Silicate Glasses and Melts: Properties and Structure (Developments in Geochemistry)

Developments in Geochemistry 10

Silicate Glasses and Melts Properties and Structure

Developments in Geochemistry 1. W.S. Fyfe, N.J. Price and A.B. Thompson FLUIDS IN THE EARTH'S CRUST 2. P. Henderson (Editor) RARE EARTH ELEMENT GEOCHEMISTRY 3. B.A. Mamyrin and I.N. Tolstikhin HELIUM ISOTOPES IN NATURE 4. B.O. Mysen STRUCTURE AND PROPERTIES OF SILICATE MELTS 5. H.A. Das, A. Faanhof and H.A. van der Sloot RADIOANALYSIS IN GEOCHEMISTRY 6. J. Berthelin DIVERSITY OF ENVIRONMENTAL BIOGEOCHEMISTRY 7. L.W. Lake, S.L. Bryant and A.N. Araque-Martinez GEOCHEMISTRY AND FLUID FLOW 8. N. Shikazono GEOCHEMICAL AND TECTONIC EVOLUTION OF ARC-BACKARC HYDROTHERMAL SYSTEMS 9. S. Mitra HIGH-PRESSURE GEOCHEMISTRY AND MINERAL PHYSICS

Developments in Geochemistry 10

Silicate Glasses and Melts Properties and Structure By

Bjorn Mysen Pascal Richet

2005

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ISBN: 0 444 52011 2

Front cover: Thin section of iron-bearing glass. Credit: Eric Boucquet, St.-Gobain/Isover

@ The paper used in this publication meets the requirements of ANSI/NISO Z39.48-1992 (Permanence of Paper). Printed in The Netherlands.

Preface A yearly production of more than 100 million tons testifies to the fact that silicate glass is ubiquitous in the modern world. From vessels and windows to lenses, screens, and insulating or optical fibers, glass fulfills an ever-increasing diversity of uses. These achievements reflect the long path followed since the beginnings of glassmaking 4500 years ago. For millennia, progress was empirical. For more than a century, basic glass research has become a key ingredient to meet successfully competition with other materials, to optimize glass production, and to develop new products tailored for specific applications. For these purposes, chemical composition is an essential factor with its strong influence on the structure and properties of silicates. Hence, deciphering the property-structure relationships as a function of temperature and chemical composition is a major goal of glass and melt science. Although magma is also essentially made up of silicates, the importance of understanding property-structure relationships of molten silicates has been perceived more recently in earth sciences. The 21 km3 (i.e., about 60 billion tons) of lava that reach the Earth's surface each year is the most spectacular manifestation of magmatic processes. This amount, however, represents just a fraction of the actual volume of rising magma that is transferring heat and matter within the Earth and is eventually forming igneous rocks at or near the surface. Magmatic activity has, in fact, been a essential agent in shaping our planet throughout its 4.5 billion years long history. Magma and industrial glass have many common features, including great compositional diversity. There are, nonetheless, also important differences. The composition of magma is not human choice but Nature's will. Chemical complexity of industrial glass is, in contrast, by design. Moreover, understanding magma and magmatic processes requires experimentation not only at high temperature but also at high pressures that are irrelevant to industrial processes. In both cases, however, the methods of investigation are the same and the results obtained in one field are generally of direct relevance to the other. Much experimental and theoretical work has been made during the last decades. In particular, a variety of spectroscopic and simulation methods have enabled dramatic progress to be made toward elucidating the microscopic constitution of amorphous silicates. A negative side effect of this emphasis recently put on structure, however, is that the actual macroscopic features to be accounted for can be either overlooked or not clearly identified. To remedy this shortcoming, this is why we first summarize physical properties before describing structural features. In this respect, it is useful to recall that density remains an essential parameter to characterize a material, and that, despite being often more than 50 years old, basic information such as phase diagrams has not lost any of its importance.

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Preface

Keeping in mind this dual natural and industrial importance, in this book we have attempted to picture in a consistent manner the physical chemistry of silicate glasses and melts. To provide this perspective, an introductory chapter is devoted to a short history of glass and magma. In the following chapters we present the general physical and structural features of glasses and viscous liquids. With pure SiO2 as a starting point, we proceed to compositions of increasing chemical complexity in the second part of the book. The effects of network-modifying cations are first exemplified by alkali and alkaline earth elements. The specific influences of aluminum, iron, titanium, and phosphorus are then reviewed. With water, fluids of the system C-H-O-S, noble gases, and halogens, the major volatile components are also dealt with. Application of these results to complex systems such as natural melts is finally discussed. By concentrating on properties of more direct relevance to phase equilibria and mass transfer, we have left aside electrical, optical or mechanical properties. Information on these themes will be found in the publications listed below, which also include a few books that reviewed the state of the art a few decades ago and remain of more than only historical interest. Assuming some familiarity with currently basic experimental and theoretical methods of investigation, we have tried to identify essential aspects and to give the reader a real grasp of the problems. To make use of this book as a reference easier, most of the chapters have been written to be read independently of the others. In a literature that is so large that it cannot be reviewed comprehensively, we have also attempted to limit the usual bias due to the authors' research interest while not overlooking important publications relevant to our story. Although a total of more than 1500 papers are quoted in the reference lists given at the end of each chapter, we apologize in advance for any such omission. At the end of our project, we thank T. Atake, J. Barton, C. Chopin, A. Choulet, L. Cormier, P. Courtial, J. Dyon, G. Gohau, B. Guillot, S. Hardy, T. Hudson, A. Jambon, M. Le Hair, D. de Ligny, V. Magnien, R. Moretti, D. Neuville, J.-L. and M.-H. Penna, E. Persikov, E. and N. Richet, M. Roskosz, and M. Wolf for information, help or comments provided at various stages of the writing. Special thanks are due to J.-L. Bernard and E. Bocquet for the picture of the cover, J. Roux for efficient phase diagram transformations, to Y. Bottinga and J. F. Stebbins for thoughtful criticism of many chapters, and to S. L. Mysen for careful proofchecking of the whole manuscript. Support from a CNRS-Carnegie Institution of Washington PICS grant is gratefully acknowledged. BOM also acknowledges an IPGP visitorship which made completion of this book easier. Finally, it is our pleasure to dedicate this book to our long-time friend and colleague, Yan Bottinga.

Preface

vii

References Bansal N. P. and Doremus R. H. (1986) Handbook of Glass Properties. Academic Press, Orlando. Carroll M. R. and Holloway J. R. (1994) Volatiles in Magmas. Reviews in Mineralogy, Vol. 30. Mineralogical Society of America, Washington DC. Doremus R. H. (1994) Glass Science (2nd ed.). John Wiley & Sons, New York. Mackenzie J. D. (1960-1964) Modern Aspects of the Vitreous State, 3 vols. Butterworth, London. Mazurin O. V, Streltsina M. V., and Shvaiko-Shvaikovskaya T. P. (1987) Handbook of Glass Data. Part A. Silica Glass and Binary Silicate Glasses. Elsevier, Amsterdam. Mazurin O. V., Streltsina M. V., and Shvaiko-Shvaikovskaya T. P. (1987) Handbook of Glass Data. Part C. Ternary Silicate Glasses. Elsevier, Amsterdam. Mazurin O. V, Streltsina M. V, and Shvaiko-Shvaikovskaya T. P. (1993) Handbook of Glass Data. Part E. Single-Component, Binary, and Ternary Oxide Glasses: Supplements to Parts A, B, C, and D. Elsevier, Amsterdam. Morey G. W. (1938) The Properties of Glass. Reinhold Publishing Co, New York. Mysen B. O. (1988) Structure and Properties of Silicate Melts. Elsevier, Amsterdam. Nicholls J. and Russell J. K. (1990) Modern Methods of Igneous Petrology: Understanding Magmatic Processes. Reviews in Mineralogy, Vol. 24. Mineralogical Society of America, Washington DC. Paul A. (1990) Chemistry of Glass (2nd ed.). Chapman and Hall, London. Rawson H. (1967) Inorganic Glass Systems. Academic Press, London. Richardson F. (1974) Physical Chemistry of Melts in Metallurgy, 2 vols. Academic Press, London. Scholze H. (1991) Glass. Nature, Structure, and Properties. Springer, Berlin. Shelby J. E. (1997) Introduction to Glass Science and Technology. The Royal Society of Chemistry, London. Simmons C. J. and El-Bayoumi O. H. (1993) Experimental Techniques of Glass Science. The American Ceramic Society, Columbus OH. Stebbins J. E, McMillan P. F., and Dingwell D. B. (1995) Structure, Dynamics and Properties of Silicate Melts. Reviews in Mineralogy, Vol. 32. Mineralogical Society of America, Washington DC. Tammann G. (1933) Der Glaszustand. Leopold Voss, Leipzig. Turkdogan E. T. (1983) Physicochemical Properties of Molten Slags and Glasses. The Metals Society, London. Vogel W. (1994) Glass Chemistry (2nd ed.). Springer, Berlin. Wolf M. B. (1984) Chemical Approach to Glass. Elsevier, Amsterdam. Zarzicki J. (1991) Glasses and the Vitreous State. Cambridge University Press, Cambridge. Zarzycki J. (1991) Glasses and Amorphous Materials. Materials Science and Technology, Vol. 9 (eds. R. W. Cahn, P. Haasen, and E. J. Kramer). VCH, Weinheim.

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Table of Contents Preface

v

Chapter 1. The Discovery of Silicate Melts —An Applied and Geological Perspective

1

1.1. The Early History of Glass 1.1a. The Beginnings of an Art 1.1b. An Industrial Revolution 1.2. Glass and Science 1.2a. A Scientific Material 1.2b. Descartes and the Foundation of a Science 1.2c. The Effects of Composition 1.3. The Discovery of Natural Melts 1.3a. The Origin of Neptunism 1.3b. From Extinct Volcanoes to Magma 1.3c. The New Importance of Silicate Melts 1.4. The Physical Chemistry of Melts 1.4a. The Measurements of Physical Properties 1.4b. Toward the Glass Transition 1.4c. The First Glimpses Into Structure 1.4d. The Search for New Compositions 1.4e. A Geological Outlook 1.5. Summary Remarks References

1 1 4 6 6 7 9 10 10 11 14 16 16 17 21 24 27 28 28

Chapter 2. Glass Versus Melt 2.1. Relaxation 2.1a. Glass Transition Range 2.1b. Vibrational vs. Configurational Relaxation 2.1c. Relaxation Times 2.1d. Maxwell Model 2.1e. Local vs. Bulk Relaxation 2.2. Glass Transition 2.2a. A Microscopic Picture 2.2b. Rate Dependence of the Glass Transition 2.2c. Fictive Temperature 2.2d. Kauzmann Paradox 2.3. Configurational Properties 2.3a. Thermal Properties 2.3b. Volume Properties 2.3c. Permanent Compaction of Glass 2.3d. Configurational Entropy and Viscosity 2.3e. Glass Formation 2.4. Summary Remarks References

35 35 35 38 40 42 44 47 47 48 51 52 53 53 54 56 57 61 63 64

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Chapter 3. Glasses and Melts vs. Crystals

69

3.1. Basics of Silicate Structure 3.1a. Oxygen Coordination Polyhedra 3.1b. Network-Formers and Modifiers 3.1c. Bond Energies 3.2. Thermodynamic Properties 3.2a. High-Temperature Enthalpy and Entropy 3.2b. Low-Temperature Heat Capacity and Vibrational Entropy 3.2c. Boson Peak 3.2d. Configurational Entropy 3.3. Liquid-Like Character of Crystals 3.3a. Glass-Like Transitions 3.3b. oc-P Transitions 3.3c. Premelting 3.4. Summary Remarks References

69 70 72 74 76 77 79 83 85 87 87 90 92 95 96

Chapter 4. Melt and Glass Structure — Basic Concepts 4.1. Bond Length, Bond Angle, and Bond Strength in Silicates 4.1a. Basic Definitions and Concepts of Bonding 4.1b. Bond Strength, Bond Angle, and Composition 4.2. Network-Formers 4.2a. Charge-Balance of Network Formers 4.2b. Aluminum Substitution 4.2c. Other Tetrahedrally Coordinated Cations 4.2d. The NBO/T Parameter, Melt Structure, and Melt Composition 4.3. Network-Modifying Cations and Linkage between Structural Units 4.3a. The Nature of Nonbridging Oxygen Bonds 4.3b. Ordering of Network-Modifying Cations 4.4. Bonding, Composition and Effects on Melt Properties 4.4a. Viscous Flow 4.4b. Interrelationships of Transport Properties 4.4c. Thermochemistry and Bond Strength 4.5 Mixing, Order, and Disorder 4.5a Viscous Flow and Mixing in Silicate Glass and Melt 4.6. Summary Remarks References

101 101 101 102 105 106 108 110 Ill 112 113 114 115 116 118 120 120 121 123 124

Chapter 5. Silica — A Deceitful Simplicity 5.1. An Outstanding Oxide 5.1a. The Archetypal Strong Liquid 5.1b. A Short Classification 5.1c. Phase Transitions: Melting and Amorphization 5.2. Physical Properties 5.2a. Thermal Properties 5.2b. Ambient-Pressure Density

