF3. The glass called ZBL, corresponding to the composition 60 ZrF 4 , 33 BaF2, 7 LaF3 and located in the middle of the vitreous area of Fig. 8-1, is a rather stable glass. The rate of crystallization can also be significantly decreased by using a small amount of A1F3. For instance, an optimized composition giving a good technical glass called ZBLA is 55ZrF 4 , 35BaF2, 6LaF 3 , 4A1F3. Many others compositions have been developed in order to decrease the nucleation rate and avoid scattering losses in optical fibers. It appears that the so-called confusion principle can be also applied in this domain of glass science and, for instance, one of the best candidates for fiber drawing is the multicomponent fluoride ZBLAN, with the molar cation composition Zr 53 Ba 20 La 4 Al 3 Na 20 . In this glass, 60ZrF4 33BaF 2 7LaF 3

8.2.1.3 The ZrF4-Based Glasses These glasses were the first of the socalled "heavy metal fluoride glasses". Their discovery in the author's laboratory in 1974 (Poulain et al., 1975) attracted considerable interest because the glasses had very promising properties for mid I.R. applications. Although ZrF 4 by itself cannot be vitrified, if it is combined with an appropriate modifier such as BaF2 it leads, by fast quenching, to simple binary glasses which are useful for structural investiga-

LaF3

ZBLA

BaF2

Glass :

ZBLAN Glass Figure 8-1. Glass forming domain in the ternary diagram ZrF 4 -BaF 2 -LaF 3 . Some compositions are given in molar percentage, for example, for the binary unstable glass ZB, the ternary ZBL and the four and five-component glasses ZBLA and ZBLAN, which are the most resistant to devitrification.

8.2 Glass Formation in Halide Systems

461

These new stable fluoride glasses have been widely investigated, and abundant literature on them exists, as discussed by Drexhage (1985). In the field of structural modelling, relationships have been established between the structure of BaZr 2 F 10 in its crystalline and vitreous states (Phifer etal., 1987). Figure 8-2 presents the 3-D aperiodic framework built up by the connection of Zr 2 F 13 bipolyhedra originating from ZrF7 and ZrF8 edge-sharing polyhedra. The Ba 2+ cations playing the role of modifier elements are inserted in the framework and interact mainly with the nonbridging ions. This model has been obtained from X-ray and neutron diffraction studies, molecular dynamics simulations, and local probe spectroscopies.

Zr

OF

Ba

Figure 8-2. A structural model for the binary glass 2 ZrF 4 -l BaF2. Elementary polyhedra ZrF7 and ZrF8 sharing corners and edges form a 3-D aperiodic framework. The large Ba 2+ cations play the role of lattice modifiers.

where the modifier Ba2 + has been partially replaced by Na + , an interdiffusion barrier to crystallization has been introduced because of the competition between Na and Ba in crystalline fluorozirconate formation. The usual way to prepare these fluorozirconate glasses is by melting the different starting fluorides in vitreous carbon or platinum crucibles in a dry atmosphere. In order to convert some materials starting as oxides to fluorides or to prevent any pyrohydrolysis during heating, it is convenient to add NH 4 HF 2 to the mixture to avoid the presence of O 2 ~ in the melt.

8.2.1.4 Multicomponent Zr-Free Heavy Metal Fluoride Glasses Research into new Zr-free fluoride glasses has been motivated by the need to synthesize glasses having the widest optical windows. The transmission range for the fluorozirconate family is limited in the multiphonon region to about 7 jim because of Zr-F, especially by Al-F vibrational modes. It has been demonstrated that heavy metal fluoride glasses not containing Zr 4 + exist but they are more difficult to prepare (Lucas, 1987), and at least three fluorides need to be incorporated to realize the conditions of glass formation. Three-Component Fluoride Glasses Depending on the quenching rate, small glassy chips can be obtained from ternary liquids. For instance, glasses have been prepared by fast quenching from the following ternary melts: BaF 2 -ZnF 2 -LnF 3 , BaF 2 -ZnF 2 -ThF 4 , BaF 2 -ZnF 2 -CdF 2 or YF 3 -ZnF 2 -ThF 4 .

462

8 Halide Glasses

Four-Component Glasses

8.2.2 Glasses Based on Heavy Halides

Systematic investigations of the quaternary diagram YbF 3 -ThF 4 -ZnF 2 -BaF 2 show that, when BaF2 is added to the glass forming composition YnThZnF9, the tendency to devitrify decreases significantly. For instance, the fluoride glass Ba 16 Th 28 Yb 28 Zn 28 , called BTYbZ, can be obtained in about a 10 mm thickness. The same kind of observation has been made in the system BaF 2 -InF 3 -ZnF 2 -ThF 4 , where the stable composition is Ba 3 0 In 3 0 Zn 3 0 Th 1 0 .

This terminology refers to glasses in which the electronegative part is a heavy halogen such as Cl, Br, I. Most of these materials suffer, in terms of their technological development, from their hygroscopicity, low softening temperature, and the tendency to devitrify. Research activity in this field (Mackenzie, 1987) has been largely motivated by the fact that, from a simple consideration of masses of anions associated with cations, chloride, bromide, and iodide glasses would be expected to be more transparent in the I.R. than the fluoride glasses.

Five-Component Glasses To demonstrate that the multiplication of cations having a flexible coordination was a suitable factor for retarding the crystallization, a systematic investigation has been done of the fluoride system Ba 30 In 20 Zn 30 _ x Y c Th 10 . For x = 10, the melt has a maximum viscosity, and samples of 20 mm thickness can be obtained. This so-called BIZYT glass, with the composition Ba 30 In 30 Zn 20 Y 10 Th 10 , is the most stable Zr-free fluoride glass and has been proven suitable for fiber drawing (Bouaggad et al., 1987). The partial substitution of In by Ga, for example, in the glass BiGaZYT with the composition Ba 30 In 18 Ga 12 Zn 20 Y 10 Th 10 allows us to decrease the critical cooling rate Rc from about 120°C/min to 10°C/min. The structure of these multicomponent glasses is obviously a subject of speculation because of the great number of pair interactions. Nevertheless, an analogy exists between these glasses and the fluorozirconate glasses in the sense that the variety of ZrFn polyhedra in these glasses are replaced by a variety of other equivalent MFn building elements.

8.2.2.1 Glasses Based on Divalent Metal Halides MX2 Vitreous materials have been prepared with M = Zn 2 + , Cd 2 + and X = C1", Br~, I~. ZnCl 2 is the best and most widely known glass former. With an I.R. edge in the 12-13 jim region, it is of interest for optics operating in the 8-12 jim atmospheric window and has a potential for ultratransparency (Van Uitert and Wemple, 1978). Many attempts have been made to increase its resistance to water corrosion and to devitrification by the addition of other halides such as KBr or PbBr 2 (Yamane et al., 1985). Nevertheless, hygroscopicity remains very high and severely affects the optical properties in the I.R. region. The glass transition temperature of such mixed halide glasses is also low, about 50 °C. The glass forming ability is explained by the formation of a 3-D aperiodic framework based on ZnCl 2 tetrahedra. The isotypic ZnBr2 is also known to be a glass former with an expected I.R. cut-off in the 20|im region (Hu et al., 1983), but vitreous ZnBr2 exhibits very poor chemical durability and a weak resistance to de-

8.2 Glass Formation in Halide Systems

vitrification. Addition of a glass modifier such as KBr (Kadono etal.? 1987) improves these two properties. Cadmium chloride CdCl 2 has also been proven to lead to vitreous materials, when associated with other halides such as Pbl 2 or PbCl 2 (Angell et al., 1987). In this case, the I.R. transmission extends to 20jLim. When CdCl2 glasses are stabilized by a mixture of chloride and fluoride such as CdF 2 -BaF 2 -NaCl (Matecki et al., 1987), the multiphonon edge is determined by the metal-fluoride bond and shifts back to the 8-12 jim region. Although they appear less sensitive to humidity than the zinc chloride-based glasses, these CdCl2 glasses cannot be kept in an ambient atmosphere without surface corrosion occurring. A large glass forming domain has been discovered by Cooper and Angell (1983) in the CdI2-based system when Cdl 2 is associated with KI and Csl as modifiers. With an I.R. edge shifted towards the 30 |im region, those glasses have the largest optical window of any known vitreous material. Unfortunately, but as expected, the mechanical properties are very poor and the hygroscopicity is high, essentially owing to a Tg ranging from 10 to 35 °C. One can speculate that these glasses contain a Cdl 4 tetrahedron as a structural module. 8.2.2.2 Glasses Based on Trivalent and Quadrivalent Metal Halides

Angell and Ziegler (1981) reported several glasses based on BiCl3 with I.R. edges located in the 14 jam region. These glasses also suffer from low glass temperatures, around 30 to 50 °C, and the rapid attack of atmospheric moisture. Hu and Mackenzie (1982) succeeded in preparing vitreous chlorides based on ThCl 4 associated with NaCl and KC1. The I.R. edge is located near 14 |im, but strong

463

corrosion due to a high sensitivity to moisture affects the optical transmission severely. In this kind of glass, the structure can be reasonably described as a 3-D framework of connected MC1 6 , MC1 7 , and MC18 polyhedra. 8.2.2.3 Miscellaneous Non-Conventional Vitreous Halides

The concept of the aperiodic framework can be applied to the previous glasses, but fails to explain the existence of some multicomponent monovalent cation halide glasses. It has been demonstrated (Angell et al., 1985, for instance), that large vitreous areas exist in the middle of the AgCl-Agl-CsCl and CuCl-PbCl 2 -RbCl systems. Even in binary systems such as AgX-CsX (X=Br, I) glasses can be obtained by rapidly quenching the melt. The addition of 2% of PbX 2 improves glass formation and allows for the preparation of samples 10 mm thick (Nishii et al., 1985). I.R. transmission occurs out to 15 |im, but the glass temperature is rather low (T g =21°C) for the stabilized glass 59AgX-39CsX-2PbX 2 . Some attack by atmospheric moisture is observed after several hours. One explanation for glass formation in multicomponent systems involving halides such as AgCl, CuCl, Agl, and CsCl can be based on the observation that the eutectic points in these systems are at relatively low temperatures, giving melts where the ionic diffusional processes are slow. Also, the nucleation and crystal growth mechanisms are highly impeded by the fact that the four halides AgCl, CuCl, Agl, and CsCl belonging to four different non-miscible structural types have to compete in forming individual crystallites.

464

8 Halide Glasses

8.2.2.4 The Tellurium Halide Glasses

The author's group recently discovered a new family (Lucas and Zhang, 1986; Lucas et al., 1987) of halide glasses based on the combination of tellurium Te with chlorine, bromine or iodine. These tellurium halide glasses, called "TeX glasses", have been obtained in the following binary or ternary systems: Te-Cl, Te-Br, Te-Cl-S, Te-Br-S, Te-Br-Se, T e - I - S , Te-I-Se. Addition of S or Se to the binary TeX glasses decreases the devitrification rate, and some of these ternary compositions are very resistant to crystallization. In Fig. 8-3 the large vitreous domains in the six different systems are shown. The glass Te3Cl2 with Tg=82°C crystallizes at 189 °C on heating, but the glass Te3Cl2S with T g =81°C shows no devitrification. Most of these TeX glasses are not corroded by atmospheric water, except for those having a high halogen content. As dis-

Q\

Q

20

20

40

40

60

60

80

80

20

B r

20

40

40

cussed in Sec. 8.3.1.2 which is devoted to the multiphonon edge, the TeX glasses can be divided into two groups: a) the light TeX glasses containing light elements such as S or Cl and having an I.R. cut-off at 13 |im, and b) the heavy TeX glasses with a multiphonon edge near 20 jim. The very large glass-forming domain in the Se-containing ternary system is due to the fact that the binary glass, Te3Cl2 for instance, has the same structure as the Se glasses. The chain-like structure of crystalline Te3Cl2 is represented in Fig. 8-4 and is obviously isotypic with the spiral-type structure of crystalline Se giving a broad domain of solid or liquid solution between the two components. Densities and molar volume measurements indicate that all the Te-Br-Se glasses are very homogeneous consisting of infinite mixed Te and Se chains and no phase separation has been observed.

60

60

j

80

80

Se

j

20

40

60

80

20

40

60

80

Figure 8-3. Glass formation in tellurium halides systems. The TeX glasses are stabilized against devitrification by S or Se addition. A large domain of glass formation is shown between the TeX glasses and the selenium due to the similarity in their chain-like structure.

8.3 Halide Glasses as Optical Materials: Passive Properties

OTe •

Cl

Figure 8-4. The chain-like structure of the crystalline form of Te3Cl2. After melting and a moderate quenching rate, Te3Cl2 easily vitrifies. The spiral structure is induced by the steric effect of the lone pair of electrons represented on one Te atom.

8.3 Halide Glasses as Optical Materials: Passive Properties 8.3.1 Optical Properties of Bulk Glasses

For definitions, see Chap. 12. 8.3.1.1 The Bandgap Absorption

The U.V. edge in halide glasses MxXy is associated with the excitation of electrons from lower to higher energy states on the molecular orbital diagram of the M - X bond. It is obvious, because of the great polarizing ability of cations such as Be2 + , Al 3+ , and Zr 4 + and the high value of the corresponding ionization energy, that the M - F bond in fluoride glasses has a strongly covalent character. Consequently, the energy gap between the bonding level and the first unoccupied antibonding level

465

is estimated to be rather high unless impurities such as cations with partly filled d or f levels or heavy halogens such Cl~, Br~, or I~ introduce parasitic levels which can strongly modify the absorption mechanisms in the U.V. A study by Brown (1982) shows that for most of the ZrF4- and HfF4-based glasses the U.V. edge is in the region E = 5 eV, corresponding to X = 0.25 jim, according to the relation /I (jam). £(eV) = 1.24. Compared to very pure vitreous SiO2 where £ = 8.0eV (vl = 0.16 jim), the fluorozirconate glasses are less interesting in terms of U.V. transmission. The U.V cut-off, of course, depends on other M - F bonds if additional metallic fluorides are added to the melt. The cut-off is also governed by the M-Cl molecular orbital diagram if Cl~ anions (Adam and Poulain, 1983) are present in the glass due to Reactive Atmosphere Processing using CC14, for example. It is often observed that CC14 treatment leads to a yellowish coloration of the glass due to a shift of the U.V edge into the visible region. Although no thorough investigation has been done in this area, it is expected that for most heavy halide glasses the U.V. edge will shift towards the visible region progressively, from Cl to I, due to the increasing size and decreasing electronegativity of the corresponding halogen. Visual observation of TeX glasses shows clearly that these "black glasses" have their band gaps in the near I.R. lying typically between 1.40 eV (0.9 \im) in TeSe6Br3 and 0.7 eV (1.8 jim) in the binary glass Te 3 Cl 2 . These glasses have a chain-like structure in which the lone pair of 5 s2 electrons associated with the Te have an important stereochemical effect. The low band gap in these glasses is due essentially to the excitation of these electrons located in non-bonding orbitals.

466

8 Halide Glasses

8.3.1.2 The Multiphonon Absorption Edges

Infrared Edge in Fluoride Glasses

The possibility of shifting the I.R. edge in halide glasses to longer wavelengths has served as a catalyst for much of the research activity on these materials. The synthesis of a glass having multispectral capabilities is of interest to many infrared technologies, especially if a potential for ultratransparency exists. It is well known that the multiphonon absorption mechanisms are among the most important for explaining the optical losses in a material (see Chap. 12). The I.R. or multiphonon edge in a transparent solid results from combinations and overtones of the far-infrared fundamental vibrational frequencies of the bonds between anions and cations. The position of the fundamental frequencies is governed by the Szigeti equation (Szigeti, 1950), which shows the dependence of the vibrational frequency v0 on the reduced mass \i of the atoms A and B and the force constant / for the bond between them: VO = (1/2TT) (//AO 1 / 2 - The reduced mass is given by fi = mAmB/(mA + mB). It is obvious that heavier atoms and weaker bonding are preferable for extended I.R. transmission. As discussed by Lines (1986) and Bendow et al. (1981 b), at the far infrared end of the optical spectrum, the attenuation is dominated by absorption from polar modes of lattice vibrations. This absorption extends as an exponential tail to shorter wavelengths from the intense single phonon band. This tail is the result of absorptions involving the simultaneous excitation of more than one phonon. The dependence of this so-called "multiphonon loss" on wavelength is expressed by the general equation a = A exp (— a/A), in which A and a are material parameters and a is the attenuation coefficient.

The fundamental vibrational modes of the fluoride glass matrix occur in the far infrared at wavelengths between 15 and 50|im. Bendow et al. (1983a, 1983b) and Drexhage (1985) have measured and discussed the reflectivity spectra of several fluoride glasses, which show the compositional variation of the I.R. edge absorption. Figure 8-5 shows the percentage of reflectivity directly related to the absorption coefficient versus the wavelength for different kind of glasses: a) a ZBL glass in the system ZrF 7 4 BaF 2 -LaF 3 ; b) a multicomponent Zr-free heavy metal fluoride glass BTYbZ having the composition 16BaF2, 28ThF 4 , 28YbF3, 28ZnF 2 ; c) the same BTYbZ glass doped with about ten percent A1F3, which often plays the role of stabilizing the glass; and d) a "BATY" glass, in which A1F3 plays the important role of glass former, with the composition 20BaF 2 , 29A1F3, 22ThF 4 , 29YF3. The interpretation of these spectra is as follows: The absorption in the region 250 cm" 1 is attributed to the B a - F bond, the bands in the range 400-450 cm" 1 are due to T h - F or Y b - F bonds, and the large absorption near 550 cm" x in the fluorozirconate is attributed to the Z r - F vibration. The Al-F vibrational mode, which corresponds to a strong M - F bond involving a small and highly charged cation Al3 + is located in the 600-650 cm" 1 region and shows the detrimental effect of A1F3 in fluoride glasses in shifting the multiphonon absorption towards shorter wavelengths. These results, obtained in the far I.R. part of the spectra, are also verified when examining the evolution of the I.R. edge in different kinds of fluoride glasses.

8.3 Halide Glasses as Optical Materials: Passive Properties

50

467

WAVELENGTH (pm) 25 20 15

Figure 8-5. Reflectivity spectra in the single phonon band for several fluoride glasses: a) a ZrF4-based glass; b) a heavy metal Zr-free fluoride glass; c) the same glass as b) but doped with A1F3, and d) an AlF3-based glass. 100

300 500 700 FREQUENCY (cm"1)

900

Figure 8-6 shows the position of the I.R. cut-off for different fluoride glasses having a thickness of about 3 mm. Spectrum 1 corresponds to a BeF2-based fluoride glass in which the strong Be-F bond between two light elements places the I.R. cut-off almost in the same region as the Si-O vibration of the silica glass (Baldwin, 1979). Spectrum 2 corresponds to fluorozirconate of Zr-free fluoride glasses doped with a few percent of A1F3, for example ZBLA glass (4% A1F3). Spectrum 3 is that of a pure fluorozirconate glass such as ZBL in which the I.R. cut-off is governed by the vibrational modes of Z r - F bonds. Finally, spectrum 4 corresponds to the so-called Zr-free multicomponent heavy metal fluoride glasses such as BTYbZ or BIZYT (see the previous

section for an explanation of the acronym). In these glasses, the multiphonon edge is governed by the T h - F or I n - F bonds, and the corresponding atomic weights and force constants are such that the I.R. cutoff is in the 8 jim region, leading to glasses having the widest optical window for stable fluoride glasses. Chung et al. (1987) have recently measured the multiphonon edges of single crystal specimens obtained from the different fluoride used for glass preparation. They also concluded that AIF3 or LiF addition to the glass shifts the I.R. edge to a higher frequency. Figure 8-7, which uses data taken from Chung et al. (1987) and from France et al. (1987) and Takahashi (1987), provides an indication of the wavelength dependence of

100

.BIZYT Glass z o

" \ ||SiO2 Glass\ 1 \ 50 .

I

ZBL Glass^ \ \ 1

I

CO

z

BeF2 Glass 1

2

3

\

3

\ V

ZBLA Glas

\ 1

\ 2

4

, 5

: 6

7

WAVELENGTH (jim)

8

9

Figure 8-6. Infrared absorption edges of several fluoride glasses compared to SiO2 glass. Spectrum 1 corresponds to BeF2-based glasses, spectrum 2 to the ZrF4based glass ZBLA stabilized by AIF3, spectrum 3 is a pure ZrF4based glass ZBL, and spectrum 4 corresponds to a heavy metal Zr-free fluoride glass such as the

468

8 Halide Glasses

the absorption coefficient or loss in dB/km for a fluorozirconate glass from the far I.R. region (50 to 15 |im), corresponding to the high absorption region of the stretching vibration, to the potential ultralow loss region in the mid I.R. region (2-4 |im). The data were obtained in the far I.R. region by reflectivity measurements, in the 5 to 10 jim region by absorption measurements on bulk samples, and in the 2 to 5 jim from optical losses in fibers ranging from a few meters to one hundred meters in length. Figure 8-7 also shows the intrinsic minimum loss expected in the 2 - 4 |im region, which is estimated to be in the range of 10" 2 dB/km. The Infrared Edge in Heavy Halide Glasses As discussed before, the metal heavy halide glasses have the general formula MxXyKz, where M = Zn 2 + , Cd 2 + , Bi3 + , Th 4 + , X = Cl, Br, I, and A is a large cation

WAVELENGTH (Mm) 3 5

2 i

From reflectivity spectra

108

i/Km)

From bulk sample

Y

104

m

From fiber

TJ


102

_i

10°

10

i

/

\

./

,

O

Intrinsic loss 10" 2

r

/

_.j_y i

i

5000

i

3000

1000 1

WAVENUMBER(cm )

Figure 8-7. Evolution of the optical loss in fluoride glasses from the far I.R. corresponding to the one phonon absorption regime to the low loss region. The theoretical intrinsic low loss around 2.6 jam is expected to be close to 10" 2 dB/km.

playing the role of modifier (Cs + , K + , Rb 2 + , Pb 2 + ,...). The position of the I.R. cut-off in such materials is associated with the atomic weight of the two glass former partners M and X and with the force constant of the M - X bond. The character of the bond in all these halides is typically ionocovalent, and the bonding forces are inversely proportional to the interatomic distances and directly proportional to the charge of M. Also, the bond distances M - X are related to the sizes of M and X, which are in turn proportional to their atomic weight. Consequently, the two factors, weight and force constant, are evolved in the same way, and it is not surprising to see that the I.R. cut-off of halide glasses is very sensitive to the nature of the halogen. In Fig. 8-8 the multiphonon absorption regions are shown for several metal heavy halide glasses. ZnCl 2 glass transmits up to 13 jim (Robinson et al, 1982) but has a multiphonon absorption region which can be strongly affected by the presence of water in this highly hygroscopic glass; similarly, the ThCl4-based glasses (Hu and Mackenzie, 1982), have their I.R. cut-off in the same region. The absorption starts at 13-14 jim and is also affected by moisture corrosion. The identical positions of the Zn 2 + -Cl and Th 4 + -Cl vibrations can be explained by the fact that the difference in atomic weight between Zn and Th is compensated by a higher force constant in Th 4 + -Cl due to the higher charge of Th 4 + compared to Zn 2 + . The same remarks can be made for the BiCl3 glass I.R. cut-off (Angell and Ziegler, 1981). For a thickness of about 1 mm, similar to that of the other chloride glasses, the I.R. absorption begins at 14jim. Examination of ZnBr2-based glass shows that the I.R. cut-off is around 20 jim when the material is not too corroded by moisture (Hu et al., 1983; Nogami et al., 1985).

8.3 Halide Glasses as Optical Materials: Passive Properties

As expected, the iodide glasses have their multiphonon edges in the far I.R. part of the spectrum around 25-30 (am (Cooper and Angell, 1983; Nasu et al., 1985). It is interesting in Fig. 8-8 to compare the positions of the I.R. edge for the four families of halide glasses. For samples of about 1 2 mm thickness, the four zones of I.R. absorption are the following: zone I, 6-8 |im fluoride glasses; zone II, 12-14 |im for the chloride glasses; zone III, 19-21 |um for the bromides, and zone IV at about 30 jim for the iodide glasses. It must be remarked that as the vibrational frequencies decrease from fluoride glasses to iodide glasses, the thermal and mechanical properties correspondingly decrease, giving soft, low Tg glasses difficult to use in practical applications. Analysis of the I.R. edges for the multicomponent halide glasses, whose glass forming concept is not well understood, shows that glassy materials such as AgClAgl-CsCl and CuCl-PbCl 2 -RbCl (Angell et al., 1985) or AgBr-CsI-PbBr 2 (Nishii et al., 1985) have their I.R. edges slightly shifted towards longer wavelengths compared to the other halide glasses. This could be explained by the low charges of

469

the different cations composing the glass. It must be noted that, at the same time, these glasses also have a low Tg, sometimes close to room temperature. The tellurium halide glasses, i.e., the TeX glasses previously discussed, form a special group of glasses due to the semi-metallic nature of tellurium and also because of their chain-like structure which is very similar to the model proposed for glassy Se (see Sec. 7.3.3.1). Figure 8-4 represents the structure of the parent crystalline material Te3Cl2 (Kniep et al., 1973), which can be taken as a model for explaining the good glass-forming ability of the TeX glasses. As discussed before, the general formula of these glasses is Te-X (S, Se). Addition of S or Se strongly decreases the devitrification rate. The vibrational modes limiting the I.R. transparency are here associated with the Te-X and Te-S or Te-Se bonds. Examination of the I.R. cut-off for several glass compositions shows clearly two families of materials: the light TeX glasses containing S or Cl, which limit the transmission to 13 jim and the heavy TeX glasses free of light elements and based on Te, Se, Br or I, with a cut-off in the 20 jim region. Figure 8-9 represents the I.R. cut-off for

Wavelength (jim) 30

40

o

25

Figure 8-8. Multiphonon absorption edges for several halide glasses including fluoride, chloride, bromide, and iodide glasses.

-

2500

1OOO

750

" '

500 1

Wavenumber (cm" )

250

470

8 Halide Glasses

Wavelength(jam) 7 8 10 12

£

80

30

1-Te3l3Se4(3.1mm) 2-Te3Br2Se(3.5mm)

c 60 CO

r

40

c

20 2000

Figure 8-9. Position of LR. cut-off for three different TeX glasses containing only heavy atoms such as Te, Se, and Br, or I.

3-Te3Br2(4.2mm)

1600

1200

800

400

Wavenumber(cm-I)

several members of the heavy TeX glass group, namely Te 3 Br 2 , Te3Br2Se, and Te 3 I 3 Se 4 . 8.3.1.3 Refractive Index of Halide Glasses Except for fluoride glasses, which have received particular attention during the last ten years, the halide glasses in general suffer from a lack of precise information on their optical properties, especially refractive index measurements which require samples of reasonable thickness, good optical quality, and resistance to moisture corrosion. Special attention has been paid to the fluoride glasses, which were considered to be the best candidates for high-power glass lasers (see Chap. 12). To minimize selffocusing effects in short pulse high-power lasers, glasses with a low non-linear refractive index n2 are necessary. As discussed by Weber et al. (1978), the materials with high Abbe numbers (see below) and low refractive indices n are the materials having the lowest n2 values. Among all the glasses examined, the BeF2-based glasses are of special interest with a refractive index near ft = 1.27, an Abbe number v = 100, and a non-linear index n? = O.25xlO~ 13 .

For comparison, the ZrF4-based glasses have the following values: n = 1.50, v = 70, and n2 = 0.7xl0~ 1 3 . Fluoride glasses have been proposed as potential candidate materials for very lowloss optical fibers, and two key parameters associated with this technology are the refractive index dispersion versus the wavelength (Jeunehomme et al., 1981; Poignant, 1981) and the possibility of controlling refractive index variation in order to realize core-clad waveguides (see Chap. 15). Several reports have been devoted to the n versus X dependence, which has been measured on different types of glasses such as ZBGA (G means Gd instead of La) by Mitachi and Miyashita (1983), ZBL by Bendow et al. (1981 d), ZBLA, ZBL AN, BZYT by Brown and Hutta (1985) and Brown and Suscavage (1987) and BIZYT by Fonteneau et al. (1987). Figure 8-10, based on data from Mitachi and Miyashita (1983), shows the index of refraction versus A for two classical glasses, ZBLA and ZBLAN. The Abbe number is a partial dispersion defined by v = (nd— l)/(ft F — nc) where nd, nF, and nc

denote respectively the indices at the following A: d = 0.589 mm, F = 0.486 mm, and c = 0.656 mm. As an indication, the

8.3 Halide Glasses as Optical Materials: Passive Properties

X

1 5 1

u

Q Z

~

^ ^ " \ ^ ^

ZBLA

1.49

h-

o <

1.47

DC UJ DC

^******^*^

1.45

ZBLAN

1.43 1

2

3 WAVELENGTH (pm)

4

5

Figure 8-10. Refractive index versus wavelength for two fluoride glasses ZBLA and ZBLAN; in the latter, half of the Ba 2+ content has been substituted by Na + .

values of v for ZBLA and ZBLAN reported by Brown and Hutta (1985) are 62 and 64, respectively. As with the oxide glasses, the refractive index of fluoride glasses is dependent on the composition. As expected, the introduction of heavy polarizable cations, especially those having non-symmetrical lone pairs such as P b 2 + or Bi3 + , increases n significantly, while light elements do the opposite. 8.3.1.4 Origin of Scattering Losses in Fluoride Glasses The total intrinsic attenuation coefficient at as a function of wavelength X in an ideal vitreous material is given by the equation: (5-1)

ax = A exp ( - a / 2 ) + B /T 4 + C exp {c/X)

The first term is associated with multiphonon absorption mechanisms, as already discussed, and is dependent on the position of the I.R. edge. The third term, also called the Urbach tail, is related to absorptions due to electronic transitions which are only important in the U.V. and can be neglected in the mid I.R. region far

471

from the U.V. cut-off. The second term, B / T 4 represents the Rayleigh scattering loss due to composition and density fluctuations on a microscopic scale. The effect of this parameter on the potential ultratransparency of fluoride glasses has recently been examined by several authors (Tran etal., 1982; Tsoukala etal., 1987; Sakagouchi and Takahashi, 1987) and the theoretical value of the Rayleigh factor B was first calculated by Poignant to be around 0.4, about half of the measured value for fused silica. Tran et al. (1982) were the first to demonstrate that the measured light scattering in fluoride bulk glasses was indeed Rayleigh in character. For all these investigations, very low losses, typically 0.01 dB/km, in the mid I.R. region are predicted. These are much lower than those observed in fused silica. When a glass follows "Rayleigh behavior", it is also observed that the B factor changes according to composition and, as demonstrated by Hattori etal. (1987), is also very sensitive to the presence of small submicron particles of ZrO 2? which cause a Rayleigh scattering about two orders of magnitude larger than that caused by ZrF 4 particles. This confirms the previous observations of Mitachi et al. (1985), who found that the optical fibers having the highest loss were made of glass with a higher content of oxygen. The oxygen impurities measured by activation analysis which are obviously at the origin of the nucleation and growth of ZrO 2 crystallites, which are known to have a high lattice energy, nucleate very easily from the glass matrix. It is also observed that the general relation between scattering loss a and wavelength X follows the relation a = BA~"4 + C, where C is a constant indicating a source of scattering independent of X. This type of scatter is, for the moment, the major limitation to low losses in fluoride glasses and

472

8 Halide Glasses

optical fibers. It is due to imperfections larger than the wavelength of light, which have been identified to be isolated crystals such as LaF 3 , A1F3 or metallic particles (Lu etal., 1987) or bubbles (McNamara and McFarlane, 1987). These sources of extrinsic scatter depend on the glass processing and especially on the quality of the raw materials. The major origin of these scattering centers is poor dissolution in the melt of a few fluoride crystals or the contamination of the melt by insoluble species originating from the crucible during the heat-treatment.

needed, it is necessary to develop new fiber materials operating in the mid I.R. region, as proposed independently by Pinnow et al. (1978), Van Uitert and Wemple (1978) and Goodman (1978) at the end of the seventies. Fluoride glasses have been widely recognized as an exellent medium for ultralow loss transmission in very long repeaterless communication links. With a minimum intrinsic loss close to 0.01 dB/km which means a factor of at least ten better than silica, this provided sufficient motivation for working on these systems.

8.3.2 Fluoride Glass Fibers

8.3.2.2 The Optical Losses in Fluoride Glass Fibers

8.3.2.1 Introduction The propagation of light through glass fibers is becoming the preferred mode of transmitting audio and visual information. Research into optical communication systems began back in 1966 and the present generation of optical fibers is based on fused silica. In twenty years, the field has developed extensively, and monomode fibers operating at 1.3 and 1.55 |im with losses close to 0.2 dB • km, form a substantial basis for many telecommunications systems around the world. (See Chap. 15.) The efficiency of an optical communication system is measured as the product of the carrying capacity, namely the number of bits of information transmitted per second, the length of fiber over which the pulses injected into the fiber remain recoverable in terms of pulse spreading due to dispersion, and the energy loss due to attenuation. The development of CVD techniques around 1970 for preparing high quality SiO2 fibers led very rapidly to optical fibers with the minimum intrinsic loss, estimated to be 0.16dB/km at 1.55 jam. This means that if lower optical attenuations are

Intrinsic Factors For a glass of ideal optical quality and free of all kinds of absorbing impurities, the total intrinsic optical attenuation at for fluoride glasses can be expressed, as discussed before, by the equation at = A exp (— a/A) + BA~4, where the first term is the multiphonon absorption and the second the Rayleigh scattering contribution. The Urbach tail contribution in these fluorides which have a U.V. cut-off around 0.25 jum is negligible in the mid I.R. The combination of those two mechanisms gives the well-known V-shaped curves shown in Fig. 8-11 for SiO2 glass and two fluoride glasses, the fluorozirconate glass ZBLA and BIZYT glass. These curves show unambiguously that the predicted loss for fluoride glasses is in the range of 10" 2 -10~ 3 dB/km in the optical window between 2 and 4 |im. As discussed before, the measured multiphonon absorption of bulk glasses and fibers is in good agreement with the predicted values, and one can estimate that the absorption in the low loss region corresponding to the six and seven phonon regime will be

8.3 Halide Glasses as Optical Materials: Passive Properties 10

10

ffi •o

o LU

id 2

Rayleigh Scattering

-3 10

104

0.3

0.5

1

2

3

4 5 678

WAVELENGTH (um )

Figure 8-11. Low loss region for SiO2 glasses and two typical fluoride glasses, a ZrF4-based ZBLA and a InF3-based BIZYT. Intrinsic absorption mechanisms are considered, namely band gap, multiphonon absorption, and Rayleigh scattering.

around 0.005 dB/km. Estimates for the Rayleigh scattering coefficient B are in the range 0.14 to 0.70 dB/km, as discussed by different authors (Drexhage et al., 1987) and by Day et al. (1987). Adding the scattering and absorption contributions in the above equation leads to an estimate of 0.02dB/km for the intrisic total attenuation of ZBLAN fibers at the wavelength close to 2.5 |im. Extrinsic Factors a) Scattering Loss As mentioned before, is has been found in many fluoride glasses that the extrinsic scattering is represented by the expression a ext = C A2 + D. The first term corresponds to the MIE scattering and results from imperfections comparable in size to the wavelength and originating from a partial devit-

473

rification of the glasses. The second term, which is wavelength-independent, is due to larger defects. Kanamori (1987) suggested that micron-sized particles, some of them several microns in diameter, were monoclinic ZrO 2 ; these particles have been identified by Raman microprobe analysis (Sakaguchi and Takahashi, 1987). According to Day et al. (1987), the value of C can be decreased by improving materials and processing. Analysis of the attenuation in ZBLAN fibers made at BTRL have yielded values of D in the range of 3 to 10 dB/km. These values are of course a function of fibre length because the larger particles which give rise to wavelengthindependent scattering are randomly distributed along the fiber. b) Absorption Loss The absorption losses in fluoride glasses are due to the intrinsic factors discussed before and due to all the parasitic absorbing impurities present in the glass. Absorption due to the hydroxyl group OH ~ is potentially the most significant because its absorption coefficients are large. According to Mitachi et al. (1987), the presence of 1 ppm of O H " introduces a loss of 3000 to 5000 dB/km at 2.9 jam. The observed loss values at 2.9 |im in the best fluoride glass optical fibers lie from 20 to 100 dB/km, indicating that the OH concentration in these fibers is in the range of 2 to 10 ppb. The transition metals Fe 2 + , Co 2 + , Ni 2 + , Cu 2 + are among the most deleterious impurities, because their absorption regions extend into the 2 to 3 jim region. The rareearth Pr 3 + , Nd 3 + , Sm 3+ , Eu 3 + , Tb 3 + and Dy 3 + are also among the most absorbing species in the mid I.R. region. Detailed absorption spectra have been published by France et al. (1968) and Ohishi et al. (1981).

474

8 Halide Glasses

By melting under oxidizing conditions a gas such as O 2 or NF 3 , the divalent Fe 2 + is converted into Fe 3 + which has no absorption in the near I.R. region. However, this operation stabilizes Cu 2 + , which remains the most absorbing cation in the 2.5 jim region. Among the rare-earths, Nd 3 + can be particularly troublesome because it has an absorption peak at 2.55 jim, exactly in the ultratransparency window. It is found as the major contaminant of La 3 + in LaF3 which is one of the constituents of the glass. It has been calculated that loss introduced by Nd 3 + at 2.55 ^im is a = 0.22(dB/km)pb. 8.3.2.3 Fluoride Glass Fiber Preparation

Fluoride glasses are known to be prone to devitrification, and fiber techniques production have to take this into account in order to avoid the formation of microcrystallites which have a drastic effect on scattering loss. In order to keep the light inside the optical waveguide, when carrying the optical signals over very long distances, the core must have a refractive index n slightly superior to the clad. This is achieved by modifying the chemical composition of both glasses; typically a small amount of PbF2 increases n, while LiF does the inverse. Present fluoride glass fiber technology relies strongly on the preform casting approach. In this approach, core melts are directly cast into cladding tubes to form waveguide preforms. Fluoride glass cladding tubes with uniform wall thickness can be obtained by rotating this mold while casting the cladding melt. The preforms are then drawn into fiber near the glass softening point, T=350°C, in order to avoid crystallization. After drawing a preform of 10 mm diameter and 20 cm length, the usual fiber diameters are about 150 jam.

The preform approach leads necessarily to limited fiber lengths, which will require the development of low-loss splicing techniques. In order to prepare ultralong fibers, a continuous fabrication process appears to be very attractive. The so-called double crucible technique, which is based on the direct preparation of core/clad fibers from two concentric melts, is in principle the most promising. Since fluoride melts are known to have very steep viscosity-temperature curves, diameter control during fiber drawing requires precise control of the melt temperatures. The major efforts conducted by Nippon Telegraph Telephon (Japan), Naval Research Laboratories (U.S.A.), and in British Telecommunication Research Laboratories (U.K.) have led to continual improvement in the absorption losses, and values as low as 0.7 dB/km at 2.55 jim have been obtained using traditional purification techniques. Figure 8-12 represents typical transmission spectra for the best fluorozirconate glass fibers prepared in England, Japan, and the U.S.A. The BTRL

140

1 :i

\NTT »

E 100

t

3

N

\

_ 2+ _

Co Cr

As "*• \ -/' | p r 3 ; Tb

NRL>c\

CO

'

3

/

w

V

V /

20 >

Ni

Cu

2+ _ ' Fe

3+

3+

3+

Nd

Sm T

If

I/

! '

V

I: Nil

0.5

•t I

1.5 2.5 WAVELENGTH (urn)

•if

3.5

Figure 8-12. Typical transmission spectra for fluoride glass optical fibers. The data are from three different research groups: NTT Japan, NRL USA, BTRL UK. Transition metals, rare-earth, and OH ~ are the most critical absorbing impurities. Also a continuous absorbing background is due to A independent scattering.

8.4 Fluoride Glasses: A new Host for Rare-Earth and Transition Metals

transmission curve is flat over a large wavelength range and shows a minimum of about 3dB/km for a 200 m fiber length. The NRL curve is for an unspecified length and shows a minimum of 0.9 dB/km. NTT data correspond to the lowest value, 0.7 dB/km on a 30 m long fiber. According to France et al. (1987) a realistic total loss of 0.035 dB/km could be expected if the impurity levels were maintained in the range 0.1 to 5 parts per billion. Also, the extrinsic scattering loss, which seems to be due essentially to ZrO 2 microcrystallites (Takahashi, 1987), could be significantly decreased by lowering the O 2 ~ impurity content. A 0.035 dB/km loss value corresponds to a capability of repeaterless information transmission over a distance of 1500 km. Recent improvements of the surface of the glass by etching the preform rod have been found to increase the strength of fibers, as described recently by Schneider et al. (1987). (See Chapter 13.) A key quantity in optical fiber communication is the pulse broadening associated with the material dispersion, which is proportional to d2n/dX2. The zero material dispersion wavelength, for most of the fluoride glasses, is located around 1.7 (im, which is relatively far from the 2.6 jim ultratransparency region. Fortunately, the slope of the dispersion curve, changes slowly compared to SiO 2 , as described by Bendow et al. (1981a). It has been demonstrated by France et al. (1987) and Takahashi (1987) that, in using a simple step index design, the dispersion characteristics of the fibers can be tuned to give zero dispersion at a 2.55 jim operating wavelength. Among the potential uses for fluoride glass optical fibers, the realization of very long repeaterless telecommunications links (for undersea systems, for example) is the most challenging and will need additional

475

research efforts, especially in chemical purification. At the moment, the actual level of transparency of fluoride glass optical fibers is such that these new waveguides can be used in many short length devices. For example, for remote sensing and thermal imaging out to about 5 jum. Other possible commercial devices include the coupling between an Er 3 + YAG laser emitting at 2.9 jum and a fluoride glass fiber for power delivery in surgical applications, since water in tissues is very absorbent at this wavelength. Gas lasers, such as HF emitting at 2.6jiim and DF emitting at 3.8 jam, can also be used as power sources. Low loss bulk optical components made of fluoride glass may also be very useful for prisms and lenses, operating in the mid I.R., as well as for optical windows with high damage thresholds for high energy lasers such as HF.

8,4 Fluoride Glasses: A new Host for Rare-Earth and Transition Metals 8.4.1 Active Optical Properties

Active optical properties of fluoride glasses have generated a great deal of interest as well (see Chapter 12). Among the various families described earlier in this review, the ZrF4-based and other multicomponent heavy-metal fluoride glasses are certainly the most attractive materials. Their relatively long wavelength I.R. edge, their good stability, and their ability to easily accommodate active rare-earth ions make these glasses preferred candidates for laser application. Except for a few studies dealing with the optical properties of divalent europium (Shafer et al., 1979), tetravalent uranium (Aliaga et al., 1978), and uranyl ions (Reisfeld et al., 1986 c), exten-

476

8 Halide Glasses

sive investigations have been carried out on fundamental or applied spectroscopy of trivalent rare-earth and transition metal ions. Either bulk glasses or fibers are suitable for practical applications. Fibers are of special interest because of their flexibility and compactness which allows for light systems with good concentration of the light and easy cooling of the medium for laser operation. This is especially important for glasses whose thermal conductivity is lower than that for crystals. Besides these applications, luminescence is a reliable technique for analysis of optically active impurities in fluoride glasses. Also, fluorescence line narrowing is a useful tool for structural investigations on heavy metal fluoride glasses and beryllium-based fluoride glasses. 8.4.2 Absorption Spectra of Rare-Earth and Transition Metal Ions 8.4.2.1 Rare-Earth Ions

Absorption spectra of trivalent rareearth ions (R.E.) in heavy-metal fluoride glasses are well-known (Adam and Sibley, 1985; Lucas et al., 1978; Ohishi and Takahashi, 1985; Adam et al., 1987a; Alonso et al, 1988; Perry et al, 1981; Adam et al, 1988; Ohera et al, 1988; Tanimura et al, 1984; Shinn et al, 1983; Jorgensen et al, 1982; Guery et al, 1988; Sanz et al, 1987; Yeh et al, 1986) except for radioactive Pm 3 + and of course Lu 3 + which is optically inactive with its completely filled 4fshell. A survey of all results will not be presented here. We have arbitrarily chosen to emphasize only the optical properties of Nd 3 + , Ho 3 + , and Er 3 + which can be considered as being among the most interesting ions with regard to their applications in photoluminescence. Glasses are well-known for having a larger distribution of different sites in com-

parison with crystals (see Chaps. 4 and 6). This results in inhomogeneous broadening of absorption bands, each site having its own spectrum. This can be observed in the absorption spectrum of Nd 3 + ions (Lucas et al, 1978) where the bands have widths at half-maximum equal to a few hundreds of wavenumber. Among the various lines, attention is directed to the 4 F 3/2 absorption at 867 nm. This level gives rise to strong emissions at 1.05 and 1.35 jim, as it will be discussed later on in this chapter. From the spectrum, it is obvious that the 4 F 3/2 level should be excited via more efficient pumping levels such as ( 4 F 5/2 , 2 H 9/2 ) at 796 nm, ( 4 F 7/2 , 4 S 3/2 ) at 741 nm, or ( 4 G 5/2 , 2 G 7 / 2 ) at 576 nm. The ability for an absorption band to efficiently excite the corresponding level is quantitatively accounted for by its oscillator strength. For Ho 3 + and Er 3 + the positions of the excited states indicate that emission, especially I.R. emission, should occur at quite a few levels. The 5 G 6 level of Ho 3 + and the 4 G 1 1 / 2 level of Er 3 + exhibit a high oscillator strength at 450 nm and 378 nm, respectively. This permits efficient pumping for applications in the VisLR. range. In addition to the experimental studies, oscillator strengths may be investigated as a function of three phenomenological parameters Qt, with t = 2, 4, 6, using the Judd-Ofelt theory (Judd, 1962; Ofelt, 1962). These parameters are characteristic of an ion-host combination. For a given ion, they vary slightly between fluoride glasses. Reisfeld and Jorgensen (1987) pointed out that Q2 was an indicator of the covalent character of bonding, higher Q2 corresponding to higher covalency. 8.4.2.2 Transition Metal Ions

Like rare-earth ions, the absorption spectra of 3d transition metals (T.M.) have

8.4 Fluoride Glasses: A new Host for Rare-Earth and Transition Metals

been widely studied (Esnault et al., 1986; Fonteneau et al, 1978; Ohishi et al, 1983; Reisfeld et al, 1986a; Feuerheim et al, 1984; Suzuki et al, 1987; Poulain et al, 1987), mainly in fluorozirconate glasses. 3d ions are very sensitive to the crystal field strength and therefore to the local environment. This of course influences the spectroscopic behavior of these ions as reported in the famous diagrams established by Tanabe and Sugano (1954 a, b) for octahedral crystal fields. Previous studies have shown that transition metal ions could reasonably be expected to occupy an octahedral-type environment in fluorozirconate glasses, with crystal fields ranging from low to medium, even though some discrepancies may occur. For example, Ti 3 + ions which, under a reductive atmosphere, may be stabilized in ZBLA glass by substitution for Al 3+ ions: the absorption spectrum analysis shows that Ti 3 + ions are not simply embedded in pure octahedral symmetries, but also in perturbed geometries such as monocapped (coordination number CN = 7) and bicapped (CN = 8) octahedra (Esnault etal, 1986). The Cr 3 + ion is probably among the most important active ions in spectroscopy, as a local probe for microcrystallization studies (Miniscalco et al, 1985) and as an efficient pumping system for energy transfer application, to Nd 3 + for instance. The analysis of the absorption spectrum of Cr 3 + ions in ZrF4-based glasses strongly suggests that Cr 3 + ions are in an Oh-type environment. The best fit to the energies gives the crystal field and Racah parameters (see Chap. 12) which are Dq = 1531cm"1 and B = 721 cm" 1 in the present case. These values correspond to low fields compared to crystals and can be interpreted as being due to a more open lattice for the glass, leading to longer T M - F average bonds.

477

Because of its transition energies, Mn 2 + is, like Cr 3 + , often used as a sensitizer of rare-earth luminescence. Actually, Mn 2 + absorption is very weak as reported by Suzuki etal. (1987) for ZBLA glass. The highest experimental oscillator strength for this ion is weak compared to transitions of Ni 2 + and Co 2 + ions, respectively. This can be overcome by using fluoride glass hosts with ZnF2 as a major constituent, such as PZG glass (22mol% ZnF2) where Zn 2 + ions are easily substituted by Mn 2 + , It has been even experimentally shown that BIZYT glass was more stable in the presence of MnF2 and valuable compositions with up to 20mol% MnF2 could be obtained (Le Gall, 1988). A number of papers deals with the optical absorption of other 3d ions in heavy metal fluoride glasses. They are V3 + (France et al, 1986; Fonteneau et al, 1978; Ohishi etal, 1983), Fe 2 + (France etal, 1986), Fe 3 + (Ohishi etal, 1983), Co 2 + (France etal, 1986; Ohishi etal, 1983; Suzuki etal, 1989; Poulain etal, 1977), Ni 2 + (France etal, 1986; Ohishi etal, 1983; Reisfeld etal, 1986a; Suzuki etal, 1987) and Cu 2 + (France etal, 1986). In summary, except for Cu 2 + , all ions were found to be in octahedral-type sites with lower crystal fields compared to crystalline materials. 8.4.3 Fluorescence Spectra of Rare-Earth and Transition Metal Ions 8.4.3.1 Radiative Emission of Rare-Earth Ions

The wide range of transparency of fluoride glasses makes them attractive materials for infrared luminescence (see Chap. 12). Emission spectra have been reported in various glasses for almost every rareearth. Many ions such as Pr 3 + (Adam and Sibley, 1985; Eyal et al, 1985), Nd 3 + (Lu-

478

8 Halide Glasses

cas et al., 1978), Eu 3 + (Adam et al, 1987 a; Blanzat et al., 1980; Reisfeld et al., 1983), Gd 3 + (Alonso et al., 1988), Tb 3 + (Perry etal., 1981), Dy 3 + (Adam et al., 1988b; Orera et al., 1988), Ho 3 + (Tanimura et al., 1984; Reisfeld etal., 1985), Er 3 + (Shinn etal., 1983) and Tm 3+ (Sanz etal., 1987) have been studied in fluorozirconate-type glasses while only Ho 3 + (Eyal et al., 1987; Adam etal, 1987b), Er 3 + (Eyal etal., 1987a), Tm 3+ (Guery etal, 1988) and Yb 3 + (Yeh et al, 1986) have been studied in (Ba, Zn, Th, Y)-based fluoride glasses. Also Reisfeld and coworkers (Jorgensen et al, 1982) have reported luminescence of Er 3 + ions in (Pb, Zn, Ga)-fluoride glasses. The first two infrared emissions of Nd 3 + ions in fluorozirconate glass are shown in Fig. 8-13. The 4 F 3 / 2 -» 4 I 1 1 / 2 transition is found to peak at 1040 nm with an experimental lifetime of nearly 450 JIS. In that same figure, the optical spectrum for Nd 3 + ions in NdZr 7 crystals is superimposed. It is important to note that the emission peaks for the glass are just as broad as they are for the crystal. This suggests that the Stark splitting of the levels involved is

io 3 cm~ 1 11.

3/2

ANM

1100

'11/2 1000 900 9/2

800 NdFG-V

Figure 8-13. Emission spectra of Nd 3 + in two parent fluoride matrices. NdFG is a 0.5 Nd 3 + doped fluoride glass of the ZBLA family. NdZrF7 is a crystalline material containing Nd 3 + in a NdF8 polyhedron. The emission bandwidth is the same in the glassy and crystalline materials.

about the same in both materials. The number of non-equivalent sites is certainly small in heavy metal fluoride glasses, compared to oxide glasses in general. This arises from the specific structure of fluoride glasses where rare-earth ions are part of the framework and, as glass formers, are in well-defined sites. Conversely, in oxide glasses rare-earth ions are in modifier sites, that is in ill-defined sites. This is confirmed by the decay time measurements of the emitting levels. Usually in glasses, because of the great number of non-equivalent sites, the decay curves are non-exponential, each type of site having its own time constant. In heavy metal fluoride glasses, the decays can generally be fitted to nearly single exponentials with a ratio between the first and third e-folding times equal to 0.80.9 (Lucas etal., 1978; Adam etal., 1988; Tanimura et al., 1984; Shinn et al., 1983). The relatively large number of isolated levels of Ho 3 + and Er 3 + ions yields rich emission spectra ranging from near U.V. to mid I.R. In the visible range, the wellknown intense green emission of these two ions ( 5 S 2 , 5 F 4 ) -> 5 I 8 for Ho 3 + and 4 S 3 / 2 -> 4 I 1 5 / 2 for Er 3 + are reported to peak at 537 and 542 nm, respectively, in fluorozirconate glasses. In the infrared region, Ho 3 + ions exhibit four emissions at 1.2 jam (5I6-5I8), 1.38 Mm ( 5 S 2 + 5 F 4 ^ % ) , 5 5 2.04 m ( I 7 ^ I 8 ) , and 3 ^m ( 5 I 6 ^ 5 I 7 ) . The 2.04 jim emission is of particular interest as it is located in a transparent window of the atmosphere. Even though that transition terminates on the 5 I 8 ground level, laser action has been demonstrated in Ho 3+ -doped fluorozirconate fibers at room temperature (Brierley et al., 1986). However, low-temperature absorption measurements have shown that 5 I 8 was made of two components in these glasses, separated by 230 cm" 1 . Er 3 + ions exhibit three I.R. emissions at 0.975 jam ( 4 In / 2 ->

479

8.4 Fluoride Glasses: A new Host for Rare-Earth and Transition Metals 4 and 1.52 {im 13/2" • I15/2), 4 e have previ2.78 pm ( I 1 1 / 2 ously reported that the minimum loss of fluoride glass fibers could be reasonably expected at 2.55 jim. At the moment, the 4 111/2 ->4113/2 emission of Er 3 + is the only one available in that region, for use with solid state lasers. That wavelength would of course be better matched by using U 3 + ions whose 4 I 11/2" I 9/2 transition peaks at nearly 2.5 jim. L

8.4.3.2 Non-Radiative Processes in Rare-Earth Doped Glasses Another important parameter for evaluating the lasing potentiality of a given transition is the quantum efficiency rj: n

= WK/{W^Wu^W^)

(8-2)

where WR is the radiative rate and WMJ> and WET are the multiphonon emission and energy transfer rates, respectively. The last two quantities correspond to non-radiative processes and have to be as small as possible in order to have a quantum coefficient equal to or near unity. The multiphonon emission rate varies exponentially according to the following empirical law: WMP = Ce-«*E

(8-3)

where C and a are constants for a given host and AE is the energy gap between the emitting level and the next lower-lying level. The evolution of WMP as a function of AE is portrayed in Fig. 8-14 for ZrF4-based glass (Adam and Sibley, 1985; Tanimura et al., 1984; Shinn et al, 1983), BeF2-based glasses (Layne and Weber, 1977), and various oxide glasses (Yeh et al., 1987; Layne et al., 1977; Reisfeld and Eyal, 1985). As far as the quantum efficiency is concerned, the superiority of fluorozirconate glass is obvious with multiphonon emission rates lower

by one to four orders of magnitude when compared with other glasses. In consequence, fluorescence is more intense and occurs from a greater number of levels in heavy-metal fluoride glasses. This special feature is directly related to the fundamental vibration mode of the host. In fluorozirconate glasses, phonon energies are as low as 500 cm" 1 , compared to 1000 cm" 1 in silicates. For a given energy gap, a greater number of phonons is then required, leading to lower non-radiative probabilities. The WMP=f(AE) curve for YAG crystals (Krupke, 1974) is also shown in Fig. 8-14. It should be noted that WMP is even lower for the ZrF4-based glass in the 2500-5000 cm" 1 region. Energy transfer between ions of the same nature causes a well-known phenomenon: 1OC

H\\\ *\ \ *\ \ \\\ \

LU <

M

en

o o CL 2 H 1O

10

•ZBLA F-BERYLLATE TELLURITE GERMANATE SILICATE PHOSPHATE YAG I L

2

3

ENERGY GAP

\ \ 4

(1O 3 cnT 1 )

Figure 8-14. Multiphonon emission rate, namely heat dissipation by phonon relaxation for different glass matrices doped with rare-earth materials. The YAG crystal is also mentioned for comparison.

480

8 Halide Glasses

fluorescence quenching. This occurs when ion-ion interactions become non-negligible, that is, when rare-earth concentration is around 1 mol%, in general. However, a peculiar behavior has been observed for the Ho 3 + - 5 I 7 - » 5 I 8 emission at nearly 2jim (Adam et al., 1987); this lifetime is reported in Fig. 8-15 as a function of concentration in various heavy-metal fluoride glasses. Examination of Fig. 8-15 shows that there is less energy transfer in BIZYT glass than in ZBLA and less in ZBLA than in BATY glass. This is explained as being due to a perturbation effect of Al3 + ions on Ho 3 + sites. From that same figure, it is to be noted that no concentration quenching is observed until 5 mol% for Ho 3 + -doped BIZYT glass. This makes this glass a promising material for luminescence applications in the infrared (Adam et al., 1988 a).

16

I 7 Level T=295K

12

BATY

8 4 E w

O 16

ZBLA

|±j 12 H

B

KH 4

=14.9ms

-J o 16 12

BIZYT -

8 '=15.8ms O

2

4

CONCENTRATION

6

8

10

(1O 2 O cm~ 3 )

Figure 8-15. Lifetime of the Ho 3 + emission 5 I 7 -> 5 I 8 versus concentration in three different fluoride glass matrices: BATY is an AlF3-based glass, ZBLA is based on ZrF4, and BIZYT contains mainly InF 3 .

8.4.3.3 Multidoped Fluoride Glasses While energy transfer between ions of the same nature is usually troublesome, energy transfer between different species can be very useful in improving the pumping efficiency of a given optical system. Sensitized luminescence of rare-earth ions has been investigated in R.E.-R.E. and T.M.R.E systems. The transfer efficiency depends directly on the emission and absorption abilities of sensitizer and activator ions, respectively. The knowledge of emission properties of 3d ions is necessary in this case and has generated a number of studies, especially dealing with Mn 2 + (Feuerhelm et al., 1984; Suzuki et al., 1979; LeGall, 1988; Jorgensen et al., 1986) and Cr 3 + (LeGall, 1988) ions. The 4 T l g ^ 6 A l g emission of Mn 2 + is observable at room temperature in fluoride glasses, rendering sensitization possible at that temperature. The peak wavelength is very sensitive to Mn 2 + concentration (LeGall, 1988; Jorgensen et al., 1986). High concentration causes a red shift of the band due to a change of the average local symmetry. Jorgensen et al. (1986) pointed out that Mn 2 + ions are mainly distributed in approximately octahedral sites, a non-negligible part is likely embedded in 7 or even 6 (nonoctahedral)-coordinated geometries. For instance, the 4 T l g -> 6 A l g emission peaks, at 568 nm in BIZYT: Mn 2 + (2 mol%) and at 602 nm in the 5%-doped glass. According to these values, Mn 2 + ion is suitable for sensitizing the 4 F 3/2 emissions of Nd 3 + . M n 2 + - > N d 3 + transfer has been investigated in PZG (Reisfeld et al., 1986d), BIZYT (LeGall, 1988) and ZBLA glasses (Jorgensen et al., 1986). The transfer efficiency was found to be as high as 0.94 for PZG glass containing 24 and 2 mol% of MnF2 and NdF 3 , respectively. Energy transfer from Mn 2 + to Tm3 + ions has been

8.4 Fluoride Glasses: A new Host for Rare-Earth and Transition Metals

observed in that same glass (Eyal et al, 1987 b) with a 0.95 efficiency. In contrast to Mn 2 + , Cr 3 + ions do not emit at room temperature because when the 4 T 4 is excited the related vibronic levels are thermally populated at room temperature. R.E.-R.E. systems are of special interest because they allow direct sensitization of I.R. emitting levels, compared to Cr 3 + and Mn 2 + in which the first excited states are located in the visible range. Depending on the purpose, combinations of Ho 3 + , Er 3 + , Tm3 + , and Yb 3 + ions have been studied (Eyal et al., 1987 a; Yeh et al, 1989; Adam et al, 1987; Rubin et al, 1987; Moine et al, 1988) as well as N d 3 + - > Y b 3 + energy transfer (Eyal et al, 1986). As pointed out before, the 5 I 7 -» 5 I 8 emission of H o 3 + at 2 jim is quite interesting. Efficient sensitization of Ho 3 + could be achieved in heavy metal fluoride glasses by the use of the appropriate concentration of Er 3 + or Yb 3 + ions. Yeh et al. recently reported energy transfer between Er 3 + and Tm 3+ in BIZYT-type fluoride glasses. Tm 3+ ions act as quenching centers for the green luminescence of the Er 3 + 4 S 3 / 2 -• 4Ii5/2 transition. Unfortunately, transfer from 3 H 4 (Tm 3+ ) to 4 I 9 / 2 (Er 3+ ) that could enhance the Er 3 + - 4 I 1 1 / 2 -• 4 I 1 3 / 2 emission at nearly 2.8 jLim is not observed. 8.4.3.4 Up-Conversion or Photon Addition in Fluoride Glasses

The conversion of infrared light to visible light has received special attention in view of applications for I.R.-detectors and improved visible sources. Two-photon upconversion processes have been demonstrated in heavy metal fluoride glasses at room temperature for the (Yb3 + - E r 3 + ) (Yeh etal, 1987; Quimby et al, 1987; Quimby, 1988; Okada et al, 1988), (Yb3 + -

481

Tm 3+ ) (Yeh et al, 1988; Yeh etal, 1989) and (Er3 + -Tm 3 + ) (Yeh et al.) systems and also for Er 3 + ions alone (Yeh et al.; Okada et al, 1988; Quimby, 1989). Quimby et al. (1987) have determined the up-conversion efficiency of infrared light ( = 1.0 |im) into green light ( = 0.55 |im) for the (Yb3 + Er 3 + ) combination in (Th, Zn, Lu)-based fluoride glasses. A very important result is that the efficiency (lxlO~ 3 ) is found to be of the same order of magnitude as that for crystalline materials such as CaF2 (2.1 x 10 ~3) and four orders of magnitude higher than that for silicate (2x 10"7) or phosphate (6 x 10 ~8) glasses. Heavy metal fluoride glasses appear to be a very good compromise that holds the good optical efficiency of crystals and easy preparation of glasses permitting the elaboration of the bulk of the fiber optical system. 8.4.4 Interest of Rare-Earth Spectroscopy in Fluoride Glasses 8.4.4.1 Analysis of Impurities by Photoluminescence

While optical properties of rare-earth and transition metal ions are of great interest with regard to laser applications, the optical properties of these elements are undesirable for ultralow loss fiber communications. 3d ion and rare-earth ion analysis can be successfully carried out by photoluminescence measurements (Miniscalco and Thompson, 1986; Freitas, 1987). In particular for rare-earth ions, the oscillator strengths of the transitions are lower and the absorption spectra are more complicated making photoluminescence a powerful tool. Ohishi et al. (1986) for instance have determined a Pr 3 + impurity content of 25 ppb in a fluorozirconate optical fiber by using this method, and Freitas et al. (1988) a Nd 3 + content of 40 ppb in similar conditions.

482

8 Halide Glasses

8.4.4.2 Crystallization and Structure Investigations

The luminescence of local probes such as Cr 3 + , Pr 3 + , Nd 3 + , or Eu 3 + ions is an efficient technique for crystallization and structure investigations. Miniscalco et al. (1985) have studied the evolution of the Cr 3 + emission in fluorozirconate glasses as a function of heat treatment. They found two crystalline phases in devitrified samples: j8-BaZrF6 for samples at 375 °C and a-BaZrF6 for higher-temperature treatment (426 °C). By use of the 1 D 2 -> 3 H 4 emission of Pr 3 + , Ferrari et al. (1988) have shown the presence of two micro-crystalline species in a fluorozirconate glass sample heated above Tg. This suggests that Pr 3 + ions are distributed in two main families of sites in the glass. This finding confirms the results obtained for Eu 3 + -doped fluorozirconate glass by fluorescence line narrowing (F.L.N.) (Adam et al., 1987 a). The study by F.L.N. of transitions from the 5 D 0 singlet state clearly shows emissions from two different types of sites. Comparison with spectroscopic data obtained for crystals, EuF3 (coordination number CN = 9) and EuZrF7 (CN = 8), indicates that the two types of sites in the glass are likely to derive from the 8-coordinated geometry of rareearth sites in EuZrF 7 . Even though the 5 D 0 -> 7 F 0 transition is forbidden (J = 0 -» -> J' = 0), one can observe it around 17 300 cm" 1 in some glasses. Its one-component structure (initial and final states are singlet) makes that transition very useful for structural investigations. F.L.N. experiments again have shown that the 5 D 0 -» 7 F 0 homogeneous line width is smaller in ZBLA glasses compared with silicate glasses (Durville et al., 1985). This is directly related to the respective structures and is explained as being due to weaker chemical

bonds and larger interatomic distances which induce smaller electron-lattice interactions in the fluoride host. A number of studies have been devoted to the structure of fluoroberyllate glasses (Brecher et al., 1978; Brecher and Risberg, 1980; Weber and Brawer, 1982). Like fluorozirconates, they exhibit narrower absorption or emission lines compared to oxide glasses, which means also fewer types of non-equivalent sites. Conversely, the local environment of rare-earth ions is found to be a 9-fold coordinated site in fluoroberyllates.

8.4.4.3 Temperature Measurements by Optical Means

Thermalization effects in emission or absorption spectra of rare-earth ions are wellknown phenomena and have been widely described in heavy metal fluoride glasses (Adam and Sibley, 1985; Shinn et al., 1983; Guery, 1988). The process for the (7F0, 7 FJ -> 7 F 6 absorption of Eu 3 + is given by Ohishi and Takahashi, 1986. At 4K, only the 7 F 0 -> 7 F 6 transition occurs. When temperature increases, the 1F1 level is thermally populated according to Boltzmann's distribution law and the 7 F 1 -• 7 F 6 transition shows up accordingly. Thus, the intensity ratio between the two transitions is directly related to the temperature. The measurements accuracy can be modulated by varying either the rare-earth concentration or the optical path length. With the above system, accuracy of 0.5 K in the 7 7 150 K temperature range could be achieved.

8.4.4.4 Lasers and Fiber Lasers

The goal of most of the studies reported above is to evaluate the potentially for

8.5 Tellurium Halide Glasses (TeX Glasses): New Materials for Low Loss Infrared Fibers

lasers of rare-earth-doped heavy-metal fluoride glasses (Reisfeld et al., 1986 b). Laser action in multimode fluorozirconate fibers has been effectively obtained for several infrared transitions such as the 1.05 and 1.3 mm emissions of Nd 3 + (Brierley and France, 1987; Brierley and Millar, 1988), the 1.38 and 2.08 mm emissions of Ho 3 + (Brierley et al., 1988) and the 2.71 and 1.00 mm emission of Er 3 + (Allain et al., 1988). These results show the feasibility of fluorozirconate fiber lasers. As already suggested by the much lower threshold obtained for Nd 3 + ions by Brierley and France (1987) and Brierley et al. (1988) compared to that of Allain et al. (1988), further technical improvements will undoubtedly be achieved in that field. These are, for instance, the optimization of rareearth concentrations and the reduction of fiber core diameter taking advantage of the optical properties of single-mode fibers. Lasing operation for the Er 3 + -2.78mm emission has also been reported in bulk heavy metal fluoride glasses (Pollack et al., 1988). From that study, it appears that very good optical quality is a more critical issue in bulk lasers than in fiber lasers.

483

8.5 Tellurium Halide Glasses (TeX Glasses): new Materials for Low Loss Infrared Fibers 8.5.1 Optical Characterization

As described before, the TeX glasses have their multiphonon edge located in the 20 |im region while the band gap absorption mechanisms start around 1 jim. In taking into account these two basic intrinsic factors of optical loss it can be seen from Fig. 8-16 that the low-loss region is situated in the 8-12 jim band. The V-shaped curve represented in Fig. 8-16 has been determined for the glass Te4Se3Br3, which is a very stable glass, versus devitrification and moisture or water corrosion. For this glass the lowest attenuation is around 11 jim and estimated to be close to 10 dB/ km. This family of vitreous materials is the only class of stable glasses showing so high a transparency in this strategic atmospheric window from 8-12 \xm and at the CO 2 laser wavelength peaking at 10.6 jim. 8.5.2 Optical Fibers Operating Between 3 and 14 fim

Monoindex optical fibers can be prepared easily from TeX glasses using either Wavelength (jim) 10

5 4

3

e o

Figure 8-16. Low loss region for the TeX glass Te4Se3Br3. Lowest attenuations are expected in 8-12 Jim region. 2000

4000

6000

Wavenumber (cm"1)

8000

484

8 Halide Glasses

the rod or crucible method (Lucas et al., 1989). The drawing temperature is around 130°C depending on the composition of the glass and the diameter of the fiber usually ranges from 100 to 300 jim. Figure 8-17 shows the optical loss curve of a fiber having the composition Te 3 Se 4 I 3 .

9-

Owing to their technological interest, only the heavy metal fluoride glasses have been deeply investigated in respect to their tendency to be corroded by moisture or other chemical reagents. Also, special efforts have been made in order to understand the devitrification mechanisms in these exotic glasses.

7"

8.6.1 Chemical Durability

5"

First it must be noted that all the chloride, bromide, and iodide glasses, except the TeX glasses are strongly corroded by moisture and that this hygroscopicity has limited the interest in them as optical materials. Fluoride glasses are strongly resistant to corroding agents such as F 2 , HF, and UF6 gases. In considering their optical transparency and good resistance to corrosion, they are ideal materials for photochemical reactors which contain these aggressive reagents. These materials are not hygroscopic and can stay in the normal laboratory atmosphere without any attack on the surface. Nevertheless, the water molecule, H 2 O, reacts with fluoride glass and the corrosion mechanisms depend on the temperature and if the water is a liquid or a vapour. When a piece of glass is immersed in water, the corrosion kinetics depend on the pH; under acidic conditions, the proton H + reacts rapidly with the F~ ions of the glass to form HF, the corresponding OH ~ takes the place of the F~ in the structure; at the same time, the modifier cations such as Ba 2+ or Na + diffuse into the solution. According to Simmons and Simmons (1986), the total mechanism leads to a dis-

11 Attenuation (dB/m)

8.6 Stability of Halide Glasses against Chemical Attack and Devitrification

n

Te3Se4l3 fiber

3-

e>

7

8

9

1 0 1 1 1 2

13

W a v e l e n g t h (jLim) Figure 8-17. Transmission spectra of a TeX glass optical fiber.

The attenuation spectrum shows that the low loss region is, as expected, in the 8 12|im region and that the loss is dominated by X independent scattering due to the imperfections of the fibers. Bubbles and fluctuations in diameter are the main reasons of loss and explain the difference between expected and experimental values. Due to the extreme hygroscopicity of the other chloride, bromide and iodide glasses, it has never been possible to draw fibers from those materials and TeX glasses are the only vitreous heavy halide materials drawn into optical fibers. These new waveguides are very promising materials for carrying the CO 2 laser light to targets for laser surgery and industrial operations such as cutting, welding, surface treatment, etc.

485

8.6 Stability of Halide Glasses against Chemical Attack and Devitrification

solution of the matrix with a very fast migration of certain species such as Li + , Na + , Al 3+ into the solution. The direct consequence is that the ZrF4-based glasses have chemical durability in non-basic solutions comparable to the poorest silicates. The direct result of these chemical modifications is the devitrification of the corroded surface which crystallizes and forms an opaque film on the surface. In basic solutions, the stability of the glass is much higher and some compositions could stay in these conditions for a few weeks without apparent corrosion. The corrosion by H 2 O vapour is quite different (Loehr et al., 1987); depending on the composition, it usually starts just below the glass temperature around 300 °C. The mechanism of corrosion is illustrated by the following reaction: ME, (glass) 4- y H 2 O (vapour) ->

/g_^

-> MF,_ y OH^ (glass) + y HF (vapour) This attack becomes significant when the temperature increases and is visually easy to detect when a fluoride glass melt is treated in a normal atmosphere due to the formation of white fumes. The result of this corrosion is the presence of a strong OH absorption peak at 2.9 jim in the glass and the potential formation of oxides playing the role of nucleation agents according to the reaction: 2OH

O2

+H.O/'

8.6.2 Devitrification of Fluoride Glasses As discussed by Moynihan and coworkers (Moynihan, 1987; Chrichton et al., 1987), one of the major problems encountered in the development of heavy metal fluoride glass has been the tendency for the glasses to devitrify above the glass transition temperature. Also, during the cooling process of the melt, a critical cooling rate is necessary to avoid nucleation (EsnaultGrosdemouge et al., 1985) and then growth of the crystallites (Bonsai et al., 1985). The main feature illustrating the special thermal behaviour of fluoride glasses is the temperature dependence of the viscosity which is represented in Fig. 8-18. It is clear that there is a large gap between the hightemperature viscosity data collected in the melt (Hu and Mackenzie, 1983) and the highly viscous zone just above Tg. This situation is due in part to the tendency of these melts to crystallize mainly because the viscosity is only a few dPa s at temperatures significantly below the liquidus allowing relatively high mobility of the

900 700

T(° C) 500 400

300

(8-5)

The practical effect of this corrosion phenomenon leading to hydroxyl and then oxide formation, is the risk of nucleation and crystallization originating from the surface; consequently the only way to prepare good optical glasses is to operate in a dry glove box.

0.001

0.0014

0.0018

Figure 8-18. Viscosity versus temperature for two different fluoride glasses ZBLA and ZBLAN. Experimental points are missing in the middle of the diagram due to crystallization on cooling TXC or heating TXH.

486

8 Halide Glasses

ions for nucleation and crystallization processes. Figure 8-18 is a comparison of two good technical glasses: 1) ZBLA with the composition Zr 55 Ba 35 La 6 Al 4 and 2) ZBLAN with the composition Zr 55 Ba 17 La 6 Al 4 Na 18 . The second has been proven to be more resistant to devitrification and is one of the best candidates for fibre drawing. This interesting behaviour is explained by an interdiffusion barrier to crystallization due to the competition between two crystalline forms. Indeed, it has been noticed that a partial substitution of the modifier cation Ba2 + by Na + cations introduces a competition between sodium fluorozirconate and barium fluorozirconate formation during the crystallization process and consequently delays the devitrification phenomena. This observation appears to be a kind of illustration of the so-called "confusion principle" and could show that one route to finding fluoride glasses compositions more stable against crystallization may be to incorporate into the melt additional components which will inhibit the first crystalline species formation.

8.7 Preparation of Fluoride Glasses and some Physical Properties The interest in fluoride glasses is mainly related to their passive or active optical properties and in both cases the search for materials having excellent optical quality is essential. The preparation route then becomes a key factor especially when ultra pure glass is the ultimate goal. This constraint is less critical for some physical investigations, such as electrical and magnetic properties.

8.7.1 Preparation of Fluoride Glasses

The conventional route for preparing fluoride glasses is the melting of the starting fluorides into an inert atmosphere using vitreous carbon, gold, or platinum crucibles. The liquidus temperature for heavy metal fluoride glasses is around 550 to 650 °C, and then heating until 800 to 950 °C is needed to obtain an homogeneous melt. Another convenient way to prepare the melt is the ammonium fluoride route using NH 4 FHF which easily converts oxides in fluorides. The conversion reaction takes place at temperatures around 300 to 400 °C and an excess of ammonium fluoride is needed to completely transform the oxides in a mixture of metallic ammonium fluorides which are then decomposed by heating at 800 °C. This treatment eliminates the excess of NH 4 FHF and produces a melt which is poured in preheated brass moulds. The glasses are then annealed at a temperature close to Tg. As mentioned before, the development of high optical quality optics or optical fibres is governed by the production of highpurity materials where one must avoid the presence of transition metal, rare-earth, complex anions such as OH, SO 4 ~, P O | ~ , ... which absorb in the optical window of fluoride glasses. Sublimation of volatile fluoride, such as ZrF 4 , as well as solvent extractions are the most common techniques used for purifying the starting fluorides from the most poisonous absorbing cations such as Fe 2 + , Cu 2 + , Co 2 + , Ni 2 + , Nd 3 + , Ce 3 + , Pr 3 + . It must be noted that 1 ppm of these impurities leads to parasitic absorption in the range of 10 to 100 dB/km and that the tolerated level of contamination for reaching the ultimate transparency values will have to be at the part per billions level.

8.7 Preparation of Fluoride Glasses and some Physical Properties

Purification based on chemical vapour deposition also seems to be a solution for separating transition metals. The vapour pressure of ZrCl 4 and ZrBr 4 is, for instance, a few orders of magnitude higher than the transition metal equivalents. Their conversion in ZrF 4 through the vapour state via a fluorinating agent is an elegant way of producing very pure starting materials (Folweiller and Guenther, 1985). The natural impurity of the fluoride material is OH~ due to hydrolysis with HF formation. In order to decrease the level of OH" which introduces a large absorption band in the middle of the optical window, a "reactive atmosphere processing" (RAP) technique has been developed, initially by Robinson (1985). A gaseous atmosphere, such as CC14, SF6, NF 3 , CS 2 used above the melt helps the substitution of OH ~ and O 2 ~ impurities by Cl~, S 2 ~, etc. An NF 3 atmosphere also maintains an oxidizing situation above the melt which allows iron impurities to be retained in the trivalent non-infrared absorbing Fe 3 + state. It must be noted that an O2~ impurity in fluoride glasses has two effects: it modifies the multiphonon absorption mechanisms by the formation of M - O vibrational modes which introduce shoulders in the multiphonon region; depending on the degree of contamination, O 2 ~ could contribute to the formation of ZrO 2 crystallite particles having a high lattice energy and producing a very poor effect on the Rayleigh scattering factor even if the particles are of the 0.2 jam range size (Takahashi, 1987). Using the RAP technique for decreasing the oxygen content in glasses is consequently justified especially for lowering the scattering loss mechanism in longdistance repeaterless optical fiber for telecommunication.

487

8.7.2 Magnetic Properties of Fluoride Glasses Fluoride glasses offer unique opportunities to study the magnetic properties of amorphous disordered systems because they exhibit a large range of glass compositions, high atomic concentrations, and various associations of magnetic ions belonging either to the 3d or 4f series. These properties have been essentially investigated by Dupas and co-workers (Dupas et al., 1981) on many FG compositions containing either high concentrations of magnetic lanthanides or 3d metals such as iron or a combination of both species. As an example, we shall select the glass PbMnFeF 7 belonging to the 3d metal system PbF 2 /MnF 2 /FeF 3 and a rare-earth rich material with the composition 20 BaF2, 30 H0F3, 45 ZnF 2 . Most of these magnetic glasses are usually not resistant to devitrification and need to be obtained by quenching. The magnetic susceptibility of doped fluoride glasses follows a Curie-Weiss law over a wide range of temperature. These systems exhibit very low values of the Curie-Weiss temperature (0 ~ 100 K) and thus evidence of antiferromagnetic interactions. At low temperatures, a cusp occurs in the thermal variation of the a.c. susceptibility, indicating the onset of spin-glass ordering. The spin-freezing temperature, Tf = 10 K is remarkably high for the glass PbFeMnF 7 which contains large amounts of 3d 5 cations Fe 3 + and Mn 2 + , compared to the Ho 3+ -containing glass where Tf ^ 1 K. Many investigations have been conducted on this type of magnetic material in order to see the effect of metallic substitutions on the properties and to clarify the nature of the spin-glass interactions in these insulating materials (see also Chap. 6).

488

8 Halide Glasses

8.7.3 Electrical Properties of Fluoride Glasses Electrical investigations on fluoride glasses have been initiated by Ravaine (1985). They concluded that the main features of the electrical behaviour of this new vitreous materials were that: (a) as expected, they are very poor electronic conductors taking into account the very electronegative character of the fluorine atoms; (b) the conductivity measured on many samples and compositions is in the range of 1 0 " 6 Q - 1 c m " 1 at200°C; (c) the conductivity mechanism is only due to F~ ion mobility which gives to these glasses solid electrolyte properties and makes them candidates for a solid-state battery involving F2 or derivatives at one electrode;

T(°C) 250

150

100

(d) the activation energy is very dependent on the composition and is in the range E = 0.66 to 0.89 eV. Kawamoto and Nohara (1985) confirmed these results and Inoue and Yasui (1987) have proposed a conductivity mechanism from molecular dynamics simulations which shows that the dominant factor of the conduction is due to the migration of the non-bridging fluorine ions. The fluorine mobility can be explained by the plurality of the ZrFn polyhedra (n = 6, 7, 8) in the glass, as discussed in the section on structure. This situation can be compared to the mixed valence effect in electronic semiconductors (see Chap. 7). Figure 8-19 shows the conductivity-temperature diagram for different crystalline and vitreous fluoride conductors. It appears that the conductivities of all fluoride glass compositions are located in the same order of magnitude, approximately between the very good fluorine conductors such as PbSnF4 and the poor fluorine conductors such as CaF 2 .

50

8.8 References

-8 1.5

Figure 8-19. Anionic F conduction in fluoride glasses based on ZrF4 or Zr-free BTYZ glass for example, versus temperature. For comparison the best F conductors, such as PbSnF4 are given.

Adam, XL., Poulain, M. (1983), in: Ilnd Int. Symp. Halide Glasses. Troy, paper 37. Adam, J. L., Sibley, W. A. (1985), / Non-Cryst. Solids 76, 267. Adam, J. L., Poncon, V., Lucas, X, Boulon, G. (1987 a), J. Non-Cryst. Solids 91, 191. Adam, X L., Guery, C , Lucas, X, Rubin, X, Moine, B., Boulon, G. (1987 b), Mater. Science Forum 1920, 573. Adam, XL., Guery, C , Lucas, X (1988a), Mater. Science Forum 32-33, 517. Adam, XL., Docq, A.D., Lucas, X (1988b), J. Solid State Chem. 75, 403. Aliaga, N., Fonteneau, G., Lucas, X (1978), Ann. Chim. Sci. Mat. 3, 58. Allain, X Y, Monnerie, M., Poignant, H. (1988), Electron Lett. 25, 28. Almeida, R. M. (1987), in: Proc. NATO Workshop, NATO ASI Series E: Appl. Science, # 123. Martinus Science Publishers. Alonso, P.X, Orera, V. M., Cases, R., Alcala, R., Rodriguez, V.D. (1988), J. Lumin. 39, 275.

8.8 References

Angell, C.A., Ziegler, D.C. (1981), Mat. Res. Bull. 16, 279. Angell, C. A., Liu, C , Sundar, H.G.K. (1985), Mater. Science Forum 5, 189. Baldwin, C. M. (1979), PhD Thesis, U. Cal. (Los Angeles). Baldwin, C M . , Almeida, R.M., Mackenzie, I D . (1981), J. Non-Cryst. Solids 43, 309. Bansal, N.P., Doremus, R.H., Moynihan, C.T., Bruce, A. J. (1985), Mater. Science Forum 5, 211. Bendow, B., Brown, R.N., Drexhage, M.G., Loretz, T. X, Kirk, R.L. (1981 a), Appl. Opt. 20, 3688. Bendow, B., Drexhage, M. G., Lipson, H. G. (1981 b), J. Appl Phys. 52, 1460. Bendow, B., Banerjee, P.K., Drexhage, M.G., Goltmann, X, Mitra, S.S., Moynihan, C.T. (1983 a), /. Amer. Ceram. Soc. 65, 11-33. Bendow, B., Banerjee, P.K., Drexhage, M.G., El Bayoumi, O., Mitra, S. S., Moynihan, C. T., Gavin, D., Fonteneau, G., Lucas, X, Poulain, M. (1983 b), «/. Amer. Ceram. Soc. 66, 11-35. Blanzat, B., Boehm, L., Jorgensen, C. K., Reisfeld, R., Spector, N. (1980), /. Solid State Chem. 32,185. Bouaggad, A., Fonteneau, G., Lucas, X (1987), Mat. Res. Bull. 22, 685. Brecher, C , Riseberg, L.A. (1980), Phys. Rev. B21, 2607. Brecher, C , Riseberg, L.A., Weber, M.X (1978), Phys. Rev. BIS, 5799. Brierley, M.C., France, P.W. (1987), Electron. Lett. 23, 815. Brierley, M.C., Millar, C.A. (1988), Electron. Lett. 24, 438. Brierley, M.C., France, P.W., Millar, C.A. (1988), Electron. Lett. 24, 439. Brown, R.N., Hutta, X (1985), Appl. Opt. 24, 4500. Brown, R.N., Suscavage, M.X (1987), /. Non-Cryst. Solids 89, 282. Brown, R. N., Bendow, B., Drexhage, M. G., Moynihan, C.T. (1982), Appl. Opt. 21, 361. Chung, K.H., Moynihan, C.T, Robinson, M., Ma, D.S. (1987), Mater. Science Forum 19-20, 615. Cooper, E.I., Angell, C.A. (1983), J. Non-Cryst. Solids 56, 75. Chrichton S.N., Mossadegh, R., Moynihan, C.T, Gupta, P. K., Drexhage, M. G. (1987), Mater. Science Forum 19-20, 327. Day, C.R., France, P.W., Carter, S.F., Moore, M.W., Williams, XR. (1987), SPIE 799, 94. Drexhage, M. G. (1985), in: Treatise on Material Sciences and Technology, Vol.26; Tomazawa and Doremus (Eds.). Academic Press: pp. 151. Drexhage, M.G., Moynihan, C.T, Robinson, M. (1987), in: Mater. Science Forum 19-20, IVth International Symposium on Halide Glasses. Monterey (USA). Dupas, C , Renard, J.P., Velu, E., Jacoboni, C , Fonteneau, G., Lucas, X (1981), Physica 108 B, 1291.

489

Durville, F., Dixon, G. S., Powel, R. C. (1987), J. Lumin. 36, 221. Esnault, M.A., Lucas, X, Babonneau, F , Livage, X (1986), Mat. Res. Bull. 21, 201. Esnault-Grosdemouge, M. A., Matecki, M., Poulain, M. (1985), Mater. Science Forum 5, 241. Eyal, M., Greenberg, E., Reisberg, R., Spector, N. (1985), Chem. Phys. Lett. 17, 108. Eyal, M., Reisfeld, R., Jorgensen, C. K., Jacoboni, C. (1986), Chem. Phys. Lett. 129, 550. Eyal, M., Reisfeld, R., Jorgensen, C. K., Bendow, B. (1987 a), Chem. Phys. Lett. 139, 395. Eyal, M., Reisfeld, R., Schiller, A., Jacoboni, C , Jorgensen, C.K. (1987 b), Chem. Phys. Lett. 140, 595. Feuerheim, L.N., Sibley, S. ML, Sibley, W. A. (1984), /. Solid State Chem. 54, 164. Folweiller, R. C , Guenther, D. E. (1985), Mater. Science Forum 5, 43. Fonteneau, G., Aliaga, N., Corre, O., Lucas, X (1978), Rev. Chim. Min. 15, 537. Fonteneau, G., Bouaggad, A., Lucas, X (1987), Mater. Science Forum 19-20, 41. France, P.W, Carter, S.F., Parker, X M. (1986), Phys. Chem. Glasses 27, 32. France, P. W, Carter, S. E, Moore, M. W, Day, C. R. (1987), Br. Telecom. Technol. # 2 . Freitas, X A., Strom, U., Busse, L., Aggarwal, I. D. (1987), Mater. Lett. 5, 235. Freitas, J. A., Strom, U., Fisher, C. E, Ginther, R. G. (1988), Mater. Science Forum 32-33, 537. Ferrari, M., Duval, E., Boyrivent, A., Bounkenter, A., Adam, X L. (1988), J. Non-Cryst. Solids 99, 210. Goodman, C. H. L. (1978), J. Sol. State. Eletr. Dev. 2, 129. Guery, C. (1988), These, Universite de Rennes I, France. Guery, C , Adam, X L., Lucas, X (1988), J. Lumin. 42, 181. Hattori, H., Sakagouchi, S., Kanamori, T, Terunuma, Y. (1987), Appl. Opt. 26, 2683. Hu, H., Mackenzie, J. D. (1982), J. Non-Cryst. Solids 74, 411. Hu, H., Mackenzie, X D. (1983), J. Non-Cryst. Solids 54, 241. Hu, H., Ma, F , Mackenzie, X D. (1983), / Non-Cryst. Solids 55, 169. Inoue, H., Yasui, I. (1987), Mater. Science Forum

19-20, 161. Jacoboni, C , Le Bail, A., De Pape, R. (1983), Glass Technol. 24, 164. Jeunehomme, L., Poignant, H., Monnerie, M. (1981), Electron. Lett. 17, 809. Jorgensen, C. K., Jacoboni, C , De Pape, R. (1982), /. Solid State Chem. 41, 253. Jorgensen, C.K., Reisfeld, R., Eyal, M. (1986), /. Less Common Met. 126, 181. Judd, B.R. (1962), Phys. Rev. 127, 750. Kadono, K., Nakamichi, H., Nogami, M. (1987), Mater. Science Forum 19-20, 63.

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8 Halide Glasses

Kanamori, T. (1987), Mater. Science Forum 19-20, 363. Kawamoto, Y, Nohara, I. (1985), Mater. Science Forum 6, 767. Kniep, R., Mootz, D., Rabeneau, A. (1973), Ang. Chem. Intern. 12, 499. Krupke, W.F. (1974), IEEE, Albuquerque, pp. 1733. Layne, C.B., Weber, M.J. (1977), Phys. Rev. B16, 3259. Layne, C. B., Lowdermilk, W.H., Weber, M.J. (1977), Phys. Rev. B16, 10. LeGall, P. (1988), These, Universite de Rennes I, France. Lines, M.E. (1986), Ann. Rev. Mater. Sci. 16, 113. Lu, G., Fischer, C , Bradley, I P . (1987), /. NonCry>st. Solids 94, 45. Lucas, J. (1986), in: 1st Int. Workshop on N.C.S. in Current Topics on Non-Crystalline Solids. World Scientific Publishing, p. 141. Lucas, J. (1987), in: NATO ASI, Series, E, #123. Martinus Nijhoff Publishers, pp. 321-330. Lucas, X, Moynihan, C.T. (1985), in: Mater. Science Forum 5-6: Illrd Internation. Symposium on Halide Glasses. Rennes (France). Lucas, I, Zhang, X. H. (1986), Mat. Res. Bull. 21, 871. Lucas, I , Chanthanasinh, M., Poulain, M., Brun, P., Weber, M.J. (1978), J. Non-Cryst. Solids 27, 273. Lucas, I , Zhang, X.H., Fonteneau, G. (1987), SPIE 843, 2. Lucas, X, Chiarrutini, I., Zhang, X. H., Ma, H.L., Fonteneau, G. (1989), SPIE 1048, 52. McNamara, P., McFarlane, D.C. (1987), /. NonCry st. Solids 95, 625. Matecki, M., Poulain, M., Poulain, M. (1987), Mater. Science Forum 19-20, 47. Mackenzie, X D. (1987), NATO ASI, Series E, # 123. Martinus Nijhoff Publishers, pp. 357-363. Miniscalco, W.X, Thompson, B. A. (1986), Electron. Lett. 22, 1278. Miniscalco, W.X, Andrews, L.X, Hall, B.T., Guenther, D.E. (1985), Mater. Science Forum 5, 279. Mitachi, S. (1982), Phys. Chem. Glasses 23, 30. Mitachi, S., Miyashita, T. (1983), Appl. Opt. 2, 1419. Mitachi, S., Sakagouchi, S., Yonezawa, H., Shikano, K., Shigematsu, T, Takahashi, S. (1985), Jap. J. Appl. Phys. 24, L827. Mitachi, S., Fonteneau, G., Christensen, P. S., Lucas, X (1987), J. Non-Cryst. Solids 92, 326. Moine, B., Pedrini, C , Boulon, G., Brenier, A., Adam XL., Lucas, X (1988), /. Lumin. 40, 692. Moynihan, C. T. (1987), Mat. Res. Soc. Bull., August Issue. Nasu, H., Yamoto, D. P., Heo, X, Mackenzie, X D. (1985), Mater. Science Forum 5, 121. Nishii, X, Kaite, Y, Yamagishi, T. (1985), J. NonCryst. Solids 74, 411. Nogami, M., Sawanobori, N., Makihara, M., Hayakawa, X (1985), J. Mat. Sci. Lett. 4, 271.

Ofelt, G.S. (1962), /. Chem. Phys. 37, 511. Ohishi, Y, Hattori, H. (1986), Jap. J. Appl. Phys. 25, L844. Ohishi, Y, Takahashi, S. (1985), J. Non-Cryst. Solids 74, 407. Ohishi, Y, Takahashi, S. (1986), Appl. Opt. 25, 720. Ohishi, Y, Mitachi, S., Shibata, S., Manabe, T. (1981), Jap. J Appl. Phys. 20, L191. Ohishi, Y, Mitachi, S., Kanamori, T, Manabe, T. (1983), Phys. Chem. Glasses 14, 135. Okada, K., Miura, K., Masuda, I., Yamashita, T. (1988), Mater. Science Forum 19-20, 557. Orera, V.M., Alonso, P.X, Cases, R., Alcala, R. (1988), Phys. Chem. Glasses 29, 59. Perry, P. B., Shafer, M. W, Chang, I. F (1981), / Lumin 23, 261. Phifer, C.C., Angell, C.A., Laval, J.P., Lucas, X (1987), J Non-Cryst. Solids 94, 315. Pinnow, D. A., Gentille, A. L., Standlee, A. G., Timper, A. X, Hobrock, L. M. (1978), Appl. Phys. Lett. 33, 28. Poignant, H. (1981), Electron. Lett. 17, 973. Pollack, S.A., Robinson, M. (1988), Electron. Lett. 24, 320. Poulain, M., Lucas, X (1978), Verres Refract. 32, 505. Poulain, M., Poulain, M., Lucas, X, Brun, P. (1975), Mat. Res. Bull. 10, 242. Poulain, M., Lucas, X, Brun, P., Drifford, M. (1977), in: Colloques Internationaux du C.N.R.S. 255; Paris: C.N.R.S., pp. 257-263. Quimby, R. S. (1988), Mater. Science Forum 32, 551. Quimby, R. S., Drexhage, M. G., Suscavage, M. X (1987), Electron. Lett. 23, 32. Ravaine, D. (1985), Mater. Science Forum 6, 761. Reisfeld, R., Eyal, M. (1985), /. Phys. 436, 349. Reisfeld, R., Jorgensen, C.K. (1987), in: Handbook on the Physics and Chemistry of Rare-Earth, Chap. 58. Amsterdam: Elsevier Sci. Publ., pp. 1-90. Reisfeld, R., Greenberg, E., Brown, R. N., Drexhage, M.G., Jorgensen, C.K. (1983), Chem. Phys. Lett. 95, 91. Reisfeld, R., Eyal, M., Greenberg, E., Jorgensen, C.K. (1985), Chem. Phys. Lett. 118, 25. Reisfeld, R., Eyal, M., Jorgensen, C. K., Guenther, A.H., Bendow, B. (1986 a), Chimia 40, 403. Reisfeld, R., Eyal, M., Jorgensen, C.K. (1986b), /. Less. Common. Met. 126, 187. Reisfeld, R., Eyal, M., Jorgensen, C.K. (1986c), Chem. Phys. Lett. 132, 252. Reisfeld, R., Eyal, M., Jorgensen, C. K., Jacoboni, C. (1986 d), Chem. Phys. Lett. 129, 392. Renard, J.P., Dupas, C , Velu, E., Jacoboni, C , Fonteneau, G., Lucas, X (1981), Physica 108 B, 1291. Robinson, M. (1985), Mater. Science Forum 5, 19. Robinson, M., Pastor, R. C , Harrington, X A. (1982), SPIE 320, 37. Rubin, X, Brenier, A., Moncorge, R., Pedrini, C , Moine, B., Boulon, G., Adam, J. L., Lucas, X, Henry, X Y (1987), J. Phys. C48, 367.

8.8 References

Sakagouchi, S., Takahashi, S. (1987), /. Lightw. Technol. 5, 1219. Sanz, X, Cases, R., Alcala, R. (1987), /. Non-Cryst. Solids 93, 311. Schneider, H. W., Schoberth, A., Staudt, A., Gerndt, C.H. (1987), SPIE799, 112. Shafer, M.W, Perry, P. (1979), Mat. Res. Bull. 14, 899. Shinn, M. D., Sibley, W. A., Drexhage, M. G., Brown, R.N. (1983), Phys. Rev. B27, 6635. Simmons, C.J., Simmons, J. H. (1986), /. Amer. Ceram. Soc. 69, 661. Sun, K.H. (1947), J. Amer. Ceram. Soc. 30, 277. Suzuki, Y, Sibley, W. A., El Bayoumi, O. H., Roberts, T.M., Bendow, B. (1987), Phys. Rev. B35, 4412. Szigeti, B. (1950), Proc. Roy. Soc. A 204, 51. Takahashi, S. (1987), /. Non-Cryst. Solids 95-96, 95. Tanabe, Y, Sugano, S. (1954 a), /. Phys. Soc. Jap. 9, 753. Tanabe, Y, Sugano, S. (1954 b), J. Phys. Soc. Jap. 9, 166. Tanimura, K., Shinn, M. D., Sibley, W. A., Drexhage, M.G., Brown, R.N. (1984), Phys. Rev. B30, 2429. Tran, D. C , Sigel, G. H., Levin, K. H., Ginther, R. J. (1982), Electron. Lett. 18, 1046. Tran, D. C , Sigel, G. H., Bendow, B. (1984), /. Lightwave Technol. LT2 # 5 , 566. Tsoukala, V. G., Schroeder, I, Floudes, G. A., Thomson, D.A. (1987), Mater. Science Forum 19-20, 637. Weber, M. J. (1986), in: Critical Materials Problems in Energy Production. New York: Academic Press, pp. 261-279. Weber, M.J., Brawer, S.A. (1982), /. Non-Cryst. Solids 52, 321. Weber, M. X, Cline, C.E, Smith, W.L., Milan, D., Heiman, D., Hellwarth, R.W. (1978), Appl. Phys. Lett. 32, 403. Van Uitert, L.G., Wemple, S.H. (1978), Appl. Phys. Lett. 33, 57.

491

Yamane, M.Y, Moynihan, C.T. (1988), in: Mater. Science Forum 32-33, Vth International Symposium on Halide Glasses. Japan. Yamane, M., Kawazoe, H., Inoue, S., Maeda, K. (1985), Mat. Res. Bull. 20, 905. Yeh, D.C., Sibley, W.A., Suscavage, M., Drexhage, M.G. (1986), J. Non-Cryst. Solids 88, 66. Yeh, D.C., Sibley, W.A., Suscavage, M., Drexhage, M.G. (1987), J. Appl. Phys. 62, 266. Yeh, D.C., Sibley, W.A., Suscavage, M.J. (1988), J. Appl. Phys. 63, 4644. Yeh, D. C , Petrin, R. R., Sibley, W. A., Madigou, V., Adam, XL., Suscavage, M.X (1989), Phys. Rev. B39 [1], 80-90. Zheng, H., Gan, F. (1986), Chin. Phys. 6, 978.

General Reading Baldwin, C M . , Almeida, R.M., Mackenzie, XD. (1981), Halide Glasses, Journal of Non-Crystalline Solids 43, 309. Comyns, A.E. (Ed.) (1989), Fluoride Glasses, Critical Reports on Applied Chemistry, Vol. 27, New York: John Wiley. Drexhage, M.G. (1985), "Heavy-metal fluoride glasses", Treatise on Materials Science and Technology, Vol. 26, Glass IV: Tomozawa, M., Doremus, R.N. (Eds.). London: Academic Press. Drexhage, M.G., Moynihan, C.T. (1988), "Infrared Optical Fibers", Scientific American 256, no. 11. France, P. W, Carter, S.F., Moore, M. W, Day, C.R. (1987), "Progress in Fluoride Fibres for Optical Telecommunications", British Telecom. Technol. J 5, no. 2. Lucas, X (1989), "Review on Fluoride Glasses", Journal of Materials Science 24, 1-13. Tran, D.C., Sigel, G.X, Bendow, B. (1984), "Heavy Metal Fluoride Glasses and Fibers", Journal of Lightwave Technol., Vol. LT2, no. 5.

9 Metallic Glasses Robert W. Cahn Department of Materials Science and Metallurgy, University of Cambridge, Cambridge, U.K.

List of 9.1 9.1.1 9.1.2 9.1.3 9.2 9.2.1 9.2.2 9.2.3 9.2.4 9.2.5 9.2.6 9.2.7 9.2.8 9.2.9 9.3 9.3.1 9.3.2 9.3.3 9.3.4 9.4 9.4.1 9.4.2 9.4.3 9.4.4 9.4.5 9.5 9.5.1 9.5.2 9.6 9.6.1 9.6.2 9.6.3 9.6.4

Symbols and Abbreviations Introduction Quenching from the Vapor The Origins of Quenching from the Liquid State Treatment of Metallic Glasses in the Series Methods of Making Metallic Glasses and Amorphous Alloys Melt-Quenching Vapor-Quenching Electrolytic Deposition Ion Implantation and Ion Mixing Amorphization by Irradiation Amorphization by Interdiffusion and Reaction Mechanically Aided or Induced Amorphization Amorphization at High Pressure Composition Ranges of Glass Formation and Glass Structures for Different Preparation Techniques Amorphizable Alloy Systems Favorable Combinations of Metals Composition Ranges for Glass Formation Criteria for Glass Formation The Special Case of Silicon Diffusion, Relaxation and Crystallization Diffusion Relaxation Thermal Embrittlement Relaxation of Magnetic and Elastic Properties Crystallization Chemical Properties Corrosion Resistance Heterogeneous Catalysis and Electrocatalysis Applications Magnetic Applications Brazing Foils Mechanical Properties Chemical Properties

Materials Science and Technology Copyright © WILEY-VCH Verlag GmbH & Co KGaA. Allrightsreserved.

495 496 496 497 498 499 499 500 501 502 502 503 506 507 507 508 508 510 510 517 518 518 521 526 528 530 535 535 536 536 537 538 539 540

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9.6.5 9.6.6 9.7 9.8

9 Metallic Glasses

Diffusion Barriers Metallic Precursors for Devitrification Acknowledgement References

542 542 543 543

List of Symbols and Abbreviations

495

List of Symbols and Abbreviations B b c#m D E G(r) H HLY Hsy KP k kF Rc r T To

magnetic flux density characteristic distance minimum solute concentration of element B diffusion constant Young's modulus total reduced atomic pair radial distribution magnetic field strength large-atom hole-formation enthalpy small-atom hole-formation enthalpy first peak of the X-ray scattering curve Boltzmann constant fc-vector of the Fermi energy critical quenching rate interatomic distance temperature temperature at which two phases of identical composition have equal free energies TBD ductile-to-brittle transition temperature Tf thermodynamic freezing temperature Tg glass transition temperature 7^° ideal freezing temperature Ts limiting glass transition temperature from entropy crisis models Tx, Tcryst crystallization temperature 7^ limiting glass transition temperature from free volume models t time vA, vB atomic volumes g rj a

strain rate viscosity stress

CALPHAD CSRO DSC GFA SRO SSAR TEM TSRO

calculation of phase diagrams chemical short-range order differential scanning calorimeter or calorimetry glass forming ability short-range order solid-state amorphization reaction transmission electron microscopy topological short-range order

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9.1 Introduction A solid alloy with a liquid-like atomic arrangement is called a metallic glass, or alternatively an amorphous (metallic) alloy. A glass is, strictly speaking, a liquid which has been cooled into a state of rigidity without crystallizing, while a material with a similar structure made by some process other than cooling is properly called "amorphous" rather than "glassy". This fine distinction, which is not always observed, will be retained here. Very few pure metals can be made amorphous, so the use of the word "alloy" is mostly appropriate in this context. Unlike the production of, say, an oxide glass, which can be accomplished by very slow cooling of a siliceous melt, the making of a metallic glass by simple cooling requires very rapid quenching of an alloy melt: with two known exceptions, a minimum cooling rate of about 103 K~ x is required, and minimum rates of 104 to 106 K " 1 are common (see Chap. 2). 9.1.1 Quenching from the Vapor

The earliest observations of amorphous alloys did not involve starting with a liquid alloy, but were made by physicists who used thermal evaporation to prepare metal films intended for the study of superconducting properties. The condensation of a metallic vapor on a cold substrate is functionally equivalent to an ultrarapid quench from the melt. In the 1930s, a German physicist, Kramer (1934, 1937) claimed to have generated amorphous Sb by this approach; he was one of the early users of electron diffraction in support of this research. Much later, Buckel and Hilsch in Gottingen evaporated metals such as Bi, Ga and Sn and Sn-Cu alloys on to substrates held at 4 K (because they were preparing their films for superconductivity

measurements). Their papers (Buckel, 1954; Buckel and Hilsch, 1952,1954,1956) have become classics. They believed, from electron diffraction findings, that their films were ultrafine-grained, and they also found that the normal, very slight solubility of Cu in Sn could be extended beyond 20 at.%, and that of Bi in Sn to 45 at.%. A little later, it had become clear that several of the films originally believed to be ultrafine-grained were in fact amorphous: this was true of Bi, Ga and Sn-Cu. Buckel and Hilsch had thus discovered, before the first researches on rapid quenching from the melt were performed, two of the key features of rapid quenching: the extension of solid solubility and vitrification. Curiously, there is still today disagreement whether the Bi films made by Buckel and Hilsch's method were truly amorphous or only microcrystalline. Thus Comberg et al. (1975) claimed, on the basis of Hall effect measurements in particular, that vapor-quenched bismuth is in fact microcrystalline, and the issue was further discussed in a review, by Bergmann (1976), of amorphous superconductivity. Bergmann also describes experiments which showed that other metals besides Sn, including Pb, In and Tl, could be forced into the amorphous state by co-depositing them with 10-20 at.% of a second component. Ge (Haug et al., 1975) and Sb (Muller et al., 1975) were made amorphous only by coevaporating them with a high concentration of solute (e.g., 50 at.% Au); this suggests that Kramer's prewar claim to have amorphized pure Sb should be regarded as suspect. - The special case of amorphous Si will be discussed later in this chapter. The continuing debate between those who believe that Bi films made by the Buckel method are amorphous and those who regard them as microcrystalline is an echo of a long-standing disagreement of

9.1 Introduction

this kind, most vigorous in the 1970s, concerning a number of supposed metallic glasses. A good discussion of this type is to be found in a paper by Dixmier and Guinier (1970): these authors examined two alloys, P t - C and N i - P , the former made by evaporation, the latter by electrolysis. Examination of the X-ray scattering pattern proved to be an uncertain basis for deciding between the amorphous and microcrystalline options, but Dixmier and Guinier discovered that the two alloys behaved quite differently on annealing. In Pt-C, the scale of the structure gradually coarsened, with a progressive sharpening of the diffraction lines, whereas in N i - P , diffraction lines due to Ni and Ni 3 P appeared and gradually strengthened while the pattern due to the N i - P itself remained unaltered. - This, they held, implied that the P t - C was microcrystalline and underwent progressive grain growth, a quasi-homogeneous process (see Vol. 15, Chap. 9) whereas the N i - P t was truly amorphous and crystalline phases were nucleated from it and grew heterogeneously. - A technique has however now been perfected which should obviate arguments as to the amorphousness/microcrystallinity of any specific phase. Chen and Spaepen (1988,1991) have used a scanning differential calorimeter (see Vol. 2, Chap. 4) in isothermal mode, to establish the form of the heat release of the contentious alloy: the "fingerprint" of the heat release of an alloy undergoing normal (i.e., uniform) grain growth is quite different from that of an alloy undergoing nucleation and growth of one or more crystalline phases from a true glass. 9.1.2 The Origins of Quenching from the Liquid State

Pol Duwez, a highly original metallurgist at the California Institute of Technol-

497

ogy, is universally regarded as the father of rapid quenching from the liquid state. He was not the first to use such methods, but earlier innovators were interested only in using rapid quenching as a production method for cheaply making the relevant shapes, whereas Duwez explicitly investigated the metallurgical consequences of rapid quenching from the melt, that is, he was using the technique from a researcher's viewpoint while his predecessors were seeing it from a production engineer's viewpoint. - The various experimental techniques of rapid quenching from the melt, alias rapid solidification processing, are

fully explained in Vol. 15, Chap. 2, and will not be further described here. - In his own account of his early researches in the field, Duwez (1967 a, b) describes his concern to resolve the paradox of the failure of the Ag-Cu system to generate a continuous series of solid solutions while the Ag-Au and Cu-Au systems did have such a series. He wrote later that "the possibility of removing this rather exceptional case from the list of binary alloys which did not follow the Hume-Rothery criteria was the main incentive for finding an experimental technique capable of achieving extreme rates of cooling from the liquid state". He concluded that quenching from the melt might force concentrated Ag-Cu alloys into a state of solid solution which was only just unfavorable from a free-energy viewpoint, if it were done fast enough, and he understood the quenching process well enough from his earlier attempts to accelerate cooling in the solid state (Duwez, 1951) to recognize the need to bring a thin layer of liquid rapidly into contact with a cold solid chill-block: thus the Duwez gun, a device for atomizing a metallic melt and impelling the small droplets against a copper sheet, was born; at about the same time Duwez also developed the piston-and-

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anvil apparatus. Duwez and his colleagues used this new equipment to show that melt-quenched Cu-Ag alloys did indeed form a seamless series of solid solutions (Duwez et al., 1960). It would be difficult to find a clearer example of the truth that the exercise of curiosity concerning fundamental scientific issues can launch an experimental programme leading to momentous technological consequences. Very soon after the first publication just cited, the same group of investigators decided to look for the formation of a metallic glass in a melt-quenched alloy and promptly found it in the Au-Si system (Klement et al., 1960). Thereupon Cohen and Turnbull, who happened to be sharing the same room at the Cavendish Laboratory at the time, wrote a key paper (Turnbull and Cohen, 1961) in which they suggested that the ready formation of a metallic glass in the Au-Si system near 25 at.% Si was connected with the existence of a deep eutectic in equilibrium near this composition: this gave the melt the opportunity to cool stably to a temperature at which its viscosity had become quite high and therefore diffusion in the melt had become sluggish. This immediately provided a logical basis for finding other glass-forming systems, and led, inter alia, to the discovery of the important glass in the Pd-Si system (Duwez et al., 1965) on which much of the early systematic work on metallic glass properties was done. Duwez began this process by examining the Pd-Si glass by transmission electron microscopy and studying its crystallization in situ. - Turnbull has analyzed the many stages in the recognition and characterization of the metallic glass state (Turnbull, 1985).

9.1.3 Treatment of Metallic Glasses in the Series

Different aspects of metallic glasses are treated in several Volumes of the Series. The structure of both molten and amorphous binary alloys is treated in Vol. 1, Chap. 4, together with a discussion of the requisite instrumental methods, including not only wide-angle X-ray diffraction but also small-angle X-ray scattering and Xray absorption methods. A more extensive treatment of models of glass structure and the problems encountered in deriving such models from diffraction and spectroscopic data is to be found in Vol. 9, Chap. 4; this treatment covers all kinds of glasses, including metallic ones. Physical properties of metallic glasses (as well as metallic melts), including particularly magnetic and electrical properties, are treated in Vol. 3, Chap. 9. A chapter on the deformation and fracture of glassy materials in Vol. 6, Chap. 11 includes some discussion of deformation and fracture mechanisms in metallic glasses. The formation of amorphous alloys by ion implantation and ionmixing is treated in Vol. 15, Chap. 6. Because of this varied coverage, and to avoid needless duplication, the remainder of this chapter will be restricted essentially to the following topics: (1) Methods of making metallic glasses and amorphous alloys; (2) the systematics of the alloy systems and composition ranges in which it has been possible to make such materials, and, more generally, criteria for glass formation in alloy systems; (3) diffusion and crystallization in metallic glasses; (4) structural relaxation of metallic glasses and its consequences for properties, including embrittlement; (5) corrosion resistance and catalytic activity of metallic glasses; and (6) applications.

9.2 Methods of Making Metallic Glasses and Amorphous Alloys

9.2 Methods of Making Metallic Glasses and Amorphous Alloys 9.2.1 Melt-Quenching The various methods currently used for rapidly abstracting heat from thin sections of molten alloys are fully described in Vol.15, Chap. 2. (See also this Volume, Chap. 2.) They include melt-spinning (in which a jet of melt is projected against a spinning polished copper wheel), to make narrow ribbons; planar flow-casting, in which a slit through which the melt flows is held within a fraction of a millimeter of the surface of the copper wheel, to make wide sheet up to about 25 cm in width; melt extraction, itself available in several variants, in which a sharp-edged wheel barely touches a molten surface and extracts a ribbon of D-shaped cross-section from it; the piston-and-anvil method, in which a free-falling melt droplet is caught between rapidly colliding metal plates to make a disc; free jet melt-extrusion, in which a jet is spun under conditions which discourage break-up into discrete droplets, so that the wire cools freely in contact with the surrounding cold gas; the twin-roller technique, in which a flat melt-jet is pinched between counter-rotating rollers; the in-rotating-water spinnning process, in which a fine jet of melt is injected into a rotating annulus of water, to make an amorphous wire; laser treatment, in which a laser beam focused to a small area is traversed across a solid surface so as to melt it in a transient fashion, the underlying solid acting as a chill-block, or else nanosecond or picosecond pulses are applied to a spot on a stationary substrate (see also Vol. 15, Chap. 3); atomization, in which an alloy melt jet is broken up by a cold, transverse liquid or gaseous jet into alloy droplets which solidify by depositing

499

their heat in the atomizing fluid, to make a melt-quenched powder; the Taylor wire method, which creates a fine alloy wire encapsulated in an oxide glass sleeve through which heat is abstracted; and several other methods such as spark erosion which are curiosities rather than mainline techniques. Four of the mainline methods are shown schematically in Fig. 9-1. In all these methods, the melt is given a geometrical shape in which one or more dimensions are small, so that heat can be removed fast. In melt-spinning or planar flow-casting, ribbon or sheet thickness is typically in the range 20-50 jam, wires made by the in-rotating-water method are typically 50-100 jim in diameter, powders have a size distribution typically 20-100 jam diameter. The cooling rate in these various methods varies with the dimensions of the melt and the experimental variables such as wheel speed or piston-and-anvil speed, and it also varies as the sample cools, being fastest when the sample is hottest. The common practice of citing a single figure for the cooling rate during a melt-quenching operation thus has little physical meaning without further information. - Fig. 9-2a shows a series of measurements on free-falling drops of pure molten iron, quenched in an electromagnetically operated piston-and-anvil apparatus; the temperature versus time plots were obtained by means of microthermocouples built into the anvil (Duflos and Cantor, 1982). It is clear that cooling rates decline greatly during the solid-state phase of cooling. - Cantor subsequently used ingenious pyrometric methods to map the cooling-rate history of glass ribbons during melt-spinning (Fig. 9.2 b) (Hayzelden et al., 1983; Gillen and Cantor, 1985); it is to be noted that none of the methods for estimating cooling rates which depend upon measurement of microstructural features such as

500

9 Metallic Glasses LEVITATION COIL

MELT

PRESSURE

/ OPTICAL SENSOR

/INDUCTION COIL

MELT DROPLET

SUBSTRATE PISTONS

(b)

(a) PRESSURE

MELT

FEED

INGOT ROD MELT DROPLET

INDUCTION COIL

\

RIBBON

SUBSTRATE WHEEL

(c) (d) Figure 9-1. Principal methods of quenching alloys from the melt: (a) Drop-smasher or piston-and-anvil method, (b) Melt-spinning, (c) Pendant-drop melt extraction, (d) Twin-roller quenching device.

dendrite arm spacing (Vol. 15, Chap. 2) can be used with metallic glasses. With regard to atomization as used to make powders, only computational methods are available for assessing cooling rates. Systematic studies (Clemens et al., 1987) have shown that metallic multilayer films (here Ni and Zr) can be converted to glass by microsecond current pulses which take the film above the glass transition temperature but not above the melting-point of the constituent metals; the effective quenching rate is I O ^ I O ^ S " 1 .

9.2.2 Vapor-Quenching

The early work of Buckel and Hilsch on vapor-quenching of a number of metals and alloys has, rather surprisingly, not had a great deal of follow-up. Dahlgren (1983) has reported on the method of highrate vapor-quenching, based on sputtering rather than thermal evaporation (Vol. 15, Chaps. 7, 8), to make glassy objects of substantial thickness. Others (Bickerdike etal., 1986; Gardiner and McConnell, 1987) developed high-rate thermal evapo-

9.2 Methods of Making Metallic Glasses and Amorphous Alloys

107

ration methods on to cold substrates to make objects up to ingot size, but these techniques appear to have been used only to manufacture crystalline, not amorphous alloys. Dahlgren's approach appears to be too expensive to have found large scale application, but vapor-quenching has been used in connection with electronic and magnetic amorphous films, as will be seen below.

7in 106 c

E io 5 c "o o o

900 V

A

A

750 V • 500 V •

D

0.5g

500

(a)

o 1g

1000 1500 Temperature, T in K

1600

1200 (b)

501

9.2.3 Electrolytic Deposition Many years ago (Brenner et al., 1950) it was discovered that N i - P alloys, containing more than about 10at.%P, can be electrodeposited in amorphous form to give an ultrahard surface coating. Much further research has been done on this family of electrodeposits (see Brenner, 1963), more recently in relation to electroplating variables such as steady or pulsed current (Lashmore and Weinroth, 1982). Indeed, it seems that N i - P amorphous layers electrodeposited by steady and pulsed currents are structurally distinct (Lashmore et al., 1982). Electrodeposition allows good control of glass production. Some account of this method will be found in Vol. 15, Chap. 11, including the generation of amorphous alloy multilayers by electrodeposition. Not much search for other amorphous alloys that can be made by electrodeposition has been reported, though apparently C o - W - B is one other candidate. Also, it has been established that bright amorphous chromium of very high hardness can be electrodeposited

t in ms

Figure 9-2. (a) Data from many cooling curves obtained from a microthermocouple built into the anvil of a piston-and-anvil quenching apparatus, during drop-smashing of pure iron. The voltages are accelerating voltages: higher values imply faster quenching. Larger specimens had greater superheat. (After Du-

flos and Cantor, 1982.) - (b) Cooling Curves for Ni5 wt.% Al ribbons melt-spun on a copper wheel, using temperature-calibrated color photography, at a superheat of 200 K, ejection pressure of 42 kPa, and circumferential wheel speeds of 12 (A), 24(B) and 36 (•) m s" 1 . (After Gillen and Cantor, 1985.)

502

9 Metallic Glasses

from a chromic acid solution with additives (e.g., formic acid or iron) (Hoshino et al., 1986; Tsai and Wu, 1990). It is also possible to deposit a few glasses by electroless deposition, and this method has been particularly used to produce glasses for magnetic investigations, N i - P in particular (Dietz, 1977). Recently, it has been shown that certain organic materials, for instance polyacetylene, can be used as catalysts to aid the deposition of glasses such as N i - C o - B and N i - C o - P (Kamrava and Soderholm, 1990). 9.2.4 Ion Implantation and Ion Mixing

A number of amorphous phases have been prepared by implanting high-energy solute ions into metallic surfaces, or by mixing successively vapor-deposited layers of different elements by means of the thermal energy of injected rare-gas ions. The most thoroughly researched such phase is the wear-resistant amorphous layer obtained by injecting Ti and C into a Fe surface. This, and other instances, are discussed in detail in Vol. 15, Chap. 6, Sec. 3.4. 9.2.5 Amorphization by Irradiation

A number of intermetallic compounds have been amorphized by irradiation with high-energy electrons, heavy ions such as Ni + or fission fragments. This was first discovered when the compound U 6 Fe was bombarded with fission fragments (Bloch, 1962); much research was then done with more familiar compounds, notably NiTi, Zr3Al and the nickel aluminides. The last of these remained crystalline, whichever irradiation projectiles were used, while the first two are instances of compounds which became amorphous, the former with electrons, the latter only with heavy ions. Primary solid solutions can never be amorphized by this approach.

There has been much dispute over the criteria which determine the ability to amorphize such compounds. The principal earlier overview was by Russell (1985): low temperature, high doses and high dose rates were generally found necessary. There is still some disagreement about the principal criterion, viz., that compounds with a narrow or vanishing homogeneity range amorphize most readily; the difficulty is that for many intermetallic compounds, the homogeneity range is not known with precision. This criterion may well prove to be generally valid: since irradiation knocks a proportion of atoms off their proper crystal sites, wrong atom pairs are generated, and compounds with a narrow homogeneity range necessarily have free energies which rise very steeply with departure from stoichiometry such compounds therefore rapidly gain free energy as they are irradiated, which would favor amorphization. Such compounds also necessarily have high ordering energies, which by implication therefore is one of the criteria for amorphizability by irradiation. Luzzi and Meshii (1986) propose as one criterion that an amorphizable compound is ordered up to its melting-point; again, this is another way of saying that its ordering energy is high. They also suggest that compounds with constituents separated by more than two groups in the periodic table and those with a relatively complex structure are favored for amorphization. None of these criteria, in the light of later evidence, appears to be watertight ... except possibly the one calling for a high ordering energy. More recently, Luzzi and Meshii (1988), concentrating on 2 MeV electron irradiation, have accumulated evidence that destruction, not necessarily complete, of longrange crystallographic order (i.e., of the superlattice) is a precondition of amor-

9.2 Methods of Making Metallic Glasses and Amorphous Alloys

phization by irradiation. Others interpret such disordering as implying a mechanical destabilization of the lattice, such as has been proposed by some as a precondition of melting also. The evidence for this is well assembled by Okamoto et al. (1988), who examined Zr3Al. It is not quite clear at present whether the crucial feature is disordering per se, or the lattice expansion which accompanies it, but the most recent analysis prefers the second alternative. - A recent, illuminating comparison of melting with amorphization in the solid state, which includes irradiation as one variant (Wolf etal, 1990), makes the point that there are two forms of melting, and two of amorphization: one involves heterogeneous nucleation at interfaces or defects, one is homogeneous. Wolf et al. conclude that the destruction of a superlattice "merely drives the crystal to a critical combination of volume and temperature at which the amorphous phase can form heterogeneously or homogeneously". These fundamental issues have also been analyzed by Fecht and Johnson (1990). - In this connection, it has been suggested (Vepfek etal., 1982) that a microcrystalline-to-amorphous transition in silicon is driven by lattice expansion. 9.2.6 Amorphization by Interdiffusion and Reaction

An extraordinary phenomenon was discovered by Schwarz and Johnson in 1983 the formation of an amorphous alloy by the interdiffusion of two pure polycrystalline metals. They deposited successive thin films of Au and La, 10-50 nm in thickness, in a multilayer configuration, and annealed the multilayers at a low temperature (50-100°C). The final composition of the mixed phase was controlled by adjusting the relative thickness of the two

503

films. This study followed an earlier, accidental discovery of a related phenomenon: the compound Zr 3 Rh, in a metastable crystalline form, could be amorphized by reacting it with hydrogen to form a metastable amorphous hydride (Yeh et al., 1983). The very fast diffusion of hydrogen was thought to be a crucial aspect of this process, named a solid-state amorphization reaction (SSAR). For the second study, the somewhat exotic combination of La and Au was chosen because Au was known to be a "fast diffuser" in crystalline La (in the technical sense that Au diffusion in La is many orders of magnitude faster than selfdiffusion in La), and it was assumed that a similar disparity in diffusion rates would extend into the amorphous phase, if one was formed. (A discussion of fast diffusion can be found in Warburton and Turnbull, 1975). The 1983 discovery that a compound (Zr3Rh) could be amorphized by hydrogen absorption has now been generalized (Aoki et al., 1991). 'Hydrogen-induced amorphization' has been found to be possible in many binary metal compounds of which one constituent is a hydride former. Examples include R2A1, R3In, R 3 Ga, RFe 2 (where R is a rare-earth metal), Zr3Al, and others. The apparent thermodynamic paradox that two stable phases can generate a metastable phase was dealt with by means of two hypotheses: (a) The amorphous phase has a lower free energy than the initial mixture of elements; this arises from entropy terms, due to the fact that the amorphous phase has a large negative heat of mixing, whereas the crystalline elements have a large positive heat of mixing, (b) There are indeed intermetallic crystalline compounds with a still lower free energy than the amorphous phase, but they cannot form because one constituent diffuses

504

9 Metallic Glasses

(relatively) very sluggishly, and apparently both constituents must diffuse reasonably fast if crystalline nuclei of an intermetallic phase are to form. The intermetallic phase cannot be prevented from nucleating if the annealing temperature is chosen too high. The essentials of the situation are shown in Fig. 9-3. In the seven years since this discovery, a very great deal of research has been done on the SSAR and hundreds of papers published. Reviews (Johnson et al., 1985; Johnson, 1986) and a conference devoted to SSAR (including amorphization by irradiation, which is now generally included in the SSAR designation) (Schwarz and Johnson, 1988) have marked this burgeoning of

-90 E o "a

L

r=373K ' •#

- u

i \

S -ioo Am+ La

Au + \ Am

c

-110
-120 --

V \/ i

0 Au

0.2

/) //

/

i

1

0.6

0.8

1.0 La

Figure 9-3. Gibbs free energy vs composition for a mixture of crystalline Au and La (dotted line) and for amorphous A% _xLax alloy. The approximate free energy curve for the amorphous phase was estimated from Miedema's predictions for liquid Au-La alloys. The tangents predicting two-phase regions were drawn on the assumption of zero intersolubility of Au and La. A wholly amorphous reaction product was found only in the central concentration range, as predicted. (After Schwarz and Johnson, 1983.)

research. A recent review which places the SSAR (including also the mechanical methods to be discussed in the next Section) in relation to more conventional quenching methods, has been published by Schwarz (1988), while another (Greer, 1990) discusses in depth the quite complex thermodynamics of amorphization by interdiffusion. A number of interesting issues have been raised in very recent work, but there is space here only for a few of them to be briefly treated. Only recently has the postulated large disparity in diffusivities between the two constituent metals in a system capable of SSAR been experimentally confirmed. The determination of the slower of the two diffusivities is an exceedingly difficult experimental problem, discussed further in Sec. 9.4.1, below. Greer et al. (1990) performed the measurement for the Ni-Zr system, on which much of the recent research on SSAR has been performed. They overcame the experimental obstacles by using a method in which the interdiffusion of Zr and Hf (an element closely similar to Zr) in a multilayer consisting of a-Ni 65 Zr 35 and a-Ni65Hf35 was measured by X-ray diffraction from the multilayer at various stages of anneal. The outcome was that, at 573 K, the diffusivity of Zr in the amorphous solid solution was ^ 1 0 6 times smaller than the diffusivity of Ni - a very large factor of disparity indeed. The disparity is attributed to the large size difference of the Zr and Ni atoms; this aspect is further discussed in Sec. 9.4.1. - One consequence of very fast diffusion of one constituent in an amorphous layer which has sometimes been observed is the formation of voids in the layer, e.g., in the Al-Pt system where Al is the fast diffuser (Legresy et al., 1988). Another issue is the nucleation of the amorphous phase at the start of the SSAR. Schroder et al. (1985) established that grain

9.2 Methods of Making Metallic Glasses and Amorphous Alloys 20 (d)

(c)

in

I 15

i

(g)

(f) i

4- —H

J ~

D CO

(b)

(a) 1

1

Ni

1

Ni 211 A

0)

225 A

a 10 -

0

(e)

-r-

0 O

Dstra

c

- \

\

boundaries in the polycrystalline Zr films played a part in nucleating the amorphous layer. The fact that such layers do indeed have to be heterogeneously nucleated was made very clear by a subsequent experiment by Vredenburg et al. (1986). They attempted to grow amorphous films in a bilayer consisting of polycrystalline Ni deposited on a Zr single crystal, and found this to be impossible. Only if the interface was first disturbed by mixing it with a bombardment of high-energy Xe + ions could the SSAR get started. - The more general issue of the "nucleation of disorder" in SSAR, melting and destruction of atomic long-range order, as posed by observations such as that just described, has been discussed by Cahn and Johnson (1986), and brought up to date in a stimulating thermodynamic approach by Wolf etal. (1990). The kinetics of growth of amorphous layers during diffusive SSAR has been deduced from continuous measurements of electrical resistivity of the multilayers during the reaction. Schroder and Samwer (1988) have done this with Co-Zr multilayers under isothermal conditions, while Rubin and Schwarz (1989) have made measurements for Ni-Zr under continuous heating (Fig. 9-4). By means of a simple model that relates resistivity change to amorphous layer thickness, Rubin and Schwarz were able to estimate the effective diffusivity of Ni in a-Ni5OZr5O. (Their findings are further discussed in Sec. 9.4.1). Schroder and Samwer found that at long times, the isothermal growth in thickness of the amorphous layer tends towards a yft law, expected for an interface-limited reaction. This law has also been established by direct microscopic examination (Johnson et al., 1985). It has been repeatedly observed that if the individual layers in a reacting multi-

505

Zr

Zr i

200 400 600 Temperature, T in °C

Figure 9-4. Electrical resistance of multilayer system of Ni and Zr thin films during continuous heating and cooling at lOKmin" 1 . The thermal cycle was repeated; during the second cycle, the resistance follows the line f-g traced during the cooling part of the first cycle, a line characteristic of a wholly amorphous material. (After Rubin and Schwarz, 1989.)

layer are too thick, then during reaction a stage is reached when the growth of the amorphous layers is interrupted by the nucleation of intermetallic compounds just ahead of the layers. Thus in Ni-Zr, at 300°C the critical thickness ^lOOnrn (Newcomb and Tu, 1986); the compound NiZr is nucleated at the interface of the amorphous layer and Zr. Meng et al. (1988) found that in this system, at a somewhat higher temperature, the freshly nucleated NiZr can grow backwards and consume the previously formed amorphous layer. Highmore (1990) has interpreted the critical thickness quantitatively in terms of transient nucleation theory (see Sec. 9.4.5): as the interface slows down progressively, a stage is reached when nucleation of NiZr becomes effective before the advancing amorphous layer can overwhelm the embryo.

506

9 Metallic Glasses

9.2.7 Mechanically Aided or Induced Amorphization

When diffusion-induced amorphization was first discovered, it was soon recognized that deposition of multilayers from the vapor phase was not the only possible approach: it was also possible to roll or wiredraw composites of foils or wires of the constituent metals, to reduce the scale of the microstructure and weld the constituents, and then anneal the product - an approach which had already proved its worth in superconductivity research. Such mechanically aided amorphization has been achieved successfully by several investigators (e.g., for Cu-Er by Atzmon et al., 1985). The amorphization reaction can also take place during the rolling itself if the end thickness of the layers is small enough, as for instance in the amorphization of rolled Al-Pt multilayers (Bordeaux and Yavari, 1990) where the layers finished up only « 60 nm thick. From this it was only a short extrapolation in technique to experiment with ballmilling, a process which combines deformation, comminution and mixing. A small amount of powder is ground in a rotating, "planetary" or vibrating container with a number of hardened steel balls. This technique has been intensively developed by metallurgists in recent years because it permits mechanical alloying, that is to say, atomic-scale mutual solution or chemical combination of two metals achieved by intensive ball-milling. The process and its various uses, including mechanically induced amorphization, are treated in detail in Vol. 15, Chap. 5. These are instances of mechanically induced

amorphization.

The first to achieve mechanically induced amorphization by co-deformation of a layered composite appears to have been Schultz (Ni-Zr), who has traced

the history of this process and also surveyed the underlying principles (Schultz, 1989). The formation of amorphous phases by mechanical alloying of elemental metal powders was first reported in Russia (Yermakov et al., 1981, 1982). Subsequently, Schwarz and Koch (1983) prepared Ni-Ti and Ni-Nb amorphous powders by ballmilling the elemental powders. The process is closely akin to that outlined the preceding paragraph, and indeed intimate layering of the constituents has been observed at an intermediate stage of the process. Lee et al. (1988), among others, showed that many amorphous phases can be produced indifferently by ball-milling or by ballgrinding a readymade intermetallic compound or indeed a mixture of two compounds in the same system. (This is not always true: thus Mg 70 Zn 30 can only be amorphized by grinding the intermetallic compound, not from the elements (Calka and Radlinski, 1989).) Careful comparative studies, using differential scanning microcalorimetry (Schwarz and Petrich, 1988) have made it clear that in the case of mechanical alloying of Ni and Ti, the amorphization reaction takes place directly between Ni and Ti zones brought into intimate contact by milling. In the case of grinding of an intermetallic compound, disordering is mechanically induced. As in the case of irradiation-induced amorphization, the lattice expansion caused by disordering can be regarded as the proximate cause of amorphization. The range of compositions in a given system which can be amorphized by one of these techniques can be extended either by grinding mixtures of intermetallics, as mentioned, or else by grinding an already amorphous powder with excess of one of the constituent metals in powder form (Weeber and Bakker, 1988).

9.2 Methods of Making Metallic Glasses and Amorphous Alloys

Various recent researches (e.g., Weeber et al., 1988) have shown that for a given system and composition, different results can be obtained according to the nature and severity of the ball-milling operation (in particular, planetary or vibrational ball-mills). Martin and Gaffet (1990) point out that in ball-milling, particles undergo repetitive and competitive shearing and annealing (healing) processes, and the endresult depends on the balance between these. A recent Soviet paper (Gerasimov et al., 1991) shows that in the Ti-Cu and Zr-Co systems, increasing ball energy led to a tendency towards a crystalline as opposed to an amorphous product. The criteria for amorphizability in the case of mechanical alloying or grinding (see, for instance, Schultz and Hellstern, 1987) are generally presumed to be the same as in the case of irradiation, but no critical comparison of the two techniques seems to have been made. An important new approach however is that due to Beke et al. (1990). They estimated the additional elastic (mismatch) energy which is stored in an ordered solid solution when its longrange order is destroyed, whether mechanically or by irradiation; this depends, of course, inter alia on the atomic sizes. This new quantity was then compared to the ordering energy, and it was concluded that amorphization is possible if (a) the (virtual) critical disordering temperature is above the melting temperature, and (b) the ratio of the elastic mismatch energy to the ordering energy is high enough. A comprehensive test against known experimental facts gives widespread though by no means universal agreement. 9.2.8 Amorphization at High Pressure

Much research on amorphization under high confining pressure has been done with non-metals, but a few experiments on

507

metallic systems have been reported (Battezzati, 1990). For instance, alloys in the Cd-Sb, Zn-Sb and Al-Ge systems have been pressurized to produce unstable crystalline phases which decay after a while to leave metastable amorphous solids. Another approach was to heat Cu-Sn alloys under confining pressure by direct electric heating and to quench them by suddenly switching off the current. In this way, amorphous Cu-12-17at.% Sn amorphous phases could be made, which is not possible under atmospheric pressure. For further details of these observations, and of the relevant thermodynamics, Battezzati's paper should be consulted. - Very recently, Ponyatovsky and Barkalow (1991) have further developed the process which they call 'thermobaric quenching', and have made glasses in the Cd-Sb, Zn-Sb and Al-Ge systems by this means. Another novel and interesting approach has just been reported and probably belongs under this heading. Suslik et al. (1991) have been able to make nearly pure amorphous iron by sonochemical synthesis, i.e., ultrasonic irradiation, of a liquid, iron pentacarbonyl. The formation, growth and collapse of liquid bubbles is associated with extremely rapid heating and cooling. 9.2.9 Composition Ranges of Glass Formation and Glass Structures for Different Preparation Techniques

A number of investigators have compared the range of compositions over which amorphous alloys can be prepared when various forms of rapid melt-quenching, vapor-quenching and SSAR are used. A good example is seen in Fig. 9-5 (Gartner and Bormann, 1990), which refers to the Co-Zr system. As a crude generalization, in agreement with theoretical expectation (Schwarz, 1988), melt-spinning favors amorphous phases near deep eutectics, mechan-

508

9 Metallic Glasses

Co-Concentration

Figure 9-5. The observed concentration ranges (from the literature) in the Co-Zr system for melt-spinning (m.s.), ion-mixing (i.m.), co-condensation (c.c), mechanical alloying (m. a.). (After Gartner and Bormann, 1990.)

ical alloying (and indeed the other methods) favor amorphous phase formation around the compositions at which compounds form. The role of deep eutectics is further discussed in the next Section. Most observers have found that the properties, as tested most often by measurements of crystallization temperatures,

(mechanically alloyed, Schwarz et al. 1985) N

UoTi6o (rapidly quenched.Wagner &Lee 1980)

10

r (A)

Figure 9-6. Total reduced atomic pair radial distribution G (r) of amorphous Ni 40 Ti 60 prepared by mechanical alloying (solid curve) and rapid solidification (dashed curve). (After Schwarz and Nash, 1989.)

are almost identical for amorphous solids of a given composition, irrespective of their mode of production (Schultz and Hellstern, 1987). Hydrogen storage capacity, which is particularly sensitive to the topological fine structure of a glass (Harris et al., 1988), is also similar. Judged more directly from radial pair distribution functions derived from X-ray scattering (see Vol. 1, Chap. 4 and Vol. 9, Chap. 4), glass structures are again seen to be very similar for melt-quenched and mechanically alloyed glasses (Fig. 9-6). A particular sensitive test is to examine viscous flow at a range of temperatures. This has been done for glasses of composition close to Pd 80 Si 20 made by melt-quenching and by sputtering, and the flow properties far below Tg were found to be closely similar (Volkert and Spaepen, 1990).

9.3 Amorphizable Alloy Systems 9.3.1 Favorable Combinations of Metals Metallic glass systems are generally divided into 5 categories, shown in Table 9-1. The two major classes are 1 and 2; originally, research attention was mostly concentrated on the metal-metalloid glasses, category 1, which were the first metallic glasses to be made by rapid solidification and are also the most useful kind, but more recently, attention has shifted towards the metal-metal glasses (more, it seems, because this kind of glass is amenable to theoretical interpretation, than because of their applicability). Metal-metalloid glasses, as a class, are the easiest to make by rapid solidification, and two of them (Pd 40 Ni 40 P 20 and Pd 7 7 5 Cu 6 Si 1 6 5 ) can be made at cooling rates as slow as 1 K s ~1 if heterogeneous surface nucleation is hindered by appropriate measures (see Sec. 9.4.5).

9.3 Amorphizable Alloy Systems

509

Table 9-1. Classification of glass-forming alloy systems. Category 1. T2 or noble metal + metalloid (m) 2. T1 metal +T 2 (or Cu) 3. A metal + B metal 4. T1 metal-f A metal 5. Actinide-f-T1

Representative systems

Typical composition range, at.%

Au-Si, Pd-Si, Co-P, Fe-B, Fe-P-C, Fe-Ni-P-B, Mo-Ru-Si, Ni-B-Si Zr-Cu, Zr-Ni, Y-Cu, Ti-Ni, Nb-Ni, Ta-Ni, Ta-Ir Mg-Zn, Ca-Mg, Mg-Ga (Ti,Zr)-Be, Al-Y-Ni U-V, U-Cr

15-25 m 30-65 Cu or T2, or smaller range Variable 20-60 Be, 10Y-5Ni 20-40 T1

A metal: Li, Mg groups; B metal: Cu, Zn, Al groups. T 1 : early transition metal (Sc, Ti, V groups): T 2 : late transition metal (Mn, Fe, Co, Ni groups). This table is a modified form of one published by Polk and Giessen (1978).

Categories 3 and 5 may be classed as curiosities, very much a minority interest. This was also true until recently of category 4 (the Be-bearing glasses excited much interest at one time as potential lowdensity, high-strength reinforcement ribbons, but were dropped because of the health hazard associated with beryllium): however, the position of category 4 glasses has been transformed by the recent discovery of Al-rich glasses, of which there is now a great variety (Inoue and Masumoto, 1990; He et al., 1988). Glasses which have been studied in categories 1 and 4 are most often ternaries, those in category 2, most often binaries. - Almost all research on methods of glass formation other than rapid solidification has been done with glasses of category 3. The metal-metalloid glasses always consist of small solute atoms dissolved in larger metal atoms; for greatest ease of glass formation, the total concentration of metalloids, which may be of more than one species, is generally around 20 at.%. At an early stage, Polk (1972) proposed that the relatively easy formability of this kind of glass was to be attributed to the ability of the metalloid atoms to "stuff" the voids in the Bernal dense random packing structure (an early model for metallic glasses),

and thereby to stabilize the structure against ready crystallization. This muchquoted idea has been critized by Gaskell on the grounds that an exact examination of the Bernal structure indicates that there are by no means enough large voids to accommodate most metalloid atoms, but this objection in turn has been thrown back into the melting-pot by TurnbulFs observation that the effective size of a metalloid atom depends on the nature of the metals in which it is dissolved. The matter is further discussed by Gaskell (Vol. 9, Chap. 4). A word is in order here about the new category of Al-rich glasses. The curious history of these materials, independently discovered in France, U.S.A. and Japan, and driven by both fundamental and practical considerations, has been outlined by Cahn (1989). The most interesting properties (very high strength combined with toughness and lightness) attach to glasses consisting, typically, of « 80 at.% Al and ^ 1 0 at.% each of a transition metal such as Ni, Co or Fe and a rare earth metal such as Y, Ce or La, though in the search for applicable alloys, complex compositions such as Al 69 Cu 17 Fe 10 Mo 1 Si 3 have been recorded. The Japanese and American researchers established that, while binary

510

9 Metallic Glasses

aluminum-rare earth combinations could be induced to form glasses, the composition ranges were narrow and could be much widened by adding a ternary constituent, a transition metal. 9.3.2 Composition Ranges for Glass Formation In a given alloy system, the range of compositions over which glasses can be made depends (in the case of rapid solidification) on the cooling rate achieved. As we saw in Fig. 9-5, the concentration ranges for different techniques can also be substantially different. Most such measurements have been for binary alloys, but some have been for ternaries also. Fig. 9-7 shows such information relating to F e Si-B glasses, which are of ferromagnetic importance, and for A l - Y - M glasses. (In these instances, the cooling rates were not specified by the investigators .) - It is generally true that wider composition ranges can be vitrified by the vapor quenching route, since the effective quenching rate is much higher than in quenching from the liquid state. 9.3.3 Criteria for Glass Formation The possible criteria determining the feasibility of making amorphous alloys, from intermetallic compounds by irradiation or mechanical grinding, by mechanical alloying of pairs of elements, or by interdiffusion, have already been briefly discussed in Sections 9.2.7, 9.2.6 and 9.2.5, respectively; here we concentrate mainly on glasses made by rapid solidification. - The generic term most commonly applied to represent what we are trying to explain here is glass forming ability, or GFA. It is usually taken to mean the critical cooling rate, Rc, which is necessary to turn a melt into a glass: when this is in the experimen-

tally accessible range for mainline rapid solidification processes such as melt-spinning, approximately up to 107 K s" 1 , then the alloy can be vitrified by such a process; if theory tells us that Rc is higher than this, then, at best, tiny amounts of glass can be made by a much faster quenching process such as picosecond quenching with a pulsed laser, which can provide cooling rates as high as l O ^ K s " 1 (Lin and Spaepen, 1984). (As we saw earlier (Fig. 9-2), cooling rates are not constant during a quench from the melt; so presumably the Rc values discussed in theories mean the maximum experimental values, which refer to temperatures at and slightly below the equilibrium freezing temperature.) Motorin (1983) calculated from first principles the expected homogeneous nucleation rates of crystals in supercooled pure metal melts, using known physical parameters as input. For Ag, Cu, Ni and Pb, minimum cooling rates of 10 1 2 -10 1 3 K s " 1 were derived, which shows clearly enough why no pure metals have been vitrified by melt-quenching. Not even picosecond laser quenching has been successful in this respect. Thus the GFA criteria refer in practice only to alloys. The range of ideas and approaches which have been proposed to get an understanding of why some alloy systems can be vitrified and others not, and of what determines the composition ranges over which glasses can be made, is almost disconcertingly wide. There are almost as many criteria for glass formation as there are for the good life, and almost as little agreement among protagonists as to which are to be preferred. A valiant early attempt to come to grips with this difficult issue was by Polk and Giessen (1978). The best comprehensive overview of the development of these criteria is by Ramachandrarao (1984). Cahn

9.3 Amorphizable Alloy Systems

511

20

Al-Y-M

,'Ni

•

20 -

\

/<0*

/ "' Cu

\

5

Figure 9-7. Glass-forming ranges for rapidly solidified ternary alloy systems, (a) Fe-Si-B alloys, showing five independent experimental estimates for the glassforming range. (After Luborsky et al., 1979.) (b) AlY - M alloys, where M = Cu, Co, Fe or Ni. (After Inoue and Masumoto, 1990.)

— 10 \

-

\

I

-e / —.^~ 10

(b)

Co i

20 M in at. %

30

(1986 a), Hafner (1986) and Massalski (1986) have published more specialised treatments. Here we can attempt only a bird's eye view. In spite of a tendency by some theorists to regard this claim as culpably naive, there can be no doubt that atomic size is the single factor that plays the major role in determining GFA. The recognition that the constituent atoms in a melt must have sufficiently different Goldschmidt radii to permit glass formation goes back to very

early experiments on vapor-quenching, in a classic study by Mader et al. (1967). A critical radius mismatch of ^ 1 5 % fitted the results, and this value has been accepted ever since. This criterion might be termed an anti-Hume Rothery criterion, since Hume Rothery's celebrated law laid it down that a radius mismatch not exceeding 15% was necessary for extensive solid solution formation in terminal alloy phases. - Mader himself had simulated glass formation by jiggling populations of

512

9 Metallic Glasses

wooden balls of different sizes on a tray, and found that the radii had to differ sufficiently for "crystallization" to be prevented; subsequently, Simpson and Hodkinson (1972) performed the first of several simulations of this kind with rafts of soap bubbles of ^ 1 mm diameter which better simulate real interatomic forces, and again found a critical radius mismatch of « 1 5 % . The next stage was a series of attempts to create GFA maps, in which radius mismatch was plotted against one axis of a graph and some measure of bond strength such as the negative heat of mixing or heat of evaporation - the idea presumably being that strong interatomic bonds render crystallization more difficult. One of several such attempts was by Giessen (1981). Such graphs suggest that the bond strength does indeed play a part, but it is a "weak" variable compared to the size mismatch. A very important development of the radius mismatch approach is due to Egami and Waseda (1984), followed by a further development of the same ideas by Egami and Aur (1987). These authors were interested in calculating the microscopic stress levels at the scale of individual atoms in a glass or a crystalline solid solution. Briefly, they concluded that in a glass, neither the local stress fluctuations nor the total strain energy vary much with solute concentration when these quantities are normalized with respect to the elastic moduli, whereas in a crystalline phase the strain energy rises steadily with solute content. Thus, beyond a critical solute content, glass becomes favored over crystal formation, and in this way, not only GFA but also the glass-forming composition range can be calculated. The conclusion is that c#in (vh-vA)&0.1, where c™n is the minimum solute concentration of B in A required for a glass to form and the v9s are atomic volumes. The agreement with observation is good for

many systems, though melt-quenching by normal melt-spinning is not necessarily fast enough to give agreement with Egami and Waseda's criterion. Fig. 9-8, for the Ni-Nb system, shows at the bottom the results of applying Egami and Waseda's criterion, and also three different experimentally determined glass-forming ranges. The "faster" methods agree very well with the theoretical criterion. This was the first theory to allow the glass-forming composition range to be interpreted, as distinct from theories which only interpret the identity of glass-forming alloy systems. Several other theories, of a thermodynamic nature, based on atomic volumes have appeared. One version is due to Ramachandrarao (1980): he estimated the departure from ideality of melts, in terms of a kind of deviation from a liquid Vegard's Law, and concluded, both theoretically

Atom fraction sputtering frx*:::*:^^ L ns laser quenching

Ni

melt-spinning

prediction

msmm

Figure 9-8. The Ni-Nb phase diagram, experimentally determined glass-forming ranges for three methods of decreasing effective quenching speed, and the range predicted by Egami and Waseda's theory. (After Greer, 1989.)

9.3 Amorphizable Alloy Systems

and by comparison with experiment, that melts with a large deviation, in the sense of having an anomalously small atomic volume, were most likely to form glasses. This finding was interpreted in terms of the enhanced viscosity associated with a small atomic volume (which implies little free volume available to support atomic motion in the melt). - Yavari et al. (1983) independently developed a closely related idea, by establishing empirically that a zero (or negative) change of specific volume on melting of a crystalline species favors glass formation on subsequent rapid solidification. In effect, their idea is that if a crystal is denser than the melt from which it grows, then in growing it rejects free volume into the melt and thereby reduces its viscosity; thus crystal growth becomes selfcatalytic. Contrariwise, a less dense crystal raises viscosity and favors glass formation. Theoretical physicists have developed a number of models to rationalize GFA. The best known is that due to Nagel and Tauc (1977). They proposed that a glass was most likely to form if its electronic energy lies in a local metastable minimum with respect to composition change. They showed that if the structure factor corresponding to the first, strong peak of the diffuse X-ray scattering curve, Kv, satisfies the relationship Kp = 2fcF,where kF is the wave vector at the Fermi energy, then the electronic energy does indeed occupy a local minimum. A number of familiar glasses, in the Au-Si, Au-Ge and C o - P systems for example, accurately obey this criterion, but there are also exceptions, e.g., some obscure glasses in the C s - O and R b - O systems. This kind of approach, using modern approaches such as pseudopotential theory, has been taken much further in recent years, but a discussion would take us too far here. For further details, the reader is referred to reviews by Hafner

513

(1981, 1986). However, as we shall see below, the ability, demonstrated by Hafner, to make theoretical estimates of the glass transition temperature of unknown glasses offers a novel way to estimate GFA. Theories based more explicitly on the need to prevent nucleation of a crystalline phase take two main forms. First, there are models based on an explicit calculation of homogeneous nucleation rates (this begs the question whether heterogeneous nucleation plays a role). The standard approach here is due to Davies (1976). He adapts a theory of isothermal crystallization kinetics due to Uhlmann and calculates the critical cooling rate necessary to bypass the "nose" of the time-temperature-transformation plot thus calculated. (The nose is the minimum time required to initiate homogeneous nucleation, at some temperature well below the thermodynamic freezing temperature). The principal difficulty here is to estimate the viscosity of a supercooled melt, but there are a number of empirical relationships which allow a rough estimate to be made. (There is now available a critical survey of known viscosities of molten metals and alloys, by Battezzati and Greer, 1989.) Fig. 9-9 shows some calculated critical quenching rates obtained in this way, and Fig. 9-10 shows how the calculated value of Rc varies with composition across a phase diagram. It will be seen from this second figure that, as a number of people have pointed out and as follows from Davies' theory, the ratio TJTf (Tg is the glass transition temperature, 7^ is the thermodynamic freezing temperature) is a crucial figure of merit in determining GFA, for purely kinetic reasons associated with the need to avoid crystallization. The lower this ratio, the more viscous the melt becomes before it is ever undercooled and the more difficult crystallization becomes, thus enhancing GFA and reducing Rc.

514

9 Metallic Glasses

0.8 Figure 9-9. Calculated critical quenching rates, Rc, for glass formation, and examples of limiting ribbon thickness. Key: (1) F e 8 9 B n ; (2) Au 78 Ge 14 Si 8 ; (3) Fe 8 3 B 1 7 ; (4) Fe 41 . 5 Ni 41 . 5 B 17 ; (5) Co 75 Si 15 B 10 ; (6) Fe 7 9 Si 1 0 B l i ; (7) Fe 80 P 13 C 7 ; (8) Pd 82 Si 18 ; (9) Ni 6 3 Nb 3 7 ; (10) Pd 77 . 5 Cu 6 Si 16 . 5 ; (11) Pd 40 Ni 40 P 20 . (After Davies, 1978.)

(a)

1600 * U00 c ^

1200

(b) 700 600 500 (c)

Experimental glass range

8 7

6

log!

c *°

1* 2

10

15

20

25

Atomic % Si Figure 9-10. Equilibrium freezing temperature, Tf, glass transition temperature, Tg, figure of merit TJT{ and calculated critical quenching rate, Rc, for a range of Pd-Si alloys.

A somewhat related, more thermodynamically biased approach derives from a paper by IW. Cahn (1980) on the thermodynamics of metastable equilibria. From this, the role of the relative values of Tg and To becomes clear; here, To is the temperature at which liquid and solid of the same composition have the same free energy. A glass forms readily if Tg > To; what this means is that the melt rigidifies before reaching the temperature at which freezing without composition change (and thus without long-range diffusion), also known as solute-trapping, becomes possible. The implications of this are clearly set out in the review by Massalski (1986) and applied to a detailed analysis of GFA across the Cu-Ti system in a paper published about the same time (Massalski and Woychik, 1985). The problem is that, before a glass has actually been made, its Tg is not known. Here, Hafner's (1983, 1986) ability to calculate glass transition temperatures comes into its own. In Fig. 9-11, for the Ca-Mg system, the calculated To values are shown, and also two estimates for Tg, an upper limit based on the "entropy-crisis" or Kauzmann model, and a lower limit based on a free-volume model. (For a fuller explanation, see Hafner (1983).) Theoretical composition ranges for glass formation are shown for two cooling rates; here the criterion Tg > To is the central consideration; agreement with experiment is quite good. - Another detailed thermodynamic analysis of metallic glass formation near eutectic troughs was published by Highmore and Greer (1989). Another set of theories is based on the postulate that metallic melts are not homogeneous in composition but contain compositional clusters. Such clusters are held to aid crystal nucleation, and their absence or weak development to aid glass formation. Contrariwise, short range order (the

9.3 Amorphizable Alloy Systems

converse of clustering), which is believed (though there is a singular absence of experimental evidence on this point) to increase with falling temperature of a glass, just as it does in a crystalline solid solution, should enhance GFA. (See, for instance, Wagner's survey of SRO in metallic glasses, 1986; at least, it has been established for Cu-Ti that a glass has higher SRO than the melt from which it is quenched (Sakata et al., 1981).) Indeed, there is some evidence that some Cu-Ti alloys show clustering in the melt whereas the glass has SRO. This field of research, which has a large literature, is at present somewhat beset by controversy: for further details, the reader is referred to Ramachandrarao (1980, 1984). A further development is the application of CALPHAD (CALculation of PHAse Diagrams) methods to calculate from first principles the part of a phase diagram in which the free energy of a supercooled melt (i.e., a glass) is particularly low relative to that of the competing terminal phases, and only slightly higher than that of a competing intermetallic phase. A successful beginning with this approach has been published by Saunders and Miodownik (1986). The method has been applied in detail to one particular system, Ni-Ti, by Nash and Schwarz (1988). NiTi has also been studied by Zollzer and Bormann (1988) who have made E.M.F. measurements on a-NiTi at 613 K to complement purely theoretical estimates of free energy. - The free energies of a-Cu/Zr phases have also been calculated by a least-squares fitting program from available thermodynamic data (Bormann et al., 1988). Finally, we return to a less sophisticated "figure-of-merit" approach which has been quite successful in rationalizing GFA. Donald and Davies (1978) long ago recognized the awkwardness of theories which

515

Figure 9-11. Calculated phase diagram, To values and upper and lower limits (Ts, 7^) for Tg for the Ca-Mg system, with theoretical and observed glass-forming ranges. (After Hafner, 1983, 1986.)

related GFA to quantities (such as TJT{) which involve Tg, when normally this is unknown unil a glass has been made and examined. They proposed that a good test of GFA is the extent to which the equilibrium freezing temperature of an alloy melt is depressed below the ideal value, which they calculated simply by linear interpolation between the freezing points of the constituent metals. This simple method was then developed by Whang (1983), who took into account the modification required to allow for possibly extensive solid

516

9 Metallic Glasses

solution of one metal in the other, in the solid state. This is necessary because solid solubility reduces the slope of the To versus composition curves (like those shown in Fig. 9-11). Whang generated figure-ofmerit maps in which one axis gave TLR, defined as TLR = AT/T£, where AT is the difference between the ideal freezing temperature for an alloy (Tj°), defined as above, while along the other axis is C er , a simple measure of the amount of the solubility of the minor constituent in the major at the eutectic temperature. - A large value of TTR implies a severely depressed liquidus, while a small Cer implies a steeply sloping To versus composition curve ... both factors favouring easy glass formation. In fact, the maps so generated show a clear boundary between glass-forming and non-glass-forming alloys. - Dubey and Ramachandrarao (1990) have developed Whang's model to show that most eutectic phase diagrams can be expected to show an asymmetry of GFA, in the sense that glass formation is easier just to one side of the eutectic composition than on the other; the melt-spinning range indicated in Fig. 9-8 shows an example of this. Whang's theory was then adapted by Tendler (1986) to show, for a series of Zrbased alloys, that alloys which according to Whang's criterion should be good glassformers are also those in which there is fast diffusion, in the special sense used before (Warburton and Turnbull, 1975). Fig. 9-12 shows one of Tendler's figures for a series of Z r - M alloys. All the alloys showing fast diffusion (Zr-Cr, Mn, Fe, Co, Ni, Cu and Be) are also glass-formers. For fast diffusion, the solute atom must be much smaller than the solvent (for details see Tendler's paper) and this clearly also favors GFA. In fact, some years ago Turnbull (Turnbull, 1974) had predicted an association between good GFA and fast diffusion.

\J.\J

o Ga Al o

Bi o

0.1 c oB

NON-GFA oRe

0.2 GFA

\ Cr Mn

*• v \

0.3 -

Pt.

iBe Co kI . Ni • • Cu» i

1.0

oAg

\

i

0.8

#

\Ru

Os • \

Rh

#

• Fe i

i

0.6

'

\ 0.4

0.2

Figure 9-12. A number of Z r - M alloys plotted on a Whang graph, separating glass-formers (GFA) from non-glass-formers. (After Tendler, 1986).

This by no means exhaustive overview of the models and theories that have been advanced to make sense of glass-forming systems and ranges might well seem discouraging, because at first sight they are mutually exclusive. In fact, hidden crossconnections undoubtedly exist: the linkage between Whang's thermodynamic approach (related to terminal solid solubilities) and Tendler's association between fast diffusion and GFA clearly comes from a correlation of both solid solubilities and fast diffusion with atomic size ratios. Perhaps in due course even the electronic criteria studied by Nagel and Tauc and by Hafner may prove to be linked with some of the other ideas, e.g., the free volume approach due to Ramachandrarao and Yavari. My own view is that simple geometry ... atomic sizes ... will prove to be the main criterion that in various subtle ways incorporates the others.

9.3 Amorphizable Alloy Systems

9.3.4 The Special Case of Silicon Metallic glasses resemble oxide glasses in that the transition from the liquid to the glassy state is a continuous, seamless one. The atomic configuration changes with temperature during cooling, fast or slow according to the type of material, until a temperature range is reached in which diffusion cannot keep up and a non-equilibrium configuration is "frozen in"; this is of course the glass transition range. "Frozen in" has been put in quotes because the glass transition is not at all like real freezing, which is a first-order phase transition with a well defined equilibrium temperature, at which the Gibbs free energies of the liquid and crystalline phases are equal. In contrast, the glass transition temperature (temperature range is a more suitable phrase) is a function of cooling rate and is kinetically, not thermodynamically, determined (see Chap. 3). Correspondingly, of course, on heating a glass, the glass transition (softening) temperature is again variable, whereas the melting of a crystal happens at a well defined equilibrium temperature. We briefly discuss silicon here because it breaks this simple, clear distinction between freezing and vitrification, between melting and softening. It is true that crystalline silicon is not metallic and so does not strictly belong to this chapter, but molten silicon does have a metallic character. Amorphous silicon is quite distinct from the liquid form, and resembles the crystalline form in having covalently bonded character. Amorphous silicon can be made, with difficulty, by quenching liquid silicon with ultrafast, picosecond laser pulses (Liu et al, 1979). The more common way, however, of making a-silicon is by ion implantation, especially by self-ion bombardment. (This process has some peculiar

517

features, such as a dependence on the orientation of the initial crystalline silicon: Yater and Thompson, 1989.) On the basis of microcalorimetric measurements of such a-silicon layers, Spaepen and Turnbull (1979), and Bagley and Chen (1979), independently proposed that a-Si (and also a-Ge) undergo first-order melting to the metallic liquid on heating. This bold hypothesis, implying a latent heat of melting for an amorphous solid, could only be tested some years later, when it became feasible (e.g., Thompson etal., 1984) to measure transient electrical conductance and reflectance of silicon films: since a-Si and 1-Si have drastically different bond character, their electrical and optical properties are also quite different. In this way, the prediction made in 1978, that a-Si melts at a well defined temperature more than 200 K below the melting temperature of c-Si, was confirmed: the a-Si melting temperature was experimentally found to be 225 + 50 K. These experiments and theoretical calculations are excellently reviewed by Poate et al. (1987). It would, however, be a mistake to assume that the melting temperature of a-Si is well defined thermodynamically, because the structure of a-Si is itself not well defined and can be altered by a relaxation anneal. Fig. 9-13 (Sinke etal., 1988 a) shows a series of estimated free energy curves, which show clearly that the intersections between the a-Si and 1-Si curves come at quite different temperatures for different degrees of relaxation; accordingly, the melting temperature should vary in the same way. Indeed, if a-Si could relax to the theoretical limit at each temperature (curve 5 in the figure) it should intersect the c-Si curve before it intersects the 1-Si curve, and thus in that hypothetical case, a-Si should not melt at all, but crystallize directly. Thus, a-Si resembles a conventional

9 Metallic Glasses

Figure 9-13. Calculation of the isobaric Gibbs free energy of a-Si (curves 1 to 5) and of /-Si relative to that of c-Si, using strain energies deduced from Raman spectra. Curves 1 to 4 represent increasing degrees of thermal relaxation of the a-Si. Curve 5 is an estimated curve for a-Si prepared in a wholly unrelaxed form, but allowing it to relax to an equilibrium degree at each temperature. (After Sinke et al, 1988 a.)

glass in having a variable melting (transition) temperature. - More will be said about relaxation of a-Si in Section 9.4.2.

9.4 Diffusion, Relaxation and Crystallization When a metallic glass of amorphous solid is heated to a sufficiently high temperature, the constituent atoms begin to diffuse. This permits the amorphous structure to relax towards the state corresponding to the ideal congealed liquid. If diffusion is fast enough, the amorphous structure begins to crystallize. These three linked phenomena are treated in this Section. 9.4.1 Diffusion The first experimental study of atomic diffusion in a metallic glass was made as

recently as 1978 (Chen et al., 1978). The reason for this tardy start was the experimental difficulty of such measurements. The duration of a diffusion anneal of a metallic glass is limited by the need to ensure that no crystallization takes place, and this in practice means that penetration of the diffusing species is limited to a few tenths of a micrometer. Normal methods depending on mechanical sectioning and chemical analysis are therefore not applicable, and investigators have mostly used Rutherford back-scattering (used in Chen et al.'s initial study), ion erosion combined with radioactivity measurements, secondary ion mass spectrometry, nuclear reaction analysis and X-ray diffraction from multilayer films. These methods can measure diffusion coefficients as small as 10~ 20 -10~ 2 6 m 2 s" 1 . In the last few years, over a hundred publications have appeared on this theme and there is room here only for a brief account of the principal generalizations that can be made with confidence. More detailed information can be found in reviews by Cantor (1986), Cahn (1986), Mehrer and Dorner (1989) and Cahn (1990). Fig. 9-14 shows a characteristic set of measured diffusion coefficients for B diffusing in a Ni-Nb glass (Kijek et al., 1986). The xl B(p,a) 8 Be nuclear reaction was exploited; this has a strong resonance for a particular proton energy and by varying the energy of the probing beam, B concentrations at different small depths below the surface could be determined. It is clear that (as first discovered by Chen et al. 1978) a relaxation anneal reduces the diffusivity. Other studies have determined the kinetics of this reduction and shown that it saturates, and have also shown that the diffusivity falls as the atomic volume reduces during an anneal ... i.e., as the amount of free volume diminishes (Chason and Mi-

9.4 Diffusion, Relaxation and Crystallization

•

Fe

519

82 B 18

A Zr 61 Ni 39

10"19 =-\ \r

:

Uu

in

C

io- 2 T

CO

\

\

:

• Sb

\

:

"5

v

Q

s,.\ \ \«Au\ \

10-,21

\

S b

10 0.12

(a) 1.2

U 1.6 1 0 0 0 / T i n K"1

0.U 0.16 Atomic radius in nm

0.18

1.8

Figure 9-14. Diffusion coefficients of X1B in Ni 6 0 Nb 4 0 glass. O unrelaxed; x relaxed 420 s at 878 K. (After Kijek et al., 1986.)

zoguchi, 1987; see also discussion by Cahn, 1990). Fig. 9-14 also shows that, after relaxation, the diffusivity obeys an Arrhenius-type temperature variation, a fact which has occasioned much surprise, because a well defined activation energy would seem to imply that all atomic jumps go over similar energy barriers, which clearly is not true in a glass. The rather unsatisfactory present situation with regard to the theory of diffusion in metallic glasses is reviewed by Frank et al. (1988) and by Mehrer and Dorner (1989). The best established generalization concerning diffusion in metallic glasses is its great sensitivity to the relative sizes of the diffusing and host atoms. Sharma has done much to establish this (see Sharma et al., 1989) and the previously cited study by Greer et al. (1990) on the asymmetry of diffusivity of Zr and Ni in a-Ni-Zr has neatly confirmed it. Fig. 9-15 shows graphs

Ni Co Fe Cu

Au Ti

Zr

10"19

10-27 20 10 12 U 16 18 (b) Atomic vol. in 10"30m3 Figure 9-15. (a) The dependence of diffusivity of different metals in two metallic glasses on atomic radius of the diffusing species. (After Sharma et al., 1989.) (b) Diffusivities of various metals in amorphous N i Zr, with a Ni content in the range 50-65 at.%, as a function of the atomic volume of the diffusion species. (After Greer et al., 1990.)

520

9 Metallic Glasses

from these two studies. This is reminiscent of the behavior of diffusing species in crystalline metals, but is particularly pronounced here. This size sensitivity of diffusivity in metallic glasses still does not tell us for sure whether the diffusing process should be regarded as being mediated by vacancy-like holes or whether it is to be regarded as primarily interstitial. A recent study, via indirect diffusion measurements under hydrostatic pressure, of the activation volume for diffusion in a metallic glass (Limoge, 1990) suggests a vacancy-like mechanism. Further, the reduction of diffusivity as a result of relaxation has been closely correlated with the loss of free volume, and this indicates that "holes" play an essential part in diffusion. It is clear that the ultrafast diffusion of H in metallic glasses is of an interstitial nature, but it is also to be noted that the small number of interstitial spaces of large sizes act as traps for hydrogen, so that (e.g., Kirchheim etal., 1982; Kirchheim 1988, Kirchheim et al., 1991) the diffusivity of H in metallic glasses becomes extremely sensitive to concentration (which has not been established for any other diffusant). Whether such large units of free volume are to be regarded as holes or interstitial spaces is really a matter of lexicography; it may turn out that the vigorous debate as to whether, in general, diffusion in metallic glasses is to be perceived as an interstitial or as a vacancy-type mechanism is a matter of shadow-boxing. The one thing which is unambiguously clear is that free volume plays a vital role in determining diffusivity. A very recent study (Faupel et al., 1990) has shown, for a Co-rich glass, that there is no pressure dependence at all of cobalt diffusivity and a very small isotope effect. The conclusion is that diffusion is not mediated through quasivacancies in thermal equilibrium, but rather takes place by a 'direct'

mechanism involving about 10 atoms cooperatively. One well-known theoretical approach to diffusion in metallic glasses is firmly predicated on the notion of diffusion via atom-sized holes. Buschow (1984) was able to estimate the heats of formation of holes in various metallic glasses, using a method introduced by Miedema, and was able to show that the crystallization temperature scales as does this heat of formation. (He assumed that the diffusion of holes of the same size as the smaller constituent atoms was the important variable.) A larger heat of formation, as with crystal vacancies, implies a smaller concentration of holes, thus a smaller diffusivity at a given temperature and, in consequence, more sluggish crystallization. Barbour et al. (1987) have developed this approach by computing also the heats of formation for holes of the same size as the larger constituent atoms of each glass, and concluded that the readiness of a particular amorphous alloy to be formed by the interdiffusion SSAR mechanism depends on a large difference between the heats of formation for the larger and smaller holes, and this of course relates to the size difference of the constituent atoms. A large size difference implies a large diffusivity difference, as we have seen. Fig. 9-16 shows the results of the calculations by Barbour et al. As we saw above, diffusion is an essential process in some of the solid-state amorphization mechanisms. It is not known what the state of relaxation of an amorphous alloy made by interdiffusion of layers is, but it is no doubt significant that the diffusivity calculated from measured growth kinetics (Rubin and Schwarz, 1989) of such an alloy layer in Ni/Zr and the directly measured diffusivity of Ni in a Ni/Zr glass made by melt-quenching, have quite different activation energies (1.01 eV/

9.4 Diffusion, Relaxation and Crystallization

521

1500 .9

11000

Figure 9-16. Crystallization temperatures for various transition metal amorphous alloys plotted against the calculated heats of formation of holes equivalent in size to the larger constituent atoms (HLV) or the smaller constituent atoms (HSY). (After Barbour et al., 1984.)

CD C

o N

5

500

o

50

100

150

200

250

HSw (A) or HLy ( • ) in kJ mole

atom in the first case, 1.45 eV/atom in the second). It will be interesting to see more critical comparisons of diffusivities in meltquenched and SSAR amorphous alloys. Relaxation does not always depress the diffusivity in an amorphous solid. a-Si is a notable exception. A recent study (Polman et al, 1990) has established that the diffusivity of Cu in a-Si made by ion implantation increases by a factor of 2 to 5 when the silicon is relaxation-annealed. The explanation is that as-implanted a-Si contains a large concentration of defects (point defects and agglomerates) which act to trap Cu atoms; relaxation destroys many of these defects and thus enhances mobility of the Cu. Free volume seems to be of secondary importance here. 9.4.2 Relaxation

As we have already seen in connection with diffusion, annealing a metallic glass below its crystallization temperature reduces the free volume and thereby decreases the self-diffusivity. (a-Si behaves differently.) The reduction in free volume

also affects many other physical and mechanical properties: changes of physical properties are briefly discussed in this section, relaxation-induced embrittlement in the next. Oxide glasses behave similarly: for instance, when an optical glass is annealed close to its glass transition, the refractive index changes steadily. Relaxation in oxide glasses is treated in Chap. 3 of this Volume. Table 9-2, modified by Cahn (1983) from a compilation by Egami, lists the properties the changes of which on thermal relaxation have been most frequently studied. A distinction is made between those phenomena which change in a primarily irreversible way and others which change in a primarily reversible way as the annealing temperature is cycled; recent research has however made it clear that no property changes in a wholly irreversible or a wholly reversible way. Thus, length changes, which are most directly tied to free volume changes, while almost wholly irreversible have nevertheless recently been shown to have a small reversible component (Huizer and van den Beukel, 1987). The principal

522

9 Metallic Glasses

Table 9-2. Changes in physical and mechanical properties during structural relaxation. (After Egami et al. (1982), slightly modified.) Properties

Volume Specific heat Young's modulus Internal friction b ' c Electrical resistivity Diffusivityb Viscosity15 Embrittlementb Thermal resistivity Curie temperature Coercive field Magnetic anisotropy, field-induced Superconductive transition temperature

Direction of Reversible (R) change during or irreversible (I) below Tg relaxationa D I I/D I I/D D I/D I/D D I I D I/D I/D

I I R I R I I R I I I I I/R I/R

I/D

R

D

I

a

I denotes increase, D decrease. These properties are conventionally (for crystalline solids) considered to be structure-sensitive, and indeed do show large changes in amorphous solids upon annealing. c This property is itself a reversible relaxation phenomenon. b

difference between these two fundamentally distinct types of relaxation-induced change was first recognized by Egami (1981). He proposed a distinction between topological short-range order, or TSRO (which in effect describes the density of packing of atoms) and chemical short-range order, or CSRO, which defines the extent to which atoms have unlike nearest neighbours. On relaxation annealing, TSRO changes through the progressive, irreversible removal of free volume, and this causes irreversible property changes. Chemical SRO, by analogy with crystalline alloys (see Cahn, 1982) is assumed to vary with tem-

perature in metallic glasses only, although no direct diffraction evidence of this has ever been reported (it would be more difficult to obtain in glasses than in crystals). Because of this postulated reversible variation of chemical SRO with temperature, changes in properties that are particularly sensitive to it, such as elastic properties or Curie temperature, have a large reversible component to their changes on relaxation. Very recently Haruyama and Asahi (1991) claim to have found calorimetric and resistometric evidence of reversible SRO in N i - C r - B glasses. One test of Egami's rationalization of the two types of relaxation effect would be to test whether the incidence of reversible changes of property are correlated with the magnitude of chemical SRO present in different glasses: thus, Cu-Ti glasses are known to order strongly, Fe-Ti glasses have recently been found to have no chemical SRO, and comparative measurements, for instance of Young's modulus, between them might serve as a test of what is still, after 9 years, no more than a very reasonable hypothesis: the association between reversibility of property changes and chemical SRO. - An excellent overview of known facts concerning relaxation of metallic glasses in the light of Egami's hypothesis was published more recently (Egami, 1986). Fig. 9-17 shows some characteristic examples of relaxation-induced property changes. The kinetics of such processes, especially reversible ones, became an interesting problem when the so-called crossover effect was discovered in metallic glasses, with respect to properties such as the Curie temperature and elastic moduli (Greer and Spaepen, 1981; Scott and Kursumovic, 1982). This effect is most easily understood by reference to Fig. 9-18, which actually refers to earlier work done with respect to

523

9.4 Diffusion, Relaxation and Crystallization jL0*?0'{5)

p Relaxed at 623 K {Pre-relaxed 30 m'm at 5/3 K)

-

;

•

Fe

40 Nl40

B

20

179-

-3623 time (s)

-4

1000

60

10

12

U tjh]

Figure 9-17. Manifestations of relaxation of metallic glasses: (a) irreversible length change of a Fe 40 Ni 40 B 20 glass; (b) short-term reversible changes of Young's modulus of Co 58 Fe 5 Ni 10 B 16 Si 11 glass cycled between 623 K and 723 K; (c) longterm change of Young's modulus in the same glass at various temperatures, from the as-quenched state; (d) changes of Curie temperature of Fe 80 B 20 glass as a function of holding time at various temperatures above the Curie temperature, substantially reversible; dashed lines indicate incipient crystallization; (e) reversible changes of coercive field of the above-mentioned Co-rich glass, a composition of low magnetorestriction, during cyclic annealing. (After Cahn, 1983.)

524

9 Metallic Glasses

1.5U60 Equilibrium line

1.51430

200 300 Time in minutes

400

Figure 9-18. Refractive index vs. time in a crossover experiment on a borosilicate glass. The glass was held at temperature Tx until the index reached the value characteristic of equilibrium at a second, higher temperature T2. The temperature was then changed abruptly to T2: instead of remaining steady, the index followed the curve shown, returning eventually to the T2 equilibrium value. (After Macedo and Napolitano, 1967.)

the refractive index of a borosilicate glass (Macedo and Napolitano, 1967). The caption indicates the treatment used. - Such behavior can only mean that two or more distinct atomistic processes, with different activation energies and different kinetics, operate simultaneously: it also implies that there is not a one-to-one relationship between measurable properties and the internal state of the glass, in the sense that the same value of a property can be associated with distinct states generated by different heat-treatment programs. A thorough analysis showed that, in fact, not two but a spectrum of activation energies has to be operative (Gibbs et al., 1983; Leake et al., 1988), and this idea has had a major effect on subsequent theories of relaxation phenomena. The idea has been used to particularly good effect in a long series of papers by van den Beukel and colleagues, in which the relaxation of a number of properties, including viscosity, length changes, resistivity, Young's modulus and Curie temperature, mostly in Fe 4 0 Ni 4 0 B 2 0 glass, was analyzed experimentally and theoretically in great detail. Their entire programme of research has been summarized (van den

Beukel, 1986). This work is too complex and extensive to treat here. Most commonly, relaxation kinetics of various properties follow a In t law, which has been shown to be consistent with the existence of a spectrum of activation energies. Not only melt-quenched glasses relax. Thus Riveiro and Hernando (1985) measured the relaxation of coercive field in an electrodeposited Co 91 P 9 glass, and found a drop by two orders of magnitude. They were able to analyze this change in terms of the spectrum of activation energies and decided that at least 4 distinct processes were in play; they also concluded that the diffusion of P atoms from "unstable" to "stable" holes was the main relaxation process. When a metallic glass is stressed at a high temperature, it undergoes homogenous flow by a purely viscous process. (At room temperature, flow proceeds inhomogeneously, along shear bands - see Vol. 6, Chap. 11). As creep proceeds, free volume is progressively annealed out and since the viscosity is directly linked to free volume (see Chap. 3, this Volume), the creep rate under constant stress progressively diminishes. The relation between viscosity, rj, stress,
9.4 Diffusion, Relaxation and Crystallization

525

1O 1;

1011

>10 1 0 -a Tensile creep

/

A

10 <100

] 104 I 117 Tensile stress f 100-400 relaxation (100-400 Bend stress { 30-330

9

10

V A

• •

relaxation

108 1.4

1.6

1.8

2.0 2.2 10 3 / T in K"1

(Nachtrieb, 1976). The rise in viscosity on relaxation due to reduced free volume is thus associated, as we have already seen, with a fall in diffusivity. The free volume model of flow and viscosity, originated by Cohen and Turnbull, can be outlined as follows: Each atom is confined in a cage defined by its nearest neighbors; that cage can vary in volume, and the free volume is that part of a cage in which the atom can move without an energy change. Normally the atom can only oscillate, but if there is a density fluctuation, there is a computable probability (dependent of course on temperature) that the atom will jump to a neighboring cage if the fluctuation generates an instantaneous local free volume exceeding a critical amount. Such jumps define both viscosity and creep rate under stress. Relaxation diminishes the average free volume and thus increases the viscosity, linearly with time as it turns out. Fig. 9-19 shows how the (linear) rate of increase of viscosity varies with temperature for a metal-metalloid glass. -

Figure 9-19. Rate of change of viscosity of Fe 40 Ni 40 P 14 B 6 glass with time as a function of temperature, as measured by three different experimental techniques. (After Spaepen and Taub, 1983.)

a O

2.4

2.6

2.8

Attempts to interpret such relaxation-induced changes quantitatively are still beset by some difficulties, notably the need to assume that the concentration of flow defects (unlike free volume collectively) to some extent changes reversibly with temperature. A "flow defect" here is a particular configuration of free volume of a kind which favors atomic jumps, as sketched out above. For details of the theoretical considerations involved, the reader is referred to Spaepen and Taub's review, and to other detailed reviews by Chaudhari et al. (1983) and Spaepen et al. (1986). It is undoubtedly very difficult to define in an acceptable operational manner what is meant by a defect in an amorphous structure; one very recent attempt to do so (Calvo, 1991) leans on a method originally introduced for quasicrystals. Although the theory of the glass transition is not discussed in this Chapter, it is worth pointing out that an effective theory linking the glass transition and relaxation in terms of free volume has recently been

526

9 Metallic Glasses

120 240 Time in min

360

Figure 9-20. Relative change in the density of Pd 82 Si 18 glass as a function of annealing time at 260 °C, determined from changes in x-ray absorption. (After Chason et al., 1985.)

published by van den Beukel and Sietsma (1990). To conclude this Section, we consider the possibility of direct experimental analysis of changes in TSRO during relaxation. On a coarse scale, one can estimate the reduction in free volume by measuring the change in length (e.g., Huizer and van den Beukel, 1987) or even more directly, the change in density resulting from relaxation. This last has been measured in an experimental tour de force by Chason et al. 20 V)

Annealed at 500°C Annealed at 230°C as implanted

S 15 ^

(1985), by measurement of the change of X-ray absorption by a foil of metallic glass. The change of density of Pd-Si based glasses in these two studies ranged from 0.14 to 0.25% (Fig. 9-20). - The most direct way of measuring changes in TSRO would be to monitor changes in the diffraction pattern. This is exceedingly difficult because the changes are so small. The first serious attempt to detect such changes was by Egami (1978): he used the highly sensitive energy-dispersive X-ray diffraction method. Later, Chason et al. (1985), in the study just cited, determined the change in the profile of the first diffuse X-ray diffraction peak from Pd 82 Si 18 and related this to the measured change in resistivity, which is closely linked with the structure factor in the neighborhood of the first peak. The observed and calculated change of resistivity matched well. The structural relaxation of a-Si (see Sec. 9.3.4) has been determined by X-ray diffraction (Roorda, 1990) and here the changes are much more substantial than in a metallic glass (Fig. 9-21). The changes correspond to enhanced ordering over a range of several atomic distances, but without any change in nearest neighbor separations. The nature and kinetics of the relaxation process in this material has also been studied by Raman spectroscopy, which is sensitive to the distortion of covalent bond angles - a method not applicable to metallic glasses (Sinke et al., 1988 b).

10

c

9.4.3 Thermal Embrittlement c 0)

0

2

4 k in A"1

6

8

Figure 9-21. X-ray diffraction pattern of a-Si made by ion implantation, before and after relaxation anneals. (After Roorda, 1990.)

Many metallic glasses are capable of a moderate degree of plastic deformation at room temperature: the process is heterogeneous and involves the formation of shear bands approximately along a plane of maximum resolved shear stress. A ductile metal ribbon can generally be plastically

527

9.4 Diffusion, Relaxation and Crystallization

350°C-2hr r BD =97°C —•—1

c o t_ In

10°

ry

-

• •••

ing

bent sharply back on itself. Some such glasses, mostly those based on iron (one might call these "glassy steels"), show (1) a ductile-brittle transition temperature and (2) the phenomenon of thermal embrittlement, which is marked by an increase in the ductile-brittle transition temperature on annealing below the crystallization temperature. Fig. 9-22 exemplifies these phenomena. The mechanism of the embrittlement process has given rise to a great deal of debate and investigation. Spaepen (1977) first put forward the idea that shear band formation (morphologically similar to slip bands in crystalline metals) is to be attributed to a multiplication of free volume at an incipient band, which reduces the flow stress locally so that the shear band develops preferentially. Cahn et al. (1984) showed that the overall density reduction in a Pd-Cu-Si glass due to a 40% rolling reduction was 0.14%, which implied a much larger density reduction within the narrow shear bands themselves. This notion was further analyzed by Argon et al. (1985), and they concluded, from measured overall density changes in heavily deformed glasses (rolling or wiredrawing) and the observed shear band geometry, that within a shear band itself the local dilatation due to free volume can be as large as 50%. - Cahn et al. (1984) further showed that the excess free volume in the shear bands was dissipated during a relaxation anneal, while Krishnanand and Cahn (1975) had earlier shown that after such a relaxation anneal and renewed plastic deformation, the new population of shear bands was not in the same sites as the old ... i.e., the old shear bands had been totally "healed" by the relaxation anneal. It can thus be taken as well established that free volume plays a central role in both homogeneous (creep) and heterogeneous plastic flow in metallic glasses.

T3

1

c 0) .a

1n -1

Q>

»

1U

•3 (_)

0 «_ li_

L

•

• •

• •

•• •

••

I •

-n

••

• •

10"2

•

• ••

1

30

(a)

1

1

1

1

1

50 70 90 110 130 150 170 Testing temperature in °C

300 260 -

Isochronal annealing, fA = 2hr \

220 -

i

180

Crystallization 1 ' *

140 O 100 o

1 1 1

-

.£ 60 .§ K

20 -20 -60

-100 \

J A

-140

-180 (b)

240

280

320 in °C

360

400

Figure 9-22. (a) Strain at fracture in a bending test as a function of temperature for a Fe 79 3 Be 16 4 Si 4 0 C 0 3 glass, annealed for 2 h at 350°C after melt-spinning. TBD is the ductile-brittle transition temperature, (b) Change of TBD with isochromal anneals at progressively increasing temperature: same glass. (After Spaepen et al., 1986.)

528

9 Metallic Glasses

The theories to explain thermal embrittlement fall into two categories: (1) the hypothesis that annealing removes excess free volume and (2) the hypothesis that the homogeneous glass structure separates into two distinct amorphous phases. The basis of the first hypothesis is clear from the foregoing: further, Wu and Spaepen (1986) have assembled detailed evidence on thermal embrittlement consistent with this model. The second hypothesis leans on observations such as that due to Walter et al. (1976), who by Auger electron spectroscopy established an enrichment of P at fracture surfaces of a Fe 40 Ni 40 P 14 B 6 glass, and Piller and Haasen (1982) who used field ion microscopy to demonstrate the formation, during relaxation annealing of Fe 4 0 Ni 4 0 B 2 0 , of minute zones enriched in boron to 25 at.%. However, tests by Xray small-angle scattering of some other glasses have failed to demonstrate phase separation of this kind, whereas other experiments have given contrary results. The literature is quite extensive. A possible marriage between the two types of hypothesis has been proposed in an interesting paper by Yavari (1986). By analyzing the volume per metal atom in Fe-B glasses of different compositions, he shows that a local enrichment of B will need to "suck" free volume from the adjacent matrix, reducing the free volume concentration there. He suggests, therefore, that the phase separation hypothesis resolves itself, indirectly, into the free volume hypothesis. According to Yavari, the fact that some additives (e.g., Ce) delay embrittlement to higher temperatures, whereas others such as Sb promote it, can also be interpreted on the basis of his model. Another observation (Yamasaki et al., 1985) to the effect that Fe-based glasses whose compositions fall close to an equilibrium eutectic composition embrittle

much more sluggishly, if at all, is attributed to a reduced tendency to phase separation for such compositions. The clearest demonstration to date of the central role of free volume in determining the incidence of thermal embrittlement comes from an important series of publications by Gerling et al. (1985, 1988, 1989, 1990) relating to Fe 4 0 Ni 4 0 B 2 0 glass. Briefly, they have established in circumstantial detail how this glass is embrittled by the loss of free volume on annealing; for instance, the embrittlement behavior varies with ribbon thickness, because the quenched-in free volume varies also. They have further shown that a glass which has been thermally embrittled can be reductilized by neutron irradiation, which creates fresh free volume. The new ductility can in turn be removed by a second relaxation anneal. 9.4.4 Relaxation of Magnetic and Elastic Properties Changes in the Curie temperature, which is particularly affected by CSRO, and of the coercive field, have already been discussed. A number of other magnetic properties have also been studied in relation to relaxation. The magnetic and mechanical properties of soft ferromagnetic metallic glass sheets, which are now widely used for transformer laminations (see Sec. 9.6.1) are considerably affected by relaxation anneals. Because of the role of magnetostriction in enhancing core losses, it is important to remove residual stresses without changing glass structure appreciably. Taub (1984) has shown that a short pulsed anneal at high temperature is much more effective in achieving this than a long anneal at a lower temperature. A comprehensive study of the effect of annealing on a range of properties,

9.4 Diffusion, Relaxation and Crystallization

with special emphasis on magnetic ones (Liebermann et al, 1989) of Fe 78 B 13 Si 9 glass has reached the conclusion that embrittlement is associated with clusters as small as 0.3 nm in size. The authors also established that stress relief was complete at annealing temperatures lower than those at which embrittlement began; it is thus possible to achieve the desirable objective of stress relief without embrittling the laminations. Another form of magnetic relaxation which is of practical importance is the generation of magnetically induced uniaxial (ferromagnetic) anisotropy. This is a form of "magnetic annealing" well known in ferromagnetic crystalline solid solutions (Graham, 1959) but less familiar in glasses. The relevant theory is well established. The phenomenon is of practical concern because an induced uniaxial anisotropy affects the response of magnetic components to applied fields. - An alloy is annealed in a magnetic field at a temperature high enough to permit exchange of places between neighboring atoms, and pairs of unlike atoms tend to line up preferentially parallel to the field, inducing a magnetic anisotropy. The statistical tendency for this to happen is very weak, but magnetic measurements are ultrasensitive even to minute amounts of directional short-range order which would be too weak to measure by X-ray diffraction. The phenomenon is best defined where two distinct kinds of metal atom are present (usually, Fe and Ni) and is most pronounced for concentrated solid solutions, since it depends on the presence of numerous pairs of unlike nearest neighbor atoms. The kinetics of reorientation of the preferred magnetic direction when the field direction is changed depends on self-diffusivities in the alloy concerned, although no attempts have been made to measure diffusivities in this

529

way. The establishment of directional SRO (which can exist at the same time as normal isotropic SRO) is reversible, in the sense that a change in direction of the applied field, or its removal, will redirect or destroy the directional SRO. The phenomenon, which deserves more exploitation than it has had as a useful way of measuring structure change kinetics in metallic glasses, is described in detail by Luborsky (1980). Evetts and Hodson (1985) have in fact analyzed the kinetics of the process (which they term 'polarization') in terms of the concept of a spectrum of activation energies, mentioned in Sec. 9.4.2. A closely related process is stress-induced ordering; here the external influence is a stress instead of a magnetic field, and the measured property is anelastic strain instead of a magnetic anisotropy. In an experimental tour de force, Suzuki et al. (1987) were able to show directly, by energy-dispersive X-ray diffraction from a stress-annealed Fe 40 Ni 40 Mo 3 Si 12 B 5 glass done successively with two orthogonal diffraction vectors, that directional order (they called it 'bond-orientational anisotropy') was induced by stress-annealing and decayed on subsequent stress-free annealing. The ordering kinetics followed In t kinetics, characteristic of a material with a spectrum of relaxational activation energies. According to their model, bond-orientational anisotropy involves a directional variation in the number of all kinds of bonds, whereas the accepted theory as applied to crystalline alloys involves, as we have seen, anisotropies in different kinds of bonds. In fact, a more recent study from the same laboratory (Tomida and Egami, 1991) recognizes that chemical as well as topological anisotropy is involved in bondorientational anisotropy. A recent study of stress-induced ordering in Fe 4 0 Ni 4 0 B 2 0 glass, by Leusink and

530

9 Metallic Glasses

van den Beukel (1988), has proved that the ordering kinetics is determined by the amount of free volume present. As these authors point out, this is a good way of estimating the kinetics of establishment of CSRO in a metallic glass; the fact that the state of order here is anisotropic rather than isotropic is of no consequence. Other special forms of relaxation, particularly magnetoelastic and thermoelastic relaxation in metallic glasses, and internal friction, are reviewed by Kiinzi (1983). Internal friction can be used to monitor structural changes; this was done, for instance, in a study by Sinning et al. (1991) on crystallization of a C o - Z r - H glass, to be cited in the next Section. 9.4.5 Crystallization

When a metallic glass is heated, it will crystallize to form some combination of intermetallic compounds and metallic solid solutions, just as an oxide glass crystallizes to form a glass-ceramic. The nomenclature of the product poses a problem: "Glass-alloy" has not found favor, "Pyromet" by analogy with "pyroceram" is excluded because the word is a registered trademark; there is a family of engineering alloys made by crystallizing, or "devitrifying" metallic glasses with the trade name "Devitrium"; probably "devitrified alloy" is the best available generic term. Crystallization mechanisms of metallic glasses are generally divided into three categories - polymorphous, eutectic and primary crystallization (Koster and Herold, 1981) - to which a fourth, crystallization with phase separation, can usefully be added: - In polymorphous crystallization (e.g., of Fe 7 5 B 2 5 glass), a single intermetallic compound crystallizes without change of composition.

- In eutectic crystallization (e.g., of Fe 8 0 B 2 0 glass), the glass transforms to two phases growing in a closely coupled form. In the example cited, the constituent phases are a-iron and Fe 3 B. There is no change in overall composition between the glass and the eutectic colony. - In primary crystallization (e.g., of Fe 8 6 B 1 4 glass), a primary phase, here airon, crystallizes out first, which involves a change in composition of the residual glass; later, a compound, here Fe 3 B, crystallizes separately (i.e., not in closely coupled form). - In crystallization with phase separation, the glass itself phase-separates into two distinct amorphous phases with different compositions and glass transition temperatures, and these then crystallize at different temperatures during further heating. A good example of a glass behaving like this is Zr 3 6 Ti 2 4 B 4 0 (Tanner and Ray, 1980). Early studies of crystallization of metallic glasses largely depended on the use of a differential scanning calorimeter (DSC), which generates curves such as that shown in Fig. 9-23. In this particular instance, it is not certain whether the double peak is due to amorphous phase separation (there is a faint indication of a second glass transition) or to primary crystallization followed by crystallization of a small amount of residual glass at a higher temperature. This uncertainty indicates that micrographic examination is really necessary as well to determine crystallization mechanisms for certain, and this has been widely done for a variety of glasses (see reviews by Koster and Herold, 1981; Scott, 1983; Koster and Schunemann, 1992). A very large literature exists on the results of such investigations, which it would not be profitable to review. Many studies have examined the effect on crystallization mechanisms and kinetics of

9.4 Diffusion, Relaxation and Crystallization

I

230

I

I

270

I

I

310 350 390 430 Temperature in °C

470

510

Figure 9-23. Differential scanning calorimeter record during heating, at 20Kmin~ 1 , of Pd 77 5 Cu 6 Si 16 5 glass. The ordinate represents power released (exotherm upwards) or absorbed (endotherm downwards). Tg is clearly differentiated from the first crystallization peak, Txl.

changing the proportion of the constituent elements. A good, very recent specimen of this literature is a paper by Sprengel et al. (1990) on the crystallization of a range of Co-Zr glasses. Other investigations, which are increasing in frequency, have examined the effect of systematically varying ternary additions to a fixed binary composition (e.g., Bhatnagar et al., 1990, with respect to NiZr 2 plus Al or Ga; Ghosh et al., 1991, with respect to "micro-additions" to Ni 24 Zr 76 ). - For detailed information the reader is referred to the cited overview articles. The crystallization temperature not only depends on the alloy system but also varies somewhat with the composition of the glass within a given system. This is exemplified by Fig. 9-24, for the Fe-B system: this shows that the same system can show single or double crystallization peaks, according as the type of crystallization

531

changes between the various categories listed above. The activation energy for the crystallization process as a whole, which is usually well defined, is obtained by varying the heating rate in the DSC and applying a theory developed by Kissinger (1957) to the measured peak values of crystallization temperature. However, as often in physical metallurgy, little useful has been done with the activation energies once they have been determined! They could be compared with activation energies for the self-diffusion of the constituent species, where known, to help define rate-determining process in crystal growth, but this does not appear to have been widely done. (However, Koster and Herold (1981) have used crystallization kinetics as an indirect way to estimate diffusion rates, without being able to determine which diffusing species is rate-determining.) DSC studies can only encompass a limited range of heating rates, approximately 5-100 K/min, and until recently no methods were available to study crystallization kinetics and mechanisms at very high heating rates or isothermally at high temperatures. This has been altered by the intro-

350,

Figure 9-24. Crystallization temperatures Tcryst (peak in DSC continuous-heating records for different heating rates) of Fe-B metallic glasses. The various symbols refer to different investigators. (After Koster and Herold, 1981.)

532

9 Metallic Glasses

duction of time-resolved X-ray diffraction, in which extremely intense monochromated X-ray beams from a synchrotron source are combined with very rapid («10 4 K s ~x) electrical self-heating of glass ribbons to constant high temperature (Sutton et al, 1989). With the aid of positionsensitive X-ray detectors, an entire diffraction pattern can be determined in as little as 3 ms. In this first study by the new technique, polymorphous crystallization of NiZr 2 was studied up to 680 K (at which temperature, 50% crystallization is achieved in 4 s) and it was established that at these high temperatures, a transient precursor phase is formed initially. From a practical viewpoint, plots like that shown in Fig. 9-25 are useful. These are obtained by isothermal anneals (less often used than continuous heating ones) at a range of temperatures. Metal-metal glasses are of particular interest because some of them have very high crystallization temperatures. Notable among these are W 65 Ru 35 , W 50 Re 50 (both with T x ^800°C, and Ta 55 lr 45 , with T x ^ ^900°C (Denier van der Gon et al., 1987). Such glasses have found an unexpected ap-

450

Temperature. T in °C 400 350

plication because of their resistance to crystallization (Sec. 9.6.5). These high crystallization temperatures have been successfully rationalized on the basis of Buschow's hole model of diffusivities (Sec. 9.4.1). Attention has recently moved from the simple determination of crystallization temperatures to the investigation of nucleation mechanisms, in particular, whether nucleation in particular case is homogeneous or heterogeneous, and to a study of the role of heterogeneous nucleation at the free surface of a glass. The leading investigator in recent years into nucleation mechanisms and kinetics has been Greer. His series of papers began with an important study of the crystallization of Fe 8 0 B 2 0 glass (Greer, 1982). His approach combines DSC and micrographic observation with modelling. Isothermal DSC runs (with elaborate corrections for various sources of error) were used to fit the parameters of the standard Johnson-Mehl-Avrami equation, x (t) = l - e x p ( - K t " ) , where x{t) is the fraction crystallized in time t and K = Ko • Qxp( — E/kT). Special steps are taken to make allowance for the mutual impinge-

300

Figure 9-25. Time for the start of crystallization of a range of metallic glasses as a function of temperature. (After Luborsky, 1980.)

Fe*oN'*opuB6

1.4

1.5 1.6 1000/7" in K"1

17

1.8

533

9.4 Diffusion, Relaxation and Crystallization

ment of growing grains. TEM established the growth rate of crystals at specific temperatures. These correspond to an exponent, n = 3 in the above kinetic equation. Putting all this information together allowed a computer model to be set up for the crystallization kinetics during continuous heating in a DSC, which permits the highest precision, and the experimental output was compared with the predictions from the model. Fig. 9-26 shows the results in the form of a dx/dt plot derived both from the DSC output and from the fitted model, both for the as-quenched glass and for a sample preannealed at a constant temperature (which initiates crystallization on preexisting nuclei). One adjustable parameter, Ko, is adjusted to give the best fit for both curves and it can be seen that a very exact fit was obtainable for experimental peaks, except for a small unfitted subsidiary peak at high temperatures. (This was shown to be due to a thin surface skin on the ribbons which was known to contain no preexisting nuclei, so that crystallization of this skin was delayed until new nuclei could form.) Greer showed that Ko is directly proportional to the nucleus density for a fixed growth rate, and was able to deduce a nucleus density (not affected by the preanneal) of3.5xl0 1 8 m~ 3 . This was checked against the grain concentration in partly crystallized specimens as determined by TEM, and fitted well. At this stage, he could not be certain as to the nucleation mechanism, but because of the very high nucleus density he deduced that it was very probably a homogeneous mechanism. - He found that the nucleus density was very sensitive to the thickness of the ribbon and thus to the quench rate. The next stage was to study both theoretically and experimentally the phenomenon of transient homogeneous nucleation; this term is applied to a nucleation

as-quenched

3

0.4

0.0

680

700 TEMPERATURE(K)

720

Figure 9-26. Crystallization kinetics, dx/dt, deduced from continuous DSC heating data, for Fe 80 B 20 glass 32 urn thick (solid curves), compared with fitted curves derived from a model. The lower peak corresponds to a preannealed sample. (After Greer, 1982.)

rate increasing from zero to a steady state value as the material is undercooled. (In the case of Fe 8 0 B 2 0 Just discussed, the observations fit the hypothesis of transient nucleation during the quench itself.) Fig. 9-27, taken from a review of nucleation mechanisms (Greer, 1988) shows schematically the different forms of nucleation

Time

Figure 9-27. Schematic variation in the number of nuclei with time in an isothermal anneal for the following nucleation types: (a) steady-state homogeneous; (b) transient homogeneous; (c) steadystate heterogeneous; (d) transient heterogeneous; (e) quenched-in active nuclei. (After Greer, 1988.)

534

9 Metallic Glasses

which can arise during crystallization of a glass (and beforehand, during the quench). Kelton and Greer (1986) published a detailed analysis of the role of transient homogeneous nucleation in glass formation and showed that a glass can sometimes form only because nucleation was of the transient rather than the steady-state type. This is exemplified by Fig. 9-28, which shows calculations, based on known material parameters, for both types of nucleation for Au 81 Si 19 . The dashed line in the lower figure indicates the low level of volume fraction transformed which has usually been taken as the condition for forming a metallic glass successfully; it can be seen that this level is achieved with transient nucleation for a quench rate of 105 K s" 1 , whereas for steady-state nucleation the unrealistic rate of 10 8 Ks~ 1 would be needed.

Au 81 Si 19

10 5

10 6

10 7

108

Quench r a t e in K / s

Figure 9-28. (a) The number of nuclei and (b) the transformed crystal fraction calculated for quenching molten Au 81 Si 19 at various rates, assuming either steady-state or transient homogeneous nucleation. (After Kelton and Greer, 1986.)

Homogeneous nucleation has been firmly established in the much-studied Fe 40 Ni 40 P 14 B 6 glass, by appeal to crystallite counting (Morris, 1982) and a few other metal-metalloid glasses. Other glasses in which homogeneous nucleation is much slower, notably Pd 4 0 Ni 4 0 B 2 0 (Drehman and Greer, 1984) crystallize predominantly heterogeneously, both from internal defects and from defects at free surfaces. Even for such alloys, homogeneous nucleation with the concomitant fine grain size can be achieved by first annealing close to the temperature of maximum nucleation frequency and then raising the temperature to allow the nuclei thus formed to grow. Contrariwise, this same alloy can be formed into large glassy volumes, « 1 cm3, by cooling at a rate as low as 1 K s ~ 1 , if the surface is cleared of local defects by immersing it in a molten flux (Kui et al, 1984). At the opposite extreme, it has recently been shown (Sinning et al., 1991) that a Co 33 Zr 67 glass containing a small amount of hydrogen can be crystallized by fairly fast heating to give a nanocrystalline structure (see Vol.15, Chap. 13). This is most simply interpreted in terms of a very copious homogeneous nucleation, with a crystal growth rate that slows down sharply at higher temperatures. Generally, heterogeneous nucleation is most clearly demonstrated at free surfaces. In some instances, the process is so dominant that columnar grains grow in from the surface while none grow in the interior - i.e., the exact converse of what is observed in Fe 8 0 B 2 0 , as we have seen above. However, a glass of this type can crystallize preferentially at the surface if the surface is chemically or otherwise modified before or during annealing. Thus, if Fe 8 0 B 2 0 is differentially oxidized so that the boron content is reduced at the surface (Koster, 1984), preferential surface nucleation is found.

9.5 Chemical Properties

The related composition Fe 4 0 Ni 4 0 B 2 0 behaves similarly; here, iron is preferentially removed. Recently, Wei and Cantor (1989) made a detailed study of surface crystallization of Fe 4 0 Ni 4 0 B 2 0 and found that it is enhanced if the alloy is first phase-separated by relaxation and then abraded at the surface, or else the surface is enriched in Ni by electroplating Ni and then annealing the glass. Sometimes, surface oxidation can have the opposite effect of inhibiting surface crystallization; with Pd 4 0 Ni 4 0 P 2 0 , a thin NiO layer protects the glass from local loss of P; such loss is the prime cause of preferential surface nucleation. - Removal of the original surface can drastically modify crystallization behavior: thus, Ni 6 6 B 3 4 glass (which normally crystallizes from the surface with a strong accompanying [100] fiber texture, loses the quenched-in nuclei responsible for this if the surface is etched off (Koster and Schiinemann, 1991). According to the same authors, another way of inhibiting surface crystallization is to remelt the original surface by means of laser pulses; the self-quenching resulting from this seems to be fast enough to obviate quenched-in nuclei. Clearly, the variegated phenomena surrounding surface nucleation during the crystallization of metallic glasses as yet defy generalization, and it must be left to future research to systematize and interpret them, as homogeneous nucleation has recently been interpreted. Certainly, there is a practical interest in gaining such understanding, because preferential surface nucleation can produce undesirable sideeffects, such as increased magnetic eddy current losses in surface-crystallized soft magnetic glass ribbons for high-frequency applications (Datta et al., 1982).

535

9.5 Chemical Properties A good deal of research has been done, mostly in Japan, on the corrosion resistance of metallic glasses, which can be spectacularly good. Much more recently, such research has extended also to the catalytic and electrocatalytic properties of suitable treated metallic glasses. A combined overview of these fields of research can be found in a recent conference proceedings (Diegle and Hashimoto, 1988) and in review papers (Hashimoto, 1985, 1992). Here we have space only for a summary.

9.5.1 Corrosion Resistance

The wet corrosion resistance of metallic glasses is greatly affected by their structural and chemical homogeneity. In particular, there are no grain boundaries with their frequent forms of chemical heterogeneity; accordingly, no electrolytic microcircuits are set up with their bad effects on corrosion resistance. Most of the research which has been done on iron-base glasses containing metalloid addition, in various acids and sodium chloride solutions, although very recently, work has been extended to some metal-metal glasses, for instance in the Ni-Ta series. With respect to Fe-based glasses, the following have been thoroughly established: 1) Most metallic solutes increase corrosion resistance; Cr and Mo are particularly effective, most so in combination. By way of example, a-Fe 72 Cr 8 P 13 C 7 passivates spontaneously in 2 N HC1 (a very powerful corrodant) at ambient temperature, while some glasses containing both Cr and Mo will passivate spontaneously even in hot concentrated HC1.

536

9 Metallic Glasses

2) Metalloids accelerate passivation by aiding the dissolution of all constituents other than the passivating one from a thin surface layer; P has been found to be particularly effective. Accordingly, even small amounts of Cr, « 3 at.%, can lead to much higher surface concentrations of Cr ion than is found on crystalline stainless steels. On Ni-Ta and N i - N b glasses, the cations in the highly effective passive films are almost pure Ta 5+ or N b 5 + . Ni-Ta glass is more resistant to hot phosphoric acid than pure Ta. 9.5.2 Heterogeneous Catalysis and Electrocatalysis Research has been concentrated on catalysts for gas-phase reactions such as the hydrogenation of CO or methanol synthesis, and on electrocatalysts for electrodes used in fuel cells and for electrowinning of metals (see Sec. 9.6.4). The recent literature makes one thing quite clear: while metalmetal glasses often make excellent catalysts, they do so only after treatments which wholly or partly crystallize the surface; unmodified glasses are not effective catalysts. One must therefore think of metallic glasses as precursors for catalysts, although according to a quite recent review (Schlogl, 1985) this was not yet clear at that time. The most comprehensive review, written more with emphasis on the chemical reactions which can be catalysed than on the state of the catalysts, is by a Hungarian group (Molnar et al, 1989); this cites 177 references. Selective oxidation of, or the absorption of hydrogen in, glasses such as Ni-Zr, Cu-Zr or P d - Z r modifies their surface (e.g., the early study by Spit et al., 1981). A recent study by Vanini (1990), using Auger electrons and X-ray diffraction, shows that

hydrogen absorption in various Cu-Zr glasses generates a Cu-enriched surface layers containing Cu microcrystals. A P d Zr glass, activated in CO, O 2 , CO 2 or H 2 , crumbles to a powder consisting of fine Pd and ZrO 2 particles. The catalytic effectiveness of such catalysts depends entirely on the fineness of the crystalline metal particles produced during activation. In both Cu-Zr (Vanini, 1990) and Ni-Zr (Spit et al., 1981) the activity is enhanced because the Cu or Ni can diffuse to the surface along the surface of cracks opened up by the hydrogen activation. Selective oxidation operates in much the same way to provide an activation mechanism as does hydrogen absorption (Schlapbach et al., 1980). Some experiments have also been done with metal-metalloid glassy precursors. Guczi and his coworkers (e.g., Kisfaludi et al., 1987), who sought to catalyze the hydrogenation of CO with Fe-B and F e - N i - B glassy catalysts, found that partially crystallized alloys were more effective than wholly crystalline ones, primarily because in that state, very small iron particles are stabilized. The important Japanese work on activated electrode alloys is outlined in Section 9.6.4.

9.6 Applications Up to the present, the only bulk use of metallic glasses has exploited the soft magnetic properties of certain Fe-based glasses in the form of transformer laminations. However, other magnetic uses, and to a lesser degree electrocatalytic uses, are in the process of developing. The exploitation of the great strength and good toughness of some metallic glasses has, somewhat surprisingly, lagged badly behind other categories of uses.

537

9.6 Applications

Since there is room here only for an outline of what has been done, especially with regard to transformer applications (which is a complex topic in its own right), we cite three important overviews of applications of metallic glasses. Luborsky (1983) has an important overview chapter on applications-oriented magnetic properties, the Proceedings of the Fifth Conference on Rapidly Quenched Metals (Steeb and Warlimont, 1985) have over 200 pages of papers specifically devoted to various types of application, mostly of metallic glasses, and a book on metallic glasses (Anantharaman, 1984) has 4 chapters on applications. 9.6.1 Magnetic Applications

The growing use of wide sheets of Febased metallic glass, made by planar flowcasting, as transformer laminations, is based essentially on two properties of the best of such glasses: a more slender magnetization (hysteresis) loop than grain-oriented Fe-Si sheet, the excellent material used for over half a century for this purpose, can achieve (Fig. 9-29); and a higher electrical resistivity, which reduces induced eddy currents in comparison to the crystalline Fe-Si alloy. The slenderer hysteresis loop is associated with a lower saturation magnetization: this is an inescapable price, because intrinsically, no glass can achieve as good a magnetization as almost pure iron. The gradual recognition that a metallic glass could outperform crystalline alloys which had been gradually perfected over many years led to a progressive improvement of glass compositions as well as technical improvements in the economic production of wide sheets, culminating in the glass composition Metglas® 2605 SC, Fe 81 B 13>5 Si 3 . 5 C 2 ("Metglas" is a trademark of Allied-Signal Corporation); an improved alternative is 2605 S2,

-1.0

-0.5

0 H in A/cm

0.5

Figure 9-29. Comparison of the hysteresis loops at mains frequency for Metglas 2605 SC (0.4 mm thick) and crystalline Fe-3 wt.% Si sheet (0.3 mm thick). (After Hilzinger, reproduced by Anantharaman, 1984.)

Fe 78 B 13 Si 9 . In a classical episode of challenge-and-response, the steel community has set about improving crystalline Fe-Si alloys by increasing the Si content from « 3 to « 6 at.% (with concomitant enhanced resistivity and reduced magnetostriction) by using rapid quenching methods to obviate extreme brittleness, but they have not caught up with the best metallic glasses yet, except for the fact that Fe-Si is still cheaper than metallic glass. Fig. 9-30 shows, on a logarithmic scale, comparative values for the core loss (hysteretic and eddy currents) and the exciting power in watts per kg of core, for oriented and unoriented Fe-Si and for the best metallic glass. The superiority of the glass is very clear. Once the problems of cutting, coating and winding metallic glass sheet on an industrial scale had been solved, a large number of experimental distribution transformers (used in the U.S.A. and Japan to transform supplies down to the domestic voltage of 110 V) were successfully made and evaluated (Natasingh and Liebermann, 1987). Competing designs have also been described (e.g., Schulz et al., 1988). The economics of glass-wound transformers well as a critical comparison with those

538

9 Metallic Glasses 10

M-19 (non-oriented) (0.36mm thick) />'

<

6.5wt%Si-Fe(0.06 mm thick) -

C

1.0

a. o a.