131 132 132 134 135 136 137 139

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5.2c. Compressibility 5.2d. Viscosity 5.2e. Element Diffusion 5.3. Structure of SiO2 Glass and Melt 5.3a. Random Network Structure 5.3b. Pseudocrystalline Structure Model 5.3c. Coexisting Structural Units 5.4. Effects of Pressure and Temperature 5.4a. Pressure 5.4b. Temperature 5.5. Summary Remarks References

142 144 146 148 148 148 150 155 156 158 160 161

Chapter 6. Binary Metal Oxide-Silica Systems — I. Physical Properties 6.1. Phase Relationships 6.1a. Phase Diagrams: Liquidus and Solvus Relations 6.1b. The Difficult Match with Q3 Species 6.1c. Energetics and Phase Stability 6.2. Thermodynamics of Mixing 6.2a. Enthalpy of Mixing 6.2b. Heat Capacity 6.2c. Activity of SiO2 in Binary Melts 6.2d. Oxygen Activity and Acid-Base Reactions 6.3. Volume and Transport Properties 6.3a. Volume and Thermal Expansion 6.3b. Compressibility 6.3c. Electrical Conductivity 6.3d. Viscosity 6.3e. Element Diffusivity 6.4. Summary Remarks References

169 169 171 171 173 174 174 176 177 179 183 183 186 188 189 192 193 194

Chapter 7. Binary Metal Oxide-Silica Systems — II. Structure 7.1. Pseudocrystalline Models of Melt Structure 7.2. Thermodynamic Modeling and Melt Structure 7.2a. Polymer Modeling 7.2b. Quasichemical Modeling of Melt Structure 7.3. Numerical Simulation of Melt Structure 7.4. Structure from Direct Measurements 7.4a. Structure Determinations 7.4b. High-Temperature Structure at Ambient Pressure 7.4c. Effect of Pressure on Metal Oxide Silicate Glass and Melt Structure 7.5. Structure and Melt Properties 7.5a. Liquidus Phase Relations 7.5b. Mixing Behavior 7.5c. The Mixed Alkali Effect

199 199 200 200 201 203 205 205 211 215 218 218 220 221

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7.5d. Transport Properties 7.6. Summary Remarks References

221 223 223

Chapter 8. Aluminosilicate Systems — I. Physical Properties 8.1. Phase Relationships 8.1a. Immiscibility Fields 8.1b. Liquidus Relations 8.1c. Glass Formation 8.2. Thermodynamics of Mixing 8.2a. Heat Capacity 8.2b. Enthalpy of Mixing 8.2c. Activity 8.3. Volume and Viscosity 8.3a. Volume and thermal expansion 8.3b. Compressibility 8.3c. Viscosity 8.3d. Element Diffusivity 8.4. Summary Remarks References

231 231 232 234 236 238 238 241 243 244 244 246 248 252 253 254

Chapter 9. Aluminosilicate Systems — II. Structure 9.1. Binary Al2O3-Bearing Glasses and Melts 9.1a. SiO2-Al2O3 9.1b.Al2O3-M1/xAlO2 9.1c. MxO-M1/xAlO2 9.2. Meta-Aluminosilicate Glasses and Melts (SiO2-M1/xAlO2) 9.2a. Charge-compensation of Al3+ and (SioAl)-Ordering 9.2b. Systematics of SiO2-M1/xAlO2 Glass and Melt Structure 9.2c. Temperature-Induced Transformations Along SiO2-M1/xAlO2 Joins 9.3. Peralkaline Aluminosilicate Glasses and Melts 9.3a. Systematics of SiO2-MxO-M1/xAlO2 Glass and Melt Structure 9.4. Pressure and the Structure of Aluminosilicate Melts 9.5. Structure and Properties of Aluminosilicate Melts 9.5a. Peraluminous Melts 9.5b. Meta-aluminous Melts 9.5c. Peralkaline Aluminosilicate Melts 9.6. Summary Remarks References

259 260 260 263 264 267 267 270 273 275 275 278 281 281 281 283 284 285

Chapter 10. Iron-bearing Melts — I. Physical Properties 10.1 Ferrous and Ferric Iron 10.1a. Redox States 10.1b. Iron Coordination and Melt Polymerization 10.1c. Oxygen Fugacity lO.ld. Analysis of Redox Ratio

291 292 292 293 294 296

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10.2. Phase Equilibria 10.2a. Ferrosilicate Phase Relations 10.2b. Ferrisilicate Phase Relations 10.2c. Phase Relations in Complex Systems 10.3. Iron Redox Reactions 10.3a. Effects of Temperature and Oxygen Fugacity 10.3b. Oxygen Activity and Glass Basicity 10.3c. Composition Dependence of Iron Redox State 10.3d. Prediction of Iron Redox Ratios 10.3e. Mechanisms of Redox Reactions 10.4. Physical Properties 10.4a. Density 10.4b. Pressure Dependence of Iron Redox State 10.4c. Thermal Properties 10.4d. Viscosity 10.5. Summary Remarks References

298 298 300 302 304 304 306 307 311 314 318 318 320 321 322 326 327

Chapter 11. Iron-bearing Melts — II. Structure 11.1. Ferric Iron 11.1a. Bond Length 11.1b. Oxygen Coordination 11.2. Ferrous Iron 11.2a. Oxygen Coordination 11.3. Ferric and Ferrous Iron in Silicate Melts at High Temperature 11.4. Iron in Silicate Melts and Glasses at High Pressure 11.5. Summary Remarks References

335 335 335 338 344 345 347 350 353 354

Chapter 12. The Titanium Anomalies 12.1. Phase Relations and Glass Formation 12.1a. Titanium Redox Reactions 12.1b. SiO2-TiO2 Phase Relations 12.1c. Ternary Phase Relations: Alkali and Alkaline Earth Titanosilicates 12.Id. Phase Relations in Chemically More Complex Systems 12.2. Physical Properties 12.2a. The Heat Capacity Anomaly 12.2b. Configurational Entropy and Viscosity 12.2c. Volume-Composition Relationships 12.3. Structure of Titanosilicate Glasses and Melts 12.3a. The System SiO2-TiO2 12.3b. Titanium in Metal Oxide-Silicate and Aluminosilicate Glass and Melt 12.4. High-Temperature Studies 12.5. Structure and Properties of Ti-bearing Melts 12.6. Summary Remarks References

357 357 357 359 360 362 364 365 367 369 372 372 374 377 378 381 381

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Chapter 13. Phosphorus 13.1. Properties of Phosphorus-bearing Glasses and Melts 13.1a. Solution Thermodynamics 13.1b. Phosphorus and Viscosity 13.1c. Properties and Phosphate Complexes 13.2. Structure of Phosphorus-bearing Silicate Melts and Glasses 13.2a. Charge-Compensation Mechanisms 13.2b. SiO2-P2O5 13.2c. Phosphate-containing Metal Oxide-Silica Glass and Melt 13.2d. Phosphate in Metal Oxide-Alumina-Silica Systems 13.2e. Temperature-Induced Transformations 13.3 Structure and Properties of P-bearing Silicate Melts and Glasses 13.4 Summary Remarks References

387 387 387 389 391 393 393 395 395 400 403 405 406 407

Chapter 14. Water — An Elusive Component 14.1. Phase Relations 14.1a. Melting in Hydrous Silicate Systems 14.1b. Water Solubility 14.1c. Water solution: OH Groups and Molecular H2O 14.2. Physical Properties of Hydrous Silicate Systems 14.2a. Volume Properties 14.2b. Heat Capacity and Enthalpy 14.2c. Viscosity Near the Glass Transition 14.2d. Diffusion Coefficients and Electrical Conductivity 14.3. Water and Silicate Melt and Glass Structure 14.3a. SiO2-H2O 14.3b. Metal Oxide-Silica Systems 14.3c. Aluminosilicate Melts and Glasses 14.4. Temperature Effects 14.5. Application to Some Properties of Hydrous Melts 14.6. Summary Remarks References

411 412 412 414 421 424 425 428 430 435 436 436 439 443 448 450 451 452

Chapter 15. Volatiles — I. The System C-O-H-S

461

15.1. Sulfur 15.2. Volatiles in the System C-O-H 15.2a. Hydrogen 15.2b. Reduced, Carbon-Bearing C-O-H Volatiles 15.2c. Carbon Dioxide 15.3. Structure and Melt Properties 15.4. Summary Remarks References

461 466 467 469 473 477 478 478

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Chapter 16. Volatiles — II. Noble Gases and Halogens 16.1. Noble Gases 16.1a. Solubility 16.2b. Solution Mechanisms 16.2. Halogens 16.2a. Chlorine 16.2b. Fluorine 16.3. Structure and Melt Properties 16.4. Summary Remarks References

485 485 485 486 487 488 491 497 498 499

Chapter 17. Natural Melts 17.1. Structure of Magmatic Liquids 17.1a. Degree of Polymerization, Network Formers, and Network Modifiers 17.1b. Qn-Species 17.2. Properties of Magmatic Liquids 17.2a. Molar Volume and Melt Density 17.2b. Viscosity 17.2c. Volatiles in Magmatic Liquids 17.2d. Mineral/Melt Equilibria 17.3. Summary Remarks References

503 503 503 507 507 508 511 514 517 520 520

Subject Index

525

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Chapter 1

The Discovery of Silicate Melts An Applied and Geological Perspective Under a thin sedimentary layer, the rocks that make up the continents and the ocean floor have formed by cooling of magma. The name igneous rocks (ignis, fire in Latin) is a reminder of this origin. Today, such a magmatic source is taken for granted although it was established only about two centuries ago. In fact, since the beginnings of glass to the end of the 18th century, for millennia molten silicates were of concern solely to glass makers and subsequently to metallurgists. Hence, it is hardly a novelty that the properties of silicate melts are as important in materials sciences as in the earth sciences. 1.1. The Early History of Glass 1.1a. The Beginnings of an Art Glass is one of the earliest man-made materials [e.g., Bimson and Freestone, 1987; Tait, 1991 ]. It appeared some 4500 years ago in the Middle-East during the Bronze age, about 5 millennia after other oxide-based materials (ceramics, plaster and lime), but closely followed the first metals, copper and lead, and even preceded iron. It is not known whether glass was first produced in Mesopotamia, Egypt or Syria, and whether it was made during ceramic or metallurgical operations. In fact, a single origin is unlikely. Similar sequences of discoveries probably lead to similar processes and products in different places in the Middle East. The earliest glasses have familiar compositions (Table 1.1). They are not translucent but opaque and vividly colored by various metals such as copper (red and blue-red), iron (black, brown and green), antimony (yellow), cobalt (blue), tin (white) [Oppenheim et al., 1970]. The substances which yielded these various colors were thus identified at these early stages. Between 2500 and 1500 B.C., glass was used as small decorative pieces like jewels or amulets, of obvious pride, or even (for antimony-bearing compositions) as drugs to be ingested as fine powders. In Egypt, it is not fortuitous that glassmakers were called "makers of lapis lazuli". As a matter of fact, this was the first time that a given property of a material — its color — could be varied almost at will. Unknowingly, glassmakers had thus discovered the rich possibilities offered by continuous solid solutions, and they also observed that small changes in ingredients (i.e., in chemical composition) can result in marked changes in a physical property.

2

Chapter 1 Table 1.1. Composition of some ancient glasses (wt %f

Babylonian, 14th cent. B.C. Egypt, 18th dynasty, translucent India (3rd - 5lh cent. B.C.) Alexandria Soda glass, Europe, 1st- 9th cent. Potash glass, Europe 9th cent. Islamic glass, 13th cent. English crystal Bohemia

SiO2

Na2O

61-71 62-66 58-71 72.7 65-73 51-54 68 57-72 55

9-14 17-22 13-19 19.0 14-20 1-2 14 0-3

A12O3 K2O CaO 1-3 1-2 2-6 1.8 2-5 1-3 3 0-1

1-3 0-1 2-5 0.39 0-2 14-18 3 8-14 32

5-8 8-12 5-9 5.2 4-9 12-16 8 0-1 12

MgO Fe2O3 PbO 3-6 4-5 1-5 0.4 0-2 5-7 4

1-2 0-1 1-2 0.12 0-3 1-3 9-29

"See Brill [iyyyj tor a comprenensive review; bnglish crystal, witn u-o7e D2L>3, trom Moretti L/UU4J.

For a very long time, glassmakers would use raw materials of variable quality and, of course, be ignorant of the importance of controlling redox conditions when working with multivalent elements. Because their knowledge was strictly empirical, their operations were tricky and not necessarily reproducible. Hence, rites were practiced to ensure success through the protection of gods. This is revealed by extant 7th-century B.C. cuneiform tablets from Niniveh, found in King Assurbanipal's library, which report the earliest known procedures for making kilns and glass [Oppenheim et al., 1970]: "When you set up the foundation of a kiln to [make] glass, you [first] search in a favorable month for a propitious day, and [then only] you set up the foundation of the kiln. As soon as you have completely finished [...] no outsider or stranger should [thereafter] enter [the building], an unclean person must not [even] pass in front of [ritual A'wi'M-images]. You regularly perform libations offerings before them. On the day when you plan to make the "metal" in the kiln, you make a sheep sacrifice before the Aj/bw-images, you place juniper incense on the censer and [then only] you make a fire in the hearth of the kiln and place the "metal" in the kiln."