MetglasR2605S2 (0.03 mm thick)

0.1 o

Exciting power Core loss

0.01 0.6 0.8

1.0 1.2 U 1.6 Induction, B in T

1.8

0.01 2.0

Figure 9-30. Core loss and exciting power vs. induction at 60 Hz for annealed grain-oriented Fe6.5 wt.% Si, non-oriented Fe-3.5 wt.% Si alloy M19 and Metglas 2605 S2. (After Das et al., 1985 a.)

ties), recording heads, saturable cores, magnetic switches, magnetometers and other devices used in light electrical engineering. These are well reviewed by Warlimont (1985,1988). Magnetic shielding using woven tubes or sheet made of narrow magnetic glass ribbon (Dismukes and Sellers, 1978) is another important application, bypassing the sensitivity of permalloy sheet (the crystalline competitor) to even the slightest deformation: the shielding achieved by a glass ribbon is not affected by elastic bending. Indeed, Fe-based metallic glasses have the unique distinction of combining magnetic softness with mechanical hardness. 9.6.2 Brazing Foils

using silicon-iron were discussed by Bailey and Lowdermilk (1985). It should be noted that metallic glasses have not yet been used for large power transformers (presumably because sheets cannot be made sufficiently wide). Metallic glasses are only just beginning to make inroads into the high-frequency (kHz) regime, though suitable glasses have been developed. Datta et al. (1982) have reported on Metglas® 2605 S3, Fe 70 B 16 Si 5 , which at up to 100 kHz shows core losses below those for supermalloy and a highfrequency ferrite. It seems also that very small fractions of a-iron precipitates in the glass help to reduce losses. Glasses do not as yet seem particularly promising for motor windings, which is a very large and lucrative market; this market is particularly sensitive to price, and this may well be the principal reason. Metallic glasses have, however, been used for a range of small-scale applications, many developed in Japan and Germany; these include sensors and transducers (exploiting magnetostrictive proper-

One of the less obvious commercial applications of metallic glasses is for brazing (DeCristofaro and Bose, 1986; Liebermann and Rabinkin, 1988). Until recently, furnace brazing of complex assemblies was performed by placing low-melting brazing alloy in powder form, as a paste, between the components to be joined. Most of the crystalline alloys used are brittle and therefore cannot be shaped as sheet. The use of powder is messy and impossible to dose accurately. It has been found that brazing alloys can also be made by melt-quenching in the form of amorphous sheets. Examples of such glass sheets are: Cu-P, Ni-Si (B, P), C o - S i - P , Cu-Ti-Ni. (Other combinations have been melt-quenched in the form of microcrystalline sheets.) Such sheets are ductile even when crystalline alloys of the same compositions are highly brittle, so that preforms can be stamped out in elaborate shapes to fit precisely between the components in a brazing operation. - The alloy compositions are chosen by criteria such as good GFA, low melting temperature, low surface tension and constituents

539

9.6 Applications

Table 9-3. Tensile properties of various continuous filaments and ribbons. Material

S-glass (SiO 2 -Al 2 O 3 -MgO) C fibre (high-yield PAN type)a B filament (on W core)a SiC microcrystalline filament3 Kevlar fibre (organic polymer)b High-C steel wire Fe 80 B 20 met glass b Ti

5oBe4oZrio

met

- Slassb

Ti6OBe35Si5 met glassb Cu 50 Zr 50 met glass b Al87Y8Ni5 met glassb a b

Yield stress
Relative density d

5.0 3.2 2.5-4.5 3.5 2.8 4.2 3.6 2.3 2.5 1.8 ~1.1

2.5 2.6 2.6 2.6 1.5 7.9 7.4 4.1 3.9 7.3 -3.0

ffytT^GPa)

2.0 1.7 1.0-1.7 1.4 1.9 0.55 0.5 0.55 0.65 0.25 0.38

Young's modulus E(GPa) 85 490 380 200 135 210 170 105 -110 85 71

Ed-^GPa) 34 153 146 77 90 27 23 26 -28 12 24

Indicates heat-resistant materials. Indicates materials with some ductility.

which reduce surface oxides on the components to be joined. 9.6.3 Mechanical Properties

The high strength and toughness of a number of metallic glasses, combined with adequate stiffness, has often been remarked, and the natural assumption has been made that such glasses should be useful for applications such as reinforcement in composites and cutting utensils. However, no signs of such uses have appeared in the market-place. For some years, representatives of razor blade manufacturers haunted conferences at which metallic glasses were being discussed, but this has ceased and no glassy razor blades have appeared yet. (One can have an enjoyable time speculating on advertisement strategies for such blades, were they ever to be marketed!) Perhaps it is impossible to grind an edge on a metallic glass without local crystallization? - Exceedingly sharply pointed metallic glass needles for eye surgery have been developed and are now in use (J. V. Wood, priv. comm.). It has not

been revealed whether the point was created by mechanical means or by an electrolytic process. - It has been pointed out (Warlimont, 1980) that some metallic glasses have exceptionally high bend fatigue resistance, and this suggests use of glass ribbons for springs exposed to numerous alternating loads. Table 9-3 (Cahn, R.W., 1980) compares mechanical properties of a number of potential and actual reinforcing fibers and ribbons, with special attention to densitycompensated strength and stiffness. It can be seen that most metallic glasses are let down by their high densities, compared with materials such as graphite and Kevlar. The Be-containing glasses were at one time considered very promising but have never been put into production because of the health hazards associated with beryllium. Much interest attaches to the new Al-bearing glasses (see Sec. 9.3.1); one of the strongest representatives of this family is included in Table 9-3. It has been pointed out (Bechet et al, 1989) that the best Al-base glasses are twice as strong as the strongest commercial crystalline Al-

540

9 Metallic Glasses

base alloys, and that their corrosion resistance is very much better than that of any commercial aluminum alloys. Experiments were done some years ago on polymer matrix composites reinforced with metallic glass ribbons (Fels et al., 1984) and reasonable reinforcement was observed. Recently, this approach has been taken to the next stage in experiments to reinforce glass ceramics with small volume fractions of metallic glass ribbons (Vaidya and Subramanian, 1990). Both 2605 SC and a N i - C o - M o - F e - B glass, each a commercial product, were tried; the latter is the stronger (1300 MPa yield strength) and has a high crystallization temperature ( « 605 °C). The glass precursor in the form of powder is assembled with parallel ribbons and heated to 400-450 °C, at which temperature the glass first sinters and then crystallizes, to give a porosity-free matrix, without crystallizing the metallic glass ribbons. The modulus of rupture was doubled by as little as ^ 1 vol.% of glass ribbon, and the fracture toughness enhanced more than 3-fold. - It has been suggested that instead of using ribbons, fine wires made by the in-rotating-water melt-quenching approach could be used, and Hagiwara etal. (1985) have shown that Fe-based glass wires, strengthened by additions of Nb, Ta, Cr or Mo, can combine high yield strengths with exceptionally high fatigue strengths. A further possible use of such wires is as reinforcement for motor tires, another very large market. This was first suggested by Ohnaka (1985), who developed the in-rotating-water melt-quenching process to make wires of ^0.1 mm diameter, and subsequently it was shown by an American company that Fe-Si-B amorphous wires, with a suitable coating, fulfilled the requirements of tire reinforcement, which are: a high tensile strength, good adhesion

to rubber, and excellent resistance to fatigue and corrosion (Ogino, 1986). Japanese investigators are also pursuing this application. Reinforcement in composites, as in the pioneering experiments just described, would seem the most likely applications exploiting the mechanical properties of metallic glasses, but it is also possible that pieces of substantial dimensions might be made by consolidating metallic glass powders; this can be done by warm isostatic pressing or explosive compaction without crystallizing the powder. Bechet et al. (1989) pointed out that Al-base glasses can readily be made in the form of powders. However, applications for Al-based glasses are at this stage still speculative. A number of experiments on the wear and frictional properties of metallic glasses have been reported, but at this stage no clear generalizations have emerged. Some amorphous coatings, notably (W 06 Re 0 4 ) 7 6 B 2 4 , have proved to give very large improvements in wear resistance over uncoated steel (Thakoor et al., 1985). 9.6.4 Chemical Properties

The excellent corrosion resistance of a number of metallic glasses suggests their use as a protection in aggressive environments. The problem is that objects such as containers can scarcely be made entirely of metallic glass, and so for some uses it is essential to think in terms of glassy coatings. This has been done successfully by laser-amorphization (Vol. 15, Chap. 3) of coatings of suitable composition on conventional substrates, for instance mild steel. The composition must be carefully chosen because, with laser amorphization, the overlap between successive passes of the focused laser beam across the surface can lead to localized crystallization. How-

9.6 Applications

ever, by the use of suitable optics, a laser can be used to amorphize difficult surfaces, for instance, the inside of a vessel. Fig. 9-31 shows the electrochemical characteristics of a Cr-rich metallic glass made in situ and compares it with the same glass made by a conventional melt-spinning process and with the corresponding crystalline alloy. An alternative process, which allows coating and amorphization to be achieved in one step, is sputtering. A number of amorphous layers have been produced in this way and some have been found to evince remarkable corrosion protection (Hashimoto, 1992; Diegle and Hashimoto, 1988). The technique has the incidental advantage, as we saw earlier, that amorphous alloys can be made over a wide composition range. Amorphous Cu-Ta (2080at.%Ta) has been found to passivate spontaneously even in 12 N HC1; it behaves much better than crystalline Ta, itself notably resistant to acids. Some applications can use melt-spun glasses directly, without any coating stage. Thus, a - F e - C r - P - C ribbons were used as the active element in electromagnetic filters to remove rust from water (Kawashima et al., 1985). Since the field is strongest at the edges of ribbons, narrow ribbons were used. Their high corrosion resistance ensured a long life for the filter elements. The Japanese group which has made much of the running in corrosion and electrochemical research concerned with metallic glasses has also developed amorphous materials for electrocatalytically active electrodes (Hashimoto, 1992). The aim is to make electrodes highly active for specific electrochemical reactions. Thus, for example, chlorine is made by electrolysis of hot concentrated sodium chloride solutions, and anodes are needed with a high electrocatalytic activity for Cl2 evolution and a low activity for O 2 evolution, a par-

541

Ni-15Cr-16P-4B 1N HCl 30°C

10:

c CD XJ

10"

-0.5

0

0.5 Potential in V

Figure9-31. Electrochemical characteristics in I N HCl of a N i - C r - P - B metallic glass prepared by melt-spinning or surface laser-amorphization, compared with the same alloy before amorphization. (After Yoshioka et al., 1987.)

asitic process. None of the platinum group metals combine the required activity with good corrosion resistance, but Pd-based glasses have been found to have the necessary combination of properties. - These alloys however were found not to be good enough for the electrolysis of seawater, which is much more dilute than the normal industrial brines. The answer to this was found to be the introduction, by low-temperature diffusion, of zinc into the surface layers of a glassy electrode followed by a leaching process in hot alkali solution to remove the zinc again. In this way, the specific surface area is greatly increased, enhancing the electrocatalytic activity. Because of the high resistivity of metallic glasses, which is a disadvantage in electrodes, the Japanese group has developed ways of coating glassy surface layers on normal high-conductivity metals. The electrodes used in extractive metallurgy to produce metals electrolytically have also been improved by exploiting metallic glasses. Here, surfaces combining electrode activity with corrosion resistance have been made by combining glasses such

542

9 Metallic Glasses

as N i - N b and Ni-Ta with a few per cent of platinum group elements (Diegle and Hashimoto, 1988). 9.6.5 Diffusion Barriers

In the manufacture of complex multilevel integrated circuits, diffusion barriers are necessary between Si and the Al metallization applied to make interconnections between circuit elements, because Si and Al would react at high temperatures, either during the later stages of circuit manufacture or (for some circuits) during high-temperature service. Many crystalline barriers have been tried, but in 1981, at the First High-Temperature Electronics Conference, the use of a metallic glass was proposed, and a variety of metal-metal binary glasses were soon shown to be effective. (The early history of this concept, with its advantages and difficulties, is surveyed by Cahn (1986 b).) The underlying principle is shown in Fig. 9-32. Gold (used as a model diffusant) diffuses much more slowly in aNi 5 5 Nb 4 5 than it does in the same alloy in crystalline form, at relatively low temperatures, because in this temperature range,

diffusion in polycrystals is dominated by grain-boundary transport, which is entirely excluded in a glass. As can be seen in the figure, at 400 °C the difference in diffusivity is seven orders of magnitude! Approximately equiatomic Ta-Ir glasses, the most resistant to crystallization known (and therefore also particularly resistant to diffusion), with T cryst «900 °C, were suggested to be the best material to use for diffusion barriers. The most recent studies of this glass (de Reus, 1990) has shown negligible interdiffusion up to 800 °C. Nevertheless, such glasses can give problems at the higher temperatures owing to chemical reaction with either Si or Al, and this may be the factor that effectively limits the maximum temperature of use. Another reputed problem with Ta-Ir diffusion barriers is that the glass is so very stable that it resists all etching processes associated with lithographic circuit-shaping procedures. Ta-Ir glassy alloy has been used to make effective diffusion barriers between Si substrates and Y - B a - C u - O ceramic superconductor layers (de Reus et al., 1988). 9.6.6 Metallic Precursors for Devitrification

_ 70Q 600 10 u

T in 500

400

300 10 urn

\ Amorphous ^ ^B Polycrystal \

10-'

1um

g

> 10" ;

10r 20 -

0.1 urn ~

\ Diffusion of Au in NiNb

\

"

1.0

100 A \ \ ,

1.2 U 1000/ T in K

, - 10 A

1.6

Figure 9-32. Diffusivity of gold in amorphous and polycrystalline Ni 5 5 Nb 4 5 . The righthand ordinate shows the diffusion distance in a period of one year. (After Doyle et al., 1982.)

The use of highly alloyed metal glasses as precursors for the production of finegrained crystalline alloys has received some attention, although very little by comparison with the effort which has gone into the design of glass-ceramics. The first serious research was by Ray (1981): his alloys were based on Fe, Ni, Al, Cr, Mo, Co and W in multiple combinations, with 5 12 at.% of B or other metalloids as glassforming aids. This interesting work has not received any follow-up until very recently, when Arnberg et al. have developed a range of tool steels by devitrification of glassy F e - C r - M o - C - B or F e - C r - M o -

543

9.8 References

C-V glasses (Arnberg, 1991). Subsequent to Ray's work, alloy developments along similar lines were by Das et al. (1985 b) and by Vineberg et al. (1985). Das et al. developed N i - M o - B and N i - A l - T i - X - B alloys, and later other N i - M o - B alloys with added Cr. These alloys were made by meltquenching, comminution and consolidation by extrusion or HIPping (Vol. 15, Chap. 4). During the processing, ordered phases including Ni 4 Mo, Ni 3 Mo, Ni 2 Mo and Ni3(Al,Ti) are precipitated from the crystallized matrix, together with stable boride precipitates. This family of alloys is now manufactured commercially under the trade name Devitrium® (Vineberg, 1985). The best of these alloys have very impressive high-temperature properties, exceeding high-grade tool steels. By far the most industrially important development of this kind is connected with rare-earth permanent magnets. The modern family of magnets based on the highcoercivity phase Nd 2 Fe 14 B can be made either by sintering an alloy powder or by melt-spinning the alloy to form a glass which is then devitrified (or, alternatively, quenching direct to a microcrystalline structure). The melt-quenching method was introduced by Croat et al. (1984) and culminated in a full-scale industrial process for making magnets. The various complications and improvements along the way are surveyed in a major review by Buschow (1986). Fig. 9-33 shows diagrammatically why there is an optimum quenching rate for this process, whether by direct quenching to a microcrystalline phase or by formation of a glass followed by reheating. The hard magnetic phase is desired, the alternative soft magnetic phase must be completely avoided, and a fine grain size is desirable for high coercivity. The process of devitrifying glass precursors in the N d - F e - B system is still receiving exten-

continuous cooling quenching and annealing onset of crystallization soft magnetic phase O \ —

hard magnetic phase I decreasing Tgrain size

W Time

Figure 9-33. Schematic time-temperature-transformation diagram to rationalize optimum conditions for producing N d - F e - B permanent magnets. (After Warlimont, 1985.)

sive attention: thus Jha et al. (1991) have established the formation of a metastable intermediate phase during the devitrification; the nature of the Nd 2 Fe 14 B phase itself was found to change progressively during the anneal, as indicated by a gradual change in the Curie temperature. A beginning has now also been made in using the devitrification approach for making nanocrystalline soft magnetic alloys, for instance a series of Fe-Cu-Nb-Si-B compositions (Herzer, 1991). Nanocrystallinity in such alloys presumably derives from exceedingly copious homogeneous nucleation during crystallization.

9.7 Acknowledgement I am greatly indebted to Dr. A. L. Greer for a critical reading of this chapter.

9.8 References Anantharaman, T. R. (Ed.) (1984), Metallic Glasses Production, Properties and Applications. Aedermannsdorf: Trans. Tech., pp. 203-292.

544

9 Metallic Glasses

Aoki, K., Li, X. G., Masumoto, T. (1991), paper presented at 7th. Conf. on Rapidily Quenched Metals, Stockholm, 1990. To be published in Mater. Sci. Eng. Argon, A. S., Megusar, I, Grant, N. I (1985), Scripta Metall. 19, 591. Arnberg, L., Larsson, E., Savage, S., Inoue, A., Yamaguchi, S., Kikuchi, M. (1991), paper presented at 7th Conf. on Rapidly Quenched Metals, Stockholm, 1990. To be published in Mater. Sci. Eng. Atzmon, M., Unruh, K. M., Johnson, W. L. (1985), J. Appl. Phys. 22, 707. Bagley, B. S., Chen, H. S. (1979), in: Laser-Solid Interactions and Laser Processing - 1978: Ferris, S. D., Leamy, H. X, Prate, J. M. (Eds.). Amer. Inst. Phys. Conf. Proc. Vol. 50, p. 97. Bailey, D.J., Lowdermilk, L. A. (1985), in: Rapidly Quenched Metals (Proc. 5th Conf.): Steeb, S., Warlimont, H. (Eds.). Amsterdam: North-Holland, pp. 1625-1628. Barbour, J. C , de Reus, R., Denier van der Gon, A. W, Saris, F.W. (1987), J. Mater. Res. 2, 169. Battezzati, L. (1990), Phil Mag. B 61,511. Battezzati, L., Greer, A.L. (1989), Acta Metall. 37, 1791. Bechet, D., Regazzoni, G., Dubois, J.-M. (1989), Pour la Science (May), n° 139, p. 30. Beke, D.L., Bakker, H., Loeff, P.I. (1990), /. de Physique France (Colloques) 51, C4, 63-69. Bergmann, G. (1976), Physics Reports 27, 159. Bhatnagar, A.K., Rhie, K.W., Naugle, D.G., Wolfenden, A., Zhang, B. H., Calloway, T. O., Bruton, W.D., Hu, C.-R. (1990), J. Phys. Condens. Matter 2, 2625. Bickerdike, R.L., Clark, D., Eastabrook, J.N., Hughes, G., Mair, W. N., Partridge, P. G., Ranson, H.C. (1986), Internat. J. of Rapid. Solidif. 2, 1. Bloch, J. (1962), /. Nucl. Mater. 6, 203. Bordeaux, R, Yavari, A. R. (1990), /. Appl. Phys., in press. Bormann, R., Gartner, F., Haider, F. (1988), Mater. Sci. Eng. 97, 97. Brenner, A. (1963), Electrodeposition of Alloys: Principles and Practice, 2nd Ed. New York: Academic Press. Brenner, A., Couch, D. E., Williams, E. K. (1950), /. Res. Nat. Bur. Stand. 44, 109. Buckel, W. (1954), Z. Phys. 138, 136. Buckel, W, Hilsch, R. (1952), Z. Phys. 131, 420; (1954), Z. Phys. 8, 109; (1956), 146, 27. Buschow, K.H.J. (1982), Solid State Commun. 43, 111. Buschow, K.H.J. (1984), J. Phys. F14, 593. Buschow, K.H.J. (1986), Mater. Sci. Reports 1, 1. Cahn, J. W. (1980), in: Rapid Solidification Processing, Principles and Technologies II: Mehrabian, R., Kear, B.H., Cohen, M. (Eds.). Baton Rouge: Claitor's Publishing Division, pp. 24-34. Cahn, R.W. (1980), Contemp. Phys. 21, 43.

Cahn, R. W. (1982), J. de Physique France (Colloques) 43, C9. Cahn, R.W. (1983), in: Physical Metallurgy: Cahn, R.W, Haasen, R.W. (Eds.). Amsterdam: NorthHolland, pp. 1779-1852. Cahn, R.W (1986a), in: Science and Technology of the Undercooled Melt: Sahm, P. R., Jones, H., Adam, C. M. (Eds.). Dordrecht: Martinus Nijhoff, pp. 73-80. Cahn, R.W (1986b), /. Vac. Sci. Technol. A4, 3071. Cahn, R.W. (1989), Nature 341, 183. Cahn, R.W (1990), in: Basic Features of the Glassy State: Colmenero, X, Alegria, A. (Eds.). Singapore: World Scientific, pp. 282-296. Cahn, R. W, Johnson, W L. (1986), / Mater. Res. 1, 724. Cahn, R.W, Pratten, N. A., Scott, M.G., Sinning, H.R., Leonardsson, L. (1984), Mat. Res. Soc. Symp. Proc. Vol. 28, pp. 241-252. Calka, A., Radlinksi, A. P. (1989), Mat. Sci. Eng. A 118, 131. Calvo, M. (1991), paper presented at 7th Int. Conf. on Rapidly Quenched Metals, Stockholm, 1990. To be published in Mater. Sci. Eng. Cantor, B. (1986), in: Amorphous Metals and Semiconductors: Haasen, P., Jaffee, R. I. (Eds.). Oxford: Pergamon Press, pp. 108-123. Chason, E.H., Mizoguchi, T. (1987), Mat. Res. Soc. Symp. Proc, Vol. 80, 61-67. Chason, E.H., Greer, A.L., Kelton, K.F., Pershan, P. S., Sorensen, L., Spaepen, F., Weiss, A. H. (1985), Phys. Rev. B32, 3399. Chaudhari, P., Spaepen, F, Steinhardt, P. J. (1983), in: Glassy Metals II: Beck, H., Giintherodt, H.-J. (Eds.). Berlin: Springer, pp. 127-168. Chen, L.C., Spaepen, F. (1988), Nature 336, 366. Chen, L. C , Spaepen, F. (1991), J. Appl. Phys. 69, 679. Chen, H.S., Kimerling, L.C., Poate, J.M., Brown, WL. (1978), Appl. Phys. Lett. 32, 461. Clemens, B.M., Gilgenbach, R.M., Bidwell, S. (1987), Appl. Phys. Lett. 50, 495. Comberg, A., Ewert, S., Wuhl, H. (1975), Z. Phys. B.20, 165. Croat, J. X, Herbst, R. W, Lee, R. W, Pinkerton, F. E. (1984), J. Appl. Phys. 55, 2078. Dahlgren, S.D. (1983), in: Proc. 3rd Int. Conf. on Rapidly Quenched Metals (Rapidly Quenched Metals III), Vol.2: Cantor, B. (Ed.). London: Metals Society, pp. 36-47. Das, S. K., DeCristofaro, N. X, Davis, L. A. (1985 a), in: Rapidly Quenched Metals (Proc. 5th Int. Conf.): Steeb, S., Warlimont, H. (Eds.). Amsterdam: North-Holland, pp. 1621-1624. Das, S.K., Okazaki, K., Adam, C M . (1985b), in: High Temperature Alloys - Theory and Design: Stiegler, X O. (Ed.). Warrendale: The Metallurgical Society, p. 451. Datta, A., DeCristofaro, N.X, Davis, L.A. (1982), in: Proc. 4th Int. Conf on Rapidly Quenched

9.8 References

Metals: Masumoto, T., Suzuki, K. (Eds.). Sendai: Japan Inst. of Metals, pp. 1007-1010. Davies, H. A. (1976), Phys. and Chem. of Glasses 17, 159. Davies, H.A. (1978), in: Proc. 3rd Int. Conf. on Rapidly Quenched Metals (Rapidly Quenched Metals III): Cantor, B. (Ed.). London: Metals Society. Vol. l,pp. 1-21. DeCristofaro, N., Bose, N. (1986), in: Rapidly Solidified Materials: Lee, P. W., Carbonara, R. S. (Eds.). Metals Park: American Society for Metals, pp. 415-424. Denier van der Gon, A. W., Barbour, J. C , de Reus, R., Saris, F.W. (1987), /. Appl. Phys. 61, 1212. de Reus, R. (1990), Doctoral Dissertation, Utrecht. de Reus, R., Saris, F. W., Bailer, T. S. (1988), /. LessCommon Metals, 145, 621. Diegle, R.B., Hashimoto, K. (Eds.) (1988), Proc. Symposium on Corrosion, Electrochemistry and Catalysis of Metallic Glasses. Pennington: The Electrochemical Society. Dietz, G. (1977), /. Magn. & Magn. Mater. 6, 47. Dismukes, I P . , Sellers, G.J. (1978), in: Rapidly Quenched Metals III, Vol. 2: Cantor, B. (Ed.). London: The Institute of Metals, pp. 205-212. Dixmier, X, Guinier, A. (1970), Fizika (Belgrade) 2 (Supplement 2), 9.1. Donald, I.W., Davies, H.A. (1978), /. Non-Cryst. Solids 30, 77. Doyle, B. L., Peercy, P. S., Wiley, J. D., Perepezko, X H., Nordman, X E. (1982), J. Appl. Phys. 5, 6168. Drehman, A. X, Greer, A. L. (1984), Acta Metall. 32, 323. Duflos, B., Cantor, B. (1982), Acta Metall. 30, 323. Dubey, K.S., Ramachandrarao, P. (1990), Int. J. of Rapid Solidif 5, 127. Duwez, P. (1951), Trans. Amer. Inst. Min. Met. Engrs. 191, 765. Duwez, P. (1967 a), Trans. Amer. Soc. Metals 60, 607. Duwez, P. (1967 b), in: Progress in Solid-State Chemistry, Vol.3: H. Reiss (Ed.). Oxford: Pergamon Press, pp. 377-406. Duwez, P., Willens, R. H., Klement, Jr., W. (1960), /. Appl. Phys. 31, 36. Duwez, P., Willens, R. H., Crewdson, R. C. (1965), / Appl. Phys. 36, 2267. Egami, T. (1978), /. Mater. Sci. 13, 2587. Egami, T. (1981), in: Structure and Mobility in Molecular and Atomic Glasses, Ann. New York: Acad. Sci. Vol. 371, pp. 238-251. Egami, T. (1986), in: Amorphous Metals and Semiconductors: Haasen, P., Jaffee, R.I. (Eds.), Oxford: Pergamon, pp. 222-240. Egami, T, Aur, S. (1987), J. Non-Cryst. Solids 89, 60. Egami, T, Waseda, Y (1984), J. Non-Cryst. Solids 64, 113. Evetts, X E., Hodson, P. E. (1985), in: Steeb, S., Warlimont, H. (Eds.): Rapidly Quenched Metals (Proc. 5th Int. Conf). Amsterdam: North-Holland, pp. 671-674.

545

Faupel, R, Hiippe, P.W., Ratzke, K. (1990), Phys. Rev. Lett. 65, 1219. Fecht, H.X, Johnson, W.L. (1990), /. Non-Cryst. Solids 117/118, 704. Fels, A., Friedrich, K., Hornbogen, E. (1984), J. Mater. Sci. Lett. 3, 569, 639. Frank, W, Horvath, X, Kronmiiller, H. (1988), Mater. Sci. Eng. 97, 415. Gardiner, R.W., McConnell, M. C. (1987), Metals and Materials 3, 254. Gartner, F , Bormann R. (1990), J. de Physique France (Colloques) 51, C4-95. Gerasimov, K. B., Gusev, A. A., Ivanov, E. Yu., Boldyrev, V. V. (1991), J. Mater. Sci., in press. Gerling, R., Schimansky, F. P., Wagner, R. (1985), in: Rapidly Quenched Metals (V): Steeb, S., Warlimont, H. (Eds.). Amsterdam: North-Holland, pp. 1377-1380, (1988), Acta Metall. 36, 575, (1989), Acta Metall. 37, 2961, (1990), Int. J. Rapid Solidification 5, 137. Ghosh, G., Chandrasekaran, M., Delaey, L. (1991), Acta Metall. 39, 37. Gibbs, M.R.X, Evetts, J.E., Leake, X A. (1983), /. Mater. Sci. 18, 278. Giessen, B. C. (1981), Proc. 4th Int. Conf. on Rapidly Quenched Metals: Masumoto, T, Suzuki, K. (Eds.). Sendai: Japan Institute of Metals, pp. 213216. Gillen, A.G., Cantor, B. (1985), Acta Metall. 33, 1813. Graham, Jr., C. D. (1959), in: Magnetic Properties of Metals and Alloys. Cleveland: Amer. Soc. Metals, pp. 288-329. Greer, A. L. (1982), Acta Metall. 30, 171. Greer, A. L. (1988), Mater. Sci. Eng. 97, 285. Greer, A.L. (1989), in: Advanced Metallic and Ceramic Materials, Proceedings of an EC/ Yugoslavia Colloquium: Rogers, M. D., Jovicevic, X (Eds.). EUR 12274 EN. Luxembourg: Commission of the European Communities, pp. 183-202. Greer, A. L. (1990), Phil. Mag. B61, 525. Greer, A. L., Spaepen, F. (1981), in: Structure and Mobility in Molecular and Atomic Glasses, Ann. N.Y. Acad. Sci., Vol. 371, pp. 218-234. Greer, A. L., Dyrbye, K., Aaen Andersen, L.-U., Somekh, R. E., Bottiger, X, Janting, X (1990), Mat. Res. Soc. Symp. Proc. 187, 3-14. Hafner, X (1981), in: Glassy Metals I: Guntherodt, H.-X, Beck, H. (Eds.). Berlin: Springer-Verlag, pp. 93-140. Hafner, X (1983), Phys. Rev. B28, 1734. Hafner, X (1986), in: Amorphous Metals and Semiconductors: Haasen, P., Jaffee, R.I. (Eds.). Oxford: Pergamon, pp. 151-167. Hagiwara, M., Inoue, A., Masumoto, T. (1985), in: Rapidly Quenched Metals (Proc. 5th Conf.): Steeb, S., Warlimont, H. (Eds.). Amsterdam: North-Holland, pp. 1779-1782. Harris, X H., Curtin, W. A., Schultz, L. (1988), J. Mater. Res. 3, 872.

546

9 Metallic Glasses

Haruyama, O., Asahi, N. (1991), J. Mater. Sci. 26, 1851. Hashimoto, K. (1985), in: Rapidly Quenched Metals (Proc. 5th Int. Conf): Steeb, S., Warlimont, H. (Eds.). Amsterdam: North-Holland, pp. 14491456. Hashimoto, K. (1992), in: Rapidly Solidified Alloys Processes, Structures, Properties and Applications: Liebermann, H.H. (Ed.). New York: Dekker. In press. Haug, E., Hedgecock, N., Buckel, W. (1975), Z. Phys. B22, 237. Hayzelden, C , Rayment, J. X, Cantor, B. (1983), Acta Metall 1, 379. He, Y, Poo, S.I, Shiflet, G.J. (1988), Science 241, 1640. Herzer, G. (1991), Mater. Sci. Eng. A133, 1. Highmore, R.J. (1990), J. de Physique France (Colloques)^, C4-37. Highmore, R. X, Greer, A. L. (1989), Nature 339, 363. Hoshino, S., Laitinen, H.A., Hoflund, G. B. (1986), /. Electrochem. Soc. 133, 681. Huizer, E., van den Beukel, A. (1987), Acta Metall. 35, 2843. Inoue, A., Masumoto, T. (1990), in: Second Supplementary Volume of the Encyclopedia of Materials Science and Engineering: Cahn, R. W. (Ed.). Oxford: Pergamon, pp. 660-667. Jha, A., Buckley, R. A., Davies, H. A. (1991), Mater. Sci. Eng. A133, 490. Johnson, W.L. (1986), Progr. Mater. Sci. 30, 81. Johnson, W. L., Atzmon, A., van Rossum, M., Dolgin, B. P., Yeh, X. L. (1985), in: Rapidly Quenched Metals V: Steeb, S., Warlimont, H. (Eds.). Amsterdam: North-Holland, pp. 1515-1519. Johnson, W. L., Yeh, X.L., Atzmon, M. (1985), in: Amorphous Metals and Semiconductors: Haasen, P., Jaffee, R.I. (Eds.). Oxford: Pergamon Press, pp. 168-177. Kamrava, S.X, Soderholm, S. (1990), /. Mater. Res. 5, 1697. Kawashima, A., Asami, K., Sato, T., Hashimoto, K. (1985), in: Rapidly Quenched Metals (Proc. 5th Conf): Steeb, S., Warlimont, H. (Eds.). Amsterdam: North-Holland, pp. 1671-1674. Kelton, K.F., Greer, A. L. (1986), /. Non-Cryst. Solids 79, 295. Kijek, M. M., Palmer, D. W, Cantor, B. (1986), Acta Metall. 34, 1455. Kirchheim, R. (1988), Progr. Mater. Sci. 32, 261. Kirchheim, R., Sommer, R, Schluckebier, G. (1982), Acta Metall. 30, 1054. Kirchheim, R., Kieninger, W, Huang, X. Y, Filipek, S. M., Rush, X, Udovic, T. (1991), /. Less-Common Metals (in press). Kisfaludi, G., Schay, Z., Guczi, L., Konczos, G., Lovas, A., Kovacs, P. (1987), Appl. Surf. Sci. 28,111. Kissinger, H.E. (1957), Analytical Chem. 29, 1702. Klement, Jr., W, Willens, R.H., Duwez, P. (1960), Nature 187, 869.

Koster, U. (1984), in: Amorphous Metals and NonEquilibrium Processing: von Airmen, M. (Ed.). Paris: Editions de Physique, p. 175. Koster, U., Herold, U. (1981), in: Glassy Metals I: Giintherodt, H.-X, Beck, H. (Eds.). Berlin: Springer, pp. 225-259. Koster, U., Schiinemann, U. (1992), in: Rapidly Solidified Alloys: Liebermann, H. H. (Ed.). New York: Dekker. In press. Kramer, X (1934), Ann. Phys. 19, 37; Z. Phys. 106, 675. Krishnanand, K.D., Cahn, R.W. (1975), Scripta metall. 9, 1259. Kui, H.-W, Greer, A.L., Turnbull, D. (1984), Appl. Phys. Lett. 45, 615. Kiinzi, H.-U. (1983), in: Glassy Metals II: Beck, H., Giintherodt, H.-X (Eds.). Berlin: Springer, pp. 169-216. Lashmore, D. S., Weinroth, X F. (1982), Plating and Surface Finishing, (August), 72. Lashmore, D.S., Bennett, L.H., Schone, H.E., Gustafson, P., Watson, R.E. (1982), Phys. Rev. Lett. 48, 1760. Leake, X A., Woldt, E., Evetts, X E. (1988), Mater. Sci. Eng. 97, 469. Lee, P. Y, Jang, X, Koch, C.C. (1988), J. Less-Common Metals 140, 73. Legresy, J.M, Blanpain, B., Mayer, XW. (1988), /. Mater. Res. 3, 884. Leusink, G.X, van den Beukel, A. (1988), Acta Metall. 36, 3019. Liebermann, H. H., Rabinkin, A. (1988), in: Encyclopedia of Materials Science and Engineering, Supplementary Volume 1: Cahn, R.W. (Ed.). Oxford: Pergamon, pp. 59-63. Liebermann, H. H., Marti, X, Martis, R. X, Wong, C.P. (1989), Metall. Trans. 20 A, 63. Limoge, Y (1990), Acta Metall. 38, 1733. Lin, C.-X, Spaepen, F. (1984), MRS Symp. Proc. Vol. 28, pp. 75-80. Liu, P. L., Yen, R., Bloembergen, B., Hodgson, R. T. (1979), Appl. Phys. Lett. 34, 864. Luborsky, RE. (1980), in: Ferromagnetic Materials: Wohlfahrt, E.P. (Ed.). Vol. 1. Amsterdam: NorthHolland, 451-529 (esp. pp. 511-514). Luborsky, RE. (1983), in: Amorphous Metallic Alloys: Luborsky, R E. (Ed.). London: Butterworth, pp. 360-380. Luborsky, RE., Becker, XX, Walter, XL., Liebermann, H. H. (1979), IEEE Trans. Magn. MAG-13, 953, 1653. Luzzi, D.E., Meshii, M. (1986), Scripta Metall. 20, 943. Luzzi, D.E., Meshii, M. (1988), /. Less-Common Metals 140, 193. Macedo, P.B., Napolitano, A. (1967), J. Res. NBS, 71 A, 231. Mader, S., Nowick, A. S., Widmer, H. (1967), Acta Metall. 15, 203, 215.

9.8 References

Martin, G., Gaffet, E. (1990), J. de Physique France (Colloques) 51, C4-71. Massalski, T. B. (1986), in: Amorphous Metals and Semiconductors: Haasen, P., Jaffee, R.I. (Eds.). Oxford: Pergamon, pp. 178-187. Massalski, T. B., Woychik, C. G. (1985), Ada Metall 33, 1873. Mehrer, H., Dorner, W. (1989), Defect and Diffusion Forum 66/69, 189. Meng, W. X, Nieh, C. W, Ma, E., Fultz, B., Johnson, W. L. (1988), Mater. Sci. Eng. 97, 87. Molnar, A., Smith, C.V., Bartok, M. (1989), Advances in Catalysis, 36, 329. Morris, D.G. (1982), Acta Metall. 29, 1213. Motorin, V.I. (1983), Phys. Stat. Sol. (a) 80, 447. Muller, W. H.-G., Baumann, R, Buckel, W. (1975), Thin Solid Films 28, 83. Nachtrieb, N. H. (1976), Ber. Bunsenges. Phys. Chem. 80, 678. Nagel, S.R., Tauc, J. (1977), Solid State Comm. 22, 129. Nash, P., Schwarz, R. B. (1988), Acta Metall. 36, 3047. Natasingh, D.M., Liebermann, H.H. (1987), IEEE Trans, on Power Delivery, Vol. PWRD-2, no. 3, 843. Newcomb, S.B., Tu, K.N. (1986), Appl. Phys. Lett. 48, 1436. Ogino, T. (1986), French patent 2 569143. Ohnaka, I. (1985), Int. J. Rapid Solidification 1, 219. Okamoto, P. R., Rehn, L. E., Pearson, I, Bjhadra, R., Grimsditch, M. (1988), J. Less-Common Metals, 140, 231. Piller, I, Haasen, P. (1982), Acta Metall. 30, 1. Poate, J.M., Peercy, P. S., Thompson, M.O. (1987), Mat. Res. Soc. Symp. Proc. Vol. 57, 466. Polk, D.E. (1972), Acta Metall. 20, 485. Polk, D. E., Giessen, B. C. (1978), in: Metallic Glasses: Gilman, XI,. Leamy, H.X (Eds.). Metals Park: American Society for Metals, pp. 1-35. Polman, A., Jacobson, D. C , Coffa, S., Poate, X M., Roorda, S., Sinke, W.C. (1990), Appl. Phys. Lett., in press. Ponyatovsky, E.G., Barkalov, O. I. (1991), Mater. Sci. Eng. A133, 726. Ramachandrarao, P. (1980), Z. Metallkde. 71, 172. Ramachandrarao, P. (1984), in: Metallic Glasses Production, Properties and Applications: Anantharaman, T. R. (Ed.). Aedermannsdorf: Trans. Tech. Publications, pp. 31-63. Ray, R. (1981), /. Mater. Sci. 16, 2924, 2927. Riveiro, X M., Hernando, A. (1985), Phys. Rev. 32, 5102. Roorda, S. (1990), Doctoral Thesis, University of Utrecht. Rubin, X B., Schwarz, R. B. (1989), Appl Phys. Lett. 55, 36. Russell, K. C. (1985), Proc. Internat. Seminar on Solute-Defect Interactions, Kingston, Ontario. Oxford: Pergamon Press.

547

Sakata, M., Cowlam, N., Davies, H.A. (1981), J. Phys. Fll, LI57. Saunders, N., Miodownik, A. P. (1986), / Mater. Res. 1, 38. Schlapbach, L., Seiler, A., Stucki, R, Siegmann, H. C. (1980), /. Less-Common Metals 73, 145. Schlogl, R. (1985), in: Rapidly Quenched Metals (Proc. 5th Int. Conf): Steeb, S., Warlimont, H. (Eds.). Amsterdam: North-Holland, pp. 17231727. Schrdder, H., Samwer, K. (1988), /. Mater. Res. 3, 461. Schroder, H., Samwer, K., Koster, U. (1985), Phys. Rev. Lett. 54, 19. Schultz, L. (1989), in: New Materials by Mechanical Alloying Techniques: Arzt, E., Schultz, L. (Eds.). Oberursel: DGM Informationsgesellschaft Verlag, pp. 53-72. Schultz, L., Hellstern, E. (1987), Mat. Res. Soc. Symp. Proc., Vol. 80, 3. Schulz, R., Chretien, N., Alexandrov, N., Aubin, X, Roberge, R. (1988), Mater. Sci. Eng. 99, 19. Schwarz, R. B. (1988), in: Advances in Phase Transitions: XD. Embury, G.R. Purdy (Eds.). Oxford: Pergamon Press, pp. 167-177. Schwarz, R. B., Johnson, W.L. (1983), Phys. Rev. Lett. 51, 415. Schwarz, R. B., Johnson, W.L. (Eds.) (1988), Proc. Conf. on Solid State Amorphizing Transformation, J. Less-Common Metals 140, 1-399. Schwarz, R. B., Koch, C. C. (1983), Appl. Phys. Lett. 49, 146. Schwarz, R.B., Nash, P. (1989), JOM 41(1), 27. Schwarz, R.B., Petrich, R.R. (1988), J. Less-Common Metals 140, 111. Scott, M.G. (1983), in: Amorphous Metallic Alloys: Luborksy, RE. (Ed.). London: Butterworth, pp. 144-168. Scott, M.G., Kursumovic, A. (1982), Acta Metall. 30, 853. Sharma, S. K., Banerjee, S., Kudleep, S., Jain, A. K. (1989), J. Mater. Res. 4, 603. Simpson, A. W, Hodkinson, P. A. (1972), Nature 237, 320. Sinke, W.C, Roorda, S., Saris, F. W. (1988a), J. Mater. Res. 3, 1201. Sinke, W. C , Warabisako, T, Miyao, M., Tokuyama, T, Roorda, S., Saris, R W (1988 b), J. Non-Cryst. Solids 99, 308. Sinning, H.-R., Nicolaus, M. M., Haessner, F. (1991), Mater. Sci. Eng. A133, 371. Spaepen, F. (1977), Acta Metall. 25, 407. Spaepen, R, Taub, A. I. (1983), in: Amorphous Metallic Alloys: Luborsky, RE. (Ed.). London: Butterworth, pp. 231-256. Spaepen, R, Turnbull, D. (1979), in: Laser-Solid Interactions and Laser Processing - 1978: Ferris, S. D., Leamy, H. X, Prate, X M. (Eds.). Amer. Inst. Phys. Conf. Proc, Vol. 50, p. 73.

548

9 Metallic Glasses

Spaepen, R, Tsao, S. S., Wu, T. W. (1986), in: Amorphous Metals and Semicondutors: Haasen, P., Jaffee, R.I. (Eds.). Oxford: Pergamon, pp. 365-378. Spit, E, Blok, K., Hendriks, E., Winkels, G., Turkenburg, W, Drijver, J.W., Radelaar, S. (1981), in: Proc. 4th Int. Conf on Rapidly Quenched Metals: Masumoto, T.5 Suzuki, K. (Eds.). Sendai: Japan Inst. of Metals, pp. 1635-1640. Sprengel, W, Dorner, W, Mehrer, H. (1990), Z. Metallkde. 81, 467. Steeb, S., Warlimont, H. (Eds.) (1985), Rapidly Quenched Metals (Proc. 5th Int. Conf.). Amsterdam: North-Holland, pp. 1589-1802. Suslick, K. S., Choe, S.-B., Cichowlas, A. A., Grinstoff, M. W (1991), Nature 352, in press. Sutton, M., Yang, Y S., Mainville, J., Jordan-Sweet, XL., Ludwig, Jr., K.F., Stephenson, G.B. (1989), Phys. Rev. Lett. 62, 288. Suzuki, Y, Haimovich, I, Egami, T. (1987), Phys. Rev. B 35, 2162. Tanner, L., Ray, R. (1980), Scripta Metall. 28, 633. Taub, A.I. (1984), IEEE Trans, on Magnetics 20, 564. Tendler, R.H. de (1986), J. Mater. Sci. 21, 64. Thakoor, A.P., Lamb, XL., Khanna, S.K., Mehra, M., Johnson, W. L. (1985), J. Appl. Phys. 58, 3409. Thompson, M.O., Galvin, G.J., Mayer, J.W., Peercy, P.S., Poate, J.M., Jacobson, D.C., Cullis, A.G., Chew, N. G. (1984), Phys. Rev. Lett. 52, 2360. Tomida, T, Egami, T. (1991), Mater. Sci. Eng. A133, 931. Tsai, R.-Y, Wu, S.-T. (1990), J. Electrochem. Soc. 137, 2803. Turnbull, D. (1974), /. de Physique 35, C 4 - 1 . Turnbull, D. (1985), in: Amorphous Metals and Semiconductors: Haasen, P., Jaffee, R.I. (Eds.). Oxford: Pergamon Press, 9-23. Turnbull, D., Cohen, M.H. (1961), Nature 189, 131. Vaidya, R.U., Subramanian, K.N. (1990), /. Mater. Sci. 25, 3291. van den Beukel, A. (1986), in: Rapidly Quenched Materials: Lee, P.W., Carbonara, S. (Eds.). Metals Park: Amer. Soc. Metals, p. 193. van den Beukel, A., Sietsma, J. (1990), Acta Metall. 38, 383. Vanini, F. (1990), Doctoral dissertation, Swiss Federal Inst. of Techn., Zurich. Vepfek, S., Iqbal, Z., Sarott, F.-A. (1982), Phil. Mag. B45, 137. Vineberg, E. X, Ohriner, E. K., Whelan, E. P., Stapleton, G. E. (1985), in: Rapidly Solidified Crystalline Alloys: Das, S.K., Kear, B. H., Adam, C M . (Eds.). Warrendale: The Metallurgical Society, 306. Volkert, C. A., Spaepen, F. (1990), Scripta Metall. 24, 463. Vredenburg, A. M., Westendorp, J. F. M., Saris, F. W, van der Pers, N. M., Keijser, Th. D. (1986), /. Mater. Res. 1, 775.

Wagner, C.N.J. (1986), in: Amorphous Metals and Semiconductors: Haase, P., Jaffee, R. I. (Eds.). Oxford: Pergamon, pp. 54-69. Walter, XL., Bacon, F , Luborsky, F.E. (1976), Mater. Sci. Eng. 24, 239. Warburton, W.K., Turnbull, D. (1975), Diffusion in Solids: Recent Developments. Nowick, A. S., Burton, X X (Eds.). New York: Academic Press, p. 171. Warlimont, H. (1980), Physics in Technology 11, 28. Warlimont, H. (1985), in: Rapidly Quenched Metals (Proc. 5th Conf.): Steeb, S., Warlimont, H. (Eds.). Amsterdam: North-Holland, pp. 1599-1609. Warlimont, H. (1988), Mater. Sci. Eng. 99, 1. Weeber, A.W., Bakker, H. (1988), X Phys. F: Met. Phys. 18, 1359. Weeber, A.W, Haag, W.X, Wester, A.J.H., Bakker, H. (1988), J. Less-Common Metals 140, 119. Wei, Gao, Cantor, B. (1989), Acta Metall. 37, 3409. Whang, S.H. (1983), Mater. Sci. Eng. 57, 87. Wolf, D., Okamoto, P. R., Yip, S., Lutsko, J.F., Kluge, M. (1990), J. Mater. Res. 5, 286. Wu, T. W, Spaepen, F. (1986), in: Mechanical Behavior of Rapidly Solidified Materials: Sastry, S. M. L., MacDonald, B.A. (Eds.). Warrendale: TMSAIME, p. 293. Yamasaki, T, Takahashi, M., Ogino, Y. (1985), in: Rapidly Quenched Metals (V): Steeb, S., Warlimont, H. (Eds.). Amsterdam: North-Holland, pp. 1381-1384. Yater, J.A., Thompson, M.O. (1989), Phys. Rev. Lett. 63, 2088. Yavari, A.R. (1986), J. Mater. Res. 1, 746. Yavari, A.R., Hicter, P., Desre, P. (1983), J. Chim. Physique 79, 572. Yeh, X.L., Samwer, K., Johnson, WL. (1983), Appl. Phys. Lett. 42, 242. Yermakov, A. Ye., Barinov, V.A., Yurchikov, Ye. Ye. (1981), Phys. Met. Metall. 54, 935. Yermakov, A. Ye., Yurchikov, Ye. Ye., Barinov, V.A. (1982), Phys. Met. Metall. 52, 50. Yoshioka, H., Asami, K., Kawashima, A., Hashimoto, K. (1987), Corros. Sci. 27, 981. Zollzer, K., Bormann, R. (1988), J. Less-Common Metals 140, 335.

General Reading Anantharaman, T. R. (Ed.) (1984) Metallic Glasses Production, Properties and Applications. Aedermannsdorf: Trans. Tech. Cahn, R. W. (1980), Metallic Glasses. Contemp. Phys. 21, 43. Giintherodt, H.-X, Beck, H. (Eds.) (1981, 1983), Glassy Metals I and II. Berlin: Springer. Haasen, P., Jaffee, R.I. (Eds.) (1986), Amorphous Metals and Semiconductors. Oxford: Pergamon. Luborsky, F. E. (Ed.) (1983), Amorphous Metallic Alloys. London: Butterworth.

10 Glass-Like Carbons Sugio Otani and Asao Oya Department of Materials Science, Gunma University, Gunma, Japan

List of Symbols and Abbreviations 550 10.1 Introduction 551 10.2 A Short History of Glass-Like Carbon 551 10.3 Preparation Procedures of Glass-Like Carbon 553 10.3.1 Preparation from Cellulose 553 10.3.2 Preparation from Thermosetting Resin 554 10.3.3 Preparation by Use of Filler Material 555 10.3.4 Porous Glass-Like Carbon 555 10.3.5 Fine Glass-Like Carbon Particles 556 10.3.6 Glass-Like Carbon Coating and Film 556 10.3.7 Glass-Like Carbon Fiber 556 10.4 Structure of Glass-Like Carbon 557 10.4.1 Structural Models of Glass-Like Carbon 557 10.4.2 Structural Change on Hardening and Initial Carbonization Processes .. . 558 10.4.2.1 Cellulose 558 10.4.2.2 Phenol-Formaldehyde Resin 559 10.4.2.3 Furfuryl-Alcohol Resin 562 10.4.3 Structural Change During the Carbonization Process 562 10.5 Properties of Glass-Like Carbon 563 10.5.1 Normal Glass-Like Carbon 563 10.5.1.1 Density, Porosity and Gas Permeability 564 10.5.1.2 Mechanical Properties 564 10.5.1.3 Electrical Properties 565 10.5.1.4 Thermal Properties 565 10.5.1.5 Chemical Properties 565 10.5.1.6 Purity 565 10.5.1.7 Comparison with other Materials 566 10.5.2 Properties of Composite Glass-Like Carbon and Porous Glass-Like Carbon 566 10.6 Applications of Glass-Like Carbon 566 10.6.1 Electronic and Magnetic Applications 566 10.6.2 Applications in Analytical Chemistry 569 10.6.3 Metallurgical Applications 569 10.6.4 Applications to Biomaterials 569 10.6.5 Applications to Fuel Cells 569 10.6.6 Other Applications 571 10.7 Acknowledgements . 571 10.8 References 571 Materials Science and Technology Copyright © WILEY-VCH Verlag GmbH & Co KGaA. All rights reserved.

550

10 Glass-Like Carbons

List of Symbols and Abbreviations d002 Lc La

interlayer distance crystallite thickness parallel to the c axis crystallite size normal to the c axis

CVD HHT PAN RVC

chemical vapor deposition heat-treatment temperature polyacrylonitrile Reticulated Vitreous Carbon

10.2 A Short History of Glass-Like Carbon

10.1 Introduction Carbon atoms have three valence states, sp, sp 2 and sp3, from which three allotropic forms are derived: carbyne (Sladkov et al., 1968; Heimann et al., 1983), graphite and diamond. Carbon materials such as coke, carbon black and graphite electrodes, however, have complex structures of sp 2 and sp 3 as well as small amounts of sp carbon atoms. Despite containing only one element, carbon materials therefore have a wide range of structures and properties. Glass-like carbon is a unique carbon material because it consists of an amorphous-like and isotropic structure including a large amount of tetrahedral sp 3 carbon. It has several characteristic properties resulting from its structure in addition to its glass-like appearance. When glasslike carbon was developed around 1960, many practical applications were expected, but were not realized because of some disadvantages described at a later date. Instead, this material served to increase fundamental and academic knowledge of carbon materials and just recently some potential applications have appeared. For successful applications, the preparation procedure as well as the structure and properties of glass-like carbon have been diversified remarkably, once again stimulating interest in this material and raising expectations of future development. Since many of the preparations and applications are described in patents, many are cited, especially from Japan where the most active development is now in progress.

10.2 A Short History of Glass-Like Carbon A short history of this material is shown in Table 10-1. The initial purpose of the

551

Table 10-1. A short history of glass-like carbon. Year 1957 1961 1962 1964

19641965 1966 1967 1969 1969 1971

1974

1975 1980

1981 1983

1983 1984

Event First glass-like carbon Cellulose Carbon by General Electric Company (UK). Vitreous Carbon derived from phenolaldehyde resin by Plessey Company (UK). Glassy Carbon derived from furfuryl alcohol by Tokai Carbon Company. Microporous glass-like carbon by Societe le Carbone-Lorraine (Development year of Carbone Vitreux is not clear). Proposal of some structural models of glasslike carbon using X-ray diffraction technique by Noda et al. Vitro Carbon derived from acetonefurfuryl resin by Nippon Carbon Company. Glass-like carbon fiber by Tokai Carbon Company. Composite glass-like carbon using filler by Lockheed. Formation mechanism of glass-like carbon by Fitzer's group. Structural model of "network of ribbon stacking" for glass-like carbon by Jenkins and Kawamura. Glass-like carbon containing the finely dispersed iron particles by Walker et al. and Yajima et al. Fine porous glass-like carbon by Hucke. Reticulated Vitreous Carbon by Chemotronics International. Glass-like carbon coating by The Aerospace Corp. Activation of study on the fuel cell. A high quality glass-like carbon (Glahard) derived from a hydrophilic resin by Kao Company. Composite glass-like carbon by Showa Denko. Development of a large-sized composite glass-like carbon by Showa Denko. New model of glass-like carbon by Shiraishi.

glass-like carbon was to develop a component of nuclear fuel. For this application, the carbon material must be gas-impermeable and of high purity. Davidson (1957) of the General Electric Company (UK) succeeded in developing the first glass-like carbon, Cellulose Carbon, from cellulose slurry. The products were small pipes. This

552

10 Glass-Like Carbons

company developed the preparation procedure of glass-like carbon from thermosetting resins in 1960 (Rivington, 1960). With this as a trigger, the race for the development of glass-like carbon had begun. Plessey in England (Redfern, 1961; Redfern and Floyd, 1962; Cowlard and Lewis, 1967) developed Vitreous Carbon from phenol-aldehyde resin. A glass-like carbon boat, disc and rod in addition to pipes were prepared. The glass-like carbon was gradually shown to have some additional attractive properties, e.g. high chemical durability, and was expected to have practical applications in the use of chemical vessels and electrodes for electroanalysis (Zittel and Miller, 1965; Yoshimori et al., 1965). These applications were later industrialized but their production quantities were quite small. At almost the same time, Tokai Electrode (at present Tokai Carbon) derived Glassy Carbon from furfuryl-alcohol resin (Yamada and Sato, 1962; Yamada and Takada, 1963 a, 1963 b). Here new techniques were developed, e.g., using a powder filler and making a mold by repeatedly coating the resin on a substrate. In 1964, the Societe Carbone-Lorraine developed porous glass-like carbon. This company also distributed a catalog for a dense glass-like carbon called Carbone Vitreux but the preparation procedure has not been published as far as we know. Nippon Carbon subsequently developed Vitro Carbon by using an acetone-furfural resin (Honda et al., 1966; Teranishi et al., 1967). In addition, Sigri GmbH (FRG) developed Sigradur (the preparation procedure is not clear, however). A unique glass-like appearance and some attractive properties of this material led to active interest in its structure, beginning around 1964. Some structural models for glass-like carbon were proposed on the basis of X-ray diffraction analysis as de-

scribed in Sec. 10.4.1. In 1971, Jenkins and Kawamura proposed a novel "network of ribbon stacking" model (sometimes called the "Jenkins nightmare" model) on the basis of high-resolution electron microscopic observations in 1971. Such fundamental work contributed favorably to the understanding of the structure of not only glasslike carbon but also other carbon materials. The pitch-based carbon fiber developed by Otani (1965, 1966) had a similar structure. Stimulated by this invention, a glasslike carbon fiber was developed by Yamada et al. (Yamada and Nakamura, 1966; Yamada and Yamamoto, 1968). However, the resulting fiber was mechanically weak compared with fibers derived from pitch material and polyacrylonitrile (PAN). It was not until around 1980 that carbon fiber from phenol resin was industrialized on the basis of its high flexibility (Kawamura and Jenkins, 1970) or because of the large specific surface area achieved through activation treatment (Miyashita, 1983). Research and development on new applications of glass-like carbon were continued. Walker's group endeavored to apply the glass-like carbon, with or without fine metals, as a catalyst (Jung et al., 1979) and as a catalyst support and molecular sieve (Walker et al., 1977). Its potential use as biomaterial was examined by Fitzer's group (1978). None of these results, however, were industrialized. The uniform dispersion of fine iron metals in glass-like carbon has been achieved by some researchers (Yajima and Omori, 1972; Kammereck et al., 1974). Recently, fine glass-like carbon particles containing dispersed fine metals have again attracted much attention as electromagnetic material, catalyst, etc. (Hirano et al., 1983; Yogo et al., 1986). However, practical applications for glass-like carbon were not developed as ex-

10.3 Preparation Procedures of Glass-Like Carbon

tensively as expected initially because of the low productivity and high price. But then again, in those days there were no high technology application fields in which the unique properties of this material would be required. Around 1980, some potential applications appeared, among which the most attractive ones were as parts of fuel cells and magnetic recording equipment. Both applications required a low priced, large and thin glass-like carbon plate; however, somewhat lower gas impermeability and structural homogeneity were needed in the first case and a high quality glass-like carbon was required in the second. Some companies entered the field of glass-like carbon and made extensive contributions to accomplish these requirements. The first was achieved successfully by the use of filler material (Saura et al, 1987; Fukuda et al., 1988). In connection with the second application, on the other hand, the chemical structure of the starting thermosetting resin itself was reconsidered, and a hydrophilic resin was developed by a structural modification technique or blending technique of the resins to result in a high quality glass-like carbon (Yamauchi et al., 1985). These materials are now undergoing extensive trials for practical uses. Also, the conventional glass-like carbon has penetrated somewhat into the semiconductor as well as other industries (Yasuda and Nakamura, 1975).

10.3 Preparation Procedures of Glass-Like Carbon 10.3.1 Preparation from Cellulose

There are three typical carbonization processes, called the liquid-phase, gasphase and solid-phase carbonizations. The

553

typical carbon materials resulting from these processes are coke, pyrolytic graphite and charcoal (or carbon fiber), respectively. Glass-like carbon is prepared through the solid-carbonization process. As seen in the case of charcoal, the carbon resulting from solid-phase carbonization tends to become porous in nature. In the preparation of glass-like carbon, therefore, the key point is the removal of the pores from the material. Many preparation procedures are disclosed in patents but expert knowledge is essential for practical production. Cellulose Carbon is prepared according to the processes shown in Fig. 10-1 a (Davidson, 1957, 1959). The fibrous structure of the cellulose is mechanically and/or chemically beaten in an aqueous medium to prepare the cellulose slurry. It is important to prepare a fine and homogeneous dispersion of the cellulose because the state of the cellulose slurry is intimately related to the cross-linking reaction in the subsequent heating process and to the properties of the final product. The close cross-linkages result in a dense and homogeneous glass-like carbon. The addition of a dispersion agent such as zinc chloride is effective in forming the homogeneous slurry. The slurry is fed into the bowl of a centrifuge, and, while the water is continuously removed, the beaten cellulose is automatically pressed against the centrifuge wall to form a long hollow tube. The moist cellulose tube is carefully and slowly dried at room temperature and, if necessary, under controlled humidity. The tube undergoes a 50% volume shrinkage. After machining to the desired size and shape, the regenerated cellulose tube is slowly carbonized under an inert atmosphere for several days and then graphitized above 2500 °C. The carbonized tube is microporous in nature, the pore size being approximately 2 nm. Graphitization results in clo-

554

10 Glass-Like Carbons (a)

Cellulose slurry

(c)

(b)

Thermosetting resin

Thermosetting resin

I Molding

Molding

Kneading

I Molding Drying

Hardening

Hardening

Machining

Machining

Machining

Carbonization

Carbonization

I

I

Graphitization

Graphitization

Graphitization

Carbonization

sure of the ends of the pores, achieving gas impermeability. The products are small tubes, as suggested by the preparation method. Glass-like carbon formation from lignin was later attempted by Tormala and Romppanen (1981) using a different procedure from that of Cellulose Carbon, but the resulting product did not exhibit high mechanical strength. 10.3.2 Preparation from Thermosetting Resin

Many kinds of thermosetting resins such as phenol resin and furfuryl-alcohol resin are used as raw materials for glass-like carbon (Rivington, 1960; Redfern, 1961), but the fundamental preparation procedure is almost the same. As shown in Fig. 10-1 b, a thermosetting resin is first shaped. Here the resin is usually poured into a mold and thereafter hardened through polymerization. In practical operations, an organic hardener such as benzoic peroxide or aniline sulfate is sometimes used (Yamada and Takada, 1963 a, 1963 b). When a tube is desired, the resin is poured into a cylindri-

Figure 10-1. Preparation procedures for glass-like carbons from (a) cellulose, (b) thermosetting resin, and (c) thermosetting resin/ filler particle.

cal mold and rotated at high speed (in order to form the resin into a tubular shape by centrifugal force), followed by hardening treatment. The product after hardening is dehydrated slowly by heating under pressure or at a very low heating rate (1 °C h~ x ) under reduced pressure (Redfern, 1961); the resulting product breaks easily since the moisture evolved is not easily released from the mold, which shrinks extensively. This is the most substantial cause of low productivity of this material. A glass-like carbon product of >10mm in thickness is difficult to prepare. According to the patents applied for by Tokai Carbon Company (Yamada and Takada, 1963 a, 1963 b), a shaped substrate is repeatedly coated with resin and then hardened, to form the product. The moisture is easily released from the mold and the resulting product is strong because of the layered structure. The product is carbonized to 10001500°C with a heating rate of about 5°C min" 1 and subsequently graphitized. The largest products attained by this method were a rod of 6.25 mm diameter x 300 mm length and a tube of 23 mm diameter

10.3 Preparation Procedures of Glass-Like Carbon

(thickness 6 mm) x 165 mm length, etc. (Redfern, 1961). 10.3.3 Preparation by Use of Filler Material Attention has concentrated recently on glass-like carbon containing filler material (here, this type of glass-like carbon is referred to as composite glass-like carbon). The addition of filler is effective in decreasing the weight loss and the shrinkage of the product, and in facilitating the release of the evolving gas during the hardening and carbonization processes. This method is used to prepare a large-sized inexpensive glass-like carbon with a lowering of gas impermeability and structural homogeneity. In the initial patent describing this method, the thermosetting resin powder after hardening was used as a filler to prepare the final product consisting of the same glass-like carbon component. Natural graphite has also been used (Bradshaw et al., 1969); and fine graphite powder of less than several microns has again attracted much attention recently (Saura et al., 1987; Fukuda et al., 1988). As shown in Fig. 10-1 c, the thermosetting resin and the filler particles are first kneaded under a vacuum to remove trapped gas. Several effective shaping techniques such as extrusion, pressing and roller forming can be used. The productivity of these methods is far higher compared with the methods without the filler (Saura et al., 1987). A plate as large as 100 x 100 cm and several millimeters in thickness is prepared commercially by using graphite powder filler. In the preparation of the glass-like carbon Strux by the Fudow Chemical Company, a woven fabric of the thermosetting resin fiber is used as a filler. The filler is first impregnated with the resin and stacked,

555

then pressed. The resulting product consists completely of the glass-like carbon component. According to a patent by Sakaguchi (1988), some kinds of ceramic powder (A12O3, SiC, etc.) are used to improve the abrasion resistance of the product. It is well known that the thermosetting resin is used as a matrix for fiber-reinforced carbon composites, further details of which can be found elsewhere (Fitzer, 1987). 10.3.4 Porous Glass-Like Carbon Porous glass-like carbon can be prepared more easily without damage than the products described in 10.3.2 and 10.3.3. In some cases, therefore, porous glass-like carbon is first prepared and then subjected to impregnation by the resin (Johnson et al., 1979) or chemical vapor deposition (CVD) (Nagle and Walker, 1973) to obtain a dense glass-like carbon. There are four fundamental methods for preparing porous glass-like carbon: (i) Polyurethane foam or non-woven fabric of carbon fiber, cellulose, etc., is impregnated with thermosetting resin, followed by removal of the excess resin which then remains on the fiber surface alone. Subsequently, the resulting skeleton is subjected to the usual preparation procedures of glass-like carbon (Franklin, 1980). (ii) The pore former, such as water or polyethyleneglycol, is added to the raw thermosetting resin (Hucke, 1975; Walker Jr. etal., 1977; Yata et al., 1986). It is released from the resin after hardening, leaving the pores, because it is not a component forming the glass-like carbon. The pore size is controlled by additional amounts of both the surface-active agent and the pore former. The procedure involving the replication of a porous sacrificial substrate, i.e., sodium chloride, is used for glass-like foam (Pekala and Hopper,

556

10 Glass-Like Carbons

1987). This technique is suitable for preparing glass-like carbons with relatively large pores. (iii) Glass-like carbon particles are shaped with a binder by pressing. The pore remains at the particle boundary. It is difficult, using this method, to prepare porous material with a large pore volume without lowering the mechanical strength. (iv) A chemical foaming agent such as a halogenated hydrocarbon is used (Murakami etal., 1985; Katsura and Shiraki, 1987). The graphite powder is added to prepare the composite glass-like carbon as stated in Sec. 10.3.3. However, when the exfoliated graphite is used instead of the graphite powder, a unique, porous glass-like carbon is obtained (Kikuchi et al., 1985). 10.3.5 Fine Glass-Like Carbon Particles

Fine glass-like carbon particles have several specific applications. So far, particles have been prepared by crushing massive glass-like carbon. Recently, some new practical preparation procedures have been developed: (i) The polymer precursor is subjected to controlled atomization, followed by hardening and heat treatment (Levendis and Flagan, 1989). (ii) A suitable viscous thermosetting resin with a hardener is added dropwise into sulfuric acid and hardened in situ. The fine particles obtained after washing are carbonized and then graphitized. (iii) An aqueous solution of phenol is dropped into a hydrochloric acid/formaldehyde mixture, stirred to convert the mixture into a slurry or resinous state and then hardened by heating. The resulting fine spheres of several tens of microns in diameter are subjected to the subsequent heat treatments (Koyama et al., 1988).

10.3.6 Glass-Like Carbon Coating and Film

To avoid the difficulties involved in preparing a large-sized glass-like carbon product, the conventional artificial graphite products can be coated with glass-like carbon. Initially, a diluted thermosetting resin was used for the coating but the technique developed recently (Murata et al., 1988) is as follows: After initial carbonization, the resin is subjected to extraction with an organic solvent. The solution is concentrated to about 20 wt.%, then used to coat the conventional graphite product - mainly high-density isotropic graphite followed by hardening, carbonization and graphitization. The resulting product is substantially gas-impermeable. When the glass-like carbon is coated on a quartz glass plate coated with a release agent, a glass-like carbon film is obtained by peeling (Ogata et al., 1987).

10.3.7 Glass-Like Carbon Fiber

The thermosetting resin is subjected to continuous melt-spinning, hardening, carbonization and then graphitization, just as the usual pitch-based carbon fiber. The preparation using Kynol-type phenol resin has already been industrialized (Miyashita, 1983). The carbon fiber has low mechanical strength on the one hand, reflecting its amorphous-like structure, but high flexibility on the other. These inherent properties of the fiber are suitable for several applications as explained later. The mechanical properties can be improved by hot stretching carbonization but this technique is not practical (Economy and Lin, 1971). The carbon fiber can be converted into an excellent active carbon fiber through activation treatment (Miyashita, 1983).

10.4 Structure of Glass-Like Carbon

10.4 Structure of Glass-Like Carbon

80 70

10.4.1 Structural Models of Glass-Like Carbon

Figure 10-2 shows changes in the X-ray parameters of two typical kinds of carbons with heat-treatment temperature. Normal pitch coke shows a decrease of interlayer distance (d002) an<^ a n increase of crystallite thickness parallel to the c axis (Lc) with increasing heat-treatment temperature, as shown by the lines in Fig. 10-2. The crystallite size normal to the c axis (La), though not presented, is almost proportional to L c . A carbon exhibiting such excellent crystal growth is called graphitizable or soft carbon. On the contrary, the glass-like carbon Glassy Carbon shows a far smaller decrease of d002 and smaller increase of L c with increasing temperature (Noda et al., 1969) compared with graphitizable carbon. Such a carbon is called a non-graphitizable or hard carbon. This structural behavior is the most substantial characteristic of glasslike carbon. When a hard carbon is heated to high temperature, it exhibits multiphase graphitization in which the graphite component suddenly appears within the low crystalline matrix (Kamiya and Suzuki, 1975). The structure of the glass-like carbon was initially studied by using the X-ray diffraction technique, including the radial distribution analysis because of its low crystalline structure. Noda and Inagaki (1964) proposed the presence of two types of carbon atoms, one having a tetrahedral (sp3) relationship, and the other a trigonal (sp2) relationship to the nearest carbon atoms in the glass-like carbon. The unique characteristic was that the presence of a fairly large amount of tetrahedral sp 3 carbon was proposed. Their model has trigo-

557

60 5040 . 30 20 10 0 5

10 15 20 25 30 Heat-treatment temperature (x 102 °C)

Figure 10-2. Changes of X-ray parameters of Glassy Carbon and a typical graphitizable carbon as a function of the heat treatment temperature.

nally bound carbon atoms forming small domains of two-dimensional graphite-like arrangements and these domains are crosslinked by tetrahedrally bound carbon atoms. Furukawa (1964) criticized this model by Noda and Inagaki in the following two points: (i) their results are questionable in view of the shape of the radial-distribution curve, and (ii) if a large amount of sp 3 carbon exists, as they proposed, the density of the glass-like carbon should be larger in view of the density of diamond (3520 kg m~ 3 ). He proposed a three-dimensional irregular network configuration model which contains all kinds of C - C bonds, i.e., tetrahedral, planar double, linear triple and also conjugated bonds. Whittaker and Tooper (1974) revealed that Vitreous Carbon gives some kinds of electron diffraction patterns including a single-crystal pattern, of which further details are unclear. Based on a paper describing an oxygen content of 5-6% in Glassy Carbon, Kaki-

558

10 Glass-Like Carbons

noki (1965) proposed a model which consists of two kinds of domains, each of which is composed of tetrahedral carbon atoms and trigonal carbon atoms, respectively, linked by oxygen bridges. The low density of the glass-like carbon is explained by the oxygen bridges. Later, it was shown that the oxygen content of Glassy Carbons, after heating to 900 and 1200°C, are 1.2 and 0.9%, respectively (Noda et al., 1969), so that his model became groundless. Takahashi and Westrum, Jr. et al. (1970) reported that the specific heat of Glassy Carbon is proportional to the square of the absolute temperature, suggesting that this carbon consists mainly of two-dimensional layers. The controversy was ended in 1971 by high resolution electron microscope observations. Figures 10-3 a and 10-3 b are high resolution electron micrographs of

a)

b)

the phenol resins after heating to 1200 and 2800 °C. The former sample consists of a random configuration of small crystallites with stacks of several layers, 2-3 nm in size. After heating to 2800 °C, however, the crystallites grew to stacks of about 10 layers, 6-7 nm in size, and were entangled with each other. Based on these photographs, Jenkins and Kawamura (1971) and Jenkins et al. (1972) proposed a "network of ribbon stacking" model for the glass-like carbon after heating to a high temperature as shown in Fig. 10-4 a, in which only small amount of sp 3 carbons exist. D'Antonio and Konnert (1981) later supported this model by the use of X-ray radial distribution analysis. The network of ribbon stacking model provides a reasonable explanation for the behavior and properties of glass-like carbon: (i) an isotropic structure, (ii) gas-impermeability in spite of its low density, and (hi) less crystalline growth by heating to high temperatures. This model was also supported by the use of electron microscopic observations (Bose et al., 1978) and has gained wide acceptance. Shiraishi (1984), however, had doubts about the gasimpermeability predicted by this structural model. He pointed out that glass-like carbon has a low He density (1500 kg m~ 3 ), determined by He pyknometry, and small CO 2 absorption capacity (2 10" 3 m 3 kg" 1 ), which means that it consists of a large proportion of closed pores. He proposed the model shown in Fig. 10-4 b. 10.4.2 Structural Change on Hardening and Initial Carbonization Processes 10.4.2.1 Cellulose

Figure 10-3. High resolution electron microphotographs and electron diffraction patterns of phenol resin carbons after heating to (a) 1200°C and (b) 2800°C.

The properties and structure of the carbon material are strongly dependent on the structure of the raw material and the carbonization process. Such relationships are

10.4 Structure of Glass-Like Carbon

559

(b)

La: Crystallite size Z.c: Crystallite thickness

especially retained in solid-phase carbonization because of the difficulty of rearranging the constituents during the carbonization process. It is important to understand the initial thermal degradation process of some raw materials of the glasslike carbon (Fitzer et al., 1971). As shown in Fig. 10-5 cellulose (I) undergoes changes when heated slowly (Tang and Bacon, 1964). After removal of the absorbed water below 150°C, a dehydration reaction starts to form keto groups (II) which have a keto-enol tautomer (III). Glucose bonds are broken at 240-400 °C, resulting in fragments (IV) and (V) together with the evolution of CO, CO 2 , H 2 O and a residue of tarry matter. As the reaction proceeds further, the volatile material (VI) is formed to a slight extent. By dehydration around 400 °C, compound (V) also changes into compound (VII) of which the carbon skeleton model is shown in (VIII). This compound converts into C 4 fragments as shown by the flame with removals of H 2 O, CO 2 and CO. The fragments slowly grow into the carbon crystal with increasing heat treatment. The structural changes involved in the carbonization of cellulose fiber were examined in detail (Tang and Bacon, 1964; Bacon and Tang, 1964).

Figure 10-4. Two structural models of glass-like carbon heated to high temperature; (a) network of ribbon stacking model by Jenkins and Kawamura, (b) Shiraishi model.

10.4.2.2 Phenol-Formaldehyde Resin

There are many reports on the initial carbonization process of phenol-formaldehyde resin (Yamashita and Ouchi, 1981). As shown in Fig. 10-6 (Fitzer and Schaefer, 1970), phenol-formaldehyde resin (II) is first subjected to dehydration polymerization by heating, leading to the formation of ether cross-linkages (III) and the triphenylmethane structure (IV) with methylene bridges. The cyclization as shown by the formation of diphenylpyran (V) also occurs at temperatures somewhat lower than 400 °C. The reaction becomes most active around 400 °C and the pyran ring is broken to change into the furan ring (VI). By heating to 450 °C or higher, the methylene bridge (VII) derived from the raw material (II) is oxidized by the resulting H 2 O and changes into the keto radical (VIII) which is finally converted into the biphenyl structure (IX), evolving CO gas. The structural model (XI) of Ouchi and Honda (1959) of phenol-formaldehyde resin after heating to 600 °C consists of a three-dimensional disordered structure. This structure remains as a memory after carbonization, leading to a homogeneous and amorphous-like structure.

560

O'

10 Glass-Like Carbons

o o

o o

CO

i

OH H2 OH

/-H2O

Figure 10-6. Initial thermal degradation mechanisms of phenol resin. CO C

.°2

CH, H2O

I

130

100

°C

200

300 1

- H 2 0 ( -CH 4 CH 2 -0H

j^

1

1

-C0 2 , - C O
1

1

600

r^

o

1

o

>450»C

=3

IV

- H 2 |>H 2 <

-C l

Figure 10-7. Initial thermal degradation mechanisms of furfuryl-alcohol resin.

"C i

C l

^C t

Ill

o

1 1

c 1

500

400

-co >460°C

I

I

c

I

•c* V Y c V I

c

I

I

1

O1

562

10 Glass-Like Carbons

Bhatia et al. (1984) and Aggarwal et al. (1988) examined in detail the carbonization processes of phenol-formaldehyde resins relevant to the number of OH in phenol and to the molar ratio between phenol and formaldehyde, and pointed out that the quality of glass-like carbon depends strongly on both factors. Kobayashi et al. (1968) reported that the phenol-formaldehyde resin fuses during the carbonization process, with increasing numbers of methyl radicals in the phenol molecule. As shown by these observations, the properties of glass-like carbon can be sensitively controlled by changing the starting molecules. 10.4.2.3 Furfuryl-Alcohol Resin

As shown in Fig. 10-7 (Fitzer and Schaefer, 1970), methylene bridges (I) are formed in furfuryl-alcohol resin by dehydration at the initial stage. Above 150°C the methylene bridge is broken to evolve methane, of which the intermediates are not clear. The furan ring itself is broken to evolve CO 2 and H 2 O. Around 450 °C a part of the methylene bridge is oxidized by the resulting H 2 O to change into a chain polymer (III). During heating above 460 °C, CO evolves from the carbonyl bond, leading first to an unsaturated conjugated system (IV) and then to the carbon crystallite. Jenkins et al. (1972) proposed a clear pathway from phenol-hexamine resin carbon to the network of ribbon stacking model.

process of Glassy Carbon derived from furfuryl alcohol was clarified, but there are few data on other resins. According to optical microscopic observations on the polished surfaces of Glassy Carbon, the pores appear at approximately 500 °C, below which no pore exists (Fitzer et al., 1969). The most abundant pores of 0.2-2 nm in diameter are observed after heating to 800 °C. Heating to even higher temperatures causes the pores to shrink and decrease and to disappear completely after heating to 1600°C. Some techniques of burying the pores are also available (Nagle and Walker, Jr., 1973; Edelson and Glaeser, 1986). Figure 10-8 shows some structural parameters of Glassy Carbon as influenced by the carbonization process (Fitzer et al., 1969). The amount of water absorbed and the specific surface area correspond to the appearance of the carbon surfaces stated above, i.e., both parameters increase up to 800 °C and then decrease to reach constant

O BET surface area • Water adsorption 1? a n l A \ Q) "U

\

A Volume change \

• Weight change

10.4.3 Structural Change During the Carbonization Process

In contrast to the hardening and initial carbonization processes, the structural change in the carbonization process is not well known because the usual chemical analyses cannot be used. By using other structural parameters, the carbonization

£00

800 ~12OOW 1600 2000 Heat-treatment temperature (°C)

Figure 10-8. Changes of some structural parameters of Glassy Carbon with heat-treatment temperature.

10.5 Properties of Glass-Like Carbon

563

ill!

Glahard

Conventional glass-like carbon

Figure 10-9. Polished surface appearance of conventional glass-like carbon and high-quality glass-like carbon Glahard.

values at 1000-1100 °C. The weight decrease of Glassy Carbon almost finishes by 800 °C. The bulk shrinkage, on the other hand, continues strongly up to 800 °C and then decreases at higher temperatures. During carbonization below 800 °C the weight loss is more substantial than the shrinkage, leading to formation of pores. Since the main change at higher temperature is shrinkage rather than weight loss, the resulting pores gradually disappear. The pores present during the carbonization process are so-called closed pores, which do not affect gas permeability but do result in some problems in applications which depend on the surface smoothness of the glass-like carbon. The behavior stated above can be somewhat changed, depending on the kind of resin used and the heat-treatment conditions. With some resins, pores are never formed during the preparation processes. The hardening treatment must be carried out carefully because it is intimately related to the subsequent thermal degradation behavior and, furthermore, to the properties of the final glass-like carbon

product. The pore-free glass-like carbon Glahard was developed recently by using a hydrophilic resin (Yamauchi et al., 1985). The water which is formed during the hardening and initial carbonization processes tends to coagulate to form fine drops, leading to pores after removal at a subsequent stage. A hydrophilic resin is so effective in dispersing the resulting water that no pores remain. The polished surface of such a glass-like carbon, after heating to 1200 °C, is shown together with that of the conventional material in Fig. 10-9. Hot isostatic pressing (HIP) is also effective in removing pores. The UDAC Carbon of the Kobe Steel Company, produced by this technique, has a surface smoothness of < 0.01 jam without pores.

10,5 Properties of Glass-Like Carbon 10.5.1 Normal Glass-Like Carbon The properties summarized in Table 10-2 are quoted from the catalogs of three com-

564

10 Glass-Like Carbons

Table 10-2. The properties of commercially available glass-like carbon products (manufacturers are listed in parentheses beside each product). Celluose Carbon (G.E.)

Property

Glassy Carbon (Tokai) GC-10

HTT (°C) Bulk density (103 kg m" 3 ) Apparent porosity (%) Gas permeability (cm2 s"1) Bending strength (MPa) Young's modulus (GPa) Shore hardness Electrical resistivity (10" 6 Om) Thermal conductivity y W Hi

Jv

>1700 1.55

io- 1 2 176.5 27.4 95 40 4.18-16.72

GC-20

1300 2000 1.47-1.51 1.46-1.50 1-3 1-3 l O - ^ - l O " 1 2 1Cr i o _ 1 0 - i 2 98.1-117.7 88.3-98.1 29.4-32.37 29.4-32.37 100-120 100-110 45-65 40-45 3.76-4.6 8.36-9.19

Glahard (Kao) GC-30

S-100

3000 1.43-1.47 3-5

1200 1.45

1 0 -7_ 1 ( ) -9

49-58.8 21.6-24.5 70-80 35-40 15.0-17.55

98.1 19.6 120 45 3.34-3.76

2.0-2.2

3.5

)

Thermal expansion coefficient .(lO-^CT 1 )

3.4

2.0-2.2

mercially available glass-like carbons: Cellulose Carbon is characterized by its unique raw material; Glassy Carbon has been the most comprehensively examined carbon until now (Yamada et al., 1964; Metrotra et al., 1983); Glahard is a high quality glass-like carbon derived from a hydrophilic thermosetting resin (Yamauchi etal., 1985).

2.0-2.2

hibit the opposite behavior, or almost no change, with heat treatment. Craievich et al. (1973) and Jenkins and Walker, Jr. (1976) used the small-angle Xray scattering technique to examine the pores in glass-like carbon. Both results agree well: glass-like carbon contains pores of 1-2 nm (mean diameter), and their shape is possibly that of oblate ellipsoids.

10.5.1.1 Density, Porosity and Gas Permeability

10.5.1.2 Mechanical Properties

The density of many glass-like carbons is around 1500 kg m~ 3 . These values are far smaller than the 3520 kg m~ 3 of diamond and 2250 kg m~~3 of graphite but glass-like carbon is gas-impermeable because of the characteristic structure shown in Fig. 10-9. The porosity of Glahard, though not disclosed, must be zero in view of the photograph shown in Fig. 10-9. With increased heat-treatment temperature, Glassy Carbon shows a decrease in density and an increase in porosity as well as gas permeability. Such behavior is not necessarily common to all glass-like carbons; for instance, there are glass-like carbons that ex-

The bending strength of glass-like carbon is 196.2 MPa at maximum but usually around 98.1 MPa as shown in Table 10-2. This material has a large Young's modulus of 19.6-29.4 GPa. These mechanical properties, in general, decrease with increased heat-treatment temperature. The dispersion of the fine iron particles is effective in improving the bending strength of glasslike carbon after carbonization but not after graphitization (Kammereck et al., 1974). As shown by the Shore hardness of 100 or higher, glass-like carbon is very hard and brittle. It retains a Shore hardness of

10.5 Properties of Glass-Like Carbon

70-80 even after graphitization. The machining of this material is so difficult that the shape and size of the product are controlled at the hardening stage. Because of the extended shrinkage during subsequent heating, however, it is also not easy to prepare a product with a close tolerance. As suggested from its characteristic structure, glass-like carbon is different from conventional artificial graphite because it has low self-lubricity and high abrasion resistance. 10.5.1.3 Electrical Properties

The specific resistivity of glass-like carbon is around 40 • 10~ 6 Qm, which is the smallest among carbon materials. The change of resistance with heat-treatment is small as a result of minor structural changes caused by heating to high temperatures (as shown in Fig. 10-2). This level of resistivity is suitable for use as a heater. In addition, isothermal heating is possible throughout the glass-like carbon heater because of its homogeneous structure. This is another reason for using it as a heater in semi-conductor technology. 10.5.1.4 Thermal Properties

There is no difference in the thermal expansion coefficients between glass-like carbon and conventional artificial graphite. The thermal conductivity of glass-like carbon is relatively small. The thermal shock resistance of this material is only one tenth of that of conventional artificial graphite because of its low thermal conductivity in addition to its high degree of hardness and high modulus. Enhancement of the thermal conductivity was an important problem from the practical point of view, and was solved later by adding a filler with high thermal conductivity such as natural graphite (Fukuda et al., 1988; Saura et al., 1987).

565

10.5.1.5 Chemical Properties

Glass-like carbon has outstanding chemical properties. Both the glass-like carbon and the conventional artificial graphite, for example, begin to react with an oxidizing gas at the same temperature; thereafter, however, the former reacts far more slowly. The reason was initially considered to be the low specific surface area of this material, but later it was attributed to its characteristic structure, as shown in Fig. 10-4a, i.e., relatively little of the reactive edge of the carbon crystallite is present in glass-like carbon. The chemical reactivity decreases with increasing heat-treatment because of the development of the crystal structure and removal of impurities which act as catalysts (Tingey, 1975). Conventional graphite reacts with H 2 SO 4 :HNO 3 (1:1) mixed acids and breaks down into powder after 40 h, but no weight loss of Glassy Carbon was observed after 150 days under these conditions (Yamada et al., 1964). Glass-like carbon can also withstand hydrofluoric acid and chromic acid but is not as stable against alkaline reagents. Glass-like carbon is far more stable toward metals at high temperatures than conventional carbon materials, leading to electrical and metallurgical applications. 10.5.1.6 Purity

For the applications described in Sec. 10.6, the purity of glass-like carbon is one of the most important factors. In contrast to the artificial graphite electrode using pitch and coke derived from natural products, glass-like carbon has a high grade of purity because of its derivation from artificial thermosetting resin. The impurity (ash) content of this class of materials - without treatment - is 0.1 to 0.5%. After specific purification treatment, how-

566

10 Glass-Like Carbons

Table 10-3. Impurity (ash) analyses of Glassy Carbon products a after purification treatment (results given in ppm; ND: not detected). Product

Total

Al

B

Ca

Co

Cr

Fe

Mg

Mn

Ni

Cu

Si

V

GC-20S GC-20SS GC-30S

<200 <10 <100

3 ND 4

<1 <1 <1

10 ND ND

ND ND ND

2 ND ND

20 <1 5

<1 <1 <1

ND ND ND

1 ND ND

<1 ND <1

7 <1 20

15 ND ND

Heat treatment temperatures: 2000°C for GC-20S, GC-20SS; 3000°C for GC-30S.

ever, it decreases remarkably: the results of ash analysis of some Glassy Carbon products show that the product with the highest purity contains < 10 ppm impurities (Table 10-3). 10.5.1.7 Comparison with other Materials

Table 10-4 shows the properties of three materials: Pyrex glass, glass-like carbon (Glassy Carbon-20) in Table 10-2 and the artificial graphite electrode without impregnation. Glass-like carbon is similar to Pyrex glass in its gas impermeability, mechanical properties and appearance, but similar to the graphite electrode in electrical and thermal properties. Glass-like carbon is therefore an intermediate material between the other two. 10.5.2 Properties of Composite Glass-Like Carbon and Porous Glass-Like Carbon

Table 10-5 shows the properties of composite glass-like carbons (SG-1 and SG-3) and porous glass-like carbons, e.g., SG200, GGC-composite and Reticulated Vitreous Carbon (RVC) (Franklin, 1980; Wang, 1981). SG-3 carbon contains a larger amount of fine natural graphite filler than SG-1. In general, gas permeability and bending strength are lower after adding the filler (see Table 10-5), but such decreases are not serious problems in some applications. The reinforcing effects of the filler are preferable, e.g., the graphite powder decreases the thermal expansion coeffi-

cient and increases thermal conductivity, leading to improvements in thermal shock resistance. The lowering of electrical resistivity is also favorable for some applications. The porous glass-like carbons SG-200 and GGC-composite were prepared by using non-woven fabric and exfoliated graphite as a filler; their pore structures differ from each other. GGC-202 contains a larger amount of filler than GGC-201. The gas permeability of GGC-202 is 100 times larger than that of GGC-201, but the other properties do not have such extreme differences. The applications of such porous materials depend on gas permeability; the control of this property is therefore important. RVC (Wang, 1981) has an entangled porous structure different from other porous carbons. Its bulk density and apparent porosity are 0.048 and 97%, respectively. The application target of this material is, of course, different from other porous carbons, as explained below.

10.6 Applications of Glass-Like Carbon 10.6.1 Electronic and Magnetic Applications

Some glass-like carbon products are shown in Fig. 10-10. The best known application is for a susceptor (heater) for the vapor phase growth of semi-conductor sili-

567

10.6 Applications of Glass-Like Carbon

Table 10-4. Comparisons of the properties of Glassy Carbon GC-20, conventional artificial graphite and Pyrex glass. Property 3

3

Bulk density (10 kg m~ ) Apparent porosity (%) Gas permeability (cm2 s"1) Bending strength (MPa) Young's modulus (GPa) Shore hardness Electrical resistivity (10 ~6 Qm) Thermal conductivity ( W m ^ K " 1 ) Thermal expansion coefficient (10~ 6o C~ 1 )

GC-20

Graphite

Pyrex glass

1.46-1.50 1-3 10-10-10'12 98.1-117.7 29.4-32.4 100-110 40-45 8.36-9.19 2.0-2.2

1.5-1.7 20-30 lO0-^"1 19.6 4.9-11.7 30 5-12 104.5-242.4 1-3.5

2.23 0 IO-^-IO- 1 2 39.2-68.6 62.8 1015 1.08 3.25

Table 10-5. Properties of the commercially available composite glass-like carbons (SG-1, SG-3) and porous glass-like carbons (SG-200, GGC-201, GGC-202, RVC) (manufacturers are listed in parentheses beside each product). SG carbon (Showa Denko)

Property

HTT (°C) Bulk density (103 kg m~ 3 ) Apparent porosity (%) Gas permeability (cm2 s" 1 ) Bending strength (MPa) Young's modulus (GPa) Shore hardness Electrical resistivity (10" 6 Qm) Thermal conductivity (Wm" 1 K" 1 ) Thermal expansion coefficient (10~ 6o C a

Tensile;

b

GGC composite (Kobe Steel)

1

3

200

201

202

1000 1.55 1.5 <10" ( 3 176.5 29.4 100 47 3.34

1000 1.60 1.6 <10~4 132.4 24.5 80 26 91.9 2.4

1000 0.55 70 0.2 22.6 0.098

0.6 65 0.3 16.5

0.6 70 30 14.7

45 4.18

45 4.18

20 1.25 0.8

RVC (ERG)

0.048 97 0.3-1.17 a 6-7b 4700

Mors

con wafers (Yasuda and Nakamura, 1975). Since the glass-like carbon is of high purity without adsorbed gas, it is possible to put this material directly into the reaction chamber. Other characteristics are: (i) moderate electrical resistance suitable for a heater, (ii) homogeneous structure (ensuring a uniform heating action), (iii) high oxidation resistance, (iv) resistance to hydrofluoric acid (the cleaning solution), etc. On the basis of its dense structure and high oxidation resistance, glass-like carbon is used for crucibles and boats to synthesize

compound semiconductors such as GaAs, which is very corrosive. Also, glass-like carbon is used for crucibles to grow single crystals - with a corrosive flux such as CaF2 (Lewis, 1963) instead of a platinum crucible. Properties required for jigs used in transistor preparation are high purity, high precision machinability, moderate electric resistance and low reactivity with metals. A perpendicular magnetic recording system now being developed has achieved higher density recording than the present

568

10 Glass-Like Carbons

Figure 10-10. Some products of glass-like carbons, (a) Glassy Carbon; (b) Glahard.

systems (Iwasaki and Nakamura, 1977). A serious problem was the development of material with high lubricity and high abrasion resistance for the magnetic head (Wakasa et al., 1987), because the magnetic head slides on the magnetic recording me-

dia in this system. Glass-like carbon was selected as the material of choice, but the surface of the conventional glass-like carbon was too rough for this purpose. Therefore a glass-like carbon with a more homogeneous structure was developed by using a hydrophilic thermosetting furan resin. Fig. 10-11 shows changes in the coefficient of friction with time when some samples were rubbed against Co-Cr-sputtered metal film. With the lubricants presently being used, no change in the friction coefficient with time was observed in the glasslike carbon (Glahard-1000) in contrast with the glass Neoceram. At present, aluminum is used as the substrate material of the so-called hard magnetic disc. In order to make a smooth surface, an aluminum plate is subjected to Ni/P chemical plating or anodic oxidation in a chromic solution, followed by polishing to attain a surface with a smoothness of better than < 0.02 fim. Conventional glasslike carbon is too rough to use as substrate material. The application of Glahard to this purpose is now under development. This glass-like carbon has a low productivity, but this is not such a serious problem in high-value applications. Glass-like carbon was to be applied to the type-wheel of high-speed printers but

Neoceram

Neocream + Lubricant A Neoceram Lubricant B Glahard

Time (min)

Figure 10-11. Changes of friction coefficient of glasslike carbon Glahard and commercially available Neoceram with rubbing time.

10.6 Applications of Glass-Like Carbon

its brittleness prevented its successful application. 10.6.2 Applications in Analytical Chemistry

Glass-like carbon is used in special electrodes for emission spectral analysis, polarography, potentiometry, etc. (de Galan etal., 1983; Linden and Dieker, 1980). Here, low reactivity and electric conductivity are mainly required. There are many reports on the electrochemical corrosion of glass-like carbon in chemical reagents (Neffe, 1988). In the case of emission spectral analysis, the usual artificial graphite electrode is used one to three times and is then thrown away. However, glass-like carbon electrodes can be used 100 times and, furthermore, they are highly sensitive and reproducible. Another application is packing for the various chromatography techniques (Fujinaga etal., 1967; Tanaka etal., 1976) because glass-like carbon can be used at a high temperature, can be packed easily and causes no tailing of chromatographic peaks. This application might be extended because of the development of new procedures to prepare the fine glass-like carbon particles stated above. Fine porous glasslike carbon particles may be used as a molecular sieve. 10.6.3 Metallurgical Applications Glass-like carbon crucibles are used as containers for molten salt electrolysis in the production of corrosive metals. Also, glass-like carbon tubes are used to blow chlorine gas to remove hydrogen from aluminum ingots. Since glass-like carbon is gas-impermeable and unreactive with metals at high temperatures, this application is expected to be extended if the cost can be lowered. There have been some tri-

569

als to replace the usual glass-like carbon with a composite glass-like carbon able to produce high yields. 10.6.4 Applications to Biomaterials

Carbon material has a high biocompatibility (Bokros etal., 1973), but problems are caused by its low moldability and diffusion of the fine carbon particles into tissue. In general, carbon materials for use as biomaterials are subjected to a hardening treatment of the surface, but glass-like carbon can be used without such treatment because of its hard and dense structure with no pores. Wear resistance, one of the most important properties, is improved by ion implantation (Pollock et al, 1987). An application has been attempted for dental implants, with unsuccessful results (Grenoble and Kim, 1973). It was difficult to prepare a thin rod with sufficient mechanical strength. Applications to joints in various parts of the body (Jenkins, 1980; Fitzer, 1980) and replacement of broken bones (Itoh et al., 1985) were reported; however, the subsequent results have not yet been reported. A well-known biocarbon material is pyrolytic carbon which is widely used as a heart valve (Bokros et al., 1973). Fitzer et al. (1978) reported that the lower-priced glass-like carbon can be used successfully, instead of pyrolytic carbon, as the valve material. 10.6.5 Applications to Fuel Cells

As shown in Fig. 10-12, separators used for fuel cells are large (60 x 60 cm100 x 100 cm, 0.5-1 mm in thickness). The phosphoric acid fuel cell (or first generation fuel cell) using a concentrated phosphoric acid electrolyte (Fig. 10-13) operates at 200 °C for long periods of time. The constituent material must have high oxida-

570

10 Glass-Like Carbons

Figure 10-12. The fuel cell separator.

tion as well as high thermal resistance. Additional properties required are as follows: (i) high mechanical strength to be handled in thin plates and to resist multiple stacking, (ii) gas impermeability, (iii) a small coefficient of thermal expansion, (iv) high electrical and thermal conductivities. Only noble metals and the carbon materials possess such properties. Initially, carbon plate separators were prepared by cutting artificial graphite out of normal bulk and subsequent impregnation with thermosetting resin. Such a method of low production yield resulted in an increase of the price of plates. The glasslike carbon plate was selected instead, but it has too small a thermal conductivity and low production yield. As a result, com-

posite glass-like carbon with graphite powder as a filler was developed and is now being tested. The use of the graphite filler results in an improvement of mechanical strength and flexibility as well as significant increases in electrical and thermal conductivities. Porous carbon is used as an electrode of the fuel cell (Stonehart, 1984). Here, the homogeneous sizes and uniform distribution of pores are required, in addition to the properties required in the separator. An electric capacitor using the active carbon fiber derived from Kynol-type phenol resin has already been industrialized in Japan; details have been reported elsewhere (Nishino et al, 1985).

Residual hydrogen Hydrogen electrode

A

uri

.— Separator ^

Oxygen electrode (with catalysis)

„

Electrolyte

• Electrolyte.

Natural. gas

V Water vapor

Air

^ Oxygen electrode • Hydrogen o Oxygen • o Water

(Phosphoric acid) -*—Hydrogen electrode (with catalysis)

-— Separator Hydrogen

Figure 10-13. Schematic model of the phosphoric acid fuel cell and assembly of the electrodes.

10.8 References

10.6.6 Other Applications

In aerospace applications, glass-like carbon is used as a rocket nozzle. Applications of the porous glass-like carbon to make heat-insulators, filters and catalyst supports are now under development. Attempts were made some years ago to use a light-weight glass-like carbon mirror in advanced optical systems (Pinoli and Bradshaw, 1975). Composite glass-like carbon with a high production yield is being considered for use as a tube for the heat exchanger. Glass-like carbon fibers are so flexible, though with poor mechanical properties, that they are used as a packing material, abrasion material, and wear-resistant material (Miyashita, 1983). A high-quality glass-like carbon may be used as a cast for optical lens preparation and as a laser mirror.

10.7 Acknowledgements The authors express their appreciation to Dr. M. Shiraishi of the National Research Institute for Pollution and Resources for useful discussions and lending of high resolution photomicrographs.

10,8 References Aggarwal, R. K., Bhatia, G., Bahl, O.P., Malik, H. (1988), J. Mater. Sci. 23, 1677. Bacon, R., Tang, M. M. (1964), Carbon 2, 221. Bhatia, G., Aggarwal, R. K., Malik, M., Bahl, O. P. (1984), J. Mater. Sci. 19, 1022. Bokros, J.C., LaGrange, L.D., Schoen, F.J. (1973), in: Chemistry and Physics of Carbon, Vol. 9, Control of Carbon for Use in Bioengineering; Walker, Jr., P.L. and Thrower, P. A. (Eds.). New York: Marcel Dekker, pp. 104-171. Bose, S., Dahmen, U., Bragg, R. H., Thomas, G. (1978), J. Am. Ceram. Society 61, 174. Bradshaw, W. G., Pinoli, P. C , Mitchel, M. J. (1969), Abstracts. 9th Biennial Conference on Carbon. Boston. Am. Carbon Society; pp. CA15.

571

Cowlard, E C , Lewis, J.C. (1967), J Mater. Sci 2, 507. Craievich, A., De Dujovny, E.P. (1973), J. Mater. Sci. 8, 1165. D'Antonio, P., Konnert, J.H. (1981), Abstracts. 15th Biennial Conference on Carbon. Philadelphia. Am. Carbon Society; pp. 476. Davidson, H. W. (1957), British Patent 860,342. Davidson, H. W. (1959), British Patent 889,351. de Galan, L., de Loos-Vollebregt, T. C , Oosterling, A.M. (1983), Analyst 108, 138. Economy, I, Lin, R. Y. (1971), J Mater. Sci. 6, 1151. Edelson, L. H., Glaeser, A. M. (1986), Carbon 5, 635. Fitzer, E. (1980), Pure and Appl. Chem. 52, 1865. Fitzer, E. (1987), Carbon 25, 163. Fitzer, E., Schaefer, W, Yamada, S. (1969), Carbon 7, 643. Fitzer, E., Schaefer, W. (1970), Carbon 8, 353. Fitzer, E., Mueller, K., Schaefer, W. (1971), in: Chemistry and Physics of Carbon, Vol. 7. The Chemistry of the Pyrolytic Conversion of Organic Compounds to Carbon; Walker, Jr., P.L. (Ed.). New York: Marcel Dekker, pp. 237. Fitzer, E., Huttner, W, Wolter, D. (1978), 3rd Int. Symp. on Newer Fibers and Composites, Bombay. pp. 389. Franklin, C. H., Japanese Patent Publication 1980 27,003. Fujinaga, T, Ogino, Y, Murai, S. (1967), Japan Analyst. 16, 492. Fukuda, H., Ouchi, K., Sagi, M. (1988), Japanese Patent Publication 1988-50,366. Furukawa, K. (1964), J. Cryst. Soc. Japan 6, 47. Grenoble, D.E., Kim, R.L (1973), Arizona State Dental Journal 19, 12. Heimann, R. B., Kleiman, I , Salansky, N. M. (1983), Nature 306, 164. Hirano, S., Yogo, T, Suzuki, H., Naka, S. (1983), J. Mater. Sci. 18, 2811. Honda, H., Sanada, Y, Furuta, T, Teranishi, H. (1966), Tanso (Carbons), No. 46, 2. Hucke, E.E. (1975), U.S. Patent Publication 3,859,421. Itoh, H., Yamashita, H., Katayama, N. (1985), Seitaizairyo (Biomaterials) 3, 45. Iwasaki, S., Nakamura, Y (1977), IEEE Trans. MAG13, 1212. Jenkins, G. M. (1980), Clin. Phys. Physiol. Meas. 3, 171. Jenkins, G. M., Kawamura, K. (1971), Nature 231, 175. Jenkins, G. M., Kawamura, K., Ban, L. L. (1972), Proc. R. Soc. (London). A327, 501. Jenkins, R. G., Walker, Jr., P. L. (1976), Carbon 14,1. Johnson, A. C , Pinoli, P. C , Keller, R. L. (1979), Abstracts. 14th Biennial Conference on Carbon, State College (Pennsylvania). Am. Carbon Society; pp. 238. Jung, H.-J. Mahajan, P.P., Castilla, C M . , Walker, Jr., P.L. (1979), Abstracts. 14th Biennial Confer-

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10 Glass-Like Carbons

ence on Carbon, State College (Pennsylvania). Am. Carbon Society; pp. 26. Kakinoki, J. (1965), Acta Cryst. 18, 578. Kamiya, K., Suzuki, K. (1975), Carbon 13, 317. Kammereck, R., Nakamizo, M., Walker, Jr., P. L. (1974), Carbon 12, 281. Katsura, S., Shiraki, M., Japanese Patent Publication 1987-162,611. Kawamura, K., Jenkins, G.M. (1970), /. Mater. Sci. 5, 262. Kikuchi, Y, Yamada, K., Fujita, J. (1985), Japanese Patent Publication 1985-65,781. Kobayashi, K., Sugawara, S., Toyoda, S., Honda, H. (1968), Carbon 6, 359. Koyama, H., Marumo, C , Kajikawa, T., Shimizu, S. (1988), Japanese Patent Publication 1988-129,006. Le Societe le Carbone-Lorraine (1964), British Patent 1,031,126. Lewis, J. C. (1963), Solid State Electronics, 6, 251. Levendis, Y A., Flagan, R. C. (1989), Carbon 27, 265. Linden, W. E., Dieker, I W. (1980), Anal. Chim. Acta 119, 1. Metrota, B., Bragg, R.H., Rao, A.S. (1983), /. Mater. Sci. 18, 2671. Miyashita, Y. (1983), Kogyo Zairyo (Industrial Materials) 31, 52. Murakami, S., Uemura, T., Yoshida, T. (1985), Japanese Patent Publication 1985-36,316. Murata, H., Nakajima, M., Terasaki, R., Ogata, Y (1988), Japanese Patent Publication 1988-74,960. Nagle, D. C , Walker, Jr., P. L. (1973), Abstracts. 11th Biennial Conference on Carbon, Catlinburg (Tennessee). Am. Carbon Society; pp. 322. Neffe, S. (1988), Carbon 26, 687. Nishino, A., Yoshida, A., Tanahashi, I. (1985), U.S. Patent 4,562,511. Noda, T., Inagaki, M. (1964), Bull. Chem. Soc. Japan 37, 1534. Noda, T., Inagaki, M., Yamada, S. (1969), /. NonCryst. Solids 1, 285. Ogata, Y, Nakajima, M., Terasaki, R., Sato, S. (1987), Japanese Patent Publication 1987-292,611. Otani, S. (1965), Carbon 3, 31. Otani, S. (1966), Japanese Patent Publication 1966 15,728. Ouchi, K., Honda, H. (1959), Fuel 38, 429. Pekala, R. W, Hopper, R. W (1987), /. Mater. Sci. 22, 1840. Pinoli, P. C , Bradshaw, W G. (1975), Abstracts. 12th Biennial Conference on Carbon, Pittsburgh. Am. Carbon Society; pp. 89. Pollock, I T . A., Clissold, R. A., Farrelly, M. (1987), J. Mater. Sci. 22, 6. Redfern, B. (1961), British Patent 956,452. Redfern, B., Floyd, L I (1962), British Patent 1,024,971. Rivington, H. L. (1960), British Patent 921,236. Sakaguchi, K. (1988), Japanese Patent Publication 1988-242,982. Saura, E., Nikaido, M., Yokoda, H. (1987), Japanese Patent Publication 1987-278,111.

Shiraishi, M. (1984), Tanso Zairyo Nyumon (Introduction to Carbon Materials, Revised Edition). Tokyo: Kagakugijitsu-sha, pp. 33. Sladkov, A. M., Kasatochkin, V. I., Kudryavtsev, Yu. P., Korshak, V. V . (1968), Izu. Akad. Nauk-SSSR, Ser. Khim. 12, 2697. Stonehard, P. (1984), Carbon 22, 423. Takahashi, Y, Westrum, Jr., E. F. (1970), /. Chem. Thermodynamics 2, 847. Tanaka, K., Ishizuka, T., Sunahara, H. (1976), Bunseki Kagaku 25, 183. Tang, M.M., Bacon, R. (1964), Carbon 2, 211. Teranishi, H., Ishikawa, T, Honda, H. (1967), Tanso (Carbons), No. 51, 11. Tingey, G. L. (1975), Abstracts. 12th Biennial Conference on Carbon, Pittsburgh. Am. Carbon Society; pp. 181. Tormala, P., Romppanen, M. (1981), J Mater. Sci. Lett. 16, 272. Wakasa, M., Yamauchi, M., Negishi, N., Imamura, T. (1987), Japanese Patent Publication 198736,011. Walker, Jr., P.L., Oya, A., Mahajan, O.P. (1977), Abstracts. 13th Biennial Conference on Carbon, Irvine. Am. Carbon Society; pp. 382. Wang, J. (1981), Carbon 26, 1721. Wang, I (1981), Electrochimica 26, 1721. Whittacker, A. G., Tooper, B. (1974), /. Am. Ceram. Soc. 57, 443. Yajima, S., Omori, M. (1972), Chem. Lett. 843. Yamada, S. (1968), Japan Analyst. 17, 1031. Yamada, S., Nakamura, S. (1966), Japanese Patent Publication 1966-15,727. Yamada, S., Sato, H. (1962), Nature 193f 261. Yamada, S., Takada, S. (1963 a), British Patent 1,033,277. Yamada, S., Takada, S. (1963 b), Japanese Patent Publication 1963-9,554. Yamada, S., Yamamoto, M. (1968), Carbon 6, 741. Yamada, S., Sato, H., Ishii, T. (1964), Carbon 2, 253. Yamashita, Y, Ouchi, K. (1981), Carbon 19, 89. Yamauchi, M., Negishi, N., Imamura, T. (1985), Japanese Patent Publication 1985-171,210. Yasuda, T., Nakamura, T. (1975), Denki Kagaku (J. Electrochem. Soc. Japan) 33, 138. Yata, S., Hatou, K., Ohsaki, T, Sakurai, K. (1986), Japanese Patent Publication 1986-222,912. Yogo, T, Tamura, E., Naka, S., Hirano, S. (1986), /. Mater. Sci. 21, 941. Yoshimori, T, Arakawa, M., Takeuchi, T. (1965), Talanta 12, 147. Zittel, H. E., Miller, F. I (1965), Anal. Chem. 37, 200.

General Reading Jenkins, G. M., Kawamura, K. (1976), Polymeric Carbons - Carbon Fiber, Glass and Char. Cambridge: Cambridge University Press.

11 Organic Glasses and Polymers Ernst Rossler Institut fur Atom- und Festkorperphysik, Freie Universitat Berlin, Berlin, Federal Republic of Germany Hans Sillescu Institut fur Physikalische Chemie, Universitat Mainz, Mainz, Federal Republic of Germany

List of Symbols and Abbreviations 11.1 Introduction 11.2 General Considerations 11.2.1 Typical Properties of Organic Glasses 11.2.2 Different Types of Glasses 11.2.3 Experimental Methods . 11.2.3.1 Thermal Methods 11.2.3.2 Viscosity, Mechanical and Dielectric Relaxation 11.2.3.3 Optical Methods 11.2.3.4 Neutron Scattering 11.2.3.5 NMR Methods 11.2.4 Theoretical Treatment 11.2.4.1 Free-Volume Theory 11.2.4.2 Thermodynamic Theories 11.2.4.3 Mode-Coupling Theory 11.2.4.4 Energy Landscapes 11.3 Typical Examples and Recent Applications 11.3.1 Simple Liquids 11.3.1.1 a Process 11.3.1.2 p Process 11.3.2 Polymeric Liquids 11.3.3 The Glassy State 11.4 References

Materials Science and Technology Copyright © WILEY-VCH Verlag GmbH & Co KGaA. Allrightsreserved.

574 577 579 579 582 585 586 586 587 588 588 593 593 595 596 597 598 598 598 605 607 608 615

574

11 Organic Glasses and Polymers

List of Symbols and Abbreviations B C

molecular-size parameter effective coupling constant heat capacity cP complex heat capacity D translational diffusion coefficient electric field E E activation energy most probable activation energy EP mean fractional free volume f Debye-Waller factor h non-ergodicity parameter distribution of spin-lattice relaxation times f(Td field F motional correlation function FA(t) ) F{x1,x2, t 2 correlation function of spin alignment experiment distribution of activation energies g(E) Fourier transform of G (co) G(t) van Hove's autocorrelation function GA*,t) G(lnr) distribution of correlation times storage modulus G'(co) G"((o) loss modulus /(CO) powder spectrum solid echo spectrum I(co,T) 7 fast exchange spectrum fast(<») slow exchange spectrum I slow (<») shear compliance J(t) J((O0) spectral density function adiabatic compressibility Ks(co) M(q,t) mode-coupling memory function distribution of correlation times PA(?) ) conditional probabilities position of a scatterer j position of a scatterer k at time t rk(t) solid echo time signal configurational entropy sc coherent dynamic structure factor incoherent dynamic structure factor Sine (9, <») spin-lattice and spin-spin relaxation times TltT2 T* transversal relaxation time critical temperature of mode coupling theory Tc glass transition temperature Ts Kauzmann temperature Tk melting point Tm

List of Symbols and Abbreviations

% V V(q,q') wtj W(T) XA(co) X'D(CO)

a Of

r 8 £*((L>)

n X

n n

kj

Q>Qo u cs u cs u cs zz yy xx

C0 0

BMO BPP CD DSC FID FRS HMB LCPS

Vogel temperature corrected glass transition temperature (reference temperature) cell volumes critical volume average free volume free volume constant molecular volume volume vertex function transition rate weight factor dynamic complex susceptibility dielectric loss curve thermal expansion coefficient differences of thermal expansion coefficients above and below Tg gamma function activation energy complex dielectric constant shear viscosity complex viscosity bulk viscosity compressibility coupling constant temperature-independent coupling parameter Prigogine-Defay ratio rate of the transitions Qt Qk density anisotropic chemical shift tensor motional correlation time cut-off time of the CD distribution response function density correlation function intermediate-scattering function excitation frequency Larmor frequencies adjustable parameters 1,1 -bis (4-methoxyphenyl) cyclohexane Bloembergen Purcell Pound Cole-Davidson differential scanning calorimetry free-induction decay forced Rayleigh scattering hexamethyl benzene liquid crystal side chain polysiloxane

575

576

KWW OTP PCS PS PDB PMMA RBS TLS TNB TTI VFT WLF

11 Organic Glasses and Polymers

Kohlrausch-Williams-Watts o-terphenyl photon correlation spectroscopy polystyrene phthalic acid di-n-butylester polymethylmethacrylate Rayleigh-Brillouin spectra two-level system 1,3,5-tri-oc-naphthyl benzene thiophene indigo derivative Vogel-Fulcher-Tammann Williams-Landel-Ferry

11.1 Introduction

11.1 Introduction Transparency and the capability of glass blowing are the most prominent features that a layman attributes to glassy materials. Transparency, specifically optical isotropy, corresponds to disorder. The similarity to a liquid is stressed by the term frozen liquid, which characterizes the structure of the glassy state. All microscopic theories introducing the concept of microcrystalline structure have failed thus far to describe the structure of glass. A glass is instead described by the predominance of local order; no translational symmetry, that is, long-range order, is observed. Topological disorder leads to a distribution of intermolecular distances, orientations, and bond angles. Many physical properties of a glass are not completely characterized by an average value; the corresponding distribution function is also of major interest. A necessary precondition of glass blowing and an important technical processing advantage as compared to crystalline materials is the possibility of controlling the viscosity of molten glass. The viscosity of a glass, or more precisely, that of a supercooled liquid, may be changed over some orders of magnitude within a narrow, but of course, temperature range. In contrast to the liquid-crystal transition, the viscosity increases continuously for the liquidglass transition. Above 1012 Pa s the supercooled liquid is conventionally called a glass. Every liquid may be solidified as a glass provided crystallization is bypassed. The competition between crystallization and vitrification may be decided in favor of the latter when sufficient high cooling rates are applied. Hence speed is the important ingredient of glass formation. Supercooled metallic melts with their high tendency of crystallization may be vitrified by quenching the melt with cooling rates of about

577

10 6 K/s (see Chap. 9). On the other hand, polymer glass forming systems- like window glass melts already have high viscosities near their melting point, and thus the tendency to crystallize is small. Molecular liquids form stable supercooled liquids only in favorable cases; however, these rare liquids are of major interest for experimentalists concerned with checking theoretical predictions. The technology of glass handicraft was already being applied in Phoenician times (see Chap. 1). Oxide glasses containing SiO 2 , Na 2 O and several further additives are nowadays used to yield high-performance window or technical glasses. Extremely high transparency glass is necessary for fiber-optical communications. Here, typical materials are SiO 2 /GeO 2 mixtures (see Chap. 15). Glass-forming compositions of particular halides work to shift the IR edge of standard glass to longer wavelengths (see Chap. 8). Chalcogenide glasses like Se or AsSe exhibiting high photoconductivity are applied in xerography. The glass-crystal transition is exploited in amorphous semiconductor memory elements like Te0 8 Ge 0 2 (see Chap. 7). Amorphous silicon containing hydrogen for photoreceptor films plays an important role in solar cell technology, and rapidly quenched metallic glasses find their application in transformer cores (see Chap. 9). All materials mentioned here consist of inorganic glasses. In many cases large area films are necessary for application, which may easily be achieved by technical control of the viscous flow. On the other hand, many new materials in daily life are made from organic polymers, in the simplest case from linear chain molecules of high molecular weight. Low specific weight, low cost and easy processing are prominent features of this class. All together, the amorphous state, as an alternative solid state to the

578

11 Organic Glasses and Polymers

crystalline state, offers a variety of exceptional properties. Two important questions may be addressed to the physics of amorphous solids. First, what structural principles characterize the glassy state, and what are the rules determining the distribution of local order? Here, the random-close-packing structure advanced by Bernal (1965), Scott and Kilgour (1969), and Finney (1970) as a model for metallic glasses is a starting point. The concept of a continuous random network proposed by Zachariasen (1932) and further developed by Polk (1971), has been used as a guide describing covalently bonded glasses, e.g., fused silica. Although long-range order is missing in a glass, intermediate-range order might play a role. In addition, the importance of structural heterogeneities or cluster formation in amorphous systems has to be clarified. Answers may be presented, for example, by X-ray, neutron, or electron scattering, by extended X-ray absorption fine structure, and by Mossbauer, IR and NMR spectroscopy. Reviews are given by Zallen (1983) and Elliot (1990) (see Chap. 4). The second challenging question for a theory on amorphous solids, which is related to the first question, involves the glass transition itself. What microscopic mechanism controls the sudden increase of viscosity below the melting point of a liquid? Many concepts have been proposed thus far. The most important ones are found in free-volume and thermodynamic theories, respectively. In particular, the widely applied Vogel-Fulcher-Tammann (VFT) equation describing the divergence of the viscosity below the melting point may be derived from both theories. The decrease of free volume and excess entropy, respectively, is related with the slowingdown of the dynamics. The free-volume theories are related to the work of Fox and

Flory (1950), Cohen and Turnbull (1959), and Williams, Landel, Ferry (1955), who proposed their famous WLF equation, a version of the VFT equation. The thermodynamic theories were first formulated by Gibbs and Di-Marzio (1958) and Adam and Gibbs (1965). Within these theories, a second-order phase transition is assumed to account for the Kauzmann paradox (1948); that is, extrapolating the entropy of a supercooled liquid should lead to lower entropies as compared to the corresponding crystal. However, the failure of the VFT equation to describe the viscosity over the entire supercooled region of simple liquids is emphasized in many publications (see Chap. 3). Not only has the divergence of viscosity or molecular time constants to be explained by a proper theory but also the appearance of a secondary relaxation process in the supercooled region, namely, the P-process. In addition, the striking anomalies of glasses at low temperatures have attracted many scientists in the last years. Heat capacity, thermal conductivity, and acoustic and dielectric absorption show peculiarities when investigated below 10K. So-called two-level systems have been introduced by Anderson et al. (1972) and Phillips (1972, 1981, 1987) to explain the anomalies; however, the physical origin of such tunneling modes is still a matter of controversy. An increasing number of publications attack the physics of the amorphous state by computer simulations, in particular, Monte Carlo and molecular dynamics simulations. Lennard Jones liquids and hardand soft-sphere systems are modeled; high quenching rates may be applied which cannot be reached by any experiment. (A review is given by Angell et al., 1981.) Polymer dynamics of systems confined to a lattice structure have shown similarities

11.2 General Considerations

with percolation phenomena, and dynamic non-uniformities have been observed (De la Batie et al., 1984). Computer models of the random-close-packing structure (Finney, 1970) and the continuous random network (Polk and Boudreux, 1973) have also been carried out. The question of the nature of the glass transition has been raised anew by recent extensions of the mode-coupling approach, which is known from the dynamics of simple liquids, and which explains the glass transition on a molecular scale. Contributions by Leutheusser (1984), Bengtzelius et al. (1984), and Sjogren and Gotze (1989) have postulated the existence of a distinguishable temperature above Tg, where traces of a dynamic phase transition may be observed. This marks the first time that a phenomenon like the glass transition has been predicted by an ab initio type theory. Indications for such a transition are substantiated by recent neutron-scattering experiments. The promising concept has inspired many new experiments, and once again, an exciting discussion concering the dynamics of the glass transition has begun. This chapter provides a review of recent applications of new methods mainly on simple supercooled liquids. The class of Van der Waals liquids is well suited to provide model systems for investigating new theoretical concepts of the glass transition. The investigations are not hampered by additional relaxation processes or structural peculiarities. Emphasis is on results from several relaxation methods, e. g., neutron and light scattering, dielectric relaxation, diffusion measurements, and, in particular, NMR studies. The survey includes relaxation studies of the glassy state of organic glasses. For comparison, results on polymers will be recalled, especially polymers with low-molecular-weight additives, as models for polymer plasticizer sys-

579

tems. The experimental picture is completed by reviewing the most influential theoretical concepts which provide a tool for understanding the experimental findings.

11.2 General Considerations 11.2.1 Typical Properties of Organic Glasses

A prominent feature of a supercooled liquid is its dramatic increase in viscosity directly below the melting point Tm. This is demonstrated in Fig. 11-1 for two organic liquids, where data for an organic and an inorganic polymer liquid are included for comparison. While viscosities of the order oflO~ 3 -10~ 2 Pas are typical for non-associated liquids above Tm, the viscosity rises continuously up to values of the order of 10 1 3 Pas within a narrow temperature range. Several approaches describing the strong non-Arrhenius temperature dependence of viscosity have been proposed, but none of them is able to fit the data over the whole supercooled region. In particular, the often-applied Vogel-Fulcher-Tammann equation, lg(rj/f]0) =D/(T- TJ (T^ < Tg), fails for viscosities below 10 2 Pas (Placzek and Magill, 1968). Recently, the equation lg(^/^ 0 ) = (T0/T)2, has been proposed by Bassler (1987), extending energy-transport kinetics in disordered solids to supercooled liquids. In the framework of the mode-coupling theory, a power law, rj =A(T— Tc)~y (Tc > Tg), is predicted for the onset of the glass transition (Sjogren and Gotze, 1989). All three fits are included in Fig. 11-1, demonstrating that only part of the dynamics is described by a single approach. The situation is even more confusing when polymer liquids are considered; the temperature dependence is much smaller as

580

11 Organic Glasses and Polymers

Igl^in Pa s) 12

Figure 11-1. Viscosity as a function of temperature: o-terphenyl (OTP) (O), 1,3,5-tri-oc-naphthyl benzene (TNB) (•), polystyrene (PS) (0), and borone trioxide (B2O3) (#•). Solid line: Vogel-Fulcher-Tammann fit; dashed line: 1/T2 fit; dotted line: power-law fit.

300

400

500

compared to simple liquids. On the other hand, the specific temperature dependence of the viscosity may be used to classify different types of liquids (see Sec. 11.2.2). When measuring the heat capacity of a supercooled liquid as a function of temperature one will notice a significant change occurring at a temperature Tg. A similar effect is observed for the thermal expansion coefficient. Although these features are characteristics of a second-order phase transition, Tg cannot be related unambiguously to an equilibrium function, such as free energy. In particular, the position and the sharpness of the transition near Tg depends on the cooling rate at which the heat capacity is monitored. Conventionally, cooling rates of about 10 K/min are used to determine Tg. Determined in this way, the glass transition temperature Tg can be used to compare different glasses. Isodynamic points are probed, as will be shown below. The interpretation of Tg as a kinetically controlled temperature is also supported by deviations from unity for the so-called Prigogine-Defay ratio, which is unity for a second-order phase transition, or more generally, when only one order parameter determines the system (see Sec. 11.2.4.2).

600

700

TinK

Viscosity as well as correlation times provided by different relaxation methods yield information on the slowing down of the dynamics. In particular, the dynamic complex susceptibility XA(co) for a given observable, A, is of major interest. Generally, XA (to) is measured when some alternating field F is applied and the response A of the systems is detected. For the linearresponse region, both are related by A = XA(co)F

(11-1)

For the case of dielectric relaxation measurements, A is identified with the polarization P, and F with the electric field E. The response of the system may be observed in the frequency domain or in the time domain. The response function
with &'X{co) = ]cos(tot)
11.2 General Considerations

tuations of the quantity A. A(t) is related to the normalized correlation function (A(0) A(t)}KA(0)2} = FA(t) by
581

Different relaxation methods report different correlation times corresponding to different dynamic windows of the dynamics typical for the glass transition. An important task is to relate these quantities to each other in order to obtain a consistent picture. In many different experiments in the supercooled region, FA (t) cannot be described by a simple exponential decay which is implied by the so-called Debye model (Debye, 1929). Non-diffusional dynamics determine the motion of the molecules. In many cases, the non-exponential correlation function may be approximated by a stretched exponential, namely, the Kohlrausch-Williams-Watts function (Kohlrausch, 1847; Williams and Watts, 1970)

quency domain, that is, XA (co), are analytical. Taking the concept of a distribution of correlation times literally and not only as a formal way to account for non-exponential correlation loss, the question arises whether a distribution of correlation times is a realistic picture for a supercooled liquid. Different molecules perform reorientation with different time constants and relax independently with an exponential correlation function. The alternative picture describes highly coupled molecules which relax collectively with a non-exponential correlation function. In the last case the cooperative nature of the glass transition is emphasized. We will come back to this question. When X"A (co) is measured in the supercooled region, pronounced asymmetric curves are found for the main a peak and its maximum shifts to lower frequencies when the temperature is lowered. In many cases the frequency-temperature superposition principle holds. The individual XA(CD, 7j) are superimposed to a master curve X"A as the frequency co is scaled by com, where com is taken from each maximum of XA(a>, Tt). Thus, we write

FA(t) = exp(-t/Ty

X'JL(co9T) = X'JL(ca)

FA®: 00

xA = lFA(t)dt

(11-3)

0

(11-4)

An alternative description is the introduction of a distribution of correlation times pA (T). The correlation function is given by a convolution of exponential decays with a distribution pA (T). (11-5) Distribution functions proposed by Cole and Davidson, Cole and Cole, or Fuoss and Kirkwood have been widely applied. (A review is given by Bottcher and Bordewijk, 1978.) In many cases analytical expressions for FA (t) cannot be given, but the corresponding expressions in the fre-

(11-6)

with co = co/com. These experimental findings imply a scaling law for the correlation function FA (t), namely FA(t,T) = FA(t/z{T))

(11-7)

Changes in temperature do not affect the shape of the correlation function but only the time scale. Applying this important result to the distribution of correlation times pA (T), all correlation times have to change by a constant factor for a given change of temperature. This implies that a distribution of correlation times originating from a distribution of activation energies violates the scaling law (Eq. 11-7). Thus, such an

582

11 Organic Glasses and Polymers

interpretation of pA (T) is not suited to describe the cooperativeness of the a process. However, the concept of a distribution of activation energies might be suited to account for motional non-uniformities of guest molecules in a glass below Tg (see Sec. 11.3.3). The temperature range for the applicability of the stretched exponential scaling law, (Eq. 11-4), is not well understood. One can argue that at the highest temperatures above the melting point, the exponent of the KWW function should return to unity (Grimsditch and Torell, 1989), and a Debye process might be a proper mechanism for the reorientation of liquid molecules at low viscosities. Returning to the operational definition of Tg by the center of the temperature range AT of the large change in heat capacity in a DSC run with cooling rate T, we note that the glass transition is related with a low-frequency excitation. For a typical rate of 10 K/min = 0.02 K/s and AT= 10 K, the excitation frequency is co = f/AT = 0.02 s" 1 , thus probing correlation times of about 50 s. The glass transition temperature defined in this manner can be understood as an isodynamical point which allows for comparing different glasses at temperature Tg. The question arises whether the different correlation times sampled by different methods have the same order of magnitude at Tg, or whether some decoupling of different motional modes may be observed. Experimental results which support a decoupling will be presented below (see Sec. 11.3.1.1). A further important feature of a supercooled liquid is the appearance of the fi process. Inspecting mechanical and dielectric susceptibility, one finds in addition to the large a peak a second smaller /? peak (McCrum et al., 1967; Johari and Goldstein, 1970, 1971; Williams and Watts,

1971). Its maximum shifts with temperature according to an Arrhenius law, whereas the a peak shifts in the typical nonArrhenius way. Relative to the a process, a faster process is responsible for the /? peak. The mean correlation times of the a and p processes merge for high temperatures. Whereas the a process is clearly attributable to the overall reorientation of the molecules, the origin of the (3 relaxation is not yet clarified. Loosely packed regions or islands of mobility (Johari, 1976, 1987), i.e., heterogeneities in the glass, might be responsible for this additional relaxation. Local vibrational modes of some kind have also been considered (Goldstein, 1969). The /? process persists in the glassy state below Tg; however, the total polarization decreases rapidly (Johari, 1976,1987). As a consequence only a few correlation times are reported for supercooled liquids. The /? process is believed to be an intrinsic feature of the glass transition, but it is not observed by all relaxation methods. In Section 11.3.1.2 recent NMR experiments are described which also provide a hint for such an additional process. The appearance of a (S process implies a more involved structure for the correlation function FA (t). For the limit of very short times (10~ 13 s), it starts with zero slope in the form of a Gauss function for free flight of liquid molecules. The development in the picosecond time domain has recently been studied by neutron-scattering techniques (Bartsch et al., 1989) and will be discussed further in Section 11.3.1.2. The traditional p process seen in dielectric and mechanical relaxation occurs on a much slower time scale merging with that of the a process at temperatures above Tg. 11.2.2 Different Types of Glasses Metallic glasses, ionic glasses, Van der Waals glasses, hydrogen-bonded glasses,

11.2 General Considerations

and covalently bonded glasses are distinguished from one another according to different kinds of intermolecular or interatomic interactions. To study the dynamics below Tm, Van der Waals liquids, ionic liquids, and hydrogen-bonded liquids may be supercooled slowly in favorable cases. Lowering the symmetry of the molecular shape by introducing bulky side groups slows down the tendency of a liquid to crystallize, and investigations might thus be facilitated. However, this introduces additional problems; i.e., the role of internal motional freedom, which gives rise to additional relaxation effects, has to be singled out from normal glassy behavior. The class of covalently bonded glasses, which includes inorganic and organic polymers, is somewhat special. Because of polymerentanglement effects, the viscosity of such polymer liquids near the melting point is much higher than that of Van der Waals liquids. Consequently, crystallization is slowed down, and the amorphous state is favored for these systems. However, with respect to dynamics, many properties are controlled by typical polymer properties, e.g., entanglement effects, decoupled molecular processes, or molecular-weight dependencies. Compared to polymer liquids, hydrogen-bridged liquids may be regarded as temporary polymers; the connectivity of the subunits is not permanent. The temperature dependence of viscosity helps to discriminate different classes of liquids. In particular, the question of universality within one class is often discussed. In 1972, Laughlin and Uhlmann proposed the use of the glass transition temperature for reducing the data. The authors extrapolated their data to a temperature corresponding to a viscosity of 10 14 Pa s. Later, Wong and Angell (1976) rescaled the data mainly for inorganic glass-forming systems by defining a glass transition temperature

583

as Tg = T{rj = 1012 Pa s). In the first case a reasonable master plot was provided for organic liquids, whereas in the second case different curves were obtained which were distinguished in terms of strong and fragile network glass formers. A different scaling procedure has been proposed recently by Rossler (Rossler, 1990 a, b) which is more in the spirit of Laughlin and Uhlmann. A better correlation was observed when minor corrections for the calorimetric Tg were carried out. The viscosity data of nonassociated liquids was rescaled in order to provide the best agreement in the range 10 2 -10 1 0 Pas. Furthermore, a reference liquid, 1,3,5-tri-a-naphthyl benzene, is introduced, where Tg = Tr is used for defining a reduced temperature scale. The result is shown in Fig. 11-2. Table 11-1 compiles Tg and Tr, and a high correlation is found among these quantities. The fundamental and experimental uncertainties in measuring Tg are minimized, and extrapolation errors are avoided by applying this reduction procedure. The isodynamic point Tg with a minor correction is taken to rescale the viscosity data of different glass-forming liquids. Three features are discovered from such a corresponding states analysis for non-associated organic liquids, (i) Universal behavior is revealed for organic liquids above 10 2 Pas. (ii) Below 10 2 Pas individual curves separate from the master curve, (iii) The viscosity at Tg is of the order of 1010 Pa s. Thus, a correlation time for heat flow of about 50 s corresponds to a viscosity of 10 10 Pa s. Judging from these results, it is believed that two dynamic regions have to be distinguished at least for simple organic liquids-namely, above and below 10 2 Pas - and have to be described separately. It has been shown that the VFT equation yields the best fit for the compiled data only above 10 2 Pas (see Fig. 11-2),

584

11 Organic Glasses and Polymers

Table 11-1. Glass transition temperatures Tg reported and reference temperatures TT given by the corresponding states analysis. Glass forming system

Non-associated organic and ionic n-butyl benzene sec-butyl benzene di-n-butyl phthalate 3-methyl pentane o-terphenyl a-phenyl-o-cresol phenyl salicylate n-propyl benzene i-propyl-benzene 1,3,5-tri-a-naphthyl benzene Hydrogen bonded propanol Polymers oligostyrene (M = 550) polystyrene (M = 4000) polystyrene (M = 37OOO) polystyrene (M = 390000) B2O3 BeF2 BSC (Oxide-glass) GeO 2 NBS-711 SiO2 Soda lime

Symbols in Fig. 11-2

References

+

1, 2 | 3 1 |3 1 1 3, 4, 5 6|7 8,9 | 10, 11, 12 8,9 5, 10 8,9 5,10 1 |3 1,2 3,12 13 | 14, 13

Tg(K)

T r (K)

liquids 125 127 176/193/181 77 242/243/244 221/230 220/230/225 122 125/127 342/345

132.5 138 185 86.4 244.2 215.3 218.8 131 131.7 345

98

98

O

15 | 3

251 353/350 378/370 380/373 526/530/539 598/570 — 853/820/810 — 1430/1453 —

258.4 343.6 370.1 373 532 584 816 810 694 1430 781

1— 2— 3— 4—

16 | 17 18 | 19, 17 18 | 19, 17 18 | 19, 17 20 | 21, 22, 10 23 | 24, 25 15 | — 26 | 24, 25, 26 15 | — 26 | 24, 22 27|-

A

•V o• O X

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O

o

References: 1) Barlow, A. I, Lamb, J., Matheson, A. J. (1966), Proc. Roy. Soc, London Ser. A 293, 322. 2) Ling, A. C, Willard, J. E. (1968), J. Phys. Chem. 72,1918. 3) Carpenter, M. R, Davies, D. B., Matheson, A. J. (1967), J. Chem. Phys. 46, 2451. 4) Hains, P. J., Williams, G. (1975), Polymer 16, 725. 5) Rossler, E. (1990), Ber. Bunsenges. Phys. Chem. 94, 392. 6) Von Salis, G.A., Labhart, H. (1968), J. Phys. Chem. 72, 752. 7) Johari, G.P., Goldstein, M. (1971), J. Chem. Phys. 55, 4245. 8) Laughlin, W.T., Uhlmann, D.R. (1972), J. Phys. Chem. 16, 2317. 9) Cukiermann, M., Lane, J. W., Uhlmann, D. R. (1973), J. Chem. Phys. 59, 3639. 10) Grest, G. S., Cohen, M. H. (1981), Adv. Chem. Phys. 48, 455. 11) Greet, R. I, Turnbull, D. (1967), J. Chem. Phys. 47, 2185. 12) Johari, G.P., Goldstein, M. (1970), J. Chem. Phys. 53, 2372. 13) Plazek, D. J., Macgill, J. H. (1968), J. Chem. Phys. 45, 3038. 14) Ehlich, D., Sillescu, H. (1990), Macromolecules 23, 1600. 15) Tweer, H., Simons, J.H., Macedo, P.B. (1971), J. Chem. Phys. 54, 1952. 16) Allen, V.R., Fox, T.G. (1964), J. Chem. Phys. 41, 337. 17) Fox, T.G., Loshaek, S. (1955), J. Polym. Sci. 15, 371. 18) Otsuka, S, Ueno, H., Kishimoto, A. (1979), Angew. Makromol. Chemie 80, 69. 19) Claudy, P., Letoffe, J. M., Camberlain, Y, Pascault, J. P. (1983), Polym. Bull 9, 208. 20) Macedo, P. B., Napolitano, A. (1968), J. Chem. Phys. 49,1887. 21) Grimsditch, M., Torell, L. M. (1989), Springer Proceedings in Physics, Vol. 37: Richter, D., Dianoux, A. J., Petry, W., Teixeira, J. (Eds.). Heidelberg: Springer, p. 196. 22) Van Uitert, L. G. (1979), J. Appl. Phys. 50, 8052. 23) Moynihan, C. X, Cantor, S. (1967), J. Chem. Phys. 48,115. 24) Wright, A. C, Etherington, G., Desa, J. A. E., Sinclair, R. N., Connell, G. A. N., Mikkelson, J. C. (1982), J. Non-Crystal. Solids 49, 63. 25) Zallen, R. (1983), The Physics of Amorphous Solids. New York: J. Wiley. 26) Wong, J., Angell, C. A. (1976), Glass Structure by Spectroscopy. New York: Marcel Dekker. 27) Doremus, R. H. (1973), Glass Science. New York: J. Wiley.

11.2 General Considerations

585

o

13

-

11 I/)

o CL

X

inorganic polymer liquids

9 7

/ 0

5 3

I

1 &"-

~$*

"

•

*®

° *

-•if

a

%"*

2.

simple organic liquids

T

-1

TC

1

• /

0.6

0.7

A—VFT Fit i

0.8 T r /T

1

i

i

0.9

1.0

whereas below 10 2 Pas a power law, rj =A(T— Tc)~y, as predicted by modecoupling theory, is well suited to fit the onset of the glass transition, where the highest curvature of r\ (T) occurs. Tc — 1.18 Tr provides a reasonable description for all liquids (Rossler, 1990 a, b). Extending the scaling procedure to inorganic polymer liquids does not allow the data to be rescaled to coincide with the master curve of simple liquids. However, we chose B 2 O 3 as a reference system with Tr = Tg and superimposed all data at highest viscosities (Rossler, 1991). Again, some degree of universality was found and the relation between Tg and Tr is satisfying (compare Fig. 11-2 and Table 11-1). Tg corresponds to 10 13 Pa s which is a considerably higher value compared to simple liquids. The two types of rescaled viscosity curves in Fig. 11-2 may be related to each other if the viscosity of organic polymers with different molecular weights are rescaled. Data for different molecular weights of polystyrene are included in Fig. 11-2 (Allen and Fox, 1964; Otsuka et al.,

Figure 11-2. Rescaled Arrhenius plot for different types of liquids. For symbols see Table 11-1.

1979). The polystyrene with the lowest molecular weight behaves like a typical simple liquid, whereas the data of high molecular weight do not at all coincide with the curves of simple organic liquids. Instead, the multitude of inorganic glassforming polymers is approached. Hence, we conclude that the differences between the class of low- and high-molecularweight liquids mainly involve a polymer effect, namely, an entanglement effect (DeGennes, 1979); the chemical character of the polymer liquid is of minor importance. The viscosity curves of hydrogen-bonded liquids lie between the two limiting curves, as demonstrated for propanol in Fig. 11-2.

11.2.3 Experimental Methods

In this Section, experimental methods for investigating physical properties of supercooled liquids and amorphous materials are briefly described. More details are given on recent NMR techniques, since most examples in Section 11.3 are related to NMR applications.

586

11 Organic Glasses and Polymers

11.2.3.1 Thermal Methods The calorimetric techniques used for measuring the heat capacity Cp of glasses are the same as used for other solid materials (see Vol. 2). In particular, differential scanning calorimetry (DSC) is used for determining the glass transition temperature Tg. Here, it is important to note the dependence of Cp and Tg on the cooling and heating rates, which has led to particular techniques for investigating the dynamics of enthalpy relaxation. Thus, one can analyze the hysteresis in heating and cooling cycles or the enthalpy relaxation after temperature jumps in terms of an order-parameter formalism that takes account of the time-dependent non-equilibrium states at and below Tg (Jackie, 1986; Kovacs, 1981). Recently, a very elegant technique has been developed which in effect allows for the determination of a complex heat capacity C* (co) at temperatures T>Tg (Birge and Nagel, 1985). Here, the temperature can be modulated at frequencies up to the kHz region, with small amplitudes (~0.1K) around some temperature T where the system is in quasi-equilibrium. C* (co) has a frequency and temperature dependence which is similar to the complex viscosity rj*(co) and dielectric constant s* (co) (see below). However, whereas the latter may only couple to part of the glass process, C* (co) depends on all motional degrees of freedom. This has important consequences for analyzing the dependence of the a process on time and temperature (Angell, 1988). 11.2.3.2 Viscosity, Mechanical and Dielectric Relaxation The shear viscosity of supercooled liquids varies over a dynamic range of about 15 decades between the liquid region and the glass transition temperature. Whereas

capillary techniques are only applicable to normal liquids, rotation viscosimetry can be used in the viscous range up to about 10 3 Pas, and sphere drag methods are applicable up to ~ 1 0 8 P a s . Since supercooled liquids and molten polymers are viscoelastic, a frequency-dependent complex shear viscosity (Ferry, 1980) is defined as

= co

-l

[G"(co)-iGf(co)]

where Gf(co) is the storage modulus, and G" (co) the loss modules. The real viscosity is then obtained as the zero frequency limit of Gff(co)/co. Since G(co) is perhaps the most important quantity for characterizing the internal dynamics of polymeric materials and rubbers, rather sophisticated techniques have been developed for its measurement and analysis, mostly by applying small oscillations in plate-plate or coneplate geometry. It is clear that the Fourier transform of G(co) is the shear relaxation function G (t) which is related to the shear compliance J(t). Other mechanical relaxation functions are related to extension and compression experiments yielding the bulk viscosity in the zero frequency limit. We refer the reader to the monograph of Ferry (1980) for a detailed description of these techniques. Recent applications to polymer glass formers have been reviewed by Pearson (1987) and to low-molecularweight glass formers by Angell (1988). Dielectric relaxation is one of the most important observables for studying the a and /? processes in glass formers (McCrum etal., 1967; Johari, 1970, 1971). Although the relation between the complex dielectric constant 8 (co) and the motion of molecular dipoles is complex due to interdipole crosscorrelations, one can often obtain approximate correlation functions for molecular reorientation over a wide time and temper-

11.2 General Considerations

ature range extending from the liquid state, through the glass transition, to the solid glass. Recent technical advances have made it possible to build measuring systems from mostly commercial components, where a frequency range from 10 4 -10 9 Hz can be scanned in 3 stages essentially automatically as a function of frequency and temperature (Kremer etal, 1989). An excellent monograph on dielectric relaxation, which includes IR and optical frequencies as well as the dynamic Kerr effect, was published by Bottcher and Bordewijk (1978). Applications to supercooled liquids and glasses have been reviewed by Johari (1976 and 1987). 11.23.3 Optical Methods Dynamic light-scattering techniques have recently been applied very successfully to the dynamics in polymers and glass-forming liquids. At high frequencies (~ 10 * ° Hz), Rayleigh-Brillouin spectra (RBS) can be analyzed in terms of the frequency-dependent bulk viscosity rjv (co) and adiabatic compressibility Ks (co) which can be related with the dynamics of density fluctuations (Berne and Pecora, 1976). In a temperature range of up to 150 K above Tg, one observes excess scattering in the central Rayleigh line which has been attributed to clusters. These clusters are also detected in static light scattering, which becomes wave vector dependent in the glass transition region, and in photon correlation spectroscopy (PCS). A first account of these findings was given by Fischer (1989) and Gerharz et al. (1990), where references to literature on the applied light-scattering techniques can also be found. PCS has mostly been used for studying the slow dynamics of density fluctuations at the glass transition (Patterson, 1983). However, the Fischer group has also analyzed the dy-

587

namics of concentration fluctuations in mixed systems where a slow mode has been detected in addition to the expected interdiffusion mode. The former can be related to a diffusional motion of clusters of approximately 100 nm in size, which must be related to the structure of the supercooled liquid close to the glass transition (Gerharz et al., 1990). These interesting new results will probably stimulate further applications of dynamic light scattering to glassforming systems. Translational diffusion at the glass transition was previously restricted to relatively rapid motions of small molecules permeating through polymer films. Recently, the application of forced Rayleigh scattering (FRS) has extended the dynamic range to diffusion coefficients D > 1 0 ~ 1 7 cm2 s" 1 (Sillescu and Ehlich, 1990). In this technique, photoreactive dye molecules serve as diffusional tracers. A holographic grating is formed in the sample exposed to two interfering laser beams, and the diffusive decay of this hologram is subsequently monitored by forced Rayleigh scattering. An example is discussed in Section 11.3.1.1 (Fig. 11-10). Photochemical hole burning has been successfully applied to the slow dynamics in glasses at low temperatures. Here, the photoreactive probe molecule is irradiated by a laser in a narrow band of the optical spectrum. Subsequently, the spectrum is recorded and the broadening of the hole is measured as a function of observation time. Eventually, the sample is annealed at higher temperatures, and the dynamics is studied as a function of temperature (Kohler and Friedrich, 1987). A review of the hole-burning technique has been given by Friedrich and Haarer (1984). Recent applications of optical spectroscopy to glasses can be found in a book edited by Zschogge (1986).

588

11 Organic Glasses and Polymers

11.2.3.4 Neutron Scattering

Neutron-scattering methods have become of particular interest recently, since they appear to be most appropriate for testing the predictions of mode-coupling theories of the glass transition (see Sec. 11.2.4.3). Whereas the structure of a supercooled liquid shows no significant change at the transition to a solid glass, the dynamics freezes in a very complex way, and dynamic neutron scattering provides information on the short-time behavior. The techniques available cover a q range of ~10~2__l nm" 1 a n c j a time range of ~10~ 8 -10~ 1 2 s. Neutron backscattering, time of flight, and spin-echo techniques are used to provide optimum conditions in the different q and t ranges. In organic glasses, neutron scattering by the protons of the organic molecules yields an incoherent dynamic structure factor Sinc (
quency Fourier transform, the intermediate-scattering function # s (q, t\ which is the space Fourier transform of van Hove's autocorrelation function Gs(r,t). The latter provides a measure of the displacement of the scattering centers, the protons, in space and time. Thus, it decays to zero in liquids where the molecules perform diffusive motions over distances of < 1 nm within the time scale of < 10" 8 s covered by neutron scattering. In a solid glass, there is a fast initial decay due to vibrational or librational displacements; however, Gs (r, t) will not decay to zero since the protons can only move within a small spacial region. The height of the long-time plateau determines the elastic peak height of the neutron-scattering spectrum and thus the Debye-Waller factor, or the non-ergodicity parameter fs (q% of the mode-coupling theory. The increased amplitudes of the local motions due to the fast ft process (see Sec. 11.3.1.2) predicted by the mode-coupling

theory cause a decrease of fs(q) with increasing temperature, which is measured at different q values in neutron-scattering experiments and allows for testing of particular scaling predictions (Eq. 11-29). At still higher temperatures, where the a process enters the neutron-scattering time window, a broadening of the elastic peak is observed and used for testing the von Schweidler law (Eq. 11-33). Neutron scattering can also provide the coherent dynamic structure factor Scoh (q, co) in deuterated organic glass formers, since the deuteron is a strong coherent scatterer. Here, the collective motion of nuclei within the scattering volume is monitored since the corresponding van Hove correlation function relates the position Vj (0) of a scatterer j with vk (t) of a neighboring scatterer k at time t. The scaling predictions of the mode-coupling theory (see Eqs. 11-29 to 11-34) are rather similar to those for incoherent neutron scattering and are currently being tested in different glass formers (see Sec. 11.3.1.2). For details of the technique, we refer to monographs on neutron scattering (Springer, 1972; Lovesey, 1986; Bee, 1988). It should be noted that neutron scattering yields information on the type or mechanism of molecular motion that is inaccessible to the relaxation and light-scattering techniques described above (see Sec. 11.2.3.2 and 11.2.3.3). This is demonstrated in Fig. 11-3, where the elastic incoherent structure factor that corresponds to / s (q) (see above) is drawn as a function of q for several motional models (Fujara et al., 1986). Similar information is available by particular NMR techniques discussed below but on a much slower time scale, 1 0 ~ 3 S < T < 1 0 2 S . 11.2.3.5 NMR Methods

As early as 1948, Bloembergen carried out a thesis together with Purcell and

589

11.2 General Considerations Quasieiastic neutron scattering

Deuteron spin alignment

nr7\

l.rir 0 A 0 (q) 1

0.75 -

—'-

0.5

"X*\ 0.25

._ —

A- ••• J V7TV-

0

10

20

.>_ —-~^.-

^^. 30

._ -,

Figure 11-3. Elastic incoherent structure factor A0(q) and normalized spin-alignment echo amplitude F^Tj) calculated for various molecular reorientation models. Dashed line: two-site jump; dotted dashed line: four-site jump; dotted line: rotational diffusion on a circle; solid line: isotropic rotational diffusion, a defines the position of the scatterer of neutron scattering; SQ is 3/4 of the quadrupole coupling constant (Fujara et al, 1986).

Pound by investigating viscous glycerol, thus demonstrating that spin-lattice relaxation is most effective when a motional correlation time x obeys the condition co0 T ~ 1 (Bloembergen et al., 1948). Applying magnetic fields of the order of 1 tesla results in proton Larmor frequencies coo of about 50 MHz; the relaxation is shortest if correlation times are of the order of 10 ~9 s. For a simple liquid, such correlation times are reached only below Tm, i.e., in the supercooled region. The first NMR application to molecular motions was concerned with the glass transition. Motional narrowing of NMR line shapes provides further information on an even slower time scale. Introducing high magnetic fields in combination with Fourier transform techniques has increased the effective signal intensity considerably and has almost completely pushed aside the old continuous wave methods. Measurements of 2 H, 13 C, 31 P nuclei have become attractive and yield information on many problems of physical chemistry. In particular, high-resolution solid-state NMR has gained more and more interest. The accessible molecu-

lar time scale was significantly extended by the advent of pulse techniques for studying slow chemical and, in particular, motional exchange in liquids and in the solid state. Here, two-dimensional NMR techniques are of major importance. A review of the application to solids is given by Fyfe (1984). 2 H N M R applied specifically to polymers is reviewed by Spiess (1984 and 1985).

Spin-Lattice and Spin-Spin Relaxation

The exponential spin-lattice relaxation of a liquid is characterized by the time constant T±, which is related to a spectral density function J(co) given by the Fourier transform of a motional correlation function FA(t) (see Sec. 11.2.1). Corresponding relations hold for the spin-spin relaxation time T2, which determines the line shape in a liquid (Abragam, 1961). l/T2 = C/2[3J{0) + 5J{(o0) + 2J(2co0)] (11-8)

590

11 Organic Glasses and Polymers

C represents an effective coupling constant, depending on the nuclei under investigation. For standard NMR, it is not possible to vary the Larmor frequency co0 over a broad range. Thus, in order to extract motional information from T± or T2, the functional time dependence of FA (t) has to be given. For XH NMR, FA(t) is governed by intra and intermolecular contributions of the dominant dipole-dipole interaction (i.e., by rotational and translational contributions), which are not easily handled. A separation of both contributions is possible by application of the deuteron dilution technique (Eisner and Mitchell, 1961; Zeidler, 1965; Lindner et al, 1981). High-resolution NMR in solids and in supercooled liquids (Mehring, 1976; Haeberlen, 1976) is achieved by systematic suppression of the dipolar coupling. Only chemical-shift anisotropy or quadrupolar interaction remain. The solid-state spectra are no longer smeared out by a dipolar broadening, and high-resolution spectra result. With respect to relaxation, only correlation functions related to rotation of the chemical-shift anisotropy or electric-field gradient are probed. The dipole-dipole interaction is eliminated most effectively by isotopic substitution. For deuterons (quadrupole coupling, 7 = 1) or for phosphorous nuclei (chemical-shift anisotropy, I = 1/2), FA (t) is given in good approximation by the normalized correlation function of the second-order Legendre polynomial (11-9) <(3 cos2 & (0) - 1 ) (3 cos2 $ (t) -1)> FA(f) = <(3cos3(0)-l) 2 > where S is the angle between the direction of the z component of the diagonalized coupling tensor and the magnetic field B. In the case of 2 H NMR, the angle is given by the direction of the a bond and B.

Hence, the reorientation of the C- 2 H bond is probed directly. For the simplest case of a Debye process, where % defines the time scale of molecular rotation. A major property of molecular reorientation in a supercooled liquid is its non-exponential correlation function, which might be modeled by a distribution of correlation times adapted to NMR (Connor, 1963; Noack, 1971). Studying Tx and T2 renders the choice of a proper distribution function less ambiguous. Both relaxation times depend differently on the correlation function. In particular, for co0 r ^> 1 the relaxation rate 1/T2 is directly proportional to the mean correlation time , which is given by the integral over the correlation function. Hence, the temperature dependence of 7\ and T2 are generally different and can be used to unravel the type of non-exponential correlation functions. Line Shape Analysis

In addition to spin relaxation measurements, motional narrowing of NMR line shapes yields information on molecular motion. Consider a proton which can be exchanged by molecular motion, located between two sites with the NMR frequencies co and co'. The two-line spectrum collapses into one line if the exchange frequency 1/T is larger than the spectral splitting \CO — (D'\. This basic phenomenon can be exploited for studying the molecular motion in the solid state or in the supercooled liquid, since the NMR frequency co oc 3 cos2 $ — 1 changes as # varies through molecular reorientation. The powder line shape depends upon the mechanism of rotational motion in the slowmotion region, where 1/T is of the order of the width of the powder spectrum. Thus,

11.2 General Considerations

rotational jumps have been confirmed as a mechanism of molecular reorientation in crystalline solids (Spiess, 1974; Alexander etal., 1974; Pschorn and Spiess, 1980; Wemmer et al., 1981). Discarding any dipolar broadening, the NMR frequency co + cocs of spin 1/2 nuclei like 13 C and 3 1 P is determined by the chemical-shift anisotropy which is described by a second-rank tensor with principal components o^, °"yy a n d ^S cocs = A cs (3 cos2 $ — 1 — rjcs sin2 S cos
^ = (a;; - o/(*2 - O

(u-io)

The angles 5 and cp characterize the orientation of the principal axes of the interaction tensor with respect to the magnetic field B. For deuterons with / = 1, two transitions are observed resulting in a doublet splitting with the frequency shifts + Q ) Q and — coQ. Here, the interaction of the electric quadrupole moment e Q and the electric-field-gradient EFG tensor aQ determines the line shape. Thus the constant in Eq. 11-10 is AQ = 3/&(eQag/h). In good approximation f7Q = 0 holds for deuterons in organic compounds. In a glass or a polycrystalline powder the orientation of the tensor is randomly distributed and typical powder spectra with distinct edges and peaks are observed. For deuterons the well-known Pake spectrum is found. According to a spectral width of the order of 100 kHz, motional correlation times of a supercooled liquid smaller than 10 ~5 s lead to a complete collapse of the broad solid-state spectrum, and for T < 1 0 ~ 6 S a Lorentzian line shape is found. Typically, such a collapse is observed 20-30 K above Tg. In the intermediate range ( 1 / T ~ 1 0 0 kHz), information on the type of molecular reorientation is accessible. The line shape is given by the Fourier transform of the

591

free-induction decay (FID), which is usually measured by standard NMR. The FID can be expressed as (11-11) » = (exp i $coQ(t')dt' o where the average is over all orientations at t = 0 (powder average) and the stochastic process. The latter is modeled by solving the set of rate equations (11-12)

(d/dt)P(Qi/Qj9t)='EP(Qi/Qk9t)nkj k

where P(Qi/Qj9t) represents conditional probabilities, and IJkj rates of the transitions Qk -> Qj where Qj represents the orientation j of the EFG tensor. For a welldefined rotational jump process, these equations can be solved in a straightforward way. For a 2 H NMR spectrum of width 100200 kHz, Eq. 11-11 can not be evaluated, because the fast time signal is partially lost in the dead time of the receiver system, and severe distortions of the spectrum occur as a Fourier transform of the time signal is performed. These problems can be overcome by applying a solid echo sequence, as depicted in Fig. 11-3. Now the time scale can be extended to a few hundred microseconds, because the dynamical range of the solid echo technique is limited only by the transversal relaxation time T2*. Beyond a time of the order of T2*, no echo is observed. The solid echo time signal starting at the echo maximum can be formulated as (Spiess and Sillescu, 1981)

= ( exp i J coQ ( 0 df -i]coQ (tr) dtf \ L o *i J where x1 is the distance between the two pulses. Again (Eq. 11-12) is applied to describe S1 if a proper motional model is given. The FID So and the solid echo time

592

11 Organic Glasses and Polymers

signal St become equal in the rigid solid limit. In the case of fast isotropic reorientation of the molecules, the solid echo spectrum disappears, and the FID spectrum shows a sharp Lorentzian line. However, fast, but anisotropic, reorientation results in a motionally averaged powder spectrum where A and rj have to be replaced by the averaged values of the tensor components (i.e., A and fj in Eq. 11-10). A typical example is the fast methyl rotation which results in a Pake spectrum reduced by a factor of three. For a fast anisotropic reorientation with a symmetry higher than C 2 , the spectral reduction is generally given by 2

A=A/2(3cos y-l)

(11-14)

where y is the angle direction of the C - 2 H bond with respect to the axis of rotation. For a lower symmetry, a characteristic nonzero fj is found which is related to the type of reorientation. Three Pulse Techniques

Ultra-slow motions with correlation times T < Tt can be probed by applying a spin-alignment echo sequence (Spiess, 1980) or a stimulated echo sequence (Gullion and Conradi, 1984; Rossler, 1986) as sketched in Fig. 11-3. In contrast to the methods mentioned above, the correlation function can now be mapped directly in the time domain. For spins I = 1 or 1/2, different pulse lengths are used; however, the same correlation function is monitored, namely "2^2) (11-15) = <sin(Q)Q(O)T1)sin(coQ(T2)t2)> In this case three time variables control the correlation loss: t2 is the running time for the second echo maximum; the mixing time T2 probes the exchange of the frequencies for a time T 2 2. The significance

of the correlation function is easily realized if, e.g., the condition COQT1<^1 is considered, and only the echo maximum as a function of T 2 is monitored, i.e., t2 = zl. Then, SHICOQT! can be expanded, and the second Legendre polynomial P2 can be measured directly. lim

F(T 1 ,T 2 )OCX OC

(11-16)

Furthermore, investigating the function F ( T 1 ? T 2 ) for t2->oo the quantity ^ ( T J can be defined ... .~ F 0 0 ( T 1 ) = F ( T 1 , T 2 - O O ) / F ( T 1 , T 2 = 0)

F^iti) is a characteristic oscillating function highly sensitive to the type of motion. This is demonstrated in Fig. 11-3 for several examples. In particular, Fo0(x1^>co) = 1/n, where n is the number of frequencies which are exchanged for a given reorientational process. As an analogy to the elastic incoherent structure factor measured by incoherent neutron scattering, F^ (T±) may be considered to represent the static structure of the motional process (Fujara et al, 1986). Details on the path followed by the orientation of a given C - 2 H bond are revealed as the spin-alignment spectrum is analyzed. Based on the ideas of two-dimensional NMR introduced by Ernst and Jeneer (Jeneer, 1971; Aue et al., 1976), a Fourier transform of Eq. 11-15 can be carried out with respect to TX and t2. The mixing time T 2 is kept as a parameter. Twodimensional exchange patterns with characteristic ridges result for powder spectra which have been used to describe motional processes in molecular crystals and polymers by Spiess and co-workers (Schmidt et al., 1986; Schaefer et al., 1990). In particular, a model-free inversion of the two-dimensional spectrum to a distribution of ro-

11.2 General Considerations

tation angles which has evolved after a given mixing time T2 was recently carried out (Hagemeyer et al., 1990). 11.2.4 Theoretical Treatment

There is hardly another single phenomenon in physics which has been treated by as many different theoretical approaches as the glass transition. In the following, we shall try to give an overview of the most important (or most influential) treatments. Only the basic ideas are reviewed, and the results are described in close relation to experiments relevant to the glass transition in supercooled, mostly organic liquids. We refer to a recent review (Binder and Young, 1986) of the theories of spin glasses; this topic is beyond the scope of this chapter. The structure of amorphous solids below the glass transition is somewhat similar to that of the corresponding liquids. However, the dynamics differs from that in liquids and in crystalline solids as well. We confine our review of the T
The first derivation of the VogelFulcher-Tammann law (see Eq. 11-20) from free-volume assumptions was given in 1959, although free-volume ideas are much older than this (Cohen and Turnbull, 1959; Ferry, 1980). They associate a different free volume with each of N molecules in the total volume V and determine the most probable free-volume distribution for the boundary conditions ^Nt=N and Z JVf % = V— Nvm, where vm is some essentially constant molecular volume, and Nt represents molecules with the free volume

593

vn. The result NJN ocexp( — yvfi) is analogous to the Boltzmann distribution NJN ocexp( —/Jef) since the condition of constant energy, X Nt ef = £, has been replaced by that of constant total free volume V—Nvm. Similarly, the parameter y is related to the average free volume v{ in analogy with the relation of /? = l/feB T and the average thermal energy kB Tper molecular degree of freedom. In the simplest version of free-volume theory, a molecule jumps into a hole of its own size (~v^3) whenever it has a free volume vn
Doc Jexp(~t;/t;f)dt;xexp(-t;*/^f)(ll-18) It is now assumed that the mean fractional free volume f=Nvf/V has a linear temperature dependence above Tg, f=fg + af(T-Tg)

(11-19)

where af is the difference of the thermal expansion coefficients above and below Tg. By combining Equations 11-18 and 11-19 one readily obtains the Vogel-FulcherTammann (VFT) law ^71 (11-20) where T^ = Tg-

is the Vogel temperature, and Do T^ = B/af relates the parameter Do with a molecular size parameter B ~ 1 which can be determined by comparison with thermal-expansion experiments (Ferry, 1980). It is plausible (Stokes-Einstein relation) that D ~* is proportional to the shear viscosity rj and the related relaxation time %n (see, however, Sec. 11.3.1.1). The Williams-Landel-Ferry (WLF) equa-

594

11 Organic Glasses and Polymers

tion, which is readily obtained by reformulation of the VFT equation, is often used to express this temperature dependence: log aT =

Clg(T-Tg) C2g + T-Tg

(11-21)

c 2g =/ g K Applications of the free-volume theory to amorphous polymers have been reviewed by Ferry (1980). Polymer diluent systems were treated most extensively by Vrentas etal. (1985). A more sophisticated treatment of the free-volume theory was given by Cohen and Grest in 1979 (Cohen and Grest, 1979; Grest and Cohen, 1981). Within the framework of a cell model they assume a local free energy that differs for cell volumes v above and below a critical value vc. It contains a term proportional to v — vc for liquid-like cells having v > vc. For solid-like cells (v
vt = a{T-TJ

+ b[{T-Tm)2 + cT] (11-22)

where a, b, c and T^ can be estimated from the details of the model and are interrelated, yielding vf oc (T- TJ for 7 > T^ and vf oc T for T^T^. The glass transition follows from the assumption that molecular displacement is only possible in liquid-like clusters of liquid-like cells having a total free volume X (^i — vc) > vc • The size of the liquid-like clusters increases with increasing temperature, and Tg is associated with the percolation temperature where the critical cluster is attained. Thus, molecular displacement over macroscopic distances is only possible at T >Tg. An essential point is the behavior of the communal entropy,

which is zero if only solid like cells are present and becomes N kB at the high-temperature limit, where the full volume, V9 is accessable to all N molecules. Clearly, the communal entropy rises sharply at the percolation transition, thus modeling the jump of the heat capacity at Tg. Additional assumptions are necessary for taking account of the cooling-rate dependence of Tg (Cohen and Grest, 1979), which otherwise should be identified with the quasistatic limit of very slow cooling, where Tg attains a value of the order of the Vogel temperature 7^. We should also note that the huge temperature dependence of transport coefficients and relaxation times (D, r\, zn,...) is essentially given by Eq. 11-22, which corresponds to Eq. 11-19 of the Cohen-Turnbull theory, and Eq. 11-18, the Doolittle equation. The main contribution to the temperature dependence above Tg is given by the slope of the linear term in the local free energy, which is a local quantity. Thus, the large apparent activation energy close to Tg is related to the cooperativity of molecular motion, not directly but rather via more or less ad hoc assumptions about free-volume properties. This is also typical of the old Cohen-Turnbull approach. It should also be noted that solidlike clusters at T>Tg correspond to the liquid-like clusters in a percolation model. Cluster-like heterogeneities have recently been detected by dynamic light-scattering experiments in supercooled liquids above Tg (Gerharz et al., 1990). In summary, the basis of the free-volume theory is given by the Doolittle equation, Eq. 11-18, which originally was formulated as a phenomenological equation but can be justified within different theoretical frameworks. Various assumptions about the dependence of v{ on temperature, pressure (Ferry, 1980), composition (Ferry, 1980; Doolittle, 1951), and time (physical

11.2 General Considerations

aging, Struik, 1980) allow for broad applicability to describing experimental results

at T>Tg. 11.2.4.2 Thermodynamic Theories

The origin of the thermodynamic approaches to the glass transition lies in the observation that a straightforward extrapolation of the entropy of supercooled liquids to a lower temperature leads to values below the entropy of the crystalline solid at a temperature Tk > 0 K (Kauzmann paradox). Therefore, a phase transition at T2 > Tk is postulated for experiments in the limit of infinitely slow cooling rates. There is still no agreement about the nature of this transition, which is experimentally inaccessible (DiMarzio, 1981; Jackie, 1986; Fredrickson, 1988). It is noteworthy, that the Prigogine-Defay ratio

n = VTaAa2

(11-23)

is larger than one for any experimental temperature Tg>T2. In Eq. 11-23, Ax, ACp, and Aa are the changes at Tg of the compressibility, the heat capacity, and the thermal expansion coefficient, respectively. It can be shown that U = 1 for a second-order phase transition (Jackie, 1986). We note further that a first-order transition is obtained if T2 is associated with the percolation transition of the Cohen-Grest theory (1979). Gibbs and DiMarzio (1958; DiMarzio, 1981) have devised a lattice model where the configurational entropy Sc of model chains can be calculated as a function of some energy difference between flexible and stiff segments and the fraction of empty cells. Thermodynamic quantities can be described within this model as a function of temperature (Sc = 0 at T2), pressure, and chain length. The model can

595

also be adapted to copolymer and polymer plasticizer systems (DiMarzio, 1981). Dynamic properties are modeled in a theory of Adam and Gibbs (1965; Jackie, 1986), where it is assumed that the supercooled liquid consists of cooperatively rearranging regions which grow to infinite size at T2. The fraction of regions where cooperative rearrangement is possible is then proportional to the transport coefficients D, rj~1, and T" 1 . The analogue of the VFT equation, Eq. 11-20 (Ferry, 1980), then becomes

D^exp

-

(11-24)

where the configurational entropy Sc is related with the Cp jump at Tg by

Sc= J(AC p /T)dT

(11-25)

T2

which yields the VFT equation if one assumes T2 — T^ and ACp oc T ~x (Angell, 1988). However, the assumption of constant ACp also results in a dependence on T which is indistinguishable from the VFT equation within the accuracy of most experiments. Although, the Adam-Gibbs equation is conceptually rather different from the VFT equation, the physics is not so different if the free volume is viewed as a dynamic quantity which somehow triggers cooperative rearrangements. This implies, for example, that the elementary process of the Cohen-Turnbull theory, where a molecule jumps into a hole of its own size, is fictitious, and no real holes exist in liquids. We should also mention the application of the coupling model of Ngai et al. (1986) to the Adam-Gibbs theory (Ngai et al., preprint). Here, a dynamic coupling is introduced between the cooperatively rearranging regions according to a coupling scheme which has been successfully applied to many types of relaxations in complex systems (Ngai et al., 1986). In contrast

596

11 Organic Glasses and Polymers

to the Adam-Gibbs theory, which predict exponential relaxation, one obtains a stretched exponential relaxation function: T* is related to T O (T) by T* = (fizo)1/P' • co~(1~1//?). The time T 0 describes relaxation within an individual cooperatively rearranging region, whereas the tightness of coupling and the number n of coupled units are characterized by the adjustable parameters coc and /? = 1 — n, respectively. 11.2.4.3 Mode-Coupling Theory

The mode-coupling theory of the liquidglass transition has emerged from treatments of dynamics in liquids. Leutheusser (1984) and Bengtzelius, Gotze, and Sjolander (1984) have proposed a mode-coupling assumption which introduces a nonlinearity into the equation of motion for the density correlation function, resulting in a singularity with properties resembling a glass transition. Thus, the q mode (q = (4n/X)• sin 0 is the wave vector) of the density correlation function (11-26)

exp (i q r) dr is assumed to follow the kinetic equation

o

—
(7zaV/£ + O(T), for / (

«

) = /

«

+

|

OiT),

e = \(Tc-T)/TJ

J

dt'M(q,t-t')

(Bengtzelius et al., 1984; Sjogren and Gotze, 1989), or the dependence on q is totally eliminated (Leutheusser, 1984). In Eq. 11-27 y is a damping coefficient, and co0 an oscillator frequency. The most interesting feature, which is obtained in the simplest version (Leutheusser, 1984), is a characteristic slowing down of $(q,t) in the vicinity of a particular value lc of the coupling constant. One can then associate E = (XC- X)/kc with the distance (Tc - T)/Tc from the glass transition temperature or r (QC~Q)/QC f° ^ e macroscopic density. The slowing down at lc is not accompanied by marked structural changes, thus describing a purely dynamical transition. Some of the most important predictions of the mode coupling theory can be summarized as follows: The long time limit TC: (H-29)

(11-27)

with a memory term subject to the modecoupling assumption (11-28)

for T>TC (11-30)

The remainder of $ (q, t) is found in a very fast fi process; (11-31)

for (11-32)

M (q91) = J dq' V(q, qf) $ (q, t)
which introduces a quadratic nonlinearity into Eq. 11-27. The discussion of numerical results often refers to the simpler case where the vertex function V(q,q') is replaced by a single coupling constant k

T
and a slower a process (11-33) for <x>~1 < t < co'e ~1 oc (
(11-34)

11.2 General Considerations

A, a, b, cog, and co'E are parameters which can be determined in numerical solutions of Eq. 11-27. The dependence of the power law on time for the a process (Eq. 11-33) was proposed long ago (von Schweidler, 1907) and is usually quoted as the von Schweidler law (Gotze, 1990). It is in agreement with the short-time limit of the stretched exponential (see Sec. 11.2.4.2), exp [ - {t/xY} = 1 - (t/xY + - . . . , which applies in many experiments. In Fig. 11-4, the density correlation function is shown for a model calculation (Gotze and Sjogren, 1989) where the glass transition is approached in the series A, B, C, .... The scaling laws for the fast (3 process (curve a) and the von Schweidler law (curve b) are also shown. A scaling law is also predicted for the shear viscosity Y\ GC8~

(11-35)

The scaling predictions (Eqs. 11-29 to 11-35) have stimulated a number of experimental tests, in particular, with neutronscattering techniques, which are discussed further in Sec. 11.3.1.2. Mode-coupling assumptions have also been introduced in hydrodynamic equations and cause nonlinearities which, however, do not result in a sharp glass transition but rather in a broader transition region (Das, 1987). 11.2.4.4 Energy Landscapes Rotational and translation motion in crystalline solids is usually characterized by a few well-defined processes, with exponential correlation functions and correlation times following an Arrhenius temperature dependence. Clearly, the amorphous structure of a glass is related with some random distribution of energy barriers leading to rather complex dynamical be-

597

Figure 11-4. Two-step correlation function as given by the mode-coupling theory. The dashed curve labeled a gives the asymptotic function f+A/ta, and the dashed curve labeled b gives the function f-B(t/T)b (Gotze and Sjogren, 1989).

havior. In most treatments of dynamics in amorphous solids, a Gaussian barrier distribution is assumed or obtained from particular model assumptions (Wagner, 1913; Tweer et al., 1971; Griinewald et al., 1984; Bassler, 1987; Richert and Bassler, 1990; Phillips, 1987; Sethna and Chow, 1985; Movaghar et al., 1986; Schirmacher and Wagener, 1989). The old proposal of a logGauss distribution of correlation times (Wagner, 1913) implies a Gaussian distribution of activation energies s if kBT)

(11-36)

G (s) de = g (lnr) (d In x/d&) ds

(11-37)

is assumed:

results from

. (11-35)

g (In T) = (2 n <72)~1 exp { - [In (T/T O )] 2 /2 a 2 } where the respective widths are related by <jx = ae/kBT (11-39) The mean energy s0 of the & distribution is related to x0 via Eq. 11-36 (Tweer et al.,

598

11 Organic Glasses and Polymers

1971) but is different from the activation energy £A, which is related to the mean correlation time . One obtains

= Tooexp(fiA/feBT)

(11-40)

eA = e0 + at/2kBT

(11-41)

from Eqs. 11-36 to 11-39. Macroscopic transport coefficients should have a temperature dependence given by Eq. 11-41 which results in a T2 law (Griinewald et al., 1984) at low temper-

atures

(2kBTs0
T2/T2)

(11-42) (11-43)

The T2 law has also been assumed to apply to shear viscosity, and agreement was found in some supercooled liquids in a certain range above Tg (Bassler, 1987). Below Tg, sA is assumed to be fixed by setting T= Tg in Eq. 11-41 which results in Arrhenius behavior of the temperature dependence (Richert and Bassler, 1990). At very low temperatures, activated hopping over the barriers of the distribution, Eq. 11-37, becomes negligible. However, the low-energy tail should contain isolated double-well potentials with sufficiently low barriers allowing for tunneling processes. Thus, the concept of energy landscapes is closely related to the description provided by the two-level system (TLS) theory for low-temperature anomalies in amorphous solids (Phillips, 1987). This has been confirmed quantitatively for the orientational glass of KBr1 _x (CN)X where a jS process with a Gaussian barrier height distribution was associated with 180° jumps of CN groups by dielectric relaxation experiments. Model calculations yielded ~O.35% of CN groups tunneling through low-energy barriers, thus account-

ing for the specific-heat anomaly at T< 1K (Sethnaetal, 1985). The concept of activated hopping over barriers in an energy landscape is only one aspect of more general treatments dealing with the transport of charges or excitons in amorphous solids (Griinewald et al., 1984; Movaghar et al., 1986; Klinger, 1988). First, a specific set of quantum states localized at randomly distributed sites is assumed. Then a master equation is solved with transition rates Wtj that depend upon the distance rtj between the sites and their energy difference Sj — st (note that W^^ Wjt in general). These models, which start from localized quantum states and introduce dynamic couplings in order to account for delocalization, should be contrasted with phonon models where anharmonicities and/or interactions with defects result in localization due to short phonon lifetimes (Buchenau, 1989).

11.3 Typical Examples and Recent Applications The examples discussed below include different experimental techniques applied to supercooled liquids, namely, simple non-associated organic liquids (see Sec. 11.3.1) and polymeric liquids, especially molten polystyrene (see Sec. 11.3.2). In Section 11.3.3, relaxation studies of the glassy state (i.e., below the glass transition temperature Tg) are reported. Here, different phenomena are addressed by the experiments. 11.3.1 Simple Liquids 11.3.1.1 a Process The drastic change of the NMR line shape as the reorientational correlation time of a supercooled liquid passes through

11.3 Typical Examples and Recent Applications

599

the NMR time window (10~5 > T > 10" 7 s) Tj in S . « % [ 2H NMR is shown in Fig. 11-5. Tricresyl phosphate was measured by 3 1 P NMR (Rossler, 101 r 1989), and 2.9% deuterated hexamethyl 10° r benzene (HMB) dissolved in phthalic acid / di-n-butylester (PDB) by 2 H NMR (Bor^ •N-1 ner and Rossler, to be published). A typical 10"' r r >k #f chemical-shift spectrum is found for tri10 - 2 cresyl phosphate at low temperatures, o-terphenyl whereas at higher temperatures the spec10 - 3 trum collapses to a narrow single line. Similar behavior is found for HMB in PDB; -4 o 10 =o o however, the characteristic Pake spectrum : °o 5 Tg"1 is found at low temperatures correspond10 — @ ing to the two transitions of a nucleus with I * 11 , 1 , 1 , 1 , " > 1 ! 1 , 1-. spin 1 = 1. 2.5 3.0 3.5 4.0 4.5 5.0 5.5 1/T in 1O'3K"1 •

%

^

f

f

l

:

31

P NMR

222

4K 40

20

0

241 243 -20

-40

kHz 2

HNMR 188

0

kHz

Figure 11-5. NMR line shapes in the supercooled region: neat tricresyl phosphate (top); 2.9% HMB-d18 in phthalic acid di-n-butyl ester (bottom).

Figure 11-6. 2 H NMR spin-lattice relaxation times (7^) and spin-spin relaxation times (T2) of o-terphenyl: T; at 2n 15 MHz (El); Tx at 2TT 33 MHz (x); T, (#) and T 2 (O)at 2n 55 MHz.

At temperatures higher than those of the line-shape changes, measurements of Tt and T2 provide information on the dynamics, whereas at lower temperatures mainly three pulse techniques in connection with measurements of Tt may be applied. 2 H spin-lattice relaxation times (T±) and spinspin relaxation times (T2) as a function of reciprocal temperature are given in Fig. 11-6 for the system o-terphenyl (Dries etal., 1988). Tx passes through an asymmetric minimum, whereas T2 decreases continuously. At temperatures below the Tx minimum, a shoulder appears for the Tx data. At even lower temperatures (i.e., below jTg) another relaxation process with a much weaker temperature dependence takes over, indicating almost rigid molecules in the glassy state. In order to extract correlation times from T± and T2 data, the spectral density is approximated by a Cole-Davidson (CD)

600

11 Organic Glasses and Polymers

distribution function yielding J(co) = sin (/?CD arctan (co TO) • (11-44)

where TO characterizes the cut-off time of the CD distribution. The distribution parameter PCD is the only free-fit parameter because the coupling constant C in Eq. 11-8 is determined from the low temperature width of the powder spectrum. The mean correlation times for o-terphenyl are drawn in Fig. 11-7. Below 10 ~ 6 s, T± and T2 yield the same correlation time, and a temperature-independent width parameter j8CD = 0.50 is found. This corresponds to /? = 0.63 of a Kohlrausch-WilliamsWatts (KWW) distribution if the relation - 0.97 jSCD + 0.144, for

(11-45)

0.2 S £CD ^ 0-6

Igd in s) 0 oc process ; a' n

e*ir B process

o-terphenyl -12

2.4

2.8

3.2 3.6 4.0 4.4 1/T in 1O"3K"1

4.8

Figure 11-7. Correlation times of o-terphenyl from 7^ ( • ) , T2 (O), spin alignment (2H NMR) ( • ) , dielectric relaxation (+), dynamic Kerr effect ( x ) (Beevers etal., 1976), light scattering (©) (Fytas et al., 1981) and dielectric relaxation, /? process (#) (Johari and Goldstein, 1970), dashed line: guide for the eye.

obtained by Lindsey and Patterson (1980) in a numerical comparison of both distributions is used. For > 1 0 ~ 7 S , there is no straightforward analysis of T2 (Dries et al., 1988), and T± yields correlation times considerably below the values obtained for the a process from other experiments. This indicates the influence of a )S process, discussed further in Section 11.3.1.2. The analysis of the spin-alignment data yields the correct correlation times for the a process (Fig. 11-7) and in addition provides information on the type of slow molecular reorientation close to Tg. Although the analysis of the spin-alignment results by Eq. 11-15 is rather complex (Dries etal., 1988; Erratum, 1989; Diehl etal., 1990), reorientations by only small angular step rotational diffusion can clearly be excluded, and some distribution of larger jump angles is in concordance with the experimental results. For tricresyl phosphate the condition cocs TX <§ 1 is more easily reached because of the smaller width of the powder spectrum which is governed by the chemical-shift anisotropy. Thus, the rotational correlation function can be obtained directly by analyzing Eq. 11-16 in the time domain (Rossler, 1989, 1990 a). In Fig. 11-8 the decay curves are shown in a presentation suited to demonstrate the stretched exponential behavior. Straight lines with temperature-independent slopes /?KWW are found. These results demonstrate nicely the scaling property of the correlation function: a shift of the time scale leads to a master plot for all temperatures. From these decay curves a mean correlation time = r KWW r(l//? KWW )//? KWW is defined, where F represents the gamma function (Lindsay and Patterson, 1980). The correlation times, together with those given by a CD analysis, are shown in Fig. 11-9. Now, ten orders of magnitude are covered by

11.3 Typical Examples and Recent Applications

601

lg[-lnFA(t)]

tricresyl phosphate 31 PNMR T/K

226 225

223

221 220

219 217 215

Figure 11-8. 31 P stimulated echo decays of tricresyl phosphate demonstrating stretched exponential scaling law behavior. lg (t in s)

correlation times provided by NMR methods. The corresponding exponents j8KWW from the stimulated echo and the 7\ and T2 analysis are 0.55 and 0.60, respectively. Included in Fig. 11-9 are the NMR correlation times for toluene-d3 and toluene-d5 for comparison, where the correlation times are extracted from T1 and T2 only (Rossler and Sillescu, 1984). o-Terphenyl and tricresyl phosphate have also been investigated by dielectric

Igd in s) 0

*

relaxation (Johari and Goldstein, 1970; Beevers et al., 1977), by the dynamic Kerr effect (Beevers et al., 1977), and by photon correlation spectroscopy (Fytas et al., 1981). The correlation times are obtained directly from the maximum of the dielectric loss curve, and X'^{co) is analyzed as a function of temperature. The maximum frequency fm is related to the correlation time by T = 1/(2 n fm). In the case of photon correlation spectroscopy, the correlation

tricresyl phosphate

a process -2

# B process

-4 -6

Figure 11-9. Correlation times of tricresyl phosphate from Tx ( • ) , T2 (O), stimulated echo <•) at 2TT 121 MHz, and from dielectric relaxation (+) and dynamic Kerr effect (x) (Beevers et al., 1976). Dashed line: guide for the eye. Correlation times of toluene from 7; and T2 at 2n 55 MHz: toluened 3 (O), toluene-d5 (#).

toluene

-10 -12

3.0

4.0

5.0 6.0 3 1 1/T in 1O" K"

7.0

602

11 Organic Glasses and Polymers

function of depolarized scattering can be fitted by a KWW function revealing a slight temperature dependence of the exponent j8KWW. Similar behavior is found for the correlation function of polarized light scattering. A mean correlation time is defined by the integral of the correlation functions. A similar analysis is carried out for the non-exponential Kerr effect rise and decay functions. Here, the /?Kww exponent also shows some temperature dependence. Correlation times from these methods are included in Figs. 11-7 and 11-9. Qualitatively, the different correlation times show the same non-Arrhenius temperature dependence. However, some scatter for the different data is found; in particular, dielectric and dynamic Kerr effect correlation times for o-terphenyl are systematically shorter than those from light scattering. In the case of tricresyl phosphate, some discrepancies are found for both the NMR correlation time and the Kerr effect correlation times for intermediate temperatures. The high temperature coefficient of the correlation times in the supercooled region might give rise to some experimental uncertainties when comparing correlation times provided by different methods. In summary, the reorientational correlation function is described by a KWW function at least for correlation times longer than 10 ~ 9 s, which clearly exhibits the features of a scaling law. For T < 1 0 ~ 9 S , T± = T2 and the relaxation data are not sensitive to the non-exponential character of the correlation function. Thus, NMR techniques are not able to probe a possible

crossover to Debye relaxation in the fluid region (Grimditch and Torrel, 1989). The j8KWW values reported for the different systems are compiled in Table 11-2. Correlation times of the first and second Legendre polynomial as given by dielectric relaxation and the other relaxation methods, respectively, are similar in favoring a rotational jump process. This is emphasized by Beevers et al. (1977). Besides viscosity and correlation time, the translational diffusion coefficient, D, is another transport coefficient that reveals information on the dynamics of a liquid. However, the very slow diffusion in the supercooled region is not accessible by most standard methods. Diffusion coefficients of dye molecules in organic liquids have recently become available through application of a holographic grating technique (forced Rayleigh scattering, see Sec. 11.2.3.3) (Eichler et al., 1986; Sillescu and Ehlich, 1990). The diffusion of dye molecules can be studied at low concentrations of approximately 0.1%. The results for a thiophene indigo derivative, namely, 2,2'bis(4,4'-dimethylthiolan-3-one) (TTI), dissolved in polystyrene, 1,3,5-tri-a-naphthyl benzene, o-terphenyl, and l,l-bis(4-methoxyphenyl)cyclohexane (BMC) are presented in Fig. 11-10. For comparison, we have included the inverse viscosity (Laughlin and Uhlmann, 1972) and the self-diffusion data of o-terphenyl (McCall et al., 1969). Again, typical non-Arrhenius behavior is observed. It is apparent that the experimental D values bend over to an Arrhenius

Table 11-2. £ K W W as reported by different relaxation methods.

o-terphenyl tricresyl phosphate

NMR

Kerr effect

Dielectric

Light scattering

0.63 0.55-0.60

0.56-0.71 0.70-0.88

0.67-0.69 0.73-0.77

0.54-0.61

11.3 Typical Examples and Recent Applications

1

603

_ 4" in (Pas)"1

in cm 2 s~ 1

Figure 11-10. Reduced Arrhenius plot of tracer diffusion data (Ehlich and Sillescu, 1990; Lohfink et al., 1991) and self-diffusion data: tracer diffusion (O) and self diffusion (0) (McCall et al., 1969) in o-terphenyl; tracer diffusion (El) in 1,3,5-tri-a-naphthyl benzene, tracer diffusion (A) in BMC; tracer diffusion (0) in polystyrene; inverse viscosity of o-terphenyl (solid line) (Laughlin and Uhlmann, 1972). Dashed line: guide for the eye.

10 10 -16

10

0.70

0.80

0.90

1.00

Tg/T

behavior with lower apparent activation energy at a temperature close to Tg. Here, the glassy state is reached, and the system is trapped in a state which is unstable with respect to the supercooled liquid; however, it is kinetically blocked. Tempering the matrix leads to a further decrease of D. Comparison of high- and low-molecular-weight matrices in Fig. 11-10 shows that tracer diffusion in a polymer is characterized by a higher diffusion coefficient near Tg, but similar slopes are observed. This behavior is in contrast to viscosity behavior, where a smaller slope is found for the polymer liquids in the Arrhenius plot near Tg (cf. Fig. 11-2). Hence, some degree of decoupling is observed if the temperature dependence of the diffusion coefficient is compared with that of the matrix viscosity rj (Fig. 11-10). The VFT equation can be applied in the form D(T)=Doexp(-fB/(r-TJ)

(11-46)

The parameters B and T^ are identical with those provided by the analysis of the viscosity data of the matrix assuming £ = 1

in the corresponding VFT equation. The temperature-independent coupling parameter £ has been introduced in a free-volume treatment of polymer liquids (Fujita, 1971; Vrentas et al., 1985) in order to account for motional decoupling of D and rj. Typically, a range of 0.8-0.9 is found for £ unless further decoupling is provided by internal matrix motions (Ehlich and Sillescu, 1990). Eq. 11-46 implies that Docrj~^ which is at variance with the classical Stokes-Einstein relation unless £ — 1. The Stokes-Einstein relation for translational diffusion and the corresponding Debye eqation for rotational diffusion can be formulated as

-kBT/(fri) vrj/(kBT)

(11-47)

where / is proportional to the size and v to the volume of a molecule dissolved in a liquid of viscosity r\. Both equations are well established for the fluid region. Hence, some crossover from £ = 1 to £ < 1 has to be observed as the temperature is lowered. In particular, the following relations may

604

11 Organic Glasses and Polymers

V(D^)inPa" 1 cm -2

in Pa

10

Figure 11-11. Test of the StokesEinstein relations (see Eq. 11-48): 71 (D), light scattering ( • ) (Ma et al., 1988) and tracer diffusion ( • ) in 1,3,5-tri-a-naphthyl benzene; T2 (O), tracer diffusion (#), and self diffusion (0) (McCall et al., 1969) in o-terphenyl; electrical conductivity (O) in 0.4 KNO 3 0.6 Ca(NO 3 ) 2 (Howell et al., 1974; Bose et al., 1970); electrical conductivity (A) (Angell et al., 1969) and dielectric relaxation ( • ) (Rhodes et al., 1966) of 0.38 KNO 3 0.62Ca(NO3)2. Dashed line: guide for the eye.

r .5 0.6

0.7 0.8

0.9

1.0

T g /T be checked (Rossler, 1990 c): T/TJccl/T 8(1/T)

fluid regime (11-48 a)

>0

viscous regime 6(1/T)

<0

(11-48 b)

A similar relation holds for the translational diffusion if we set T = r trans oc 1/D. In Fig. 11-11 reorientational correlation times of 1,3,5-tri-a-naphthyl benzene (Fujara, 1990) and o-terphenyl, as given by T± and T2, respectively, as well as by depolarized light scattering (Ma et al., 1988), are used to plot T/TJ as a function of the reduced temperature Tg/T. In addition, 1/(D rj), as given by forced Rayleigh scattering of TTI (see above) as a dye molecule and by self-diffusion data, is included. In fact, although some scatter shows up in the data, a crossover in the temperature coefficient can clearly be identified. For high temperatures a positive temperature coef-

ficient in accordance with the hydrodynamic equations is found, but a negative coefficient is revealed at low temperatures. It has been known for a long time from studies of supercooled ionic liquids that a decoupling of correlation times from electric conductivity and other correlation times occurs (Moynihan et al., 1971; Angell, 1990). A comparably high conductivity is observed near Tg. This phenomenon might have the same origin as the decoupling found in supercooled organic liquids. For the system xKNO 3 (l - x)Ca(NO 3 ) 2 , the corresponding ratios T/TJ are included in Fig. 11-13 (Rhodes et al., 1966; Angell et al., 1969; Bose et al., 1970; Howell et al., 1974). Again, a crossover is observed at comparable reduced temperatures. The degree of decoupling is much higher. The Stokes-Einstein relation does not even hold at the highest temperatures. Accordingly, the crossover is less sharp. In summary, indications are given which demonstrate a breakdown of the StokesEinstein relation at some temperature between Tm and 71. A change in the diffusion

11.3 Typical Examples and Recent Applications

mechanism occurs. In view of predictions of the mode-coupling theory, this crossover might be related with traces of a dynamic phase transition at a temperature Tc. For T>TC, correlation times provided by different methods as well as the translational diffusion coefficient show approximately the same temperature dependence as that of viscosity, whereas below Tc some degree of decoupling is observed, which is different in different systems (Rossler, 1990 c). 11.3.1.2 p Process

Correlation times derived from 2\ measurements in the low-temperature region are consistently shorter than those of the a process. This is clearly seen in Figs. 11-7 and 11-9. The only additional process discussed for simple liquids is the /? process as reported, e.g., by dielectric relaxation (McGrum et al., 1967; Johari and Goldstein, 1970, 1971; Williams and Watts, 1971), where an additional small maximum at high frequencies is observed for X^(co). The corresponding dielectric relaxation times for o-terphenyl are also plotted in Fig. 11-7. Obviously, the apparent activation energies are different. However, extrapolating the data to higher temperatures shows the relaxation times of the /? process intersecting those of the a process at the same temperature. Here, the correlation times are of the order of 10~ 7 s and the reduced temperature is T r /T^0.85. It is believed that the CD distribution is not appropriate for analyzing Tx data at temperatures where the /? process predominates, and a different analysis leads to different mean correlation times, perhaps closer to those from dielectric relaxation. On the other hand, the dielectric loss maximum is very broad, inferring formally a broad distribution of correlation times.

605

Different methods yield rather different mean correlation times for this complex process. Nevertheless, a two step correlation function appears in the supercooled region, which at least shows up in dielectric and NMR experiments. Since the NMR line shape is not altered by the /? process, it may be related to slow low-amplitude librations. It is worthwhile to emphasize that the /? process does not always show the same temperature dependence as the high-temperature end of the a process. At least for simple organic liquids, a and /? processes merge within the supercooled region, and the bifurcation is close to the temperature Tc given by the power-law analysis of the viscosity data and also by the failure of the Stokes-Einstein description (see Fig. 11-2 and Fig. 11-11). Hence, it might be related to traces of the predicted dynamic phase transition. However, the crossover predicted by the mode-coupling theory refers to a much faster process. Before discussing this difference, we shall report some recent results which substantiate predictions from the mode-coupling theory. The first indications for a critical temperature above Tg have been reported by neutron-scattering experiments; an anomaly of the Debye-Waller factor, / q , determined from elastic scattering (see Sec. 11.2.4.3), is observed. / q drops significantly within a narrow temperature range. An additional softening appears which starts already below Tg and increases its amplitude as the temperature is raised. This is not caused by the a relaxation but due to some very fast process. In the frame of the modecoupling theory, such a process yields a correlation loss for the density-density correlation function and shifts the plateau / q of the a process to lower values. Because of some similarities with the conventional /J process, it has also been called a jS process.

11 Organic Glasses and Polymers

606

o. - A

&--A... .

A "•MM

n finc ( q )

-. 5 • \

-

A

-1.0Tc i

100

1,

i

Figure 11-12. Debye-Waller factor, fmc (q), determined from neutron scattering in o-terphenyl at q = 1.39 A" 1 . (See text for explanation of solid triangles.) (Bartsch et al, 1989).

300

200 T in K

butadiene (Frick and Richter, 1989). It is rather remarkable that Tc values obtained from neutron scattering, from a power-law fit of viscosity, and from the breakdown of Stokes-Einstein relations are in agreement to within a few degrees, as demonstrated in Figs. 11-11 and 11-12. The mode-coupling theory in its present from accounts for only part of the dynamics and makes no predictions about the ; + O(T) T>TC dynamics of the a process below Tc. In parHence, a discontinuity of / q is predicted at ticular, no singularity of the viscosity is a temperature Tc, whereas for T^TC the observed at Tc. Only the highest curvature typical behavior of solids is observed, shows up in the data. The assumption that namely, In / q oc — T. At temperatures above activated-hopping processes govern the Tc, quasielastic neutron scattering can be slow dynamics below Tc leads to a smearanalyzed in terms of a two-step function ing out of the dynamic phase transition where the long-time behavior is attributed anticipated in the idealized form of the theto the a process, and the short-time portion ory. However, traces of the transition (t ^ 10 ~1X s) can be separated and is represhould survive in real supercooled liquids, sented by the solid triangles in Fig. 11-12. and judging from the experiments, Tc lies No indications of the conventional /? well above Tg. process are seen. Apparently, it has The question has been raised whether merged with the a process at T>TG. The the fast (I process observed by neutrondiscontinuity of fq at Tc has also been obscattering experiments is related to the served in coherent neutron scattering of slow P process reported by NMR and deuterated o-terphenyl (Petry et al., 1991) dielectric relaxation. At a first glance, the and is indicated in neutron-scattering recorresponding time scales are completely sults obtained in supercooled 0.6 KNO 3 • different. Typical times for the fast p pro0.4Ca(NO 3 ) 2 (Mezei, 1989) and in polycess are of the order of 10" 13 -10"" 11 s,

In Fig. 11-12, the logarithm of the Debye-Waller factor is shown as a function of temperature (Bartsch et al., 1989). The fit included is provided by predictions of the theory. For the additional drop of the Debye-Waller factor, the theory yields (see Sec. 11.2.4.3) (11-49)

11.3 Typical Examples and Recent Applications

whereas for the same temperatures, dielectric and NMR correlation times are in range oflO~ 2 -10~ 7 s. However, there are indications (Rossler and Schnauss, 1990) that the slow and fast ft processes have the same origin and can be understood within the framework of mode-coupling theory. It should be noted that activated "hopping" processes that account for the finite shear viscosity at T< Tc (Fig. 11-11) are also related to the /? process (Gotze and Sjogren, 1987; Sjogren, 1990). Finally, we mention that the fast process can be related with a softening of the low-frequency phonons, as discussed by Buchenau (1989). 11.3.2 Polymeric Liquids

The dynamic behavior of polymeric liquids above the glass transition was already discussed in Section 11.2.2, where we noted that the connectivity along the chain places polymer glass formers between inorganic networks (window glass) and supercooled van der Waals liquids (Fig. 11-2). This is also true for the transition from Arrhenius behavior at low viscosities to the VFT behavior close to Tg where the characteristic temperature Tc has been identified in polybutadiene by neutron scattering (Frick and Richter, 1989), but the changes are less pronounced than in o-terphenyl (Bartsch et al., 1989). The chain connectivity also results in large density (free-volume) fluctuations due to the problem of reconciling the random coil shape with the dense packing of the chains. As a consequence, the motion of low-molecular-weight additives is less coupled to matrix motion in polymer glasses than it is in monomer glasses, as was shown in Fig. 11-10 for translational diffusion of probe molecules. The rotational motion was studied by 2 H NMR of deuterated toluene added to polystyrene (PS) (Rossler, 1987). The rotational corre-

607

lation times were found to be significantly shorter than those characterizing PS segment motion, which also indicates decoupling from the a process. The various NMR techniques described in Sec. 11.2.3.5 have been extensively applied to the segmental motion in chaindeuterated PS-d3 and phenyl-groupdeuterated PS-d5 (Lindner et al., 1981; Rossler et al., 1985; Wefing et al., 1988; Kaufmann et al., 1990; Pschorn et al., 1990). The results can be summarized as follows: At temperatures above Tg, chain reorientation via small angular steps can be clearly identified in the shapes of deuteron ID- and 2D-spectra and fitted by a rotational diffusion model allowing for a distribution of correlation times. The width of the distribution - as seen by C- 2 H reorientation of PS-d3 chains - increases from about 1 decade at T>T g + 50K to about 5 decades a few K above Tg. This is different from the results of other relaxation techniques which detect fluctuations of larger volume elements (Patterson, 1983). Nevertheless, the mean rotational correlation time detected by 2 H NMR has the temperature dependence as mechanical relaxation. This is shown in Fig. 11-13 where the NMR results are fitted by a WLF equation with almost the same parameters as obtained for viscoelastic behavior. Thus, local chain dynamics must be closely linked to the collective dynamics of the a process. It is remarkable that reorientation by small angular steps predominates in PS, whereas larger angular rotational jumps are seen in supercooled o-terphenyl (see above). Although we cannot exclude the additional occurrence of rare rotational jumps in PS, we have to conclude that motion in different glass formers can indeed differ on a local scale. Due to the faster time window of Tx measurements, which are most sensitive at

608

11 Organic Glasses and Polymers

650 UP

A30

£20

T I IK] KI £10 Z.00

390

380

'9 J370

360

1-10

Figure 11-13. Average rotational correlation times TC for C - 2 H bond reorientation in chain-deuterated polystyrene, determined from 2D-spectra (O), solid echo spectra (O), broad line spectra (•), and spinlattice relaxation times (A,A).(C l g =15.9, C2g = 49.9, see Eq. 11-21 and Pschorn et al, 1991).

1-10 2.7

the Larmor frequency, the correlation times extracted from Tt data are related to the /? process. This parallels our findings in supercooled o-terphenyl (compare Figs. 11-7 and 11-13). It should be noted, however, that T± provides little information on the type of molecular motion. We expect that the amplitude of the /? process decreases on approaching Tg from above. This is not properly taken into account in the conventional analysis of Tx data and may imply large errors in the correlation times shown for the /? process in Figs. 11-7 and 11-13. 11.3.3 The Glassy State The glassy state of simple organic systems is characterized by the absence of large-scale motion. Because of the structural arrest, the liquid-like short-range order is frozen. The dielectric absorption maximum attributed to the /? process decreases and is finally lost in the experimental background as the temperature is low-

ered. Thus, the remaining dynamics of the glassy state is determined by vibrational and electronic excitations only. Due to the absence of periodicity, Bloch states can not be introduced in order to simplify the theoretical treatment. As a consequence, the density of states is smeared out. For nonmetallic solids, observables such as heat capacity and thermal conductivity are determined by the phonon spectrum, where in amorphous solids pronounced peculiarities show up at low temperatures, i.e., below 10 K. These properties are attributed to low-frequency modes which are modeled by assuming two-level systems. A review is given by Phillips (1987). At present, it is not clear whether these two-level systems also account for properties of amorphous solids above 10 K. Regarding NMR studies, only a few experiments have been reported on the glassy state. In most cases inorganic glasses have been studied. It is a common feature that the spin-lattice relaxation is faster than the corresponding relaxation in the crystalline

11.3 Typical Examples and Recent Applications

solid. At low temperatures (T<100K), power-law behavior characterized by Tx oc T~y(y = 1.1-1.5) is usually observed and can be related to the two-level system (TLS) theory (Szeftel and Alloul, 1978; BalzerJollenbeck et al., 1988). At temperatures closer to Tg, activated processes lead to further reduction of T±. In spin 1/2 systems, the mechanism of spin diffusion causes a common spin temperature, and it then becomes difficult to identify the processes determining the experimental T± (Miiller-Warmuth and Eckert, 1982). Spin diffusion plays a minor role in 2 H NMR (/ = 1) where non-exponential spin-lattice relaxation was found for several organic glasses. Interestingly, the spin relaxation function becomes exponential at about 20 K above Tg, where Tx becomes larger than the structural relaxation time (a process). Thus, non-exponential 2 H spin-lattice relaxation can be looked upon as a signature of the glassy state, and it contains information on the spatial heterogeneity frozen within the glass (Schnauss et al., 1990). The problem of long relaxation times for Tx in solid glasses can be circumvented by using deuterated guest molecules, which are characterized by fast intrinsic rotational motion in a protonated glassy matrix. The molecular rotation, e.g., C6-rotation in benzene, persists also in the glassy state (Miiller-Warmuth and Otte, 1979). In contrast to investigations of the pure matrix, a well-known relaxation mechanism, namely, the molecular reorientation around the symmetry axis, simplifies the interpretation, resulting in comparatively fast relaxation. The rotational correlation times T of the individual guest molecules reflect the local structure. In particular, the activation energy E depends on the local arrangements of the molecules. According to a distribution of local environments in

609

the glass, the guest molecules probe a distribution of activation energies g (E), Here, the concept of a distribution of correlation times is well suited to account for the guest dynamics, as will be demonstrated. Although 2 H NMR is not sensitive to spatial heterogeneities, the corresponding motional non-uniformities should be observable in an NMR experiment. Again, absence of spin diffusion leads to a non-averaged spin-lattice relaxation. Further results are provided by 2 H NMR line shape studies. Hence, we believe that structural information may be obtained by studying the dynamics of small, mobile probes in disordered systems (JansenGlaw et al., 1989; Rossler et al., 1989 a). In Fig. 11-14, highly non-exponential spin-lattice relaxation curves are shown for two systems, namely, benzene-d6 in a liquid crystal side chain polysiloxane (LCPS) (Rossler et al., 1991) and adamantane-d 16 in phthalic acid di-n-butyl ester (PDB) (Rossler et al., unpublished data). The shapes of the curves can be understood in terms of a superposition of exponentials

= [M0-M(t)]/M0 (11-50) where /(T x ) is a distribution of spin-lattice relaxation times. It is now assumed that each individual 7\ is related with a rotational correlation time of the deuterated probe molecule at one particular site by applying the Bloembergen-Purcell-Pound (BPP) equation (see Eq. 11-8) T + K)T)

4l 2

+

1 + (2COOT)

Since / ( 7 \ ) can extend over many decades from the high-temperature branch (co0 r 1, 7\OCT) of Eq. 11-51, it is

610

11 Organic Glasses and Polymers

H EBEBBBEEB fflEBEBfflEBffleiBfflESBHlBmai

%

• a

20 K 32 49 60 69 88 96 105 156

•

l O ' 1 r~

o a

I

o

• •

10

-2

t

• ^

3

^

7

O

S3

ffl

*°0D

•

\

n O

%

03 O

^ T

^

i

10"

2

10"

1

.

no • O o°

"

•

v

i # l A ,,„•• , 1

10° t in s

O

O

V

,,,1

1 M M l i

10~

OQ

10

o

v

A1I1I

D

^

10

,n

1 ,

2


Figure 11-14. Non-exponential 2H NMR spin-lattice relaxation. 10.0% benzene-d6 in a liquid crystal polysiloxane (top); 4.1% adamantane-d16 in phthalic acid di-n-butyl ester (bottom).

10"

•,-2

10"1 10° t in s

not surprising that rather unusual shapes result (Fig. 11-14) which allow for the determination of the distribution of correlation times G(lnt) corresponding to / ( T J . In particular, NMR relaxation is sensitive to asymmetric G (In T) (Rossler et al., 1989 b). A detailed analysis of the curves shown in Fig. 11-14 (Rossler et al., 1989 a; Rossler et al., 1990 b) has revealed that the distribution of correlation times G(lnt) has a temperature dependence which results in a temperature-independent distribution of activation energies g(E) if an

101

102

Arrhenius temperature dependence for % is assumed for the molecular probe reorientation, where r = zoexp(E/RT)

(11-52)

The width of G (In T) is found to be proportional to 1/T, a behavior completely different from features of a scaling law, discussed for the dynamics of the a process and often described by a distribution of correlation times (see Sec. 11.2.1). Since g(E) reflects the probe environment of many different sites, it should provide an excellent picture

11.3 Typical Examples and Recent Applications

of the energy landscape (see Sec. 11.2.4.4) within a glass. Furthermore, studying the reorientation of mobile guest molecules in a glass may be useful for checking consequences of the energy landscape models, which are also applied to explain the temperature dependence of the dynamics above Tg (see Sec. 11.2.4.4). The relaxation can be fitted by a Gaussian distribution in the high-temperature region. However, at low temperatures the linear portion of the double logarithmic plot can only be accounted for by assuming that g (E) is asymmetric with its maximum on the low E side. From model calculations shown in Fig. 11-15 it is seen that the power-law behavior observed at low temperatures is in agreement with g (E) oc ocexp[ — (Eo — E)/e], whereas Gaussian E distributions provide $ (t) curves with only positive curvature not in agreement with Fig. 11-14 (Taupitz et al, 1990). Unraveling the exact shape of g (E) is difficult, due to the stringent requirement that allows only one g (E) to fit all relaxation curves over a wide temperature range. In particular, the role of spin diffusion, which leads back to a more exponential relaxation and is recognized by a bending off of the relaxation for t ^ 10 s (see Fig. 11-14) has to be incorporated in the relaxation theory. However, an exponential E distribution with some Gaussian broadening yields a fair interpolation of the relaxation data over a large temperature range (Rossler et al., 1990 b, 1991). Information on g (E) is also povided by line shape analysis of the deuterated guest molecules. Fig. 11-16 shows 2 H NMR spectra of benzene in LCPS (Rossler et al., 1990 a). A motional-averaged Pake spectrum is found at high temperatures according to fast rotating molecules (T < 10" 7 s), whereas at low temperatures a broader spectrum is found corresponding to

10" 3

10" 2

10"1

101

10°

icr

q(E)

611

102

10

Exponential \ distribution

10"

10" \^051^\90K

10

I/SKUX 10"

10"

10u t in s

101

Figure 11-15. Simulated spin-lattice relaxation for a Gaussian distribution (top); an exponential distribution of activation energy (bottom).

molecules in the limit of slow rotation ( T > 1 0 ~ 5 S ) . In the intermediate temperature range, the line shapes can be described by a superposition of only two sub-spectra corresponding to molecules in the limit of fast and slow reorientation with temperature-dependent fractions. No contribution from intermediate exchange spectra is observed where the correlation time is of the order of the reciprocal spectral width. These results confirm the existence of a very broad distribution of correlation times. The spectra have to be compared with those in Fig. 11-5, where no such twophase spectra are observed for the slowing down of the a process. Hence, a comparatively uniform motional process governs the a process above Tg in contrast to the

612

11 Organic Glasses and Polymers

150

100

50

0

-50

-100

-150

150

kHz

100

50

0

-50

-100

-150

kHz

Figure 11-16. 2 H NMR line shapes of 10.0% benzene-d6 in a liquid crystal polysiloxane (bottom, left) and corresponding simulations (bottom, right).

dynamics of mobile guest molecules below Tg. We should mention that similar spectra have been reported for gas hydrates by Ripmeester and co-workers (Davidson and Ripmeester, 1984). The disorder of the cage is reflected by the dynamics of mobile guests. The spectra can be explained by a distribution of correlation times which passes through the NMR spectral window as the temperature is lowered. It can be shown that in the case of a broad distribution the solid echo spectrum is given by the weighted sum of the fast and the slow ex-

change spectrum (Rossler et al., 1990 a) / (Q), T) = Itast M 7 G (In T) d In T + (11-53) + / sIOW M J G(lnT)dlnz lnt*

It is apparent from the example of Fig. 11-16 that the distribution of correlation times G(lni) can be determined by measuring the weight factor W(T) given by the first integral in Eq. 11-53, where the second integral is i — W(T). It has also been shown that the distribution of activation energies, g(E) is equal to (d/dT) W(T) up

613

11.3 Typical Examples and Recent Applications

to a constant factor / = R In (T*/TO)> which is 133 Jmol" 1 K " 1 if one assumes T* = = 10~ 5 s and TO = 1 0 ~ 1 2 S , where T* is roughly the inverse width of the powder spectrum I(co) (Rossler etal., 1990 a). The factor / relates the E scale with the T scale used for evaluating the experimental weight factor W{T\ see Fig. 11-17. (This T scale should not be confused with the energy scale E/R often used in the literature.) In Fig. 11-17, the E distributions obtained by analyzing the 2 H NMR line shapes of the two probe molecules in some monomer and polymer glasses are shown (Rossler et al., 1990 a). For all systems, the shape of g(E) is asymmetric. The main difference among the systems is the position of the most probable activation energy E p . For benzene as guest molecule, g(E) is shifted to lower activation energies compared to HMB. This reflects the smaller molecular size and mass of benzene relative to HMB. Comparing high and low-molecular-weight matrices for the same guest molecule, one finds that £ p is lower for the high-molecular-weight matrix, indicating a higher degree of local free volume in the polymer systems. For HMB in PDB with the highest £ p , the asymmetric character of the distribution is almost lost. Both NMR methods yield comparable results; asymmetric distribution functions determine the dynamics of mobile guest molecules in glassy systems. A Gauss distribution, as often discussed for the glassy state, does not fully describe the experimental results. The method is well suited to characterize disordered systems; the local packing of the molecules is probed. Different types of disordered systems may be investigated and a relation to mechanical properties of a matrix may be attempted. Although a quantitative correlation between structural and motional properties is not yet known, we think that this

g(E)

/-x P D B 0.02

LCPS//

x\

\PDB \\ V \ \> * \

0.01

i

i

10

15

20

E in kJmol'1

Figure 11-17. Activation energy distribution g(E) in different glasses as given by 2 H NMR lineshape analysis. Solid line: benzene, dashed line: HMB as probes; PS: polystyrene; LCPS: liquid crystal side chain polysiloxane; PDB: phthalic acid di-n-butyl ester.

method yields information on the first coordination shell of a given guest molecule. In favorable cases guest concentrations of 2% are sufficient to provide a reasonable signal-to-noise ratio. We should mention that distributions of correlation times have also been observed for side group motion in polymers (Schmidt etal., 1985; Wehrle etal., 1988). The distributions found are less broad as compared to those reported here. Large intramolecular contributions to the rotational potential have to be expected for such internal motions which result in a high mean activation energy and less sensitivity to the disorder of the environment. Broad distributions of the equilibrium constants of isolated bistable dye molecules inbedded in glassy solids have also been reported by 15 N NMR (B. Wehrle et al., 1987). On the other hand, the asymmetric distribution functions are similar to distribution functions found by Frauenfelder (1984) for the recombination kinetics of CO in proteins. This supports the assumption that a single protein resembles a glassy state. The distribution revealed by optical hole-burning experiments is also asymmetric with Ep on the low E side

614

11 Organic Glasses and Polymers

(Kohler and Friedrich, 1987). A distribution g(E)ocl/y/E is observed which is explained within the framework of the twolevel system theory. Two-phase spectra are also observed when deuterated low-molecular-weight additives in polymers are investigated by 2 H NMR. Fig. 11-18 shows typical spectra for 3% HMB in polymethylmethacrylate (PMMA) indicating that in addition to C 6 rotational jumps of HMB, isotropic reorientation is observed in the polymer glass (Borner and Rossler, to be published). Similar spectra are observed in the system toluene-polystyrene (Rossler et al., 1985 and Rossler 1987). On top of the broad Pake spectrum a narrow line is observed representing liquid-like molecules. Its relative intensity increases as the temperature is raised. The solid-like spectrum disap-

Figure 11-18. Spectra of 3.0% HMB-d 18 in PMMA demonstrating two-phase spectra.

pears completely above Tg. The temperature dependence of the fraction of the liquid-like molecules is plotted in Fig. 11-19. Clearly, there is fast molecular motion in the mixed PS-toluene glasses well below Tg as determined by DSC. The temperature interval for a coexistence of liquid-like and solid-like molecules becomes narrower as more toluene is added, and the thermal Tg lowered. Apparently, the mixed system becomes a rigid glass at the glass transition of the additive, Tg = 117K. This is also observed for HMB motion in PMMA, where Tg of HMB should be around 260 K if we apply the rule of thumb T g =0.6T m with Tm = 439K. In Fig. 11-18 the two-phase behavior of HMB starts above 280 K and extends to temperatures above the thermal T g =378K of neat PMMA. Of course, HMB motion is never slower than that of PMMA; however, the rigid Pake spectrum is already obtained for relatively short correlation times T ^ 10 ~5 s. It is tempting to perform the same analysis as described above. Consequently, the NMR behavior would be explained in terms of a distribution of correlation times related with a distribution of activation energies for liquid-like motion in the rigid polymer matrix (Rossler etal., 1990 a). Rigid polymer molecules have been confirmed by investigating the matrix of polystyrene itself. According to Fig. 11-19 the distribution of activation energies should become narrower if more toluene is added to polystyrene, and a correspondingly greater intensity from intermediate spectra should appear where the correlation time is of the order of the reciprocal spectral width. However, the opposite behavior is observed. Hence, the precondition of line shape analysis, namely the presence of an activated process which governs the slowing down of the molecular motion, is not given for the isotropic motion in

11.4 References

615

W(T)

3% HMB in PMMA 0.0 -

Figure 11-19. Fraction of liquid-like spectra as a function of temperature for the systems toluene/polystyrene and HMB/PMMA. Concentration in mass percent.