As testifies in this tablet the term "metal", which would be used in Europe until the late 19th century, early glassmakers shared many points with metallurgists in their use of earthy materials and operation of their furnaces. More important, glassmakers were good observers. In Mesopotamia, they were well aware of the deleterious effects of fumes (through vapor-melt interactions) and thus kept recommending "You keep a good and smokeless fire burning". They used bellows to achieve sufficiently high temperatures and knew which colors would be obtained (through redox reactions) depending on whether their pots were covered or not and the door of their kilns open or closed. They were familiar with sintering, grinding and stirring (to achieve chemical homogeneity). Glassmakers also mastered quenching procedures by dipping or immersing glass pots in water, and practiced annealing at appropriate temperatures in dedicated furnaces to prevent

The Discovery of Silicate Melts

Figure 1.1 - Millefiori glass cup (size: 10 cm) from Alexandria probably made about 2000 years ago (Corning Glass Museum, Corning, New York). a piece from breaking spontaneously on cooling (as a result of the internal stresses that build up through the glass transition). A testimony of high achievements was the ability of early glass makers to imitate obsidians, which thus belonged to two different categories, namely, "genuine" and "from the kiln" [Oppenheim et al., 1970]. The very existence of these cuneiform tablets shows that keeping written records of technical processes was already considered important in Mesopotamia. This first kind of quality control included instructions on how to estimate the most important practical property of glass, viscosity. For this purpose, tablets from the 14th or 12th century B.C. advised the glassmaker to observe how droplets of glass were sticking to the tip of the rake used to stir the melt. Such records would eventually be lost after the collapse of Mesopotamian states, to be recovered only in the early 20th century A.D. when these tablets would be deciphered and their meaning ascertained. An abrupt transformation took place in the 15th century B.C. when glass was made translucent and produced in a variety of shapes. At that time, the chemical inertness and nonporous nature of glass were put to good use to conserve unguents or perfumes. To make small containers, the viscous melt was, for example, spread over a core made up of a mixture of dung and clay which was subsequently scraped from the inside of the newly made piece. Many other ways of working or molding glass were invented at the same time [see Stern and Schlick-Nolte, 1994; Sternini, 1995]. Although (or because?) glass remained an expensive material, a very high level of artistry was rapidly reached. These skills are attested by pieces made up of glasses of different colors, sometimes intermingling in a very complex pattern like the so-called millefiori glass cup of Fig. l.l [cf. Charleston, 1980; Richet, 2000]. Glass of similar composition was also deposited as thin layers on a variety of surfaces [Matson, 1985]. The vitrified bricks of Mesopotamian monuments of the 6-4th centuries B.C. are famous for their ornamental value. For such fragile building materials, glass was also valuable because it offered protection against alteration. When deposited on metals, glass is called enamel. In this form, it was extensively used in jewelry. And, from the 4th century B.C., very fluid lead-based glasses gave rise to glazes thanks which made pottery

4

Chapter 1

Figure 1.2 - Making of crown, flat glass from a bulb rapidly rotated in front of a furnace, which was opened opposite to the end through which it was first blown [Diderot and d'Alembert, 1751]. Alternatively, as described by the German monk Theophilus in the 12th century, flat glass could be made from a large cylinder which was split longitudinally and flattened in an annealing furnace after its two ends had been cut out. In both cases, controlling the viscosity at the various stages of the process was of paramount importance.

impermeable to liquids. When welding different glasses or depositing glass onto another substrate, glassmakers had to use materials having similar thermal expansion coefficients. In all these endeavors, thermal expansion had thus to be controlled empirically. Lib. An Industrial Revolution Slowly, glassmaking had spread from the Middle-East. Beads made during the late 2nd millenum B.C. have been found from Italy to central Asia and China. Glass vessels later followed suit, reaching Greece, Italy and China toward the 13th, 8th, and 5thcentury B.C., respectively, France in the 1st century A.D. and then Belgium and the Rhine valley in the 3rd-4th centuries. Glass did not gain importance in andesitic Japan because of the lack of siliceous sand. It would remain unknown in America until the Spanish conquest. Two most important inventions were made at the beginning of the Christan era, probably in Phoenicia, in the large workshops of Sidon. These inventions were transparent glass and glass blowing. Transparency requires the raw materials to be of high purity with less than 0.1 wt % of iron oxides, in particular. This could be achieved only in places where sand and natron, i.e., naturally occurring sodium carbonate, were available. The border between Phoenicia and Egypt owes its importance to the local availability of such materials. Glass blowing was an early industrial revolution. With this new process, shaping glass became much easier, less time consuming and, thus, less expensive [see Grose, 1986]. The size and shape of pieces were no longer restricted as they were with earlier methods, thus allowing glass to become a basic commodity in the Roman empire [e.g., Stern, 1995; Sternini, 1995]. To be possible, glass blowing required a strict control of viscosity during the alternating periods of working and reheating before the final annealing. Good use was also made of thermal shock to cut the piece at the desired place, as for severing it from the blowing pipe. Because glasses found in widely different places show a definite similarity of chemical composition, Velde [1990] suggested that, until the 8th or 9th century, glass was essentially made in the Middle East and exported as ingots or final products to the western world

The Discovery of Silicate Melts

5

Figure 1.3 - Viscosity of antique glasses [Vo Thanh et al., unpub. results]. Glass is said to be short or long when the temperature interval of the 105-108 Pa s working viscosity interval is narrow or large, respectively. Compositions listed in Table 1.1 for Bab (Babylonia), Bohe (Bohemia) and Alex (Alexandria). Na: 66% SiO2, 20% Na2O, 8% CaO 2.5% A12O3; K: 54% SiO2,20% K 2 0,15% CaO, 6% MgO and 2% A12O3 (other oxides as in Table 1.1 for soda and potash glass).

where only small furnaces were operated for remelting the imported ingots along with cullet (scrap glass) that was extensively recycled. This view is supported by glass cargo found in ships wrecked in the Mediterranean Sea and by the fact that remains of glassworks from this period have not been unearthed in Europe [Foy et al, 1998]. The composition of this glass (Table 1.1) is similar to that of modern window glass. When the ancient trade routes were cut following the Arab conquest, glass had to be made from starting materials available locally. In Western Europe, the ashes of ferns, which are potassium-rich, were commonly used as a flux to melt siliceous sand. In the long run, this change had the unfortunate consequence that the resulting glasses were more prone to alteration by atmospheric and meteoric waters than the former soda-lime glasses. Then, around the 11th century A.D., the soda-rich ashes of marine plants such as Salicornia were imported from Spain so glass compositions became more similar to the ancient ones. This is the reason why stained glass from the late middle ages tends to be better preserved than those of earlier periods. By that time, flat glass had already been made for a long time from blown glass by the two different processses that would be used until the end of the 19th century (Fig. 1.2). Variations of chemical composition also resulted in changes in the melting, working, and annealing conditions because viscosity depends strongly on the nature and amount of the constituting oxides. Everything else being equal, the difference between the annealing temperatures of the sodium- and potassium-based glasses of Fig. 1.3 reaches 120 degrees, whereas the former had to be melted and homogenized at temperatures about 200 degrees higher than the latter. As shown by Turner [1956a,b], much can be learned about glass technology in Antiquity from modern investigations of the physics and chemistry of ancient glasses.

6

Chapter 1

Figure 1.4 - One of the earliest representations of alchemical glassware, in a 13th century manuscript copy of a work by the 3rd century A.D. Greek alchemist Zosimus [MS 2327, BN Paris, in Berthelot, 1887].

1.2. Glass and Science 1.2a. A Scientific Material In the Middle Ages, glass was poised to become a material of considerable scientific interest. Since the beginning of their art, alchemists had taken advantage of glass transparency, chemical inertness and plasticity to make vessels of any shape for any purpose (Fig. 1.4). A most important piece from this period is the still, which led to the discovery of alcohol. Another was the philosophical egg, a large egg-shaped vessel in which the desired transmutation of base metals into silver or gold was supposed to operate, under the right heat conditions, in contact with the mysterious philosophical stone. Chemists then followed suit and kept diversifying the shape and use of glass vessels for their own operations. In physics, the manner in which glass distorts vision had already been noticed in Antiquity. For a long time, this effect was judged to be more a problem than an asset because the shape of objects could not be reliably observed. This drawback was, for instance, emphasized by Seneca (4 B.C. - 65 A.D.). Hence, glass attracted little interest from the first Arab and Western theoreticians of optics. It is only when it was realized that distortion of images is determined by the shape of glass, and not by its nature, that optical applications became possible. Apparently, this happened in the 13th century in Italy when glass was ground to form concave lenses to be used to correct shortsightedness [Clay and Court, 1932]. Because of the isotropy of its optical properties and relative ease of production, glass rapidly proved to be more appropriate for optics than crystals like quartz and beryl which were also used. Later on, convex and various sorts of lenses

7

The Discovery of Silicate Melts

Figure 1.5 - Hooke's [1665] microscope. Glass was used not only for the two lenses of the instrument, but also for the fuel flask (on the left side) and the spherical water bulb which served to focus the light on the small lens placed near the sample holder.

allowed other kinds of visual impairments to be corrected. In this way, glass transformed the daily life of laymen and scholars. Of fundamental importance were also the inventions that glass made possible in the 17th century when lenses became used in telescopes and microscopes (Fig. 1.5). With these new instruments, scientists like Galileo Galilei (1564-1642), Robert Hooke (1635-1703) and Antonie van Leeuwenhoek (1632-1723) began to explore the marvels of the outer and inner reaches of the world. Glass, in the form of prisms, also had the intriguing ability to decompose natural light in a rainbow-like manner. This was the basis of Isaac Newton (1642-1727)'s famous 1666 investigation on the nature of light. All branches of physics would, in fact, depend on glass to a very large extent. To give a single example, Robert Boyle's (1627-1691) law was determined in 1662 from measurements of the volume of air compressed by mercury in glass tubes (Fig. 1.6). Indeed, without glass there would have been no thermometers or barometers and it would have been more difficult to arrive at the concepts of temperature and pressure. (For thermometers, however, problems raised by the nonequilibrium nature of glass would last more than two centuries!) Thanks to its insulating properties, glass would also play a major role in electrostatics through rubbing of various materials on glass rods and disks [Hackmann, 1978]. When he discovered in 1733 two different kinds of electricity, Charles Du Fay (1698-1739) thus called them "vitreous" [positive] and "resinous" [negative], a nomenclature that would hold until the end of the 19th century. 1.2b. Descartes and the Foundation of a Science Figure 1 6 - The Of course, curious minds were not satisfied with empiricism. Rene U-shaped glass Descartes (1596-1650) had a strong interest in glass because of his optical tube used by research activities. He had for instance explained theoretically the law Boyle [1662].

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Chapter 1

Figure 1.7 - Prince Rupert's drops [Peligot, 1877]. Their weak point is their thin tail, which lacks a core, so that a slight shock on it triggers shattering of the whole piece.

of refraction discovered in 1620 by Willebrord Snell (1580-1626) in the Netherlands. The famous philosopher was especially fascinated by the "transmutation of ashes into glass". This wide-ranging interest led him to give, in 1644, a correct picture of vitrification in his extremely ambitious Principles of Philosophy, a treatise aimed at deriving a comprehensive description of the world from a few first mechanical principles. A glass, thus wrote Descartes, "when still glowing with heat, is fluid because its particles are easily moved [separately from one another] by that force of fire which previously smoothed and bent them. However, when it begins to be cooled, it can take on any figures whatever. And this is common to all bodies which have been liquefied by fire; for while they are still fluid, their particles effortlessly adapt themselves to any figures whatever, and when such bodies subsequently harden with cold, they retain the figures which they last assumed".

At a time when nothing was known about the microscopic constitution of matter, Descartes was able to describe in this way what we refer to as atomic configurations of a material and the manner in which these vary with temperature. Descartes went on to explain why glass should be annealed because of differential volume contraction on cooling and build-up of what we call internal stress: glass "is also more fragile when it is cooled quickly than when it is cooled slowly; for its pores are fairly open while it is glowing with heat [...]. However, when glass cools naturally, these pores become narrower. [...] And if the cooling occurs too rapidly, the glass becomes hard before its pores can thus contract: as a result, those globules subsequently always make an effort to separate its particles from one another."