120 160 200 240 280 320 360 400 T in K

these mixed systems. We find instead that the motion of a probe molecule at a particular site has a temperature dependence resembling that of the a process, but with the local Tg differing from the macroscopic glass transition. It is not possible to quantify this scenario, which characterizes a motional non-uniformity within the mixed glass and could also be looked upon as a spatial distribution of free-volume aggregates, each related to molecular motion by the Doolittle equation (see Sec. 11.2.4.1). Summarizing the experimental findings of the last section, polymer glasses, in contrast to low-molecular-weight glasses, are characterized by a higher fraction of local free volume. Static density fluctuations are considerably larger. Local motion of guest molecules is facilitated. The distribution of activation energies of mobile guest molecules acting as a probe, e.g., by the C 6 rotation of benzene, is shifted to lower energies. In addition, motional decoupling is observed for low molecular additives; i.e., the guest molecules perform liquid-like isotopic reorientation in a rigid polymer matrix.

11.4 References Adam, G., Gibbs, J. H. (1965), J. Chem. Phys. 28, 373. Alexander, S., Baram, A., Luz, Z. (1974), Mot. Phys. 27,441. Allen, V. R., Fox, T. G. (1964), /. Chem. Phys. 41, 337. Anderson, P.W., Halperin, B.I., Varma, C M . (1972), Phil. Mag. 25, 1. Angell, C.A. (1988), /. Non-Cryst. Solids, 102, 205. Angell, C.A. (1990), Chem. Rev. 90, 523. Angell, C.A., Pollard, L.J., Strauss, W. (1969), J. Chem. Phys. 50, 2694. Angell, C.A., Clarke, J.H.R., Woodcock, L.V. (1981), Advances Phys. Chem. 48, 387. Aue, W.P., Bartholdi, E., Ernst, R. R. (1976), /. Chem. Phys. 64, 2229. Balzer-Jollenbeck, G., Kanert, O., Steinert, I, Jain, H. (1988), Solid State Commun. 65, 303. Bartsch, E., Fujara, R, Kiebel, M., Petry, W. (1989), Ber. Bunsenges. Phys. Chem. 93, 1252. Bassler, H. (1987), Phys. Rev. Lett. 58, 767. de la Batie, R.D., Viovy, XL., Monnerie, L. (1982), /. Chem. Phys. 81, 567. Beevers, M.S., Crossley, J., Garrington, D.C., Williams, G. (1977), Trans. Faraday Soc. 18, 540. Bengtzelius, U., Gotze, W, Sjolander, A. (1984), J. Phys. C17, 5915. Bernal, J. D. (1965), in: Liquids: Structure, Properties, Solid Interactions. Hughel, T. J. (Ed.). Amsterdam: Elsevier Sci. Publ. Binder, K., Young, A. P. (1986), Rev. Mod. Phys. 58, 801. Birge, N. O., Nagel, S. R. (1985), Phys. Rev. Lett. 54, 2674. Bloembergen, N., Purcell, E. M., Pound, R. V. (1948), Phys. Rev. 73, 679.

616

11 Organic Glasses and Polymers

Bose, R., Weiler, R., Macedo, P. B. (1970), Physics. Chem. Glasses 11, 117. Buchenau, U. (1989), Springer Proceed. Phys. 37, 172. Cohen, M. T, Turnbull, D. (1959), J. Chem. Phys. 31, 1164. Cohen, M.H., Grest, G.S. (1979), Phys. Rev. B20, 1077. Connor, T.M. (1963), Trans. Faraday Soc. 60, 1574. Das, S. P. (1987), Phys. Rev. A 36, 211, and references therein. Davidson, D.W., Ripmeester, J.A. (1984), in: Inclusion Compounds. Atwood, XL., Davies, J.E.D., MacNicol, D.D. (Eds.). London: Academic Press. De la Batie, R. D., Viory, J. L., Monnerie, L. (1984), /. Chem. Phys. 81, 567. Diehl, R.M., Fujara, R, Sillescu, H. (1990), Europhys. Lett. 13, 257. Doolittle, A.K. (1951), J. Appl. Phys. 22, 1471. Dries, Th., Fujara, R, Kiebel, M., Rossler, E., Sillescu, H. (1988), J. Chem. Phys. 88, 2139. Erratum (1989), /. Chem. Phys. 90, 7613. Ehlich, D., Sillescu, H. (1990), Macromolecules 23, 1600. Eisner, M., Mitchell, R.W. (1961), Bull. Amer. Physic. Soc. 6, 363. Finney, I L . (1970), Proc. Roy. Soc. (London) A 319, 479. Fischer, E.W. (1989), Proc. 2nd. Int. Workshop on Non-cryst. Solids, World Publ. Co. Fox, T. G., Flory, P.J. (1950), /. Appl. Phys. 21, 581. Frauenfelder, H. (1984), Helv. Phys. Acta 57, 165. Fredrickson, G. H. (1988), Ann. Rev. Phys. Chem. 39, 149. Frick, B., Richter, D. (1989), in: Springer Proceedings in Physics, Vol.37: Richter, D., Dianoux, A.X, Petry, W., Teixeira, X (Eds.). Berlin: Springer, pp. 38-52. Friedrich, X, Haarer, D. (1984), Angew. Chem. Internatl. Ed. Engl. 23, 113. Fujara, R, Wefmg, S., Spiess, H. W. (1986), /. Chem. Phys. 84, 4579. Fujara, F. (1990), private commun. Fujita, H. (1971), Fortschr. Hochpol. Forsch. 3, 1. Fytas, G., Wang, C.H., Lilge, D., Dorfmuller, T.H. (1981), J. Chem. Phys. 75, 4241. Gerharz, B., Meier, G., Fischer, E.W. (1990), /. Chem. Phys. 92, 7110. Gibbs, XW, DiMarzio, E. A. (1958), J. Chem. Phys. 28, 373. Goldstein, M. (1969), J. Chem. Phys. 51, 3728. Gotze, W, Sjogren, L. (1987), Z. Phys. B65, 415. Gotze, W, Sjogren, L. (1989), J. Phys. Condens. Matter 1, 4183. Grimsditch, M., Torell, L.M. (1989), in: Springer Proceedings in Physics, Vol. 37: Richter, D., Dianoux, A.X, Petry, W, Teixeira, X (Eds.). Berlin: Springer, pp. 196-210. Griinewald, M., Pohlmann, B., Movaghar, B., Wurz, D. (1984), Phil. Mag. B49, 341.

Gullion, T., Conradi, M.S. (1984), Phys. Rev. B30, 1133. Hagemeyer, A., Brombacher, L., Schmidt-Rohr, K., Spiess, H.W. (1990), Chem. Phys. Lett. 167, 583. Howell, F. S., Bose, R. A., Macedo, P. B., Moynihan, C.T. (1974), /. Phys. Chem. 78, 639. Jansen-Glaw, B., Rossler, E., Taupitz, M., Vieth, H.M. (1989), /. Chem. Phys. 90, 6858. Jeener, X (1971), Proc. Ampere Inter. Summer School II, Basko Polje. Johari, G.P. (1985), /. Chim. Phys. 82, 283. Johari, G. P. (1976), Ann. N. Y Acad. of Sci. 279, 111. Johari, G. P. (1987), in: Lecture Notes in Physics 277, 90. Berlin: Springer, pp. 90-112. Johari, G.P., Goldstein, M. (1970), J. Chem. Phys. 53, 2372. Kaufmann, S., Wefmg, S., Schaefer, D., Spiess, H. W. (1990), /. Chem. Phys. 93, 197. Kauzmann, W. (1948), Chem. Rev. 43, 219. Klinger, M.I. (1988), Phys. Repts. 165, 275. Kohler, W, Friedrich, X (1987), Phys. Rev. Lett. 59, 2199. Kohlrausch, R. (1847), Ann. Phys. (Leipzig) 12, 393. Kovacs, A.I. (1981), Ann. N. Y. Acad. Sci. 371, 38. Kremer, R, Boese, D., Meier, G., Pischer, E.W. (1989), Progr. Colloid and Polym. Sci., 80, 129. Laughlin, W.T., Uhlmann, D.R. (1972), J. Phys. Chem. 76, 2317. Leutheusser, E. (1984), Phys. Rev. A 29, 2765. Lindner, P., Rossler, E., Sillescu, H. (1981), Makromol. Chem. 182, 3653. Lindsay, C.P., Patterson, G.D. (1980), J. Chem. Phys. 3, 3348. Lohflnk, M., Sillescu, H., Fujara, F , Fleischer, G. (1991), to be published. Ma, R.X, He, T.H., Wang, C.H. (1988), /. Chem. Phys. 88, 1497. McCall, D.W., Douglass, D. C , Falcone, D.R. (1969), J. Chem. Phys. 50, 3839. Mezei, R (1989), in: Springer Proceedings in Physics, Vol.37: Richter, D., Dianoux, A.X, Petry, W, Teixeira, X (Eds.), pp. 164-169. Movaghar, B., Grunewald, M., Ries, B., Bassler, H., Wiirz, D. (1986), Phys. Rev. B33, 5545. Moynihan, C. X, Balitactac, N., Boone, L., Litovitz, T. A. (1971), J. Chem. Phys. 55, 3013. Muller-Warmuth, W, Otte, W. (1979), /. Chem. Phys. 72, 1749. Muller-Warmuth, W, Eckert, H. (1982), Phys. Repts 88, 91. Ngai, K. L., Rendell, R. W, Rajagopal, A. K., Teitler, S. (1986), in: Ann. N.Y. Acad. Sci. 484, 150. Otsuka, S., Ueno, H., Kishimoto, A. (1979), Angew. Makrom. Chem. 80, 69. Patterson, G. D. (1983), Adv. in Polymer Sci. 48, 125. Pearson, D. (1987), Rubber Chem. and Technol. 60, 439. Petry, W, Bartsch, E., Pujara, R, Sillescu, H., Farago, B. (1991), Z. Phys. B, in press. Phillips, W. A. (1972), /. Low Temp. Phys. 7, 351.

11.4 References

Placzek, D. I, Magill, J. H. (1968), /. Chem. Phys. 45, 3038. Polk, D. E. (1971), J. Non-Cryst. Solids 5, 365. Polk, D. E., Boudreux, D. S. (1973), Phys. Rev. Lett. 31, 92, Pschorn, U., Spiess, H.W. (1980), 1 Magn. Res. 39, 217. Pschorn, U., Rossler, E., Kaufmann, S., Sillescu, H., Spiess, H.W. (1991), Macromolecules 24, 398. Rhodes, E., Smith, WE., Ubbelohde, A.R. (1966), Trans. Faraday Soc. 63, 1943. Richert, R., Bassler, H. (1990), J. Phys. Condensed Matter 2, 2273. Rossler, E., Sillescu, H. (1984), Chem. Phys. Lett. 112, 94. Rossler, E., Sillescu, H., Spiess, H.W (1985), Polymer 26, 203. Rossler, E. (1986), Chem. Phys. Lett. 128, 330. Rossler, E. (1987), in: Lecture Notes in Physics, Vol. 277, Berlin: Springer, pp. 144-154. Rossler, E. (1989), in: Proceedings of the 24th Ampere Congress, Magnetic Resonance and Related Phenomena, Poznan: Stankowski, I , Pislewski, N., Hoffmann, S.K. (Eds.). Amsterdam: Elsevier, pp. 1019-1026. Rossler, E. (1990 a), /. Chem. Phys. 92, 3725. Rossler, E. (1990 b), Ber. Bunsenges. Chem. Phys. 94, 392. Rossler, E. (1990 c), Phys. Rev. Lett. 65, 1595. Rossler, E. (1991), /. Non-Crystall. Solids, in press. Rossler, E., Schnauss, W (1990), Chem. Phys. Lett. 170, 315. Rossler, E., Taupitz, M., Yieth, H.-M. (1989a), in: Springer Proceedings in Physics, Vol. 37: Richter, D., Dianoux, A.J., Petry, W, Teixeira, J. (Eds.), Berlin: Springer, pp. 114-119. Rossler, E., Taupitz, M., Vieth, H.-M. (1989 b), Ber. Bunsenges. Phys. Chem. 93, 1241. Rossler, E., Taupitz, M., Borner, K., Schulz, M., Vieth, H.-M. (1990 a), / Chem. Phys. 92, 5847. Rossler, E., Taupitz, M., Vieth, H.-M. (1990 b), /. Phys. Chem. 94, 6879. Rossler, E., Borner, K., Schulz, M., Taupitz, M. (1991), J. Non-Crystall. Solids, in press. Schaefer, D., Spiess, H.W, Suter, U.W, Fleming, W W (1990), Macromolecules 23, 3431. Schirmacher, W, Wagener, M. (1989), Springer Proceed. Phys. 37, 231. Scott, G. D., Kilgour, D. M. (1969), J. Phys. D 2, 263. Schmidt, C , Kuhn, H.-I, Spiess, H. W (1985), Progr. Coll. &Polym. Sci. 71, 71. Schmidt, C , Bliimich, B., Wefing, S., Spiess, H.W (1986), Chem. Phys. Lett. 130, 84. Schnauss, W, Fujara, R, Hartmann, K., Sillescu, H. (1990), Chem. Phys. Lett. 166, 381. Schweidler, E. Ritter von (1907), Ann. Phys. 24, 711. Sethna, J. P., Chow, K. S. (1985), Phase Transitions 5, 317.

617

Sillescu, H., Ehlich, D. (1990), in: Lasers in Polym. Sci. and Technol, Vol. Ill: Fouassier, I P . , Rabek, J. F. (Eds.). CRC Press, Boca Raton, p. 211. Sjogren, L. (1990), Z. Phys. B79, 5. Sjogren, L., Gotze, W (1989), in: Springer Proceedings in Physics, Vol. 37: Richter, D., Dianoux, A. X, Petry, W, Teixeira, J. (Eds.). Berlin: Springer, pp. 18-37. Spiess, H.W. (1974), Chem. Phys. 6, 217. Spiess, H.W. (1980), /. Chem. Phys. 72, 6755. Spiess, H.W, Sillescu, H. (1981), J. Magn. Reson. 42, 381. Szeftel, X, Alloul, H. (1978), J. Non-Crystall Solids 29, 253. Taupitz, M., Rossler, E., Schulz, H., Vieth, W (1990), in: Basic Features of the Glassy State, World Scientific Publishing Co. Tweer, H., Simmons, X H., Macedo, P. B. (1971), /. Chem. Phys. 54, 1952. Vrentas, I. S., Duda, I.L., Ling, H.-C, Hou, A.C. (1985), /. Polym. Sci. Phys. 23, 275, 289, 2469, and references therein. Wagner, K. W (1913), Ann. Physik (4), 40, 817. Wefing, S., Kaufmann, S., Spiess, H.W (1988), /. Chem. Phys. 89, 1234. Wehrle, B., Limbach, H.-H., Zimmermann, H. (1987), Ber. Bunsenges. Phys. Chem. 91, 941. Wehrle, M., Hellmann, G. H., Spiess, H.W. (1988), Colloid & Polymer Sci. 265, 815. Wemmer, D. E., Ruben, D. X, Pines, A. (1981), J. Am. Chem. Soc. 103, 28. Williams, M. L., Landel, R. F , Ferry, X D. (1955), J. Am. Chem. Soc. 77, 3701. Williams, G., Watts, D.C. (1970), Trans. Faraday Soc. 66, 80. Zachariasen, W.H. (1932), J. Am. Chem. Soc. 54, 3841. Zeidler, M.D. (1965), Ber. Bunsenges. Phys. Chem. 69, 659.

General Reading Abragam, A. (1961), The Principles of Nuclear Magnetic Resonance. Oxford: Oxford University Press. Bee, M. (1988), Quasielastic Neutron Scattering. Bristol: Hilger. Berne, B.X, Pecora, R. (1976), Dynamic Light Scattering. New York: Wiley. Bottcher, C.J.F., Bordewijk, P. (1978), Theory of Electric Polarization, Vol. II. Amsterdam: Elsevier. Debye, P. (1929), Polare Molekel. Leipzig: Hirzel. DeGennes, P.-G. (1979), Scaling Concepts in Polymer Physics. Ithaca: Cornell University Press. DiMarzio, E.A. (1981), Ann. New York Acad. Sci. 371, 1. Eichler, H. X, Giinther, P., Pohl, D. W. (1986), LaserInduced Dynamic Gratings. Berlin: Springer. Elliot, S.R. (1990), Physics of Amorphous Materials. 2nd. Edn. London: Longman.

618

11 Organic Glasses and Polymers

Ferry, I D . (1980), Viscoelastic Properties of Polymers, 3rd. Ed. London: J. Wiley. Fyfe, C.A. (1984), Solid State NMR for Chemists. Guelph: Guelph CFC Press. Gotze, W. (1990), in: Liquids, Freezing and the Glass Transition; Hansen, I P . , Levesque, D., ZinnJustin, J. (Eds.). North-Holland Publ. Grest, G. S., Cohen, M. H. (1981), Adv. Chem. Phys. 4K455. Haebeflen, U. (1976), Adv. ofMagn. Reson., Suppl 1. New York: Academic Press. Jackie, I (1986), Rep. Progr. Phys. 49, 171. Lovesey, S.W. (1986), Theory of Neutron Scattering from Condensed Matter, Vol. 1. Oxford: Clarendon Press. McCrum, N.G., Read, B.E., Williams, G. (1967), Anelastic and Dielectric Effects in Polymer Solids, London. Mehring, M. (1976), NMR - Basic Principles and Progress, Vol. 11. Berlin: Springer. Noack, F. (1971), in: NMR - Basic Principles and Progress, Vol.3. Berlin: Springer.

Phillips, W.A. (1981), Topics in Current Physics, Vol. 24, Amorphous Solids Low-Temperature Properties. Berlin: Springer. Phillips, W.A. (1987), Repts. Progr. Phys. 50, 1657, and references therein. Spiess, H. W. (1984), Colloid & Polymer Sci. 261, 193. Spiess, H. W (1985), Adv. Polym. Sci. 66, 23. Springer, T. (1972), Quasielastic Neutron Scattering for the Investigating of Diffusive Motions in Solids and Liquids. Berlin: Springer. Struik, L. C. E. (1980), Physical Ageing in Amorphous Polymers and other Materials, 2nd impr., Amsterdam: Elsevier Sci. Publ. Williams, G., Watts, D.C. (1971), in: NMR Basic Principles and Progress, Vol. 4. Diehl, P., Fluck, E., Kosfeld, R. (Eds.). Berlin: Springer, pp. 271-285. Wong, I , Angell, C.A. (1976), Glass - Structure by Spectroscopy. New York: Marcel Dekker. Zallen, R. (1963), The Physics of Amorphous Solids. New York: Wiley. Zschogge, I. (1986), Optical Spectroscopy of Glasses. Dordrecht: D. Reidel Publ.

12 Optical Properties of Glasses Marvin J. Weber Lawrence Livermore National Laboratory, University of California, Livermore, CA, U.S.A.

List of Symbols and Abbreviations 12.1 Introduction 12.2 Fundamental Optical Phenomena 12.2.1 Absorption 12.2.2 Refraction 12.2.3 Reflection 12.2.4 Scattering 12.2.5 Photoelastic Properties 12.2.6 Thermal-Optical Properties 12.2.7 Magneto-Optical Properties 12.2.8 Nonlinear Optical Properties 12.2.9 Luminescence and Stimulated Emission 12.2.10 Optical Damage 12.3 Optical Glasses 12.3.1 Classification and Designation 12.3.2 Transmission 12.3.3 Refractive Index and Dispersion 12.3.4 Thermal Properties 12.3.5 Mechanical Properties 12.3.6 Chemical Durability 12.3.7 Quality and Forms 12.4 Special Glasses 12.4.1 Abnormal Dispersion Glass 12.4.2 Gradient Index Glass . . . . 12.4.3 Mirror Substrate Glass . 12.4.4 Optical Filter Glass 12.4.5 Nonlinear Glass 12.4.6 Laser Glass 12.4.7 Faraday Rotator Glass 12.4.8 Acoustooptic Glass 12.4.9 Radiation Detection Glass 12.4.10 Radiation Shielding Glass 12.4.11 Photosensitive Glass 12.5 Future 12.6 Acknowledgements 12.7 References Materials Science and Technology Copyright © WILEY-VCH Verlag GmbH & Co KGaA. All rights reserved.

620 622 622 623 625 627 629 630 631 632 634 637 639 639 639 641 642 644 646 647 648 649 649 649 650 651 652 654 657 658 659 660 661 661 662 662

620

12 Optical Properties of Glasses

List of Symbols and Abbreviations B B c c

a

C

P

e E E

f

F 9 G h H I J Kc K kB k

I m M n, n*

n0 n2 OD P P(co)

P, P*y

P P q Q r R RT S T V

bulk modulus Kerr constant velocity of light in vacuum elastic stiffness constant specific heat at constant pressure electron charge electric field Young's modulus energy gap oscillator strength force constant Lande g factor modulus of rigidity Planck's constant magnetic field intensity angular momentum quantum number fracture toughness stress-optical coefficient Boltzmann's constant extinction coefficient length electron mass figure of merit index of refraction, complex index of refraction linear index of refraction nonlinear index of refraction coefficient optical density elastic-optic constant polarization acoustic power partial dispersion thermo-optic coefficient pressure piezo-optic constant thermo-optic coefficient reflectivity reflection factor Landau-Placzek ratio thermochemical figure of merit optical path length temperature Verdet constant

List of Symbols and Abbreviations

w

thermo-optic coefficient velocity longitudinal sound velocity

a a aB as

ll/F

coefficient of thermal expansion linear absorption coefficient Brillouin loss coefficient scattering loss coefficient Bohr magneton cubic coefficient of thermal expansion two-photon absorption coefficient damping factor linewidth stress dielectric constant complex dielectric constant permittivity flux Bragg angle Brewster angle susceptibility thermal conductivity wavelength Poisson's ratio reduced mass Abbe number frequency density stress angular frequency Faraday rotation angle magnetic linear birefringence magnetic linear dichroism Faraday ellipticity

AO ESCA FR GRIN LG MCD

acousto-optic glass electron spectroscopy for chemical analysis Faraday rotator glass gradient index laser glass magnetic circular dichroism

V

P P P y y

s 8

oB X X

I \i

fi V V

Q G

CO

0L

621

622

12 Optical Properties of Glasses

12.1 Introduction Of the properties of glass, none combines science, technology, and aesthetics to the extent exhibited by optical properties. Glass has enabled mankind to observe nature from the minuscule to the vastness of space, yet understanding its linear and nonlinear optical behavior and their dependence on glass structure and composition remains a scientific challenge. Technologically, the benefits of glass transparency range from simple windows for buildings to optical fibers for ultra-long-distance communications. And the beauty of glass its clarity, color, and art forms - is one of the most appealing features of its optical properties. Optical glass epitomizes an engineered material (Stokowski, 1987). In contrast to a crystal which has a specific chemical composition, glass has a variable chemical composition (Kreidl, 1983). This compositional versatility has been exploited to tailor glasses to achieve an optimal compromise of properties for specific applications. Hundreds of optical glasses now exist with extremely well characterized and reproducible properties for numerous optical components and systems. These include glasses for passive applications such as lenses, windows, prisms, and substrates, and for active applications such as laser sources and magnetooptic and acoustooptic modulators. Today, optics encompasses not only the visible spectral region but extends from the vacuum ultraviolet through the mid-infrared. Optical glasses of high quality are available for use throughout this spectral range. Compared to window glass, optical glass is distinguished by demands for quality (high homogeneity, transparency, and the absence of imperfections), for varied sizes

and forms (from disks measured in meters to fibers measured in microns), and for a multitude of special properties (linear, nonlinear, electrooptic, magnetooptic, acoustooptic, etc.). Over one hundred and fifty years ago Michael Faraday (1830) in his Bakerian lecture noted that "Perfect as is the manufacture of glass for all ordinary purposes, and extensive the scale upon which its production is carried on, yet there is scarcely any artificial substance in which it is so difficult to unite what is required to satisfy the wants of science." To the glass technologist of today, his comments are still apropos. In this chapter we begin with a brief review of fundamental optical phenomena and properties characteristic of optical glasses. Oxide glasses are by far the most advanced of the optical glasses and their properties are discussed in detail. These glasses were developed mainly for the visible portion of the spectrum, but present science and technology require materials with optical properties covering a wider spectral range than can be satisfied by oxide glasses. Hence considerable current research and development are devoted to non-oxide glasses. A number of the optical properties of these glasses are covered in the earlier chapters in this volume on halide and chalcogenide glasses. Here we emphasize the characteristics of oxide glasses but also present data for other glasses to display the range of physical properties available. We conclude with descriptions of a number of glasses having special optical properties for special applications.

12.2 Fundamental Optical Phenomena The interaction of light with a solid can be specified by various optical response

12.2 Fundamental Optical Phenomena

functions. To describe the amplitude and phase of the response, these functions are generally frequency-dependent complex quantities. The complex dielectric constant £*, for example, relates the amplitude of an optical electric field E of frequency co to the polarization wave P(co) induced in the material. It is related to the complex index of refraction /i* (co) by s* (co) = /i*2 (co). The index of refraction, in turn, can be related to the amplitude and phase of the reflectivity. For each of these complex quantities the real and imaginary components are related by Kramers-Kronig integral equations (Kittel, 1976). Thus if one of the components is known over a sufficiently large frequency range, the other component can be obtained from an integral transform. Because glass is a disordered medium, it is

isotropic on a macroscopic scale and does not exhibit sharp spectral features characteristic of crystalline materials. This simplifies the treatment of most optical properties. 12.2.1 Absorption

Optical glass absorbs strongly in the infrared and the ultraviolet spectral regions. The former is associated with the interaction of light and molecular vibrations giving rise to multiphonon absorption processes; the latter is associated with electronic transitions between the valence band and the conduction band or exciton levels. The absorption spectrum for a sodalime-silicate glass (Bagley et al., 1976) shown in Fig. 12-1 illustrates the region of transparency and of strong infrared (IR)

Wavelength (nm) 1240

12398

10 8

124

Visible Infrared 10

l • i

Ultrai/iolet

w

6

/

104

A i

1

S10 2 o

"5

8

.1 fr

o

O

10- 2

10" 4

0.01

0.10

\J 1.0

623

10

100

Energy (eV)

Figure 12-1. Absorption spectrum of a soda-lime-silicate glass [see Bagley et al. (1976)].

624

12 Optical Properties of Glasses

and ultraviolet (UV) absorption typical of an optical glass. The positions of both the long- and short-wavelength absorption edges depend on the glass composition and can be varied by the choice of glass network former and network modifier ions. The region of transparency is shifted into the mid-infrared for chalcogenide glasses and into the ultraviolet for fluoride glasses. Oxide glasses typically have a broad transmission window in the visible and near infrared; fluoride-containing glasses can have a more extended range of transparency. The intensity / of light transmitted through a sample of length / is given by the Lambert-Beer law as = Io exp( — a I

(12-1)

where J o is the incident intensity and a is the absorption coefficient. As evident from Fig. 12-1, the range of absorption coefficients for glass over the entire spectrum covers many orders of magnitude, from 106 cm" 1 in the UV to less than 1(T 4 cm" 1 in the near IR for ultrapure glass. The fundamental absorption edge at short wavelengths in Fig. 12-1 can be described by an absorption coefficient <xl]y(co) = = a0exp{-G[Eg(T)-hco]/kBT}

(12-2)

where ao, a and the temperature-dependent energy gap Eg are fitting parameters independent of the frequency co. This empirical relation, known as Urbach's rule (Urbach, 1953), has been well verified experimentally (see, for example, Mohler and Thomas, 1980). The UV absorption edges of many different glasses and the dependence of the edge on composition have been reviewed by Sigel (1977). In oxide glasses the excitation of non-bridging oxides requires less energy than the excitation of bridging oxygens, thus the absorption

edge occurs at longer wavelengths for multi-component silicate glasses than for simple fused silica. From photoelectron spectra it is possible to distinguish between bridging and non-bridging oxygen atoms and, in the case of phosphate glasses, double-bonded oxygen atoms (Bruckner et al, 1980). Studies of silica, alkali silicate, and aluminosilicate glasses show a clear shift of the non-bridging oxygen 1 s line corresponding to progressively lower bonding energies in the series Li-Na-K-Rb-Cs. This, in turn, shifts the UV absorption edge to longer wavelengths (Smith and Cohen, 1963). The long-wavelength absorption edge in solids arises from multiphonon excitation of overtone and combination bands of fundamental vibrational modes and can also be fitted to an exponential dependence on energy similar to Eq. (12-2) of the form (Bendow, 1973, 1977) (12-3) where N(co) = [exp (h co/kB T) — 1] ~ x , coo is

an average optical phonon frequency, and C is a material constant characterizing the vibrational anharmonicity. The highest frequency vibrations in glass are usually associated with the network former, such as the silicon-oxygen SiO4 tetrahedron. The frequency varies with the strength of the force constant F and inversely with the reduced mass fi = m1rn2/(m1 + m2) of the component ions and is found empirically to obey the Szigeti equation (Szigeti, 1950) co = (F/n)1/2/2nc

(12-4)

Thus with respect to silicate glasses the IR absorption moves to long wavelengths for germanate or tellurite glasses or for heavy metal (Zr, Hf) fluoride glasses due to the changes in bond strength and reduced mass. Similarly, the absorption edge moves to

12.2 Fundamental Optical Phenomena

longer wavelengths for chalcogenide glasses in the series As-S
In vacuum the propagation velocity is the same for all wavelengths, but in a transmitting medium the velocity and refractive index vary with wavelength. Using a classical oscillator model, the refractive index due to absorption of a system of N atoms per unit volume is described by Ne /r -1 =

JflSn

/;

co2 — co2

(12-6)

where e0 is the electric permittivity, / is a dimensionless oscillator strength, and the summation is over all oscillators of frequency ojj and linewidth y^ contributing to the absorption (Born and Wolf, 1980). Separating Eq. (12-6) into its real and imaginary parts yields /JK-M2)

(12-7)

and

(12-8) msn

Figure 12-2 illustrates the general wavelength dispersion of the refractive index for a simple case where X± and X2 are the wavelengths of two effective oscillators corresponding to the ultraviolet and infrared absorption bands, respectively. In regions far removed from absorption, wherefc^O,Eq. (12-7) reduces to (12-9)

12.2.2 Refraction The index of refraction n for monochromatic radiation is the ratio of the velocity of light in vacuum to the velocity of light in the medium, that is, n — c/v. For an absorbing dielectric medium, the index of refraction at wavelength X is complex and given by n* = n-ik (12-5) where the extinction coefficient k is related to the absorption coefficient by k = a X/4 n.

625

men

The wavelength dependence of the refractive index in this case is frequently expressed by the Sellmeier relationship m 2

4 22

n (A)-l=Z^rr

(12-10)

where Aj and Xj are the effective strength and mean wavelength of the jth absorption band and the summation is over all infrared and ultraviolet bands. The static dielec-

626

12 Optical Properties of Glasses •Ultraviolet -j

Visible | - Infrared>

/ *1/

Wavelength •

Figure 12-2. Schematic dispersion curve for an optical glass. Dashed portions correspond to regions of strong absorption.

trie constant 8 of the material is equal to n2, where n is given by Eq. (12-9) for co = 0 (* = oo). Other simplified models involving more physically meaningful phenomenological parameters can be used to describe the wavelength dependence of n. A two-parameter Sellmeier expression for the electronic contribution and a single-parameter asymptotic expression for the lattice contribution of the form '<-l =

EdE0/(E2-h2co2)-Ef/h2co2

(12-11)

where Eo is an average electronic energy gap, Ed is the electron oscillator strength or dispersion energy, and El is the lattice oscillator strength fits refractive index data satisfactorily for a wide range of crystalline and amorphous materials (Wemple, 1973, 1977). Eo scales with the fundamental energy gap and is a strong function of bond length d, that is, Eoccd~s, where 2 < s < 3 . The macroscopic oscillator strength Ed is related to the cation coordination number, anion valency, and ionicity by

Ed=fncZa(NAd3)

(12-12)

where ne is the number of valence electrons per anion (usually ne = 8), Z a is the anion valence (2 for oxides, 1 for fluorides), and iVA is the anion number density. The normalized oscillator strength / for crystals and glasses is unaffected by disorder. This indicates that the bond lengths remain essentially unaltered and illustrates the insensitivity of bond-dependent optical properties to the absence of long-range order. This is consistent with a picture of a glass as a loosely-packed version of a crystal in which no significant bonding changes occur within the basic molecular unit (SiO4, PO 4 , BO 3 , etc.). Ed is also nearly independent of £ 0 . The lattice energy El in Eq. (12-11) is ~0.1 eV and in the short wavelength regime its contribution is negligible. In the simple formalism of Eq. (12-11), EQ and Ed represent weighted averages of the absorption band energies and oscillator strengths. For selected optical glasses (n values ranging from 1.46 to 1.81), changes in n correlate with changes in the band gap energy Eo (DiDomenico, 1972). There is little change in Ed with composition. For most binary, ternary, and more complex lanthanide silicate glasses, £ d ^ 1 5 e V ± 1 0 % (Wemple, 1973). Larger

12.2 Fundamental Optical Phenomena

values of Ed for lanthanide and mixed oxide glasses are attributed to changes of coordination number.

Compositional Dependence; Additivity

Physical properties of solids may be divided into two groups: (1) structure sensitive - those dependent on long-range order and only weakly dependent on composition, and (2) bond sensitive - those dependent on the nature, local arrangement, and interactions of neighboring constituent ions but not dependent on long-range structural order. Examples of structuresensitive properties are thermal and electrical conductivity, fracture characteristics such as breaking strength and yield point, acoustic attenuation, and dielectric, ferromagnetic and other losses. These properties can differ greatly for crystalline versus amorphous solids. Bond-sensitive properties such as thermal expansion, specific heat, specific volume, elastic and photoelastic coefficients, band gap, and refractive index depend strongly on composition; however the values of these properties for crystalline and amorphous solids exhibit only small differences. Structure-insensitive properties of glass can, within limits, be represented by regarding the material as a simple mixture of components each of which contributes independently to the overall effect. Therefore a glass property P can be described by an additive relation of the form '=a+

btxt

(12-13)

where a is a constant dependent on some other property or procedure, N is the number of constituents, xt is the weight or mole fraction of each component, and the bt are experimentally determined factors for each

627

component z. The b{ vary within a given glass former and for different formers. Over the region where this simple linear relationship has validity, if sufficient measurements are made to determine the bi accurately, Eq. (12-13) provides a valuable method for selecting and adjusting glass compositions to obtain desired property values (Volf, 1988). An early and classic example of this approach is the work of Winkelmann and Schott (1894) on glass density. For large compositional variations, Eq. (12-13) can be extended to include nonlinear terms (Huff and Call, 1973). The refraction and dispersion of glasses can be expressed by additivity relations of the form in Eq. (12-13) (Huggins and Sun, 1943; Goldstein and Sun, 1979). This is a useful procedure for finding approximate values of the refractive index and dispersion of a glass from its chemical composition. Morey (1954) cites many experimental investigations of refractive index versus composition. Glass properties such as density and refractive index have also been expressed in terms of the bridging oxygen to non-bridging oxygen ratio derived from ESCA studies (Jen and Kalinowski, 1980). This ratio has direct implications for glass structure and therefore is more physically meaningful than simple glass composition. 12.2.3 Reflection

When a flux of light $ traversing a medium of refractive index nf is incident on a glass of index n, it is partially reflected and partially refracted as shown in Fig. 12-3. By Snell's laws, 9r1 = 91 on reflection and n sin 62 = n'sind1 on refraction (Born and Wolf, 1980). The amount of light reflected is a function of the angle of incidence. For light incident from a less dense to a more dense medium, the reflectivity

628

12 Optical Properties of Glasses ° incident

/

n

nf

transmitted

Figure 12-3. Reflection, refraction, and transmission of light at material boundaries (n' < n).

becomes very large as 61 approaches grazing incidence. If n>n\ 62<0l and light is refracted toward the normal. If n! > n, at a critical angle determined by sin 6C = n/ri, light is totally reflected. Light becomes polarized due to reflection, refraction, absorption, and scattering. At Brewster angle 9V, given by ri/n = tan 6p,

only the component of light polarized perpendicular to the plane of incidence is reflected and the intensity is plane polarized; at other angles of incidence the reflected light has mixed polarization. If the glass surface is oriented at Brewster's angle with respect to the direction of propagation of a plane-polarized beam, light is propagated through the glass with no reflective losses. The dependence of the reflectivity on wavelength and angle of incidence (Fresnel

laws) is complex, especially near an absorption band (Born and Wolf, 1980). The index of refraction and the absorption coefficient of a material can be derived from reflectivity data integrated over a broad range of wavelengths beyond the IR and UV absorption edges using a KramersKronig analysis (Powell and Spicer, 1970). The fraction of light reflected by a glass in air (nf«1) for normal incidence is given by the Fresnel reflectivity

In the transparent region where k w 0, this reduces to r = 4% for a glass of refractive index 7? = 1.5. The fraction of light transmitted when multiple reflections at both entrance and exit surfaces are considered is

12.2 Fundamental Optical Phenomena

given by the reflection factor R-

2n

(12-15)

For high-index glasses, Fresnel reflective losses become very large. In addition to spectral reflection depicted by Fig. 12-3, the transmitted flux may also be reduced by diffuse reflection from rough or irregular entrance and exit surfaces and imperfections in the interior of the glass. 12.2.4 Scattering

The flux transmitted in Fig. 12-3 is reduced from the incident flux by a combination of losses due to absorption, reflection, and scattering. Scattering of light in glass may be due to extrinsic causes or it may be intrinsic in nature. The former include discrete scattering centers such as bubbles, inclusions, impurities or flaws introduced during production. The latter includes Rayleigh scattering caused by stationary density, temperature, and compositional fluctuations, and Brillouin scattering caused by propagating fluctuations in the dielectric constant. Spontaneous and stimulated Raman and Brillouin scattering involve optic and acoustic phonons and nonlinear optical processes (Shen, 1984). Scattering processes may also be distinguished by the size and absorptivity of the active centers (Van de Hulst, 1957). Rayleigh scattering is caused by scattering centers that are small compared to the wavelength of light and exhibits a characteristic A~4 dependence on wavelength. As the particle size increases, scattering occurs increasingly in the forward direction and exhibits a l " 2 dependence (Rayleigh-Gan scattering). Mie scattering occurs when the scattering centers have a size comparable to the wavelength of light. Scattering in

629

glass begins to be visible for centers > lOnm in size. For large numbers of centers of dimensions ~100nm, glass appears cloudy. For high densities of centers having dimensions >1000nm, glass is usually opaque. Colloidal particles (crystals) that diffract light - the Tyndall effect - also contribute to light scattering. The color of the scattered light changes with the size of the colloidal particles. This particle size property is used to obtain optimum color characteristics, for example, in gold ruby glass. The spectrum of intrinsically scattered light consists of an unshifted central Rayleigh line and frequency-shifted Brillouin lines, the theoretical and experimental aspects of which are reviewed by Schroeder (1977). The ratio of the intensities of the central component to the total Brillouin components is given by the LandauPlaczek ratio RhP. The scattering loss coefficient as at wavelength X and temperature T is given by (12-16) where 8TI 3 kBT

n8p212

(12-17)

QV\

In Eq. (12-17), p12 is the longitudinal elastooptic constant (see Sec. 12.2.5), and vl is the longitudinal sound velocity (Pinnow et al., 1973). A similar expression applies to Rayleigh scattering where the temperature T is now the fictive temperature Tf at which density fluctuations are frozen in (near the glass transition temperature Tg). Light scattering losses in single-component glasses such as SiO2 are small and limited by microscopic density fluctuations associated with the random molecular structure. Losses in multi-component glasses and mixtures are generally larger because of additional concentration fluctu-

630

12 Optical Properties of Glasses

ations. Compositional studies of scattering losses show, for example, that for simple binary alkali silicate glasses, density fluctuations decrease with decreasing molecular weight of the alkali oxide. Thus glasses composed of low-atomic-number cations have reduced scattering losses. Since Tf > T, Rayleigh scattering is greater than Brillouin scattering. For single-component glasses, RLP~ 20. Scattering losses in optical fibers (Chap. 15), where ultralow losses are important, have been investigated extensively. For these materials, scattering is the major loss mechanism when absorption is successfully reduced. For most bulk optical and laser glasses, losses due to extrinsic imperfections and impurity absorptions are usually larger than intrinsic scattering losses. 12.2.5 Photoelastic Properties While glass is normally considered to be an isotropic material, it becomes birefringent under stress. Photoelastic properties describe the effects of elastic deformation on the refractive index; these result in distortions of the optical wavefront. The piezo-optic and elasto-optic coefficients determine the effects of stress and strain, respectively. In general a material may possess 36 independent piezo-optic or elasto-optic constants, but because glass is isotropic, there are only two independent coefficients for each. The change in refractive index An caused by a change in stress o for light polarized parallel or perpendicular to the line of stress is given by n3 An = Anl]-An1= — (q11-q12)a (12-18) where the g's are the piezo-optic constants and ^44 = ^ii — ^i2- The change in refractive index for uniform hydrostatic pressure P i s An = n3(q11+q12)P/2.

Corresponding relations involving elastic-optic constants p (Pockels coefficients) describe changes in refractive index and the state of strain in the glass. The p's and g's are related by (12-19 a)

Pn = and P12 = Cn «i2 + cii(«n

+«i2>

(12-19b)

where the c's are elastic stiffness constants. Also, p 4 4 = (p 11 ~p 12 )/2. Photoelastic constants have been measured for many optical glasses (Schaefer, 1953; Waxier, 1971) and studied as a function of glass composition. The dependence of the elastic-optic coefficients (measured from Brillouin line shifts) on composition for binary and ternary silicate glasses have been correlated with the degree of ion overlap and covalent bonding as the amount of alkali oxide in the base glass was varied (Schroeder, 1980). Stress-Optical Coefficient Mechanical stress, either developed internally during production, applied externally, or as a consequence of fluctuating temperature, changes the refractive index. The resulting change in optical path length S for a sample of length / caused by stress birefringence is AS = Anl = Kla

(12-20)

where, from Eq. (12-18), the stress-optical coefficient K is defined by K = Y(
(12-21)

Pockels (1903) was the first person to study the stress-optical effect, including the variations of K with PbO content in a lead silicate glass. K was found to decrease with increasing PbO content, was zero at

631

12.2 Fundamental Optical Phenomena

«75wt.%, and became negative at higher PbO concentrations. Several studies have been made to reduce the stress-optical coefficients of oxide and oxyfluoride glasses (Tashiro, 1956; Galant, 1979) with the result that to reduce K the glass composition should contain strongly polarizable cations (e.g., Cs + , Tl + , Ba 2+ , Pb 2 + , La 3+ ) and weakly polarizable anions (F~). Additivity relations have been applied (Nissle and Babcock, 1973) which are useful for estimating K for contiguous fields in the glass compositional space. Partial stress-optical coefficients have been tabulated for alkali, alkaline earth, and other oxide components in silicate and phosphate glasses (Shchavelev et al., 1978). The birefringence varies with both temperature and wavelength. The wavelength dispersion of K over a large wavelength range can be fitted using an empirical expression involving ultraviolet and infrared absorption frequencies (Sinka, 1978).

fects. At a given wavelength, the change in refractive index resulting from the temperature-dependent shift in absorption and thermal expansion is given by dn/dT = dn/dT -0Q dn/dg

(12-23)

where dn/dT is the change in refractive index at constant density Q and /? is the cubic expansion coefficient. Because both dn/dT and dn/dg are always positive, dn/dT can be either positive or negative. By adjusting the glass composition so that the change in path length change due to thermal expansion is compensated by a negative value of dn/d7^ the thermo-optic coefficient can be positive, negative or zero (Shchavelev and Babkina, 1970). Pump-induced optical distortions in laser rods affect both radially and tangentially polarized light propagating along the axis. For a rod of radius r0 at a temperature To, refractive index fluctuations for light polarized parallel or perpendicular to the radius are

12.2.6 Thermal-Optical Properties

dnr(r) = (P + Q/2) To [1 - (r/r0)2]

Partial absorption of intense light traversing a glass or, in the case of laser glass, optical pumping lead to the formation of temperature gradients and stress in the glass. Thermally-induced optical distortions in laser materials have been the subject of many theoretical and experimental studies (see Quelle, 1966; Riedel and Baldwin, 1967). The optical path length of light passing through a glass varies with temperature owing to thermal expansion and to changes in the refractive index and is given by

and

dS/dT = (n - 1 ) a + dn/dT = W

(12-22)

where a is the linear coefficient of thermal expansion and W is one of three coefficients used to define the thermo-optic ef-

(12-24 a)

6n& (r) = (P- 2/2) To [1 - (r/r0)2]

(12-24 b)

where the two additional thermo-optic coefficients P and Q are defined by dn dT

n3aE 4(1-^

L

+ 3
(12-25)

and 4(1-/

2(1-A*)

(12-26)

The coefficient P can be positive or negative. Studies (Shchavelev et al., 1976) of silicate, phosphate and fluorophosphate glasses show that P can range from approximately 40x 10" 1K'1 to - 2 5 x l O ~ 7 K - 1 . Since E and \x in Eq. (12-26) are positive, the sign of Q is generally determined by the

632

12 Optical Properties of Glasses

stress-optical coefficient K. As discussed in Sec. 12.2.5.1, by compositional variations K, and hence Q, can be made equal to zero for some glasses. All coefficients and moduli that enter into W9 P and Q are, in varying degrees, dependent on the glass composition and the temperature. In principle, with the proper combination of glass properties, no optical distortions would appear in the presence of a nonuniform temperature distribution. Even if this ideal athermal glass is not achieved, thermo-optic distortions in optical glass can be reduced by compositional tailoring. 12.2.7 Magneto-Optical Properties Optical rotation occurs in a medium when the refractive indices n+ and n_ for right and left circularly-polarized light are unequal. The microscopic origin of magnetic optical rotation is the inequality that is created by the splitting of the ground or excited-state energy levels due to an applied magnetic field or magnetization. Magneto-optical effects are described by the dielectric tensor elements (Zeiger and Pratt, 1973). When the magnetic vector is parallel to the light propagation vector, measurable optical qualities are (12-27) and 71

(12-28)

where <9F is the angle of Faraday rotation (also called magnetic optical rotation and magnetic circular birefringence) and \j/¥ is the Faraday ellipticity or the magnetic circular dichroism (MCD). The sense of rotation is positive if the rotation is in the direction of the positive current in the coil that produces the magnetic field. When the

magnetization vector is perpendicular to the light propagation vector, measurable optical quantities are 271

(12-29)

and (12-30) where @L is the magnetic linear birefringence (also called the Voigt or CottonMouton effect) and \/JL is the magnetic linear dichroism. The four quantities <9F, \j/F, 0 L , i/fL are usually measured in transmission experiments. Although Faraday rotation occurs in both nonabsorbing and absorbing regions, magnetic circular dichroism occurs only in absorbing regions. In regions of strong absorption, reflection measurements are possible using magnetization Kerr effects (Sec. 12.2.8). The real and imaginary parts of the off-diagonal dielectric tensor elements are again related by a Kramers-Kronig transform. Therefore Faraday rotation can be calculated from magnetic circular dichroism measurements. Measurements of Faraday rotation and magnetic circular dichroism in the vicinity of absorption yield information about ground and excited states of paramagnetic ions and about intra- and interband transitions (Buckingham and Stephens, 1966). For the Faraday effect the rotation of the plane of polarization of light is given by 0F = VlHs

(12-31)

where H is the strength of the applied field, £ is a unit vector in the direction of light propagation, and the constant of proportionality V is the Verdet constant. In terms of the electric susceptibility x for right and

12.2 Fundamental Optical Phenomena

left circularly-polarized light,

Becquerel (1897) is (12-32)

The term in brackets in Eq. (12-32) is the local field correction derived from the Lorentz-Lorenz model. For a system of N atoms per unit volume, the susceptibilities are given by the Kramers-Heisenberg dispersion relation (Zeiger and Pratt, 1973) Qa

(Ea-Eb)

(12-33)

where the summation is over transitions between all ground states a and excited states b (E^>kB T). The transitions are weighted by the Boltzmann factor Qa. Although Eq. (12-33) involves electric-dipole transition matrix elements, it can be generalized to include all types of transitions. Combining Eqs. (12-32) and (12-33) the quantum mechanical expression for Faraday rotation is ACD2N

[>2 +

633

2)2~|

V

dia

=

eX

dn

(12-35)

2

2 m c dX

This expression holds for most materials if a multiplicative factor y, the magneto-optic anomaly, is introduced (Serber, 1932). This factor varies with the nature of the bonding in the material and ranges from near unity for predominantly ionic bonding to 0.28 for strongly covalently bonded diamond. Generally, the larger the refractive index of a material, the larger the diamagnetic Verdet constant; however, a better correlation is obtained if V is plotted as a function of the Abbe number (Cole, 1950). Plots of V for similar glasses as a function of other partial dispersions also yield satisfactory predictions of Verdet constants at a given wavelength. Because of the wavelength dependence of the dispersion dn/dX and the magnetooptic anomaly y, Fdia increases as the wavelength approaches the fundamental absorption edge. The frequency dependence of the diamagnetic term derived from the quantum mechanical expression in Eq. (12-34) has the form

exp(-hcoa/kBT) Zexp(-ftcofl/feBTV a,b

0) —CO a,b

where coa is the ground state splitting, co is the light frequency, coab is the frequency difference of the ground and excited states, and X and Y are components of the electric-dipole moment. The frequency wa is dependent on the magnetic field. Therefore in the small-field limit where ® F depends linearly on if, the Verdet constant is a function of co, T9 and n. The classical formula for the Verdet constant of diamagnetic materials derived by

where C (a, b) is a function of the transition moments between the ground state and excited states. The Verdet constant of diamagnetic materials exhibits only a small temperature dependence and in the longwavelength limit (X^>Xab) varies as 1/X2. When paramagnetic ions are present in a material, their contribution to the Faraday rotation is given by Eq. (12-34), where now N is the number of paramagnetic ions and coab is the frequency of electronic transitions of the ions. Magnetic optical rotation occurs for ions from various transition metal groups, ions of the iron transition

634

12 Optical Properties of Glasses

group and lanthanide series being the most thoroughly studied (Buckingham and Stephens, 1966). The paramagnetic Verdet constant is given C(a,b)

V para

=

3ch

kBT

frequency co can be expressed by the power series <}1)(co)E{(o) + E(coi)E(co2)

a,b

(12-37) where g is the Lande factor, J is the total angular momentum quantum number of the ground state, and p is the Bohr magneton. In the long wavelength limit, Fpara again varies as I/A2 and, except for extremely low temperatures, is inversely proportional to temperature. All glasses exhibit diamagnetic Faraday rotation; however, when paramagnetic ions are present in sufficient quantities, paramagnetic Faraday rotation can dominate. Because the diamagnetic and paramagnetic effects produce opposite rotations, the sign of the net Verdet constant can change with paramagnetic ion content. The wavelength and concentration dependences of the Verdet constant for a rareearth doped silicate glass are illustrated in Fig. 12-4. 12.2.8 Nonlinear Optical Properties

The polarization P induced in a medium by an external optical electric field E of

E((D1)E(co2)E(co3)

(12-38)

where the complex dielectric susceptibilities X(n) are tensors of rank (rc + 1) and are related to the microscopic (electronic and nuclear) structure of the material (Bloembergen, 1965; Shen, 1984). Classical or linear optics is concerned with the first-order term x(1). The linear refractive index n0 and the linear absorption coefficient k are proportional to the real and imaginary parts of x(1) (Born and Wolf, 1980). In regions of no absorption, n2 — 1 = 4TT %(1). Second-harmonic generation and the electro-optic effect are both described by the second-order nonlinear susceptibility y(2) j n gq (12-36). In the first process an optical signal is generated at twice the frequency of the incident optical field, that is, co1=(o2 and co = 2(o1. In the second process, an optical signal is changed by the application of the strong DC field. The generated signal is at the same frequency as the incident optical signal and a)2 = 0 and co = co1. This latter process can also be de-

40

20

2.

8 8 -20

-40

Figure 12-4. Faraday rotation of a sodium silicate glass at 4.2 K for several concentrations of Ho 2 O 3 (wt.%) [from Collocott and Taylor (1978)].

12.2 Fundamental Optical Phenomena

scribed in terms of a DC-field-dependent change of the refractive index. The secondorder nonlinearity term x(2) is important in materials having no center of inversion. In isotropic materials that possess inversion symmetry such as glasses, the second-order contributions are ruled out although electric quadrupole, magnetic dipole and surface terms can produce weak harmonic generation even in centrosymmetric materials. The third-order contributions to the polarization are given by jkl

(12-39) where Ej9 Ek, Ex are three separately applied electric fields each having its own frequency (co1? co2, co3) and polarization direction. Many different third-order nonlinear processes are possible because three incoming electric fields are involved (Hellwarth, 1977). Processes involving x(3) are thirdharmonic generation, Raman and Brillouin scattering, self focusing, optical phase conjugation, and a large number of fourwave mixing processes. The optical (AC) Kerr effect is a four-wave mixing process involving optical frequency fields. In the DC Kerr effect, the modifying electric field is at microwave or lower frequencies. Raman and Brillouin scattering arise from the imaginary part of x(3) and involve interactions with optical and acoustic vibrations of the material. Nonlinear optical properties also depend upon whether the frequency co is resonant or nonresonant with an electronic transition in the material (Borrelli and Hall, 1991). The resonant case applies when the operating wavelength is near a fundamental absorption. Near resonance part of the light beam is absorbed which can lead to redistribution of electron energies, shifts in

635

the absorption frequency, and changes in the refractive index. The response time depends on the relaxation time of the carriers that are excited by the optical field. Thermally-induced nonlinearies associated with absorption generally have much longer relaxation times. The nonresonant case applies for wavelengths far removed from any fundamental absorption in the glass. Nonresonant optical nonlinearities are predominantly of electronic origin and exhibit subpicosecond response times with minimal heating; however, the nonlinearities are much smaller than for the resonant case (Vogel et al., 1991). When the optical Kerr effect is included, the refractive index becomes intensity-dependent and is given by n = n0 + n21

(12-40)

where n0 is the linear index of refraction, / is the time averaged-intensity of the incident optical beam, and n2 is the nonlinear refractive index coefficient. n2 is derived from the real part of / (3) . For an isotropic medium and a linearly-polarized monochromatic beam of frequency co, 480**

(12 41)

"

If a high-intensity beam propagating through a glass has a non-uniform spatial profile, the spatial variation of the induced refractive index will lead to whole-beam or small-scale self-focusing (or defocusing depending on the sign of n2) (Bliss et al., 1974). The intensity-dependent refractive index also causes the phase at the peak of an optical pulse to be retarded with respect to its leading or trailing edges. This selfphase modulation produces a frequency chirp and spectral broadening of the pulse (Stolen and Lin, 1978). Depending upon the sign of the dispersion, the pulse may expand or contract. In addition, certain so-

636

12 Optical Properties of Glasses

lutions of the nonlinear wave equation, called solitons, propagate without any change in shape (Tomlinson, 1988). The above nonlinear optical phenomena are observed in optical fibers at more modest power levels than in pulsed high-power lasers because of the longer path length possible due to the beam confinement and low-loss propagation. Four physical processes contribute to self focusing (Feldman et al., 1973): electronic-arising from induced distortions of the electron orbit about the nuclei (response time 10" 1 4 -10~ 1 6 s), nuclear-optical induced changes in the motion of the nuclei (response time ~ 10~ 12 s), electrostriction-electric-field induced strains (response time 10~ 7 -10~ 9 s), and thermalresulting from absorption (response time ~ 10 ~1 s). The nuclear contribution can be determined from Raman scattering spectra and is only about one-third of the total n2 for many glasses (Heiman et al., 1978). In the DC Kerr effect, an applied field induces a birefringence where B is the Kerr constant and <£2> is the time-averaged square of the modifying electric field amplitude. B is proportional to the difference of two components of x(3) and is given by n

3Xn0

[X(i3Ai(- a, co, Q,-Q) -co,co,Q,-Q)]

-

(12-43)

where the frequency Q <^co (Borrelli and Hall, 1991). The imaginary part of %(3) contributes to two-photon absorption. For the case above, a beam of intensity / propagating in the z-direction is attenuated as ^

(12-45)

P= — T ^ T

I m

Xuii (~co, co, co, - co)

The specific linear combinations of x (3)

components that define n2 and (3 are dependent on the geometry. In the same way that the linear refractive index exhibits dispersion as a fundamental absorption is approached, the nonlinear refractive index exhibits dispersion and changes sign as one transverses a two-photon absorption (Sheik-Bahne et al., 1990). The linear absorption coefficient and refractive index are related by a KramersKronig transformation, therefore a change in the absorption coefficient due to nonlinear effects can be correlated with a change in refractive index via the relationship (Olbright and Peyghanbarian, 1986) An(co) =

Aa(cof) n I co'2 - co2

da/

(12-46)

(12-42)

An n — .

B=

where a is the linear absorption coefficient and P is the two-photon absorption coefficient given by

= al-pi2

(12-44)

Photoinduced Nonlinearities

Several nonlinear optical effects are observed after a glass has been exposed to light for periods of time varying from minutes to hours. Photoinduced nonlinearities include refractive index gratings and second harmonic generation in fibers. In the first effect, when a laser beam is injected into an optical fiber, a standing wave pattern is set up by the transmitted beam and the counterpropagating beam reflected from the fiber end. This intensity grating leads to a permanent photoinduced modulation of the refractive index which acts as a Bragg grating for the incident light (Hill et al., 1978). Gratings can also be formed by side illumination using the interference pattern generated by two coherent, over-

12.2 Fundamental Optical Phenomena

lapping laser beams. These so-called Hill gratings are extremely wavelength specific and can be used as narrowband filters. Laser-induced refractive index gratings have also been produced in bulk glasses doped with trivalent rare-earth ions using four-wave mixing geometries (Behrens et al., 1990). Permanent gratings are attributed to a change in the local structure of the glass at the rare-earth site caused by vibrational energy released by the nonradiative relaxation of the rare earth following optical excitation. Glass is macroscopically isotropic, therefore it is not expected to exhibit second harmonic generation due to the second-order nonlinear susceptibility x(2)- Osterberg and Margulis (1986) found, however, that a fiber that had been irradiated for several hours with a very intense laser beam at 1.06 |im showed a strong second-harmonic signal which grew exponentially with the time of the irradiation. Moderately high conversion efficiencies are obtained because the second harmonic beam can be phase-matched to the input beam by a periodic variation of y}2) (Stolen and Tom, 1987). Both photoinduced refractive index gratings and second harmonic generation have only been reported for Ge-P or Ge doped silica fibers. Germanium-related defects are believed to play an important role in the processes, although the origins of the phenomena are not understood in detail (Vogel et al., 1991). 12.2.9 Luminescence and Stimulated Emission

Luminescence from glass can arise from the presence of various transition metal ions (principally iron group and lanthanide series elements having partially filled electron shells), filled shell and post-transition group elements, semiconductor clus-

637

ters, molecular complexes, organic dyes, and defect or color centers (Bamforth, 1977; Hiifner, 1978; Nassau, 1986). While many of the general features of the luminescence from a given species are similar whether the host is a glass or an insulating crystal, site-to-site variations in the local environments in glass result in a distribution of energy levels and radiative and nonradiative transition probabilities. This appears spectrally as inhomogeneous line broadening and in the time domain as nonsingle-exponential excited state relaxation (Weber, 1981). High frequency vibrations associated with the glass network former determine the probability of nonradiative decay of excited ions by multiphonon emission, hence the radiative quantum efficiency and number of fluorescing states are generally smaller for a borate or silicate glass than for a heavy metal fluoride glass (Layneetal, 1977). Stimulated emission (laser action) requires an inverted ion population. The essential features necessary to achieve this condition are illustrated in the energy level scheme in Fig. 12-5. The laser ion is excited by optically pumping the 1 -> 4 transition with a flashlamp or another laser. This is followed by rapid relaxation to a metastable level 3, thereby creating a population inversion AN = N3 — N2 with respect to level 2. The gain coefficient for the 3 -• 2 transition is given by a AN, where a is the stimulated emission cross-section. If the probability for stimulated emission is greater than that for excited-state absorption 3 -> 4 and if the resulting gain is greater than losses due to absorption and scattering at the lasing wavelength and losses in the optical resonator, laser oscillation will be obtained. The electronic states of the unfilled 4f" shell of the trivalent lanthanide ions provide many energy level schemes suit-

638

12 Optical Properties of Glasses

Excited state absorption

i

\

Pump transition

Laser transition

\

Figure 12-5. Schematic diagram of energy levels and transitions important for four-level laser action. Wavy lines denote nonradiative transitions.

able for laser action. Lasing has been obtained for all ions of the 4P1 series in either crystals or glasses, in many cases involving several different transitions (Weber, 1991). Lanthanide ions are readily incorporated into most glasses in concentrations of up to ~ 1 mol% needed for flashlamp-pumped lasers. Other ions with complementary ab-

sorption band may also be added to the glass as fluorescence sensitizers to increase the optical pumping efficiency. Host glass requirements include transparency at the pump and lasing wavelengths. The overall performance of glass lasers depends upon the efficiency and limitations of energy storage and energy extrac-

12.3 Optical Glasses

tion. The energy storage is affected by the spectral match of the laser ion absorption bands to the pump source, excited-state absorption of pump radiation, and the lifetime and efficiency of decay to the upper laser level. The rate of energy extraction is proportional to a 1/Pico and thus is limited by the effective stimulated emission cross section a and the beam intensity / that can be propagated in the glass without self focusing or optical damage. Because energy is extracted only from those ions resonant with the lasing wavelength, in large-signal or saturated gain operation a hole develops in the gain profile (spectral hole burning) which reduces the energy extraction efficiency (Hall et al, 1983). 12.2.10 Optical Damage The extremely large optical electric fields associated with the high peak powers and fluences of lasers can lead to damage of reflecting and transmitting optical components (Wood, 1990). Owing to the intensitydependent index of refraction, a light beam having a non-uniform spatial profile will self-focus as it traverses a glass. If uncontrolled, whole beam or small-scale self-focusing will lead to catastrophic damage in the form of bubbles or tracking along the light path. Self-focusing is minimized by using glasses with small nonlinear refractive index coefficients n2 and by controlling spatial nonuniformities in the beam profile. Interaction of intense light with structural or chemical imperfections in the surface leads to damage in the form of pitting of the glass. Because the ratio of the optical intensities at the exit and entrance faces of a glass of refractive index n is 4n2/(n +1) 2 (Crisp et al., 1972), the threshold for damage is lower at the exit face. Accumulation of surface damage may eventually render the optical component useless.

639

Laser-induced damage usually arises from extrinsic rather than intrinsic glass properties. Glasses melted in platinum, for example, have the potential problem of metallic platinum inclusions which, if present, are heated by the absorption of light. At high fluences, absorbing inclusions vaporize and cause internal cracking in the glass. Most of the platinum in glass is introduced in the early stages of the melt cycle, the primary source being the reduction of PtO 2 vapor to metallic Pt on the melt surface due to thermal gradients or other nonequilibrium conditions. By using strongly oxidizing conditions, small metallic Pt particles are oxidized and dissolved in the melt. Although the resulting ionic Pt introduces a near-ultraviolet absorption band in glass, this is usually more tolerable than damaging metallic Pt inclusions.

12.3 Optical Glasses Commercially available glasses for optical components and ophthalmic use are principally colorless oxide glasses. They provide a wide range of refraction, dispersion, specific gravity, and other optical, thermal, and mechanical properties. 12.3.1 Classification and Designation Optical glasses are characterized and designated by their refractive index and dispersion. The most common measure is the refractive index at the wavelength of the He d line (587.6 nm) or the Hg e line (546.1 nm). The difference in the refractive index at the hydrogen F (486.1 nm) and C (656.3 nm) lines, nF — nc, is called the average or principal dispersion. The ratio (nF — nc)/(nd — 1) is called the relative dispersion; the reciprocal of this quantity is the Abbe number vd. A six-digit number is used to specify optical glasses, where the

640

12 Optical Properties of Glasses

Table 12-1. Designation, type, and major compositional components of optical glasses. Designation

Glass type

Compositiona

FB FA FP (FK) FZ FK (FC) BK (BSC) PK (PC) PSK (DPC, PCD) K(C) ZK (ZC, ZnC) BaK (BaC, LBC) SK (DBC, BCD) SSK (EDBC, BCDD) LaK (LaC, LaCL) LaSK LgSK TiK TiF TiSF (FF) KzF (CHD, SbF) KzFS (ADF) KF (CF, CHD) LLF (BLF, FEL) LF (FL) F (DF, FD) SF (EDF, FDS) SFS BaLF (LBC, BCL) BaF (BF, FB) BaSF (DBF, FBD) LaF (LaFL) LaSF TaK TaF TaSF NbF NbSF

Fluoroberyllate Fluoroaluminate Fluorophosphate Fluorozirconate Fluorocrown Borosilicate crown Phosphate crown Dense phosphate crown Crown Zinc crown Barium crown Dense barium crown Extra dense barium crown Lanthanum crown Dense lanthanum crown Special long crown Titanium crown "J Titanium flint v Dense titanium flint J Short flint Dense short flint Crown flint Extra light flint Light flint Flint Dense flint Special dense flint Light barium flint ^ Barium flint > Dense barium flint J Lanthanum flint Dense lanthanum flint Tantalum crown "1 Tantalum flint / Dense tantalum flint J Niobium flint Dense niobium flint

BeF2-AF3-RF-MF2 AlF 3 -RF-MF 2 -(Y,La)F 3 P2O5-A1F3-RF-MF2 ZrF 4 -RF-MF 2 -(Al,La)F 3 SiO2-B2O3-K2O-KF SiO 2 (P 2 O 5 )-B 2 O 3 R 2 O BaO P 2 O 5 ~(B,A1) 2 O 3 -R 2 O MO SiO 2 -R 2 O-(Ca,Ba)O SiO 2 (B 2 O 3 )-ZnO SiO 2 (B 2 O 3 )-BaO-R 2 O SiO 2 -B 2 O 3 -BaO B 2 O 3 (SiO 2 )-La 2 O 3 -ZnO MO B 2 O 3 -A1 2 O 3 -MF 2 SiO 2 (B 2 O 3 )-TiO 2 -Al 2 O 3 -KF SiO 2 -B 2 O 3 -R 2 O-Sb 2 O 3 B 2 O 3 (Al 2 O 3 )-PbO-MO

SiO7-R9O-PbO-MO

SiO3-R?O-MO-TiO? SiO2-B2O3-BaO-PbO-R2O B 2 O 3 (SiO 2 )-La 2 O 3 -MO-PbO B 2 O 3 -La 2 O 3 -(Gd,Y) 2 O 3 -(Ta,Nb) 2 O 5 B2O3-La2O3-ZnO-Nb2O5 B 2 O 3 (SiO 2 )-La 2 O 3 -ZnO-(Ti,Zr)O 2

R and M denote one or more alkali or alkaline earth elements, respectively.

first three digits designate the refractive index nd with the preceding " 1 " omitted and the last three digits designate the Abbe number vd with the decimal point omitted. Thus a borosilicate glass BK 7 having an nd = 1.51680 and vd = 64.17 has a designation 517-642. This six-digit refraction in-

dex-Abbe number code is the most universally useful way of designating optical glasses. Glasses having nd > 1.60, vd > 50 or nd < 1.60, vd > 55 are called "crown" (K) glass; other glasses are called "flint" (F). These letters, plus others, are usually con-

12.3 Optical Glasses 2.0

I

1

1

1

1

1.9 - -

1

LaSF LaSK TaF NbF LaK

-

BaF

.1 1.6 - -

SK PSK

/ //

TaSF

1.8 -

641

^

1

LaF

7/SFS_

BaSFy/ /TiSF

A/

SSK KzFS

-

8aLF


'BaK

PK

FZ 1.5

-

/ XBK

FP

FK

#

_ [TiKl

SiO2 FA

1.4 - -

-

FB 1.3 ; B e F 2

(

100

1 80

1

60

40

20

Abbe number vH

Figure 12-6. Location of the optical glasses in Table 12-1 in a refractive index-Abbe number diagram.

tained in the manufacturer's designation of optical glasses. Representative manufacturer's designations, descriptive names, and principal compositional components of commercial optical glasses are given in Table 12-1 (Fig. 12-6) (Gliemeroth, 1983; Izumitani, 1986; Marker and Scheller, 1988). (Designations vary with the country of origin and some alternate designations are given in parentheses.) "Light" or "dense" indicate the relative amounts of heavy metal oxides such as PbO or La 2 O 3 . Glasses with prefixes U or IR denote extended ultraviolet or infrared transmitting glasses. Other designators are used for glasses for special applications such as LG-laser glass, FR-Faraday rotator glass, and AO-acousto-optic glass. Only a few non-oxide optical glasses such as heavy metal fluorides and chalcogenides are available commercially. These

are specified by the manufacturer's name or by the composition if it is simple. 12.3.2 Transmission

Glasses exist that are optically transparent in the vacuum ultraviolet and in the mid-infrared. Figures 12-7 and 12-8 illustrate the variation of the ultraviolet and infrared absorption edges of representative optical glasses. The optical transmission in these figures depends on the wavelength dependence of the absorption, reflection, and scattering of the glass. The transmission of optical glasses is frequently given in terms of the internal transmission Tt after correction for reflective losses, that is, 7] - T/R, where R is the reflection factor given by Eq. (12-15). The deviation of Tt from 100% is a measure of absorption due to impurities and scattering due to defects.

642

12 Optical Properties of Glasses

100 Fused silica^-

80

'

/^Pluoropho sohate (LG-810JL.—"*^

-

-—

60

; 40

/

( /

•

/

-

1

20 -

/Borosilicsrte (BK7)

/

/

/

150

'

200

1

i

1

250 300 Wavelength (nm)

f

/

/Lead / silicate / (SF6) 350

400

Figure 12-7. Ultraviolet absorption edge of representative optical glasses. Sample thickness: 5 mm except for SiO2 and LG 810 which are 2 mm [from Cook and Mader (1982); Schott (1982)].

The internal transmittance is usually reported at a number of standard wavelengths from the ultraviolet to the infrared. Transmittances of near unity for millimeter thick samples attests to the high quality of most optical glasses. The transmission (I/Io) and the absorption coefficient a for a sample of length / are related by ln(/ 0 /J) a=- I

2.303 OD

I

(12-47)

where OD = log 10 (/ 0 //) is the absorbance or optical density. The absorption cross section a is derived from a = oN, where N

2

4

6

is the number of absorbing centers to unit volume. 12.3.3 Refractive Index and Dispersion

Optical glasses cover a general range of refractive indices nd = 1.4 to 2.0 and reciprocal dispersions vd = 20 to 90. These are almost exclusively oxide glasses. The location of the glasses in Table 12-1 on an nd — vd map is shown in Fig. 12-6, where the lines divide the main compositional types. Optical glass companies supply such a figure with dots scattered throughout this parameter space representing avail-

8 10 12 Wavelength (jam)

Figure 12-8. Infrared absorption edge of representative optical glasses. Sample thickness: 2 mm [from Dumbaugh (1985)].

643

12.3 Optical Glasses

able glasses. The range of nd — vd in Fig. 12-6 is larger than that given in the ordinary glass catalog so as to include low-index, low-dispersion fluoride glasses. Amorphous SiO2 and BeF2 are added in Fig. 12-6 to indicate the extrema for oxide and fluoride glasses. Higher index chalcogenide glasses cannot be located in an nd — vd plot because the absorption edge extends into the visible and it is not always possible to measure vd. Therefore, for infrared materials, plots are made using a reciprocal dispersion based on measurements of refractive index at longer wavelengths. For example, for the atmospheric window at 8-13 jim, a relative dispersion v l o = (n lo — l)/(ns 0 — n12) is used, where the wavelengths are in microns (Feltz et al, 1991). Similarly, for more ultraviolet-transmitting glasses, relative dispersions such as v313 = (n 3 1 3-l)/(n 2 6 5 -n 4 0 5 ) have been used, where here the wavelengths are in nanometers (Gerth et al., 1991). Data sheets usually report the refractive index (the mean value for a number of melts) at a number of specific wavelengths. Wavelengths of a number of commonly used spectral lines are given in Table 12-2. Refractive indices may also be given for common laser wavelengths, e.g., the He-Ne gas laser at 632.8 nm and the N d : YAG laser at 1064 nm. Hg lines at 1530, 1970, and 2325 nm are frequently used to report values in the infrared. The wavelength dependence of the refractive index of a number of representative optical glasses is shown in Fig. 12-9 to illustrate the range of values and dispersions obtainable. These depend upon the relative positions of the intrinsic absorption bands in the ultraviolet and infrared. Figure 12-9 represents only a small portion of the overall dispersion indicated in Fig. 12-2. In general, the smaller the fundamen-

Table 12-2. Wavelengths of spectral lines used for refractive index measurements. Wavelength (nm)

Spectral line

Element

365.0 404.7 435.8 480.0 486.1 546.1 587.6 589.3 643.8 656.3 706.6 768.2 852.1 1014.0

i n g F F e d D C C r A' s t

Hg Hg Hg Cd H Hg He Na Cd H He K Cs Hg

tal band gap, the greater the refractive index and dispersion at a given wavelength. For interpolating values of the refractive index at the other wavelengths, glass manufacturers use an approximate dispersion formula derived from a power series expansion of Eq. (12-10) of the form n2 = Ao r i ^ 2

•A3X~4

(12-48) where the constants At are determined from a least squared fit of the measured values. Using this equation, refractive indices in the wavelength range 365-1014 nm can be calculated to an accuracy of ± 5 x 10" 6 or better. Various relative partial dispersions _nx-ny

(12-49)

are defined for other wavelengths x and y. A century ago Abbe found an empirical rule that the relative partial dispersion of most glasses obeyed a linear relationship on vd of the form L

x,y

(12-50)

12 Optical Properties of Glasses

400

600

800 Wavelength (nm)

1000

Figure 12-9. Dispersion of the refractive index of representative optical glasses [from Schott (1982)].

where a and b are constants. As discussed later in Section 12.4.1, it is not possible to correct for second-order chromatic aberrations using so-called "normal" glasses that satisfy Eq. (12-50). Optical glass catalogs therefore list deviations of the relative partial dispersions from the normal for glasses covering a wide range of vd values. 12.3.4 Thermal Properties

The temperature range in which a glass transforms from its solid state into a "plastic" state is called the transformation region. A (glass) transformation temperature Tg is used to define this region and is determined from a standard thermal expansion measurement. The viscosity of the melt at Tg is approximately 10 13 poise. The softening temperature is that temperature at which in a standard test the glass deforms under its own weight and corresponds to a melt viscosity of 10 7 6 poise. A low Tg is important for molded optical elements.

Thermal expansion varies the dimensions of glass and affects refractive optics subject to either uniform or gradient temperature variations. The coefficient of thermal expansion, a, of glass ranges from near zero for special low expansion glasses such as titania-doped SiO2 and tailored glass ceramics to values greater than 20 x 10~ 6 / K. For optical glasses a ranges from about 4 to 16 x 10" 6 /K. The thermal expansion coefficient increases with increasing temperature, exhibiting a nonlinear increase up to about room temperature, followed by an approximately linear range until the glass begins to exhibit plastic behavior, and then a rapid increase with increasing structural mobility in the glass. Therefore mean thermal expansion coefficients are given for a specific temperature range. Some representative values around room temperature are listed in Table 12-3. The thermal coefficient of refractive index depends on the wavelength, temperature, and pressure. Examples of the varia-

12.3 Optical Glasses

645

Table 12-3. Thermal properties of optical glasses. Glass type

x(W/mK)

Fused silica (SiO2) Fluorophosphate (FK 54-487 865) Fluorosilicate (FK 5-487 704) Fluorozirconate (ZBLAN) Borosilicate (BK 7-517 642) Barium silicate (SK 14-603606) Alkali lead silicate (F 2-620 364) Barium alkali silicate (BaFNlO-670471) Lanthanum borate (LaFN2-744448) Lanthanum silicoborate (LaK 9-691547) Lead silicate (SF 2-648 339) Lead silicate (SF 6-805 254) Lead silicate (SF 59-953 204) Arsenic trisulfide (As2S2) a

0.55 16.9 10.0 17.2 8.3 7.0 9.3 7.9 9.1 7.6 9.2 9.0 10.3 2.6

1.38 1.06 0.92 -0.6 1.11 0.85 0.78 0.80 0.67 0.91 0.73 0.67 0.51 0.17

c p (J/gK)

T<°C)

0.75 0.71 0.81 0.62 0.85 0.64 0.56 0.59 0.48 0.65 0.50 0.39 0.31 -

1175 403 464 265 559 649 432 630 616 650 441 423 362 163

Temperature range: 20-300°C.

tions with wavelength and temperature for representative optical glasses are shown in Figs. 12-10 and 12-11. Both positive and negative values of dn/dT are included. In the pressure range 0-10 5 Pa, the thermal

coefficient of refraction for a borosilicate glass (BK 7) glass changes by «1.3 x 10~ 6 / K at 546 nm and temperatures of 20-40 °C. Because of its disordered atomic structure, the thermal conductivity of glass is

20

-

10 ^

-

—

_ .

"

SF6

—

— —

—

PK3

-10

I

400

i

I

600

800 Wavelength (nm)

1000

1200

Figure 12-10. Absolute thermal coefficient of refractive index for representative optical glasses as a function of wavelength [from Schott (1982)].

646

12 Optical Properties of Glasses

20

I

I

I

^ ^

I

^

^

10

LaK10

I

—

—

-

—

—

—

" BK7

• — '

—_

_

•o

—

- — • — "

" ,

—

-

—

-

___ -10

I -40

—r—" 0 Temperature (°C)

I 40

PK51 I 80

Figure 12-11. Absolute thermal coefficient of refractive index for representative optical glasses as a function of temperature [from Schott (1982)].

much lower than that for crystalline materials. This limits its use as an optical material for high average power applications where linear or nonlinear absorption is present to cause heating. The thermal conductivity of optical glasses ranges from about 0.5 to 1.5 W/m • K, being high for silica and low for glasses containing large quantities of heavy elements such as lead, tantalum, barium and lanthanum. The thermal conductivity of glass increases with temperature but only slightly above 300 K. Representative values of the thermal conductivity, %, and specific heat at constant pressure and room temperature of optical glasses are included in Table 12-3.

12.3.5 Mechanical Properties The mechanical response of a glass to an applied force is described by various moduli. Optical glass catalogs usually list moduli such as Young's modulus E (extension in tension) and the modulus of rigidity or shear G which are important for thermal and mechanical stress determinations. These are related to Poisson's ratio pt (ratio of lateral to longitudinal strain under unilateral stress) by (12-51)

"-SO"1

The bulk modulus B (1/isothermal compressibility) is related to the above moduli by -H)

(12-52)

647

12.3 Optical Glasses

Values of E and jn for glasses at room temperature are included in Table 12-4. Elastic moduli can also be expressed in terms of the longitudinal and transverse sound velocities and the density. Ultrasonic pulse-echo, Brillouin scattering, and other methods are used to measure sound velocities to determine elastic and photoelastic constants. The hardness of a glass is an indication of its vulnerability to surface damage and the ease with which the glass can be polished. It is usually measured from the indentation of Knoop or Vickers penetrators. Values (Knoop) for oxide glasses range from ~ 250 for high-lead-content glasses to > 600 for lanthanum crown glasses. Representative values for a variety of glass types are summarized in Table 12-4. The Knoop hardness generally correlates with Young's modulus. The stress-optical coefficient K varies with glass type and wavelength. It is usually positive, although it can become negative (so called Pockets glasses) for silicate glasses having a high lead content. The stress-optical coefficient is measured in

units of 1 Brewster = (TPa)" 1 = 10~ 12 m 2 / N. Values of K are included in Table 12-4 and generally range from —2
An important consideration for many optical glasses is their chemical reactivity with slurries during cutting and polishing of components such as lenses, windows, and prisms and with its environment where it may be subject to chemical attack by water, water vapor, gases, acids, etc. In the presence of water, there is dissolution of glass and a coating develops as hydrogen from the solution exchanges with alkali ions in the glass. This and other forms of corrosion, dimming, and straining occur and vary greatly depending on the chemical composition of the glass. Whereas SiO2, A12O3, TiO 2 and La 2 O 3 resist leaching by aqueous or acid solutions, alkali

Table 12-4. Mechanical properties and stress-optical coefficients at 589 nm for representative optical glasses. Glass type (designation)

Fused silica (SiO2) Fluorophosphate (FK 54-487 865) Fluorosilicate (FK 5-487 704) Fluorozirconate (ZBLAN) Borosilicate (BK 7-517642) Barium silicate (SK 14-603606) Alkali lead silicate (F 2-620 364) Lanthanum borate (LaFN2-744448) Lead silicate (SF 2-648 339) Lead silicate (SF 6-805 254) Lead silicate (SF 59-953 204) Arsenic trisulfide (As2S3)

Knoop hardness (N/mm2) 450 320 450 250 520 490 370 450 350 310 250 180

Stress-optical coefficient (TPa)" 1 3.5 0.01 2.91 2.74 2.00 2.81 1.65 2.65 0.63 -1.46 -1.1

Young's modulus (103 N/mm2) 70 76 62 54 81 86 58 87 55 56 51 16

Poisson's ratio

0.170 0.286 0.205 0.31 0.208 0.261 0.225 0.294 0.231 0.248 0.269 0.240

648

12 Optical Properties of Glasses

and alkaline earth oxides do not. Also, B 2 O 3 and P 2 O 5 are more soluble glass network formers than SiO2. No simple test and parameter is sufficient to characterize chemical reactivity under all conditions. Thus many terms and tests are used to rank glasses with respect to their resistance to acids, straining, climate, weathering, etc. Glasses may be described by several grades ranging from those exhibiting no surface deterioration in normal humidity conditions to those exhibiting increased surface scattering within a few hours and for which protective coatings are recommended after polishing and before storage. Ion-exchange reactions create a surface layer of lower refractive index. This appears as colors when the product of n and the optical thickness becomes a multiple of 1/4 and interference occurs between the incident and reflected light. Staining is a surface change resulting from contact with acidic conditions or small quantities of slightly acidic water (e.g., perspiration). It appears as a coloration for standard acetate (pH = 4.6). Glasses range in their resistance to staining from those showing virtually no interference coloring after many days exposure to those that change color in minutes in sodium acetate buffer (pH = 5.6). The latter glasses require special care in processing. Acidic or alkali aqueous solutions also cause decomposition of glass surfaces. The time lapse before a layer of 0.1 jam is dissolved is used as a measure of acid resistance. For optical glasses in 0.5 N nitric acid this time can range from more than 100 h to only a few minutes. In sodium hydroxide, pH 10 at 90 °C, some glasses show no visible effects in hours whereas other glasses show color or whitish strains and develop coatings in a few minutes. Manufacturers typically list several cate-

gories of acid and alkali resistance to cover the above ranges. 12.3.7 Quality and Forms

By careful batching, processing, and annealing, optical glasses can be made with very reproducible properties. The refractive index is controlled by the rate of annealing in the transformation range. Tolerances for nd of ±0.001-0.002 and for vd of ±0.8% are standard. Closer tolerances for nd and vd of ±0.0002 and ±0.2% can usually be obtained by precision annealing. The homogeneity of the refractive index is important for imaging systems and is documented interferometrically. From selected melts or selected blanks, homogeneities of ± 1 0 " 5 - 1 0 ~ 6 are possible. At 633 nm, the wavefront distortion after transmission through 100 mm of a glass of index homogeneity 10" 6 is only 0.3 wave. Residual stress birefringence varies with glass size and type. For some glasses values of < 20 nm/cm are achievable for large ( ^ l m ) diameter blanks. For smaller pieces (~ 100 mm), values of ^ 4 nm/cm are possible by special annealing. Striae (cords) are localized regions of glass that differ slightly in chemical composition from that of the base glass. If present, they can be observed by examining the glass in one or more directions, depending upon the intended use, in a shadowgraph or Foucault knife-edge test. Other macroscopic defects such as bubbles or inclusions may also be present. The total content of inclusions above a specific dimension, e.g., those measuring ^ 0.05 mm, is specified by giving their measured cross section area in mm 2 per 100 cm3 of glass. Most glasses can be produced virtually striae and inclusion (bubble) free. Optical glass is available in many forms including (1) slabs and blocks with two or

12.4 Special Glasses

more machined and polished faces used for test purposes, (2) strips, rods and rolled glass with unfinished surfaces, (3) semi-finished and pressings of some required form, and (4) simple gobs. Several hundred optical glass types are available commercially. These are multicomponents glasses whose chemical compositions have been tailored to achieve the range of refractive indices and other physical properties discussed above. All glass types cannot be produced in the same sizes or with the same quality, however. Manufacturers may indicate "preferred" glass types which can be melted more easily and obtained in the size and quality required.

12.4 Special Glasses 12.4.1 Abnormal Dispersion Glass The partial dispersions of optical glass are important in the design of compound lenses. By combining a positive lens of a crown glass with a negative lens of a flint glass, chromatic aberration can be avoided at two wavelengths. For such an achromatic lens composed of different glasses of local lengths f1 and f2 to have the same focal length at the wavelengths of the C and F lines, the condition Vid/id + v 2 d / 2 d = 0

(12-53)

must be satisfied. There will, however, be a residual error in the intermediate wavelength range. The difference in the focal length of the compound lens at wavelengths x and y is given by the relationship (Rawson, 1980) , < < ( 12 " 54 ) L

fy

l-V2d)

Because of the linear relationship between the relative partial dispersions and Abbe

649

number in Eq. (12-50), the difference in partial dispersion will always be the same for normal glasses. Correction for second-order chromatic aberration (secondary spectrum) is accomplished using glasses with equal partial dispersions for different Abbe values. The corrected systems are called apochromats. Socalled abnormal dispersion glasses depart from the "normal line" and the linear relationship in Eq. (12-50). Figure 12-12 plots the relative dispersion (ng — nF)/(nF — nc) of optical glasses and shows the magnitude of the deviations from the normal line that are possible. The deviations can be either positive or negative. A glass with the same nd and nx as a flint glass, but for which the increase in refractive index from the blue to the ultraviolet is steeper, is called a "short" flint. Abnormal dispersion glasses are produced by tailoring the chemical composition of the glass so as to alter the relative strength and positions of the ultraviolet and infrared absorption bands of the constituents and thereby change the dispersion. 12.4.2 Gradient Index Glass A conventional glass lens consists of a homogeneous material with a single index of refraction. Imaging occurs by means of discrete refraction at the lens surfaces. In the design of a compound lens, the curvature, thickness, and refractive index of each element are varied to control aberrations and curvature of the imaging field. Glass elements, however, can also be manufactured in which the index of refraction varies continuously within the material. These are called gradient index or GRIN materials. The refractive index gradient may be axial (varying along the optical axis), radial (varying outwardly from the optical axis), or spherical (varying symmetrically from a

650

12 Optical Properties of Glasses 0.65

•

0.60

• • •

0.55

•

0.50

100

• •

80

60

v

40

20

d

Figure 12-12. Absolute thermal coefficient of refractive index for representative optical glasses as a function of temperature [from Schott (1982)].

point) (Moore, 1980). For imaging systems, gradient index glass provides an alternative to the generation of complex aspheric lens surfaces to control aberrations. Gradient-index rods and fibers are used in microoptics, imaging optics, and optical fiber communication systems (Iga et al., 1984). In a rod or fiber having a radial index gradient, light propagates in a sinusoidal fashion because rays passing through the center travel more slowly than those further away from the optical axis. Several techniques have been developed to create refractive index variations in glass. These include neutron irradiation of boron-rich glasses such as borosilicates, chemical vapor deposition of layers of glass of slightly different refractive indices, and ion exchange by immersing the glass in an appropriate solution. These methods differ in the size of components that can be treated and the magnitude and gradient of the index that can be produced. Changes in refractive indices of An < 0.04 are achievable by the above techniques (Moore, 1980). Ion stuffing in porous glass and sol gel

techniques can also be used to create gradient index glass. Production of large pieces of glass having index variations of An ~ 0.5 has been demonstrated (Blankenbecker et al., 1991). The process is based on controlled fusion of glass layers of different physical properties. Diffusion within and between layers creates a gradual change of properties. The smoothness of the gradient profile is a function of the concentration gradient and the diffusion rate of the major index determining components. In practice, powders of different glasses are mixed in varying proportions and layered in a mold or homogenous plates of different glasses are fabricated and stacked together; the composite material is then fused together in a furnace to produce the gradient index material. 12.4.3 Mirror Substrate Glass The selection of glass for mirror substrates involves many factors. For front surface mirrors where retention of the opti-

651

12.4 Special Glasses

cal figure is important, the thermal stability of the environment is a major consideration. In a temperature-controlled environment, low-cost borosilicate glasses can be used. If, however, the substrate is subject to temperature variations, materials with the lowest possible coefficient of thermal expansion are needed. Silica containing small quantities of titanium dioxide or other heavy metal oxides and transparent glass ceramics can be produced which have extremely small, near-zero coefficients of thermal expansion. The latter materials (such as lithium-aluminum silicates) are solid solutions in which the very small or even negative thermal expansion coefficient of the crystalline phase compensates for the positive expansion coefficient of the remaining glass matrix. Glass ceramic mirror blanks with diameters of more than eight meters have been produced for telescope mirrors, (see also Vol. 11, Chap. 5). Because optical coatings are not 100% reflective, some light is always transmitted to the substrate. Thus UV-transmitting silica is used for mirrors intended for highpower ultraviolet applications. Homogeneity of the glass is a consideration for substrates for partially reflecting elements. Variations in the chemical composition of the glass and the presence of striae produce spatial variations in the thermal expansion that can result in optical distortions. Bub-

bles, if at the surface, cause coating problems. For airborne or space applications, weight of the substrate is a factor. In all cases, fabrication - the ease of grinding and polishing the mirror - is an additional consideration. Properties of several low-expansion glasses used for mirror substrates are listed in Table 12-5. Barnes (1979) gives more detailed descriptions of the properties of substrate glasses and compares them with other insulating materials and metals. 12.4.4 Optical Filter Glass Transmitting filter glasses change the spectral properties of optical radiation and provide selective filtering for scientific and technological applications, for color enhancement in ophthalmic lenses, and for contrast enhancement in displays. Filters are categorized as band passing and band blocking filters, short-wavelength and longwavelength cutoff filters, and neutral density and color conversion filters. The transmission characteristics are determined by a combination of the base glass and ion doping or colloidal coloration (Cook and Stokowski, 1986). As can be seen from Figs. 12-7 and 12-8, the UV and IR cutoff wavelengths vary greatly depending on the glass composition; thus the composition can be tailored

Table 12-5. Common mirror substrate glasses. Material (supplier)

Fused silica (various) ULE (Corning) Zerodur (Schott) Pyrex (Corning) BK 7 (various)

Hardness (Knoop)

(g/cm3)

Thermal expansion coefficient (KTVKT 1 )

Stress-optical coefficient (TPa" 1 )

2.20 2.21 2.53 2.23 2.51

0.55 0.03 0.10 3.2 8.3

450 460 630 418 520

3.5 4.0 3.0 3.9 2.7

Density

652

12 Optical Properties of Glasses

to achieve selected transmission characteristics. Other cutoff and bandpass filters are produced by doping with transition metals (Ti3 + ' 4 + , V3 + , Cr 3 + , Mn 3 + , Fe 2 + ' 3 + , Co 2 + , Ni 2 + , Cu 2 + ), rare-earths (Ce3 + ' 4 + , Pr 3 + ,Nd 3 + ,Sm 3 + ,Eu 2 + ,Ho 3 + ), and uranium (U6 + , [UO 2 ] 2+ ). The 3 d - 3 d transitions of iron group ions generally produce broad absorption bands. The 4f-5d transitions of the rare-earths are also broad, whereas the 4f-4f transitions are narrower and provide more selective filtering (Bamforth, 1977). The fundamental absorption edge of semiconductor-doped glasses depends on the size and absorption characteristics of the colloidal particles. By careful heat treatment and processing of Cd(S, Se) and CdTe doped silicate and borosilicate glasses, a series of long pass filters can be manufactured with sharp cutoff wavelengths varying over a wide spectral range in the visible and near infrared. The wavelength Xc of the absorption edge of these colloidally-colored filters increases with temperature; values of d/l c /dT<0.4nm/K are typical. Glass can also be colored by the incorporation of metallic particles, such as the ~ 5 nm gold spheres in ruby glass. Metaldoped glasses are much more limited in their use as optical filters. Optical filter glass, like other optical glasses, is manufactured in high optical quality, free of striae and inclusions, and in a variety of forms. Transmission is carefully controlled. Filter glass catalogs present extensive data on transmittance; data on refractive index and other thermal and mechanical properties and chemical durability are also listed. To define the color, the chromaticity coordinates x and y of the color focus, the dominant wavelength 2 d , the color saturation Pe, and the photooptic transmission Y are specified for three light

types: a Planck black body at 2856 K (light from an incandescent bulb), a Planck black body at 3200 K (halogen lamp light), and standard daylight (D 65). These conform to the Commission Internationale d'Eclairage (CIE) standard colorimetric system (Fanderlik, 1983). Under prolonged exposure to high-intensity ultraviolet radiation, some filter glass may solarize and exhibit reduced transmission, particularly at shorter wavelengths. Some ionically or colloidally colored glasses also exhibit photoluminescence (Turner, 1973). 12.4.5 Nonlinear Glass

Optical nonlinearities in glass arising from the Kerr effect are of interest in two extremes: in high power lasers where glass with a small nonlinear refractive index n2 is desired to reduce self-focusing and optical damage, and in all optical switching devices where glass with a large n2 is desired to minimize the optical power requirements. The magnitude of the optical Kerr effect is known for a wide range of undoped and doped glasses (Borrelli and, Hall, 1991; Vogel et al., 1991) and, given a glass composition, reasonable estimates of the nonresonant n2 can be made. Although there is a wavelength dispersion of n2, most measurements have been made in the longwavelength limit where hcop Eg. Nonlinear Refractive Index

Glasses with small values of linear refractive index and dispersion generally have small n2 values (Adair et al., 1987). Accurate first-principles calculations of nonlinear indices of glasses are not possible; however, estimates of the nonresonant n2 can be obtained from the linear index

12.4 Special Glasses I

'

i

'

-

1

1

1.8 -

\

V

\

X X

y

1.4 —

x

\

N

X^^+

\

20 "

/ /

C ^

sio2

/

\ 10

N X

^

/

\ \\

\ \

-

/

X

Fluoride glasses -

1.6 -

i

\ X \\

Oxide glasses^

-

1

653

\ \

N

5

N

—

3

^

/ ^

n 2 (i
^ 1

-

BeF2 1 0

i 100

I 80

1

60 Abbe number ud

I 40

20

Figure 12-13. Oxide and fluoride glasses on an nd — vd diagram with lines of constant nonlinear refractive index coefficient n2 predicted from Eq. (12-55).

and dispersion via the expression (Boling et al, 1978) (12-55)

n1 =-

K(nd-l)(nj

+ 2]

where K is an empirical constant obtained from a fit to experimental data (Weber etal., 1978 a; Adair et al, 1987). Lines of constant n2 predicted from Eq. (12-55) are plotted as a function of nd and vd in Fig. 12-13 and are superimposed on regions of known oxide and fluoride glasses. For these glasses n2 can be estimated from Eq. (12-55) with an accuracy of ~ 10-20%. The equation is not generally applicable to chalcogenide glasses. The smallest linear and nonlinear refractive indices for glass occur for simple BeF2 (Weber et al, 1978 b). The addition of alkali, alkaline earth, and aluminum fluorides produces durable fluoroberyllate glasses with only a small increase in n2 and with excel-

lent ultraviolet transmission (Dumbaugh and Morgan, 1980). Comparing Figs. 12-6 and 12-13, fluorozirconate glasses have significantly larger n2 values than fluoroberyllate glasses and overlap the lower index region of oxide glasses. The refractive indices of halide glasses increase when the network former anion is changed in the series F < Cl < Br < I. Simple SiO 2 has the smallest linear and nonlinear refractive indices of the oxide glasses. These values increase as modifier ions are added. For laser applications where lower n2 values are needed, oxygen can be replaced in part by fluorine to reduce n2 (e.g., in fluorophosphate glass). For all-optical switching devices, materials are sought having a large n2 and a small absorption loss coefficient at the operating wavelength. Hall et al. (1989) has established an upper limit of n2 ~ 10~ 1 8 m 2 /W for oxide glasses containing

654

12 Optical Properties of Glasses

heavy metal ions (Pb, Bi). Although high purity silica has a much lower n2 value, it has the best overall figure of merit for this application due to its extremely low absorption (Vogel, 1989). Doped Glass Very large resonant optical nonlinearities are observed in doped glasses. Jain and Lind (1983) showed that enhanced resonant third-order optical nonlinearities could be obtained in semiconductor-doped glasses (colloidally-colored filter glass), where n 2 - 1 0 ~ 1 4 m 2 / W , x ( 3 ) - 1 0 - 8 - 1 0 - 9 esu, and response times were <10~ 1 1 s. The nonlinear behavior appears as intensity-dependent changes in absorption and refractive index originating from the generation of a short-lived free electron plasma and band filling effects. The size of the semiconductor microcrystals in the glass affects the linear and nonlinear optical properties due to quantum confinement effects (Borrelli et al., 1987; Potter and Simmons, 1988). Very strong dispersion and a change in sign of n2 are observed in the vicinity of the band gap of these materials (Olbright and Peyghambarian, 1986). Semiconductor doped glasses have included I-VII [CuCl, CuBr, Ag(Cl,Br,I)] compounds, II-VI [CdS, CdSe, C d S ^ S e ^ , CdTe] compounds, and III-V compounds (Vogel etal., 1991). Organic dye molecules have intense singlet-singlet transitions and have been added to low-melting-point glasses such as boric-acid glass (Kramer et al., 1986) and lead-tin fluorophosphate glass (Tompkin etal., 1987) without decomposition. Saturation of the ground state absorption of the dye produces optical nonlinearities with very large effective x(3) ~ 1 esu. Because the response time is governed by the relaxation time of the triplet state of the dye, recovery

of the saturated nonlinearity is very slow compared to that of nonresonant electronic nonlinearities. Glasses containing very small metallic particles also exhibit an efficient, fast optical Kerr effect with x(3) ~ 10" 8 esu. A large enhancement of the intrinsic x(3) of the metal arises from a surface-mediated plasmon resonance effect analogous to surfaceenhanced Raman scattering (Hache et al., 1986). 12.4.6 Laser Glass A large number of different lasing ions and host glasses have been used for glass lasers (Patek, 1970). Table 12-6 summarizes the dopant ions, representative of lasing wavelengths (the exact wavelength varies with host), and host glasses that have been reported (Hall and Weber, 1991). Fluorescence sensitizing ions are sometimes added to the glass to improve the optical pumping efficiency. The forms used for laser glasses include bulk, fibers, and planar waveguides. Thus far all glass lasers have used trivalent lanthanides as the active ion. Figure 12-14 shows the 4 f electronic energy levels and transitions for which stimulated emission has been observed. The spectral range of glass lasers extends from ~ 0.5 to 3.0 }im; this is smaller than the ~ 0.2-5.0 |im range of crystalline lasers (Weber, 1991). The spectral range of glass lasers can undoubtedly be expanded by the use of appropriate ions and transitions in wide-band-gap fluoride glasses or fused silica as hosts for the ultraviolet and in heavy metal halide or chalcogenide glasses as hosts for the infrared. Because the optical spectra of ions in glass are inhomogenously broadening, glass lasers provide some tunability (<10%) that is not possible in crystalline hosts.

12.4 Special Glasses

655

Table 12-6. Rare-earth glass lasers and representative lasing wavelengths (from Hall and Weber, 1991). Wavelength (um)

Host glassa

Cu+b Pr 3 + Nd 3 +

0.56-0.58, 0.63 0.61, 0.64, 0.70, 0.72, 0.91, 0.89, 1.08, 1.31 0.93, 1.06, 1.34

Pm 3 + Sm3 + Tb 3 + Ho 3 + Er 3 +

0.93, 1.10 0.65 0.54 0.55, 0.75, 1.38, 2.05, 2.9 0.85, 0.99, 1.55, 1.66, 1.72, 2.75

Aluminoborosilicate (b), fluorohafnate (b) Silica (i), fluorozirconate (f) Silica (b, f), silicate (b, f, w), borosilicate (w), phosphate (b, f, w), germanate (b), tellurite (b), fluoroberyllate (b), fluorophosphate (b), fluorozirconate (f) Phosphate (b) Silica (f) Borate (b) Silica (f), silicate (b), fluorozirconate (f) Silica (f, w), silicate (b), phosphate (b, f), fluorophosphate (b), fluoroaluminate (b), fluorozirconate (b, f) Silica (f), silicate (b), fluorozirconate (b, f) Silica (f), silicate (b), borate (b) Silica (b)

Ion

Tm3 + Yb 3 + Organic dyes b a b

0.46, 0.48, 0.82, 1.48, 1.51, 1.88, 2.25 1.03 -0.53-0.65

Form of the laser glass: b - bulk, f - fiber, w - planar waveguide. Optical gain rather than laser oscillation was observed.

The spectroscopic properties important for laser action vary with the chemical composition of the host (Jacobs and Weber, 1976). These include absorption and stimulated emission cross sections, homogeneous (natural) and inhomogeneous linewidths, and radiative and nonradiative transition probabilities. An extensive database exists of spectroscopic properties associated with the 4 F 3/2 -> 4 Iii/2 transition of Nd 3 + (Weber, 1990). The stimulated emission cross section, for example, can vary by one order of magnitude depending upon the host glass. This arises from combined changes in the oscillator strength of the transition, the linewidth, and the refractive index of the host. From systematic compositional studies, rules can be derived for tailoring laser parameters. The variations in spectroscopic properties observed for Nd 3 + usually also apply to other trivalent rare-earth ions. In contrast to the large number of experimental laser glasses listed in Table 12-6,

commercial laser glasses are almost exclusively silicates and phosphates. Fluorophosphate glasses have also been developed for applications requiring low n2 values (Neuroth, 1987). Phosphate glasses generally have narrower linewidths and for ultraphosphates have less fluorescence concentration quenching than for silicate glasses, thus they are more appropriate for applications requiring high gain and efficient energy extraction (Marion and Weber, 1991). Laser glass shares with optical glass the requirements of refractive index homogeneity (variations <10~ 6 ), high purity (absorption coefficient at the lasing wavelength of <10" 3 cm~ 1 ), freedom from bubbles and striae, low birefringence (< 5 nm/cm), good chemical durability, and capacity of being finished to high optical tolerances (A/20). High-quality phosphate laser glasses satisfying these requirements have been produced with dimensions greater than 0.5 m.

1.51

30

25

f

0.48

0.46 |

0.85 I

1.72 I

ess

2

• H,

1.66 II

O 0.75

u o

W

1.38 11

_ ~ 20

X 15 1

o u

\f

CD

2.25

f

Pm 3 +

Sm3+

f

Ho 3 +

1.88

5

^H6

\

Tb 3 *

4

f

| _

}f

1.55

0.99

F

2.05 ••H. Nd 3 +

1.48

f

t

Pr 3+

f

f

0.82

2.9

V r^

2.75

10

Er 3+

Tm 3 *

Figure 12-14. Energy levels and transitions of trivalent rare earth glass lasers. Typical transition wavelengths are given in microns.

Yb 3

12.4 Special Glasses

Thermooptic properties control the beam quality of flashlamp-pumped, highaverage-power lasers. A thermal phosphate glasses have been developed in which the change of optical pathlength with temperature dS/dT^O (Izumitani, 1986). Fracture of the laser glass from thermally induced stress is a primary limitation on performance (Marion, 1986). A thermomechanical figure of merit for the fracture resistance of a large plate of isotopic material that absorbs light and is convectively cooled on its major faces is RT = Kcx(l~fi)/(xE

(12-56)

where Kc is the fracture toughness (MPa/ m 1/2 ). The fracture toughness is a measure of the inherent resistance of the glass to crack propagation and is determined either by direct crack measurements or from the indentation produced by a microhardness tester, but the accuracy is usually not very high. As evident from Eq. (12-56), the intrinsic resistance of a laser glass to fracture can be increased by increasing the thermal conductivity, decreasing Poisson's ratio, and reducing the thermal expansion coefficient and Young's modulus. 12.4.7 Faraday Rotator Glass

The rotation of the plane of polarization of light propagating through a glass parallel to an applied magnetic field, the Faraday effect, has been utilized in the construction of fast optical switches, modulators, circulators, isolators, and sensors for magnetic fields and electric currents. Diamagnetic and paramagnetic glasses have been used in bulk and fiber forms for these applications. To minimize the magnetic field and length of material needed to produce a given rotation, the Verdet constant should be as large as possible. For uniformity of rotation and isolation, the Faraday rotator

657

glass must also be optically homogeneous and free of birefringence. In high-power laser applications, the nonlinear refractive index and optical damage threshold are further considerations. Thus the stringent requirements characteristic of optical and laser glasses are usually also applicable to Faraday rotator glasses. The largest diamagnetic Verdet constants are found for high-index, high-dispersion glasses located in the upper righthand corner of Fig. 12-6. Oxide glasses containing cations with large, easily polarizable outer electron shells, such as Te4 + , Bi 3 + , and P b 2 + network formers and Tl + , In 3 + , Sb 3 + , La 3 + , Ti 4 + , Nb 5 + , and Ta5 + network modifiers have large Verdet constants (Borrelli, 1964). Of the nonoxide glasses, beryllium and aluminum fluorides exhibit little dispersion and hence have corresponding small Verdet constants. At the other extreme, chalcogenide glasses have very high dispersion and large Verdet constants and are appropriate for use in the infrared (Stepanov, 1974). Since the diamagnetic Verdet constant varies at I/A2 in the long wavelength limit hc/A<^Eg, Vdia is increased by selecting materials for which operation is nearer the fundamental band gap energy. If, however, the material figure of merit for the applications is VdiJa, then the wavelength dependencies of both Fdia and the absorption coefficient a must be considered. The Verdet constants of several representative glasses are given in Table 12-7. The temperature dependence of Fdia is very small which makes diamagnetic glasses attractive for high-stability Faraday effect sensors. Measured values of (dV/dT)/V for SiO 2 , BK 7, and SF 57 glasses are approximately 10~4/K (Williams et al., 1991). The magnitude and the wavelength and temperature dependences of paramagnetic Verdet constants vary depending upon the

658

12 Optical Properties of Glasses

Table 12-7. Verdet constants of glasses (at 633 nm and 300 K). Paramagnetic

Diamagnetic F(rad/Tm)

Glass Arsenic trisulfide Lead-bismuth gallate Lead silicate (SF 59) Alkali silicate (F2) Borosilicate (BK 7)

_ 20 36 64

74 42 29 11 4.1

choice of the paramagnetic ion. For lanthanide series ions Faraday rotation involves 4P-4f"~ 1 5d electric-dipole transitions, therefore ions with low-lying 5d states such as Ce 3 + , Tb 3 + , and Eu 2 + have large F para . These ions also have large regions of transparency in the visible-near infrared region. Because Fdia and Fpara have opposite signs, the best host glasses are those having low dispersion (therefore small Fdia) and capable of incorporating large quantities of the paramagnetic ion. Values of Fpara for several rare-earth containing glasses are included in Table 12-7. The wavelength dependence of Fpara is also I/A2 at long wavelengths. Near sharp resonances Vpara is enhanced and changes sign as the wavelength of the incident light passes through the resonance (Collocott and Taylor, 1978). Except for very low temperatures (T<20K), Fpara varies as 1/T and hence is increased by operating at low temperatures. A figure of merit for Faraday rotator materials used in high power lasers where self-focusing is important is V/n2. As evident from Figs. 12-6 and 12-13, low-index fluoride glasses are attractive hosts for paramagnetic ions for this application because both Fdia and n2 are small. 12.4.8 Acoustooptic Glass

Acoustic waves create a time-varying refractive index grating in a material via the photoelastic effect. The grating spacing is

Glass Borosilicate (FR-5) Metaphosphate Metaphosphate Fluorophosphate (FR-7) Phosphate (FR-4)

Ion

F(rad/Tm)

Tb 3 + Tb 3 + Pr 3 + Tb 3 + Ce3 +

-71 -54 -40 -35 -31

equal to the acoustic wavelength; the grating depth is determined by the drive power of the transducer. A light beam traversing the medium is deflected by the grating at the Bragg angle <9B from the normal to the sound propagation direction given by 1 k

(12-57)

17

where X and A are the wavelengths of the light and sound beams. This phenomenon provides fast deflection or modulation of light and is used in display technology. The diffraction efficiency for a transducer of height H and interaction length L is (see, for example, Gottlieb, 1986) K2

L P, n6

2\l/2

V*J 7

(12-58)

where Pa is the acoustic power, p is the photoelastic constant, Q is the density, and v is the sound velocity. Thus an acoustooptic material, in addition to having low losses at the acoustic and optical wavelengths, should also have a large index of refraction and small sound velocity. These include materials containing heavy cations such as lead silicate or tellurite glasses and chalcogenide glasses. From Eq. (12-58), a figure of merit for an acoustooptic material is M =

n6p2 QV3

(12-59)

659

12.4 Special Glasses

Table 12-8. Properties of acoustooptic glasses (from Gottlieb (1986) and Izumitani (1986)). Material

Transmission range Refractive index (urn) (0.633 urn)

Fused silica (SiO2) Lead silicate (SF 59) Tellurite(AOT5) TeO2 (crystal)

0.2 0.460.470.35-

4.0 2.5 2.7 5

Arsenic trisulfide (As2S3)

0.6 - 1 1

1.46 1.95 2.09 2.26 2.61

Sound velocity (km/s) 5.96 3.20 3.40 4.20 (L) 0.616 (S) 2.6

Relative Ma 1.0 12.6 21.5 22.8 525 256

L - longitudinal wave, S - shear wave. a Figure of merit M = n6 P2/QVZ relative to that of SiO 2 .

Properties and figures of merit for several glasses are compared in Table 12-8. The selection of glass also depends upon the operating wavelength. Compared to crystals, glasses are attractive because they are isotopic and can be prepared in large sizes of excellent optical quality. 12.4.9 Radiation Detection Glass Glass is used in two forms for detection of high energy radiation and particles: as a pure glass for the generation of Cerenkov radiation by energetic particles and as a doped glass for scintillation caused by Xrays, gamma rays, charged particles, and neutrons. If a particle travels through of medium of refractive index n at a speed greater than that of light (c/n\ Cerenkov radiation is created. Since the Cerenkov radiation is in the blue-violet, for the radiation to be detected the glass must maintain good transparency in this spectral region. Large blocks of optical glass having a high refractive index, rc^l.7 are used in Cerenkov counters capable of detecting particles traveling at 0.6 of the speed of light in vacuum. High energy particles and ionizing radiation are detected by scintillation from glass activated by a fluorescing species

(transition metal ion, organic dye, molecular group, etc.). Absorption causes core level excitations followed by secondary radiation and relaxation processes. These lead to the creation of large numbers of electron-hole pairs, subsequent excitation of the activator, and fluorescence which is detected by a photomultiplier tube or other appropriate detector. Scintillation glasses are available in bulk form for energy calorimetry and in fiber form for particle tracking. Scintillation glass is produced by doping glass with ions such as those used for phosphors and lasers. The fluorescence efficiency for excitation by ionizing radiation, however, is not the same as for optical radiation. The development of scintillation glass was pioneered by Ginther (Ginther and Schulman, 1958; Ginther, 1960). Among the glasses investigated were cerium-activated lithium-magnesium-aluminum silicate glass. Variants of this glass are still currently in use. The 5 d -> 4 f transition of Ce 3 + provides fluorescence at ~ 400 nm which is well matched to the peak spectral sensitivity of photocathodes. Because the absorption of Ce 4 + overlaps the emission of Ce 3 + , the glasses are prepared under reducing conditions to keep the cerium in the trivalent state. The com-

660

12 Optical Properties of Glasses

position of the host glass affects the stopping power and overall detection efficiency. Cerium-activated glasses containing large quantities of BaO to increase the density have been investigated for electronic and hadronic calorimetry (Bross, 1986). Cerium-activated glass is also used for neutron detection where 6 Li is the neutron sensitive component (Spowart, 1976,1977). 6 Li interacts with a neutron to produce a 2.72 MeV triton and a 2.04 MeV alpha particle; these lead to excitation of the Ce 3 + fluorescence. Scintillation glasses are produced with lithium present in its natural isotopic abundance, as enriched 6Li (95%), or depleted (99.9% 7Li); weight percentages are in the range 2.5-7.5%. The Ce 3 + fluorescence decay from these glasses consists of a fast component (~ 20 ns) and a slow component (~60ns). Longer lifetime decay(s) associated with trapping centers may also be present in scintillation glass. The inertness of the glass to radiation damage (color center formation) is important for use in high radiation intensity environments. Trajectories of highly ionizing charged particles can be recorded in glass and revealed by etching with concentrated hydrofluoric acid or sodium hydroxide to remove material selectively along the track. The half-angle of the resulting cone-shaped etchpit is a measure of the ionization rate of the particle. Of the many glasses investigated for this application, phosphate glasses provide the greatest sensitivity (etching rate along the particle trajectory to general etching rate) and the highest charge resolution (Wang et al., 1988). Among the uses of these glasses are identification of the mass and atomic number of relativistic heavy cosmic rays and high resolution studies of relativistic heavy nuclei at accelerators.

Phosphate glasses containing cobalt or silver are used for personnel dosimeters. When exposed to radiation, the cobalt containing glass becomes colored due to the formation of color centers. Irradiation of silver phosphate glass produces silver particles. The fluorescence stimulated by ultraviolet radiation of the glass is then used to measure the radiation dose.

12.4.10 Radiation Shielding Glass

Glass is used for remote viewing of radiation environments such as X-ray facilities, hot cells in nuclear research, irradiation facilities for food preservation, and medical sterilization and therapeutic installations. In these applications the optical glass must provide both adequate shielding and not discolor during exposure to the radiation. High-lead-content glasses are used for radiation shielding glass. These glasses have about one-half the absorption of lead of comparable thickness. When normal fused silica and multicomponent glasses are exposed to ionizing radiation and high energy particles, charge carriers and a variety of atomic defects are produced. This results in electronic (charge rearrangement) damage and, if the particles have sufficient momentum, atomic or ionic displacement damage (Williams and Friebele, 1986). Coloration (browning) of optical glass begins at radiation doses of ~10 2 Gy and becomes very dark at ~ 5 x l O 4 G y . Radiation-resistant glasses have been developed to overcome this coloration. This is accomplished by the introduction of a small quantity of polyvalent ions that act as electron acceptors and reduce the probability for generating stable color centers. A commonly used ion is cerium which is added as CeO 2 in the range of 0.3-3.0 wt.%.

12.5 Future

12.4.11 Photosensitive Glass Photosensitive glasses are a special class of glasses whose optical properties are changed by optical/thermal treatment. Among these are photochromic glasses that change color under ultraviolet or short wavelength light, then revert back to the original state when the light is reduced. In ophthalmic and architectural applications, the transmission of such glasses in the 400-700 nm region can be reduced by more than 50% when exposed to bright light. Photochromism is observed in strongly reduced alkali silicate and other multicomponent silicate and borosilicate glasses, in glasses containing suspensions of crystallites, and in glasses colored by silver halides (Araujo, 1977). Transparent photochromic glasses are produced by starting with a homogenous glass containing dissolved silver and halide ions, then heating it to precipitate the silver halide (Stookey etal, 1978; Mauer, 1958). Many different base glasses can be used; the choice of composition, especially the halide, and thermal treatment influence the photochromic properties. The large range of possible compositional variations and careful control of the thermal treatment result in a wide range of transmission spectra, rates of color induction, and recovery times. The mechanisms involved in photochromism are complex and include treatment of precipitation kinetics and charge carrier diffusion (Araujo, 1977). Using small-particle scattering theory, the color variation in polychromatic glasses are attributed to the specific geometric shape of the silver on the alkali halide monocrystal (Borrelli et al., 1979). Another example of a photosensitive glass is lithium silicate glass containing CeO 2 as an optical sensitizer and silver,

661

gold, or palladium oxide as nucleating agents. This glass photonucleates when subjected to ultraviolet or ionizing radiation via the process Ce 3 + +hv -* Ce 4 + -f e~, followed by heating and diffusion of the electron to a nearly silver ion where Ag + +e~->Ag°. Upon further heat treatment Ag° atoms agglomerate to form silver colloids. These are dispersed through the glass and act as nucleation sites for crystal growth which proceeds upon heating at higher temperatures. Because crystallization occurs only in areas exposed to the ionizing radiation, spatially selective chemical machining, photo engraving, and photographs are possible, (see Vol.11, Chap. 5). As noted in Sec. 12.4.10, most glasses are photosensitive in the negative sense that they become colored (solarize) after exposure to ultraviolet or ionizing radiation. To prevent solarization in optically-pumped laser glass and in glass used for UV lamps (e.g., xenon and mercury lamps), small quantities (<1%) of polyvalent ions such as cerium, antimony, and molybdenum are added. Solarization is also associated with changes in the valence state of transition metal ions. Examples of such reactions include Mn 2 + +/iv-+Mn 3 + +e~~, F e 3 + + e " -> Fe 2 + , and Eu 2 + + T i 4 + -+ Eu 3 + +Ti 3 + .

12.5 Future A history of the chemical composition of optical glasses shows significant evolution during the past century (Marker and Scheller, 1988). Demands continue, however, for optical glasses with extended transmission in the infrared or ultraviolet, improved mechanical properties and ease of fabrication, lighter weight, better chemical durability, and composed of less costly or less hazardous raw materials. In recent years, efforts have been devoted not only to

662

12 Optical Properties of Glasses

seeking new and improved optical glasses with a wider range of properties, but to maintaining existing glass properties. Health and environmental concerns have necessitated reformulating optical glass compositions while still maintain their positions in the glass map. For example, radioactive thorium oxide has been replaced by yttrium, gadolinium, and ytterbium oxides and cadmium oxide by zinc and niobium oxides. Elements such as beryllium, which have several attractive properties for glass, are not used commercially because of the hazards associated with their use. There are also concerns about heavy metals such as lead, arsenic, antimony, and mercury. Although the compositional space of glass-forming systems has been widely explored and exploited (Izumitani, 1986), new glass compositions tailored to optimize a property(s) for specific applications continue to appear. These developments occur empirically, guided by past investigations and observations. Our ability to perform reliable ab initio calculations of physical and optical properties of simple glasses, let alone complex, multi-component compositions, is still very limited and is expected to remain so for some time (Weber, 1990). Today the search for and selection of optical glasses can be done using computerized databases of glass compositions and properties (Suzuki, 1991). With these, one has ready access to the complete glass map, partial dispersions, and numerous other properties. As a further boon to the optical designer, software is available to create new glass maps composed of selected glasses satisfying particular property criteria. Expert systems are also being used to derive multicomponent compositions of glasses having desired physical properties (Makishima, 1991).

12.6 Acknowledgement Work performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract W-7405-ENG-48. Reference herein to any specific commercial products by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United State Government or the University of California.

12.7 References Araujo, R. J. (1977), in: Treatise on Materials Science and Technology Vol. 12: Tomozawa, M., Doremus, R. H. (Eds.). New York: Academic Press, p. 91. Adair, R., Chase, L. L., Payne, S. A. (1987), J. Opt. Soc. Am. B4, 875. Bagley, B. G., Vogel, E. M., French, W. G., Pasteur, G. A., Gan, J. N., Tauc, X (1976), /. Non-Cryst. Solids 22, 423. Bamforth, C. R. (1977), Color Generation and Control in Glass. Amsterdam: Elsevier. Barnes Jr., W. P. (1979), in: Applied Optics and Optical Engineering Vol. 7. New York: Academic Press, p. 97. Bartholomew, R. F. (1982), in: Treatise on Materials Science and Technology Vol. 22: Tomozawa, M., Doremus, R. H. (Eds.). New York: Academic Press, p. 75. Becquerel, H. (1897), Compt. Rend. 125, 679. Behrens, E. G., Powell, R. C , Blackburn, D. H. (1990), /. Opt. Soc. Am. B 7, 1437. Bendow, B. (1973), Appl. Phys. Lett. 23, 133. Bendow, B. (1977), Ann. Rev. Mater. Sci. 7, 23. Blankenbecker, R., Hagerty, J. X, Pulsifer, D. N., Rindone, G. E. (1991), /. Non-Cryst. Solids 129, 109. Bliss, E. S., Speck, D. R., Holzrichter, X F , Erkkila, X H., Glass, A. X (1974), Appl. Phys. Lett. 25, 448. Bloembergen, N. (1965), Nonlinear Optics. New York: Benjamin. Boling, N. L., Glass, A. X, Owyoung, A. (1978), IEEE J. Quantum Electron. QE-14, 601. Born, M., Wolf, E. (1980), Principles of Optics, 6th ed. Oxford: Pergamon Press. Borrelli, N., Hall, D. W. (1991), in: Optical Properties of Glass: Kreidl, N. X, Uhlmann, D. R. (Eds.). Cincinnati, OH: American Ceramic Society. Borrelli, N., Hall, D. W., Holland, H. X, Smith, D. W. (1987), J. Appl. Phys. 61, 5399.

12.7 References

Borrelli, N. R, Chodak, J. B., Nolan, D. A., Seward III, T. P. (1979), /. Opt. Soc. Am. 69, 1514. Borrelli, N. F. (1964), J. Chem. Phys. 41, 3289. Bross, A. D. (1986), IEEE Trans. Nucl. Sci. 33, 144. Bruckner, R., Chun, H. U., Goretzki, H. (1978), Glastechn. Ber. 51, 1. Bruckner, R., Chun, H. U., Goretzki, H., Sammet, M. (1980), /. Non-Cryst. Solids 42, 49. Buckingham, A. D., Stephens, P. J. (1966), Am. Rev. Phys. Chem. 17, 399. Cole, H. (1950), /. Soc. Glass Tech. 34, 220. Collocott, S.J., Taylor, K. N. R. (1978), J. Phys. C17, 562. Cook, L., Mader, K. H. (1982), /. Am. Ceram. Soc. 65, 597. Cook, L. M., Stokowski, S. E. (1986), in: Handbook of Laser Science and Technology Vol. 4. Boca Raton, FL: CRC Press. Crisp, M. D., Boling, N. L., Dube, G. (1972), Appl. Phys. Lett. 21, 364. DiDomenico Jr., M. (1972), Appl. Optics 11, 652. Dumbaugh, W. H. (1985), Opt. Eng. 24, 257. Dumbaugh, W. H., Morgan, D. W. (1980), /. NonCryst. Solids 38/39, 211. Fanderlik, I. (1983), Optical Properties of Glass. Amsterdam: Elsevier, p. 38. Faraday, M. (1830), Trans. Roy. Soc. (London) 120, II, 1. Feldman, A., Horowitz, D., Waxier, R. M. (1973), IEEE J. Quantum Electron. QE-9, 1054. Feltz, A., Burckhardt, W, Voigt, B., Linke, D. (1991), / Non-Cryst. Solids 129, 31. Galant, V. E. (1979), Sov. J. Glass Phys. Chem. 5, 604. Gerth, K., Kloss, Th., Pohl, H.-J. (1991), /. NonCryst. Solids 129, 12. Ginther, R. X (1960), IRE Trans. Nucl. Sci. NS-7, 28. Ginther, R. X, Schulman, X H. (1958), IRE Trans. Nucl. Sci. NS-5, 92. Gliemeroth, G. (1983), /. Non-Cryst. Solids 47, 57. Goldstein, N. P., Sun, K. H. (1979), Am. Ceram. Soc. Bull. 58, 1182. Gottlieb, M. (1986), in: Handbook of Laser Science and Technology, Vol.4, Boca Raton, FL: CRC Press, p. 319. Hache, R, Ricard, D., Flytzanis, C. (1986), J. Opt. Soc. Am. B3, 1647. Hall, D. W., Newhouse, M. A., Borrelli, N. R, Dumbaugh, W. H., Weidman, D. L. (1989), Appl. Phys. Lett. 54, 1293. Hall, D. W., Weber, M. J. (1991), in: Handbook of Laser Science and Technology, Supplement I Lasers. Boca Raton, FL: CRC Press, p. 139. Hall, D. W, Haas, R., Krupke, W R, Weber, M. X (1983), IEEE J. Quantum Electron. QE-19, 1704. Hellwarth, R. W (1977), Prog. Quantum Electron 5, 1. Heiman, D., Hellwarth, R. W, Hamilton, D. S. (1978), J. Non-Cryst. Solids 34, 63. Hill, K. O., Fujii, Y, Johnson, D. C , Kawasaki, B. S. (1978), Appl. Phys. Lett. 32, 647. Huff, N. X, Call, A. D. (1973), /. Am. Ceram. Soc. 56, 55.

663

Hiifner, S. (1978), Optical Spectra of Transparent Rare-Earth Compounds. New York: Academic Press. Huggins, M. L., Sun, K. H. (1943), /. Am. Ceram. Soc. 26, 4. Iga, K., Kokubum, Y, Oikawa, M. (1984), Fundamentals of Microoptics. New York: Academic. Izumitani, T. S. (1986), Optical Glass. New York: Amer. Inst. Physics. Jain, R. K., Lind, R. C. (1983), J. Opt. Soc. Am. 73, 647. Jacobs, R. R., Weber, M. X (1976), IEEE J. Quantum Electron. QE-12, 102. Jen, X S., Kalinowski, M. R. (1980), /. Non-Cryst. Solids 38139, 21. Kittel, C. (1976), Introduction to Solid State Physics, 5th ed. New York: Wiley, p. 324. Kramer, M. A., Tompkin, W P., Boyd, R. W. (1986), Phys. Rev. A 34, 2026. Kreidl, N. X (1983), in: Glass: Science and Technology Vol. 1. New York: Academic Press, p. 105. Layne, C. B., Lowdermilk, W. H., Weber, M. X (1977), Phys. Rev. B 16, 10. Makishima, A., Mitomo, M., Monma, H., Mizutani, N., Yasui, I., Futagami, T. (1991), in: Computer Aided Innovation of New Materials: Doyama, M., Suzuki, T., Kihara, X, Yamamoto, R. (Eds.). Amsterdam: Elsevier, p. 891. Marion, X E., Weber, M. X (1991), Eur. J. Solid State Inorg. Chem. 28, 271. Marion, X E. (1986), Appl. Phys. Lett. 47, 694; (1986) /. Appl. Phys. 60, 69; (1987) J. Appl. Phys. 63,1595. Marker, A. X, Scheller, R. X (1988), in: Advances in the Fusion of Glass. Cincinnati, OH: American Ceramics Society, p. 4.1. Mauer, R. D. (1958), J. Appl. Phys. 29, 1. Mohler, E., Thomas, B. (1980), Phys. Rev. Lett. 44, 543. Moore, D. T. (1980), Appl. Optics 19, 1035. Morey, G. W. (1954), Properties of Glass, 2nd ed. New York: Reinhold. Nassau, K. (1986), in: Defects in Glass: Galeener, R L., Griscom, D. L., Weber, M. X (Eds.). Pittsburgh, PA: Materials Research Society, p. 427. Neuroth, N. (1987), Opt. Eng. 26, 96. Nissle, T. K., Babcock, C. L. (1973), J. Am. Ceram. Soc. 56, 596. Olbright, G. R., Peyghambarian, N. (1986), Appl. Phys. Lett. 48, 1184. Osterberg, U., Margulis, W. (1986), Opt. Lett. 11, 516; (1987) Opt. Lett. 12, 57. Patek, K. (1970), Glass Lasers. London: Butterworths. Pinnow, D. A., Rich, T. C , Ostermayer, R W, DiDomenico, M. (1973), Appl. Phys. Lett. 22, 527. Pockels, F. (1902), Ann. Physik 9, 220; (1903) Ann. Physik 11,651. Potter, B. G., Simmons, X H. (1988), Phys. Rev. B 37, 10838. Powell, R. X, Spicer, W E . (1970), Phys. Rev. B2, 2182.

664

12 Optical Properties of Glasses

Quelle Jr., F. W. (1966), Appl. Optics 5, 633. Rawson, H. (1980), Properties and Applications of Glass. Amsterdam: Elsevier. Riedel, E. P., Baldwin, G. D. (1967), /. Appl Phys. 38, 2720. Schaefer, CL, Nassenstein, H. (1953), Z. Naturforschung 8 a, 90. Shchavelev, O. S., Babkina, V. A. (1970), Sov. J. Opt. Technol. 37, 604. Shchavelev, O. S., Babkima, V. A., Elina, N. N., Didenko, L. A., Mit'kin, V. M., Molev, V. I. (1976), Sov. J. Opt. Technol. 43, All. Shchavelev, O. S., Plutalova, N. Y. (1978), Sov. J. Glass Phys. Chem. 4, 81. Schott Optical Glass Catalog (1982), Schott, Mainz, Germany. Schroeder, J. (1977), in: Treatise on Materials Science and Technology Vol. 12: Tomozawa, M., Doremus, R. H. (Eds.). New York: Academic Press, p. 157. Schroeder, J. (1980), /. Non-Cryst. Solids 75A, 163. Serber, R. (1932), Phys. Rev. 41, 489. Sheik-Bahne, M., Hagen, D. X, Van Stryland, E. W. (1990), Phys. Rev. Lett. 65, 96. Shen, Y. R. (1984), The Principles of Nonlinear Optics. New York: Wiley. Sigel Jr., G. H. (1977), in: Treatise on Materials Science and Technology Vol. 12: Tomozawa, M., Doremus, R. H. (Eds.). New York: Academic Press, p. 5. Sinka, N. K. (1978), Phys. Chem. Glass 19, 69. Smith, H. L., Cohen, A. J. (1963), Phys. Chem. Glass 4, 173. Spowart, A. R. (1976), Nucl. Instr. Meth. 135, 441. Spowart, A. R. (1977), Nucl. Instr. Meth. 140, 19. Stepanov, S. A. (1974), Sov. J. Opt. Technol. 41, 179. Stokowski, S. E. (1987), in: Lasers, Spectroscopy and New Ideas: Yen, W M., Levenson, M. D. (Eds.). Berlin: Springer, p. 47. Stolen, R. H., Lin, C. (1978), Phys. Rev. A 17, 1448. Stolen, R. H., Tom, H. W. K. (1987), Opt. Lett. 12, 585. Stookey, D., Beall, G. H., Pierson, J. E. (1978), /. Appl. Phys. 49, 5114. Suzuki, Y (1991), Ceram. Bull. 70, 219. Szigeti, B. (1950), Proc. Roy. Soc. (London) A 204, 51. Tashiro, M. (1956), /. Soc. Glass Technol. 195, 353. Thompkin, W. R., Boyd, R. W, Hall, D. W, Tuk, P. A. (1987), /. Opt. Sci. Am. B4, 1030. Tomlinson, W. J. (1988), Phys. Stat. Sol. 150, 854. Turner, W. H. (1973), Appl. Optics 12, 480. Urbach, F. (1953), Phys. Rev. 92, 1324. Van de Hulst, H. C. (1957), Light Scattering by Small Particles. New York: Wiley. Vogel, E. M. (1989), J. Am. Ceram. Soc. 72, 719. Vogel, E. M., Weber, M. J., Krol, D. M. (1991), Phys. Chem. Glass, in press. Volf, M. B. (1988), Mathematical Approach to Glass. Amsterdam: Elsevier.

Wang, S., Barwick, S. W, Ifft, D., Price, P. B., Westphal, A. X, Day, D. E. (1988), Nucl. Instr. Meth.

B35,A3. Waxier, R. M., Gleek, G. W, Malitson, I. H., Dodge, M. X, Hahn, T. A. (1971), J. Res. Nat. Bur. Stand. 75 A, 163. Weber, M. X (1990), /. Non-Cryst. Solids 123, 208. Weber, M. X (1981), in: Laser Spectroscopy in Solids: Yen, W M., Selzer, P. M. (Eds.). Berlin: Springer, p. 189. Weber, M. X, Milam, D., Smith, W. L. (1978 a), Opt. Engin. 17, 463. Weber, M. X, Cline, C. R, Milan, D., Smith, W L., Heiman, D., Hellwarth, R. W. (1978 b), Appl. Phys. Lett. 32, 403. Weber, M. X (1991), Handbook of Laser Science and Technology, Supplement 1 - Lasers. Boca Raton, FL: CRC Press. Wemple, S. H. (1973), Phys. Rev. B 7, 1161. Wemple, S. H. (1977), J. Chem. Phys. 67, 2151. Williams, P. A., Rose, A. H., Day, G. W, Milner, T. E., Deeter, M. N. (1991), Appl. Opt. 30, 1176. Williams, R. T, Friebele, E. X (1986), in: Handbook of Laser Science and Technology Vol. 3. Boca Raton, FL: CRC Press, p. 299. Winkelmann, A., Schott, O. (1894), Ann. Phys. Chem. 51, 697. Wood, R. M. (Ed.) (1990), Selected Papers on Laser Damage in Optical Materials Vol. MS 24. Bellingham, WA, SPIE Press. Zeiger, H. X, Pratt, G. W. (1973), Magnetic Interaction in Solids. Oxford: Clarendon Press.

General Reading Bamford, C. R. (1977), Color Generation and Control in Glass. Amsterdam: Elsevier. Bamford, C. R., Nicoletti, F., Gliemeroth, G., Russo, V, Marechal, A. (Eds.) (1982), "Proc. Conf. on Optical Glass and Optical Materials", /. NonCryst. Solids 47, 1-296. Fanderlik, I. (1983), "Optical Properties of Glass", Glass Science and Technology Vol. 5. Amsterdam: Elsevier. Izumitani, T. S. (1986), Optical Glass. New York: American Institute of Physics. Kreidl, N., Uhlmann, D. (Eds.) (1991), Optical Properties of Glass. Cincinnati, OH: Am. Ceram. Soc. Tomozawa, M., Levy, R. A., MacCrone, R. K., Doremus, R. H. (Eds.) (1980), "Electrical, Magnetic and Optical Properties of Glasses, Proc. 5th Intern. Conf. on Glass Science", J. Non-Cryst. Solids 40, 1-640. Weyl, W A . (1951), Coloured Glasses. Sheffield, U. K.: Society of Glass Technology. Weber, M. X (Ed.) (1986), "Optical Materials", Handbook of Laser Science and Technology Vol. 3, 4 and 5. Boca Raton, FL: CRC Press.

13 Mechanical Properties of Glasses Rolf Bruckner

Technische Universitat Berlin, Anorganische Werkstoffe, Berlin, Federal Republic of Germany

List of Symbols and Abbreviations 13.1 Introduction 13.2 Glass as an Elastic Solid Material 13.2.1 Elastic Properties of Glasses 13.2.1.1 Fundamentals 13.2.1.2 Composition Dependence 13.2.1.3 Temperature Dependence 13.2.1.4 Dependence on Thermal and Mechanical Prehistories 13.2.2 Inelastic Properties of Glasses 13.2.2.1 Densification 13.2.2.2 Mechanical Losses 13.3 The Phenomenon of Uncontrolled Brittle Fracture 13.3.1 Theoretical and Practical Strength 13.3.1.1 Theoretical Strength 13.3.1.2 Real Strength: Griffith's Theory 13.3.2 Fracture Mechanics 13.3.2.1 Energy Balance 13.3.2.2 Fractography and Crack Velocity 13.3.3 The Phenomenon of the High Strength of Glass Fibers 13.4 Controlled Fracture Propagation and Time Dependent Phenomena 13.4.1 Subcritical Crack Propagation 13.4.2 Fatigue and Lifetime 13.4.2.1 Static Fatigue 13.4.2.2 Lifetime and Proof Test 13.4.2.3 Dynamic Fatigue 13.5 Techniques for Increasing Strength and Toughness of Glasses 13.5.1 Strengthening by Thermal Tempering 13.5.2 Chemical Strengthening 13.5.3 Fiber-Reinforcement of Glasses 13.6 Mechanical Behavior Above the Glass Transition Temperature 13.6.1 High-Temperature Strength 13.6.1.1 High-Temperature Strength as a Surface Property 13.6.1.2 High-Temperature Strength as a Volume Property 13.6.2 Non-Linear Relaxation Behavior 13.6.3 Non-Newtonian Flow Behavior Materials Science and Technology Copyright © WILEY-VCH Verlag GmbH & Co KGaA. Allrightsreserved.

667 669 669 669 669 670 672 673 675 675 675 678 679 679 679 681 681 683 686 688 690 691 691 693 694 694 695 696 697 698 699 699 699 701 704

666

13.7 13.7.1 13.7.1.1 13.7.1.2 13.7.1.3 13.7.2 13.7.2.1 13.7.2.2 13.8

13 Mechanical Properties of Glasses

Further Properties Microhardness Indentation Process and Phenomena Influence of Chemical Composition Temperature Dependence and Thermal Prehistory Stress-Optical Coefficient Stress-Optical Coefficient within the Elastic Range of Glass Stress-Optical Coefficient within the Viscoelastic Range References

705 705 705 706 706 707 707 708 709

List of Symbols and Abbreviations

List of Symbols and Abbreviations a A b c C

P

C D E Et £(0 m ax

/ F Fz G Gi GSp

h k K Kad Kiso Ki

Klc I Mt m An N Pi

Q r r t T % TD Te U *>\ V{

v, v,

length crack propagation parameter broadness spring back value specific heat stress-optical coefficient relative distribution of the tensile strength Young's modulus specific elastic factor for the i-th oxide relaxation modulus factor load in Newtons drawing force shear modulus specific fracture energy specific fracture energy deformation rate Boltzmann constant compression modulus adiabatic compressive modulus isothermal compressive modulus stress intensity factor for mode I critical stress intensity factor for mode I length molecular weights mass flow birefringence interference order content of z-th oxide in wt.% or in mol% activation energy distance mean atomic distance time absolute temperature surface temperature interior temperature drawing temperature glass transition temperature dissociation energy longitudinal sound velocity fracture or crack velocity specific factors calculated from the ionic radii package density of the ions

667

668

13 Mechanical Properties of Glasses

p

cubic thermal expansion shear or torsion angle surface energy relative path difference Kronecker symbol deformation tensor viscosity compressibility wavelength Poisson ratio free surface energy density of the glass density stress tensor tensile or compressive stress amplitudes applied stress pre-stress working stress strength under inert environment axial compressive stresses relaxation time shear stress phase angle frequency

y y 5 £

n X V

Q Q

L o

^ax T T

CD

ht MH

MHK MHV

high temperature microhardness Knoop microhardness Vickers microhardness

13.2 Glass as an Elastic Solid Material

13.1 Introduction In this chapter the mechanical properties not only of glasses but also of their melts will be treated, because there is a continuous transition from the stable state of the melt via the metastable state of the undercooled melt to the thermodynamically unstable state of the glass (vitreous state) without significant change of structure and of phase. Therefore, the properties of glasses are sometimes understood much better if the stable and/or metastable state is understood, even only partly, and vice versa. Additionally, there are characteristic differences in the properties of the rigid glasses and their melts, particularly due to the molecular dynamics. Following the usual way of description of a material at room temperature and of the most common and typical glasses, the silicate and oxide glasses, the starting point will be the vitreous state clearly below the glass transition temperature, Tg. Only then will the temperature region around and above Tg be treated when the mechanical properties are altered and relaxation and flow phenomena become more and more dominant.

669

tensors are symmetric if the structure of the solid body is cubic or isotropic which is the case for a slowly cooled glass. Thus, the number of components are reduced to six for each tensor. The relationship between the two tensors are the so-called stressstrain- and strain-stress-equations depending on which physical property is given and which property is to be calculated. If the strains are given and the stresses have to be calculated the stress-strain-equations are applied: (13-1) E with Sik the Kronecker symbol = 1 for i = k and = 0 for i ^ k. The indices i, k denote the spatial directions x, y, z. Stress and strain components with i = k are normal or orthogonal components, while components with i 7^ k are shear components. If the stresses are given, the strain-stressequations are applied: 1 E Syy

~ E°yy'~E

^Gxx + °z^ (13-2)

13.2 Glass as an Elastic Solid Material

£zz = T7 <*zz - 7T (°XX + °yy)

13.2.1 Elastic Properties of Glasses 13.2.1.1 Fundamentals If a solid body is deformed by a force, both the deformation and the outer force or the applied stresses on this body are described by the components of the stress tensor, E, and by the components of the deformation tensor, 8. These usually consist of nine components, for each of the tensors. If no stresses are present within the body, as for instance cooling stresses, the

In these equations the elastic constants are properties of the material used: E the Young's modulus or elasticity modulus, G, the shear modulus and \i the Poisson ratio. If K is the compression modulus, the relationship between the elastic constants is given by:

,-§-.

(13-3)

670

13 Mechanical Properties of Glasses

Methods for measuring these material properties are described in many standard books, such as those by Schreiber et al. (1973), Davidge (1979) or Scholze (1988). Since very early on measurements have shown that glasses are excellent elastic materials for which Hooke's law is fulfilled: E =

G/S

(13-4)

(j is the applied tensile or compressive stress and e the deformation in the special case of a glass rod, s = Al/l91 the length and Al the elongation of the rod. Thus, glass is usually an elastic body at room temperature. The larger its elastic modulus is, the less it can be deformed by a certain stress. Similar behavior shows the shear or torsion modulus, G = i/y, where T is the shear stress and y the shear or torsion angle. The relationship to K and fi is given by Eq. (13-3). 13.2.1.2 Composition Dependence

Silica glass with its three-dimensionally connected network is expected to have a large £-value £ = 72 GPa (Deeg, 1958). If alkali oxide is introduced the network is weakened and E decreases (Fig. 13-1). At comparable alkali concentrations the Young's modulus decreases with decreasing field strength of the cations. In this way E decreases from Li- to K-silicate glasses (Deeg, 1958; Kozlovskaya, 1959; DeGuire

Figure 13-1. Young's modulus, E, of binary alkali silicate glasses at room temperature from various authors, composed by Scholze (1988).

and Brown, 1984). The introduction of cations with still larger field strengths, such as Ca2 + , leads to correspondingly higher E-values, as do additions of A12O3 and B 2 O 3 which reduce the number of nonbridging oxygen atoms, B 2 O 3 by the socalled boron oxide anomaly (Scholze, 1988) provided enough alkali oxide is present to ensure a network-forming quality for Al3 + and change to four-fold coordination for B 3 + . Livshits et al. (1982) showed that E increases from 59 to 74 GPa within the series 25Na 2 OxAl 2 O 3 (75-x)SiO 2 when x varies from zero to 25. As in the case of many other properties the borate glasses show a totally other dependence on E with increasing alkali oxide as compared with the silicate glasses. Starting from the very low £-value of 17.5 GPa for B 2 O 3 glass, the elastic modulus increases with alkali oxide concentration up to 60 GPa (Takahashi et al., 1983). Two structural reasons are responsible for this behavior. The B 2 O 3 glass has a very open structure and the network is much less interconnected than that of silica glass due to the disc-like triangular BO 3 groups. If alkali oxide is added, the free volume is filled at least partly by the alkali ions and the BO3-groups are changed to BO4-tetrahedra in proportion to the alkali oxide content, an effect which is well-known as boron oxide anomaly (see Chap. 5). A similar coordination change takes place in alkali germanate glasses, from the pure GeO 2 glass in which Ge 4 + is four-fold coordinated to six-fold coordination in proportion to the alkali oxide concentration up to about 12 to 17 mol% depending on the type of alkali. In this way the Young's modulus changes from 43 GPa for GeO 2 glass to a maximum value of 73 GPa at a Na 2 O content of 17 mol%. Above that value the coordination is retrograde and the ^-modulus is also (Osaka et al., 1985).

13.2 Glass as an Elastic Solid Material

The shear modulus has been investigated much less than the Young's modulus. But the shear modulus can be discussed in the same manner as the Young's modulus because G « 0.4 to 0.3 £, as follows from Eq. (13-3). From its definition the Poisson ratio fi = (Ar/r)/(Al/l) theoretically exhibits values between 0 and 0.5. For many glasses \x is between 0.2 and 0.3. A low /i-value indicates that at a certain elongation Al/l the radial contraction Ar/r is low. This is the case for relatively rigid structures, e.g. for silica glass with \i = 0.17. By the incorporation of network modifying cations, particularly large ones, the /i-values increase (increasing polarizability). More relationships to structural aspects may be deduced from the compressibility, x, which is the reciprocal of the compression modulus K. Starting from silica glass with its open structure and abundant free volume, a large compressibility is expected: x = 2.7 • 10" 1 1 Pa" 1 . The introduction of alkali oxide leads to a decrease of free volume which is connected with a decrease of compressibility, particularly for small cations with a high field strength (Li2O, see Fig. 13-2). However, for cations with larger (ionic) radii and with a large polarizability (K + , P b 2 + , Ba 2+ ), the compressibility is increased. These two counteracting effects are still more pronounced in binary R 2 O - B 2 O 3 and R O - B 2 O 3 systems (Fig. 13-3). Of special interest is one of many anomalies of silica glass: in contrast to nearly all other solids, x increases with increasing compressive stress up to a maximum value at a compressive stress of 350 MPa. Above that value the compressibility decreases in the usual way (Bridgman and Simon, 1953). Many attempts have been made to calculate the elastic constants by so-called specific factors found empirically by sys-

671

0.04

10 20 30 40 — R20 in mol % —

50

Figure 13-2. Compressibility, x, of binary silicate glasses at 21 °C and at 1 GPa (Weir and Shartsis, 1955). 0.05

Ratio

number of oxygen ions

Figure 13-3. Compressibility of binary alkali and alkaline earth borate glasses at 21 °C and extrapolated to 0.1 GPa (Weir and Shartsis, 1955).

tematic measurements: n

E= £

EiPi

(13-5)

where Et is the specific factor for the i-th oxide and pt the content of this i-th oxide in wt.% or in mol%, respectively, depending on the authors who determined the specific factors. Similar treatments are given for G, \i and K. Numerous authors have applied such treatments for various homologous series: Appen et al. (1961), Kozlovskaya (1959), Winkelmann and Schott (1894), Makishima and Mackenzie (1973, 1975). A useful and comprehensive

672

13 Mechanical Properties of Glasses

summary of these specific factors is given by Scholze (1988). Apart from the purely empirically evaluated specific factors, Makishima and Mackenzie (1973,1975) calculated the elastic properties using a physical background. They regarded the Young's modulus as dependent on the packing density of the ions, Vt9 and on the dissociation energy, (7, related to the unit of volume. In this way they obtained for single component glasses: E = 2VtU

(13-6)

For multi-component glasses, the sum over all components must be calculated:

z

(13-7)

i =1

with Q the density of the glass, p{ portions in mol%, Mt the molecular weights, and V{ the specific factors which can be calculated from the ionic radii. Together with the factors Ut in KJ/cm3, Makishima and Mackenzie obtained: E = 0.2VtZUiPi = 0.2ZVipiZUipi/?1Mipi

145 GPa is obtained (Williams and Scott, 1970). It is well known that a high Young's modulus is usually connected to a high strength, apart from or under comparable surface conditions (see Sees. 13.3.1 and 13.3.2). 13.2.1.3 Temperature Dependence Usually bonding forces decrease with increasing temperature. This leads to a decrease of the elastic constants as was measured by Spinner (1956) and McGraw (1952) for silicate glasses (Figs. 13-4 and 13-5). The increase of /a with temperature is 750 700-

650350 300-

250 0.24

(13-8)

0.220.20

and in a similar manner they calculated the compression modulus: K = Vt2ZUiPi=l/x

(13-9)

and the Poisson ratio: ju = 0.5-0A39/Vt

100 200 300 400 500 600

T in °C

—

Figure 13-4. Elastic constants and Poisson ratio versus temperature of a borosilicate glass below Tg (Spinner, 1956).

(13-10)

The consequence of Makishima and Mackenzie's considerations is that a glass with a high Young's modulus should contain components with high dissociation energies and high package densities but small molecular weights. Oxides with cations of medium field strengths are most advantageous in this respect. As an example for a glass with the composition 40.7 SiO 2 , 7.2A12O3, 26.7 MgO, 25.4 BeO (in mol%) an extreme Young's modulus of

0

200 400 600 800 T in °C —

Figure 13-5. Young's modulus of a sodium calcium silicate glass versus temperature below and above Tg (McGraw, 1952).

13.2 Glass as an Elastic Solid Material

due to the fact that the glass structure approaches with increasing temperature the value fi = 0.5 of melts and fluids. The decrease of E and G depends on the glass composition. Increasing alkali oxide concentration leads to a steeper decrease of E and G, the steepest decrease for Li 2 O-SiO 2 glasses following the series K 2 O -> Na 2 O -• Li 2 O according to Galyant and Primenko (1978). These authors also found that A12O3 diminishes this effect drastically. One exception exists again for silica glass: it shows an increase of E and G with temperature by 9% for E at 900 °C which might be due to its low thermal expansion and other thermodynamical effects, such as the entropy effect, based on an elastic anisotropy of the glass network (Coenen, 1983). 13.2.1.4 Dependence on Thermal and Mechanical Prehistories

Most properties of glasses are dependent on the prehistory. Among the various prehistories (Bruckner, 1990), the thermal and the mechanical are the most important ones. A typical consequence of the structure of glasses, with its failure of long range order, is that the structure can be changed continuously by thermal and mechanical influences. If these influences are removed, the properties will change back to their previous values. This process takes time depending on temperature and on the distance from the metastable state of the glass. With respect to elasticity this phenomenon is called elastic aftereffect and is closely related to relaxation effects (see Chap. 3 of this volume). The fact that the Young's modulus usually decreases with increasing temperature makes plausible that very quickly cooled glasses have lower E-values than slowly cooled glasses. Stong (1937) has found a change of the Young's modulus

673

from 74.5 and 71.5 GPa for a sodium calcium silicate glass which had been cooled normally and quenched. After having annealed the same glass near Tg for several hours they found E = 16 GPa. Similar results were obtained by Halleck et al. (1986). Investigations on glass fibers have shown very drastically the effects of thermal and mechanical prehistory on the elastic constants. Typical of these effects are the two following examples for £-glass fibers produced under different drawing conditions (Pahler and Bruckner, 1985 a, b): First, Figs. 13-6 a toe show that the Young's and the shear moduli are decreasing with decreasing fiber diameter. Since the square of the fiber diameter is reciprocal to the fictive temperature of the fibers (that temperature at which the glass structure is frozen-in), the fictive temperature increases with decreasing diameter and the moduli decrease. This tendency is independent of the drawing temperature, TD, and drawing force, but it depends on the mass flow which is kept constant in Figs. 13-6 a to c by variation of the pressure on the nozzle. The strength, on the other hand, increases with decreasing fiber diameter, a phenomenon which will be discussed in Sec. 13.3.3. Second, if using the Young's and shear moduli the Poisson ratios as a function of the reciprocal radius at constant mass flow are calculated, one gets values which are not only near 0.5 but partly above 0.5 (Figs. 13-7 a to c). This indicates that these Poisson ratios are apparent ones because the formula fj* = E/G — 1 is only valid for isotropic materials (Pahler and Bruckner, 1985 a, b). The fibers, however, are anisotropic and show birefringence (see Sec. 13.3.3). Thus, the first example indicates preferentially the thermal prehistory, while the second example shows both influences, the

674

13 Mechanical Properties of Glasses

1L

33-

8 f"

2523: 80: 757066:

30-

V \

\

c)

^"""""^--•^

s x

^ ^ *——-—

3500-

u

T

Q) \

TD = 1623K m =5mg/s -x F z =1.2mN

T D =1423K m =5mg/s F 2 =3,8mN

/

0.05

0,1

2500-

?_

__5_

T

h

1500-

0

0,15

0,2

0

0.05

0,1

0,15

0

0,2

Reciprocal fiber radius in urn"

0,05

0.1

0,15

0,2

1

Figure 13-6. Shear and Young's moduli and strength of E-glass fibers versus the reciprocal of fiber radius under various fiber drawing conditions (a to c) but at constant mass flow. Fz = drawing force, m = mass flow.

v

11

»w

b)

a)

0#4^ D

0,2-

T D =1623K m =5mg/s Fz = 1#2mN

E-Glass

a

; c) TD=1073K ffi =3mg/s F 2 =0,8mN

CaBa

[

T D =773K m =243mg/s F z =0 f 8mN

NaPoLi

0,4-

a ex ^f

TD = 673K %—

TD=1023K m =3mg/s F z =0,9mN

m =5mg/s F 2 =1.3mN

0.2-

%

ent Poissor

0.6-

m =2.3m/s Fz =2.45mN

0.6-

0A-

T D =973K m =3mg/s F z =3.0mN

,/#

0,2-

0

0,05

0,1

0.15

0.2

0

0.05

0.1

0J5

0.2

^f^=648K m = 1.7mg/s Fz =3,24mN 0

0.05

0.1

0.15

0,2

Reciprocal fiber radius in u.m~1

Figure 13-7. Apparent Poisson ratio of glass fibers versus the reciprocal of fiber radius under various drawing conditions but at constant mass flow for a) £-glass, b) Ca-Ba-metaphosphate glass and c) Na-Li-metaphosphate glass.

thermal and the mechanical prehistory, the latter one produced by the stress during the fiber drawing process which causes the freezing-in of strains and, at least in the case of Na-Li-metaphosphate glass fibers, also orientations of PO 4 -chains (Stockhorst and Bruckner, 1982, 1986).

It is plausible that time-dependent effects occur during phase-separation processes. This because to the progress of phase separation constitutes a kind of prehistory for glasses which have compositions within a solubility gap. Usually these effects are found to be low, within changes

13.2 Glass as an Elastic Solid Material

of 2 to 5% (Pye etal., 1974; Shaw and Uhlmann, 1969, 1971; Tille etal., 1978). A common phenomenon which is not only connected to the glassy but also to the crystalline state is the dependence of the elastic constants on thermodynamic properties, such as heat capacity, thermal conductance and thermal expansion. Therefore a distinction has to be made between the isothermal and adiabatic elastic constants. If the Young's modulus or the compressibility is measured by static methods, the isothermal moduli are obtained. When, however, dynamic methods are applied, the adiabatic moduli are measured, if the frequency of the dynamic method is high enough that no temperature equilibration during torsional or tensile and compressive stresses can take place. Therefore, if Kad is the adiabatic compressive modulus, which may be measured easily by ultrasonic velocity and density, the isothermal modulus can be calculated by the following equation and vice versa: = Kis

TH2/cp

(13-11)

with T the absolute temperature, /? the cubic thermal expansion coefficient, and cp the specific heat. The difference between the isothermal and adiabatic compressibilities is about 5%. 13.2.2 Inelastic Properties of Glasses 13.2.2.1 Densification

Elastic deformations are by definition reversible. At very high pressures, however, the deformation can be irreversible; this means that plastic flow takes place and the result is an increase of density. This densification can be reversed by annealing around Tg as was shown first by Bridgman and Simon (1953) and later by Cohen and Roy (1961) and by Mackenzie (1963,1964). The results indicate that the degree of den-

675

sification of silica glass (up to 16%) depends strongly on the experimental conditions of the compression process, specifically, on whether it is uniaxial or isostatic. A uniaxial compression process provides much higher shear stresses which act during the compression experiment, and thus a higher degree of permanent densification compared with an isostatic compression process. Seifert et al. (1983) showed by means of Raman spectrocopy that this process is accompanied by a decrease of the mean S i - O - S i angle. The degree of densification is, of course, also dependent on the glass composition and on the starting condition of the glass structure. Uhlmann (1973/74) showed that the densification is increased with increasing temperature and pressure, and no limit seems to exist. The dependence on the composition is more complicated: in the systems Na 2 O-SiO 2 and K 2 O-SiO 2 , densification at 200 °C and 3 GPa increases with R2O-concentration from pure silica glass with 2.2% to R 2 O = 10 mol% up to 6.5%. Above 10mol% R 2 O densification decreases again. Two effects are in conflict. On the one hand the mobility of the glass structure increases with increasing alkali content, which increases the densification; on the other hand, the free volume is filled by the alkali ions which leads to a reduced densification effect. Fig. 13-8 shows this latter influence in comparable uniaxial compression experiments as a function of pressure and alkali concentration (Mackenzie, 1963, 1964; Bridgman and Simon, 1953). 13.2.2.2 Mechanical Losses

Another inelasticity effect in glasses is the internal friction. There are several acting mechanisms which are responsible for the internal friction or mechanical losses. If

676

13 Mechanical Properties of Glasses

0%NaoO-

10%Na2023%Na2Q 31%Na 2 CT

U 8 12 16 20 Pressure in GPa —m"

Figure 13-8. Densification of silica glass and sodium silicate glass versus uniaxial compressive stress with increasing Na 2 O content (composed from various authors).

a sinusoidal stress (usually a torsional or a bending one), a = a0 sin co t or a — a0 eicof, is applied on a glass rod, the deformation, 8? lags behind the stress by the phase angle, cp: a = e0 sin(cot — cp) or: s = 8 0 e l(wr ~^, where a0 and e0 are the amplitudes, co — 2 n v the frequency and t the time. If mechanical energy is dissipated in the form of heat in real materials, the phase angle cp is identical with the loss angle. In ideal elastic materials cp = 0, inelastic portions give rise to cp ^ 0. As in the analogous case of electrical vibration losses, the dynamic shear modulus of torsional vibrations (or in the case of longitudinal waves the dynamic elastic modulus) and the loss factor, tan cp, depend on frequency, co, and on the relaxation time, T, of that relaxation mechanism which causes the mechanical loss. These relationships are given (Ferry, 1970; Kirby, 1953 and 1954) for the simplest case by:

G = G0-(G0-GJ(l

+ co2T2r1 COT

typical absorption curve with a maximum at the inflexion point of curve G (Fig. 13-9). The maximum of a mechanical loss mechanism with a relaxation time, T, occurs at a frequency when COT = 1. This corresponds to a loss factor of tan cp = (Go— G^)/2G0 and a modulus G = 0.5 (Go + G J . The temperature dependence of the relaxation time, T, is given by the typical Boltzmann equation T = ToeQ/fcT, from which it follows for co x = 1 the temperature, 7^, at which the loss factor, tan cp, has its maximum: TM = Q//cln(l/coTo)

(13-14)

where Q is the activation energy of the relaxation process, k the Boltzmann constant and T 0 the pre-exponential factor (TO^10-13S).

From the logarithmic decrement of attenuation, the loss factor can be obtained by simple torsional or longitudinal vibrations as well. The relationship is: tan cp = 8/n.

In order to study relaxation mechanisms in glasses it is more convenient to vary the temperature instead of frequency, because from Eq. (13-14) it follows that a linear alteration of temperature at constant frequency is equivalent to an exponential alteration of frequency at constant tempera-

(13-12) (13-13)

where G is the dynamic shear modulus, Go that at co -+oo, and G^ that at co = 0. The dynamic shear modulus, G, versus frequency, co, is a typical dispersion curve (a) and the curve of the loss factor (b) is a

Figure 13-9. Typical dispersion curve for the dynamic shear modulus G (curve a) and for the loss factor tan (p versus frequency co• = 2 n v multiplied by the relaxation time r of a distinct relaxation or loss media-

677

13.2 Glass as an Elastic Solid Material

ture. Therefore, most experiments were made at constant frequency with variation of temperature. In simple alkali and multicomponent silicate glasses three different loss mechanisms are acting, as is shown in Fig. 13-10 (Coenen and Amrhein, 1961). With respect to a frequency of 5 cps the low temperature maximum is caused by the diffusion of alkali ions, the medium temperature maximum is due to the mobility of non-bridging oxygen ions, connected with a combined loss produced by the interaction of two different mobile cations (two different alkali and/or hydrogen ions). The main loss maximum in the glass transition range is related to the mobility of the whole network. An interesting point in Fig. 13-10 is the existence of double maxima at medium and high temperatures for the sodium silicate glass with 24 mol% Na 2 O, indicating phase separation into high and low silica portions with somewhat higher and lower amounts of non-bridging oxygen atoms and with higher and lower glass transition temperatures, respectively. All loss maxima show a shift to lower temperatures with increasing Na 2 O content due to decreasing network strength. Directly connected to the loss maxima are step-wise decays of the shear modulus as was shown by Coenen and Amrhein (1961) in Fig. 13-11. Further features of loss maxima measured by various authors (Fitzgerald, 1951; Kirby 1953,1954,1957; Day and Rindone, 1962; Coenen and Amrhein, 1961) are as follows. The height of the loss maxima increases with increasing sodium oxide content and with increasing cooling rates of the glass samples. The loss peak is shifted at lower temperatures and the activation energy is decreased from 21 kcal/mol (annealed) to 16 kcal/mol (quenched glass) as was shown by Fitzgerald (1951). This author also demonstrated that the activa-

500

1000

- Temperature in

Figure 13-10. The logarithmic decrement of attenuation of binary sodium silicate glasses (Na2O-content from 20 to 40 mole%) versus temperature under torsion vibrations with a frequency of 5 rps (Coenen and Amrhein, 1961). Courtesy of flnstitut National du Verre.

0

400 Temperature in °C

•

Figure 13-11. Logarithm of the shear modulus at constant frequency of 5 rps for a sodium disilicate glass versus temperature (Coenen and Amrhein, 1961). Courtesy of l'lnstitut National du Verre.

tion energy for the alkali oxide loss peak corresponds with that for the ionic conductivity, thus both processes are based on the mobility of the alkali ions. The activation energy decreases with decreasing field strength, i.e. from Li + to K + .

678

13 Mechanical Properties of Glasses

It is of distinct interest that the medium temperature loss maximum has no relation to a conductivity effect, thus, it should be electrically neutral. If A12O3 is added to a silicate glass as a substitute for SiO 2 the number of non-bridging oxygen ions decreases and the loss peak intensity should decrease. This is confirmed by Kirby (1954) and by Day and Rindone (1962), who showed that the peak height decreases and the peak is shifted towards higher temperatures, indicating together with the shift of Tg towards higher temperature a stronger and more cross-linked network. The method of internal friction has frequently been applied to study the so-called mixed alkali effect, an effect which is most pronounced for alkali ion mobility in an electric field by which the specific conductivity is decreased up to several orders of magnitude if two alkali ions are exchanged by molar fraction of 0.5. Also the mechanical mobility in an alternating field of stress is very pronounced as was shown by Coenen (1961), Shelby and Day (1969, 1970), vanGemert et al. (1974), and in a review by Zdaniewski et al. (1979).

13.3 The Phenomenon of Uncontrolled Brittle Fracture It is well known that glasses, particularly oxide glasses, are highly brittle. The term brittleness is related to the fracture behavior and is closely connected to Hooke's law: brittle fracture occurs at a certain point on the elastic line without any indication or deviation from the stress-strain straight line (Fig. 13-12, curve a). A ductile polycrystalline metal, however, breaks after a significant deviation from linearity at much higher strains and after a certain deformation which may be described as plastic flow under a certain stress (Fig. 13-12,

Strain, relat. units —•Figure 13-12. Stress-strain straight line (Hooke's law) with sudden (brittle) fracture of a bulk glass (curve a) and with a ductile fracture (toughness) of a metal (curve b).

curve b). This kind of fracture behavior is called toughness and is explained by plastic gliding of layers in crystalline lattices, a phenomenon occurring particularly in metals and for instance in graphite, which has been shown experimentally. Therefore, it was believed that the brittleness of oxide glasses is due to their disordered network without any long-range order where gliding layers cannot be formed. However, when the high ductility of metal glasses (see Volume 6) was discovered, this explanation could not be maintained any longer. The main origin of ductility of a material seems to lie in metallic bonding and that of brittleness seems to be in an ionic and covalent or mixed bonding character and not (or at least not only) the ordered or disordered structure of a material. In this way it becomes plausible that not only are glasses brittle materials but also ceramic materials with and without glass phase, quartz and even diamond and silicon carbide with their dominant covalent bonding character. Another point connected with the term "brittleness" is the question: is the behavior of a glass as a brittle material really characterized by curve a in Fig. 13-12 or is this produced by effects which reduce only the strength of the glass, e.g., by surface or internal cracks?

13.3 The Phenomenon of Uncontrolled Brittle Fracture

It is a very long-established fact, recognized since the key work by Griffith (1920), that the strength of glass fibers is two or three orders of magnitude larger than that of bulk glass. Only this fact has the consequence that the stress-strain curves of glass fibers and bulk differ from each other not only by magnitude of stress, <x, and strain, s, but also by the character of the curves (see Fig. 13-32 in Sec. 13.5.3). A comparison of curve 1 for bulk glass to curve 2 for glass fibers shows a curvature at stresses which are clearly beyond the strength values of bulk glass. Thus, the non-linear part of curve 2 cannot be measured for bulk glass because fracture occurs before these stress-strain values are reached. As will be shown later (in Sec. 13.3.3) this non-linearity is reversible at least within the experimental error of one cycle of the stress-strain curve, as a result of the nonlinear interaction potential between the stressed and strained atoms which is obviously induced to a certain degree (Pahler and Bruckner, 1985 b). If such high stresses are repeated numerous times, bondings may be broken more and more, microcracks will be produced and finally the stress-strain curve will no longer be reversible, indicating that deviation from ideal elasticity occurs, if fracture can be prevented during the stress-strain cycles. If any deviation from Hooke's straight line indicates toughness, at least a very slight one, the non-linear part of curve 2 in Fig. 13-32 characterizes such a property and this property should be dependent on the composition of the glass. However, as will be shown in the next sections, the strength of glasses below Tg is usually not a volume, but primarily a surface property. Above Tg, however, strength becomes a volume property (see Sec. 13.6.1).

679

13.3.1 Theoretical and Practical Strength

Strength is not a material constant such as the elastic constants, thermal expansion, density, etc. which can be determined with an error of less than 3%. Strength depends on various influences, e.g. the size of the specimen, the sample preparation, duration of load, surrounding media etc. Therefore a scatter of strength values of 15 to 25% is normal. This indicates that fracture is broadly connected to statistics. 13.3.1.1 Theoretical Strength

The ultimate strength of a material is determined by the mutual bonding forces of its atoms, ions or molecules and can be calculated in various ways. Usually that energy which is necessary to produce a new surface is considered. Supposing a planary stress strain state, this leads to the theoretical strength (Griffith, 1920): (13-15) where E is the Young's modulus, y the free surface energy and a the atomic distance. A rough estimation with the help of mean values for silicate glasses, E = 70 GPa, y = 0.3 N/m and a = 1.6 • 10" 1 0 m, leads to a value for <7theOr.~ 13 GPa. Other estimations are within the same order of magnitude, e.g. the so-called Orowanian rule leads to <7 theor ^£/10 = 7GPa. A somewhat modified estimation (Bartenev and Sanditov, 1982) is: <7theor. = (l -2/x)£/(l + pi) with fi the Poisson number. 13.3.1.2 Real Strength: Griffith's Theory

The experimentally measured real strength values of glasses are usually lower than the theoretical strength values by several orders of magnitude. The origin of this discrepancy is that real bulk glasses and real materials all contain faults, micro-

680

13 Mechanical Properties of Glasses

f theoret. strength 10*> glass fibers I pristine and acid| polished glasses normal glass products > scratched glasses

structural defects surface defects and microcracks

heavy surface defects macrocracks

Figure 13-13. Overview of the strength of glasses (Kruithof and Zijlstra, 1959).

cracks and cracks, of which those at the surface diminish the strength in the most drastic manner. Figure 13-13 gives an overview of the strength of glasses and the origin of the reduced values (Kruithof and Zijlstra, 1959). Most interesting are the strength values of glass fibers which are close below that of the theoretical strength. This was recognized already by Griffith (1920), who observed a drastic increase of strength with decreasing fiber diameter. After having explained the difference between theoretical and experimental strength with his famous equation: (13-16) where / is the length of that crack which leads to fracture, Griffith interpreted the high strength of glass fibers as being due to very short crack lengths in pristine fibers. An important point is the size of a sample, because the probability for the occurrence of voids and cracks increases with the size of a specimen. Thus, the strength of fibers decreases with increasing fiber length at comparable diameters (Anderegg, 1939) and the strength of a bulk glass with a much larger volume than that of a fiber is much lower. This size effect is also wellknown for the strength of sheet glass (Blank et al., 1990; Struck and Briinner,

1989). The reason that cracks at the surface influence positively the strength of glass as compared with cracks in the interior may be seen in the fact that the tensile strength is about one order of magnitude less than the compressive strength; the flexural strength is in between because one side is under compressive, the other one under tensile stress before fracture. Thus if surface cracks are removed by etching with HF or by flame polishing, the strength of a glass sample is increased. The real strength is influenced not only by the size of the specimen but also by corrosion phenomena. Norville and Minor (1985) have investigated 20-year-old window panes and have found clearly higher strength values on the inner side compared to the outer side. Still higher strength values resulted for the inner surfaces of insulating double glazed windows. Very large surface cracks are created by collisions with small particles or stones. The loss of strength is dependent on the impact of the projectile (Wiederhorn et al., 1979). Smaller cracks can be observed by electron microscope, as was done by Varner and Oel (1975), in order to attribute the strength to certain faults and to study the action of HF-etching of the surface. A combination of electron microscope and strength measurements was also applied by Pavelchek and Doremus (1974), who were able to show that the cracks produced by grinding the surface with SiC paper, which determines the strength of the glass, have a depth of 6 jam, a value which Griffith (1920) had already found by his estimates from real strength values of bulk glasses. The reason for the difference between the theoretical strength (10 to 30 GPa) and the strength of glasses with crack-free surfaces (about 4 GPa) is a question of special

13.3 The Phenomenon of Uncontrolled Brittle Fracture

interest. Rawson (1953) and Dietzel (1981) explain this discrepancy by inhomogeneities within atomic regions where stresses occur by phase separation tendency or by formation of swarms of alkali-rich regions. In glasses with real phase separation small cracks at the phase boundaries were found by Vogel (1964). In normal glasses without phase separation, Hillig (1962) explained the low strength values of bulk glasses with thermal motions within atomic regions (fluctuations). It has also been discussed that fluctuations at the surface may lead to a kind of surface roughness which might act as cracks in the sense of fracture mechanics (see Sec. 13.3.2). These small surface cracks are not detectable, not even by electron microscope. Therefore attempts have been made to enlarge these surface faults in order to convert them to visible cracks. This was done by evaporation of gold (Adams and McMillan, 1977) or sodium vapor (Andrade and Tsien, 1937), or by ion exchange (Acloque et al., 1960; Ernsberger, 1962). The latter method was the most successful one. Ernsberger produced tensile stresses in the surface by ion exchange Na-»Li + (15 min. at 250 °C) and counted the cracks which became visible as a result of these surface tensile stresses. The results for normal sheet glass was 50000 cracks/cm2. He could show that the cracks originated from surface damages or surface decompositions already produced by small amounts of impurities. Rauschenbach (1981, 1983) has applied the method of implantation of noble gas ions. A thermal treatment after implantation leads to formation of small bubbles which make visible the finest defects at the glass surface. Defect densities up to 10 11 cm" 2 are measurable by this method.

681

13.3.2 Fracture Mechanics 13.3.2.1 Energy Balance

In order to produce glasses with higher mechanical strength and to understand brittle fracture behavior it is necessary to investigate the processes that occur during the fracture. Since about 1960, fracture phenomena have been treated by the increasingly developed discipline of fracture mechanics (see also Vol. 6). Kerkhof (1970) has summarized the knowledge in a book. Conference proceedings were published by Bradt et al. (1974, 1986) and by Kurkjian (1985), and a long series of review articles appeared, such as Charles (1961), Chermant et al. (1979), Cottrell (1964), Doremus (1982), Ernsberger (1977), Evans (1974, 1978), Freiman (1980), Hillig (1962), Holloway (1986), LaCourse (1972), Lawn and Wilshaw (1975), Lawn (1983) and Wiederhorn (1974). The development of fracture mechanics is closely linked with the names of Inglis, Griffith and Irwin. In contrast to the more statistical treatment of fracture strength, the behavior of a single crack (or flaw) is treated within a homogeneous and isotropic continuum. If linear elastic behavior can be presupposed, the term linear elastic fracture mechanics is also used. As in the case of Griffith's theory, the origins of fracture mechanics are located in continuum mechanics and the difficulty is the transformation to atomic scales if the stress field at the flaw tip is treated during the fracture process. This is the main task of fracture mechanics. The stress fields around a crack tip are complex and are dependent on the kind of loading. According to Irwin (1958), one has to distinguish between three fundamental types (modes) of crack loadings which are characterized by the relative shifts of the crack tips (Fig. 13-14). The first mode (I) is the most important and is the typical crack opening mode.

682

13 Mechanical Properties of Glasses

II

III

Mode II is the first shear mode or the edge mode, and mode III is called the second shear mode or the tearing mode. Mode I is best realized if the fracture is a brittle one, which again is best realized for glasses. The stresses for mode I before the crack tip are (see Fig. 13-15): G

' «xx

u

yy

=

Kr

= (7™ = 0

Figure 13-14 The three modes of crack loading (Kerkhof, 1970).

sin (p/2 • cos (p/2 • cos 3 (p/2 (13-17d) (13-17e)

zy

Figure 13-15. The crack tip front with the corresponding coordinates and the components of stresses in the advanced field of the crack (Kerkhof, 1970).

where KY is the stress intensity factor for mode I by which the stresses before the crack tip, r, can be easily calculated. For a crack with the length of 2 a which is under an overall tensile stress, cr, the stress intensity factor is given by: (13-18) na For the special case of a long plane plate with a broadness b and with a crack at one side of depth a which is under tensile stress, cr, perpendicular to the crack, the stress directly before the sharp crack tip, ar9 at the distance r is given (see, e.g. Kerkhof, 1970 or Paris and Sih, 1965) by:

x,=

(13-19)

or = 2o«

!f t he condition a
(13-20)

13.3 The Phenomenon of Uncontrolled Brittle Fracture

This is a material-specific property and is important as a fracture criterium. From the energy balance, the specific fracture energy, GI? is obtained for the plane stress condition:

G, = Kf/E

(13-21)

If the critical stress is exceeded, the crack propagation becomes unstable and GY becomes the critical specific fracture energy, GIC = K2C/E. For an ideal brittle material Gj = 2y (y the surface energy) which leads, together with Eq. (13-18) to a)

(13-22)

which is equivalent with Eq. (13-16), if a = 1/2. This equation leads to an unstable equilibrium, because, if 2 y > a2 n a/E the crack would be closed and if 2 y < a2 n a/E the crack would be opened, an effect which was realized by Stavrinidis and Holloway (1983) in load-changing experiments where fracture has to be prevented. In real fracture experiments with glasses it was found that the fracture energy is clearly higher than that for ideal elasticity. Marsh (1964) interpreted this problem to mean that something other than elastic energy still has to be considered, such as plastic deformation at the crack tip. Irreversible chemical reactions may also take place (Wiederhorn and Townsend, 1970).

683

This is the reason why today the critical specific fracture energy, GIC, is measured indirectly by the determination of the critical stress intensity factor, Klc. It must be emphasized, however, that the fracture criterion,
The usual brittle fracture of glass is characterized by the fracture or crack velocity

Table 13-1. Fracture mechanics data for some glasses (Wiederhorn, 1969). Glass

Young's modulus in GPa

Silica glass 96% silica Lead-alkali Soda-lime Aluminosilicate Borosilicate

72.1 65.9 65.3 73.4 89.1 63.7

Fracture surface energy in Jm at various temperatures (K)

2

KIC-value in MPam 1 / 2 at various temperatures (K)

11

196

300

77

196

300

4.56 4.17 4.11 4.55 5.21 4.70

4.83 4.60 4.48 _

4.37 3.96 3.52 3.87 4.65 4.63

0.811 0.741 0.734 0.820 0.963 0.774

0.839 0.779

0.794 0.722 0.680 0.754 0.910 0.768

0.812

684

13 Mechanical Properties of Glasses

V{. Schardin and Struth (1937) found that after a relatively slow start the crack tip propagates to a maximum value V[max which is typical for each glass, e.g. for silica glass Vu max = 2200 m/s, for sheet glass Vf, max = 1-500 m/s. They calculated from the elasticity theory: = 0.38

(13-23)

while Kerkhof (1963) calculated from molecular considerations: (13-24) where Q is the density, y the surface energy and f0 the mean distance of the ions. For a mirror glass with E = 74 GPa, Q == 2.520 g/cm3, y = 0.305 N/m and r 0 = 2.0 • 10" 1 0 m (Scholze, 1988), the maximum fracture velocity is 2059 with Eq. (13-23) and 1556 m/s with Eq. (13-24). The latter value agrees very well with the experimental value of 1520 m/s. The most exact experiments on crack velocity were performed using the ultrasonic modulation technique of fracture surfaces developed by Kerkhof (1980). Fig. 13-16 a shows the principle and the result from which the crack velocity V{, can be directly determined by V{ = X • v, where X is the wavelength of the modulated crack surface and v the frequency of the ultrasonic wave. If X becomes too small at low V{ or too large at the beginning or end of the fracture process, v should be chosen smaller or larger, respectively. In this way the increase of V{ with crack propagation can be obtained in an elegant manner (Fig. 13-16 b). For further methods, the reader is referred to work by Kerkhof (1970, 1980, 1983), Kerkhof and Richter (1987), and Scholze (1988) which also contains a great variety of fracture phenomena with glasses. Two very frequently observed typical phenomena may be mentioned here, the so-called fracture mirror and the Wallner lines. If a glass rod or a sheet glass speci-

Figure 13-16 a. Principle of crack surface modulation with ultrasonic waves during crack propagation, V{ = Vh, under tensile stress, a0 • Vt = velocity of transversal waves, T = transversal ultrasonic source (Kerkhof, 1980).

—

direction of crack propagation

Figure 13-16 b. Microscopic interference field of the crack surface in the starting range of the ultrasonically modulated crack propagation: v = 923 kHz, height of the photon graph is 0.4 mm, Crack velocity at the right-hand end about 100 m/s (Kerkhof, 1980).

men is broken, one can observe (Fig. 13-17) fracture mirrors; these are regions with a smooth surface around the fracture origin (below) which corresponds with the area of the starting fracture. At a certain distance when the crack propagates with high velocity, the fracture mirror becomes coarser. This distance, am9 is proportional to the reciprocal of the square stress, a~2, or in other words the product am a2 is constant (Kerkhof, 1970, 1980). This constant is called the fracture mirror constant and al-

13.3 The Phenomenon of Uncontrolled Brittle Fracture

685

lows one to calculate the specific fracture energy, GSP: GSJ> = 4(1-^)

a2 aJ(nE)

(13-25)

The roughness of the fracture surface is a criterion that in this region the maximum fracture velocity has been reached. The Wallner lines can be detected on the fracture mirror area as many fine crossing curves (Fig. 13-18 a) from which the crack velocity can be measured and calculated in a much more laborious way and with a larger error than by using the ultra-sonic modulation technique. Fig. 13-18 b gives the explanation for the evaluation of the crack velocity and the origin of the Wallner lines: supposing a constant fracture velocity, Vf the production of a single Wallner line (ABCDE) is shown in Fig. 13-18 b (Schardin, 1950). Around the crack origin P are drawn 5 concentrical successive fracture fronts with equal time differences At. They correspond to 5 ultrasonic lines with the same time difference At as if the moving crack had been treated with transversal ul-

Figure 13-18 a. Fracture surface of a broken glass rod (diameter about 6 mm) with Wallner lines. Crack from below (Kerkhof, 1980).

Figure 13-18 b. Schematic sketch for the construction of a Wallner line (ABCDE). P: origin of crack (Schardin, 1950; Kerkhof, 1980).

Figure 13-17. Fracture mirror of a glass rod with 9.4 mm diameter (Kerkhof, 1980).

trasonic waves. The first cycle through point A is the fracture front after the time t0 corresponding to the distance V{ t0. Suppose that at point A a small surface crack exists at which the stored elastic energy will be set free the moment the fracture front arrives at A. Suppose further that the elastic energy expands radial-symmetrically as a transversal wave with a velocity, Vt9 and that this wave coincides with the fracture fronts at the points B, C, D and E always after the time differences = *2-'o>

13 Mechanical Properties of Glasses

etc. In this way a single Wallner line is formed as a trace by the superposition of the fracture process with the velocity, V{9 and the elastic ultrasonic wave released at point A. In order to calculate V{, the pulse velocity Vt must be known. For that reason it is necessary to determine the whole fracture process from a field of crossing Wallner lines or to determine the crack velocity point by point from angle measurements at one or two crossing Wallner lines (see for example Kerkhof, 1970, 1980). 13.3.3 The Phenomenon of the High Strength of Glass Fibers

The famous investigation of Griffith (1920) and the results on the increasing strength of glass fibers with decreasing diameter has not only enormously increased knowledge on the large scale of strength values, especially for glasses, bulk glass samples, glass fibers and glass products, but has also suggested for a long period that the strength of glass fibers depends only on the diameter (170 to 3400 MPa for 1 mm to 3 jam diameter). This was at least partly confirmed by various other authors: Anderegg (1939), Hasegawa et al. (1972) and Rexer (1939). In contrast, radiusindependent strength was measured by Thomas (1960). During various discussions about these contradicting results the question arose about the influence of the size effect on strength measurements (see Sec. 13.3.1.2). Anderegg (1939) found that the strength of fibers of constant diameter decreases with increasing length, an effect which is also found for float glass plates (Struck and Briinner, 1989; Blank et al., 1990) with different extensions (Kerper and Scuderi, 1964 a, b). Thus, the interpretation of Griffith's results was changed to the argument that the radius effect is due to de-

creasing probability for the presence of cracks with decreasing radius or volume. Of all possible cracks, surface cracks are most important for the strength values. Thus, Thomas (1971) found that rods with 1.3 cm diameter showed a mean strength value which was about 35% lower than that of fibers with 3 to 50 \xm diameter made from the same glass. The measured highest strength values, however, did not differ. This observation is related to that of Bartenev (1968) who has found repeatedly that industrial glass fibers exhibit no simple distribution of strength values, but a distribution with three distinct strength maxima as is shown in curve 1 of Fig. 13-19. Very carefully prepared pristine glass fibers show a distribution like curve 2 and annealed fibers that like curve 3. The maximum at 3000 MPa is due to a defectfree glass fiber while the maximum of curve 2 at 2000 MPa is due to ultrafme defects at the surface and that at 900 MPa is due to very fine cracks or surface defects of first order according to Bartenev. Ritter et al. (1978) have produced surface defect-free silica fibers with strength values of up to 6 GPa (see also Kurkjian et al., 1982). Decreasing strength values from 6 to 2.6 GPa may be explained by corrosion effects or by the action of very small atmospheric dust particles (Maurer, 1977). 1

ibu fion-

686

2 3

1 \

/~ 'f\ \

y

1 A 1

\

0 2000 4000 — Strength in MPa*-

Figure 13-19. Relative distribution D of the tensile strength of alumino-borosilicate glass fibers (diameter 10 um) with different surface defects according to Bartenev (1968). Curve 1: industrial fibers, curve 2: pristine glass fibers, curve 3: annealed glass fibers.

687

13.3 The Phenomenon of Uncontrolled Brittle Fracture

According to extended investigations by Pahler and Bruckner (1981, 1985 a, b) and Stockhorst and Bruckner (1982, 1986), the properties of pristine glass fibers depend on two main factors: thermal and mechanical prehistory. Only if the detailed and complete rheological variables (temperature, velocity and pressure (or mass flow)) during the drawing process are known and varied and the drawing force, drawing stress, fiber diameter and quenching rate can be estimated, is a separation of thermal and mechanical prehistory possible. With respect to the properties of pristine glass fibers it is necessary to coat the fibers with a protective layer of polymer or to catch the fibers by electromagnetically operated clamps during the fiber drawing process. A typical criterion for a flawless pristine fiber is that the fiber explodes into very small pieces at fracture without leaving any pieces between the two clamps. In this way maximum strength values were obtained by Pahler and Bruckner (1981) at low drawing rates or low mass flow rates, at low relative humidity (< 30% for £-glass) and at a viscosity of lg rj = 2.8, rj in dPa s. In such a way tensile strength values up to 4000 MPa were obtained for E-glass fibers. The fiber radius itself is not the only parameter which is responsible for high strength values - much more important are the temperature profile, the deformation rate, cooling rate and drawing stress within the originating fiber (along the gob), which are all related to the inverse fiber radius and the wetting condition of the nozzle (Fig. 13-20). Thus, Griffith is confirmed, but only partly and in an indirect manner. Young's modulus, the shear modulus, and calculated from these values the apparent Poisson ratio as a function of the mentioned drawing parameters all give direct evidence of the anisotropic structure of the fibers when compared with the

Independent parameter nozzle temperature Tn

pressure on the nozzle p

drawing speed Vz

mass flow m-a^p exp (- Z?1 / 7"n) + 6

t drawing force F - a2 / n 1 / 3 e x p ( 6 2 / r n )

fiber radius /? =

T drawing stress cr=Fz/[jrR2)

[ffi/[pjrVz)]v2

T cooling rate

T=a3/R

Figure 13-20. The most important parameters for fiber preparation by the nozzle-drawing method and their mutual dependence.

isotropic structure of bulk glass (Pahler and Bruckner, 1985 a). £-glass fibers as well as metaphosphate glass fibers show values of the apparent Poisson's ratio which are very different from those for the bulk glasses and sometimes exceed the value ^ = 0.5 (Fig. 13-7 in Sec. 13.2.1.4). Another interesting point is that the elastic moduli do not parallel the strength, as is usual for bulk glass when the composition is altered, but follow a contrary course to the strength (Fig. 13-6 in Sec. 13.2.1.4). Thus, something must be changed, if the Griffith Eq. (13-15) is to remain valid. This change may be seen in the difference between bulk and fiber glass structure, as will be shown later in this section. Deviations from Hooke's law at high stress levels (Fig. 13-21) indicate that the measured tensile strength can reach 50 to 90% of the maximum attainable theoretical strength (Pahler and Bruckner, 1985 b), which is determined largely by the ionic portion of the bonding. Flaws on which fracture depends lie in the nanometer range and tend to be sharply angular and oriented along the length of thefibers.In such a way only the much smaller cross section of an elongated microcrack perpendicular to the fiber axis is acting when frac-

688

13 Mechanical Properties of Glasses

• 75-

1 2 3 — Relative fiber strain in % •

Figure 13-21. Stress-strain diagram of E-glass fibers with 10 \xm radius and the differentiated curve as strain-dependent Young's modulus.

ture occurs and not the larger cross section parallel to the fiber axis. Measurements on other, more structuresensitive properties of £-glass fibers (Stockhorst and Bruckner, 1982), as well as alkali and alkaline earth metaphosphate glass fibers (birefringence, density, shrinkage at Tg and X-ray diffraction, Stockhorst and Bruckner, 1986), have shown that glass fibers are more anisotropic the larger the stress was during the drawing process (mechanical prehistory) and the larger the nozzle temperature and the cooling rate (thermal prehistory) were. For alkali metaphosphate glass fibers, the orientation effect of the PO 4 chains along the fiber axis can be shown by wide angle X-ray diffraction patterns (Stockhorst and Bruckner, 1986). A measure of anisotropy or even of orientation of structural units is the birefringence, An, shown for the three glass types men-

tioned versus drawing stress during fiber fabrication in Figs. 13-22 a to d. In all three cases An increases with drawing stress and with nozzle temperature and values are obtained from An « 40 (£-glass fibers) up to 10000 nm/mm (alkali metaphosphate glass fibers). The latter value is comparable with those found in stretched organic polymers. From these structure-sensitive measurements it is easy to understand that cracks, microcracks and flaws within and at the surface of fibers will be oriented with their longest axis parallel to the fiber axis; thus, only the smallest cross-section dimension of very flat and elongated cracks will be responsible for fracture. It may therefore be concluded that the high strength of pristine glass fibers can be explained by the anisotropic arrangement of the structural units (flow units) and their sharply elongated structural defects and microcracks. Otherwise it is impossible to understand that an open network such as that produced by very high quenching rates (thermal prehistory of thin fibers) can produce much higher strength values than an annealed glass or glass fiber. The drastic decrease in strength of annealed fibers as shown in Fig. 13-19, curve 3, can also be understood with the anisotropic structure of the fibers: the rearrangement of the fiber structure and reelongation of microcracks to an isotropic network results in a drastic decrease in strength.

13.4 Controlled Fracture Propagation and Time Dependent Phenomena In Sec. 13.3 stresses were applied which lead immediately to fracture with unstable crack propagation. If, in contrast, very low stresses are applied, the glasses will not

13.4 Controlled Fracture Propagation and T i m e Dependent P h e n o m e n a

689

10000 9000 8000 |

7000

g

6000

c <

S

5000

CT1

£

4000 3000 2000

25Na2 O-25Li 2 O-50P 2 0 5 TD = 375°C

1000 20

(a)

—

40

60 0-

Drawing Stress o z in MPa

(c)

50 100 Drawing stress o in MPa

150

10000 9000 8000

m=3,0mg/s J& / / m=2,0mg/s

(b)

20 40 60 80 — — Drawing stress in MPa

100

120 •-

Figure 13-22. Birefringence of glass fibers versus drawing stress during fiber spinning; parameter: nozzle temperature, a: £-glass fibers; b: calcium-barium metaphosphate glass fibers; c and d: sodium-lithium metaphosphate glass fibers with the mass flow, m, as parameter and TD = drawing temperature.

fracture but will show birefringence, if the stress optical constant is not zero. At intermediate stresses, however, glass does not fracture immediately but supports the stress only for a certain time interval. The higher the stress, the shorter this time in-

25Na2O-25Li2O-50P2O5 TD=400°C

50 100 Drawing stress o in MPa •

150

terval will be, and the strength becomes time dependent. This kind of fracture is called static fatigue. This is equivalent with the fact that the Klc value will be reached only after a certain time during loading. The origin of this dependence of load on

690

13 Mechanical Properties of Glasses

loading duration is that flaws and cracks increase slowly under load until they have reached the critical crack length of Klc at which rapid crack propagation or failure occurs. Therefore it is important to know the dependence of fracture propagation velocity on various effects such as stress, temperature and surrounding medium. On the basis of a detailed analysis of these effects and from exact measurements of subcritical crack propagation the proof test was developed, particularly by Wiederhorn and Evans (1974). If stresses are applied to glasses at constant stress rates, the fracture stress, that is, the strength of a glass, depends on the stress rate. The higher the stress, the larger the stress rate. This phenomenon is called dynamic fatigue. 13.4.1 Subcritical Crack Propagation In carefully performed measurements it is possible to apply just those intermediate stresses to a glass sample provided with a well-defined crack before experiment so that the velocity of the crack propagation can be controlled and varied over many orders of magnitude. Wiederhorn (1974) has reported this in a review article. A very strong dependence on the surrounding atmosphere or fluid media and on temperature has been found. Measurements in vacuum at constant temperature indicated that the logarithm of the subcritical fracture velocity, \gVf, increases proportionally to the stress intensity factor, KY (not to the stress!), and increases with rising temperature (Wiederhorn et al, 1974), with an activation energy of about 500 kJ/mole. The interpretation of this activation value is not yet quite clear. It should be emphasized that a subcritical V{ could not be measured for a few glasses, such as silica glass and borosilicate

glass, because fracture happened immediately. This shows a dependence of the elastic constant on temperature and pressure (see Sec. 13.2.1.3) other than that for usual silicate glasses. Possibly, the stress at the crack tip is released first and when the pressure dependence becomes normal at higher load, the fracture velocity is turned immediately into the unstable condition. The main results obtained from subcritical crack propagation in glass in various environments may be summarized by the following generalization, in addition to those already mentioned: - The Vf — Klc curves may be divided into three different regions (Wiederhorn, 1967), all of which can occur in a material but do not necessarily need to occur (Fig. 13-23): Region I is determined by the velocity which is needed for the surrounding medium to react with the glass at the crack tip. Region II, the horizontal part of the curves in Fig. 13-23, is determined by the velocity which is necessary to transport the surrounding medium to the location of the crack tip. This velocity limits the influence of the medium on the crack propagation velocity. Region III is independent of a gaseous medium. This region corresponds to the behavior in vacuum. Liquid media, however, can influence the subcritical crack propagation up to still higher velocities due to physical processes (Fig. 13-24). - The Klc value is a point on the lg V{ — KY curve within region III at about 10 mm/s < Vf < 100 mm/s, and is somewhat arbitrary. - At extremely low crack velocity values (Vf < 10 ~6 mm/s), a value Klo can be assumed below which no crack propagation happens. This is called the static fatigue limit.

13.4 Controlled Fracture Propagation and Time Dependent Phenomena

Figure 13-23. Crack velocity, V{, of glass versus stress intensity factor Kx in air with various relative humidities and under liquid water (Wiederhorn, 1967).

691

Wiederhorn (1967) suggested, with the help of the stress-corrosion theory of Charles (1958) and Hillig and Charles (1965), that an accelerated chemical reaction takes place under the influence of the enhanced stress at the crack tip. In aqueous solutions, however, this interpretation is not satisfying. Therefore Freiman et al. (1985) and Michalske and Freiman (1983) assume that the reaction with the glass network at the crack tip is important for crack propagation and that those reactions only happen when the absorbing molecules dissociate at the stressed bondings of the glass network. More investigations are necessary, particularly because no one knows the exact geometry of the crack tips. Doremus (1982) assumes a crack tip radius of about 10 atomic distances and Lawn et al. (1985) assume about one atomic distance (0.14 nm), where a radius has no physical sense; at this point the continuum character of the theory of fracture mechanics has its limit. 13.4.2 Fatigue and Lifetime 13.4.2.1 Static Fatigue

Figure 13-24. Crack velocity, V{, versus Xj for glass under liquids with various viscosities. The numbers at the curves indicate the same regions as in Fig. 13-23. The larger the viscosity, the more the crack propagation under liquids is reduced. The regions 2, 3 and 4 coincide in the case of water (Richter, 1985).

From the results of fracture velocity versus KY one may state that fatigue occurs only in the presence of water, not in vacuum, that no fatigue takes place at very low temperatures because of the very low reaction rates, and that fatigue increases with increasing temperature. The consequence of the existence of subcritical crack propagation is that at a certain stress in or on a glass specimen a crack elongation can be expected. After a certain time under this stress a critical crack length can be reached at which fracture occurs spontaneously. This time-dependent fracture or strength is called fatigue. It can be measured with static, dynamic and cyclic methods and is connected to fracture me-

692

13 Mechanical Properties of Glasses

chanical data. Wiederhorn (1975) has given detailed descriptions in a review article on this topic. The interpretation of this phenomenon is usually based on the stress corrosion theory of Charles (1958) and Hillig and Charles (1965), which was mentioned in Sec. 13.4.1: the crack elongates by the reaction of an agent, e.g., water, with the glass network until the critical length is reached. With this interpretation a blunting effect at the crack tip should occur parallel to the elongation. Doremus (1973), on the other hand, thinks that the reaction with water produces a sharpening of the crack tip which leads to a decrease of strength when the tip radius is very small. Oka et al. (1981) remind one that the surface energy should decrease upon contact with water. It should be emphasized that the reaction with water can also lead to the opposite effect, an increase of strength, if a crack is corroded in such a way that blunting (increase of the crack tip radius) and shortening of the crack occurs. This is called aging (Fig. 13-25), and happens preferably when a low stress, or no stress, is applied during corrosion (Bando et al., 1984; Hirao and Tomozawa, 1987). This explains the old observation that glass breaks more easily immediately following scratching than after a certain time has elapsed. Going back to the effect of stress corrosion and fatigue, the so-called universal

uniform dissolution

Figure 13-25. Schematic sketch of the alteration of a crack tip in the presence of water (blunting and aging, Bando et al., 1984).

0.5-

0

4

8

tog (i-/t os )

Figure 13-26. Universal fatigue curve. Curve 1: ground sodium calcium silicate glass according to Mould and Southwick (1959-1961); curve 2: E-glass fiber; curve 3: silica glass fiber; curve 4: acid-etched sodium calcium silicate glass. Curves 2 to 4 are from Ritter and Sherburne (1971).

fatigue curve (Fig. 13-26), according to Mould and Southwick (1959, 1961), may be mentioned here. Curve 1 was obtained from many experiments under various conditions: sodium calcium silicate glass samples were roughened by defined grinding of the surface. It was found that the strength, a, relative to the strength at liquid N 2 temperature (77 K),
13.4 Controlled Fracture Propagation and Time Dependent Phenomena

pared to a surface with deep cracks. Various equations were proposed to describe the fatigue curves, e.g., lg t = at + b± lgcr or Igt = a2 + b2/(T.

693

13.4.2.2 Lifetime and Proof Test

One of the main reasons that great efforts were made with experiments on slow crack propagation in glasses was a wish to get information about the long-time strength and/or life-time of real structural components of glasses from short-time experiments. Starting from Eq. (13-18) for Kl9 it follows by differentiation that

A special point of interest is the static fatigue limit. Evidence for the existence of such a limit requires measurements at extremely low subcritical fracture velocities and stresses. Such measurements were performed by Wiederhorn and Bolz (1970) who found deviations from the lg V{ — Kx n da Vf with Vf=da/dt curves within region I (see Fig. 13-23) at a dt 2KX 1/2 (13-26) K r values < 0.3 MPam becoming nearly stress-independent (Fig. 13-27). This is if <ja, the applied stress, is assumed to be equivalent to a limit of fatigue for the inconstant. From the experimental results vestigated glasses of about 20-25% of the (Figs. 13-23 and 13-24) the empirical Eq. critical stress intensity factor, Klc. This (13-27) follows for the crack velocity, V{: limit seems, however, to be variable and Vf = AK? = da/dt (13-27) can be changed to 50% of Klc for glasses with low chemical stability (Gehrke et al., where the constant, n, represents the slopes 1986), which is usually combined with low of the curves in Figs. 13-23 and 13-24, strength. The reason for this may be seen in which are about n = 20 to 30 for the range I the formation of corrosion layers, as was and n = 80 for range III. A, the crack propdescribed above in connection with aging. agation parameter, is within +0.5 to —0.5 in region I and + 7 in region III for V{ in m/s and KY in MPam 1 / 2 . The lifetime, tf, the time at failure, can be easily obtained from Eq. (13-26) after integration over KJVf from K Ia , the value at the beginning of loading with the starting crack length a, to Klc, where the dependence of KY versus Vf is given by Eq. (13-27)

tf = 2anlc2a;n/[^(n-2)AK^2]

0.2

0.3 0.4 0.5 0.6 K} in MPam1/2 - —

Figure 13-27. Crack velocity, V{, versus J^ of various glasses under water at 25 °C at very low Vi-values. Curve 1: sodium calcium silicate glass; curve 2: borosilicate glass; curve 3: alumino-silicate glass; curve 4: silica glass (Wiederhorn and Bolz, 1970).

(13-28)

where aIC is the strength in an inert environment. An example from Scholze (1988) may be given here. From Fig. 13-23, it follows that for 10 and 100% relative humidities n = 25 and 22, and A = 2.8 and 4.0, respectively. For usual sodium calcium silicate glasses XIC = 0.75 MPam 1 / 2 . With a crack depth of 10 nm a critical strength results from Eq. (13-18):
694

13 Mechanical Properties of Glasses

ical strength, oa = 1410 MPa, is calculated from Eq. (13-18) to be t{ = 4 days in 10% relative humidity and in 100% relative humidity only ti = 75 minutes. The calculation of reliable lifetimes demands some critical remarks: - the values for K1C and olc must be determined exactly because of the high exponents of n, - for different experimental methods different equations are applied (see Kerkhof etal., 1981), - cracks usually have different depths and the largest one determines the strength. Statistics have been applied, as described for instance by Jakus et al. (1978), in an attempt to overcome these restrictions. Frequently Weibull statistics are used; however, Doremus (1983) argued that this is not always necessary. A prognosis or a guarantee of the lifetime can be obtained by proof testing (Ritter et al., 1980). This procedure starts with a pre-loading of the samples by a prestress, crp, which is larger than the working stress o-w, applied later. All those specimens for which Klc < op < 'n ap will be fractured. The rest comprises specimens with cracks a < ap, which means Klc > <rp^Jna. For the practical application of the structural component the specimen should show oa > <7p, thus, with oa yfna = Kla it follows: <jp/<ja
or

l/X I a ><rp/(<7aKIC).

With a < olc Eq. (13-28) is altered to: tf>

n(n-2)A

ona,

i - 2

(13-29)

From plots of lg t versus lg oa one can estimate how large the value for op has to be in order to achieve a certain desired lifetime (Ritter etal., 1980).

13.4.23 Dynamic Fatigue The parameters n and A of Eqs. (13-27 to 13-29) can also be obtained from the dynamic fatigue. If Eq. (13-26) is integrated not for a = constant but for da/dt = at, that means for linearly increasing stress as is the case for usual fracture stress measurements, one obtains for the fracture stress, af: (13-30) with

B = 2/[n(n-2)AK?c2] fna

and: (13-31)

where ain is the strength in an inert environment, a condition for which slow crack propagation is fairly excluded. Eq. (13-30) means that the fracture stress is lower the slower the loading rate is. The reason is that the cracks have more time for elongation at slow rates compared with larger rates, and the longer the crack depths, the lower the stresses needed to reach Klc. In a plot lg o versus lg(do-/dt), Eq. (13-30), a straight line results with a slope l/(rc + l). These dynamic fatigue measurements are the simplest method for the determination of crack propagation parameters.

13.5 Techniques for Increasing Strength and Toughness of Glasses Three possibilities for increasing the strength of glasses are described in this section: thermal, chemical and fiber-reinforced strengthening. A special problem for glasses, with exception of metallic glasses (see Chap. 9 of this volume), is the restriction of their application as structural components because of their brittleness or very low toughness. Typical values for Klc are

13.5 Techniques for Increasing Strength and Toughness of Glasses

695

only around 1 MPam 1 / 2 . The only way to increase the toughness of glasses is to incorporate ceramic fibers. In this way not only is the strength increased by a factor of up to more than 10, but the toughness also increases by a factor of up to more than 30 (Sec. 13.5.3). 13.5.1 Strengthening by Thermal Tempering

This kind of strengthening is based on quenching glass (flat glass) in air (Gardon, 1980) or in liquids (flat glass and glass piping, Gora et al., 1977). The result is that compressive stresses are built up in the surface area which contract the surface cracks. When loading occurs the surface compressive stress must first be turned into tensile stress before the specimen breaks under a certain tensile stress value. In order to build up permanent compressive stresses in the surface, the quenching process has to start from a To above Tg. If the quenching rate is kept constant, a parabolic temperature profile in the cross section of, e.g. a flat glass plate, is built up and kept constant. No stress will be built up as long as To > Tg because viscosity is too low. When To at the surface, Ta, undergoes Tg, the thermal expansion mismatch (Hagy and Ritland, 1957; Oel et al., 1979) between surface layers (Ta
0 1 2 3 4 Thickness x in m m - * -

Figure 13-28. Parabolic stress distribution of thermally strengthened glass plates. Solid curve: normally quenched in one way; dashed curve: quenched and heat-treated in a second step (Dannheim and Oel, 1983).

treatment does not consider the visco-elastic behavior of glasses around Tg, where solidification and stress-forming processes are time-dependent and thus dependent on cooling rate dT/dt, characterized usually by a distribution function of stress relaxation times. Additionally, structure-related changes in viscosity, density and Young's modulus have to be considered within the rg-region during quenching for a more refined approach to stress profile formation (Gardon, 1980; Scherer, 1986; Rekhson, 1986). All the above-mentioned effects and properties depend strongly on glass composition and geometry but also on surfacerelated properties such as the heat transfer coefficient, surface tension, contact angle, thermal conductivity, and specific heat. Also of importance are the properties of the quenching medium, its temperature relative to that of the specimen and its boiling tendency which influences the heat transfer coefficient (Singh et al., 1981). Strength can be increased in these ways by a factor of up to four (Gardon, 1980). The stress profile shown in Fig. 13-28, solid curve, with the maximum compressive stress at the surface is optimal only

696

13 Mechanical Properties of Glasses

with respect to strength experiments. If a surface crack is produced in practice, it propagates towards lower stresses and will grow. On the other hand, if the compressive stress profile has its maximum beneath the surface, the crack propagation will be hampered and suppressed within the region of increasing compressive stress (stress barrier effect, see dashed curve in Fig. 13-28). This can be done by multi-step methods in two ways: by an inverse thermal quench, e.g., by rapid heating in metal melts in order to relax the surface compressive stress partly (Schaeffer, 1985), or by a. subsequent ion exchange below Tg (see Sec. 13.5.2). 13.5.2 Chemical Strengthening

As early as 1892, Schott proposed to strengthen a glass by coating it with a glass having a smaller thermal expansion coefficient. This can be done easily today by the sol-gel method, described by Fabes et al. (1986) (see also Chap. 2). Another way to produce compressive stress in the surface layers is in principle the ion-exchange method with its various combinations. If the sodium ions of a glass are exchanged with lithium ions from a LiNO 3 salt melt above Tg, the surface layers exhibit a smaller thermal expansion coefficient than the interior and give rise to compressive stresses after cooling down to room temperature. This method (Hood and Stookey, 1957) has the disadvantage that the specimens will be more or less easily deformed. This disadvantage is also present for some variations of this method with ion-exchange treatments above Tg, by which surface layers are produced consisting of transparent glass ceramic based on lithium alumino silicates with their wellknown extremely low thermal expansion coefficients. The strength values of normal

glass products with such surface-modified layers are up to 800 MPa (Stookey et al., 1962; Schroder and Gliemeroth, 1970). In contrast to ion exchange treatments above Tg, there is the mechanism of ion exchange below Tg. When a Na 2 O-containing glass is treated in a KNO 3 salt melt, a lattice dilation (ion stuffing) is produced by the ion exchange Na + ^ K + , and compressive stresses are built up by the incorporation of the larger K + ions into the glass surface layer (stress-induced diffusion). Interdiffusion processes determine this procedure, which is of great practical importance. The A12O3 content of the glasses improves the diffusion rate of the alkali ions. Too high temperatures close to Tg enhance the exchange rate, but the compressive stresses will be destroyed by the increasing rates of the relaxation processes. This phenomenon is noticeably active down to Tg - 100 K (Sane and Cooper, 1987). If the glass specimens are quenched before the ion-exchange process, a larger ion exchange results because of the larger free volume as compared with a slowly cooled glass sample (Zheleztsov and Yanbeeva, 1983). The ion exchange depths are usually 100 to 300 jim. Compressive stresses up to 1000 MPa are reached at the surfaces, and must be overcome before fracture occurs in a tensile stress situation. Fig. 13-29 gives a comparison of the stress profiles between low temperature (below Tg) ion exchange and thermal strengthening (Olcott, 1963).

surface

surface 200 0 200 400 600 800 -«-tensile compressive stress in MPa-*-

Figure 13-29. Stress profile through the cross section of a flat glass plate after ion exchange (dashed curve) and after quenching (solid curve) (Olcott, 1963).

13.5 Techniques for Increasing Strength and Toughness of Glasses

100 200 , 300 Layer thickness in u

400

Figure 13-30. Relaxed stress profiles after ion exchange in Na 2 SO 4 + ZnSO 4 (Zijlstra and Burggraaf, 1969). Curve 1: 10 min. at 590°C; curve 2: 15 min. at 580 °C; curve 3: 25 min. at 585 °C.

The above-mentioned effect of a relaxed stress profile is shown in Fig. 13-30, and is due to a stress relaxation caused by viscous flow and seems not to be directly connected to the mixed-alkali effect (Tomandl and Schaeffer, 1977). 13.5.3 Fiber-Reinforcement of Glasses As was shown in the previous sections, glasses usually show low tensile and flexural strength, except for pristine thin glass fibers, and a pronounced brittle fracture behavior. This is the main reason for their limited technical application as construction elements of engines and other products. Strength-increasing effects as described in Sees. 13.5.1 and 13.5.2 by thermal or chemical means enhance the strength indeed, but do not influence the brittle fracture behavior. One possible way to overcome these disadvantage is the incorporation of ceramic fibers (SiC- and Cfibers) into glass matrices. This principle was first energetically promoted by Prewo etal. (1981). One of the most successful and economical procedures is the so-called slurry technique for preparing the "prepregs" (Sambell et al, 1972; Levitt, 1973), where an organic binder is used to glue the glass particles to

697

the fibers. If, however, an alkoxide solution is used as a binder material (Hegeler and Bruckner, 1989; Hegeler etal, 1989), the wetting of glass particles and fibers as well as interfacial properties can be optimized. The strength of the "prepregs" can then be increased by sol-gel transition (see Chap. 2) up to such a hardness that the prepregs can be well-handled and cut into pieces by a diamond saw. Any suitable alkoxide solution may be applied. The finished prepregs are densified by means of an inductively heated hydraulic press in a graphite die and in N 2 or Ar atmosphere. Optimization procedures with respect to optimum mechanical and thermal properties are possible by variation of the following parameters (Hegeler and Bruckner, 1989, 1990): First, thermal and mechanical treatment - an optimum is at about 1250 °C for DURAN glass (viscosity around 10 4 dPas), at a pressure of lOMPa. Second, the fiber content - for which an optimum also exists at a volume concentration of about 50%. Third, the forces acting between fibers and matrix - chemical and mechanical forces. Optimum values for flexural strength and toughness are obtained if these forces are neither too low nor too high. If on the one hand the contact between fibers and matrix is too high, e.g., for a strong chemical bonding, the strength will be moderate and the toughness will be low; if on the other hand the forces are too low, the strength will be also very low and toughness will be good. The best effect will be produced in between, for which the thermal expansion mismatch, as well as the condition of the interfacial layer of fiber and glass matrix, are important. The thermal expansion mismatch is responsible for the stress (with its three components - radial, axial and circumferen-

698

13 Mechanical Properties of Glasses

cial), between fibers and glass matrix, and primarily determines, together with the hot-pressing pressure, the strength of the composite. In addition to, the friction coefficients, the adhesive and gliding friction coefficient, between the two components of the composite determine not only the strength but also the toughness. This influence is determined largely by the interface composition and properties (Hegeler and Bruckner, 1990). It was found that a thin carbon layer (Brennan, 1988) is very advantageous for a good (not too low and not too high) adhesion to optimize the socalled pull-out effect (Fig. 13-31), which should neither be too large nor too small. If no pull-out effect is observed after fracture, the composite is usually brittle. Much more investigation has to be done to optimize the interfacial layers (see also Vol. 13, Chaps. 7 and 11). Some typical results are presented here. Fig. 13-32 is an example of the stress-strain behavior for two composites. The high strength and the large work of fracture (integral over the stress-strain curve) are remarkable compared with those of a usual bulk glass. The effect is tremendous, an increase in strength by a factor of up to more than 10, and an increase in Klc values by a factor up to more than 30 are possible. The great disadvantage of low strength perpendicular to the fiber orientation may be overcome by a layered structure, e.g. by 0o/90° cross-ply composites. Figs. 13-33 a and b show the strength of composites with unidirectionally and bidirectionally oriented SiC-fibers versus the angle of loading. In Fig. 13-33 a it is noteworthy that no decrease in strength is reached before 30°, and in Fig. 13-33b a reduction in strength of only 30% occurs at 0° and 90°, compared with 0° in Fig. 13-33 a. The anisotropic strength decrease is only 100 MPa at 45°.

pull out

delaminafion of fibers crack fiber fractures

Figure 13-31. Pull-out effect of a fiber-reinforced glass composite, schematically.