Unfortunately, Descartes' groundbreaking conceptions on glass probably suffered from the general criticism laid upon the Principles of Philosophy. This treatise was judged by many as a "romance" even before the vortices, which played so prominent a role in his system, had rightly been attacked by the Newtonians. Although they were heralding the beginnings of glass science, Descartes' ideas, thus, did not attract much attention. They

The Discovery of Silicate Melts

9

have even remained completely forgotten until the present time [Richet, 2000]. Yet, these concepts would have helped find explanations to a great many glass properties. A case in point is tempered glass, which was presented in 1661 as Prince Rupert's drops before the Royal Society of London [Merret, 1661]. Brought from Germany by the English Prince Rupert, these glass beads are produced through quenching of melt droplets into water (Fig. 1.7). Their particularity is to be remarkably shock resistant until a final blow make them explode and shatter into a very fine powder. 11 In a dramatic way, this phenomenon illustrates the role played by internal stresses that develop when glass is not annealed. Tempered glass would remain a scientific curiosity until the late 19th century, however, when fast cooling by compressed air came into use and made it possible to cool a piece of glass in such a way as to ensure a smooth, homogeneous distribution of internal stress. 1.2c. The Effects of Composition Environmental issues have long confronted the uses of glass. As early as the beginning of the 17th century, excessive consumption of charcoal for metallurgy and glassmaking in England gave rise to laws designed to preserve forests. But substitution of coal for charcoal resulted in serious difficulties because the glass had to be protected from the corrosive (sulfurous) fumes released by the burning of coal. Melting pots had to be covered, with the consequence that heating was made more difficult because of the lack of heat radiated from the furnace vault. Consequently, new, more effective fluxes had to be found to alleviate the problem. A result was the invention in 1676 of crystal glass by George Ravenscroft (1632-1683) through addition of large amounts of lead oxide to the composition [Moody, 1988; Moretti, 2004]. Even though lead oxide had been used in Antiquity, crystal glass was a forerunner of future changes made in glass composition to yield new, special properties. Because index of refraction scales with density, crystal glass had a distinctly bright and vivid appearance which instantly met with popular success. Of course, it also proved valuable to optics, a branch of physics where it became known as flint glass because it was made from ground flint in a country (England) where pure enough siliceous sand was badly lacking. Another new family of glass appeared at about the same time in Bohemia. There, potash-lime glass was made as a substitute for quartz, which had been extensively mined for the purpose of carving beautiful vessels out of large single crystals. The new glass ensured great clarity, even for big pieces, and it could be ornamented with enamel thanks to the high temperatures it could sustain without softening. 11

In modern terms, the explanation is as follows. Owing to faster cooling, the surface of the drop is slightly less dense that its core. As a result, the core is under extension whereas the surface is under compression. Because a material breaks much more readily under extension than under compression, strong shocks are needed to produce the extensive stresses needed to initiate rupture on the glass surface. The mechanical energy that was stored through tempering is then released so violently that the glass shatters completely.

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Chapter 1

Figure 1.8 - Reaumur's porcelain, an engraving from Peligot [1877].

Actually, glassmakers had long noticed that excessive time spent at temperatures appropriate for blowing induces partial transformation to a whitish material that could no longer be blown. It is only in 1727 that the naturalist and physicist Rene-Antoine Ferchault de Reaumur (1683-1757) observed that this was the result of devitrification of the melt. Reaumur also discovered that porcelain was a partially melted material and was, thus, an intermediate product between terracotta and glass. Through extensive devitrification, he could then create new products later called Reaumur's glass porcelains (Fig. 1.8). Reaumur's experiments exemplified the extensive ceramic work of the period connected with the search for raw materials which would allow imitation of China's porcelain. Rocks appeared to differ widely in the way they reacted at high temperature. Granite, for instance, was readily melted. To Georges Louis Leclerc, count of Buffon (1707-1788), this observation suggested that granite had formed by cooling of a melt. For reasons that will be given below, however, the evidence was not considered overwhelming by many scientists of the time. 1.3. The Discovery of Natural Melts 1.3a. The Origin ofNeptunism Early glassmakers were familiar with an uncommon rock, obsidian. As already noted, they even succeeded in imitating this rock as small pieces because its special aspect, color, luster, and fracture made it a valuable commodity used for a wide variety of tools, jewels or even mirrors. Long before the emergence of agriculture, these natural glasses had been traded far and wide within Eurasia, North and South America, and other parts of the world. In Eurasia, outcrops were mined in Sardinia, Lipari Islands (north of Sicily), Pantelleria (between Sicily and Tunisia), Armenia, Ethiopia or Turkey. Today, these obsidians are of interest for archaelogical purposes because the specific trace element composition of the mined outcrops makes it possible to reconstruct trade routes [see

Dixonetal, 1968].

Before the beginnings of geology, however, the origin of rocks in general, and obsidians in particular, was not of great concern. Without adequate means of investigation, people were mostly interested in the practical uses of different kinds of rocks. Until the middle of the 18th century, volcanic products were identified as such only when their

The Discovery of Silicate Melts

11

origin was obvious from field relationships. This applied to cinders, ashes, scoriae, and solid lava that had been clearly issued from the crater of a volcano. At a time when the world was believed to have been created about 6000 years earlier, it was difficult to think of extinct volcanoes because the Earth could not be much different from what it had been at the Creation. Since Antiquity, it had been held that volcanoes resulted from subterranean fires fueled, not by exhalations of subterraneous winds as guessed by Aristotle (-384~322 B.C.), but by bitumen, sulfur or coal as reported by Lucretius (~98-~55 B.C.) or Strabo (—64 B.C. +25 A.D.). Hence, volcanoes were just considered as local accidents, scattered throughout the Earth's surface, which could not have been of any real importance in the past. As a result, volcanoes were known only in volcanically active regions. In contrast, there were good reasons for thinking that most rocks had formed in water. Water was the ubiquitous agent at the Earth's surface. The Scriptures asserted that the sole extraordinary episode of the Earth's history had not been a volcanic conflagration, but the Deluge. When laying the foundations of geology in 1669, Nicolaus Steno (16381686) indeed explained that strata had first been sediments deposited at the bottom of the sea before being consolidated as rock. In addition, chemists had observed that aqueous solutions precipitated solid material with a geometrical shape. The prismatic shape of rocks such as basalt (Fig. 1.9), thus, was indicative of an aqueous origin. Even the bold theoreticians who followed Descartes and wrote their own Theories of the Earth did not challenge such ideas. Descartes himself thought that the Earth was an "encrusted" sun whose center was filled with a fiery matter. But he did not make any connection between such hot, deep interiors of the Earth and volcanism, which he also ascribed to as subterranean fires. When Gottfried Wilhelm Leibniz (1646-1716) and Buffon later considered the Earth as still cooling from an initially molten state, they, too, held that water was the main geological agent. They were both neptunists, as they would have been called at the beginning of the 19th century. Following the ideas that Leibniz expounded in the 1690's in his Protogaea, published posthumously, it was generally assumed instead that granite, the rock considered at that time to be primordial because it was consistently overlaid by sedimentary rocks, had deposited from a primitive, strongly mineralized ocean. 1.3b. From Extinct Volcanoes to Magma To appreciate better how the existence of igneous rocks came to be recognized, we must start with the field trip made by the naturalist Jean-Etienne Guettard

Figure 1.9 - Basalt prisms whose idealized apices are a testimony of the confusion that would beset the distinction between minerals and rocks until the end of the 18th century [Gesner, 1565].

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Chapter 1

Figure 1.10 - Basalt prisms in Chenavari, near Montelimar in the Rhone valley [Faujas de SaintFond, 1778]. (1715-1786) in central France in July 1751. In Moulins, he was struck by the town's fountains which were made from a stone that resembled some Italian lavas of the Parisian rock collection of which he was curator. By asking where this stone was quarried, he ended up near Clermont-Ferrand where he discovered the typical volcanoes which make up the now-famous Chaine des Puys. Far away from any active volcanic province, Guettard pointed out, there were extinct volcanoes which some day would perhaps erupt anew. Guettard, however, was himself a neptunist. He was a proponent of subterranean fires as the source of volcanic activity, and he was sharing the common idea held since Antiquity that volcanoes are located near the sea because eruptions are triggered by interactions of infiltrated sea water with molten lava. He would also long believe that basalt could not have a volcanic origin because its columnar nature was a testimony to an order inconsistent with the confusion that is the hallmark of the action of fire [Guettard, 1770]. Later, however, Guettard [1779] would yield to the new ideas that were being propounded by Nicolas Desmarest (1725-1815), a government official who was also a part-time naturalist. Of still greater importance was the second step made in 1763 when Desmarest travelled to Auvergne to see for himself the volcanoes described by Guettard. Near the Puy de Dome, he immediately realized that basalt had been flowing out from the crater of volcanoes. This, he demonstrated by careful observations that led him to make a detailed cartography of lava flows in the whole region. Thanks to its prismatic nature, basalt was

The Discovery of Silicate Melts

13

soon identified not only in various parts of France by Faujas de Saint-Fond [1778], Guettard [1779], and other naturalists, but throughout Europe (Fig. 1.11). As made in Hessia by Rudolf Erich Raspe (1737-1794) — better known as the author of the Adventures of Baron Miinchausen — the existence of former volcanoes was recognized in Italy, Spain, Portugal, Germany, Ireland, and Scotland. In the past, volcanism thus appeared to have been much more important than previously thought. But Desmarest and his fellow naturalists were also neptunists. They held that lavas were just rocks melted at shallow depths in which phenocrysts were the remnants of former rocks that had been incompletely melted. The mineral pyroxene \pyros, fire, and xenos, foreign] described by Buffon's aide Louis Jean-Marie Daubenton (1716-1800) and by the famous mineralogist ReneJust Haiiy (1743-1822), is a reminder of these ideas. At that time, thermodynamics was still in limbo so that it is not surprising that the nature of "volcanic fire" was debated. Was it the same as that of "common fire"? Scientists like the abbot Lazzaro Spallanzani (1729-1799) thought that melting experiments could solve the problem. But the answer remained elusive because the difference between temperature (an intensive thermodynamic property) and heat (an extensive property) had not yet been worked out properly. Spallanzani [1792-1797], himself, incorrectly believed

Figure 1.11 - The basaltic Fingal cave in Staffa island (Hebrides, Scotland) as depicted by Faujas de Saint-Fond [1797].

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Chapter 1

that, over long enough periods of time, the fire of furnaces would reach an intensity sufficient to melt lavas. A more lasting observation reported by Spallanzani in his great book was that exsolution of dissolved gases is the driving force of volcanic eruptions, as he daringly recognized in 1790 during an eruption of Vesuvius. The breakthrough on the origin of lava eventually came from Deodat de Dolomieu (1750-1801), a famous geologist of the period who left his name to the dolomite rock and the Dolomites mountains. Back from volcanological field work in Italy and Auvergne, he elegantly demonstrated in 1797 that lavas originate from a great depth below the primordial granite, an idea that ruled out water-melt interactions as the cause of eruptions. Although Dolomieu remained cautious about the source of lava, he correctly concluded that it extends all over the Earth. Announcing the concepts of isostasy and asthenosphere, he also inferred that this reservoir is "viscous and pasty" and can, thus, feed the biggest volcanoes indefinitely without causing any underground collapse [see Richet, 2005a]. It was at that time that the word magma began to take on its modern meaning [Gohau, 1998]; until then, it had meant viscous or gelatinous pastes used in pharmacy. 1.3c. The New Importance of Silicate Melts In Scotland, the physician James Hutton (1726-1797) had already assumed that the Earth was hot at depth. He was, in fact, claiming that fire, and not water, is the main natural agent. According to the theory he first sketched in 1785 — late in his life — the Earth is a heat engine that gives rise to the great geological cycles of erosion, sedimentation, petrification, and finally mountain-building. For Hutton, there was no doubt that granite had an igneous origin, a term whose oldest known occurence is in a 1792 book by the Irish scientist Richard Kirwan (1733-1812). Although Dolomieu's view fit well within this plutonist scheme, there was considerable reluctance to admit that basalt is indeed a volcanic rock. During the first decades of the 19th century, the neptunist school would follow Abraham Gottlob Werner (1749-1817), the most famous geologist of his time, and continue to defend the old ideas of an aqueous origin for granite and basalt through deposition of both rocks in highly mineralized primitive solutions [e.g., Werner, 1791]. Another Scot, James Hall (1761-1832) resolved to provide an experimental basis for his friend Hutton's ideas. With great ingenuity, and a certain contempt of danger, he showed that pressure is an important factor for phase stability within the Earth [Hall, 1806]. Limestone, for instance, does not decompose when heated under pressure, but transforms into marble. Hall's other main achievement was his discovery, in 1790, that glass forms when the cooling rate of the melt is too high for crystallization to proceed, a result that he published only eight years later. This discovery marked an abrupt change in perspective because phenocry sts could no longer be considered as the remnants of former rocks, but were recognized to be the first minerals to form on cooling. These conclusions were soon put to practical use. In France, the chemist Jean-Antoine Chaptal (1756-1832) attempted to use basalt as a starting product to make bottles, but his efforts ended in failure because devitrification could not be avoided on cooling.

The Discovery of Silicate Melts

15

Figure 1.12- A 19th century concept which is still present in the popular mind: the sea of fire with its direct connection with active and extinct volcanoes [With, 1874].