1200

900-

45vot.%>

bulk glass MPa 100

U 0

0.1 %

600-

300-

0.2

0.4

0.6

0.8

1.0

1.2

Strain in % Supremax glass/SiC fibers

Figure 13-32. Stress-strain diagrams of SUPREMAX glass/SiC-fiber composites with 40 and 45 vol% fiber content compared to that of bulk glass (inserted figure).

13.6 Mechanical Behavior Above the Glass Transition Temperature While the tensile and flexural strength of glasses is primarily a surface property which depends on the most severe flaws at the surface and which is valid within the pure elastic and brittle region of glasses, the question arises as to what happens with the characteristic mechanical properties if viscoelastic and viscous influences become

13.6 Mechanical Behavior Above the Glass Transition Temperature

600-

Bending strength

^00-

200-

0

(a)

30 60 90 Loading angle a indegrees —•»-

600-

400-

t

Bending strength

200Shear strength

I 0

(b)

30 60 90 —Loading angle oc in degrees-—••

Figure 13-33. Bending and shear strength of a DURAN glass/SiC-fiber composite with unidirectionally oriented fibers (a) and of a composite with 0°/90° crossply oriented fibers (b) versus loading angle a; 40 vol% fiber content each.

more and more dominant with increasing temperature around and above Tg, a question which is also of great importance for practical forming processes. 13.6.1 High-Temperature Strength 13.6.1.1 High-Temperature Strength as a Surface Property

If the flexural strength of a commercial silicate glass is measured at elevated tem-

699

peratures, the influence of different stress rates on the strength becomes more and more pronounced. At temperatures above r g , a strongly temperature-dependent critical deformation rate can be identified as a necessary condition for brittle fracture at small bending deflections which are well within the linear elastic theory (Manns and Bruckner, 1983). This critical deformation rate may be taken as a limiting criterion as between plastic-viscous (or visco-elastic) and brittle-elastic behavior of the supercooled glass melt (Fig. 13-34). Strength measurements on glass plates using the double ring method within the brittle-elastic region, where the linear elastic theory is still valid, are shown in Fig. 13-35 for a commercial borosilicate glass with original surfaces versus temperature. A steep increase in bending strength occurs around Tg and above. In order to be able to measure bending strength up to the Littleton temperature (where rj = 10 7 6 dPas), sufficiently large deformation or strain rates have to be applied, characterized by the rate-dependent values of the elastic modulus E* = 25 or 40 GPa. A possible interpretation of the results of Fig. 13-35 is that viscous flow within surface cracks, and particularly at the crack tips, takes place and leads to a blunting of the crack tip and therefore to an increase in strength. As will be seen from Sec. 13.6.3, even non-Newtonian flow (decrease of normal viscosity under high deformation rates and stresses) has to be considered under the applied stresses and strain rates. 13.6.1.2 High-Temperature Strength as a Volume Property

A totally different kind of high-temperature fracture and strength was found recently, which is not a surface property but

700

13 Mechanical Properties of Glasses

600

Figure 13-34. Curve of minimum deformation rate for the brittle bending fracture of float glass plates (double ring method). As received surfaces are plotted versus temperature with the restriction that the bending of the plate at fracture is smaller than the plate thickness. The symbols indicate the applied deformation rates for the strength measurements, characterized by the observed apparent (that means rate-dependent) elastic moduli £* in GPa.

700

650 Temperature in °C

300/

I / / o

• o -- 2MPa/s o E* < 25 a E*^40

250-

a/

a/

2001

1°

/ a T 9 5 % confidence

-t

i

limits of mean

100-

0

100

200

Flow range

0.4

0.8

1.2

Figure 13-35. Bending strength of borosilicate flat glass plates with as received surfaces versus temperature at various loading rates, characterized by £*. (J): strength of annealed samples.

300 400 Temperature in °C

first crack

0

-

a

o

150-

o

1.6

2.0

2.4

2.8

3.2

Axial compressive deformation in mm

3.6 — •

Figure 13-36. Typical force-deformation diagram of a compressed cylindrical glass sample (DGG standard glass I, T = 658 °C, s = 8 mm/s) with viscoelastic range, viscous flow range and situation of the first macrocrack at the equator-line of the deformed cylinder.

a volume property. Starting from simple experiments in which a glass cylinder is compressed between the pistons of a universal servo-hydraulic test machine at different deformation rates, the response of the glass sample above Tg is a curve like that in Fig. 13-36 at a moderate rate. After the viscoelastic and flow range has been passed, the first axial macro-crack appears at the equator line of the deformed cylinder. The tensile strength of the specimen can be calculated from the values of the stress strain curve (Hessenkemper and Bruckner, 1989). Results are given in Fig. 13-37, where the tensile strength is plotted

13.6 Mechanical Behavior A b o v e the Glass Transition Temperature

701

Figure 13-37. High-temperature tensile strength for various glass melts versus axial compressive stress at constant Newtonian equilibrium viscosity rj0 = 10 8 Pas and in one case also at t]0 = 10 12 Pas. 100 200 300 400 500 - A x i a l compression stress in MPa — » -

versus the axial compressive stress for various silicate glasses at constant Newtonian equilibrium viscosity r\0 = 10 8 Pas, and in one case also at rj0 = 10 1 2 Pas. There are differences in the tensile strength values of up to 300% depending on the composition of the glasses, which are given in Tables 13-2 and 13-3. The temperature dependence of the high-temperature tensile strength is seen from the glass containing CaO-MgO, with 4 and 8 mol%, respectively, as an example (Fig. 13-37): the strength decreases by 60 MPa when the temperature is changed from 557 to 697 °C or the viscosity from 1012 to 10 8 Pas. The increasing strength with increasing axial compressive stress in Fig. 13-37 is interpreted as a load-dependent change of structure of the glass melts and agrees with both stress-dependent relaxation behavior (see Sec. 13.6.2) and non-Newtonian flow behavior (see Sec. 13.6.3). It is remarkable that high-temperature tensile strength within the viscous flow range is a volume property, as was shown by Hessenkemper and Bruckner (1989). While surface-dependent strength values within the brittle and viscoelastic range are connected to a relatively high variation of 30% and more, which is typical for statisti-

cally acting surface influences, the variation of the tensile strength values within the viscous range is only around 5% and the fracture strength values are strictly independent of the surface roughness. 13.6.2 Non-Linear Relaxation Behavior

When glass melts are treated in such a way that the stress limit of fracture is reached the relaxation behavior will no longer be linear. This was shown by Hessenkemper and Bruckner (1989, 1990 a) in numerous experiments. The main results of these investigations are shown in Figs. 13-38 a and b, where the relaxation modulus E(t)max is plotted versus the deformation rate, h, of a compressed glass cylinder within the viscoelastic range (Fig. 13-38), and for various glass melts and at various equilibrium viscosities, rj0. The large differences in E (Omax n o t o n ly between different viscosities, rj0, but also between the various compositions of the glass melts (see Tables 13-2 and 13-3) are evident. The relaxation modulus increases with h and with increasing viscosity. Of special interest is that the shift factor of the Wiliams-Landel-Ferry equation is no longer constant above 20 MPa axial compressive stress, <7ax, but decreases with

702

13 Mechanical Properties of Glasses

Table 13-2. Compositions and properties of industrial glasses. Borosilicate glass

SiO 2 B2O3 A12O3 Na 2 O K2O MgO CaO BaO ZnO Sb 2 O 3 SO 3 Sum Tg in °C a in l O ^ K " 1 E in GPa G in GPa Density Q in g/cm3

Float glass

Optical glass

in mol%

in wt.%

in mol%

in wt.%

in mol%

in wt.%

81.8 8.8 1.8 5.0 1.5 1.1 -

80 10 3 5

73.0

69

70.1

71.3

0.35 13.3 0.02 5.9 10.1

0.6 14 0.03 4.0 9.6

0.22

0.31 99.84

1 1

8.2 6.1 9.1 0.8 2.7 0.1

100

100 550 3.25 59 25 2.226

2 3.5 0.5

546 8.96 73 32 2.495

529 9.35 64.5 26 2.565

Table 13-3. Compositions and properties of glasses with exchanged CaO/MgO contents. Glass no. 1

SiO 2 A12O3 Na 2 O K2O MgO CaO Sb 2 O 3 Tg in °C a in 10" 6 K~ 1 (100 to 200 °C) E in GPa G in GPa Density Q in g/cm3

Glass no. 2

Glass no. 3

in mol%

in wt.%

in mol%

in wt.%

in mol%

in wt.%

74 1.5 12 0.5 O0 12

73.33 2.52 12.27 0.78 0.00 11.1 0.5

74 1.5 12 0.5 4 8

74.11 2.55 12.4 0.78 2.68 7.48 0.5

74 1.5 12 0.5 8 4

74.5 2.58 12.53 0.79 5.42 3.77 0.5

565 8.7 75 31 2.52

increasing aax (Hessenkemper and Bruckner, 1990 a). As a result, above this loading limit thermorheological simplicity (Ferry, 1970; Kurkjian, 1963; Mills and Sievert, 1973) is not achieved, relaxation behavior is load- and/or rate-dependent, and the re-

547 8.25 72 30.5 2.479

548 7.6 71 30.5 2.45

laxation time T at a constant temperature or constant equilibrium viscosity, rj0, is no longer a constant but depends on the deformation rate, h (Fig. 13-39). This means that relaxation processes are faster under load than without load.

13.6 Mechanical Behavior Above the Glass Transition Temperature

- 2 - 1 (a)

0

703

1

•Deformation r a t e : log h',K in m r n / s -

a 32-

/

Q_

ID

/glass 3

/

24-

no^O12Pas

glass 3 Pas

16/

8^

-3 (b)

^^--^glass 1 ^ no-1O12 Pas

/

/ /

7

glass 1 vio

8

Pa^

Figure 13-38. Relaxation modulus versus axial deformation rate of the samples, lg/i, at various equilibrium viscosities, rj0; a) optical glass, b) glasses no. 1 and 3 (see Table 13-3).

-2 -1 0 1 Deformation rate : log h, h in mm/s

h in mm/s

Figure 13-39, Relaxation time, T, of an optical glass melt versus deformation rate, h, at a Newtonian equilibrium viscosity rj0 = 10 8 Pas.

Another point of interest is that a correlation between the relaxation modulus and the high-temperature tensile strength exists: the larger the relaxation modulus the lower the ht-tensile strength and vice versa (compare Figs. 13-38 a and b with Fig. 13-37!). In this way a clear definition for the brittleness of a glass melt is given which has important consequences for the concept of workability of a glass melt in glass forming processes (Hessenkemper and Bruckner, 1990 b).

704

13 Mechanical Properties of Glasses

to 1 0 1 4 > ^ 0 > 2 • 10 5 Pas, where special care was taken to eliminate the heating effects of dissipated mechanical energy (Hessenkemper and Bruckner, 1988). At high deformation rates the observed stressstrain curves (see, e.g. Fig. 13-36) exhibit a pronounced temporary stress maximum. The measured data reveal a continuous decrease in glass viscosity during pressing at high pressing rates of more than a factor of 10 compared with the Newtonian values (Fig. 13-40). These data agree very well with the above-mentioned data obtained by the fiber elongation method in comparable ranges. The enhanced fluidity of the glass melt is explained mainly by structure-viscous flow behavior produced by a load-dependent alteration of the structure of the glass melt in connection with orientation, at least with anisotropic effects. The phenomenon of non-Newtonian flow behavior increases clearly with increasing temperature at constant axial

13,6.3 Non-Newtonian Flow Behavior

In this section the well-known effects of time-dependent viscosity due to thermal non-equilibrium processes (see, e.g., Chap. 3 of this volume and Scherer, 1986; Rekhson, 1986) are excluded and only load-dependent viscosity effects will be regarded. The first measurements of non-Newtonian flow behavior of silicate glasses were done by Li and Uhlmann (1970) at constant tensile stresses and by Simmons et al. (1982) at constant tensile strain rates using the fiber elongation method. These measurements are restricted to the (Newtonian) viscosity ranges 1 0 1 6 > ^ 0 > 1 0 1 2 5 P a s and 10 13 >77 0 >10 10 Pas. Studies of glass cylinders under compressive stresses with a parallel plate plastometer have also been made under nonNewtonian flow conditions, first in the range of 1011 >rj0 > 1 0 8 3 Pas (Manns and Bruckner, 1988), which was then extended

o-~o

0,2-

T581 •

"5, 0.6-

' \

T*

u*

O i l

.629 a 634 • 648

o

-1

\

v 596

^ 0,4
Figure 13-40. Viscosity of a float glass melt normalized by the Newtonian equilibrium viscosity, r\0, versus axial compression rate at various temperatures; a) normalized initial viscosity, igrjJrjQ, at the beginning of the compression process; b) normalized final viscosity, lgrjf/fj0, at the end of the compression process or at the moment of the first crack occurrence.

o657

1.00i

° OA

-

0.8

b)

-*v-*^

3 in °C: • 581 v596 A 611 . 629 • 634 • 648 o 657

\

\

\ \ V \ \D^ N

A\

1

\

1210"

10'

10"

10"

Axial compression rate e in s"

10

13.7 Further Properties

compressive stresses. This effect is similar to the increasing birefringence and shrinkage of glass fibers at To with increasing fiber drawing temperature at constant drawing stress (see Sec. 13.3.3). It also confirms that the isotropic structure of a glass melt changes to an anisotropic and even to an oriented structure under high enough load, which influences not only the flow behavior but also the relaxation behavior (see Sec. 13.6.2) and the high-temperature tensile strength (see Sec. 13.6.1.2) in the manner described. Up to what temperature does this increasing effect continue? Is there a limit, and what kind of limit - a saturation or a maximum? The answer is given by flow birefringence measurements of various melts, e.g. borate, sulphide and metaphosphate melts, which indicate maxima of the specific birefringence (zlft/stress)at viscosities between about 104 to 102 Pa s, a region at which the fiber drawing process is possible (Bruckner, 1987). Thus, at temperatures below this maximum the anisotropic and orientation effect increases and above this maximum it decreases with rising temperature.

13.7 Further Properties 13.7.1 Microhardness 13.7.1.1 Indentation Process and Phenomena

The term microhardness is occasionally called diamond indentation hardness. Two different diamond tools may be applied: the Vickers diamond, which is a regular pyramid with a peak angle of 136°, and the Knoop diamond, which is an elongated rhombus pyramid with angles of 172.5° and 130° at the diamond peak. The two

705

microhardnesses are given by Eq. (13-32): MHV= 0.1855 F/d2 and MHK = 1.4233 F/d2

(13-32)

where F is the load in N, and d the diagonal line in mm. In the case of the Knoop diamond, d is the longer diagonal line of the indentation. The microhardness is obtained then in 10 7 N/m 2 or lOMPa. The diamond penetrates into the glass until the load is compensated by the increasing contact area. This process is a combination of elastic and plastic deformation of the glass as long as no cracks at the edges are produced. If no elastic component is acting, the microhardness should be independent of the load, F But this is not the case: it increases with decreasing load due to elastic springback at the moment when the sample is unloaded. If, as is usual, the indentation is observed after loading, one has to regard and evaluate the so-called springback value, c, in Eq. (13-33) MHKcorr, = 1.4233 F/(d + c)2

(13-33)

in which c as well as MHKcorr are really load-independent values as was shown by Kranich and Scholze (1976), but c depends on moisture. It decreases with increasing relative humidity and increasing loading time. This was also found by Hirao and Tomozawa (1987). Water penetratres into the stressed glass surface during the measurement and increases the plastic component of the deformation process. In order to avoid the elastic springback effect, which is about 50% at the peak, measurements of d have been made under load by observation through the glass sample from below (Kranich and Scholze, 1976; Michels and Frischat, 1982) or by measuring and recording the indentation depth (Frohlich et al., 1977, 1979; Weiss, 1987). However, the elastic components

706

13 Mechanical Properties of Glasses

are not totally eliminated by this method because both the glass and the diamond react elastically under load. In this respect, the experiments of Bartenev et al. (1969) are of interest, because the plastic deformation is also related to a densification of the glass (Ernsberger, 1968) in a way similar to permanent densification, as was treated in Sec. 13.2.2.1. Bartenev et al. annealed the glass sample after the indentation process and showed that small indentations are healed completely, whereas large indentations lead to smaller ones which show at the border of the indentation elevations. This indicates a very complicated flow and densification process on which more research needs to be done. 13.7.1.2 Influence of Chemical Composition

The indentation process is at least partly a deformation or flow process which is comparable as a first approximation with the Newtonian, or (according to Douglas 1958), with a non-Newtonian viscosity at low temperatures. Therefore, it is expected that alkali oxides, as substitutes for SiO 2 , decrease (Fig. 13-41) and CaO, MgO, ZnO, B 2 O 3 and A12O3 increase the microhardness. This was confirmed by Ainsworth (1954) with MHV and by Kennedy et al. (1980) with MHK measurements. Besides

the viscosity, a certain connection to the polarizability of the various components may be appropriate for interpretation of these results (Petzold et al., 1961). In this way there seems to be a parallel also to the elastic constants (see Sec. 13.2.1.2), particularly the compressibility. It is understandable that OH groups in glasses reduce microhardness as well (Sakka et al., 1981; Takata et al., 1982). The mentioned relation to the elastic constants was treated by Yamane and Mackenzie (1974), who treated the microhardness (MH) as the resistance against elastic and plastic deformation and densification, as given by the expression MH « 19(a GK) 1/2 , where a is the thermal expansion coefficient, and G and K the shear and compression moduli, respectively. Bartenev and Sanditov (1982) deduced the relation between MH and the elastic constants Young's modulus £ and Poisson ratio ix\ MH = (1 - 2 p)E/[G (1 + //)] which is a rough estimation that the MH is about 6 to 10% of the Young's modulus of a glass. Last but not least, Kerkhof and Schinker (1972) found the relation between the MH and the flow stress, which is proportional to the molecular strength expressed by the equation: H ~ v^gy/f)112 in which vl is the longitudinal sound velocity, Q the density, y the surface energy, and f the mean atomic distance. 13.7.1.3 Temperature Dependence and Thermal Prehistory

10

20

30

R 2 0 in mol. %

•

Figure 13-41. Knoop microhardness of binary alkali silicate glasses (Kennedy et al., 1980).

The microhardness of glasses decreases with increasing temperature in a similar way as bonding strength and viscosity. The trend of the temperature dependence is shown in Fig. 13-42 for silica glass and for a sodium calcium silicate glass (Westbrook, 1960). Therefore, if a state of higher

13.7 Further Properties 1000

£

750-

500-

x

250-

-200

\ / S i O 2 -glass

Na-Ca-silicate glass

0 400 Temperafure in °C

\

800

Figure 13-42. Temperature dependence of Vickers microhardness (Westbrook, 1960).

temperature is frozen-in, as in the case of a tempered glass, the microhardness will be lower than that of an annealed glass because the structure of a tempered glass is more open (larger specific volume) than that of an annealed one. Attention should be paid to the elastic springback effect which will be much larger if the surface of the glass sample is under compressive stress (Kranich and Scholze, 1976). Therefore such measurements have to be done under load (see Sec. 13.7.1.1). Hara and Kerkhof (1962) have shown that the microhardness of tempered glass is about 4% lower than that of annealed glass.

707

nary borate and silicate glass is given in Fig. 13-43. For more details concerning C and chemical composition see Chap. 12 of this volume. In the present section the stress-optical coefficient will be regarded as a tool to measure stress distributions in glasses. The essence of all stress-optical methods is to conclude from the relative path difference, 3 = AndjX {X = wavelength of light), and from the known stress-optical coefficient, C, the difference between the principal stresses, which is equal to twice maximum shear stress. Two cases have to be distinguished: a) the stress differences are so large that they can be made visible by isochromates: S = N = ±1, ±2, ± 3 , etc., where N is the interference order, and b) the stress differences are so small that the corresponding path differences can be compensated and measured by compensators: (5 < + 1. The situation for silicate glasses is such that a tensile stress of (T^lOON/mm 2 ^

13.7.2 Stress-Optical Coefficient 13.7.2.1 Stress-Optical Coefficient within the Elastic Range of Glass

The stress-optical coefficient, C, is defined by the well-known linear connection between stress difference, Aa, and birefringence, An: An = 3/d = CAa, where 3 is the path difference and d the geometric length of the light beam through the glass. It is also called the photoelastic or the Brewster constant (1 Brewster = 10~ 6 mm 2 /N) and is a value which is characteristic for a glass composition. The range of C is from about — 3 to -1-5 Brewster. An example for bi-

10 20 30 40 R 2 0 in mol. % - » -

Figure 13-43. Stress-optical coefficient, C, of binary alkali borate and alkali silicate glasses according to Matusita et al. (1984 a, b), composed by Scholze (1988).

708

13 Mechanical Properties of Glasses

1000 kp/cm2 ^100 MPa (a2 = 0) for a sheet glass of 2 mm thickness has to be applied to produce a path difference of 5 = 1, i.e., to produce the first isochromate. This stress is of the order of magnitude of the strength of bulk glasses. Therefore it is more suitable to use model materials such as polymers (Araldite B) in order to determine stress distributions in certain constructions, at cracks, edges or holes, because these materials have much larger Brewster constants (25 to 55) than silicate glasses (about 3). In this way (see case b) it is necessary to use a polarizer and an analyzer (e.g. "crossed Nicols") or a polarizing microscope with a Berek compensator, a Babinet or a Brace-Kohler compensator in order to determine the path difference, S (Kerkhof, 1980). With the help of a X/A plate it is possible to distinguish between tensile and compressive stress by the color change from the red of first order to blue or yellow. Besides pure mechanical stresses produced in glasses by external forces, other stresses, such as temporary and permanent thermal stresses, stresses produced by flaws and crystalline inclusions in glasses with different thermal expansion coefficients are also important.

£ 3.4-

I & 3.3-

I 3.2S

13.7.2.2 Stress-Optical Coefficient within the Viscoelastic Range

The stress-optical coefficient depends on temperature because the polarizability is also temperature dependent. From room temperature to Tg this dependence is small (about 7%, van Zee and Noritake, 1958), but at and above Tg this dependence is very large and time or rate dependent (Manns and Bruckner, 1981), thus, there is a certain influence of thermal prehistory. Figs. 13-44 a and b show the stress-optical coefficient as a function of temperature at various load velocities within the viscoelastic range of two glasses, a commercial colorless sodium calcium container glass and a laboratory glass of the same composition in which Na 2 O is substituted by K 2 O. The lower the stress rate, the larger is C. This particular stress rate dependence is illustrated particularly in Figs. 13-45 a and b for the same two glasses (Manns and Bruckner, 1981). The conclusions which may be drawn from these results are that, first, the K 2 O containing glass generally shows the larger C-values due to the larger polarizability. Second, the large temperature coefficients

Q) container glass (Na) + 1 MPas"1 • 10 MPas"1 x 100 MPas"1 o 500 MPas~1

Figure 13-44. Temperature dependence of the stress-optical coefficient of a commercial Na-Casilicate container glass (Na); a), and of a modified K-Ca-silicate glass (with K 2 O as substitute for Na 2 O), (K); b), at various stress rates.

31.

"5 £ 3.0o

g 2.9 500

Tg 600

500

Temperature in °C

600

Tg 700

13.8 References

709

flow by which an anisotropic effect or even an orientation effect will be produced. This mechanism is similar to effects which are described in Sec. 13.6.2 and is also similar to flow birefringence (Wasche and Bruckner, 1986a, b, 1987; see also Bruckner, 1987).

13.8 References

3.1-

N 638,9 © 628.7 • 608.9 • 589,3

3.0

10-

10Z 10 • Stress rate o in MPas"-

10°

103

Figure 13-45. Stress-optical coefficient versus stress rate for the two glasses (Na) and (K) at various temperatures, a) industrial container glass, (Na), b) modified container glass (K); see Figs. 13-44 a and b.

C of the glasses above Tg may be interpreted to be due to a thermally induced depolymerization of the glass network (reversible network splitting and reconnecting process), the mechanism for which is the statistical network splitting effect (bond opening) which increases with rising temperature and vice versa. It is also a mechanism for the statistical network closing effect (bond connection), which increases with decreasing temperature; thus, in total it is a matter of a bond switching process. Third, under the influence of mechanical stresses, the network fragments and ions need a certain time interval in order to change energetically into other positions than those of the unstressed state. This is related to viscous, or better viscoelastic,

Acloque, P., Le Clerc, P., Ehrmann, P. (1960), Compte Rendu du Colloque U.S.C.V. sur la Nature des Surfaces Vitreuses Polies. Charleroi: Union Scientifique Continental du Verre, pp. 43-63. Adams, R., McMillan, P. W. (1977), /. Mater. ScL 12, 2544-2546. Ainsworth, L. (1954), /. Soc. Glass Techn. 38, 479547. Anderegg, F. O. (1939), Ind. Eng. Chem. 31, 290-298. Andrade, E. N., Tsien, L.C. (1937), Proc. Roy. Soc. A159, 346-354. Appen, A. A., Kozlovskaya, E.J., Fu-Si, H. (1961), J. Angew. Chemie UdSSR 34, 975-981. Bando, Y, Ito, S., Tomozawa, M. (1984), J. Am. Ceram. Soc. 67, C36-37. Bartenev, G. M. (1968), /. Non-Cryst. Solids 1, 6 9 90. Bartenev, G. M., Rasumowskaja, J. W, Sanditow, D.S. (1969), Silikattechn. 20, 89-93. Bartenev, G.M., Sanditov, D.S. (1982), /. NonCryst. Solids 48, 405-421. Blank, K., Griiters, H., Hackl, H. (1990), Glastechn. Ber. 63, in print. Bradt, R.C. (Ed.) (1974-1986), Fracture Mechanics of Ceramics. New York, London: Plenum Press, Vol. 1 (1974) to Vol. 8 (1986). Brennan, J. J. (1988), Journal de Physique Colloqu. C5 Supplement no. 10, 49, C5 791-809. Bridgman, P. W, Simon, J. (1953), J. Appl. Phys. 24, 405-413. Bruckner, R. (1987), J. Non-Cryst. Solids 95 and 96, 961-968. Bruckner, R. (1990), in: Uhlmann, D. R., Kreidl, N. (Ed.): Glass Science and Technology, Vol.9, 3 3 118. Charles, R. J. (1958), J. Appl. Phys. 29, 1549-1560. Charles, R. J. (1961), in: Progress in Ceramic Science: Burke, I E . (Ed.). Oxford etc., Pergamon, Vol. 1, pp. 1-38. Chermant, J. L., Osterstock, R, Vadam, G. (1979), Verres Refract. 33, 843-857. Coenen, M. (1961), Z. Elektrochem. 65, 903-908. Coenen, M. (1983), Glastechn. Ber. 56, 188-195. Coenen, M., Amrhein, E. M. (1961), Compte Rendu du Symposium sur la resistance mechanique du

710

13 Mechanical Properties of Glasses

verre, Florence, 529-550. Compte Rendu; Union Scientifique Continentale du Verre, 24 Rue Dourlet, Charleroi, Belgique. Cohen, H. M., Roy, R. (1961), /. Am. Ceram. Soc. 44, 523-524. Cottrell, A.H. (1964), The Mechanical Properties of Matter. New York, Wiley, 430 p. Dannheim, H., Oel, H.J. (1983), in: Festigkeit keramischer Werkstoffe. DFG (Ed.), Deutscher Verband fur Materialpriifung, e.V., Berlin 87, pp. 17-32. Davidge, R. W. (1979), Mechanical Behaviour of Ceramics. Cambridge, London, New York: Cambridge Univ. Press. Day, D.E., Rindone, G. (1962), J. Am. Ceram. Soc. 45, 496-504. Deeg, E. (1958), Glastechn. Ber. 31, 1-9, 85-93, 124-132, 229-240. DeGuire, M.R., Brown, S.D. (1984), J. Am. Ceram. Soc. 67, 210-213. Dietzel, A. (1981), Glastechn. Ber. 54, 49-51. Doremus, R.H. (1973), Glass Science. New York: Wiley. Doremus, R.H. (1983), J. Appl. Phys. 54, 193-198. Doremus, R.H. (1982), in: Treatise on materials science and technology: Tomozawa, M., Doremus, R.H. (Ed.). New York, San Francisco, London: Academic Press, Vol. 22, pp. 169-239. Douglas, R. W. (1958), /. Soc. Glass Technol. 42,145157. Ernsberger, F. M. (1962), Advances in Glass Technology, New York: Plenum Press, pp. 511-524. Ernsberger, F. M. (1968), /. Am. Ceram. Soc. 51, 545547. Ernsberger, F.M. (1977), /. Non-Cryst. Solids 25, 295-321. Evans, A.G. (1974/78), in: Fracture Mechanics of Ceramics. New York, London: Plenum Press, Vol. 1 (1974), pp. 17-48; Vol. 3 (1978), pp. 31-49. Fabes, B. D., Doyle, W E , Zelinski, J.J., Silverman, L. A., Uhlmann, D. R. (1986), J. Non-Cryst. Solids 82, 349-355. Ferry, I D . (1970), Viscoelastic Properties of Polymers. 2nd ed., New York, London, Sydney: Wiley. Fitzgerald, IV. (1951), J. Am. Ceram. Soc. 34, 314319, 339-342, 388-391. Freiman, S. W (1980), in: Glass: Science and Technology. New York, London: Academic Press, Vol. 5, pp. 21-78. Freiman, S.W, White, G. S., Fuller, E. R. (1985), J. Am. Ceram. Soc. 68, 108-112. Frohlich, E, Grau, P., Grellmann, W. (1977), Phys. stat. solidi (a) 42, 79. Frohlich, E, Grau, P., Grellman, W. (1979), Wiss. Ztschr. Friedr. Schiller Universitat Jena, Math.Nat. R. 28, 449-463. Galyant, V.I, Primenko, V.I (1978), Glass Ceram. USSR 35, 14-15. Gardon, R. (1980), in: Glass: Science and Technology, Vol. 5, Elasticity and Strength in Glasses: Uhl-

mann, D. R., Kreidl, N. I (Eds.). New York: Acad. Press, pp. 145-216. Gehrke, E., Hahnert, M., Ullner, Ch. (1986), /. NonCryst. Solids 80, 269-276. Gora, P., Kiefer, W, Sack, W, Seidel, H. (1977), Glastechn. Ber. 50, 319-327. Griffith, A. A. (1920), Phil. Trans. Roy. Soc. (Lond.) A221, 163-198. Hagy, H.E., Ritland, H.N. (1957), /. Am. Ceram. Soc. 40, 436-442. Halleck, P. M., Pacalo, R. E., Graham, E. K. (1986), /. Non-Cryst. Solids 86, 190-203. Hasegawa, H., Nishihama, K., Imaoka, M. (1972), /. Non-Cryst. Solids 7, 93-102. Hegeler, H., Bruckner, R. (1989), /. Mater. Sci. 24, 1191-1194. Hegeler, H., Bruckner, R. (1990), J. Mater. Sci. 25, 4836-4846. Hegeler, H., Reich, Ch., Bruckner, R., Pannhorst, W (1989), Patent Schott Glaswerke, P 3731650. Hessenkemper, H., Bruckner, R. (1988), Glastechn. Ber. 61, 312-320. Hessenkemper, H., Bruckner, R. (1989), Glastechn. Ber. 62, 399-409. Hara, M., Kerkhof, E (1962), Rep. Asahi Glass Comp. Res. Lab. 12, 99-104. Hessenkemper, H., Bruckner, R. (1990 a), Glastechn. Ber. 63, in print. Hessenkemper, H., Bruckner, R. (1990b), Glastechn., Ber. 63, in print. Hillig, WB. (1962), in: Modern Aspects of the Vitreous State. Mackenzie, I D . (Ed.), London, Butterworths. Vol. 2, pp. 152-194. Hillig, W.B., Charles, R . I (1965), in: High strength materials: Zackay, V. E (Ed.). New York: Wiley, pp. 682-705. Hirao, K., Tomozawa, M. (1987), /. Am. Ceram. Soc. 70, 43-48. Holloway, D.G. (1986), Glass Technol. 27, 120-133. Hood, H.P., Stookey, S.D. (1957), US Pat. 2,779, 136. Irwin, G.R. (1958), Fracture, in: Handbuch der Physik, Bd. 6. Fliigge, S. (Ed.). Springer, Berlin, Gottingen, Heidelberg, pp. 551-590. Jakus, K., Coyne, D. C , Ritter, I E . (1978), /. Mater. Sci. 13, 2071-2080. Kennedy, C. R., Bradt, R. C , Rindone, G. E. (1980), Phys. Chem. Glasses 21, 99-105. Kerkhof, F. (1963), Naturwiss. 50, 565-566. Kerkhof, E (1970), Bruchvorgdnge in Gldsern. Frankfurt/M., Deutsche Glastechn. Gesellschaft. Kerkhof, E (1980), Bruchentstehung und Bruchausbreitung, in: Glastechn. Fabrikationsfehler: JelsenMarwedel, H., Bruckner, R. (Ed). Berlin, Heidelberg, New York: Springer, pp. 523-587. Kerkhof, E (1983), in: Ceramic Monographs - Handbook of Ceramics, Schmid-Verlag GmbH, Freiburg i. Br., FRG, pp. 1-13. Kerkhof, E, Richter, H. G. (1987), Sprechsaal 120, 430-437, 659-667.

13.8 References

Kerkhof, R, Schinker, M. (1972), Glastechn. Ber. 45, 228-233. Kerkhof, R, Richter, H.-G., Stahn, D. (1981), Glastechn. Ber. 54, 265-277. Kerper, M. X, Scuderi, T. G. (1964a), Proc. Am. Soc. Test. Mat. (ASTM) 64, 1073-1143. Kerper, M. X, Scuderi, T. G. (1964b), Bull. Amer. Ceram. Soc. 43, 622-625. Kirby, P. L. (1953), /. Soc. Glass Technol. 37, 7-26. Kirby, P.L. (1954), J. Soc. Glass Technol. 38, 383420. Kirby, P. L. (1957), J. Soc. Glass Technol. 41,95-116. Kozlovskaya, E.X (1959), in: The Structure of Glass: Vol. 2. Porai-Koshits, E. A. (Ed.), pp. 299-301. Kranich, X R, Scholze, H. (1976), Glastech. Ber. 49, 135-143. Kruithof, A.M., Zijlstra, A. L. (1959), Glastechn. Ber. 32K, 111/1-6. Kurkjian, C. R. (1963), Phys. Chem. Glasses 4, 128136. Kurkjian, C.R. (1985), NATO Conference Series, 6. Material Science, Vol. 11: Strength of Inorganic Glasses. New York: Plenum Press. Kurkjian, C.R., Krause, XT., Paek, U.C. (1982), /. Physique 43, Suppl. 12, Coll. C9, 585-586. LaCourse, W. C. (1972), in: Introduction in Glass Science: Pye, L.D., Stevens, H.X, LaCourse, W.C. (Eds.). New York, London: Plenum, pp. 451-512. Lawn, B.R. (1983), J. Am. Ceram. Soc. 66, 83-91. Lawn, B.R., Wilshaw, T.R. (1975), Fracture of Brittle Solids, 2nd ed.: Lawn, B.R. (1992). Cambridge: Cambridge University Press. Lawn, B.R., Jakus, K., Gonzales, A.C. (1985), J. Am. Ceram. Soc. 68, 25-34. Levitt, S.R. (1973), J. Mater. Sci. 8, 793-796. Li, X H., Uhlmann, D. R. (1970), /. Non-Cryst. Solids 3, 127-147, 205-224. Livshits, V. Ya. et al. (1982), Sov. J. Glass Phys. Chem. 8, 463-468. Mackenzie, X D. (1963), /. Am. Ceram. Soc. 46, 461 476. Mackenzie, XD. (1964), J. Am. Ceram. Soc. 47, 76-84. Makishima, A., Mackenzie, XD. (1973), /. NonCryst. Solids 12, 35-45. Makishima, A., Mackenzie, XD. (1975), /. NonCryst. Solids 17, 147-157. Manns, P., Bruckner, R. (1981), Glastechn. Ber. 54, 319-331. Manns, P., Bruckner, R. (1983), Glastechn. Ber. 56, 155-164. Manns, P., Bruckner, R. (1988), Glastechn. Ber. 61, 46-56. Marsh, D. M. (1964), Proc. Roy. Soc. A279,420-435. Matusita, K., Yokota, R., Kimijima, T., Ihara, Ch. (1984a), J. Am. Ceram. Soc. 67, 261-265. Matusita, K., Ihara, Ch., Komatsu, T., Yokota, R. (1984b), J. Am. Ceram. Soc. 67, 700-704. Maurer, R.D. (1977), Appl. Phys. Lett. 30, 82-84.

711

McGraw, D.A. (1952), /. Am. Ceram. Soc. 35, 22-27. Michalske, T.A., Freiman, S.W. (1983), /. Am. Ceram. Soc. 66, 284-288. Michels, B.D., Frischat, G. H. (1982), /. Mater. Sci. 17, 329-334. Mills, X X, Sievert, X L. (1973), J. Am. Ceram. Soc. 56, 501-505. Mould, R.E., Southwick, R.D. (1959-1961), J. Am. Ceram. Soc. (1959) 42, 542-547, 582-592; (1960) 43, 160-167; (1961) 44, 481-491. Norville, H. S., Minor, X E. (1985), Am. Ceram. Soc. Bull 64, 1467-1470. Oel, H.X, Dannheim, H., Helland, G. (1979), Glastechn. Ber. 52, 127-130. Oka, Y, Wahl, J.M., Tomozawa, M. (1981), /. Am. Ceram. Soc. 64, 456-460. Olcott, XS. (1963), Science 140, 1189-1193. Osaka, A., Takahashi, K., Ariyoshi, K. (1985), /. Non-Cryst. Solids 79, 243-252. Pahler, G., Bruckner, R. (1981), Glastechn. Ber. 54, 65-73. Pahler, G., Bruckner, R. (1985a), Glastechn. Ber. 58, 33-39. Pahler, G., Bruckner, R. (1985 b), Glastechn. Ber. 58, 45-51. Paris, P.S., Sih, G.C.M. (1965), Stress analysis of cracks, in: Fracture Toughness Testing and its Applications. ASTM Spec. Techn. Publ. No. 381, pp. 30-83. Pavelchek, E.K., Doremus, R. H. (1974), / Mater. Sci. 9, 1803-1803. Petzold, A., Wihsmann, F.G., Kamptz, H. (1961), Glastechn. Ber. 34, 56-71. Prewo, K.M., Thompson, E.R. (1981), Reinforced Glass Matrix Composition. NASA contract report 165711. Pye, L.D., Ploetz, L., Manfredo, L. (1974), /. NonCryst. Solids 14, 310-321. Rauschenbach, B. (1981), Silikattechn. 32, 137-139. Rauschenbach, B. (1983), Silikattechn. 34, 299-302. Rawson, H. (1953), Nature 171, 169. Rekhson, S. (1986), in: Glass: Science and Technology: Uhlmann, D.R., Kreidl, N.X (Eds.). New York: Acad. Press, Vol. 3, pp. 1-118. Rexer, M. (1939), Z. Techn. Physik 20, 4-13. Richter, R. (1985), in: Strength in Inorganic Glasses: Kurkjian, C. R. (Ed.). New York, London: Plenum Publ. Corp., pp. 219-229. Ritter, J.E., Sherburne, C. L. (1971), /. Am. Ceram. Soc. 54, 601-605. Ritter, XE., Oates, P.B., Fuller, E.R., Wiederhorn, S.M. (1980), J. Mater. Sci. 15, 2275-2295. Ritter, X E., Sullivan, X M., Jakus, K. (1978), /. Appl. Phys. 49, 4779-4781. Sakka, S. et al. (1981), J. Ceram. Soc. Japan 89, 577584. Sambell, R.A.X, Bowen, D.H., Phillips, D.C. (1972), J. Mater. Sci. 7, 676-680.

712

13 Mechanical Properties of Glasses

Sane, A. Y, Cooper, A. R. (1987), J. Am. Ceram. Soc. 70, 86-89. Schaeffer, H.A. (1985), in: Strength of Inorganic Glass: Kurkjian, C.R. (Ed.). New York, London: Plenum Publ. Corp., pp. 469-483. Schardin, H. (1950), Glastechn. Ber. 23, 325-336. Schardin, H., Strath, W. (1937), Z. Techn. Physik 18, A1A-A11. Scherer, G. (1986), Relaxation in Glass and Composites. New York, Toronto, Singapore: Wiley. Scholze, H. (1988), Glas; Natur, Struktur und Eigenschaften. Berlin, Heidelberg, New York: SpringerVerlag. Schreiber, E., Anderson, O. L., Soga, N. (1973), Elastic Constants and their Measurement. New York, Diisseldorf, London etc.: McGraw-Hill Book Comp. Schroder, H., Gliemerodt, G. (1970), Naturwiss. 57, 533-541. Seifert, F. A., Mysen, B.O., Virgo, D. (1983), Phys. Chem. Glasses 24, 141-145. Shaw, R. R., Uhlmann, D.R. (1969), /. Non-Cryst. Solids 1, 474-498. Shaw, R.R., Uhlmann, D.R. (1971), /. Non-Cryst. Solids 5, 237-263. Shelby, I E . , Day, D.E. (1969), J Am. Ceram. Soc. 52, 169-174. Shelby, J.E., Day, D.E. (1970), J. Am. Ceram. Soc. 53, 182-187. Simmons, J.H., Mohr, R.K., Montrose, C. J. (1982), /. Appl. Phys. 53, 4075-4080. Singh, I P . , Tree, Y, Hasselmann, D.P.H. (1981), / Mater. Sci. 16, 2109-2118. Spinner, S. (1956), J Am. Ceram. Soc. 39, 113-118. Stavrinidis, B., Holloway, D. G. (1983), Phys. Chem. Glasses 24, \9-25. Stockhorst, H., Bruckner, R. (1982), J. Non-Cryst. Solids 49, 471-484. Stockhorst, H., Bruckner, R. (1986), J Non-Cryst. Solids 85, 105-126. Stong, G. E. (1937), /. Am. Ceram. Soc. 20, 16-22. Stookey, S.D., Olcott, I S . , Garfmkel, H. M., Rothermel, D. L. (1962), in: Advances in Glass Technology. New York: Plenum Press, pp. 397411. Struck, W, Briinner, W. (1989), Bautechnik 66, 351361. Takahashi, K., Oska, A., Furuno, R. (1983), J Ceram. Soc. Japan 91, 199-205. Takata, M., Tomozawa, M., Watson, E. B. (1982), J. Am. Ceram. Soc. 65, C156-C157. Tille, U., Frischat, G.H., Leers, K.J. (1978), Glastechn. Ber. 51, 8-16. Thomas, W. F. (1960), Phys. Chem. Glasses 1, 4-18. Thomas, WF. (1971), Glass Technology 12, 42-44. Tomandl, G., Schaeffer, H.A. (1977), in: Non-Crystalline Solids, Fourth Internal. Conf. in ClausthalZellerfeld: Frischat, G. H. (Ed.). Trans. Techn. Publ., pp. 480-485.

Uhlmann, D.R. (1973/74), J. Non-Cryst. Solids 13, 89-99. vanGemert, W.J.Th., van Ass, H.M.J.M., Stevels, J.M. (1974), J. Non-Cryst. Solids 16, 281-293. Varner, J. R., Oel, H. J. (1975), J Non-Cryst. Solids 19, 321-333. Vogel, W. (1964), Z. Chemie 4, 190-192. Wasche, R., Bruckner, R. (1986a), Phys. Chem. Glasses 27, 80-86. Wasche, R., Bruckner, R. (1986 b), Phys. Chem. Glasses 27, 87-94. Wasche, R., Bruckner, R. (1987), Phys. Chem. Glasses 28, 139-142. Weir, Ch.E., Shartsis, L. (1955), /. Am. Ceram. Soc. 38, 299-306. Weiss, H. J. (1987), Phys. stat. solidi (a) 99, 491. Westbrook, J.H. (1960), Phys. Chem. Glasses 1, 32-36. Wiederhorn, S.M. (1967), J. Am. Ceram. Soc. 50, 407-414. Wiederhorn, S.M. (1969), J. Am. Ceram. Soc. 52, 99-105. Wiederhorn, S. M. (1974), Subcritical crack growth in ceramics, in: Fracture mechanics of ceramics: Bradt, R.C. etal. (Ed.). New York, London: Plenum Press, Vol. 2, pp. 613-646. Wiederhorn, S. M. (1974), in: X. Intern. Congr. Glass, Ceram. Soc. Japan, Vol. 11, pp. 1-15. Wiederhorn, S.M. (1975), /. Non-Cryst. Solids 19, 169-181. Wiederhorn, S. M., Bolz, L. H. (1970), J. Am. Ceram. Soc. 53, 543-548. Wiederhorn, S. M., Evans, A. G. (1974), Int. J. Fracture 10, 379-392. Wiederhorn, S. M., Lawn, B. R., Marshall, D. B. (1979), /. Am. Ceram. Soc. 62, 66-74. Wiederhorn, S.M., Johnson, H., Dienes, A.M., Heuer, A.H. (1974), J. Am. Ceram. Soc. 57, 336341. Wiederhorn, S.M., Townsend, P.R. (1970), / Am. Ceram. Soc. 53, 486-489. Williams, M. L., Scott, G. E. (1970), Glass Technology 11, 76-79. Winkelmann, A., Schott, O. (1984), Ann. Physik 51, 697. Yamane, M., Mackenzie, J.D. (1974), /. Non-Cryst. Solids 15, 153-164. Zdaniewski, W.A., Rindone, G.E., Day, D.E. (1979), J. Mater. Sci. 14, 763-775. van Zee, A. F , Noritake, H. M. (1958), J. Am. Ceram. Soc. 41, 164-175. Zheleztsov, V.A., Yanbaeva, G.U. (1983), Sov. J. Glass Phys. Chem. 9, 323-326. Zijlstra, A. I, Burggraaf, A.J. (1969), /. Non-Cryst. Solids 1, 163-185.

13.8 References

General Reading Bartenev, G. M. (1970), The Structure and Mechanical Properties of Inorganic Glasses. Groningen: Wolters-Nordhoff. Kerkhof, R (1970), Bruchvorgdnge in Gldsern. Frankfurt: Deutsche Glastechnische Gesellschaft. Kurkjian, C.R. (Ed.) (1988), Strength of Inorganic Glasses - Nato Adv. Workshop, 21-25 March, 1988, Algarve, Portugal Paris: North Atlantic Treaty Organization, pp. 643. Lawn, B. R., Wilshaw, T. R. (1975), Fracture of Brit-

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tle Solids, 2nd ed.: Lawn, B. R. (1992). Cambridge: Cambridge Univ. Press. Scholze, H. (1988), Glas, Natur, Struktur und Eigenschaften. Heidelberg: Springer-Verlag. Tomozawa, M., Doremus, R. H. (Eds.) (1982), Treatise on Materials Science and Technology, Vol. 22. New York: Academic Press. Uhlmann, D.R., Kreidl, N.J. (Eds.) (1980), Glass Science and Technology, Vol. 5 - Elasticity and Strength of Glasses. New York: Academic Press. Zarzycki, J. (1991), Glasses and the Vitreous State. Cambridge: Cambridge Univ. Press.

14 Electrical Properties of Glasses Malcolm D. Ingram Department of Chemistry, University of Aberdeen, Aberdeen, Scotland, U.K.

List of Symbols and Abbreviations 14.1 Introduction 14.2 Phenomenological Aspects of Ion Transport 14.2.1 Cationic and Anionic Conductors 14.2.2 Impedance Analysis and Conductivity Measurement 14.2.3 Typical Vitreous Electrolytes 14.2.4 Systematic Variations in Conductivity 14.2.5 The Mixed Alkali Effect 14.2.6 The Conductivity Spectrum 14.2.7 Electrical Relaxations and the Decoupling Index 14.3 Mechanisms of Ion Transport 14.3.1 Basic Theory 14.3.2 The Weak Electrolyte Theory 14.3.3 The Anderson Stuart Model 14.3.4 Pathway Models 14.3.5 Ionic Interaction Theories 14.3.6 Ion-Correlation Effects and Defect Models 14.4 Transition Metal Oxide Glasses 14.4.1 Polaronic Hopping Mechanism 14.4.2 High Frequency and High Voltage Effects 14.4.3 High Pressure Effects 14.4.4 Switching Phenomena 14.4.5 Double Injection of Ions and Electrons 14.4.6 Electrochromic Devices 14.5 Semiconducting Glasses 14.5.1 General Principles 14.5.2 Amorphous Silicon (a-Si and a-Si:H) 14.5.2.1 Electrical Properties 14.5.2.2 Chemistry of the Defect States 14.5.2.3 Glassy Properties of Hydrogenated Films 14.6 Applications of Amorphous Silicon and Related Materials 14.6.1 Range of Device Technologies 14.6.2 Photovoltaic Devices 14.6.3 Spatial Light Modulators 14.6.4 Reflective Coatings 14.7 Conclusion 14.8 References Materials Science and Technology Copyright © WILEY-VCH Verlag GmbH & Co KGaA. Allrightsreserved.

716 718 719 719 720 721 722 723 724 725 727 727 728 729 730 732 733 734 734 736 738 738 739 740 741 741 743 743 743 744 745 745 746 747 747 747 748

716

14 Electrical Properties of Glasses

List of Symbols and Abbreviations a B c c D* EA EX £ gap e e~~ F / G H HR J

intersite distance lattice parameter velocity of light fraction in lower oxidation state tracer diffusion coefficient microscopic activation energy measured activation energy band gap energy electronic charge electron Faraday's constant frequency elastic modulus enthalpy Haven ratio electronic transfer integral

k M* M\ M" JV n (co) R Rz r T Tg Te t t+ u WH WP X{ Z* Z', Z" z

Boltzmann's constant complex electric modulus, (e*)" 1 real and imaginary electric modulus number per unit volume frequency dependent refractivity the universal gas constant decoupling index (ratio) cation radius absolute temperature glass transition temperature equilibration temperature time cationic transport number electrical mobility polaron hopping energy polaron binding energy charge fraction complex electric impedance real and imaginary impedance charge (or valency) of an ion

a p y e 80

optical absorptivity parameter in the KWW equation co valency parameter (relative) permittivity permittivity of free space

List of Symbols and Abbreviations

s* e\ E" A ft v a ^a.o Gd.c. T TS , iff cp co

complex permittivity real and imaginary permittivity optical basicity parameter chemical potential frequency electrical conductivity electrical conductivity for alternating and stationary currents relaxation time structural and conductivity relaxation time decay of the electric field angular frequency (2nf)

a-Si a-Si:H DSC EXAFS f.w.h.m. GD KWW SAXS

amorphous silicon hydrogenated amorphous silicon differential scanning calorimetry extended X-ray absorption fine structure full width at half maximum glow discharge Kohlrausch-Williams-Watts small angle X-ray scattering

717

718

14 Electrical Properties of Glasses

14.1 Introduction Ionic conductivity in glass has been studied for over a hundred years and there are indications that glassy (and amorphous) electrolytes are showing promise for use in all-solid-state batteries and in electrochromic devices. These developments are at an early stage, and much effort is still being directed toward discovering new glassy systems and to optimising the levels of ionic conductivity in these materials. Remarkably, the main electrical application of ionic conductivity is still in the use of glass electrodes in analytical chemistry where very low levels of conductivity suffice, and the dominant effect is the surface interaction. By way of contrast, the existence of semiconducting glasses has been clearly recognised for only some twenty years, but already their technological applications, as e.g. in xerography and in solar cells for pocket calculators, are extensive and are increasingly affecting everyday life. This difference in the pace of technological development is part of a wider experience in the field of solid state ionics, and points up the difficulties in establishing reliable electrode-electrolyte interfaces and in avoiding unwanted chemical and electrochemical side reactions. To complicate matters further, many of the glasses which are good ionic conductors are either very hygroscopic or else sensitive to light. By contrast, materials widely used in microelectronics applications such as amorphous silicon (a-Si) are remarkably robust, and can also be used in architectural applications. Apart from these technical aspects, considerable progress has been made in recent years in understanding the mechanisms of both ion and electron transport in glasses and amorphous materials. In this context,

"glasses" are taken to mean bulk solids quenched from the melt, and exhibiting a glass transition temperature Tg, whereas "amorphous" materials include thin films deposited by sputtering or evaporation. It is a moot point if such a distinction has physical significance, and certainly for all these materials there are important consequences arising from the influence of disorder and thermal history. In the case of ionic conductivity, the focus is naturally on identifying the links between ion mobility on the one hand and glass structure and chemical bonding on the other. Some theoretical approaches, such as the weak electrolyte and ionic interaction theories, draw attention to more general parallels with solution electrochemistry. With electronic conductors, controversy related at first to the existence (on nonexistence) of band gaps. These issues were largely resolved as a result of the work of Mott and others (see e.g. Mott and Davis, 1979). It now emerges that the electrical properties (and especially the key role of dopants) are also very much influenced by chemical equilibria involving electron donors and acceptors, as well as defects in the glass structure. In effect, there is a growing tendency for theoretical discussions in the fields of ionic and electronic conductivity to converge on problems in glass chemistry. However, historically there has been some tendency for ionic and electronic processes to be treated as distinct phenomena, with chemists concentrating largely on ionic, and physicists on electronic systems. In the present chapter the main features of ionic and electronic processes in glass are reviewed, so as to clarify the remarkable diversity of phenomena which are observed and to highlight some of the applications which are currently envisaged.

14.2 Phenomenological Aspects of Ion Transport

719

Ionic and mixed ionic-electronic conductors are dealt with first (this is essentially the field of solid state ionics), and then there is a discussion of the growing importance of amorphous silicon and other "tetrahedral" semiconductors. The important properties of chalcogenide glasses and of metallic glasses will not be discussed here, since these are described in Chap. 7 and Chap. 9 of in this Volume.

14.2 Phenomenological Aspects of Ion Transport 14.2.1 Cationic and Anionic Conductors

The electrolytic properties of ordinary glass were demonstrated over one hundred years ago by Warburg, who electrolyzed Na + and other alkali cations through the walls of thin glass tubes and showed that Faraday's laws were obeyed. More recently Hughes and Isard (1972) employed Tubandt's method, with a series of disks of glass pressed together, to prove unequivocally the cationic nature of the conduction process in a range of single and mixed alkali silicate glasses. The cation mobility (and the corresponding immobility of the anions) can be understood intuitively by reference to the widely cited Warren Biscoe version of the structure of alkali silicate glasses (reduced to two dimensions) shown here in Fig. 14-1. According to this simplified picture, cations are placed in "holes" in a glass structure, whose shape is largely predetermined by the partially broken (or modified) silicate network. Glasses are thus members of an important class of solid electrolytes, which includes fast-ion conductors like jS-alumina and oc-Agl, where the cationic transport number, t+ = \.

Na

Figure 14-1. A schematic 2-dimensional representation of the "classical" Warren-Biscoe structure of alkali silicate glasses, showing the possibilities of localized and extended cationic motion within an anionic framework.

This form of monopolar conduction is prevalent in a wide range of borate, phosphate and silicate glasses of varying stoichiometries. Nevertheless, O 2 " migration can also occur in certain special circumstances. Layers of PbO have been observed to form on sodium borate glasses during electrolysis at Pb anodes. Apparently, O 2 ~ migration occurs in preference to the electrolysis of Pb 2 + ions into the glass. Baucke and Duffy (1983) attributed this to a structure-switching mechanism involving the ability of boron to adopt both 3 and 4 fold coordinations. Measurable levels of anionic conductivity are found only in fluoride glasses (see

720

14 Electrical Properties of Glasses

Chap. 5). A typical conductivity, e.g. for 62ZrF 4 -30BaF 2 -8LaF 3 glass (Ravaine etal., 1983) is 3 x l O " 6 S c m ~ 1 at 300°C This is very similar to the cationic conductivity found in 20Na 2 O-80SiO 2 glass. As remarked above, mixed anionic-cationic conductivity is not common in glass. However, very recently, Kulkarni and Angell (1988) have reported a "mobile-ion crossover", from anions to cations, occurring as LiF is replaced by PbF 2 in the system LiF-PbF 2 -Al(PO 3 ) 3 . The glasses discussed in the rest of this Chapter will mainly be cationic conductors. This reflects the greater interest shown in these systems, and the evidence that electrical properties of anionicallyconducting fluoride glasses are otherwise rather unexceptional.

n

glass

AVWW

1

\[ ^glass

(a)

N

c a -a
a. E

t

14.2.2 Impedance Analysis and Conductivity Measurement

The most common way of measuring the conductivity of glass (see e.g. Grant et al., 1978; Tuller et al., 1980) is to affix gold or aluminum blocking electrodes, and to determine the complex impedance diagram using a variable frequency admittance bridge (typically in the frequency range 10°-10 6 Hz) or an equivalent frequency response analyzer. The simplest equivalent circuit for such a conductivity cell is shown in Fig. 14-2 a. The glass is represented here by a parallel RC element, and the electrical double layer (and the resulting space charge effect) by a series capacitance. The value of R, the resistance of the glass, will be found directly from the intercept on the Z' axis. This "ideal" electrolyte behaviour is illustrated in Fig. 14-2b. In general, the "real" behaviour only approximates to this ideal; the semicircular arc is usually somewhat flattened, and the electrode "spike" angled somewhat away from the vertical.

Real impedance, Z ' (b)

Figure 14-2. (a) A simple equivalent circuit for a solid (glassy) electrolyte with blocking electrodes, (b) The complex impedance plot expected for such "ideal" behavior.

More will be said later about the causes of this nonideal or dispersive behaviour. Conductivities measured in this way are usually referred to as d.c. quantities, and it is assumed that identical values would be obtained at "true" d.c. using electrochemically reversible (i.e. ionically nonblocking) electrodes. Support for this assumption comes in some cases from direct experiment, and from the very general observation of a frequency-independent admittance region (the conductivity plateau - see Fig. 14-7 below).

721

14.2 Phenomenological Aspects of Ion Transport

Although it is certainly more convenient to evaporate Au electrodes onto a glass than to arrange for the preparation and handling of liquid sodium electrodes, care needs to be taken if blocking electrodes are to be used in conjunction with fixed frequency measurements. Depending on the resistance of the glass and the measurement frequency, the resistance actually recorded could move significantly away from the intended Z' intercept shown in Fig. 14-2 b. If the value of R is small (as in the case of a highly conductive glass) then the frequency would have to be high (even as much as 1 MHz) to avoid moving onto the electrode spike, while if R is large (as in conventional silicate glasses at ca. 100 °C) then the frequency would have to be low (say < 1 kHz) to avoid moving onto the electrode semicircle. These two circumstances will lead to the measurement of incorrectly low and high conductivities, respectively. Generally, the ionic conductivity of glass is thermally activated (see next section) so fixed-frequency measurements on any given sample are useful only over limited temperature ranges.

800

Temperature, T in °C 300 100 0 -100 KN03 melt

0 --

\<

f

melt \

T Kg -6-

Na 2 0-3Si0 2 \ glass \ •*-— — - ^\ i

1

. i

2

^

\

\ \

Ag5l4B03 ^ \ ^ glass ^

^

I

i

i

3 4 1O3/7" in K"1

5

6

"

Figure 14-3. Arrhenius plots showing temperaturedependent ionic conductivities in "typical" glass-melt combinations (Ingram, 1987, reproduced by kind permission of The Society of Glass Technology).

where E£ is the apparent conductivity activation energy. For this particular glass, E% = ca. 65kJmol~ 1 . The value of the activation energy is high enough to ensure that although there is a reasonable conductivity at Tg (> 10~ 3 S cm" 1 ), cooling to ambient reduces a to below 10~ 9 Scm~ 1 . Above 300 °C silicate glasses can be regarded as electrolytes, whereas at 25 °C they behave much more like insulators (or dielectrics). 14.2.3 Typical Vitreous Electrolytes The Ag 5 I 4 BO 3 glass is an example of a Figure 14-3 taken from Ingram (1987) recently discovered class of optimized (or shows Arrhenius plots (graphs of log o fast ion conducting) glasses, which contain versus 1/T) for two rather different cation Agl as a major ingredient. The conductivconductors. The corresponding behaviour ity is very high at Tg (ca. 5 x 10" x S cm"% of a typical molten salt, KNO 3 , is included but this glass also differs from sodium for comparison. trisilicate in its low energy of activation (ca. The conductivity data of sodium trisili20kJmol - 1 ). As a consequence, the concate glass (Na 2 O • 3 SiO2) illustrate a numductivity falls off very slowly with deber of typical features. Above Tg, the creasing temperature; values greater than Arrhenius plot is curved (the characteristic 10~~4 S cm" 1 can be measured right down "free volume" behaviour). Below Tg, a to - 1 0 0 ° G straight line is obtained in accordance with The Arrhenius plot shown here is virtuthe Arrhenius equation ally a direct extension of the line for molten potassium nitrate, continuing down to sub-EX/RT) (14-1)

722

14 Electrical Properties of Glasses

ambient temperatures. Somehow therefore, "liquid-like" ion mobilities (reminiscent also of Ag + ions in crystalline a-Agl) have become trapped within the rigid glass matrix. How this comes about is obviously a very important question in the context of "glassy state ionics". It is considered further in Sec. 14.3. 14.2.4 Systematic Variations in Conductivity

Among the characteristic features of vitreous electrolytes are the wide variations of conductivity to be found within many "binary" systems. Data in Fig. 14-4 for sodium borate glasses at 300 °C illustrate this phenomenon very clearly. The concentration of network modifier (mainly Na 2 O, but augmented with Na 2 SO 4 , "Na 2 Cl 2 ",

i

i

r

-3

-5

Z. -6 o

• o A • •

-9

Glasses Na 2 0-B 2 0 3 plus "Na2Cl2" plus "Na 2 F 2 " plus Na2S04 plus AI2O3

-10 10

20 30 40 50 mol % (Na20 + Na2SO4, etc.)

Figure 14-4. Compositional dependence of ionic conductivities in sodium borate glasses, where the range of glass-formation has been extended by various substitutions (Hunter and Ingram, 1984).

etc.) is varied from 10 to 50mol%. Over this range of composition the conductivity rises by seven orders of magnitude. This is clearly out of all proportion to the increase in the concentration of Na + ions. Such effects are common to all glassforming systems (M 2 O-SiO 2 , P 2 O 5 , etc.), see e.g. Martin and Angell (1986) and Pradel et al. (1989). Always there is a smooth increase in the logarithm of the conductivity with increasing mole fraction of the ionogenic component, which is also the network modifier. Only at very high modifier concentrations, and in certain systems, is there any indication that the conductivity reaches a maximum value. Very generally the rise in isothermal conductivity parallels a decrease in the activation energy. For many practical purposes, it is necessary only to know that E£ varies from 50 to 100 kJ mol" 1 over most oxide glasses, and where in this range a particular composition lies. Hunter and Ingram (1984) showed that in Na + -ion glasses, E£ decreases continuously with increase in the calculated optical basicity parameter, A (Fig. 14-5). Using the empirical "master curve" it is possible to forecast E% values directly from the chemical stoichiometry, since A = X1A1 -\-X2A2 ... where X±, X 2 , etc. are the charge fractions of different oxide components (Na 2 O, SiO2 ...), and A1, A2 are assigned basicity values. Such a correlation of E£ with A will account for increases in conductivity with Na 2 O content and for the higher conductivities of silicate as compared with phosphate glasses. Reference has already been made in Sec. 14.2.3 to the existence of glasses containing silver iodide, which are outstandingly good ionic conductors. In fact there is a whole family of such glasses (see e.g. Martin and Schiraldi, 1985) where Agl can be mixed either with recognized glass-formers like

14.2 Phenomenological Aspects of Ion Transport 1

120 •

Glasses Na2O-SiO2

i

O

Na 2 0-B 2 0 3 -Si0 2

i

o Na 2 0-Al 2 0 3 -Si0 2

• 110 -

•

1\ •

100 ~

\

c

Na 2 0-B 2 0 3 -

Na 2 0-Al 2 0 3 -B 2 0 3 u Na 2 0-P 2 0 5

0 2 -Si0 2 -P 2o5

Na2O-

90-

723

similar to silver iodide. Other examples of glasses where such effects are found include the Cul-containing glasses (Minami and Machida, 1989), and the so-called "Bordeaux" glasses which typically are lithium borates doped with lithium chloride (Levasseur et al., 1979; Button et al., 1981). In these latter glasses the presence of LiCl is useful both in extending the range of glass formation in regard to total lithium content, and also in enhancing the mobility of Li + ions.

\ D

80-

-

C \ "

> 70-

•

••o D 1 e£\ •

-

\

o €

-

60-

•o 50-

^

• o

1

0.45

1

° 1

N\ 1

0.55 0.65 Optical basicity parameter, A

Figure 14-5. The variation of the apparent activation energy for d.c. conductivity, £*, with the calculated (optical) basicity parameter in a range of Na + -ion conducting glasses (Hunter and Ingram, 1984).

AgBO2 and AgPO 3 or with non-glassformers like Ag 2 MoO 4 and Ag 3 AsO 4 . In all these systems the conductivity increases substantially with increasing silver iodide content. To give an example, in the case of AgI-AgPO 3 glasses, the conductivity increases smoothly from 3xlO~ 7 to 7xlO~ 3 Scm~ 1 , as the Agl content increases from zero to 50 mol%. In recent years, effort has been devoted to finding other salts which will show a conductance enhancement (dopant) effect

14.2.5 The Mixed Alkali Effect The trends outlined in Sec. 14.2.4 imply a direct link between ionic conductivity and glass stoichiometry, and would suggest that variations in conductivity are related to the presence of certain chemical entities in glass (see also Mueller et al., 1987). It is remarkable therefore that the mixing of different alkalis in glass produces a pronounced minimum in the conductivity. This effect is illustrated in Fig. 14-6. Although many physical properties (such as the molar volume, shown here) do show the expected additivity relationship, the conductivity of a mixed lithium-potassium disilicate glass is some four orders of magnitude lower than either of the corresponding single alkali disilicates. This effect appears to be "universal" to all ion-conducting glasses, even though there is no obvious analog in electronic conductors. Very probably it is a mismatch effect arising from the differing sizes and coordination requirements of different cations. EXAFS studies (Greaves, 1989) clearly indicate that each type of alkali modifies the network structure to suit its own requirements. Li + -ions create for themselves smaller sites than do K + -ions. There can therefore be no rapid "exchange of sites" reaction involving Li + and K + (or

724

14 Electrical Properties of Glasses

ance of flattened semicircles and other nonideal impedance behaviour. These effects are widespread and emerge as a natural consequence of the ionic hopping process. This conclusion can be reached from a consideration of Fig. 14-7 (Angell, 1989) showing data for the conductor, 3AgI-2(Ag 2 O-2B 2 O 3 ). Figure 14-7, often referred to as the conductivity spectrum, is a log-plot of conductivity versus frequency. It features the characteristic "d.c." plateaux, which correspond directly to the interceps (R) on the corresponding complex impedance diagrams, illustrated schematically in Fig. 14-2b. Clearly, a (plateau) = <7dc. = (l/A)/R

Mole fraction, Figure 14-6. The mixed alkali effect in (Li2O/ K 2 O): 2 SiO2 glasses at 150°C Note the linear variation in molar volume (reproduced by courtesy of D. E. Day, 1976).

other pairs of dissimilar ions), since such an exchange entails expanding the network around the former and contracting it around the latter. The mixed alkali effect is undoubtedly of practical importance, as e.g. in the formulation of glasses with high electrical resistivity and good chemical durability. Mainly, however, its elucidation is seen as presenting a severe test of all theories of ionic conduction in the vitreous state (Tomandl and Schaeffer, 1985). 14.2.6 The Conductivity Spectrum

Reference has already been made in Sec. 14.2.2 to the dispersive properties of ionic conductors which lead to the appear-

(14-2)

Another salient feature is the steady rise in "a.c." conductivity, which follows approximately a power law dependence when n is tending towards unity. <Ja.c. = Bcon

(14-3)

especially at higher frequencies. This conductivity increase continues into the far infrared region (where the absorption band arising from cations vibrating in their lattice sites is reached). The inclusion of data from far infrared spectroscopy is made possible by converting the spectral absorbtivity, a, into conductivity units through the equation o = c - n(co) • s0 - a

(14-4)

where c and e0 have their usual significance, n(co) is the frequency dependent refractive index (ca. 2.0) and a is the measured absorptivity in Neper cm" 1 . The d.c. conductivity is thermally activated, which is shown more explicitly by transferring the d.c. conductivities from Fig. 14-7 a onto the Arrhenius plot in Fig. 14-7 b. Comparison of these two graphs shows the far infrared conductivity emerg-

14.2 Phenomenological Aspects of Ion Transport

725

Figure 14-7. (a) The conductivity spectrum of a silver iodoborate glass (3AgI-2Ag 2 O-2B 2 O 3 ) over a range of temperatures, (b) The corresponding Arrhenius plot showing the near equivalence of the limiting high frequency conductivity obtained from the far IR absorption with the limiting high temperature conductivity in the liquid state (reproduced by courtesy of C. A. Angell, 1989). k

6

8

10

12

log10 (f/Hz)

ing (Angell, 1989) as the effective maximum value for the d.c. conductivity in the glassmelt system. This value, which is approximately lOScm" 1 , corresponds either to the vibrations of Ag + ions within their sites, or to the (fully-activated) diffusion of Ag + ions at higher temperatures. Returning again to the discussion of the dispersive or power law region, it can make more sense to think of the conductivity as "falling away" from the maximum (infrared) value, rather than as "rising above" the (much lower) values found on the d.c. plateaux. With falling temperature, the effect of the activation energy is that the vibrating Ag + ion must wait for longer periods before it has enough energy to complete a jump. The processes which give rise to ion migration are thus moved to progressively lower frequencies. The sloping region of the conductivity spectrum is thus a direct indication of this waiting process. The longer this sloping region, the more slowly the ions diffuse, and the lower is the d.c. conductivity. Conductivity spectra similar to that illustrated in Fig. 14-7 a are found for all the glass systems which have been investigated so far. Extensive data for sodium trisilicate

2 4 6 10 3 / T in K"1

glass (Wong and Angell, 1976; Burns et al., 1989) exist for the whole spectral range from audio, through radio and microwave frequencies, into the far infrared region. Some of this latter data set is used in the discussion of conductivity relaxations which follows. 14.2.7 Electrical Relaxations and the Decoupling Index

Further consideration of the conductivity spectra in Fig. 14-7 a could suggest that the low-frequency limit of the power law region (note the arrows on the diagram) corresponds to some kind of hopping rate (see e.g. Almond, 1989) or to the inverse of a conductivity relaxation time, xa. This latter viewpoint underlines the use of electric modulus spectroscopy which was pioneered by Macedo and Moynihan in the early 1970's. The complex electric modulus, M*, was defined (Macedo et al., 1972) as the reciprocal of the complex permittivity and can be calculated from normal permittivity or impedance data using equations of the kind M* = i

= jco

(14-5)

726

14 Electrical Properties of Glasses

Typical loss modulus spectra (plots of M" versus log / ) in this case for a sodium trisilicate glass (Burns et al., 1989), are shown in Fig. 14-8. The spectra are broad peaks (with full widths at half maximum, f.w.h.m. = ca. 2.3 decades) which are shifted progressively towards higher frequencies as the temperature increases. Indeed, the activation energy, d(ln/ max )/ d(l/T) = ca. 65kJmol~ 1 , which is very close to the measured E% value for d.c. conduction. This is indicative of a process involving the migration of ions, and a resulting relaxation of the electric fields within the glassy material. The conductivity relaxation time is defined as the inverse of the (angular) peak frequency, ^ T I / ^ J " 1 . It can either be measured directly or else estimated from a knowledge of the d.c. conductivity using the equation, TG = £0S(G)-1 (Howell et al., 1974).

0.03-

0.02T O

E 0.01 -

Figure 14-8. Electric loss modulus spectra (graphs of M" versus log/) for Na 2 O • 3 SiO2 glass over a range of temperatures (reproduced by courtesy of W. M. Risen, Burns et al., 1989).

Several points emerge from these modulus spectra which are of very general significance. First, the loss peaks are much broader than the simple "Debye" peaks (f.w.h.m. = 1.14 decades) which would be expected on the basis of the equivalent circuit shown in Fig. 14-2 above. Such dispersive behaviour can formally be attributed to distributions of conductivity relaxation times, and could be modelled by including a series array of parallel RC elements in the equivalent circuit in Fig. 14-2 a. However, it is more useful in the context of current viewpoints to look for an explanation in terms of the transition from localized to long range ionic motions (already discussed in connection with Fig. 14-7 a) and to regard the width of the electric modulus spectrum as a measure of the inherent complexity of the conduction mechanism. One way of expressing this complexity is by means of the Kohlrausch-WilliamsWatts (KWW) equation (Moynihan et al., 1973; Howell et al., 1974). The decay of the electric field cp within the glass follows the stretched exponential law
(14-6)

where TP is characteristic relaxation time, and 0 < / ? < l . /? would equal unity for a simple exponential relaxation, which would correspond to the simple Debye peak in the electric modulus spectrum. Moynihan has prepared tables of M' and M" evaluated for a wide range of "normalized" frequencies, which facilitate the fit of the modulus spectrum to the KWW equation, and determination of /? from experimental data. In many glasses, /? = ca. 0.5, even where the chemical compositions and the actual conductivities are very different. There is some evidence that (I is higher in glasses with low concentrations of mobile ions (e.g. low-alkali silicates) or having high activation energies, and also, perhaps

14.3 Mechanisms of Ion Transport

surprisingly, that /? increases with increase in temperature. Ngai et al. (1984) have shown how the jS-parameter can be used to calculate a true microscopic activation energy EA from the measured activation energy, Ejf, using the equation EA=P-EX

(14-7)

The energy EA is associated with single-ion processes, while the measured "d.c." activation energy includes a variety of additional interactions and cooperative effects associated with a net flow of ions in the conductor. The microscopic relaxation time is in fact much shorter than the observed relaxation time, (27c/max)'"1. Within this concept, it is not necessary to postulate a distribution of relaxation times in order to explain the breadth of the modulus spectrum. Instead it is simply an indication of the effect of the interactions between individual mobile ions. Experimentally, these electric modulus peaks correspond quite closely in frequency to the ^-relaxations (ultrasonic absorptions or internal friction peaks) seen in the mechanical loss spectra (Angell, 1989; see also Sec. 11.3.1.2). They occur therefore at much higher frequencies (or lower temperatures) than do the primary a-relaxations, which are manifested by the glass transition temperature, Tg. Angell (1983) has highlighted this distinction by defining a decoupling index, Rx = Ts/Tff, which is the

ratio of the structural (mechanical) to the electrical relaxation times at Tg. For Tg as determined in the normal differential scanning calorimetry experiment (DSC), TS = ca. 200 s, and the value of xa can be taken as approximately 10 ~ 12 (a) ~* s. A typical sodium silicate glass could have a conductivity of 5 x 10~ 3 S cm" 1 at Tg, and so the value of RT obtained is 200 x 1012 x 5 x 10" 3 = 1012.

727

The motion of cations in glass is thus strongly decoupled from the normal processes of structural relaxation. This is especially true for the fast-ion conducting glasses like Ag 5 I 4 BO 3 . Figure 14-3 shows that the mobile silver ions below Tg seem to have escaped completely from the structural "entanglements" which led to vitrification. In this latter respect vitreous conductors differ quite markedly from the important class of polymer electrolytes, where ion mobility is a melt property and ionic motions are strongly coupled to segmental motions of the polymer chains (McLin and Angell, 1988; see Chap. 11). For this reason polymer electrolytes (unlike the inorganic glasses) can only be used in electrochemical applications well above their glass transition temperatures.

14.3 Mechanisms of Ion Transport 14.3.1 Basic Theory

Appropriate Arrhenius equations (Eq. 14-1 in Sec. 14.2.3), summarize the main facts concerning the ionic (d.c.) conductivities of most glasses. The important parameters would seem to be the pre-exponential factors (a0) and the activation energies (£*)• A complete theory of ionic conductivity would be expected therefore to provide these parameters for any given glass, and plausible interpretations of trends and changes on a molecular basis. It is customary to concentrate on the variations in activation energy. This is partly because the conductivity nearly always rises as the activation energy falls and this largely overshadows any variations in the pre-exponential factor. Also, melt behaviour is generally nonarrhenian above Tg (see Figs. 14-3 and 14-7 above), so the values of d0 for the glass and the high-temper-

728

14 Electrical Properties of Glasses

ature limiting conductivity in the glassmelt system do not coincide. For practical purposes, it in fact makes more sense to specify the experimental values of Tg,
According to Ravaine and Souquet (1977), there exists in any sodium silicate glass (or similar material) an ionic dissociation equilibrium which can be written formally as Na 2 O ^± Na + + ONa~

(14-8)

+

where Na is a free cation and ONa" represents a cation firmly bound (at least temporarily) to the anionic framework. From conventional thermodynamics, 0 = 0Na2o + Krinfl N a 2 o (14-9) If the dissociation constant is small, so that the concentration of free ions is also small, this may be written more informatively as M = /4, 2 o + R r i n [ N a + ] 2

(14-10)

where activity coefficients have been discarded and charge neutrality has been assumed. Quite generally a =N -z-e-u

(14-11)

where N9 z and u are respectively the number, valence and mobility of the charge car-

riers. For a given series of alkali silicate or similar glasses, experiments have shown that a - const • (aNa2O)1/2

(14-12)

By combining Eqs. (14-9) through (14-12), Ravaine and Souquet concluded that the variation in conductivity in such a series of glasses is effectively determined by the equation a = const • [Na + ]

(14-13)

In other words, the huge variations in conductivity which are observed both as a function of temperature and composition, see e.g. Figs. 14-3 and 14-4, reflect changes in the number of free Na + ions and not changes in their mobility. Such an approach has since been extended to include Agl-containing and mixed network glasses (see Ingram, 1987; Pradel et al., 1989 for further references). The value of this theory is firstly that it establishes a firm link between certain kinetic and thermodynamic quantities, and secondly that it draws an important distinction between the "mobile" and the "average" cations in glass. If this distinction can be substantiated, then it is possible to envisage a more sophisticated kind of conduction mechanism. However, such a development hinges upon the use of appropriate spectroscopic techniques to identify the mobile ions, and/or independent electrical methods to determine their mobility. At present, the constant mobility hypothesis has not been conclusively verified. One attempt to measure concentrations of mobile ions using the mixed-alkali effect (Moynihan and Lesikar, 1981; Ingram et al., 1988) indicated apparently that it is the number of mobile "defects" which are more nearly constant, rather than the mobility. However, recently Denoyelle et al. (1990) have measured Hall-effect mobilities

14.3 Mechanisms of Ion Transport

729

which are, as predicted by the weak electrolyte theory, much larger than values calculated on the assumption that all the ions are mobile. One of the attractive features of this approach is that it enables the observed activation energy, E%, to be expressed, as the sum of two terms (Ec = AH/2, and £ M ) which express the contributions from the dissociation enthalpy and the mobility energy, respectively. The factor of lA enters here from the law of mass action since the ionogen dissociates into two ions (Eq. (14-8)). Some interesting parallels can be drawn with the Anderson Stuart model, described below. Cationic displacements

14.3.3 The Anderson Stuart Model

Given that the variations in thermodynamic activity in binary or ternary mixtures are not usually predictable from first principles, some other method of calculating variations in the activation energy is required. The Anderson Stuart approach (1954) is the one most commonly employed. The basic model is illustrated schematically for silicate glasses in Fig. 14-9 (see Martin and Angell, 1986). It is assumed that when an ion makes a hop into an adjacent site (which is also vacant), it has to overcome two energy barriers. First, it must overcome the electrostatic binding energy EB pulling it back towards its original site; then there is an elastic strain energy Es which is associated with the expansion of the local structure and the opening up of suitable "doorways" through which the ion can move. By various approximations it can be shown that for an ion of valency z (14-14) "o)

Figure 14-9. A schematic view of the Anderson-Stuart model for ion hopping processes in glass. The diagram shows a shallow energy well where an ion can residue after overcoming the electrostatic binding energy, Eh (reproduced by courtesy of S.W. Martin, Martin and Angell, 1986).

where z0 and r0 are the valency and radius of the non-bridging oxygen (or other anion) respectively, B is a lattice parameter depending on the distance between neighbouring sites, r is the cation radius, rD is the radius of normal (unexpanded) doorways in the glass, G is the elastic modulus, and y is a "co valency parameter". Values of G can often be found in the literature, and rD can be estimated from the diffusion constants of inert gases. Generally, the procedure for assigning numerical values to the B- and y-parameters is somewhat arbitrary, so this is not a truly quantitative theory. Another drawback to this theory is that there are "too many" parameters. The large increases in conductivity which accompany compositional change (as for example in the

730

14 Electrical Properties of Glasses

sodium borate or silicate glasses) can therefore be explained in several ways. Looking in more detail at Eq. (14-14), a fall in activation energy could be associated with a rise in Na 2 O content, either because of (i) a decrease in the lattice parameter, J3, consequent upon the cation sites being moved closer together, (ii) an increase in the covalency parameter, y, consequent upon a rise in the basicity (polarizability) of the oxide ions (see also Fig. 14-5), or (iii) decreases in G and in r D , consequent upon a disruption of the network and an increase in the number of nonbridging oxygens. Where "anomalies" occur, as in the rather low activation energies seen in the sodium aluminosilicate glasses, then these can be conveniently explained by focusing on other parameters such as r0, the radius of the oxide ion or alternative anionic groupings in these glasses involving tetrahedral aluminium. None of these explanations is entirely convincing in the absence of independent structural information. However, Eq. (14-14) is a useful guide to the experimentalist in the choice of glass compositions which are likely to exhibit the best ionic conductivities. Since the aim is to reduce the contributions to E% from both the electrostatic binding energy and the electrostatic strain energy, then it is advantageous if the oxide ion is replaced by a larger, more polarizable anion. Such a change will tend to maximize the values of y and r 0 , and, conversely, minimize the values of G and (r — rD). Such reasoning is consistent with the fast-ion conductivity found in Agl-containing glasses, Fig. 14-3. It has led later to the discovery of LiI-Li 2 S-P 2 S 5 and LiI-Li 2 S-GeS 2 glasses (Malugani et al., 1983; Pradel and Ribes, 1989). These are among the best room-temperature Li + -ion conducting solid electrolytes known at the present time.

The original Anderson Stuart model has been modified very slightly in Fig. 14-9 to include in the energy profile subsidiary minima corresponding to ions which have escaped from their sites, but have not yet progressed to another stable position. These ions may correspond to the free ions in the weak electrolyte theory. Martin and Angell (1986) suggest in fact that EB and Es of the Anderson Stuart theory correspond to Ec and EM of the Ravaine Souquet theory. If this is valid, these two theories are simply different versions of the same underlying physical model. The main attraction of the Anderson Stuart theory is the emphasis on calculating the energy of activation. The seeming simplicity of the theory means it is easy to see what other effects have been ignored. First, there is no discussion of disorder, and whether or not the microscopic (local) activation energies are influenced by the existence of defects or medium range order in the vitreous state. Secondly, there is no discussion of long-range ionic interactions, and whether or not cooperative effects influence the activation energies. Ways of considering some of these factors will now be considered. 14.3.4 Pathway Models The need for considering the possible existence of pathways becomes more evident in systems of chemical complexity, where an exotic constituent such as silver iodide imparts a substantial increase in conductivity. Thus, Minami (1985) postulated the existence in such glasses of conduction pathways "tracked by iodide ions". This basic model has been extended, and further elaborated, to include the presence of aAgl like clusters (Tachez et al., 1986), and their linking together to form percolation pathways (Mangion and Johari, 1987).

14.3 Mechanisms of Ion Transport

Another approach (Ingram et al., 1988, 1990; Ingram, 1989) is based on existing cluster-tissue theories of glass structure (Hayler and Goldstein, 1977; Phillips, 1979; Rao and Rao, 1982; Goodman, 1985) where relatively close-packed regions, or clustered "pseudophases", are surrounded by a more open and disordered connective tissue. The solidification of this connective tissue near to or just below Tg, when the long-range structure is already determined by the interlocking clusters, puts the clusters under compression and leaves the tissue in a highly stretched condition. Some of the principal attributes of this model are sketched in Fig. 14-10. The main point is the location of preferred pathways for ion migration within the connective tissue. The model is relevant to several aspects of glass behaviour in that: (i) The steep falls in conductivity associated with the mixed alkali effect arise because the foreign ions block off the best conduction pathways within the connective tissue. (ii) The evidence for medium range order in silver-iodide containing glasses, which comes mainly from neutron scattering experiments (Boerjessen et al., 1989; Tachez et al., 1989) is consistent with a connective tissue of Agl-rich material surrounding clusters of borate or phosphate units. The tendency for Agl to stabilize glass formation in many such systems (molybdates, arsenates, etc.) is also consistent with its tendency to form a stable connective tissue. (iii) Evidence from vibrational spectroscopy for the existence of two distinct cationic environments in alkali borate glasses (Kamitsos et al., 1987) is also consistent with the presence of the cluster and tissue phases, and provides information on their relative amorphicities. (iv) The existence of a network of preferred pathways leads directly to the ap-

731

Clusters v N

Connective tissue

Conduction pathway

Blocking by foreign cations

Figure 14-10. A schematic of the cluster-bypass model, showing preferred pathways for ion migration located in a connective tissue surrounding microdomains or "clusters" of more densely packed material.

pearance of topological constraints, which various authors have linked to the occurrence of dispersive behaviour in glass (Yamamoto and Namikawa, 1977; Shlesinger and Montroll, 1984; Palmer et al., 1984). Put very simply, the accumulation of charge carriers at junctions or constrictions in the connective tissue could introduce delays, and be responsible for the appearance of a "distribution of waiting times" in the ionic hopping process. The universal character of the relaxation processes in glass (as seen in the broad modulus spectra and the near constancy of the KWW jS-parameters, ca. 0.5, see Sec. 14.2.7 above) could reflect the existence of similar pathway topologies in different glasses. (v) Finally, the mechanical loss peaks which are observed in all conducting glasses (Sec. 14.2.7 above) could be attributed to the exchange of mobile ions between the cluster and tissue phases (where the greatest differences in compression/ tension occur). It is noteworthy (Angell, 1989) that the strongest mechanical relaxations occur either in mixed-cation glasses where stress can be released because the

732

14 Electrical Properties of Glasses

cations differ in size, or else in the Aglcontaining glasses where the chemical differentiation between clusters and tissue is probably most highly developed (so again cation exchange will involve significant volume relaxations). Clearly, this cluster-tissue model marks a decisive move away from the random network theory of Zachariasen (1932) towards the "microcrystallite" or "pseudophase" concepts of Porai-Koshits (1985) and his school. In that respect it obviously has implications for development of theory in other branches of glass science. It is useful here to see what additional light it can shed on earlier theories of ionic conductivity. The presence of the clusters and tissue phases under different conditions of compression and extension introduces an important element of disorder not present in the original Anderson Stuart picture. If the ions in glass are moving in the tissue phase with a relatively open structure, then this will minimize the contributions from the elastic strain energy. As a consequence, the predominant factors influencing ion mobility will be electrostatic in origin, see also Martin and Angell (1986), Mueller et al. (1987). On the other hand if these compressive stresses force the chemical potential (or indeed the chemical composition) of the tissue to differ from the average value for the glass, then large variations in the local thermodynamic activity are possible. This could be another way to lead into the weak electrolyte theory and the connection between ion mobility and to establish thermodynamic data. 14.3.5 Ionic Interaction Theories

Mention has just been made above to the way in which topological factors associated with the pathway model could influence the distribution of relaxation times.

An alternative and more general mechanism would involve the kinds of long range ion-ion interactions which form the basis of the standard Debye Hueckel theory of dilute electrolyte solutions. Various authors have in the past attempted to extend this classical theory to glassy electrolytes (Ingram, 1987; Hyde et al., 1987). The problem is that the concentration of ions is usually too high for the detailed electrolyte theory to apply. An alternative mathematical approach is given by Funke (1988, 1990), which also has some resemblance to Jonscher's screened charge model (1975). The essence of the idea (inherent in the Debye-Hueckel theory) is that any cation will disturb the other mobile ions (in this case cations) in its immediate vicinity. Generally, there will be less cations around (i.e. they will have moved further away) than if the initial cation were absent. According to choice, this perturbation can be called the "screening charge" or the "ion atmosphere", and as the ion moves about in the glass this perturbation must accompany it also. However, see Fig. 14-11, the "ion atmosphere" around any cation cannot reconstitute itself as soon as an ion has hopped into its neighboring site. Indeed, immediately after the hop has occurred, the disturbance in the surrounding cations remains centred on the original site, and so there is a net force tending to restore the cation to this initial position. It is this "backwards correlation" effect, diminishing with time, which can be thought responsible for the existence of high a.c. conductivities and for the observed conductivity dispersions. Only after the ion atmosphere has reformed around the new cation site is the electric field relaxed and the ion hop completed. For this reason, the d.c. conductivity is lower than the a.c. value, and the observed hopping

14.3 Mechanisms of Ion Transport

733

.Q O

E

before hopping

immediately after hopping

after relaxation of ion-atmosphere

Figure 14-11. A schematic representation of the "charge screening effect" implicit in both the Jonscher and Funke theories of power law behavior.

rate is slower than the microscopic hopping rate. The ion atmosphere model is thus entirely consistent with Ngai's phenomenological approach to relaxation and dispersive behaviour in glass (Sec. 14.2.7), and provides additional mechanistic insights into the nonexponential relaxation process. Recently, Elliott (1988) has revived interest in the "diffusion-triggered" version of the ion-hopping process. Essentially, an ion cannot hop until another ion (in effect an interstitial defect) has moved towards it. This is almost like saying that the ion does not hop until there has been an appropriate change in its ion atmosphere. In a sense, this model is very like Funke's (except that "cause" and "effect" have been reversed) in that ionic transport is envisioned as a highly concerted process, involving both the "moving" ion and its neighbors. Work presently in progress (Dieterich et al., 1990; Bunde et al., 1990) makes use of Monte Carlo simulation methods. It suggests, however, that a combination of "pathway constraint" and coulombic interaction is needed to obtain good agreement between theoretical and experimental conductivity dispersions. Discussion of ion atmospheres, therefore, does not preclude a discussion of disorder and pathway effects in glass.

14.3.6 Ion-Correlation Effects and Defect Models Ionic diffusion in glass has been studied for many years, and provides information concerning the transport mechanism, and support for various "defect" hypotheses, including mobile cation vacancies and paired interstitialcies. Usually, this approach involves a comparison of the measured conductivities and diffusivities. Quite generally, the Nernst-Einstein equation can be written as okT

(14-15)

where D* is a tracer diffusion coefficient, and HR is the charge correlation factor or Haven ratio, and cr, k, AT, e and T have their usual meaning. For dilute aqueous solutions, where the diffusional processes of ions are completely uncorrelated, the Haven ratio is exactly unity; i.e. the Nernst-Einstein equation is obeyed. For molten salts, the Haven ratio is generally greater than one, because the strong coupling of cations to anions leads to the appearance of "nonconductive diffusional transport" processes. For typical sodium silicate glasses, however, values of the Haven ratio lie in the range 0.44 to 0.55, and HR approaches

734

14 Electrical Properties of Glasses

unity only occasionally as in nearly pure SiO2 (where the cations are so far apart for their motions to be uncorrelated). The lower figures for the alkali silicate glasses have variously been interpreted as indicating a mixture of vacancy and interstitial processes, cation clustering, phase separation, and preferred conduction pathways (Beier and Frischat, 1985; Ingram, 1987). The confusion arises because any constraint which encourages the sequential hopping of the cations, such as e.g. along the pathways in the connective tissue (see Sec. 14.3.4), will mean that the amount of charge transported will be larger than is calculated from the movement of individually labeled cations. (Two cations making a concerted hop carry twice the charge of the single cation which is radioactively labeled.) Such cations moving along pathways of low dimensionality will of course have enhanced opportunity to move backwards as well as forwards. This introduces additional correlation effects in diffusion, which also lead to a reduction in the Haven ratio. To date, it is still not even clear if ionic diffusion and transport in glass is primarily a vacancy or an interstitialcy process. The Anderson Stuart and Funke theories (Sec. 14.3.2 and 14.3.5, respectively) are very much in the spirit of "vacancy" mechanisms. In both cases, it is assumed that the primary process is the jumping of a cation into a nearby (equivalent) site. By contrast, the Elliott model (Sec. 14.3.5) must be seen as an "interstitialcy" mechanism, since the jumping process is itself triggered by the arrival of an additional cation. It could be argued perhaps that the interstitial mechanism would be favoured by a homogeneous glass structure, where the extra cation is free to trigger ionic motions in all directions. On the other hand, if cationic motion is channelled along prede-

termined pathways, then the free flow of ions will occur only if these passages (and especially the junctions) are not allowed to become blocked or overcrowded. This might suggest a preference for a vacancy mechanism. This kind of uncertainty concerning the primary transport mechanism serves to emphasise the conclusion already drawn in this Section. The mechanism of ion migration in glass cannot be separated from a discussion of all aspects of the glass structure.

14.4 Transition Metal Oxide Glasses 14.4.1 Polaronic Hopping Mechanism

One class of electronically conducting glasses shows many similarities to the ionic conductors. This includes some binary compositions like TiO 2 -SiO 2 , V 2 O 5 -P 2 O 5 , and FeO-P 2 O 5 , where the oxidation state of the transition metal ion changes as a result of reactions in the molten state involving the gain or loss of oxygen. Typically, glasses in the V 2 O 5 -P 2 O 5 system prepared by melting in normal ambient atmospheres will contain a mixture of V4 + and V5 + , and the electronic conductivity will arise from the intervalence transfer of electrons from V 4 + to V 5 + ions. This process can also be regarded as the migration of a polar on. The presence of the "extra" electron (i.e. the one in the d-shell of the V 4 + cation) results in a deformation of the local environment (changes in bond length, etc.). In effect, the electron and its induced deformation can be regarded as a pseudoparticle which can only migrate by a thermally activated (or phonon assisted) process. This is the process of polaronic hopping (Sayer and Mansingh, 1987; Levy and Souquet, 1989) and it has a number of characteristic features.

735

14.4 Transition Metal Oxide Glasses

The somewhat nonlinear Arrhenius behaviour is exemplified by the conductivity of various glasses in Fig. 14-12. The deviations from the Arrhenius equation are seen more clearly in the more highly conducting glasses and always at subambient temperatures. The detailed theory involves a discussion of both disordering effects and "variable range hopping" and will not be attempted here. It is fully discussed by Sayer and Mansingh and in a number of standard texts, listed below. A number of useful points can be made, however, concerning the mobility of polarons in glass. The basic idea is that electrons are always transferred between levels of equal energy, and that the energy required WH to permit this is supplied by phonon scattering. WH depends both on the polaron binding energy WP, and on the electronic transfer integral J, which can be considered as an interaction (binding) energy between two nearby sites. The effective activation energy is therefore the difference between two terms WH = ±WF-J

(14-16)

Two limiting cases are: (i) When J is almost as big as lA WP. (The factor of Vi enters through the law of mass action for similar reasons to those mentioned in connection with ionic dissociation, Sec. 14.3.2 above.) Wu is therefore relatively small, and the electron always avails itself of an opportunity to move. The time during which adjacent sites have the same energy is thus much longer than the time it takes for the electron transfer to occur. This is the so-called "adiabatic" regime. (ii) When J is small and Wn and WP are large. The time required for an electron to jump is then large compared to the time for lattice motion. An electron will miss many

-3 -5 -

\ . TiO2-SiO2 ~ -7 -

-V \

-

-9 -

) 3 -P 2 0 5

'-10-11 -12

-13-

\

\ \ Mo0 3 -P 2 0 5

N

JiO 2 -P 2 O 5 " X

\

^ FeO-P2O5

\ BaO-B2O3-SiO2 - T i 0 2 1

2

3

4 5 6 1 0 3 / r in K"1

1

7

Figure 14-12. Arrhenius plots showing the variation of conductivity with temperature in a range of electron conducting glasses. Note the nonlinearity in the plots which is found in the more highly conducting glasses at low temperatures. (Reprinted with permission from: Noncrystalline Semiconductors, Vol. Ill, Pollak, M. (Ed.). Copyright CRC Press, Inc., Boca Raton, FL, Sayer and Mansingh, 1985.)

opportunities to hop from one site to another. This is "non-adiabatic" hopping. Generally, in glasses the effect of disorder is to reduce the extent of overlap between neighboring sites and thus to reduce the magnitude of the overlap integral J. This reduces the likelihood of adiabatic behavior. This point is illustrated in Fig. 14-13 by the variation in the effective hightemperature activation energy (WH) with transition-metal ion spacing for a series of glassy systems (Sayer and Mansingh, 1983). Only in the vanadium system is it possible to introduce sufficient transition metal ions to enhance the intersite interaction to trigger a changeover to the adiabatic hopping process.

736

14 Electrical Properties of Glasses

FeO-CaO-P2O5 0.6

FeO-P2O5 Mo0 3 -P 2 0 5

0.5

W0 3 -Zn0-Ba0

2
£ 0.3

0.2 V205 (gel) I I I A 5 6 Spacing between transition metal ion in

The electronic conductivity depends not only on the proximity of other transition metal ions, but also on the fraction c which exists in the lower oxidation or valence state. Quite generally, for the high temperature region, one expects ad.c = const • c(l - c) • exp [ - WH/R T] (14-17) The prediction is that the maximum conductivity would be obtained with a 50:50 distribution between the two oxidation states. However, many systems (Sayer and Mansingh, 1987) deviate from this predicted behavior. For V 2 O 5 -P 2 O 5 glasses, for example, the maximum occurs at c = 0.16, and only for FeO-P 2 O 5 and certain vanadate-borate glasses is there a maximum at c = 0.5. Some kind of chemical ordering effect is clearly apparent in these systems, which is presently not well understood.

Figure 14-13. Variation of high-temperature value of EJ with site spacing in transition metal ion glasses (reproduced by courtesy of M. Sayer, Sayer and Mansingh, 1983).

14.4.2 High Frequency and High Voltage Effects

The strong parallels between ionic and electronic conduction processes in glass are apparent in both the frequency-dependent conductivities (see Sec. 14.2.6 and 14.2.7 above) and the high-voltage effect. Owen (1977) reports that the dielectric loss curves (and therefore also the a.c. conductivities) for BaO-V 2 O 5 -P 2 O 5 glasses effectively replicate the corresponding pattern of behavior seen in sodium silicate glasses (Fig. 14-14). The characteristic loss spectra (actually peaks in [&" — odc Jco] versus log / where co = 2nf is the angular frequency) lead at higher frequencies into "low loss" regions (where aac = Boo1), and are indicative presumably of the same kind of (complex) hopping process. Even more remarkably, in electronic conductors the above mentioned dielectric loss peaks are accompanied by mechanical losses which can be observed by internal friction, acoustic attenuation and related

737

14.4 Transition Metal Oxide Glasses

techniques. Chomka et al. (1978) report the appearance of mechanical loss peaks upon addition of Fe 2 O 3 to MgO-P 2 O 5 glasses. The temperature at which these peaks appear decreases with increasing Fe 2 O 3 content, and moves to higher temperatures with increasing frequency of measurement. The activation energies for mechanical and dielectric relaxation are in fact very similar. This is a clear indication that the electron does possess particle properties and that electron migration in these glasses is strongly coupled to local relaxations in the glass structure. Another type of dispersive behavior is observed when large electric fields are applied. The transition metal oxide glasses are ohmic up to fields of 105 Vcm~ \ but at higher fields the conductivity increases. To a fair approximation, the data, see Fig. 14-15, obey the equation

sinh[eaF/2kT] eaF/lkT

(14-18)

Here a(F) and a0 are respectively the fielddependent and zero-field conductivities, "a" is the intersite distance, and all other

3

Sodium silicate glasses • V2O5-P2O5 glasses

3 -1

Jii

\ -2

"Debye" relaxation

_2

J Figure 14-14. Characteristic "dielectric loss" (e" — oAcJw versus log / ) curves in BaO -V 2 O 5 -P 2 O 5 glasses which superpose the curves for the corresponding behavior in ionic systems, e.g. sodium silicate glasses (reproduced with permission, Owen, 1977).

1000 2000 Normalized field. FT in

3000

Figure 14-15. High field (non-ohmic) effects in some ionically and electronically conducting glasses. The increase in the conductivity of sodium borosilicate glass is commensurate with the effects seen in two typical "polaronic" systems (reproduced with permission, Owen, 1977).

symbols have their usual significance (Owen, 1977). The values of "a" needed to fit Eq. (14-18) generally lie within the range 20-40 A, which is about five times the average separation of the transition metal ions. Large jump distances are also needed to fit Eq. (14-8) for the ion-conducting glasses (Owen, 1977; Ingram et al., 1980). The origins of the high-field dispersion are still under investigation (see e.g. Hyde et al., 1987). It is evident that (with the exception of the chalcogenide glasses; Owen, 1977) the conductivity remains ohmic until the "added" electrical energy (eaF) becomes comparable with the thermal energies. The excess electrical energy might be utilized either (i) to release ions (or polarons) from deeper than average traps, or (ii) to lift ions (or polarons) over larger than average energy barriers, or else (iii) to overcome the "ion atmosphere" effects which can retard the hopping process (Sec. 14.3.5). This last alternative would be the direct analog of the Wien effect, which is well known in solution electrochemistry. Whatever the details of the high field mechanism, it is noteworthy that these characteristic distances of 20-40 A seem to be required to balance the overall energetics of ion migration. Indirectly, this could

738

14 Electrical Properties of Glasses

be yet more evidence which supports the cluster/tissue model of glass, described in Sec. 14.3.4 above, where correlations are implicated well beyond the normal range of short range order in glass.

14.4.3 High Pressure Effects

Differences between ionic and electronically conducting glasses are apparent in the effects of external pressure. Figure 14-16 shows how the conductivities of As 2 Se 3 , 25Fe 2 O 3 -75P 2 O 5 ,and20Na 2 O-80B 2 O 3 glasses are influenced by moderate increases in pressure (Arai et al., 1973,1974). These are examples of respectively: (i) semiconducting (see Sec. 14.5 below), (ii) polaronic, and (hi) ionically conducting glasses. The behavior of the iron phosphate glass lies midway between the typical semiconductors (where the conductivity strongly rises) and typical electrolytes (where it

3.0 As2Se3 (25°C)

20Na20-80B203(61°C)

1.0 2.0 Pressure. P in kbar

Figure 14-16. Pressure effects on electronic and ionic conductivities in glass. The pressure coefficient changes from positive to negative as the mechanism changes from a semiconducting, through polaronic hopping, to a simple ionic mechanism (reproduced by courtesy of H. Namikawa, Arai et al., 1973-74).

falls). This could be a "self-cancellation effect" involving the two contributions to the hopping energy given in Eq. (14-16). Increase in pressure will slow down polaron migration (because there is a finite activation volume associated with the displacement of the polaron), but there will also be a counterbalancing increase in mobility, associated with increased orbital overlap between electron orbitals in neighboring transition metal ions.

14.4.4 Switching Phenomena

Another way in which electronic and ionic conductors differ is in the contrasting effects of devitrification. Usually the conversion of glass into crystals results in a conductivity decrease in ionic systems, whereas in electronic conductors the conductivity always increases. This could be the origin at the switching effect which is found both in chalcogenide (Ovshinsky, 1968) and transition metal oxide glasses (Sayer and Mansingh, 1987) (see Sec. 7.6.5). Many of the switching-effect studies have been made on V2O5 based glasses and on V2O5 films (Gattev and Dimitrev, 1981; Nadkarni and Shivodar, 1983). Above a certain threshold voltage, the glass sample enters a low resistance state, which returns to a higher value (closer to its initial state) when the current is reduced to zero (Tatsumisago et al., 1983). After this forming process, switching occurs at lower threshold voltages. The process is not fully understood, but it may be related to the reversible formation and decay of crystalline nuclei along pathways of high conductivity. At present the applications of these materials in commercial devices seems unlikely, but there are still important questions which merit further investigation.