These advances had obvious consequences on the still fledging discipline of petrology. The presence of coarse minerals pointed to very slow cooling, whereas that of glass was clear evidence for a volcanic origin. From careful observations made on crushed rocks with the use of the optical microcope and the blowpipe, Louis Cordier (1777-1861) concluded in 1816 that all volcanic rocks are essentially made up of a few minerals: feldspar, pyroxene, olivine and iron titanates first, and also amphibole, mica, leucite, and hematite. Of course, the same minerals were observed in coarse-grained rocks, consistent with their igneous origin. Another significant result achieved at that time was melting of quartz under the blowpipe. Vitrification of pure SiO2 was achieved in tiny amounts by Marcet [1813] and in larger quantities by Marc-Antoine Gaudin (1801-1880) who, in 1839, drew fibers which were "resembling steel in elasticity and tenacity". After four millennia of glassmaking, it had at last become possible to melt silica without a flux. Considerably more important were the temperature measurements made by Cordier in mines. He reported in 1827 that the geothermal gradient is about 1°C per 30 m and concluded that, at some depth, temperatures are much higher than the melting point of any rock. Below a solid crust thinner than 100 km was lying a boundless "sea of fire" from which all igneous rocks derived (Fig. 1.12). This view of an Earth made up mostly

16

Chapter 1

of silicate melts would be immensely popular. Temperatures of about 2 105 °C were estimated at the center of the Earth from the hypothesis of a constant geothermal gradient, even though this assumption was inconsistent with the theory of heat conduction published in 1822 by Joseph Fourier (1768-1830). In fact, Fourier's main goal when he set up his famous theory had been to determine the age of the Earth from its cooling history [see Richet, 2005b]. For lack of relevant thermal conductivity and heat capacity data, however, Fourier [1820, 1824] had himself refrained from any real numerical application. The real attack against the sea of fire would come from one of the founders of thermodynamics, William Thomson (1824-1907), later known as Lord Kelvin of Largs. As a great pioneer of geophysics, Thomson set out to place geology on a rigorous, quantitative footing. In 1863, he first demonstrated that the Earth is not liquid, but essentially solid and "at least as rigid as steel". By using Fourier's theory of heat conduction, he then attempted to determine the age of the Earth from current surface temperature and geothermal gradient [e.g., Burchfield, 1990; Richet, 2005b]. When following Buffon and Fourier, without their cautiousness, Thomson [1895] thus was mistaken when he eventually limited the age of the Earth to about 24 million years. But the stress he had put on the need for good physical measurements for rocks and melts was already bearing fruit. 1.4. The Physical Chemistry of Melts 1.4a. The Measurements of Physical Properties For basalt, Thomson inspired in England the first measurements of the enthalpy of melting [Roberts-Austen and Riicker, 1891] and in the U.S. of the variation of the melting temperature of a rock with pressure [Barus, 1893]. It was at that time that geologists began to show serious interest in melt viscosity. While Becker [1897] tried to estimate it from field observations, Doelter [1902] was measuring it to compare that of various molten minerals and rocks. Such physical work complemented well the systematic efforts made since the middle of the 19th century to reproduce the mineralogy and texture of igneous rocks in the laboratory [see Gohau, 1997; Young, 2003]. Following Kelvin's recommendations, a group of scientist was willing to make geology benefit from the new science of chemical thermodynamics whose principles had been laid out by Josiah Willard Gibbs (1839-1903). With the support of the steel tycoon Andrew Carnegie (1835-1919), they created in 1905 the Geophysical Laboratory of the Carnegie Institution of Washington. One of the first goals was establishment of a thermodynamic temperature scale up to 1755°C [see Sosman, 1952]. Besides, the quenching method was designed to determine phase equilibria of materials whose transformations tend to be extremely sluggish [Day et al., 1906; Shepherd et al., 1909]. Interest in the physical chemistry of silicate melts and glasses ranked high in the geological work to be performed and in its potential industrial applications [e.g.,Bowen, 1918; Fenner and Ferguson, 1918; Morey, 1919; Morey and Merwin, 1932]. Other early major achievements were the determination of the CaO-Al2O3-SiO2 phase diagram by Rankin and Wright [1915], the annealing studies (see below) of Adams and Williamson [1920], the recognition of the

The Discovery of Silicate Melts importance of experimental studies of diffusion by Bowen [1921], and the discovery by Greig [1927] of liquid immiscibility in binary alkaline earth silicates. Glass also played a major role in the theory of rupture published in 1920 by Alan A. Griffith (18931963). For practical reasons, glass fibers had been selected by Griffith to demonstrate the considerable lowering of breaking stress by surface defects. A tremendous increase of this stress with decreasing fibre diameter was indeed observed (Fig. 1.13); this effect was ultimately due to the fact that "a fibre consisting of a single line of molecules must possess the theoretical molecular tensile strength". In the form of fibers, glass had more strength than iron but it would take two decades to put this advantage to practical use for . . .vc & v materials reinforcement.

17

Diameter, mm Sure 1 1 3 " BreakinS stress a ainst diameter of S §lass fibers. Data of Griffith 1920 , .e. , c c for a glass of unspecified c o m p o s i t i o n ( 1 M P a = 1 0 bars].

Fi

The physical chemistry of liquid silicates also became of great importance to metallurgy. Slags, which are silica-poor melts, had been known ever since the beginnings of iron metallurgy because the ore impurities, mostly silicates, melted and coalesced as inclusions in the metal sponge that was obtained at the end of the process [e.g., Tylecote, 1990]. The smith was getting rid of them by hammering the sponge, but there was no apparent need to pay attention to their properties. This situation had began to change when the blast furnace was invented in the 15th century and pig iron — a liquid carbon-metal alloy — was recovered at the bottom of the furnace, with the molten slag left above. Then, it was realized in the 19th century that desulfurization and dephosphorization of the metal could be controlled through exchange reactions with the slag phase. Eventually, thermodynamic modeling of such reactions became an important goal. Hence, metallurgists were among the first to measure extensively activities of oxides in melts [e.g., Rein and Chipman, 1965] and to perform phase equilibria calculations [see Richardson, 1974]. Especially in Germany, metallurgists also pioneered measurements of physical properties such as density and viscosity [see the studies listed by Bottinga and Weill, 1970, 1972]. Likewise, it is with the support of the metallurgical industry that Bockris and coworkers measured the electrical conductivity [Bockris et al., 1952] and viscosity [e.g., Bockris and Lowe, 1954] of silicate melts and arrived at the modern picture of partially ionic liquids made up of groups of various sizes. 1.4b. Toward the Glass Transition From the mid-19th century, glass, in turn, had benefited from the progress of chemistry and physics to which it had contributed so much. It was known that vitrification is not restricted to silicates, but can also obtain in organic substances such as sugars. Even an element — selenium — had a vitreous form. These substances had strange properties, as

18

Chapter 1

Supercooling

Figure 1.14 - Rates of crystal growth and nucleation against extent of supercooling for a glass-forming liquid whose viscosity increase is also illustrated [from Tammann, 1925].

revealed by measurements that had either fundamental or industrial motivations. Chevandier and Wertheim [1845] observed that the density and "elasticity coefficient" of quenched glass increases upon annealing, on average by 4.5%o for the density. Because of their rigidity, glasses were considered as particular forms of solids but their relationships to crystalline polymorphs were not clear. As they were assigned definite melting temperatures, another curious observation was made in 1851 by Johann Wilhelm Hittorf (1824-1914) when he noticed that selenium glass was melting without any heat effect. At the end of the 19th century, work by Gustav Tammann (1861-1938) marked an important turning point. While investigating the relationships between glass and crystal, Tammann [1898a] found that crystallization proceeds in two steps, namely, formation of "crystallization centers", followed by growth of crystals. For both nucleation and growth, the rate varies with temperature according to a bell-shaped curve (Fig. 1.14). From cooling experiments performed on scores of liquids of many kinds, Tammann [1898b], in addition, established the kinetic nature of the glass transition and stated that, at least in small amounts, most liquids could vitrify if cooled rapidly enough. Because the glass-forming ability of a liquid was determined by its reluctance to crystallization, Tammann could define glass as "a non-crystalline, strongly supercooled melt." Abrupt variations of properties were observed when a glass is heated during measurements of thermal expansion [Callendar, 1887] or dielectric constant [Flemming and Dewar, 1897]. Curiously, however, these anomalies elicited little interest. The development of platinum-based thermocouples, calibrated through gas thermometry, made accurate measurement of high temperature possible at the beginning of the 20th century. The improved measurements of physical properties made over large temperature ranges lead to a better understanding of the glass and melt relationship. Viscosity, for instance, was extensively studied for soda-lime compositions by Washburn and Shelton [1914]. In his pioneering high-temperature calorimetric investigation of silicate glasses and crystals (Fig. 1.15), White [1919] lucidly reported that several of the glasses "show a decided increase in specific heat at some fairly elevated temperature. No explanation has been established for any of these facts. It seems probable that the increase in specific heat would have appeared if they had been carried higher. It may be a phenomenon of considerable importance." At about the same time, So [1918] and Tool and Eichlin [1920] also observed anomalous thermal effects for silicate glasses in narrow temperature intervals near the empirical

The Discovery of Silicate Melts

19

Figure 1.15 - Glass transition of NaCaAlj 5 Si 2 5 0 8 observed in drop calorimetry experiments [White, 1919] as a break in the mean heat capacity curve, Cm = (HT- H29S)/(T- 298), where H is enthalpy.

annealing temperatures (Fig. 1.16). Similar observations were made by Gibson et al. [1920] for some alcohols while Peters and Cragoe [1920] described analogous variations of the thermal expansion coefficient of silicate glasses [see Richet and Bottinga, 1983]. Glass formation was thus associated, not with any discontinuous change in first-order thermodynamic properties (e.g., volume, enthalpy), but with rapid variations of secondorder thermodynamic properties. It is during this period that Adams and Williamson [1920] investigated the internal stresses that build up when a glass-forming liquid is cooled and published their famous analysis of the rate at which the ensuing strain and birefrigence can be realeased on annealing. This work was of particular importance for optical glass. It heralded the beginning of relaxation studies. An important practical outcome would be standardization of working operations in terms of viscosity for the strain point (10135 Pa s), the annealing point (1012 Pa s), the deformation point (10103 Pa s) and the softening point (1066 Pa s). Before any structural information was available, even for silicate crystals, Alexander A. Lebedev (1893-1969) noted that the birefringence of optical glass disappeared on annealing near the 575°C temperature of the a - 3 transition of quartz. In 1921, he assumed that glass contains "minute quartz crystals", forming themselves solid solutions, such that "annealing is not so much the removal of stress as the attaining of complete polymorphic transformation". These views formed the basis for the microcrystalline

Figure 1.16 - Glass transition of annealed and quenched samples of window glass in differential thermal analysis experiments [Tool and Eichlin, 1925].

20

Chapter 1

Figure 1.17 - Structural relaxation in viscosity measurements at 486.7°C on fibers of a window glass [Lillie, 1933]. The lower curve refers to a newly drawn sample whose fictive temperature was higher than the run temperature, the upper curve to a sample first annealed at 477.8°C for 64 hours. The convergence of the curves indicates attainment of thermodynamic equilibrium in about 2000 min.

hypothesis, according to which glass is made up of a disordered arrangement of very small crystals whose structure is similar to that of a stable crystalline form [see Evstropyev, 1953]. In other measurements, Tool and Eichlin [1924] observed that thermal effects in the annealing range depend on cooling rate, which in turn causes glass properties to depend on thermal history (Fig. 1.16). Extensive work by a number of investigators, especially Tool and Eichlin [1924,1931, and references therein], revealed that a state of equilibrium could be attained through "molecular rearrangement" in crystallite-free materials. There was, therefore, still no hint of a glass-to-liquid transition. Tool and Eichlin [1931] noted that these transformations were taking place at "effective" temperatures, later called fictive temperatures [Tool, 1946], which were slightly higher than the annealing temperatures. For viscosity, Lillie [1933] then showed how equilibrium properties can be measured through reversal experiments made on samples whose fictive temperature is initially higher and lower than the run temperature (Fig. 1.17; see also section 2.1a). Another important step was recognition that the viscosity of glass-forming liquids does not follow Arrhenius laws, ri=rioexp(AHr/RT),

(1.1a)

log ri = A + 2.303 AHJRT,

(1.1b)

where A = log rj0 is a pre-exponential term and AH the activation enthalpy for viscous flow. To account for the nonlinear variations of log t] against reciprocal temperature, Fulcher [1921], Vogel [1925], and Tammann and Hesse [1926] used instead the equation logr1 = A + B/(T-Tl),

(1.2)

where A, B, and Tx are constants. This TVF equation12 embodies the fact that viscosity would become infinite at the Tx temperature. This intriguing feature is intimately connected with the still unsolved fundamental problem of the glass transition. Further work would 12

Even though "VFT" equation is more common than "TVF" equation, we prefer the latter expression. Not only is it more euphonic, but it also acknowledges more clearly Tammann's outstanding contribution to glass science.

21

The Discovery of Silicate Melts

Figure 1.18 - Heat capacity changes of organic substances in the glass transition region [Parks and Huffman, 1927]

show that equations of the same form also account for the temperature dependence of other transport and relaxation properties (i.e., electrical conductivity, atomic diffusivity, dielectric and structural relaxation times, or even spin-lattice relaxation). However, the parameter Tv which is sometimes called the Vogel temperature, is specific to each property considered. Although they could not determine unambiguously the nature of glass, Parks and Huffman [1927] recognized early its specificity as a distinct state of matter. Relying on their heat capacity measurements on organic substances (Fig. 1.18), they wrote "While there is no definite temperature, comparable to the melting point of a crystal, at which all properties undergo a sharp change, there is nevertheless a temperature interval, definite and reproducible, in which a number of properties change with a rapidity approaching that observed in the case of the melting process of a crystal. In brief, there is a softening region instead of a melting point. The glass as it exists below the softening region differs so markedly from the liquid existing above that it might well be considered as a different state of the substance. For this reason we have recently suggested the possibility of regarding glass as a fourth state of matter, distinct from both the liquid and crystalline states and yet showing to some extent characteristics of both these states."