14.4 Transition Metal Oxide Glasses

14.4.5 Double Injection of Ions and Electrons

A major application which is envisaged for these transition metal oxide glasses is as solid electrodes in electrochemical devices. This is because they exhibit mixed ionic and electronic conductivity, and can accommodate varying amounts of hydrogen or alkali metal by variations in the oxidation state of the transition metal ion. This is the process of ionic intercalation or double injection of ions and electrons. Using Li + ions and glassy V2O5 as examples, we can write = Li^

^2-

(14-19)

In this reaction (which is usually reversible), Li + ions will arrive from the electrolyte and electrons from the external circuit. Crystalline intercalation materials have been used for many years in electrochemical cells. The best known is probably y-MnO 2 which is used to store hydrogen (H 3 O + + e~) in Lechanche type cells, and /?-MnO2 which is used to store Li in most commercially available Li-batteries. Such a battery can be written schematically as ~Li | Li+-ion electrolyte | mixed conductor+ (14-20) where the positive plate (or cathode) is the intercalation electrode. The output voltage of such a device depends on the difference in the chemical potentials of lithium in the pure metal and in the transition metal oxide phases, respectively. Many such electrode materials exist; all are characterized by an open structure, offering many vacant sites for intercalable cations, and empty electronic orbitals on the transition metal ions. Examples include TiS 2 , V 6 O 13 , WO 3 and MoO 3 .

739

According to Levy and Souquet (1989), the use of glassy electrodes is especially advantageous because additional cations are welcomed into the disordered structure with a substantial release of free energy. This of course increases the amount of energy which can be stored in electrochemical cells (Eq. (14-20), above). Another advantage of glassy electrodes (Levy and Souquet, 1989) is that ionic mobilities are generally higher in glasses than in the corresponding crystals. This leads to improved (i.e. lower) response times, which means that the electrochemical cells can be discharged and recharged more quickly. Within the context of solid state ionics, the development of solid state devices involving both glassy electrolytes and/or glassy intercalation electrodes has been a major activity in the last ten years. Some of this effort has gone into the synthesis of Li + -ion conducting glasses (and polymer electrolytes), and otherwise into the construction of multilayer devices, containing thin layers of electrolyte and electrode material. See, for example, Jourdaine etal. (1988). A major achievement has been the development of Li + -ion conducting vitreous electrolytes based on the thio-analogs of the phosphate, borate and silicate glasses (see Sec. 14.2.4 above). Gabano (1985) incorporated the iodothiophosphate glasses of Malugani et al. (1983) into cells of the type -Limetal|47LiI-37Li 2 S-18P 2 S 5 |TiS 2 + (glassy electrolyte) (14-21) Such cells usually contained a mixture of electrolyte and crystalline TiS2 as the cathode material (to improve the interfacial contact), but also performed better when the temperature was raised to 110°C. Subsequently, Akridge and Vourlis (1988) have incorporated several design

740

14 Electrical Properties of Glasses

improvements, including the use of an isostatic compression technique to minimize interfacial impedances. These lithium batteries can operate in the temperature range — 40 to + 200 °C, and have now been commercialized. However, at present other ways of utilizing the special properties of amorphous materials with mixed ionic/electronic conductivity are now commanding attention. One of these potential areas of application is electrochromism. 14.4.6 Electrochromic Devices Following the classic work of Deb (1973), there has been continued interest in the phenomenon of electrochromism in thin films of both amorphous and polycrystalline tungstic oxide. The process involves a simultaneous injection of electrons and cations (as in Eq. (14-19)) but the interest is less in electrochemical energy storage than in the production of a colour change. The electrochemical write-erase mechanism can be given as WO 3 + x e + x H + = H,WO 3 (pale yellow) (deep blue) (14-22) where the blue colour (and also the electronic conductivity) in WO 3 arise from a

(W 5 + /W 6 + ) intervalence transfer reaction. The maximum of the broad absorption band appears in the near infrared region (at about 1.5 eV), so the electrochromic effect cuts out a fair amount of the energy in the solar spectrum. The optical properties are not changed if H + is replaced by Li + , etc. Applications of electrochromism include electroptic displays (Faughnan and Crandall, 1980), daylight modulation (Lampert, 1984; Cogan etal., 1987) and variable intensity sunglasses. An electrochromic mirror which is being developed for automotive applications (Baucke and Duffy, 1985; Baucke, 1990) is illustrated in Fig. 14-17. The light (from passing cars) passes through the layer of WO 3 before being reflected by a rhodium mirror. The device functions in effect as a rechargeable battery. The protons are normally stored in a WO 3 layer behind the mirror, but are brought forward electrochemically when the mirror needs to be darkened. The electrical properties of WO 3 films illustrate several aspects of the polaronic conduction mechanism, and also some important effects of structural disorder. In amorphous WO 3 (normally prepared by thermal evaporation or electron-beam sputtering), an electron hopping mechanism predominates until x reaches a value

Viewing face of mirror Transparent electrode W03 Layer Electrolyte Reflector W03 Layer Electrode

Figure 14-17. A schematic design for an electrochromic mirror intended for automotive applications (reproduced by courtesy of I A. Duffy, Baucke and Duffy, 1985).

14.5 Semiconducting Glasses

741

amorphous films. In the crystalline films, the polaronic hopping will be more adiabatic in character so the transition to metallicity will be favoured. Alternatively in the language of band theory, there is a much cleaner "mobility edge" in the crystalline systems and so it is easier to populate the extended electronic states. In the next section, a class of amorphous materials will be discussed where the explicit use of band theory is essential. 0.2 0.3 (U Composition parameter, x

0.5

Figure 14-18. Conductivities of amorphous HXWO3 films plotted versus x at 300 and 4.2 K. Note the sharp rise in o occurring when x = ca. 0.33 at the very low temperature, indicative of an insulator to metal transition (after Crandall and Faughnan, 1977).

of about 0.33 (Crandall and Faughnan, 1977). At this point an insulator-to-metal transition occurs, and the d-electrons on the tungsten atoms become fully itinerant. This transition and the associated minimum in the metallic conductivity can be readily seen in Fig. 14-18. Tungstic oxide films with x>0.33 are essentially metallic in nature, and can be used to reflect the sun's rays. They are especially attractive therefore for "smart window" applications. In polycrystalline films (DautremontSmith etal, 1977; Goldner and Rauh, 1983) there is less structural disorder, and the insulator-to-metal transition occurs at lower x-values. For this reason the polycrystalline films are sometimes preferred for the window applications, but display devices containing amorphous films may benefit from the higher cation diffusivities within the WO 3 and the shorter response times. Referring again the Eq. (14-16) above, it seems that the overlap parameter J will be larger in the crystalline as compared to the

14.5 Semiconducting Glasses 14.5.1 General Principles

Much of the basic understanding of semiconducting glasses comes from the extensive work of Mott and his co-workers. The starting point is the conception that in optically transparent glasses a "true" gap exists between the valence and conduction bands. In effect this can be seen as a straightforward consequence of chemical bonding, and of the energy separation existing between bonding and antibonding orbitals. In SiO2 glass this gap is as high as 10 eV, which means this material is transparent well into the far ultraviolet region. Typical semiconducting glasses, such as amorphous silicon, have much lower bandgaps and find important applications which rely on their photovoltaic and photoconductive properties. These materials have been intensively studied within the context of solid state physics. They are well characterized using a variety of techniques, including thermoelectric power, the Hall effect, and drift mobility measurements. A fuller discussion of these methods is given in standard texts which are listed at the end of this chapter (see also Chap. 7). The emphasis now will be on the special properties of amorphous semiconductors.

742

14 Electrical Properties of Glasses

Amorphicity (or disorder) shows up in the electrical properties several ways. First, there is the Anderson localization (see e.g. Mott, 1972, 1977) which affects electrons near the bottom of the conduction band and also, correspondingly, those holes near the top of the valence band. Such electrons in the "tail states" diffuse slowly through the glass, moving from one shallow trap to another. Only electrons above the mobility edge are free to occupy extended states within the conduction band. Figure 14-19 is a schematic representation of the resulting "mobility gap". Figure 14-19 also shows the presence of "states in the gap". According to Mott these do not arise as a necessary consequence of amorphicity (as would be the case in the Cohen-Fritzsche-Ovshinsky model, 1969) but depend on the presence of

Mobility edge

"Tail states

Fermi level

CD c LU

Defect states

Density of states

—

Figure 14-19. A schematic density-of-states diagram for an amorphous semiconductor, based largely on Mott's ideas. The Fermi level is "pinned" between partially occupied donor and acceptor states deep in the band gap.

specific defects. These could be non-bridging oxygens (nBO's) in SiO 2 or "dangling bands" in amorphous silicon (see below). These defects on "gap states" provide a home for the most energetic electrons in the system, and so they serve to pin the Fermi level in a restricted range of positions within the mobility gap. The effect of this "pinning" is very important in chalcogenide glasses (see Chapter 7) where there seems to be little possibility of raising or lowering the Fermi level even by normal doping procedures. There is also another way in which amorphicity reduces the possibility of controlling the electronic properties of glassy materials. This is Motfs 8-AT rule, which states that all atoms in glass are free to select coordination numbers best suited to their bonding requirements. Thus, silicon can complete its "octet" (or valence shell) when it is 4-coordinate, and similarly for oxygen the preferred coordination number is 2. This rule explains, for example, why so many multicomponent oxide glasses are optically transparent, and are also good electronic insulators. It is convenient to classify the different types of glass reviewed in this Chapter by reference to the simple band scheme of Fig. 14-19. The ionic conductors described in Sec. 14.2 and 14.3 are large band-gap materials, where electronic semiconduction can be ignored in most circumstances. The transition metal oxide glasses (Sec. 14.4) may also possess large band gaps, since conduction involves d-electrons effectively localized in gap states. The semiconducting glasses to be discussed below have band gaps typically around 1 to 2 eV, and exhibit a range of distinctively new electrical phenomena. However, as these systems are becoming better understood, it is apparent that their behavior is susceptible to many of the

14.5 Semiconducting Glasses

structural and chemical influences encountered in ionically conducting glasses (see also Chap. 7, which covers the electrical behavior of chalcogenide glasses). 14.5.2 Amorphous Silicon (a-Si and a-Si:H) 14.5.2.1 Electrical Properties The story of amorphous silicon is one where scientific advance has led fairly quickly to successful commercial exploitation. The decisive step forward was the discovery by Spear and Le Comber (1976) that amorphous silicon prepared by the glow-discharge (GD) decomposition of silane (SiH4) could be doped with phosphorus and boron to produce n- and p-type semiconductors respectively. This is clearly shown in Fig. 14-20, which is taken from Spear and Le Comber (1976). The "intrinsic" n-type conductivity is enhanced by the introduction of phos-

743

phine (PH3) into the silane gas stream. By contrast, introduction of diborane (B2H6) causes a reversal to p-time semiconductivity. The conductivity is increased by many orders of magnitude on doping (in p.p.m. levels) in either direction. The introduction of electrons into the valence bond or holes into the valence band must therefore be linked to significant upwards and downwards movements in the Fermi level. How has this effect come about? Is the 8-iV rule still valid? What has happened to the gap states which should (as in Fig. 14-19) restrict the movement of the Fermi level? The answer to all these questions lies in the special role of hydrogen, and in a complex interplay of defect/dopant controlled equilibria. 14.5.2.2 Chemistry of the Defect States Amorphous silicon prepared by the GD process is strongly hydrogenated. Typically, it contains 5 to 10at.% H and is properly written a-Si: H. Most of this hydrogen will be present (see e.g. Street et al., 1987 b) as a result of a chemical reaction involving a breakup of the tetrahedral network of the silicon = Si — Si = + 2H = 2( = Si:H) (14-23) (silicon network) (hydrogenated silicon)

Figure 14-20. The doping of amorphous silicon (a-Si:H) with B and P. The conductivity rises are indicative of both p- and n-type semiconductivity (reproduced by courtesy of P. G. Le Comber, Spear and Le Comber, 1976).

where ":" represents here an electron pair bond formed between Si and H, and the other three Si-Si bonds are undisturbed. By the same reaction the hydrogen will remove any "dangling bonds", i.e. single or paired electrons on three-coordinate Si atoms. It is this absence of "states in the gap", which can act either as electron donors or acceptors, which opens up the possibilities for doping with boron and phosphorus.

744

14 Electrical Properties of Glasses

Moreover, the doping of a-Si:H does seem to be strongly influenced by the 8-JV rule (Street, 1982; Street etal., 1985), and only some 1% of added phosphorus, for example, enters dopant positions. Much of the dissolved phosphorus is 3-coordinate, as would be expected from 8 — 5 = 3. Street argues that the formation of 4-coordinate phosphorus involves chemical reactions like Si3" + P4

(14-24)

where the superscripts refer to formal charges and the subscripts to the coordination numbers. The appearance of phosphorus in a doping position (P4) is compensated by the appearance of a charged silicon atom (Si 3"). Both charged species satisfy the 8-N rule and have a completed octet of outer electrons. Equation (14-24) does not in itself result in n-type conduction since the "liberated" electron has been trapped within a dangling bond (or lone pair) on the Si 3" entity. Alternatively (Street etal., 1985), reaction (14-24) might be written in two steps, involving electrons from tail states near the bottom of the conduction band (14-25) Si3

tion of phosphorus in the solid phase. This is a highly suggestive result. It parallels to a remarkable degree the correlations between the thermodynamic activity of ionic dopants and ionic conductivity (see Eq. (14-12), Sec. 14.3.2), which formed the basis of Ravaine and Souquet's weak electrolyte theory of glass. Le Comber (1989) has remarked on the significant effect which doping has on the position of the Fermi level, which would be surprising if the nature of donor (e.g. Si3") and acceptor levels (e.g. P4) were to remain fixed with changing dopant concentration. Very likely the situation is more complicated and more chemical species are involved. Very recently, Boscherini et al. (1989) have determined the local bonding configurations of phosphorus using the EXAFS method. They report the existence of 5-fold as well as 3-fold coordinated phosphorus, which clearly requires a modification to existing models of the doping process. For a further discussion of (hydrogenated) a-Si, see Vol. 4, Chap. 10. For a discussion of the relaxation and crystallization of a-Si, see Chap. 9, Sec. 9.3.4 of this volume. 14.5.2.3 Glassy Properties of Hydrogenated Films

(14-26)

Applying the law of mass action to Eqs. (14-25) and (14-26), it can be shown that both the concentration of electrons in tail states and in dangling bonds should vary as the square root of the total con-centration of phosphorus (strictly with [P^]172). Actually, this square root dependence is observed experimentally, but the correlation is better when the activity of phosphorus (as expressed by the concentration of PH 3 in the gas phase) is used rather than the actual (or stoichiometric) concentra-

Reference has already been made to the role of hydrogen and the large concentrations which have been incorporated within a-Si:H films. It is thought (see e.g. Street et al., 1987 b) that much of this hydrogen accumulates along internal surfaces (compare the "connective tissue", Sec. 14.3.4) or inside internal microbubbles and voids. Recently, Williamson etal. (1989) have used small angle X-ray scattering (SAXS) to prove the existence of such microvoids containing 5-9 atoms of hydrogen even in device quality a-Si: H.

14.6 Applications of Amorphous Silicon and Related Materials

n-type a-Si: H

745

(Eq. (14-6)), which has already been used to describe electrical relaxations in ionic glasses. There seems indeed to be no sharp distinction between the properties of amorphous semiconductors and conventional glassy materials.

-2 -2 Cooling rate K s' 5-10 • 1-2 • 0.03-0.05 • "rested"

A

-3 2.0

3.0 1O3/7" in

Figure 14-21. Arrhenius plots of conductivity in a-Si: H showing the influence of thermal history (cooling rate). Te is an effective "equilibration temperature" above which annealing effects are absent (reproduced by courtesy of R. A. Street, Street et al., 1987 a).

This hydrogen retains some mobility in a-Si: H at higher temperatures, but it seems to "freeze" on cooling. This argument has been used by Street et al. (1987 a) to explain the unusual shapes of the Arrhenius plots shown in Fig. 14-21. Below an equilibration temperature, Te = 130°C, we see "glass like" behavior where the conductivity depends not only on the actual temperature, but also on the cooling rate. One could postulate that the clusters of Si:H bonds act as "percolation impedances" (McLeod and Cord, 1988), whose presence tends to divert electrons away from more favorable pathways through the material. If the process of hydrogen clustering is arrested at Te, then the d.c. conductivities will be higher than expected on the basis of continuing structural change. Further evidence for this "glass-like" behavior comes from monitoring the decreasing concentration of electrons in tail states, when rapidly quenched a-Si: H is annealed below Te (Kakalios et al., 1987). This decay process obeys the same KWW equation

14.6 Applications of Amorphous Silicon and Related Materials 14.6.1 Range of Device Technologies

The present scope for the industrial and commercial exploitation of amorphous silicon devices (Le Comber, 1989) is summarized in Table 14-1. It is apparent that all these devices in one way or another relate to topical issues such as energy conservation or information storage and retrieval. For a fuller discussion of the technical and scientific details, the reader is referred to the original literature (see e.g. Le Comber, 1989) and to the standard texts on the physics of amorphous materials, some of which are listed below. Three examples are supplied here to give a general idea of the advantages stemming from the use of amorphous materials.

Table 14-1. Applications of amorphous silicon. Device

Commercial product

Photovoltaic cell

Calculators, watches, battery chargers, etc.

Photoconducting layers

Spatial light modulators, xerography, etc.

Reflective coatings

Heat reflecting float glass (architectural applications)

Thin film field-effect transistors (FETS)

Displays, televisions, logic circuits, etc.

746

14 Electrical Properties of Glasses Electrons

14.6.2 Photovoltaic Devices

The basic principle of photovoltaism is illustrated schematically in Fig. 14-22. This shows the band bending which occurs at a p - n junction (formed e.g. from B and Pdoped a-Si:H). At equilibrium the Fermi levels are equalized, so as to keep the chemical potential of the electrons constant across the interface. When the junction is illuminated with light of sufficient energy (£ gap < h v), electrons are promoted into the conduction band, and flow across in the direction indicated by the arrows. The output voltage will be determined by the amount of band bending which has occurred. One application to be envisaged for these devices is in the area of solar energy conversion. Optical absorption data (Gibson et al., 1978) for amorphous and crystalline silicon are compared with the energy profile of the solar spectrum in Fig. 14-23. The shift of absorption edge to longer wavelengths in the amorphous material means that more of the solar energy can be utilized. Very thin films (a few jim thick) of the amorphous material will absorb most of the useful sunlight. Another advantage of a-Si: H is that it can be alloyed with other elements such as C or Ge by mixing in either methane (CH4) or germane (GeH4) into the gas feed for the GD process. These substitutions have the effect of increasing the bandgap with C (useful in light emitting diodes) or decreasing the bandgap with Ge, which means that longer wavelength light can be used for solar energy conversion. According to Le Comber (1989) energy conversion efficiencies of 13-15% have been reported for small area devices using combinations of a-Si:H and a-SiGe:H cells. The advantages of such composite devices are discussed by Catalano et al. (1989). For larger

n-type conductor

p-type conductor

Figure 14-22. The basic principle of the photovoltaic effect showing band bending and equalization of the Fermi level (schematic).

scale a-Si:H devices, conversion efficiencies are typically 8-9% (Hamakawa, 1987). Such solar cells are routinely installed in wrist watches and pocket calculators. One can easily envisage the electrical energy which is generated during periods of strong illumination being stored in Li batteries of the kind described in Sec. 14.4.5. Such hybrid photovoltaic/electrochemical systems could indeed be "all-vitreous-state" in concept. 106 a-Si:H

E 0.20 o

10'

0.16

0.12 CL

I 10*

0.08

0.04

0.8

0.6 A in (jm

0.4

Figure 14-23. Optical absorption spectra for c-Si and a-Si: H compared with the solar energy spectrum. The shift to longer wavelengths favors the use of amorphous silicon for solar energy conversion (reproduced by courtesy of R. A. Gibson, Gibson et al., 1978).

14.7 Conclusion

14.6.3 Spatial Light Modulators The structure of an a-Si: H spatial light modulator is illustrated in Fig. 14-24 (Le Comber, 1989). This device depends on the photoconductive properties of a-Si: H, which allows an activating voltage to reach the liquid crystal display only in those regions where the write beam has impinged upon the a-Si:H coating. Writing times as short as 0.4 ms have been reported for such devices. There is no special reason for restricting use to a-Si:H in combination with liquid crystal displays. One might also envisage a combined photoconductive/electrochromic device (see Sec. 14.4.6) which would again depend entirely on the electrical and electrochemical properties of amorphous materials for its operation. 14.6.4 Reflective Coatings One product based on amorphous silicon, which does not stem directly from its electrical properties, is the "Reflectafloat" glass which is now marketed for its archi-

Transparent electrodes

Read beam

Write beam >

-Glass

Glass

a-Si;H

Liquid crystal

Figure 14-24. A spatial light modulator based on the photoconductive properties of a-Si:H (reproduced with permission, Le Comber, 1989).

747

tectural applications. According to Le Comber (1989), a very thin (only 35 nm) and uniform layer of a-Si is deposited industrially onto float glass in a 3.5 m wide reactor. This a-Si layer has a large reflectivity in the visible and infrared regions, and thereby reduces the amount of light energy entering or leaving a building through its glass windows. A remarkable property of this film is its chemical and mechanical durability. It is hard enough to be used on glass without additional protection. This is indicative of possibilities for other applications, where the electrical properties could be of more direct interest and a durable coating is required.

14.7 Conclusion A broad review of electrical phenomena in glass has been presented in this Chapter. The aim has been to focus attention on the growing importance of amorphous materials in both electrochemistry and solid state electronics. Already in the latter field, new knowledge has led directly to important technological advances. Attention has also been focussed on the problems relating to the underlying theory. This problem, as stated by Mott as long ago as 1972, is that "in amorphous materials we are faced with two difficulties: the lack of a rigorous theory, and a great uncertainty about the structure". This statement was clearly intended for electronic properties, but it relates also to ionic behavior. To some extent electrons are easier to study than ions because at least they obey the Pauli Exclusion Principle. It is known that they must occupy available atomic or molecular orbitals, whose presence and nature can be inferred from various spectro-

748

14 Electrical Properties of Glasses

scopic techniques and with the help of chemical intuition and molecular orbital theory. Also the electron energy levels are predetermined by short-range-order effects, which even in glass are quite well understood. In the case of ionic transport no such quantum effects exist, and it may not be possible even to distinguish the "mobile" from "immobile" ions, without some knowledge of medium-range-order in glass. To date, no general consensus exists on how best to approach this topic but this situation should improve as the structure of glass becomes better understood.

14.8 References Akridge, J.R., Vourlis, H. (1988), Solid St. Ionics, 28-30, 841. Almond, D.P. (1989), Mater. Chem. and Phys. 23, 211. Anderson, O. L., Stuart, D. A. (1954), J. Am. Ceram. Soc. 37, 573.

Angell, C. A. (1983), Solid St. Ionics 9-10, 3. Angell, C. A. (1989), Mater. Chem. and Phys. 23,143. Arai, K., Kumata, K., Kadota, K., Yamamoto, K., Namikawa, H., Saito, S. (1973-74), /. Non-Cryst. Solids

13,131.

Baucke, F.G.K. (1990), in: Vol. IS4 of Proc. SPIE, Granqvist, C. G., Lampert, C. M. (Eds.). Washington (D.C.): Int. Soc. Opt. Engineering, pp. 518538. Baucke, F.G.K., Duffy, J.A. (1983), Glastech. Ber. 56K, 508. Baucke, F.G.K., Duffy, J.A. (1985), Chem. in Brit. 21, 643. Beier, W, Frischat, G. H. (1985), /. Non-Cryst. Solids 73, 113. Boerjesson, L., Torell, L.M., Howells, W. S. (1989), Phil. Mag. B59, 105. Boscherini, R, Mobilio, S., Evangelisti, K, Klank, A.M. (1989), J. Non-Cryst. Solids 114, 223. Bunde, A., Maass, P., Roman, H. E.; Dieterich, W, Petersen, J. (1990), Solid State Ionics 40-41, 187. Burns, A., Chryssikos, G. D., Tombari, E., Cole, R. H., Risen, W. M. (1989), Phys. Chem. Glasses 30, 264. Button, D. P., Tandon, R. P., Tuller, H. L., Uhlmann, D.R. (1981), Solid St. Ionics 5, 655. Catalano, A., Arya, R, R., Fieselmann, B., Goldstein, B., Newton, X, Wiedeman, S., Bennett, M., Carlson, D. E. (1989), /. Non-Cryst. Solids 115, 14-20.

Chomka, W., Gzowski, O., Murawski, L., Samatowicz, I. (1978), J. Phys. Chem. 11, 3081. Cogan, S.F., Plante, T.D., McFadden, R. S., Rauh, R. D. (1987), Solar Mater. 16, 371. Cohen, M. H., Fritzsche, H., Ovshinski, S. R. (1969), Phys. Rev. Lett. 22, 1065. Crandall, R.S., Faughnan, B.W. (1977), Phys. Rev. Lett. 39, 232. Dautremont-Smith, W. C , Green, M., Kan, K. S. (1977), Electrochim. Ada 22, 751. Day, D. E. (1976), J. Non-Cryst. Solids 21, 343. Deb, S. K. (1973), Phil. Mag. 27, 801. Dieterich, W., Peterson, X, Bunde, A., Roman, H.E. (1990), Solid St. Ionics, 40-41, 184. Denoyelle, M. X, Duclot, M. X, Souquet, X L. (1990), Solid St. Ionics 31, 98. Elliott, S.R. (1988), Solid St. Ionics 27, 131. Faughnan, B. W., Crandall, R. S. (1980), in: Topics in Appl. Phys. 40, Pankove, XL (Ed.). Berlin: Springer. Funke, C. (1988), Solid St. Ionics 28-30, 100. Funke, C , Hoppe, R. (1990), Solid St. Ionics 40-41, 200. Gabano, XP. (1985), in: Glass, Current Issues, Wright, A.F., Dupuy, X (Eds.), NATO ASI Series E, No. 92, Dordrecht: Martin Nijhoff Publishers, pp. 457-480. Gattev, E. M., Dimitriev, Y. (1981), Phil. Mag. B43, 333. Gibson, R. A., Le Comber, P. G., Spear, W. E. (1978), IEE: J. Solid St. and Electron Devices 2, 83. Goldner, R. B., Rauh, R. D. (1983), in: Optical Materials and Process Technology for Energy Efficiency and Solar Applications SPIE Vol. 428, pp. 38-44 (Soc. Phot-Opt. Instr. Engineers, U.S.A.). Goodman, C. H. L. (1985), Phys. Chem. Glasses 26,1. Grant, R.X, Ingram, M.D., Turner, L.D. S., Vincent, C. A. (1978), /. Phys. Chem. 82, 2838. Greaves, G.N. (1989), Phil. Mag. B60, 793. Hamakawa, Y. (1987), in: Non-Crystalline Conductors, Pollark, M. (Ed.). Florida: C.R.C. Press, p. 229. Hayler, L., Goldstein, M. (1977), J. Chem. Phys. 66, 4736. Howell, F. S., Bose, R. A., Macedo, P. B., Moynihan, C.T. (1974), J. Phys. Chem. 78, 639. Hughes, K., Isard, XO. (1972), in: Physics of Electrolytes, Vol. 1: Hladik, X (Ed.), London: Academic Press, pp. 355-400. Hunter, C. C , Ingram, M. D. (1984), Solid St. Ionics 14, 31. Hyde, J.M., Tomozawa, M., Yoshiyagawa, M. (1987), Phys. Chem. Glasses 28, 174. Ingram, M.D. (1987), Phys. Chem. Glasses 28, 215. Ingram, M.D. (1989a), Phil. Mag. B60, 729. Ingram, M.D. (1989b), Mater. Chem. and Phys. 23, 51. Ingram, M. D. Moynihan, C. T., Lesikar, A. V. (1980), J. Non-Cryst. Solids 38-39, 371.

14.8 References

Ingram, M.D., Mackenzie, M.A., Mueller, W., Torge, M. (1988), Solid St. Ionics 28-30, 677; (1990), Solid St. Ionics, 40-41, 671. Jonscher, A.K. (1975), Nature 256, 566. Jourdain, L., Souquet, XL., Delford, V., Ribes, M. (1988), Solid St. Ionics 28-30, 1490. Kakalios, I, Street, R.A., Jackson, W.B. (1987), Phys. Rev. Lett. 59, 1037. Kamitsos, E. I., Karakassides, M. A., Chryssikos, G.D. (1987), /. Phys. Chem. 91, 5807. Kulkarni, A.R., Angell, C.A. (1988), J. Non-Cryst. Solids 99, 195. Lampert, C M . (1984), Solar Energy Mater. 11, 1. Le Comber, P. G. (1989), J. Non-Cryst. Solids 115, 1. Levasseur, A., Brethaus, J. C , Reau, J. M., Hagenmuller, P. (1979), Mater. Res. Bull. 14, 921. Levy, M., Souquet, XL. (1989), Mater. Chem. and Phys. 23, 171. Macedo, P.B., Moynihan, C.T., Bose, R. (1972), Phys. Chem. Glasses 13, 171. Magistris, A., Chiodelli, G., Schiraldi, A. (1979), Electrochim. Ada 24, 203. Malugani, J.P., Fahys, B., Mercier, R., Robert, G., Duchange, X P., Banstry, S., Broussely, M., Gabano, XP. (1983), Solid St. Ionics 9-10, 659. Mangion, M., Johari, G.P. (1987), Phys. Rev. B36, 8845. Martin, S.H., Angell, C.A. (1986), /. Non-Cryst. Solids 83, 185. Martin, S. W., Schiraldi, A. (1985), J. Phys. Chem. 89, 2070. McLeod, R.D., Cord, H. C. (1988), / Non-Cryst. Solids 105, 17. McLin, M., Angell, C.A. (1988), J. Phys. Chem. 92, 2083. Mercier, R., Tachez, M., Malugani, XP., Rousselot, C. (1989), Mater. Chem. and Phys. 23, 13. Minami, T. (1985), J. Non-Cryst. Solids 73, 273. Minami, T., Machida, N. (1989), Mater. Chem. and Phys. 23, 63. Mott, N.F. (1972), J. Non-Cryst. Solids 8-10, 1. Mott, N. F. (1977), The Structure and Non-Crystalline Materials. London: Taylor and Francis, pp. 101 — 107. Mott, N. R, Davis, E. A. (1979), Electronic Processes in Non-Crystalline Materials, 2nd ed. Oxford: Oxford University Press. Moynihan, C. T., Lesikar, A. V. (1981), J. Am. Ceram. Soc. 64, 40. Moynihan, C.T., Boesch, L. P., Laberge, N. L. (1973), Phys. Chem. Glasses 14, 122. Mueller, W., Krushke, D., Torge, M., Grimmer, A. R. (1987), Solid St. Ionics 23, 53. Nadkarni, C. S., Shivodar, V. S. (1983), Thin Solid Films 105, 115. Ngai, K.L., Rendell, R.W., Jain, H. (1984), Phys. Rev. B 30, 2133. Ovshinsky, S. R. (1968), Phys. Rev. Lett. 21, 1450. Owen, A.E. (1977), /. Non-Cryst. Solids 25, 372.

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Palmer, R. G., Stein, D. L., Abrahams, E., Anderson, P. W. (1984), Phys. Rev. Lett. 53, 958. Phillips, XC. (1979), Physics Today 35 (2), 27. Porai-Koshits, E.A. (1985), /. Non-Cryst. Solids 73, 79. Pradel, A., Ribes, M. (1989), Mater. Chem. and Phys. 23, 121. Pradel, A., Henn, F., Souquet, X L., Ribes, M. (1989), Phil. Mag. B60, 741. Rao, K. X, Rao, C. N. R. (1982), Mater. Res. Bull 17, 1337. Ravaine, D., Souquet, XL. (1977), Phys. Chem. Glasses 18, 27. Ravaine, D., Perera, G., Poulain, M. (1983), Solid St. Ionics 9-10, 631. Sayer, M., Mansingh, A. (1983), J. Non-Cryst. Solids 58, 91. Sayer, M., Mansingh, A. (1987), in: Noncrystalline Semiconductors, Vol. Ill, Pollak, M. (Ed.). Boca Rotan, Florida: C.R.C. Press, p. 1. Shlesinger, M.F., Montroll, E. W. (1984), Proc. Natl. Acad. Sci. U.S.A. 81, 1280. Spear, W. E., Le Comber, P. G. (1976), Phil. Mag. 33, 935. Street, R.A. (1982), Phys. Rev. Lett. 49, 1187. Street, R. A., Biegelsen, D. K., Jackson, W. B., Johnson, N. M., Stutzmann, M. (1985), Phil. Mag. B 52, 235. Street, R.A., Kakalios, X, Tsai, C.C., Hayes, T.M. (1987 a), Phys. Rev. B35, 1316. Street, R. A., Tsai, C. C , Kakalios, X, Jackson, W. B. (1987b), Phil. Mag. B56, 289. Tachez, M., Mercier, R., Malugani, XP., Dianoux, A.X (1986), Solid St. Ionics 18-19, 372. Tatsumisago, M., Hamada, A., Minami, T, Tanaka, M. (1983), J. Non-Cryst. Solids 56, 423. Tomandl, G., Schaeffer, H.A. (1985), /. Non-Cryst. Solids 73, 179. Tuller, H.L., Button, D.P., Uhlmann, D.R. (1980), J. Non-Cryst. Solids 40, 93. Williamson, D.L., Mahan, A.H., Nelson, B.P., Crandall, R. S. (1989), /. Non-Cryst. Solids 114, 226. Wong, X, Angell, C.A. (1976), Glass Structure by Spectroscopy, New York: Marcel Dekker, p. 750. Yamamoto, K., Namikawa, H. (1988), Jap. J. Appl. Phys. 27, 1845. Zachariasen, W. H. (1932), /. Amer. Ceram. Soc. 54, 3841.

General Reading Cox, P. A. (1987), The Electronic Structure and Chemistry of Solids, Oxford: Univ. Press (General Background to Electronic Properties of Solids). Duffy, X A. (1990), Bonding, Energy Levels and Bands in Inorganic Solids. Harlow, Essex: Longman (A

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14 Electrical Properties of Glasses

Chemist's Approach to Semiconduction and Glass Properties). Duffy, J.A., Ingram, M.D. (1976), J. Non-Cryst. Solids 21, 373. (Review of the Optical Basicity Concept). Elliott, S. R. (1990), Physics of Amorphous Materials, 2nd ed. Harlow, Essex: Longman (Glass Structure, Defects and Electronic Properties). Maclnnes, D.A. (1961), The Principles of Electro-

chemistry. New York: Dover Publications, Inc. (Ionic Interactions and Solution Electrochemistry). Mott, N. (1987), Conduction in Non-Crystalline Materials. Oxford: Clarendon Press (Band Theory of Amorphous Solids). Zallen, R. (1983), The Physics of Amorphous Solids. New York: Wiley Interscience (General Properties of Glass and Selected Applications).

15 Materials Technology of Optical Fibers John B. MacChesney and David J. DiGiovanni AT&T Bell Laboratories, Murray Hill, NJ, U.S.A.

List of Symbols and Abbreviations 15.1 Introduction 15.1.1 Digital Transmission 15.2 Signal Propagation 15.2.1 Total Internal Reflection 15.2.2 Numerical Aperture 15.2.3 Attenuation 15.2.3.1 Intrinsic Mechanisms 15.2.3.2 Loss Induced During Processing 15.2.4 Dispersion 15.2.4.1 Intermodal Dispersion 15.2.4.2 Chromatic Dispersion 15.2.4.3 Dispersion-Shifted Fiber 15.3 Fiber Fabrication Technologies 15.3.1 Double-Crucible Technique 15.3.2 Vapor-Deposition Techniques 15.3.3 Outside Processes: Outside Vapor Deposition 15.3.4 Vertical Axial Deposition 15.3.5 Inside Processes: Modified Chemical Vapor Deposition 15.3.5.1 Chemical Equilibria: Dopant Incorporation 15.3.5.2 Reduction of Hydroxyl Contamination 15.3.5.3 Thermophoresis 15.3.6 Plasma Chemical Vapor Deposition 15.4 Fiber Draw 15.4.1 Dimensional Control 15.4.2 Strength 15.4.3 Polymer Coating 15.4.4 Loss 15.5 Overcladding 15.5.1 Sol-Gel Processes 15.5.1.1 Alkoxide Sol-Gel Processing 15.5.1.2 Colloidal Sol-Gel Processing 15.6 Minimizing Defects 15.7 Active and Passive Fiber Devices 15.7.1 Optical Fiber Sensors Materials Science and Technology Copyright © WILEY-VCH Verlag GmbH & Co KGaA. Allrightsreserved.

753 754 754 756 756 756 757 757 757 758 758 758 759 760 760 761 761 761 764 764 766 766 767 768 769 769 769 770 770 770 771 771 773 774 774

752

15.7.2 15.7.2.1 15.8 15.9 15.10

15 Materials Technology of Optical Fibers

Optical Fiber Lasers and Amplifiers Fabrication of Rare-Earth Doped Optical Fiber Fluoride Glasses for Fibers Summary References

775 776 777 778 778

List of Symbols and Abbreviations

List of Symbols and Abbreviations a at Ci I /0 Kt L / n± n2 Pt r T 7^ Trxn V xt

core radius chemical activities of solid species i concentration of species i intensity measured after distance / input light intensity equilibrium constant of species i optical loss distance refractive index of the cladding refractive index of the core partial pressure of gaseous species radius temperature temperature at which the gas and the tube wall equilibrate gas reaction temperature normalized frequency mole fraction of species i in solid

a yt A 0O X

refractive index profile parameter activity coefficient =(n1 — n2)/n2; relative refractive index difference critical angle wavelength of light in vacuum

AC CVD DC IR MCVD NA OVD PCM PCVD UV VAD

alternating current chemical vapor deposition direct current infrared modified chemical vapor deposition numerical aperture outside vapor deposition pulse code modulation plasma chemical vapor deposition ultraviolet vertical axial deposition

753

754

15 Materials Technology of Optical Fibers

ited by the availability of frequency bands. Further improvements are realized with coaxial cable, but since losses are high, amplification is required every mile or two. Both microwave and coaxial transmission are currently being supplanted by transmission through hair-thin glass fibers made of exquisitely pure fused silica. Such fibers provide both enormous bandwidth and low loss. Glass as a transmission medium (Kompfner, 1965) was first explored in the 1960's, but at the time, the quality of commercially available glass was totally inadequate for optical transmission. Optical loss due to impurities was 104 —105 times higher than it is routinely today. This chapter will first outline the architecture and requirements of optical communications systems and then describe the development of materials processing of glass having unprecedented transparency into waveguide structures of precisely controlled dimensions and composition.

15.1 Introduction Communication by means of light pulses transmitted through glass fiber is rapidly replacing that of electronic messages transmitted over wire. Optical communication is superior because the frequency of visible or infrared radiation used as the signal carrier is vastly higher than the frequency of the electronic carrier used in wire transmission. Since the information carrying capacity increases directly with the carrier frequency, the potential afforded by optical communication is enormous. The message capacity of communications systems has increased progressively over the last century, as illustrated in Fig. 15-1, culminating in the development of optical communication. In the original telephone, two wires were required to transmit a single conversation using a DC carrier. With an AC carrier, greater than 10000 voice circuits per channel can be accommodated at frequencies up to one gigahertz (109Hz). However, since the resistance of copper wires increases with frequency, greater message capacity requires the use of other transmission media. Single sideband microwave radio transmission allows frequencies up to 10 GHz but is lim-

CD

107

c o x: o

106

CD O O

10*

To better understand the issues faced in the development of optical fiber, it will be helpful to understand the architecture of

Terrestrial system (1.7 Gb/s) Undersea cable (274Mb/s) Coaxial system

105 ~ Communication satelitesMicrowave links, 1800 channels

1000 100 CD

15.1.1 Digital Transmission

v

10

Coaxial cable. 600 channels

-12 Voice channels

1

First telephone lines j

|

I

I

|

I

i__

1890 1910 1930 1950 1970 1990 2010 2030 2050 Year

Figure 15-1. Chronology of message capacity showing exponential increase with time. Number of voice circuits transmitted per fiber pair increases rapidly with signal frequency.

755

15.1 Introduction

Electronic processing

3 1 2 Input signal

Encoder

Driver

Optical transmission

Laser Fiber

JM/L 11 01 10 Encoded signal

Electronic processing

•-1 Amplifier Detector

Decoder

3 1 2 Output signal

JIM/L 11 01 10 Reconstructed signal

Figure 15-2. Diagram illustrating digital transmission. Analogue waveform is sampled periodically and converted to digital code which is transmitted through fiber and reconstructed after detection.

current communication systems. As diagrammed in Fig. 15-2, an electronic circuit is used to modulate the output of a laser whose light is coupled into the fiber and carried to an electronic detector such as a photodiode. After detection, the information is reconstructed electronically. Instead of transmitting the analogue electronic signal directly, better light propagation is achieved by transforming the analogue waveform into a digital signal and transmitting a sequence of light pulses in a scheme called pulse code modulation, PCM. This is accomplished by sampling the analogue waveform periodically and assigning each sample a value between 0 and 256. Since a voice circuit has a maximum frequency of 4000 Hz, the waveform must be sampled 8000 times per second. This forms a string of numbers which is converted to binary code. That is, each number is represented by a string of 0's and l's. This string is used to turn the laser on and off at a frequency of 64000 times per second, generating a sequence of discrete light pulses, each of the same amplitude, which is transmitted through the fiber. As the light propagates, it is attenuated so that

the signal which reaches the photodetector after traveling tens of kilometers is much diminished in amplitude. However, for accurate reconstruction, it is necessary only to determine whether the laser was on or off; the light intensity is not important. Examination of the pulses as they arrive at the detector shows that the pulses may be considerably broadened in time, as illustrated by the pulse shapes shown in Fig. 15-2. This is the result of dispersion and eventually limits both the transmission distance and signal frequency since it causes initially discrete pulses to run into one another. Thus, for accurate reconstruction of the original waveform, the digital pulses must only be intense enough to register over background noise as long as they are not so broadened as to merge into one another. The challenge to materials science has been to fabricate a glass structure which can minimize both loss and dispersion and allow transmission of pulses at high frequency over long distances. While the drive of the past two decades has greatly increased the message capacity of communications systems, this increase is expected

756

15 Materials Technology of Optical Fibers

to continue into the future as higher frequency systems use an ever greater fraction of the available optical bandwidth.

15.2 Signal Propagation Before describing the evolution of fiber processing, it will be useful to describe some of the concepts used in the technology and some of the terms which define the waveguiding structure (cf. Chap. 12).

from the normal to the interface, is totally reflected. The upper diagram of Fig. 15-3 illustrates propagation through a step-index multimode fiber. The fiber is called multimode since there are many paths the light may follow. Those rays following paths which "graze" the interface are totally reflected. Such "total internal reflection" provides the means by which light can be transmitted for long distance without radiative losses. 15.2.2 Numerical Aperture

15.2.1 Total Internal Reflection

The refractive index of a material is a measure of the ratio of the speed of light in a perfect vacuum to its speed through the material. The higher the refractive index, the more the light is retarded or the slower it travels. When light travels from one medium to another, it is refracted or "bent" by an angle whose sine is proportional to the relative indices of the two media. This is known as "SnelFs Law". Light which travels in a higher refractive index medium and impinges on the interface with a lower refractive index medium at an angle greater than a critical angle, 0O measured

Cross section

Index profile

Input pulse

A basic parameter of lightguides is known as the numerical aperture (NA). The NA is a measure of the light collecting capability of the fiber and defines the minimum angle, @0, of incident light that can be totally internally reflected: (15-1)

NA = i

when the relative index difference A and where A

(15-2)

=•

n1 is the refractive index of the cladding and n2 is the index of the core.

Light path

Output pulse

Multimode stepped index

Multimode graded index

a Single mode stepped index

Figure 15-3. Structure of optical fiber showing light trajectories for different refractive index profiles.

15.2 Signal Propagation

The number of modes that can propagate in a fiber is governed by Maxwell's electromagnetic field equations and is related to a dimensionless quantity V called the normalized frequency:

757 10-1

r §2

(15-3) where X is the wavelength of light in vacuum and a is the core radius. For example, as the core radius becomes smaller, there are fewer paths which the light may follow and still undergo total internal reflection. When V is less than 2.405 for a step index core profile, only a single mode of light, the fundamental mode, can propagate; all other modes are cut-off. This governs the design of single mode fibers shown in the lower of the diagrams of Fig. 15-3. 15.23 Attenuation 15.2.3.1 Intrinsic Mechanisms Probably the mose important characteristic of an optical material for communication is the amount of absorption of the light as it propagates through the material (see Chap. 12 of this volume). Optical loss, L, is measured in terms of dB/km where L = 10 - log —, where J o is the input intensity, / is the intensity measured after a distance /. The first challenge to be faced in developing optical communications was finding a glass which is transparent at a desirable wavelength. In general, the intrinsic transmission window of glass is bounded at short wavelengths by ultraviolet absorption due to electronic transitions of the glass cations, and at longer wavelengths by molecular vibration. Between these limits, transparency is determined by Rayleigh scattering. These mechanisms and their wavelength dependence are

0.1

1.0 Wavelength ((jm)

Figure 15-4. Optical loss window is limited by electronic transitions, molecular vibrations and Rayleigh scattering. Also shown are losses due to 1 ppm of impurities.

shown in Fig. 15-4. Ultraviolet absorption is determined by the electronic band-gap of the materials. It decays exponentially with increasing wavelength and becomes negligible in the near IR. Rayleigh scattering results from glass composition and density fluctuations with size scale less than the wavelength of light. Losses from this source decrease as the fourth power of wavelength but tend to increase as dopants are added to the glass. The steeply rising absorption curve at longer wavelengths (> 1.55 jim) is due to cation-oxygen (molecular) vibrational modes in the glass lattice, such as Si-O. 15.2.3.2 Loss Induced During Processing Superimposed on these intrinsic loss mechanisms are losses arising from imperfections created during fabrication of the glass fiber. Scattering can be increased by perturbations to the waveguide structure such as imperfections at the core-clad interface or bubbles or cracks. Perturbations larger than the wavelength of light, such as diameter fluctuations, cause Mie scattering. Even in perfect fibers, impurities incorporated in the glass from the starting mate-

758

15 Materials Technology of Optical Fibers

rials or introduced during processing cause specific absorption bands. In glass, such absorption bands can be quite broad and dominate the loss spectrum. Transition metal ions and hydroxyl (OH~) impurities are the most common and the most bothersome. Representative impurity bands (Schultz, 1974), are shown in Fig. 15-4 in which the loss levels are those expected from about 1 ppm of individual impurities. In addition, defects in the glass network such as suboxide species of silicon and germanium can be formed during high temperature processing or from exposure to radiation. These defects also have characteristic absorption bands. In practice, a typical fiber loss curve is dominated by the intersection of the UV absorption edge and the X~A dependence of Rayleigh scattering. Thus, lowest loss exists in the range 1.3 jim to 1.55 jim, though the Si-OH overtone at 1.38 jum splits this zone into two separate telecommunications windows. Until recently, communications systems could not exploit the lowest loss at 1.55 (im due to problems with signal dispersion, as described below.

sion resulting from the different paths individual modes travel and chromatic dispersion which is quantitatively much smaller. [For a detailed discussion of propagation characteristics see Midwinter (1979) and Miller and Chynoweth (1979).] 15.2.4.1 Intermodal Dispersion Intermodal dispersion arises since different modes may travel zig-zag or helical courses within the fiber's core while the fundamental mode travels a shorter straight line. Each mode thus arrives at a different time. To diminish delay, fibers are designed so that modes which travel the furthest propagate through lower refractive index glass within which their speed is faster. This is accomplished by grading the index profile of the core as shown at the center of Fig. 15-3. Minimum intermodal dispersion is achieved with an index distribution which varies as n2[\— A (r/a)*], where n2 is the index of the core, A is the relative index difference, a is the core radius and the profile parameter, a, has a value of approximately 2, though the optimum value is wavelength dependent.

15.2.4 Dispersion

While the importance of lower attenuation is obvious, the effects of dispersion are subtle but equally important. As described above, current communications systems use digital transmission in which discrete light pulses propagate through the fiber. After traveling many kilometers they are diminished by absorption and broadened by dispersion. Eventually these pulses become so broadened as to be indistinguishable from each other. The distance the signal can travel before this happens depends upon how well dispersion is controlled. In multimode fibers there are two sources of dispersion, intermodal disper-

15.2.4.2 Chromatic Dispersion In singlemode fibers where intermodal dispersion is not a factor, the main source of pulse broadening is chromatic dispersion. Optical sources have finite spectral width, that is, they emit light over a small range of wavelengths, and the slightly different wavelengths travel at different velocities owing to two effects, material and waveguide dispersion. The total chromatic dispersion which exists in a singlemode fiber is the sum of these two components, illustrated in Fig. 15-5. In this figure, dispersion is presented as picoseconds of pulse spreading per kilometer of fiber tra-

15.2 Signal Propagation 20.0 Material

-p 10.0

Total chromatic dispersion

in

3r c o

0

U) 0)

Waveguide

1-10.0

-20.0

1.1

1.2 1.3 U 1.5 Wavelength (jjm)

1.6

Figure 15-5. Total chromatic dispersion is the sum of material dispersion and waveguide dispersion.

versed per nanometer of spectral width of the optical source, ps/km-nm, and is plotted against signal wavelength for a typical fiber. Material dispersion is the intrinsic refractive index variation of the bulk material, with wavelength. For glasses of high silica composition it increases with wavelength, passing through zero close to 1.3 jam. Since current waveguides are composed principally of SiO2 lightly doped with other ions, material dispersion is essentially independent of the fiber design. Waveguide dispersion, on the other hand, depends upon the spread of optical power beyond the fiber core into the surrounding cladding, which has a different wavelength/ velocity relationship since it is a different material. Light propagating in different physical regions of the fiber travels at slightly different speeds and arrives at different times. 15.2.4.3 Dispersion-Shifted Fiber

Since waveguide dispersion is a function of the fiber design, it may be controlled by

759

proper design of the fiber core diameter and refractive index profile. The conventional step index profile produces a shallow wavelength dependence, while a triangular shaped fiber core having higher index and smaller core radius results in a steeper wavelength dependence. It is thus possible to balance waveguide dispersion against material dispersion and shift the point where they cancel. As illustrated in Fig. 15-6, step index profiles show zero dispersion at 1.3 jim, but this point may be shifted to 1.55 jLim by using a small core and high refractive index. Such a dispersion-shifted design is important for more advanced systems, just now being planned, since the lower intrinsic absorption at 1.55 |im can now be exploited. More complex index profiles can yield low dispersion over a broad wavelength region (Cohen, 1983), as indicated by the dispersion-flattened profile in Fig. 15-6. Total chromatic dispersion crosses zero at two wavelengths and has a broad spectral region of low dispersion between. Such fibers are important for systems where

1.3 pm Operation

20.0 Smaller core higher index

10.0

JLVJL

More complex structure

Q. in Q

1.6 1.7 Wavelength (|jm) -10.0 Dispersion shifted -20.0 L.

Figure 15-6. Waveguide dispersion depends on the index profile and can be balanced against material dispersion to shift the zero-dispersion wavelength to 1.55 jim. More complex profiles can yield dispersionflattened fibers.

760

15 Materials Technology of Optical Fibers

many channels operating at wavelengths around 1.3 or 1.55 }im are multiplexed on a single fiber.

Core glass Cladding glass

Inner crucible Outer crucible

Furnace

15.3 Fiber Fabrication Technologies The foregoing has attempted to put into perspective the challenge presented by optical communications to materials science: fabrication of a fiber having the highest purity to achieve low losses and with a precise index profile to achieve low dispersion at the particular wavelength of operation. Pioneering work on fibers began in the 1960's with the intention of producing multimode fibers with acceptably low loss. At that time, optical quality glass exhibited losses on the order of 1000 dB/km, but losses of less than 20 dB/km were required if this new transmission mode was to compete with existing copper wire systems. It was quickly realized that reduction of transition metal impurities was the major obstacle. 15.3.1 Double-Crucible Technique

The first attempt at producing high purity glass, the so-called double-crucible technique, proceeded along the lines of conventional glass melting but used specially prepared constituents (Pearson and French, 1972; Beals and Day, 1980). Soda-lime-silicate and sodium-borosilicate glasses were made from materials purified to parts per billion levels of transition metal impurities by ion exchange, electrolysis, recrystallization or solvent extraction. These starting glasses were melted, fined, drawn to cane and fed into an ingenious continuous casting system composed of concentric platinum crucibles, shown in Fig. 15-7. A thin stream of core glass

Fiber

Figure 15-7. Double crucible process for making multicomponent glass fibers.

flowed from the upper crucible, passed through the reservoir of cladding glass and was concentrically surrounded by the cladding as it flowed through the orifice of the lower thimble. The time and temperature of core-cladding contact in the cladding reservoir were controlled enabling diffusion to produce the index gradient needed to minimize intermodal dispersion. Despite its elegance, overwhelming problems beset this method from the start. First, contamination during processing raised the impurity level from the ppb level in the constituents to ppm levels in the fiber. Many attempts were made to eliminate this contamination and improvement was achieved by using the oxygen partial pressure of the atmosphere during processing to control the redox conditions within the molten glass. Absorption by iron and copper, the two principal contaminants, could thus be minimized by altering their valence state. Iron could be oxidized primarily to the Fe 3 + state and copper retained in the monovalent state by processing in a controlled oxygen atmosphere. Thus, strong absorptions by Fe 2 + and Cu 2 + at near infrared wavelengths were diminished.

15.3 Fiber Fabrication Technologies

Fibers adequate for commercial systems of the time were made this way. Losses as low as 5 dB/km were achieved at 0.9 jam but the lower losses offered by the 1.31.5 jam window were unattainable using this technique. Fundamental electronic vibrations as well as severe OH ~ contamination were intrinsic to the starting materials as well as the glass composition and could not be appreciably lowered by improved processing. The method was still-born as it was introduced to the market owing to the advent of a superior technology. 15.3.2 Vapor-Deposition Techniques

The double crucible technique was short lived because vapor deposition techniques soon appeared which were capable of lower losses from the visible into the infrared (see Chap. 2 of this volume). These techniques appeared in the early 1970's and may be categorized as either inside or outside processes. Both use oxidation of silicon tetrachloride vapor to produce submicron amorphous silica particles. Other chloride vapors such as germanium tetrachloride and phosphorus oxychloride are used as sources of dopants in the silica. Outside deposition utilizes flames hydrolysis whereby chloride vapors pass through a methane-oxygen or hydrogen-oxygen flame to produce a "soot" of SiO2 particles. The particles partially sinter as they collect on a mandrel. The inside process uses these same reactants together with oxygen, but the reaction occurs inside a silica tube in the absence of hydrogen. The high temperature needed to react halide vapors with oxygen are provided by an oxygen-hydrogen burner which traverses along the tube as it rotates on a glass working lathe. The reactions produce particles by oxidation rather than hydrolysis. These particles are deposited on the inside wall of the tube

761

downstream of the torch and are sintered to form a vitreous layer as the torch moves past the deposit. 15.3.3 Outside Processes: Outside Vapor Deposition

Two versions of outside processes have been developed. These are the Outside Vapor Deposition (OVD) (Keck et al., 1973) process developed by Corning Glass Works, and the Vertical Axial Deposition (VAD) (Izawa and Inagaki, 1980) version developed by a consortium of Japanese cable makers and Nippon Telephone and Telegraph Corporation. In the former, shown in Fig. 15-8, soot is deposited layer by layer on a horizontal, rotating mandrel at sufficiently high temperatures to partially sinter the particles to form a porous silica cylinder. A core of GeO 2 -SiO 2 composition is deposited first, followed by an SiO2 cladding. At the conclusion of deposition, the mandrel is removed and the tube is sintered at 1500-1600 °C to vitreous silica in a furnace having an atmosphere of He, O 2 and Cl 2 . The central hole is collapsed either during the sintering or subsequently as the preform is drawn to fiber. 15.3.4 Vertical Axial Deposition

The VAD process also forms a cylindrical body using soot, but deposition occurs end-on as shown in Fig. 15-9. Here a porous soot cylinder is formed without a hole by depositing the core and cladding simultaneously using two torches. When complete, the body is sintered under conditions similar to those used for OVD. A fundamental difference between the two processes is that while the composition profile of the OVD preform is determined by changing the composition of each layer, the VAD profile depends upon subtle control of the gaseous constituents in the flame

762

15 Materials Technology of Optical Fibers

0 2 + Metal halide vapors

a)

Burner .Soot boule

Mandrel

Soot preform cross section

Preform sintering

Fiber drawing

-Soot

Furnace

Air gap

A I A IAI *

I *• Core

Furnace

Glass Clad

b)

C)

d)

Figure 15-8. Outside Vapor Deposition (OVD) process. Diagram shows four steps: (a) deposition on a mandrel; (b) profile of soot preform after removal of mandrel; (c) preform sintering; (d) fiber drawing.

and the shape and temperature distribution across the face of the growing soot boule. Critical to the development of VAD was the design of torches composed of up to ten concentric silica tubes. Typically, reactant vapors pass through one or more of the central passages where they are protected from premature reaction by a ring of inert shield gas. The outer series of tubes alternate between hydrogen and oxygen to compose the flame. By manipulation of gas flows, the temperature and particle distri-

bution in the flame can be controlled to determine the surface temperature distribution and the shape of the boule. In spite of this rather fragile control of composition, VAD had one significant advantage over first generation OVD. Recall that at this time, transmission systems were using graded index, multimode fiber. The high refractive index differences between core and cladding required by such fiber was obtained with heavy core doping. This produced a large mismatch in thermal expansion between core and cladding and

15.3 Fiber Fabrication Technologies

I

a) Cladd torch

in9

763

To elevator drive

-fB

Core torch

Soot preform cross section

Preform sintering

Fiber drawing

Soot

Furnace

Furnace

Glass

c)

d)

Figure 15-9. Vertical Axial Deposition (VAD) process, (a) End-on growth of boule; (b), (c), (d) see Fig. 15-8.

caused cracking of consolidated OVD preforms at the inner surface as the preform cooled below the glass transition temperature. Since VAD preforms do not have a central hole, they can better withstand thermal stress. The major challenge to VAD was how to create an optimized index profile to minimize mode-dispersion. Initially it was thought that control of the GeO 2 distribution across the boule required several GeCl4 sources, each of different composition. However, it was found that such grad-

ing could be accomplished by control of the boule surface temperature distribution. Eventually, process development focused critically upon the shape of the growth face and the temperature profile across it. Fig. 15-10 (Edahiro et al., 1980) shows GeO 2 incorporation into silica as a function of the temperature of the boule endface. Below 400 °C, GeO 2 is lost by vaporization of discrete crystalline particles when the boule is sintered at high temperature.

764

15 Materials Technology of Optical Fibers

Non-crystalline form j

o o t_

"c

I

Q>

O

/

Hexagonal crystalline form

c o o

a*

/

N

O

/

\

f

\

\ I 0

/ i

i

200 400 600 800 Substrate temperature (°C)

Figure 15-10. Relation between substrate temperature and GeO 2 concentration in VAD process.

15.3.5 Inside Processes: Modified Chemical Vapor Deposition

Inside processes such as Modified Chemical Vapor Deposition (MCVD) had a different origin. Following the tradition of the electronics industry, chemical vapor deposition (CVD) techniques were used to produce doped silica layers inside silica substrate tubes (MacChesney et al, 1973). The concentration of reactants was very low to inhibit gas phase reaction in favor of a heterogeneous wall-reaction which produced a vitreous, particle free deposit on the tube wall. The tube was collapsed to a rod and relatively low loss fiber obtained. However, deposition rates were impractically low and attempts to increase them always produced silica particles which deposited on the tube wall and resulted in excess loss. The solution was to exactly reverse CVD practice: intentionally produce a gas phase reaction by increasing the reactant flows by more than ten times. Submicron particles were thus produced which deposited on the tube wall and were fused into clear, pore-free glass as the torch traversed along the tube.

MCVD was thus developed (MacChesney et al., 1974) to the process diagramed in Fig. 15-11. High purity gas mixtures are injected into a rotating tube which is mounted in a glass working lathe and heated by a traversing oxy-hydrogen torch. Homogeneous gas phase reaction occurs in the hot zone created by the torch to produce amorphous particles which deposit downstream of the hot zone. The heat from the moving torch sinters this deposit to form a pure glass layer. Torch temperatures are sufficiently high to sinter the deposited material, but not so high as to deform the substrate tube. The torch is traversed repeatedly to build up, layer by layer, the core or cladding. Composition of the individual layers is varied between traversals to build the desired fiber index structure. Typically 30-100 layers are deposited to make either singlemode or graded index multimode fiber. 15.3.5.1 Chemical Equilibria: Dopant Incorporation

After the initial demonstration of feasibility, fundamental investigations established the knowledge required to create a commercial process. For instance, it was necessary to better understand the chemistry of the MCVD process in order to control the incorporation of GeO 2 and limit hydroxyl impurities. In addition, to increase fabrication efficiency, it was necessary to understand the mechanism by which particles deposit on the substrate tube as well as the manner in which the silica particles are sintered into pore-free glass. Although process development preceded quantitative understanding, optimization of the commercial process required this knowledge. The chemistry of SiCl4 and GeCl 4 oxidation was investigated by infrared spec-

765

15.3 Fiber Fabrication Technologies

I. Tube setup V> >-»v

II. Deposition

7^ i ( J

^ V>

/ N

»

Heat source

^


S N Heat source

»

Figure 15-11. MCVD process consists of deposition of glass layers inside silica tube, collapse of tube to solid rod and drawing of preform into fiber.

III. Collapse

^3^^^/ \ ^ Heat source

IV. Fiber drawing

^_ Fiber Heat source

troscopy (Wood et al., 1987). Samples of effluent gases from typical MCVD reactions demonstrated that as the maximum hot zone temperature reaches 1300 K, SiCl4 begins to oxidize to Si 2 OCl 6 . This is shown in Fig. 15-12. Up to 1450 K, the amount of oxychloride increases to a maximum, while at higher temperatures the SiCl4, Si 2 OCl 6 , and POC13 content decrease until their concentration in the effluent is insignificant above about 1750 K. Above this temperature, all reactants are converted to oxides. The behavior of GeCl 4 is different. Its concentration in the effluent gas stream decreases between 1500 K and 1700 K, but above 1700 K remains approximately 50 percent of its original value. It is clear that the major part of the initial germanium is unreacted and escapes in the effluent. These results indicate that at low temperatures (T<1600K) the extent of the reaction for SiCl4, GeCl 4 , and POC1 3 is controlled by reaction kinetics, while at higher temperatures thermodynamic equilibria become dominant. It is clear from rate studies that the residence times in the hot zone are sufficient to produce equilibrium above 1700 K. The SiCl4 and GeCl 4

concentrations at high temperatures are strongly influenced by the equilibria: SiCl4(g) + O2(g) (15-4)

-> SiO2(s) + 2Cl2(g) and GeCl4(g) + O2(g) - GeO2(s) + 2Cl 2 (g).

1000

U00

(15-5)

1800

2200

T(K)

Figure 15-12. MCVD effluent composition as a function of hot zone temperature. Starting reactants: 0.5g/min SiCl4, 0.05 g/min GeCl 4 , 0.016 g/min POC1 3 , 1540cm 3 /niinO 2 .

766

15 Materials Technology of Optical Fibers

Equilibrium constants for these reactions may be written (15-6) K GeO 2

(15-7)

where Pt are the partial pressures of gaseous species and a{ represent the chemical activities of the solid species. The activities can be approximated by ytxi9 where xt is the mole fraction of the particular species in the solid and yt is the activity coefficient. An activity coefficient of unity implies an ideal solution obeying Raoult's law. The equilibrium constants for these reactions have been determined as a function of temperature and indicate that Eq. (15-4) strongly favors the formation of SiO2 at high temperature, as verified by the experiments described above. Oxidation of GeCl4 by Eq. (15-5), on the other hand, is incomplete since the equilibrium constant, i£ GeO2 , is less than unity at temperatures above 1400 K. This means that only a fraction of the germanium starting concentration will be present as GeO 2 . The presence of significant Cl2 concentration resulting from the complete oxidation of SiCl4 shifts the equilibrium further toward GeCl 4 by the law of mass action. Low oxygen partial pressure has the same effect. 15.3.5.2 Reduction of Hydroxyl Contamination

A second important aspect of MCVD chemistry is the incorporation of the impurity OH" (Walker et al., 1981). Reduction of OH" in optical fibers to ppb levels is essential for realization of low attenuation in the 1.3-1.55 jum region. Hydrogen species originate from three sources: diffusion of OH~ from the substrate tube during processing, impurities in the starting

reagents and carrier oxygen gas, and contamination from leaks in the chemical delivery system. The OH ~ level in the fiber is controlled by the reaction (15-8)

H 2 O + Cl2 with equilibrium constant

(15-9) The concentration of OH incorporated into the glass, CSiOH, is described by

\2(P

\i/2

(Po2)1/4

(15-10)

During deposition in MCVD, Cl2 is typically present in the range 3-10% due to oxidation of the chloride reactants. This is sufficient to reduce OH~ by a factor of about 4000. However, chlorine is typically not present during collapse and significant amounts of OH ~ can be incorporated by diffusion of torch byproducts through the silica tube. Fig. 15-13 shows the dependence of the SiOH concentration in the resultant glass as a function of typical POl and P cl2 concentrations used during MCVD deposition and collapse with 10 ppm H 2 O in the starting gas. The figure also shows typical contamination of the VAD and OVD soot processes. 15.3.5.3 Thermophoresis

Turning now from the reaction equilibria, we consider the mechanism of deposition of particles on the tube walls. The SiO2 particles produced by vapor phase reaction have diameters in the range 0.02-0.1 |im and are thus entrained in the gas flow. Without the imposition of a temperature gradient they would remain in the gas stream and exit from the tube end. However, temperature gradients in the gas

15.3 Fiber Fabrication Technologies

767

MCVD collapse conditions

"|.MCVD deposition & consolidation 10-9

Figure 15-13. Typical incorporation of OH ~ during processing stages of MCVD, for 10 ppm H 2 O in chemical precursors.

10" 108

106

10*

102

10°

10"

10"

D 1/2

stream produced by the traveling torch give rise to the phenomenon of thermophoresis (Simpkins et al, 1979). Here, particles residing in a thermal gradient are bombarded by energetic gas molecules from the hot region and less energetic molecules from the cool region. A net momentum transfer forces the particle toward the cooler region. Within an MCVD substrate tube, since the wall is cooler than the center of the gas downstream of the torch, particles are driven toward the wall where they deposit. The MCVD process is shown schematically in Fig. 15-14 in terms of: 1) heat transfer in the hot zone, 2) reaction, 3) particle formation, 4) particle deposition beyond the hot zone where the tube wall

Reaction zone

Thermophoretic deposit

POCl3 GeCL ^ He

Consolidated deposit

Quartz substrate

f\

becomes cool relative to the gas stream and 5) consolidation of previously deposited particles in the hot zones as the torch traverses to the right. A mathematical model for thermophoretic deposition (Walker et al., 1980 a), experimentally verified, concluded that deposition efficiency (ratio of SiO 2 equivalent entering tube to that contained in exhaust) may be expressed as e = 0.8 [1 — Te/TTxn] where Trxn is the gas reaction temperature and Te is the temperature downstream of the torch at which the gas and the tube wall equilibrate. Typically, Te is about 400 °C and Trxn about 2000°C, giving an efficiency on the order of 60%. Note that the efficiency is not a function of the maximum tube temperature. Examination of the process of consolidation of the soot layer on the inner surface of the silica tube revealed the mechanism to be viscous sintering (Walker et al., 1980 b). By this mechanism the rate of consolidation is proportional to the sintering time and surface tension and inversely proportional to the void size, initial soot density and glass viscosity.

Torch

15.3.6 Plasma Chemical Vapor Deposition Traverse

Figure 15-14. Particle formation and thermophoretic deposition in MCVD.

A second inside process, Plasma Chemical Vapor Deposition PCVD (Kuppers

768

15 Materials Technology of Optical Fibers

2.45 GHz

1200°C Furnace

Mirrnwnvp

cavity I

Reactants

I

•

c

~ ~ ^ — I — Plasma

I

- Pump (10"3bar)

I

Substrate tube Traverse

Figure 15-15. Schematic representation of PCVD process.

and Lydtin, 1980) is similar to MCVD in that it uses the same reactants inside a silica substrate tube which is collapsed after deposition and drawn to fiber. However, the oxidation of reactants in the tube is initiated by a non-isothermal microwave plasma inside the tube rather than by heating the exterior of the tube, as shown in Fig. 15-15. In addition, the generation of the plasma requires a reactant vapor pressure of only a few torr. A microwave cavity, operating at 2.45 GHz, traverses along the substrate tube and promotes chemical reaction. However, a particulate soot is not produced but instead, deposition occurs directly on the tube wall to form a thin glass layer. Furthermore, the reaction and deposition of both GeO 2 and SiO 2 is much more efficient than in MCVD, approaching 100%. Another advantage, especially for multimode preforms, is that since the plasma involves no latent heat, it can be traversed very rapidly to produce hundreds of layers. The resulting deposit thus has a very smooth and precise index profile essential for minimizing intermodal dispersion.

15.4 Fiber Draw Typical preforms produced by the above methods are about a meter in length and between 2 and 7.5 cm in diameter. These

are drawn into 125 jim diameter fiber by holding the preform vertically and heating the end of the preform above the glass softening temperature until a gob of glass falls from the end. This forms a neck-down region which provides transition to a small diameter filament. Uniform traction on this filament results in a continuous length of fiber. Before this fiber contacts a solid surface, a polymer coating is applied to protect the fiber from abrasion and preserve the intrinsic strength of the pristine silica. The fiber is then wound on a drum. While the basic principles of fiber drawing were established prior to the advent of optical fiber technology, stringent fiber requirements necessitated improvements in process control and understanding of the effects of draw conditions on optical performance. Fiber is now drawn without inducing excess loss while maintaining high strength, dimensional precision and uniformity.

Feed mechanism Preform Furnace \

Fiber diameter monitor Fiber cooling distance Coating applicator

"I

Coating concentricity monitor

Curing furnace or lamps

Coating diameter monitor Capstan Figure 15-16. Schematic of draw process.

15.4 Fiber Draw

The essential components of a draw tower, shown schematically in Fig. 15-16, are a preform feed mechanism, a furnace capable of 1950-2200 °C? a diameter monitor, a polymer coating applicator, a coating curing unit, a traction capstan and a take-up unit. The furnace is typically either a graphite resistance type or an inductively-coupled radio frequency zirconia furnace. The former requires an inert atmosphere to prevent oxidation of the graphite element. The zirconia furnace may be operated in air but must be held above 1600°C, even when not in use, since the volume change associated with the crystallographic transition of zirconia at this temperature can cause stress-induced fracture. Its advantage is that the heater element emits fewer contaminating particles. 15.4.1 Dimensional Control

The uniformity of the fiber diameter depends on control of the preform feed rate, the preform temperature and the pulling tension. Over long lengths of fiber (>100cm) diameter variations can result from changes in preform diameter and drifts in furnace temperature and the speeds of the feed and capstan motors. Diameter variations with shorter length period arise from perturbations in the temperature of the neck-down region caused by thermal fluctuations. These may be minimized by control of convective currents and nonuniform gas flows inside the furnace as well as acoustical and mechanical vibrations. The diameter monitor positioned below the furnace provides feedback to the capstan, adjusting the draw tension to maintain constant fiber diameter.

769

15.4.2 Strength

Although the intrinsic strength of silica is extremely high, about 14 GPa, in practice, long lengths of fiber are considerably weaker due to mechanical flaws which act as stress concentrators (see Chap. 13 of this volume). The strength of a given length of fiber is thus a reflection of the most serious flaw. Flaws are due to either chemical attack or mechanical abrasion from contact of the preform or fiber with a solid material. Strength degradation due to mechanical abrasion of the preform may be eliminated by fire-polishing the preform before draw, but dust evolved from the furnace element may degrade strength. A clean atmosphere in the path from the furnace to the coating applicator afforded by filtered air can greatly reduce damage. Flaws which are present after draw generally do not cause immediate failure but require a period of growth, introducing the concept of fatigue. Although the exact mechanisms have not yet been established, it is currently believed (DiMarcello et al, 1985) that corrosion by OH~ causes growth of subcritical flaws to the point where fracture occurs. Fatigue may be minimized by preventing OH ~ from reaching the silica surface, for example by drawing in a dry environment and simultaneously applying hermetic coatings to the fiber surface. Hermetic coatings are currently being developed since the susceptibility of the fiber to fatigue is a major concern for longterm reliability. 15.4.3 Polymer Coating

As the optical fiber exits the furnace, ideally it has a flaw-free, pristine surface. Exposure to the atmosphere and physical contact would rapidly degrade this surface if it were not immediately protected. Once the fiber has been given sufficient time to

770

15 Materials Technology of Optical Fibers

cool, it enters the coating cup, a vessel filled with a liquid polymer. As the fiber emerges from the bottom of the die, a uniform coating is formed and is subsequently cured. The best coatings are those which may be induced to cross-link rapidly, such as thermally-cured silicone rubbers and UVcured urethane acrylates. The primary function of the coating is to protect the fiber from abrasion, but the coating may degrade the optical properties of the fiber if not free of particles, applied concentrically and without defects. Otherwise, the coating causes nonuniform stress upon solidification and increases the fiber loss. Low modulus coatings can actually improve the optical properties of the fiber by reducing microbending losses since they tend to cushion the fiber from stress induced during cabling or deployment. 15.4.4 Loss As mentioned above, optical loss may be increased in the draw process by nonuniformities in fiber diameter and coating thickness. These are waveguide losses, but additional loss mechanisms are also present. For example, increased losses can occur for high draw tension in pure silica core fiber as a result of ruptured Si-O bonds. High draw temperature can cause defects, such as a germanium suboxide species, which have well-defined absorption bands. Similar GeO 2 defects may be induced by the UV lamps used to cure the coatings. These latter defects may be controlled by filtering out the short UV light and using UV-absorbing coatings on the fiber.

15.5 Overcladding Drawing technology and each of the processes OVD, VAD, MCVD, and PCVD

have been developed to the point where they yield both multimode and single mode fiber whose loss is limited only by the intrinsic properties of fused silica, their principal constituent. In their initial form, each produced a preform yielding only about 10 km of fiber. However, as singlemode replaced multimode fiber, a third generation of fiber processing evolved. In multimode fiber, the ratio of core diameter to fiber diameter is typically about 0.5 while this ratio is less than 0.1 for singlemode fiber. Thus, the processing time of singlemode preforms is shortened considerably due to the smaller core region. However, since the glass from the substrate tube comprises the bulk of the fiber, the yield from each preform is limited by the size of this tube. The yield of each preform may be increased by using an "overcladding" technique, as follows. After a preform core rod with an oversized core region is fabricated by conventional means, the outer diameter is built up to attain the proper proportions. The outer diameter is increased either by jacketing the preform with a second silica tube or by using it as a bait rod for subsequent OVD or VAD soot deposition. This procedure increases the length of fiber produced from a vapor deposited preform, yielding up to a hundred kilometers of fiber. 15.5.1 Sol-Gel Processes Given a singlemode fiber technology based on overcladding core rods with silica tubes or soot, it is natural to consider other means of preparing overcladding material. Alternate overcladding processes become particularly appealing since fibers can be designed so that negligible optical power penetrates beyond a radius of 30 to 40 jim (MacChesney et al, 1985). Thus, the vapor derived core and cladding need comprise

15.5 Overcladding

only about 5% of the fiber mass while the remaining 95% may be derived from lower quality, less expensive materials. 15.5.1.1 Alkoxide Sol-Gel Processing Suitable overcladding material may be prepared by sol-gel and powder forming techniques (see Chap. 2 of this volume). In one instance, a chemical precursor, typically a silicon alkoxide such as Si(OC 2 H 5 ) 4 , is reacted with water in the presence of ethanol and an acid catalyst. The sol is cast into cylindrical molds and polycondensation of the resulting silanol groups produces a filamentary siloxane gel network. The gel body is dried and consolidated to form silica glass as films or bulk bodies. Alternatively, commercial colloidal powders obtained from flame hydrolysis, commonly known as "fumed silica", are formed into bodies by mechanical compaction (Dorn et al, 1987), centrifugation (Buchmann et al., 1988), or casting/gelation (Shibata et al., 1986). In this last approach, the silica particles (generally 0.05-0.5 jim) are dispersed in water to form a sol. Control of pH or addition of surface active agents is used to promote electrostatic or steric stabilization to inhibit interparticle attractive forces which cause agglomeration. The dispersed colloid containing up to 60wt.% silica is cast after the stabilizing forces are dissipated. Gelation by van der Waals attractive forces soon follows to produce a semirigid body. After drying, the porous silica body can be sintered to glass much like the soot boules formed in the OVD and VAD processes. Drying of the gel body is accompanied by large stresses due to shrinkage and capillary forces which generally cause the body to fracture. To date, alkoxide derived bodies as large as overcladding tubes have not been successfully fabricated using this

771

approach. However, there has been much effort to fabricate all-gel preforms since the chemical precursors are available in high purity and the refractive index of the glass may be altered by adding dopant alkoxides. Fibers with a raised-index cores, doped with alkoxides such as Ge(OC 2 H 5 ) 4 , have not yielded fiber with losses comparable to that produced by vapor technique since the germanium dioxide either dissolves in the liquor or precipitates in some crystallized form. The usual product after consolidation contains pores and its index is raised only marginally, suggesting that any germanium present in the gel is lost in firing. The alkoxide route has achieved its best success in fabricating fibers with a silica core and lowered index cladding (Shibata et al., 1987). Hydrolysis and polycondensation of Si(OC 2 H 5 ) 3 F lowers the index by incorporating fluorine. The sol is cast, gelled and dried to yield a porous silica body with surface area of 200-650 m2/gSuch high surface area allows consolidation at low temperatures in a fluorine containing atmosphere. The result is a downdoped tube (A = - 0.62%) which is collapsed with a stream of oxygen flowing down the center. This removes the fluorine from the inner tube wall and produces a core region with higher refractive index than the fluorine doped cladding. Losses as low as 0.4 dB/km have been reported for such fiber. 15.5.1.2 Colloidal Sol-Gel Processing The colloidal approach has achieved more success in producing large bodies for overcladding. The starting material is commercial fumed silica such as Aerosil OX-50 (Degussa A.G., Frankfurt, FRG). This is distinguished from other colloidal silicas by its comparatively large size (mean parti-

772

15 Materials Technology of Optical Fibers

"Fumed" silica

TEOS (C2H5O)4Si

SiCl,

Gel granulate/consolidate

Synthetic sand Gel tube

1Dry

Core rod

1 iI

Particle feed to Plasma torch

1

Preform assembly

Dehydrate/, Draw consolidate

Fiber

c: - •• •* -

Preform overclad

MCVD core rod Draw

Fiber

Figure 15-17. A hybrid sol gel strategy in which gel is cast into tubes and used to overclad a core rod. Alternatively gel is granulated then fusion-sprayed on a preform to accomplish overcladding.

cle size 40 nm). It is produced by flame hydrolysis and is similar to "soot" produced by OVD and VAD. The larger particles result in gel bodies of lower density and larger pore size. Thus, drying stress is reduced since the capillary forces are decreased. Furthermore, lower density enhances permeation of the porous silica body by reactive gasses such as Cl 2 . Consolidation in a chlorine containing atmosphere inside a non-contaminating silica muffle allows removal of impurities such as OH~, transition metal and alkali ions introduced during processing as well as those initially present. Recall that this situation is just the reverse of that encountered in the earlier Double Crucible process, which failed because very pure starting materials were contaminated during processing.

Purification from transition metals may be enhanced by use of a low oxygen partial pressure atmosphere, as indicated by the reaction Fe 2 O 3 + 2Cl 2 -> 2FeCl 2 + 3/2O 2 (15-11) By firing in an atmosphere protected from air intrusion, oxygen partial pressures can be in the range of 10 ~6 atm. Thus, at temperatures between 600 and 1000°C, iron and other impurities are effectively removed (MacChesney et al, 1987 b; Clasen, 1988). This was demonstrated by intentionally contaminating a gel body with 1 wt.% hematite. After a two step dehydration/consolidation treatment, the residual iron content was only 40 ppb. The process of overcladding with gelderived material may be accomplished using two strategies, as diagrammed in Fig.

15.6 Minimizing Defects

15-17. On the left, in the "rod-in-tube" process, an overcladding tube is formed from gel and then consolidated directly onto a core rod (MacChesney et al, 1987 a). Tubes for the rod-in-tube process are formed by dispersion, milling, casting and gelation of colloidal silica. After removal from the mold and air drying, they are placed over a core rod and the assembly is dehydrated, consolidated and drawn into fiber. A satisfactory interface, free of bubbles and other defects, must be obtained between the core rod and the gel-derived overcladding tube. By proper cleaning of the core rod and under appropriate consolidation conditions, the loss of the eventual fiber can be as low as that of the original core rod. On the right, instead of casting a tube, the wet gel is granulated into particles which are fed through an oxygen plasma torch to deposit glass droplets onto the core rod (Fleming, 1987). Since these particles are 100 jim in diameter, they deposit on the rod by impaction, rather than by weak thermophoretic forces. Deposition efficiency is thus quite high. Although, commercial development of sol-gel or powder methods for making fiber has not yet appeared, the necessary conditions for the technology have been demonstrated.

15.6 Minimizing Defects It might appear at this point that the fabrication of telecommunication fibers is well controlled and understood and that the only remaining goal is to make optical fiber cheaper. This is not so. As processing technology has improved, more stringent reliability and performance requirements demand further improvements in processing. To wring out the last few hundredths of a dB/km of loss, to minimize dispersion in the 1.3 and 1.55 jim communications windows, to achieve theoretical fiber strength and to protect the fiber from environmental effects such as radiation and exposure to hydrogen and moisture, the nature of silica and the effects of processing parameters must be understood. Both moisture and molecular hydrogen diffuse rapidly through the polymer coating which protects the fiber from abrasion. Moisture attacks the fiber surface and lowers the strength by static fatigue (Kurkjian etal, 1989) while hydrogen and ionizing radiation produce defect centers which increase the optical loss. Fig. 15-18 (Itoh etal., 1986) shows the effect of hydrogen and radiation on GeO 2 -P2O 5 -SiO 2 core and GeO 2 -SiO 2 core fiber. Gamma radiation causes an increase in loss across the

Ge0 2 -Si0 2

GeO 2 -P 2 O 5

100

773

10 \

1.0

0.1

Initial "*^-~ • - - - ^-Radiation — H2 diffusion

Initial • - - - ^-Radiation —— H2 diffusion 200°C Heating I I I

0.8

1.0 1.2 U Wavelength (|jm)

V Figure 15-18. Effect of hydrogen and radiation on (a) GeO 2 -P 2 O 5 -SiO 2 and (b) GeO 2 -SiO 2 core fiber, from Itoh et al, (1986).

/

200°C Heating _|

1.6

0.8

I

I

|

1.0 1.2 U Wavelength (JJP

1.6

774

15 Materials Technology of Optical Fibers

spectrum by introducing defects in the silica network. H 2 incorporated interstitially introduces several distinct peaks between 1.0-1.2 jim while defects caused by the reaction of hydrogen with GeO 2 species results in broadband loss. At temperatures above 200 °C, H 2 reacts with the silica network to form OH ~~ groups which increase loss at 1.38 jim. Removal of P 2 O 5 , once commonly used as a processing aid, alleviates some of the degradation caused by radiation and H 2 , but the presence of GeO 2 , the principal core dopant, still contributes to fiber loss. It is thus essential that H 2 be prevented from penetrating the fiber. Since the polymer coating is not an effective diffusion barrier, additional hermetic coatings have been developed. These are applied by chemical vapor deposition to the virgin fiber surface during draw and before application of the polymer coating. Thin films (50-100 nm) of aluminum, SiC, SiO2 and TiO 2 have been used but amorphous carbon coatings (Huff et al., 1988) appear the most satisfactory. These compact and pinhole free films result in negligible rates of H 2 permeation and dramatic reduction in strength degradation by both static and dynamic fatigue (Kranz et al., 1988).

15,7 Active and Passive Fiber Devices In the development of optical fiber for communications described above, success was measured by how well the glass medium did not interact with the transmitted light or the surroundings. However, it is possible to intentionally induce interactions for specific purposes. Passive fiber devices such as modulators, polarizers, isolators and couplers may be made from either standard or specially prepared optical

fiber (Miller and Chynoweth, 1979). In addition, sensors (Giallorenzi et al., 1982); Culshaw, 1984; Arditty et al., 1989; Scheggi, 1987), may be fabricated by using optical fibers to carry light signals to and from an active "optrode". In such an extrinsic sensor, the fiber merely transmits the signal to and from the sensing device. Active fiber devices may be fashioned into intrinsic sensors which exploit the active properties of either the glass or special dopants added to the fiber. Intrinsic sensors use the optical fiber itself to interact with the environment and modulate an optical signal. Fiber lasers and amplifiers (Urquhart, 1988), may also be fabricated if rare earth ions are added to the fiber core. Such active fiber devices take advantage of several properties unique to optical fibers such as long interaction length, small size, high light intensity and an optical as opposed to electronic carrier. 15.7.1 Optical Fiber Sensors

Fiber sensors carry an optical signal which is constant in some property such as intensity, polarization or phase. Perturbation of the fiber environment is detected as a variation in this property. Light intensity is the simplest property to modulate and detect. Extrinsic sensors can measure acoustical fields using a Fabry-Perot cavity at the fiber tip, strain using microbending induced by placing the fiber between corrugated plates, environment by incorporating fiber in a structural unit, or chemistry using chemically active materials placed at the fiber end or as a coating. Intrinsic sensors have been fabricated by measuring optical absorption of fibers doped with neodymium or erbium. These ions have a number of absorption bands and since the thermal population of the ground state of these ions changes with

775

15.7 Active and Passive Fiber Devices

temperature, changes in the absorption spectra can be used to accurately monitor temperature (Snitzer et al., 1983) over hundreds of degrees. Phase modulation may be detected with the greatest sensitivity by means of a fiber interferometer (Dandrige and Kersey, 1987). Fiber gyroscopes, for example, make use of this detection scheme since interference between counter-propagating beams within a loop of fiber allows detection of less than 10 ~ 4 rad. due to the different distances that light propagates in the two arms. Intrinsic sensors which exploit various physical phenomena such as the Faraday, electro-optic and photo-elastic effects may be used to measure stress and acoustic, magnetic or electric fields. These phenomena may also be used to induce changes in polarization for use as photonic devices. Interaction of the fiber with the field to be measured may be enhanced further by applying special active coatings to the fiber. For example, an acoustic sensor may use a piezoelectric coating to alter the phase of the propagating light. These examples illustrate the vast number of schemes which may be used to form fiber optic sensors and the field remains fertile for materials solutions. The field of optical fiber sensors has vast potential but is beset by practical problems. Owing to the long interaction length and high light intensity, optical fibers are extremely sensitive, not only to the property to be measured but to environmental influences as well. These limitations must be overcome by advances in materials and clever detection schemes. Currently, optical fiber sensors have only been used in areas which exploit their small size, immunity to electromagnetic interference and potentially remote nature. Thus, they have been used for high electric fields, corrosive

environments and in biomedical applications. Although there have been many laboratory demonstrations, widespread application has been inhibited mainly by thermal stability problems and cost. 15.7.2 Optical Fiber Lasers and Amplifiers

Optical lasers and amplifiers (Urquhart, 1988), may be created by using a more sophisticated perturbation of the light carried in an optical fiber (see Chap. 12 of this volume). If the core of a fiber is doped with optically active elements such as rare earth ions, it may act as a lasing medium in addition to guiding light. Pump light coupled into the fiber core excites the active ions in the glass and causes a population inversion between their ground state and some upper electronic energy level as shown in Fig. 15-19. The radiative transition back to the ground state emits a photon and may be either spontaneous or stimulated. Stimulated emission occurs when a signal photon at the lasing wavelength interacts with an ion in an excited state and promotes

'VPump

Transmission fiber vv X Signal = 1.53-1.55 Mm

Splice

jm

Er-doped fiber amplifier X

w

Transmission fiber

Splice

=1.48 |jm

Figure 15-19. Energy level schematic of Er3 + ion and configuration of optical amplifier in which pumplight is coupled to Er3 + containing fiber.

776

15 Materials Technology of Optical Fibers

de-excitation. This creates a second photon in phase with the first. A laser may be made by placing semitransparent mirrors at the fiber ends. This forms a Fabry-Perot cavity and causes resonance at a wavelength which is an integral fraction of the cavity length. The advantages of using a rare earth glass laser in fiber form are the long interaction length between pump and active species, high light intensity, the availability of diode laser pumps, and, for lightwave communications applications, the compatibility with standard optical fiber. An optical amplifier may be made using the device shown in the lower half of Fig. 15-19. If the optical signal (1.53 jam) is in an emission band of the active ions, the signal will stimulate depopulation of the excited states, creating photons in phase with the incident signal, thus amplifying the optical signal. Pump light is introduced through a directional coupler, so it is advantageous if the geometry of the active fiber matches that of the transmitting fiber. Fiber amplifiers promise superior performance over semiconductor amplifiers because of low noise, high bandwidth, high gain and fiber compatibility. 15.7.2.1 Fabrication of Rare-Earth Doped Optical Fiber

Rare earth doped fibers can be fabricated by several techniques. In the MCVD case (Poole et al., 1985), a volatile chloride vapor of the desired ion (generally Er 3 + or Nd 3 + ) is generated by heating a chamber contained within the substrate tube. The vapor is carried into the reaction zone along with SiCl4, GeCl 4 , A12C16 and O 2 used to produce the core deposit. Rare earth ion concentrations on the order of 100's to 1000's ppm can be achieved in this manner. However, since phase separation

occurs with even small additions of rare earths to silica, it is beneficial to have a homogenizor ion such as Al 3+ present. A second technique uses solution-doping (Townsend et al., 1987) of a partially sintered soot layer deposited in the MCVD substrate tube. The tube is soaked in a solution containing the desired ions, dried and dehydrated in an atmosphere containing O 2 , He and perhaps Cl 2 . After sintering, the tube is collapsed and drawn into fiber. Alternatively, the solution technique can be used to treat a soot-form produced by VAD (Gozen et al, 1988). Here also, a soot cylinder is soaked in an aqueous solution of rare earth ion, dried and dehydrated in an atmospheric containing SOC12 or Cl 2 . After sintering at about 1500 °C, the preform is overclad and drawn to fiber. In place of a solution, the sootform can be "soaked" in an atmosphere containing rare earth chloride species volatilized by a furnace temperature in the vicinity of 1000 °C. Efforts to optimize the amplifiers concentrate on fiber structure and the core composition. Amplifier efficiency seemingly would be improved by concentrating the rare earth dopants in the core center where the optical intensity is highest. Variations in the host glass can alter the population of various energy levels, in particular to diminish excited state absorption. This occurs if photons produced as stimulated emission from excited rare earth ions are subsequently reabsorbed by an excited ion, populating energy levels above the upper lasing level. This effect decreases the efficiency of 1.53 |im Er 3 + amplification and destroys 1.3 jim Nd 3 + amplification. Among the alternate hosts being investigated are those of fluorozirconate glasses.

15.8 Fluoride Glasses for Fibers

777

15.8 Fluoride Glasses for Fibers Interest in fluoride glass fibers began over a decade ago because they are predicted to have extremely low loss (see Chap. 8 of this volume). Since the loss of silica fibers is ultimately limited by Rayleigh scattering which decreases as A~4, improvement can be achieved by using a material transparent further into the infrared. In addition, it has been shown that the scattering coefficient of a number of fluoride glasses should be lower than that of silica. Lines (1988), describes the theoretical basis which allows prediction of the wavelength of minimum loss as well as estimation of its lower limit. Predictions of minimum loss versus wavelength for a number of fluoride glasses as contrasted to silica is shown by Fig. 15-20. Initial work concentrated on BeF2 glasses, but more recent effort has centered on ZrF4-based glasses (Poulain et al., 1977). The most common of these are socalled ZBLAN glasses, which have typical composition: 50(mol%) ZrF 4 , 20BaF 2 , 4 LaF 3 , 3 A1F3 and 23 NaF. Zirconium concentration can vary between 50-58%, the alkali can be eliminated, other rare earth may be substituted for lanthanum, and constituents such as InF 3 and PbF 2 can be added. Although estimates of lower loss limits range from 10 " 2 to 10" 3 dB/km, the lowest loss achieved to date is just below 1 dB/ km, but only on a length of several tens of meters. Significant progress toward lower loss has not been achieved during the past five years. The problem is mainly one of purification and the tendency for crystallites to form during processing. Crystallization occurs because fluoride glasses, with the exception of BeF2, are not very stable and thus require rapid cooling rates to inhibit formation of crystallites. In addition,

10

1.0 10 Wavelength (|jm)

Figure 15-20. Predicted minimum loss vs. wavelength for halide fibers compared to silica.

the task in removing impurities, especially oxygen, is momentous. Sublimation techniques and reactive gas processing are of some use, but Zr oxides are persistent and result in high scattering losses relative to the potentially low values predicted. In addition to the difficulties of fabricating the glass, preparation of a long length of fiber is beset by durability problems. The material must be protected from the atmosphere during melting, casting and drawing. Various innovative means have been devised to do this. By the standard method, the cladding melt is poured into a cylindrical mold and the periphery allowed to solidify. The center is drained and the core melt is poured to replace it. Crystallization caused by moisture at the core/clad interface is suppressed since the material remains above the crystallization temperature. A reactive atmosphere is frequently used to suppress crystallization and prevent contamination. One technique (Nakai et al., 1986) uses a carbon double crucible in an NF 3 atmosphere. The NF 3 is bubbled through core and cladding melts in the crucible at 725 °C for purification. The temperature is lowered to 375 °C and fiber

778

15 Materials Technology of Optical Fibers

is drawn from concentric orifices at 1 0 30 mm/min to obtain long length. In spite of these and other innovative processing procedures, the comparative failure of fluoride glasses to achieve performance equivalent to that of silica has led to renewed interest in other low intrinsic scattering oxide glasses. Sodium alumino-silicate has long been known (Van Uitert et al., 1973) to have substantially lower scattering losses than silica, but its preparation as low loss fiber has not been successful. In this instance, the stability of NaCl relative to Na 2 O prevents use of chlorine to purify and dehydrate the glass. Recently (Lines et al., 1989), calcium aluminate glasses have been shown to have low scattering loss (0.04 dB/km compared to 0.16 dB/km for SiO2). Since the minimum loss is near 1.55 j^m rather than further in the infrared, this material is thus compatible with existing communications systems. Processing of these oxide glasses appears much easier than it is for the fluorides. However, to date there has been little serious work to develop fibers exhibiting these desirable properties.

15.9 Summary This article has sought to describe the materials base upon which optical communication has been built. After an initial brief attempt at adapting traditional glass making processes to fiber fabrication, vapor deposition of vitreous silica was rapidly developed to become the transmission medium for optical communications. Work continued toward the ultimate engineering of silica fiber, to attain minimum loss and dispersion as well as insuring optimum mechanical reliability. Degradation by moisture and hydrogen was greatly diminished by protecting the fibers with her-

metic coatings. Meanwhile, investigations were undertaken to produce less expensive fiber using sol-gel techniques and new glasses were explored to yield enhanced performance. Currently, there are major efforts directed at both active and passive fiber devices. One fact emerges from this work: vitreous silica has exceptional suitability for optical waveguides. Its thermal expansion, high intrinsic strength, low absorption and scattering losses in the visible and infrared make silica a material as ideally suited to photonics as its parent, silicon, is to electronics. By making use of SiCl4 developed by the electronics industry, vapor phase processing has yielded ultimately pure materials with impurity levels in the range of parts per billion compared to the parts per million achieved for electronic applications. Simple and efficient vapor deposition techniques yield not only the requisite purity and optical quality but also the means for making precisely controlled waveguide structures.

15.10 References Arditty, H.J., Dakin, J.P., Kersten, R.T. (Eds.) (1989), Proc. 6th International Conf. on Optical Fiber Sensors. Berlin: Springer Verlag. Beals, K.J., Day, C.R. (1980), A Review of Glass Fibers for Optical Communication, Phys. Chem. Glasses 21, 5-19. Buchmann, P., Geittner, P., Lydtin, H., Romanowski, G., Thelen, M. (1988), Preparation of Quartz Tubes by Centrifugational Deposition of Silica Particles, Proc. 14th European Conf. on Opt. Comm., Brighton, UK. Clasen, R. (1988), Preparation of Glass and Ceramics by Sintering Colloidal Particles Deposited from the Gas Phase, Glastech. Ber. 61, 119-126. Cohen, L. G. (1983), Ultrabroadband Single-Mode Fiber, Tech. Proc. Conf. Opt. Fiber Comm., New Orleans, LA. Culshaw, P. (1984), Optical Fibre Sensing and Signal Processing. London: Peregrinus, P. Ltd. Dandridge, A., Kersey, A.D. (1987), Overview of Mach-Zender Sensor Technology, Proc. SPIE, Vol. 985: Fiber Optic and Laser Sensors, p. 184.

15.10 References

DiMarcello, F.V., Kurkjian, C. R., Williams, J.C. (1985), Fiber Drawing and Strength Properties, in: Optical Fiber Communications, Vol. 1, Yi, T. (Ed.). New York: Academic Press. Dorn, R., Baumgartner, A., Gutu-Nelle, A., Rehn, W. R., Schneider, S., Haupt, H. (1987), Glass from Mechanically Shaped Preforms, Glastech. Ber. 66, 79-32. Edahiro, T., Kawachi, M., Sudo, S., Tomaru, S. (1980), Deposition Properties of High-Silica Particles in the Flame Hydrolysis Reaction for Optical Fiber Fabrication, Jpn. J. Appl. Phys. 19, 20472054. Fleming, J. W. (1987), Sol-Gel Techniques for Lightwave Applications, Tech. Digest, Conf. on Optical Fiber Comm., Reno, Nevada, MH-1. Giallorenzi, T. G., Bucaro, J. A., Dandrioge, A., Sigei, G. H., Jr., Cole, J. H., Rashleigh, S. C , Priest, R. G. (1982), Optical Fiber Sensor Technology, IEEE J. Quantum Electronics QE-18, 627-675. Gozen, T, Kikukawa, Y, Yoshida, M., Tanaka, H., Shintani, T. (1988), Development of High Nd 3 + Content VAD Single Mode Fiber by Molecular Stuffing Technique, Tech. Digest, Conf. Opt. Fiber Comm., New Orleans, LA. Huff, R.G., DiMarcello, F.V., Hart, Jr., A. G. (1988), Amorphous Carbon Hermetic Optical Fiber, Comm. Conf., New Orleans, LA. Itoh, H., Ohmori, Y, Nakahara, M. (1986), GammaRay Radiation Effects on Hydroxyl Absorption Increase in Optical Fibers, /. Lightwave Tech. LT-4, 431-1. Izawa, T, Inagaki, N. (1980), Materials and Processes of Optical Fiber Fabricating, Proc. IEEE, 1184-1187. Keck, D.B., Schultz, P.C., Zimar, F. (1973), U.S. Patent 3 737292. Kompfner, R. (1965), Optical Communications, 5c/ence 150, No. 3693, 149-155. Kranz, K. S., Lemaire, P. I , Huff, R. G., DiMarcello, F.V., Walker, K.L. (1988), Hermetically Coated Optical Fiber: Hydrogen Permeation and Fatigue Properties, SPIE 992, 218-222. Kuppers, D., Lydtin, H. (1980), Preparation of Optical Waveguides with the Aid of Plasma Activated Chemical Vapor Deposition at Low Pressures, Topics in Current Chemistry. Heidelberg: Springer Verlag, p. 109. Kurkjian, C.R., Krause, I T , Matthewson, M.J. (1989), Strength and Fatigue of Silica Optical Fibers, IEEE J. Lightwave Tech. 7, 1360-1370. Lines, M. E. (1988), Theoretical Limits of Low Optic Loss in Multicomponent Halide Glass Materials, /. Non-Cryst. Solids 103, 265. Lines, M. E., MacChesney, J. B., Lyons, K. B., Bruce, A.J., Miller, A.E., Nassau, K. (1989), Calcium Aluminate Glasses as Potential Ultralow Loss Optical Materials at 1.5-1.9 jam, /. Non-Cryst. Solids. 107,251-290.

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MacChesney, I B . , Jaeger, R. E., Pinnow, D.A., Ostermeyer, F.W., Rich, T.C., Van Uitert, L. G. (1973), Phys. Lett. 23, 340-341. MacChesney, I B . , O'Connor, P. B., DiMarcello, F.V., Simpson, J.R., Lazay, P.D. (1974), Preparation of Low Loss Optical Fibers Using Simultaneous Vapor Phase Deposition and Fusion, Xth Int. Congress on Glass, Kyoto, Japan, pp. 6-40. MacChesney, I B . , Johnson, Jr., D. W., Lemaire, P. I , Cohen, L. G., Rabinovich, E. M. (1985), Fluorosilicate Substrate Tubes to Eliminate Leaky-Mode Losses in MCVD Single-Mode Fibers with Depressed Index Cladding, Tech. Digest, Conf. on Opt. Fiber Comm., San Diego, CA, WH2. MacChesney, I B . , Johnson, Jr., D.W., Fleming, D.A., Walz, F.W. (1987 a), Hybridized Sol-Gel Process for Optical Fibers, Electron. Lett. 23, 1005-1007. MacChesney, I B . , Johnson, Jr., D.W., Fleming, D. A., Walz, F. W, Komentani, T. Y. (1987b), Influence of Dehydration/Sintering Conditions on the Distribution of Impurities in Sol-Gel Derived Silica Glass, Mat. Res. Bull. 22, 1209-1216. Midwinter, I E . (1979), Optical Fibers for Transmission. New York: John Wiley. Miller, S. E., Chynoweth, A. G. (Eds.) (1979), Optical Fiber Telecommunications. New York: Academic Press. Nakai, T, Mimura, Y, Shinbori, O., Tokiwa, H. (1986), Jpn. J. Appl. Phys. 25, L704. Pearson, A.D., French, W.G. (1974), Low Loss Glass Fibers for Optical Transmission, Bell Laboratories Record 50, pp. 103-106. Poole, S.B., Payne, D.N., Ferman, M. E. (1985), Fabrication of Low Loss Optical Fibres Containing Rare Earth Ions, Electron. Lett. 21, 737-738. Poulain, M., Chanthanasin, M., Lucus, I (1977), Mater. Res. Bull. 12, 131. Scheggi, A.M. (Ed.) (1987), Fiber Optic Sensors II, SPIE Proc, Vol. 798. Schultz, P.C. (1974), J. Am. Ceram. Soc. 57, 309. Shibata, S., Kitagawa, T. (1986), Fabrication of SiO 2 -GeO 2 Glass by the Sol-Gel Method, /. Appl. Phys. 25, L323-L324. Shibata, S., Kitagawa, T, Horiguchi, M. (1987), Wholly Synthesized Fluorine-Doped Silica Optical Fibers by the Sol-Gel Method, Tech. Digest, 13th European Conf. on Opt. Comm., Helsinki, Finland. Simpkins, P. G., Kosinski, S. G., MacChesney, I B. (1979), Thermophoresis: The Mass Transfer Mechanism in Modified Chemical Vapor Deposition, /. Appl. Phys. 50, 5676-5681. Snitzer, E., Morey, W. W, Glenn, W. H. (1983), Fiber Optic Rare Earth Temperature Sensor, IEE Publication 221, 79-81. Townsend, I E . , Poole, S.B., Payne, D.N. (1987), Solution-Doping Technique for Fabrication of Rare-Earth-Doped Optical Fiber, Electron. Lett. 23, 329-331.

780

15 Materials Technology of Optical Fibers

Urquhart, P. (1988), Review of Rare Earth Doped Fibre Lasers and Amplifiers, IEEE Proc. 135, 385405. VanUitert, L.C., Pinnow, D.A., Williams, J.C., Rich, XL., Jaeger, R. E., Grodkiewicz, W. H. (1973), Borosilicate Glasses for Fiber Optical Waveguides, Mat. Res. Bull. 8, 469-476. Walker, K.L., Geyling, FT., Nagel, S.R. (1980a), Thermophoretic Deposition of Small Particles in Modified Chemical Vapor Deposition Process, /. Am. Ceram. Soc. 63, 96-102. Walker, K.L., Harvey, J.W., Geyling, F.T., Nagel, S. R. (1980b), Consolidation of Particulate Layers in the Fabrication of Optical Fibers Preforms, /. Am. Ceram. 63, 92-96. Walker, K.L., MacChesney, I B . , Simpson, J.R. (1981), Reduction of Hydroxyl Contamination in Optical Fiber Preforms, Tech. Digest 3rd Int. Conf. on Integ. Optics and Opt. Fiber Comm., San Francisco, CA, pp. 86-88. Wood, D.L., Walker, K.L., MacChesney, J. B., Simpson, J.R., Csencits, R. (1987), The Germanium Chemistry in the MCVD Process for Optical Fiber Fabrication, /. Lightwave Tech. LT-5, 277283.

General Reading Chai Yeh (1990), Handbook on Fiber Optics: Theory and Applications. New York: Academic Press. Fleming, J. W, Sigel, G. H., Takahashi Jr., S., France, P. W (1989), Optical Fiber Materials and Processing, Vol. 172. Pittsburgh, PA: Materials Research Society. Li, T. (Ed.) (1985), Optical Fiber Communications, Vol. I. Orlando, FL: Academic Press. Miller, S. E., Chynoweth, A. G. (Eds.) (1979), Optical Fiber Telecommunications. New York: Academic Press. Miller, S. E., Kaminow (Eds.) (1988), Optical Fiber Telecommunications II. Boston: Academic Press. Nagel, S. R., Fleming, J. W, Sigel, G. H., Thompson, D. A. (Eds.), Optical Fiber Materials and Properties, Vol. 88. Pittsburgh, PA: Materials Research Society. Suematsue, Y. (Ed.) (1982), Optical Devices and Fibers. Amsterdam: North Holland.