At last, consistent with Descartes' ideas, a new kind of transition, the glass transition, was to be defined from such variations of second-order thermodynamic properties. Without any reference to the polymorphic-like transformations assumed by Lebedev, Tool and Eichlin, or other workers, the very viscous liquid (at high temperature) was separated from the glass (at low temperature) by a transition at a temperature denoted by the symbol T . This new field of glass science was ably reviewed in books by Tamman [1933] and by Morey [1938] for silicates. Glass had definitely taken a much broader meaning by designating any material that does not crystallize on cooling from the molten state, such as the ubiquitous organic polymers today known as plastics. 1.4c. The First Glimpses Into Structure Whereas a glass is a hybrid phase characterized by a fixed atomic arrangement, like in a crystal, and by the lack of long-range order, like in a liquid, a liquid is a phase whose structure changes rapidly in response to temperature or pressure variations. Since the

22

Chapter 1

Figure 1.19- The x-ray radial distribution function of SiO2 glass [Warren et al., 1936], the first to be determined for silicate glasses. The peak positions yield the distances between first- and secondnearest neighbors, which can be assigned from known ionic radii or interatomic distances in relevant crystals. For well-resolved peaks, the number of neighboring atoms involved can be derived from the peak areas.

term configuration designates any microscopic arrangement of matter consistent with a given macroscopic state of the system, in the 1930s the physicists Franz Simon (18931956) and John D. Bernal (1901-1971) termed configurational those contributions to physical properties that are associated with structural changes within the liquid. Deciphering the nature of these changes has proven to be an extremely difficult task. For a long time, structural studies have been restricted to glasses. Conclusions have often been applied without the necessary caution to the liquid state whose direct investigation at high-temperature has become possible only recently. This will be described in later chapters. The starting point is that glass lacks long-range order, but also that some short-range order necessarily exists because the bonding requirements of each kind of atom prevent complete bond disorder. From the mid 1920s, x-ray diffraction methods allowed the structure of the main crystalline silicates to be determined [e.g., Bragg, 1937]. The young William H. Zachariasen (1906-1979) was struck by the small energy and volume differences between glasses and crystals. Assuming that the principles of structural chemistry newly established for crystal should also apply to glass, Zachariasen posited that both phases share the same basic structural elements. Because glasses lack symmetry and periodicity, they differ from crystals by the fact that disorder begins right at the scale of first-neighbor distances. In his famous 1932 paper, Zachariasen went on to summarize in three rules the conditions for glass formation: "An oxide glass may be formed 1. if the sample contains a high percentage of cations which are sourrounded by oxygen tetrahedra or by oxygen triangles; 2. if these tetrahedra or triangles share only corners with each other; 3. and if some oxygen atoms are linked to only two such cations and do not form further bonds with any other cations."

From the beginning, two extreme situations have thus been depicted by Lebedev and Zachariasen's schools, the disagreement dealing with the extent of medium-range order that prevails in glass. For lack of adequate methods to deal with the experimental x-ray scattering curve of amorphous substances, the first structural studies of glass made with x-ray diffraction had been inconclusive [e.g., Wyckoff and Morey, 1925; Randall et al, 1930]. The situation changed when the method of Fourier analysis was designed by Zernicke and

23

The Discovery of Silicate Melts

Figure 1.20 - Two-dimensional projection of the structure of a soda-silica glass [from Warren and Biscoe, 1938]. As derived from x-ray data, this random network also accounted structurally for the existence of gradual (instead of abrupt) softening, viscosity decrease upon Na2O addition (through fragmentation of the silicate network), and electrical conduction (through hopping of the loosely bound Na atoms). Prins [1927] to determine radial distribution functions of liquids. As shown in Fig. 1.19, the method was pioneered by Bertram E. Warren (1902-1991) for oxide and silicate glasses. In studies of SiO 2 and B 2 O 3 glass, Warren [1934] and Warren et al. [1936] confirmed Zachariasen's first rule by showing that Si and B are coordinated by four and three oxygens, respectively, and each oxygen by two Si or B. They also coined the term random network to describe the three-dimensional disordered arrangement described by Zachariasen. Work on soda silica glass [Warren, 1934, Warren and Biscoe, 1938] then showed that two different kinds of oxygen (later called bridging and nonbridging) must be distinguished depending on whether they are bonded to only one or to two silicons (Fig. 1.20). Other methods began to be used to investigate glass structure. Right after the discovery of the Raman effect [Raman and Krishnan, 1928], the spectrum of quartz was recorded by a number of spectroscopist [e.g., Pringsheim and Rosen, 1928]. The resemblance of the Raman spectrum of quartz with those of silica, crown and flint glasses was rapidly pointed out by Gross and Romanova [1929]. Despite the technical difficulties of work made with mercury lamps, a variety of glasses were studied in more detail by Kujumzelis [1935,1936]. His spectra for SiO 2 and B 2 O 3 glasses (Fig. 1.21) compare remarkably well with modern results (for SiO 2 , see the background corrected spectrum of Fig. 5.21). Each glass was found to have a characteristic spectrum that was determined by the kinds of molecular groups present in the structure. In accord with the ideas of Zachariasen and

Raman shift, cm-1

Figure 1.19- Raman spectra of SiO2 and B2O3 glasses [from Kujumzelis, 1936]. The sharp peak at 808 cm"1 in the B2O3 spectrum would later be shown to be characteristic of the so-called boroxol rings.

24

Chapter 1

Warren, Kujumzelis correctly attributed the bands below 550 cm"1 to lattice modes or noted that Al could substitute for Si without marked structural changes. Although the basis for such work would not be available for a few more decades, he also pointed out that systematic measurements were needed to make reliable specific band assignements. Together with the notion of bridging and nonbridging oxygens, the distinction between network-former and network-modifier cations was another concept of fundamental importance. Warren and Pincus [1940] used it to discuss liquid immiscibility in binary metal oxide-silica systems in terms of competition of cations for bonding with nonbridging oxygens, whose outcome is determined by the ratio Z/rc of the electric charges and ionic radii of cations. Along similar lines, Adolf Dietzel (1902-1993) introduced in 1942 the notion of field strength, / = Zla2, where a is the distance between ions (metal cation and oxygen, in general), to rationalize the systematic variations of devitrification, compound formation and melting temperatures as a function of the nature of cations. Later, Stevels [1953, 1954] would recognize the control exerted on physical properties by the degree of polymerization through a parameter X designating the average number of nonbridging oxygens per tetrahedrally coordinated cation (which is now more explicitely denoted by NBO/T). As will be described in other chapters of this book, random network models are probably too extreme in denying significant medium-range order. Nonetheless, Zachariasen's rules still represent a useful starting point for discussion of glass structure. On the other hand, it is ironic that the strongest evidence for structural microheterogeneity presented by the microcrystalline school [see Evstropyev, 1953] was the result of metastable liquid-liquid phase separation which would be discovered in the early 1960s [see Mazurin et al, 1984]. 1.4d. The Search for New Compositions From prehistory until the end of the 19th century, the oxides of very few elements had been used for making glass. Leaving aside coloring elements, whose concentration is low, these were silicon, sodium, calcium, aluminum, potassium and lead. In England, a minister named Harcourt and the physicist George Gabriel Stokes (1819-1903) succeeded in incorporating a variety of other elements in glass [see Vogel, 1994]. Harcourt even discovered the glass-forming ability of B2O3 and P2O5, but his efforts had little practical applications. In Germany, the great optician Ernst Abbe (1840-1905) wondered whether the narrow range of chemical composition of glass was the reason why both refractive index and dispersion were always increasing in a way similar to density. Was it also the reason why lenses had known little improvement since the invention of flint glass? At Abbe's instigation, Otto Schott (1851-1935) had begun in 1881 systematic investigations of the density-optical property relationships of silicate glasses in a work supported by a scientifically oriented German government. By using all the elements known at that time, he could incorporate 28 of them in concentrations higher than 10 wt % [see Hovenstadt, 1900]. Introduction of barium, a heavy element, for instance caused an increase of the

25

The Discovery of Silicate Melts Table 1.2. Composition of some industrial glasses and melts (wt %)a SiO2 A12O3 Window glass Thermometer" CRT, panelc CRT, funnel" FDPe Pyrex Neutral glassf E glass Vycorg Glass woolh Rock wool" Ash1 SlagJ

72.6 53.0 60.5 50.0 69.0 81.1 74.8 56.5 62.7 65.0 46.6 41.7 36-7

0.6 21.0 2.0 4.0 11.5 0.43 6.2 14.3 3.5 2.5 13.3 11.0 5-35

B2O3 Fe2O3

FeO

MgO

CaO

Na2O

0.8

3.6 10.0

8.7 5.0

14.3

0.2 7.5 8.5

0.5

2.6

4.0 5.0 1.1 0.5 18.4

8.0 6.0

0.2

2.0 1.4 0.3

4.8 2.6

2.5 9.1 2.3 16-4

8 10.0 48.0 43-54

10.0

7.3 22.0 10.5 6.4 26.9 4.5 6.4

1.5 7.5 0.4 6.6 16.5 5.6 2.4

K2O TiO2

0.5

0.8 0.4

0.6

0.7 1.4 1.3

2.4 3.3

a

Compositions may vary from a manufacturer to another, and with time for a given manufacturer. 2003 world glass production: 120 106 tons. In the European Union (29 106 tons), container glass: 63 %; flat glass: 27 %; tableware: 4%; reinforcement fibers: 2 %; specialty glasses: 4 %. bJena 2950111 (supremax);cCathode ray tube for color television, with 9.5 SrO, 9 BaO, 0.5 ZnO, 1.5 ZrO2, 0.2 CeO2, 0.3 Sb2O3;d with 23 PbO, 1 SrO and BaO, and 0.3 Sb2O3; eFlat display panel, Corning code 1737, with 4.4 BaO, 1.2 SrO and 0.2 As 2 O 3 ; f for Pharmaceuticals, with 2.3 ZnO; 8 as melted, vitroceramics;h for thermal insulation;' from incineration of household waste;' optimal sulfur retention for slags with two extreme A12O3 contents.

refractive index of glass without increasing the dispersion. Such observations proved especially useful for microscopy and photography applications. From this work, it was becoming possible to tailor a glass composition for a given specific application. At the turn of the 20th century, the various processes used to make flat and container glass underwent mechanization [see Cable, 1990], but such an industrial mutation did not induce any important change in glass composition. Further progress in this respect resulted from specific needs. In the U.S., a search was for example made for glasses with low thermal expansion coefficients because the lights of train cars were breaking under the thermal shock caused by heavy rains. The special properties of boron oxide had already been used by the Schott company to make glass for thermometers. In 1908, they resulted in the invention of Nonex glass by Corning Glass Works. This lead borosilicate glass was an instant success, but sales soon dropped because the material no longer needed replacement [see Dyer and Gross, 2001]. The use of glass for cookingware was then considered, but lead-bearing materials were unsuitable for such an application. Further research eventually resulted in 1915 into the famous sodium borosilicate glasses dubbed Pyrex, which have extremely small coefficients of thermal expansion due to the presence of about 12 w t % B 2 O 3 .

26

Chapter 1 Table 1.3. Compositional diversity of natural glasses and igneous rocks (wt %) a SiO 2

A12O3 Fe 2 O 3

Fulgurite (Lybia) Darwin glassb Obsidian0 Rhyolited Obsidian c Trachyte glassf Phonolite 8 Pele hair (Hawaii) Basalt glass11 Tephrite8 Peridotite8-' Dunite 8 '

97.6 87.0 74.7 71.6 67.5 60.1 56.2 50.8 50.3 47.8 42.3 38.3

1.5 8.0 13.7 12.4 15.7 17.7 19.0 14.7 15.5 17.0 4.2 1.8

Lunar glasses Silica glass, Luna 20 Granite glass Basalt glassj Low SiO 2 glass

98.8 73.0 51.7 32.3

0.7 14.8 15.1 38.9

0.2 1.0 1.0 1.0 3.7 2.8 2.9 4.1 3.6 3.6

0.2

CaO

Na 2 O

0.4

0.3 0.1 3.9 4.2 4.1 6.8 7.8 2.7 2.2 3.7 0.5 0.2

1.0 4.0 3.8 2.8 4.4 5.2 0.9 0.2 4.5 0.3 0.1

0.5

0.1 2.2 1.1

0.1 4.2 1.1

0.2 0.5 1.7 0.1

FeO

MgO

0.2 1.9 0.6 0.6 1.0 3.4 2.0 9.8 9.0 5.2 6.6 9.4

0.8 0.1 1.9 1.1 0.5 1.1 6.5 8.5 4.7 31.2 37.9

0.8 3.3 2.5 2.4 2.7 11.0 12.0 9.2 5.0 1.0

2.5 9.8 0.1

0.3 6.7 7.1

2.7 10.6 21.6

K2O TiO 2

0.2 0.3 0.6 1.2 1.8 0.6 0.1

a

See Richet and Bottinga [1983] or Cox et al. [1979] for references of analyses; H 2 O + and H 2 O' not listed. b Tasmania;c Obsidian Cliff, Yellowstone;d Burton Peak, Montana; e Big Butte, Montana; f Heard Island; s average compositions, see Cox et al. [1979]; h Mid-ocean ridge, Famous zone; ' melt not vitrifying;' Fra Mauro. The increasing diversity of chemical composition made it useful to predict a given physical property from the composition of the glass. Near room temperature, linear variations of various properties of silicate glasses were observed as a function of the concentration of oxide components [e.g., Winkelmann, 1893]. Further experimental work revealed deviations from additivity, which were incorporated in more complex models [Gehlhoff and Thomas, 1926]. But no such effort could be attempted for melts because experimental data would be badly lacking for a very long time. Chemistry could also help improve properties without changing the bulk composition of the glass. This is the case of chemical tempering which ensures shock resistance much greater than with the usual quenching procedure: the internal stresses that ensure resistance to shocks are achieved through replacement of sodium by potassium via chemical exchange between the surface of the glass and a molten salt. New applications could otherwise be found for existing glasses. A calcium borosilicate, the so-called E glass, was extensively used for electrical insulation before its excellent mechanical properties were recognized. From the middle of the 20th century, it is with this glass that mechanical reinforcement by glass fibers has been realized in composite materials.

The Discovery of Silicate Melts

27

More recently, new uses of silicate glasses have been made possible by the very wide extent of their solid solutions. As an example, glasses have been selected for nuclear waste disposal because of their low fusion temperature, ability to dissolve large amounts of many different nuclides, and resistance to corrosion by aqueous solutions [see Wicks, 1985]. Likewise, calcium aluminosilicate glasses can be made to dispose of the residue of incineration in trash plants [de Labarre, 1997]. Referring to Kurkjian and Prindle [1998] for a more comprehensive discussion, we will conclude this short review by mentioning the new glass families discovered in fluoride, chalcogenide or metallic systems which have found a variety of original applications thanks to their specific optical, mechanical or chemical properties. 1.4e. A Geological Outlook At the end of this fast journey through time, the considerable interest raised by silicate melts in earth sciences does not need to be emphasized. The data of Table 1.3 illustrate the diversity in chemical composition of lavas. A noteworthy feature of these analyses is the continuous increase in SiO2 content observed throughout magmatic evolution. This trend is the result of partial melting and fractional crystallization events grouped under the term of magmatic differenciation [see Young, 1998]. In the late 19th century, it was assumed that liquid-liquid immiscibility was another process effective in nature. Ironically, the observation of liquid unmixing in simple iron and alkaline earth silicates by Greig [1927] ruled out this process as a cause of magmatic differentiation because it was also observed that miscibility gaps disappear rapidly upon addition of alumina at concentrations much lower than found in igneous rocks. This was not the final answer to the question, however. The actual occurrence of liquid immiscibility in terrestrial and lunar lavas has later been demonstrated [Roedder, 1970], triggering new exprimental studies [e.g., Philpotts, 1976] and illustrating once more the fruitful interplay of field and laboratory observations. Magmas are important not only in continents, but also in the oceanic crust. In the 1950s, exploration of sea revealed that ocean floors are made up of basalt, implying that this igneous rock covers 70% of the earth's surface [Shand, 1949; Heezen et al., 1959]. In the theory of Plate Tectonics [Dietz, 1961; Hess, 1962], magma plays a key role in creating new ocean floor when emerging at mid-ocean ridges. Adiabatic melting in the rising part of the convection cells that circulate through the mantle is a fundamental aspect of the Earth's activity. Planetary exploration has also shown volcanic activity to be present in Mars and Venus and in the satellites of giant planets. Glass more than 4 billion years old has been brought back from the Moon's surface. It even appears that the surface of the primitive Earth was probably covered by a magma ocean, more than 1000 km deep, at temperatures higher than 2000°C [Abe, 1997; Rama Murthy and Karato, 1997]. From the long-gone magma ocean to the smallest currently active volcano, magma owes its fundamental importance to the fact that, at all scales, it is most efficient agent for transporting matter, and energy, throughout the Earth.

28

Chapter 1

1.5. Summary Remarks 1. Ever since glass was invented, it has found new uses whenever improvements were made either in manufacturing process or in properties of the final product. The present differs from the past in the degree of sophistication required to understand better the composition-property relationships that will allow glass to meet the competition that originates from other kinds of materials and, especially, to meet the ambitious goal of tailoring glasses or melts for specific applications. 2. In the earth sciences, the relevant ranges of pressure, temperature, and chemical compositions are wider still than in industry. Experimental studies are much simpler and more restricted than processes that have actually taken place on the Earth since (and during) its formation. Hence modeling must be introduced to interpolate or extrapolate to real processes the necessary limited number of experimental data. As stated by Kelvin [Thomson, 1871], "The essence of science, as is well illustrated by astronomy and cosmical physics, consists in inferring antecedent conditions, and anticipating future evolutions, from phenomena which have actually come under observation." 3. A key step in this effort is the understanding of the relationships between composition, structure and physical properties of silicate glasses and melts. Such relationships are fairly simple for a property like melt density at room pressure so that empirical modeling can be adequate. For viscosity, in contrast, the complex composition and temperature dependences will need a great deal of fundamental information to be understood quantitatively. The purpose of this book is to review the current state of the art in that matter. References Abe Y. (1997) Thermal and chemical evolution of the terrestrial magma ocean. Phys. Earth Planet. Inter. 100, 27-39. Adams L. H. and Williamson E. D. (1920) Annealing of glass. J. Franklin Inst. 190, 597-631 and 835-870. Aristotle. Meteorology, book II, ch. 8 (transl. by E.W. Webster, in The Complete Works of Aristotle, Princeton University Press, Princeton, 1984). Barus C. (1893) The fusion constants of igneous rock. III. The thermal capacity of igneous rock, considered in its bearing on the relation of melting-point to pressure. Phil. Mag. 35, 296-307. Becker G. F. (1897) Some queries on rock differentiation. Amer. J. Sci. 3, 21-40. Bernal J. D. (1936) An attempt at a molecular theory of liquid structure. Disc. Farad. Soc. 336, 27-40. Berthelot M. (1887) Collection des anciens alchimistes grecs, vol. I. Georges Steinhel, Paris. Bimson M. and Freestone I. C. (1987) Early Vitreous Materials, British Museum Occasional Papers N°56, British Museum, London. Bockris J. O. M. and Lowe D. C. (1954) Viscosity and the structure of molten silicates. Proc. Roy. Soc. A226,423-435. Bockris J. O. M., Kitchener J. A., Ignatowicz S., andTomlinson I. W. (1952) Electric conductance in liquid silicates. Trans. Farad. Soc. 48, 75-91.

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Glass Versus Melt The ease with which a liquid adjusts to the shape of its container is a familiar consequence of atomic mobility, the hallmark of the molten state. Atomic mobility is the very reason why liquids flow, even though another salient feature evident through daily experience is that viscosity (77) increases with decreasing temperatures. If crystallization does not occur when a liquid is cooled below its liquidus temperature, viscosity eventually becomes so high that flow can no longer take place during the timescale of an experiment. The liquid transforms to a glass, i.e., to a solid with a disordered atomic arrangement. From an essentially phenomenological perspective, the glass transition and the resulting close connection between glasses and melts are the main themes reviewed in this chapter. A variety of other relaxation mechanisms operate in glass-forming liquids [e.g., Debenedetti, 1997; Angell et al., 2000; Donth, 2001]. As a result of difficulties in high-temperature experiments, such secondary relaxation mechanisms have been little documented for silicate melts. This is not a serious problem as they are of little influence on the structural and physical properties dealt with in this book. 2.1. Relaxation The glass transition is not abrupt but typically occurs over a few tens of degrees. Depending on heating or cooling rate, it can take place at widely differing temperatures. In all cases, however, the time-dependence of the investigated physical property reveals that the kinetics of structural relaxation are slow at the timescale of the measurement. 2.1a. Glass Transition Range In general, the glass transition temperature (T) is defined as the temperature at which the tangents to the glass and liquid curves of a given property intersect (Fig. 2.1). At the particular time scale of the experiment, T is that temperature at which the configuration Figure 2.1 - Dilatometric glass transition temperature of E glass (composition in Table 1.2), as determined from the break in the thermal expansion curve. The decrease of the sample length (/) above 600°C is due to flow of the sample under its own weight slightly above the glass transition.

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Chapter 2

Figure 2.2 - Time-dependence of the glass transition for CaAl 2 Si 2 0 8 [from data of Askarpour et al., 1993]. The transition curve separates the fully relaxed liquid from the unrelaxed glass. It is plotted against experimental timescale to show the conditions under which the glass transition takes place for the three kinds of experiments indicated.

of the liquid is frozen in (here, configuration designates any microscopic arrangement of the material consistent with a given macroscopic state of the system). Contrary to the temperature of an equilibrium transition, T is not a fixed point because it varies with the experimental conditions. It is higher for higher cooling rates or shorter experimental time scales. This effect demonstrates the kinetic, nonequilibrium nature of the glass transition. Such variations of T can amount to hundred of degrees. They are shown in Fig. 2.2 for the glass transition of CaAl2Si208 as determined under the experimental conditions of viscometry, ultrasonic, and Brillouin scattering experiments, which are made at experimental timescales of the order of 102, 10~6 and 10~10 s, respectively (see section 2.2b). Hence, the glass or liquid nature of the substance does not depend only on temperature but also on the timescale at which its properties are probed. More precisely, the glass transition does not manifest itself as a sharp discontinuity, but as a temperature interval where the properties of the material depend on time as well as on thermal history. Under given experimental conditions, the width of this glass transition range is typically a few tens of degrees as illustrated in Fig. 2.3 by the viscosity of a window glass. These viscosities were measured with time scales of minutes, first in order of decreasing temperatures and then in order of increasing temperatures. A time dependence was observed from about 800 to 775 K. The viscosity increased with time when the liquid was cooled down to the temperature of the measurement, whereas it decreased with time if it was heated up first. Like any physical property, the viscosity of a liquid in internal thermodynamic equilibrium is determined by only two variables:

Figure 2.3 - Time dependence of the viscosity of a window glass (see Table 1.2) at several temperatures in the glass transition range. Isothermal measurements made in order of decreasing (open symbols) and then increasing (solid symbols) temperatures [Sippet al, 1997].

Glass Versus Melt

37

pressure (ambient, in this case) and temperature (that of the experiment). The differences between the values observed at the beginning of each series of isothermal measurements (i.e., after cooling and after heating) demonstrate that the melt was not in internal equilibrium until a common, constant value was attained. As shown in Fig. 2.3, equilibrium viscosities of up to about 1015 Pa s can be reached through complete relaxation achieved in reversal experiments lasting a few days. Still higher viscosities could be measured, but on experimental timescales that would rapidly exceed the lifetime of the experimentalist!2A Leaving aside for the moment a discussion of the configurational changes that take place during relaxation, we emphasize that equilibrium is out of reach if experiments are made quickly well below the glass transition range. Measurements can nevertheless be made under such conditions: the resulting viscosity is lower than the equilibrium value because the sample has been previously held at a temperature higher than that of the experiment (Fig. 2.3). This viscosity is termed isostructural, so called because the structure of the sample cannot adjust to the new temperature conditions during the timescale of the experiment. It varies with temperature according to an Arrhenius law [Mazurin etal., 1979], in contrast with the generally strong departures from Arrhenian variations found for the liquid [see Bottinga and Richet, 1996]. It is even possible to determine at which temperature the structure of the glass has been frozen in. This temperature is given by the intersection of the Arrhenius law of the glass with the non-Arrhenian curve of the liquid (Fig. 2.4).

Figure 2.4 - Equilibrium (open circles) and isostructural (solid squares) viscosity of window glass. For the latter data, the fictive temperature of the material is indicated by the arrow. Measurements from Mazurin et al. [1979] and Sipp et al. [1997].

Depending on the kind of measurement performed, the glass transition thus manifests itself either as a continuous or as a discontinuous transformation. As for first-order thermodynamic properties (volume, enthalpy, entropy), there is no discontinuity of transport properties (viscosity, electrical conductivity, etc.), but a change in temperature dependence. In contrast, the variations of second-order thermodynamic properties across 21

It is often said that thicker stained glass at the bottom of panes in medieval churches resulted from long-term flow at room temperature under the own weight of the material. As pointed out by Zanotto and Gupta [1999], timescales of the order of 1023 years would be needed to produce such an effect. The likely explanation is that stained glass masters simply installed the thickest side of glass panes at the bottom when they were not getting panes of even thickness.

38

Chapter 2

Figure 2.5 - Heat capacity change at the glass transition for a sodium silicate. Adiabatic measurements (solid points) by Yageman and Matveiev [1982] and drop calorimetry data (solid line) by Richet et al. [1984]. The bump near 800 K is the relaxation peak discussed in section 2.2b.

the glass transition range are rapid enough to be considered practically as discontinuities. Such a rather abrupt variation is illustrated in Fig. 2.5 by the heat capacity of a sodium silicate. 2.1b. Vibrational vs. Configurational Relaxation Relaxation does not represent a response of the material to temperature changes only, but to variations of any intensive variable. In experiments made at constant temperature, stress changes can cause viscosity to be time-dependent. Relaxation tends to be much faster after a stress change than after a temperature change, however, as illustrated by the 9-fold difference between the data plotted in Fig. 2.6 for a window glass. When the socalled Boltzmann [1874] superposition principle holds true, relaxation after simultaneous different perturbations is the sum of the individual responses [see Hodge, 1994]. This is illustrated in Fig. 2.6 by the stress and temperature perturbations and their combined effects on a window glass. Specifically, two kinds of relaxation, vibrational and configurational, must in general be distinguished. When energy is delivered quickly to a substance, for instance with laser pulses, the conversion oflight into heat takes place at the 10 -10 s timescale of atomic vibrations. Because of such very short timescales, vibrational relaxation can always be considered as instantaneous during physical measurements. The observed relaxation results

Figure 2.6 - Approach to equilibrium of the viscosity of a window glass: (a) After a stress change at constant temperature; (b) After a temperature change at constant stress, (c) And after a combination of such two changes [Sipp et al, 1997]. The departure from equilibrium in (c) is the sum of the responses in (a) and (b).

Glass Versus Melt

39

instead from configurational changes within the substance. In accordance with Le Chatelier's laws, they represent additional entropy and volume changes allowing the Gibbs free energy to decrease further in response to variations of temperature and pressure. Configurational changes thus take place whenever the structure of a substance can vary. This is the case of liquids, of course, as well as of crystals during phase transitions or at high temperatures as will be described in the following chapter. Now consider any first-order thermodynamic property, Y, such as volume, enthalpy, entropy, etc. In view of the very strong temperature dependence of relaxation kinetics, three cases must be distinguished with regard to the variation of a property following a temperature jump AT (Fig. 2.7): 1. At high temperatures, relaxation is short with respect to the timescale of a measurement. The equilibrium value Yx is reached instantly in such a way that an apparent discontinuity, AY, is observed, which is the sum of vibrational and configurational contributions. 2. At lower temperatures, relaxation takes longer because the time needed to reach the equilibrium value Y2 becomes similar to the experimental timescale. A smaller jump of Y is first observed, which is due to instantaneous vibrational relaxation. It is followed by a configurational relaxation, which progressively brings Y to its new equilibrium value. The lower the temperature, the longer is the time required to reach equilibrium as shown by the plots of Y2 and Y3 in Fig. 2.7.

Figure 2.7 - Vibrational and configurational relaxation shown in (a) at four different temperatures for a given property Y, consecutive to an abrupt change in temperature 4 7 represented in (b). In order of decreasing temperature, Yx refers to a fully relaxed phase (e.g., a liquid), Y2 and F3 to a relaxing material, and F4 to a fully unrelaxed phase (e.g., a glass). For Y2 and K3, the equilibrium values are shown by a dashed line.

3. When the temperature has decreased even further, relaxation has become so long that no configurational changes can take place in the course of the measurement. The structure of the phase has been frozen in. Only a small instantaneous change in Y due to atomic vibrations is observed. The glass transition has occurred because configurational changes are no longer possible at an appreciable rate. When relaxation requires times that are long with respect to the 10 -10 s period of atomic vibrations, vibrations in a liquid can be considered as taking place in a fixed structural environment. Physical properties can then be separated into independent vibrational and configurational contributions. As will be shown below from the simple Maxwell model, this situation occurs in liquids when the viscosity is higher than about

40

Chapter 2

Figure 2.8 - Vibrational (instantaneous) and configurational (delayed) contributions to volume relaxation in dilatometry experiments made on supercooled liquid CaMgSi2O6 [Toplis and Richet, 2000]. In response to the temperature change from 982 to 972 K shown in (a), the vibrational component of length change is much faster than the changes due to relaxation of the liquid structure apparent in (b). Sample length: 12 mm.

0.1 Pa s. An example of volume relaxation is provided by the dilatometry experiments of Fig. 2.8 where both vibrational and configurational contributions can be observed directly. The former is instantaneous, whereas the latter is delayed and leads slowly to the equilibrium length of the sample. 2.1c. Relaxation Times Relaxation is relevant to silicate melts from both a theoretical and practical standpoint. This has been reviewed elsewhere [Moynihan et al., 1976; Hessenkemper and Bruckner, 1989, 1990; Dingwell and Webb, 1990; Dingwell, 1995; Moynihan, 1995] or shown by a variety of measurements [e.g., Webb, 1992a,b; Stevenson et al, 1995; Sipp et al, 1997]. To characterize the rate at which a given property, Y, approaches the new equilibrium value, Ye, one defines the relaxation time, x, as: Ty=-(Y,-Ye)l{dY/dt),

(2.1)

where Yt is the value actually measured at instant t. If Ty were constant, i. e., not depending on the instantaneous value of Y, relaxation would be described by a simple exponential law (Y, - Ye) = (Yo - Ye) exp (- t/Ty),

(2.2)

where Yo is the initial Y value. In other words, after a time xY the variation of Y would represent a fraction 1/e of the initial difference from the equilibrium value. Relaxation times depend not only on temperature (Fig. 2.3), but also on the extent of departure from the equilibrium state, i.e., on thermal history. In addition, relaxation kinetics do not follow exponential laws of the form (2.2) at constant temperature because either individual relaxation times are intrinsically nonexponential or the actual transformation is made up of many mechanisms with different relaxation times. In a phenomenological way, quantitative modeling of experimental relaxation measurements can be achieved in two different ways. One can assume that there is a distribution of relaxation times and

Glass Versus Melt

41

Figure 2.9 - Correlation between the volume and enthalpy glass transition temperatures as measured by dilatometry (TDjj) and by differential thermal analysis (TDTA), respectively [Sipp and Richet, 2002]. Abbreviations: Ab (NaAlSi3Og); Di (CaMgSi2O6); K (K2O); N (Na2O); S (SiO2); T (TiO2); Ca x.y (x mol % SiO2, y mol % A12O3, (100-x-y) mol % CaO); BNC and E: complex calcium borosilicates [see Sipp et ai, 1997].

then expresses relaxation as the sum of a number of equations of the form (2.2). Alternatively, nonexponentiality can be built into equation (2.2) through replacement of the variable (- t/tY) by (- t/tY) , where /3 is a constant, ranging from 0 to 1, first introduced by Kohlrausch [1863] in torsion experiments on rubber and glass fibers. Because a review of relaxation studies and models is beyond the scope of this book [see Scherer, 1986; Hodge, 1994; Angell et al., 2000], we will now turn to a few points of more direct relevance. The first point is whether or not the relaxation kinetics (and relaxation times) are the same for various physical properties of the same substance. From comparisons between their own photon correlation spectroscopy results with literature data on enthalpy or viscosity, Siewert and Rosenhauer [1997] for instance concluded that relaxation in SiO2NaAlSiO4 melts is slower for thermal than for mechanical perturbation. It is not easy to answer such a question rigorously, however, because the effects of differing samples, temperature conditions, experimental timescale, thermal history or data analysis are not readily disentangled. Because the glass transition takes place when relaxation times become greater than the timescale of an experiment, differences between the glass transition temperatures measured under similar conditions for different properties reflect possible differences in relaxation kinetics for a given substance. Such comparisons made for many silicates and aluminosilicates by Webb and Knoche [1996] show that these temperatures agree to within experimental errors for enthalpy and volume. Webb and Knoche [1996] also concluded that, for all their samples, the viscosity at the glass transition lies in the rather narrow range 10971-101208 Pa s, with a standard deviation from the mean of only 10033 Pa s. From simultaneous enthalpy and volume measurements, Sipp and Richet [2002] investigated a wider composition range in which titano- and borosilicates were included. The correlation between glass transition temperatures (Fig. 2.9) is still better and the viscosity interval at T narrower than reported by Webb and Knoche [1996]. In spite of glass transition temperatures spanning the wide range 750-1160 K, the viscosity interval is 10'°'-10117 Pa s with a standard deviation from the mean of 10°" Pa s.

42

Chapter 2

Figure 2.10 - Viscosity and volume relaxation for E glass shown in a normalized form with equation (2.3). Data from Sipp and Richet [2002], with viscosity measurements from Sipp etal. [1997].

The similarity of relaxation times for different properties can be confirmed directly by measurements performed on samples with the same thermal history. For such comparisons, the results are expressed as dimensionless variables

Y=(YrYe)/(Y0-Ye),

(2.3)

where Yr Ye and Yo are the values of property Y at time t, at equilibrium, and at time 0, respectively. Over a few-hour intervals, the volume and viscosity of a window glass relaxed at the same rate [Rekhson etal., 1971]. The same conclusion has been arrived at for E glass (Fig. 2.10) over longer duration for wider departures from equilibrium [Sipp and Richet, 2002]. Although relaxation is a complicated function of temperature and thermal history, the equivalence of relaxation rates for different properties of silicate melts is a welcomed simplifying feature. It is of great practical use, especially in allowing relaxation times for any property to be estimated from viscosity through Maxwell's model. 2. Id. Maxwell Model The Maxwell model of viscoelastic media represents a convenient way to describe important features of relaxation [Maxwell, 1868]. Its starting point is the flow of liquids where shear stresses resulting from interatomic forces yield velocity gradients perpendicular to the stream direction (Fig. 2.11). The simplest case holds when "the resistance arising from the want of lubricity in the parts of a fluid is, other things being equal, proportional to the velocity with which the parts of the fluid are separated from one another" [Newton, 1725]. Shear stresses then are proportional to velocity gradients. For a homogeneous relative deformation, or strain, e (= Al/l, I = sample length), one has

Figure 2.11 - Schematic plot of velocity gradients in a liquid between two infinite planes separated by a distance d, the upper plane moving at a speed V.

Glass Versus Melt G=r] de/dt,

43 (2.4)

and the shear viscosity, rj, is Newtonian as long as r\ is independent of the stress, a, and strain rate, deldt, of the sample. In view of the continuous pathway between the liquid and glass states, glass-forming liquids cannot be purely Newtonian when they approach the glass transition. In fact, they are viscoelastic, with an elastic component that becomes increasingly important near T . More precisely, application of a shear stress first causes an elastic strain, which would be recovered if the stress were released, and then a viscous deformation. The relation between the elastic stress and strain is given by Hooke's law. Originally stated as "Ut tensio, sic vis, That is, the power of any spring is in the same proportion with the tension thereof, this law is written in modern terms as a=G^e

(2.5)

where GTO; also known as the shear rigidity, is the shear modulus at infinite frequency. Hence, the elastic stress rate is: da/dt = GM de/dt.

(2.6)

The second component is the aforementioned Newtonian, non-recoverable viscous deformation that tends to relax the stress built up macroscopically through strained bond lengths and angles. The applied stress does not remain constant but tends to disappear at a rate depending on the value of
(2.7)

and introduced in this way the stress relaxation time x as a measure of the rate of the process. In practice, stress and structural relaxation times are about the same and both terms are used synonymously in the viscoelastic literature. If the strain e is constant, Maxwell noted that a=Gaoesxp(-t/t),

(2.8)

so that the stress eventually vanishes and the pressures are distributed as in a fluid at rest. If, alternatively, the deformation rate de/dt is kept constant, the instantaneous stress is readily obtained by integration of equation (2.7) a=r] deldt + Ce'/T,

(2.9)

where C is a constant. By combining the simplest representations of elasticity and viscous flow, the Maxwell model has as a mechanical analogue a spring and a dash pot placed in series. The response

44

Chapter 2

of a viscous melt subjected to stress thus is made up of an instantaneous, elastic response, which is vibrational in origin, along with a delayed response whose nature is configurational. We refer to Richet and Bottinga [1995] for a discussion of the usefulness and limitations of the Maxwell model. Here, we simply note that da/dt in equation (2.7) becomes very small when stresses are applied at low frequencies, in which case one finds: (2.10)

r\ = Gjc.

Another important point is that the shear modulus GM is insensitive to composition. From a review of literature data for amorphous silicates, Dingwell and Webb [1989] pointed out that G^ varies by less than a factor of ten with either temperature or composition, with a mean value of 10 GPa. Since atomic vibrations typically have a period of 10"12 - 10"14 s, configurational relaxation remains much slower than vibrational relaxation as long as viscosity is higher than about 0.1 Pa s. By rewriting equation (2.10) as (2.11)

r}(T) = GJT)T(T),

we see that the variations of GM can be estimated from the width of the viscosity interval at the glass transition. Consistent with the conclusion of Dingwell and Webb [1989], the value of io 1O9±o " Pa s given for this interval in the preceding section points to a possible spread of only half an order of magnitude for G^. Compared to the tremendous variations of viscosity with temperature and composition, GM thus is almost constant. If the viscosity is known, structural relaxation times can be readily estimated from equation (2.10). The temperature dependence of GTO can be determined directly from sound velocity measurements made at extremely short time scales because G^ = p vs2, where p is the density and vs the velocity of shear acoustic waves at infinite frequency. This is the situation in Brillouin scattering experiments during which inelastic scattering of phonons by photons take place at timescales of about 10"10 s [see Askarpour et al, 1993]. Above the glass transition range, Brillouin and density data yield values of G^ in the range 34-36 GPa and indicate that dGJdT is about -0.02 GPa/K for pure SiO2 [Polian et al, 2002] and CaMgSLO,, CaALSi O and Ca.ALSLC) melts [Askarpour et al, 1993]. As a result, Zo

z

z

o

J

Z

i

\Z

G^ decreases by less than 8 GPa in the 400 K interval spanned by the data of Fig. 2.9 and remains close to the 3-32 GPa range delineated by Dingwell and Webb [1989]. 2.1e. Local vs. Bulk Relaxation Even though G^ is a property closely connected to viscosity, it is insensitive to temperature and composition. Hence, there is not much structural information to be drawn from its determination. For silicates, it is tempting to assume that this value of 34-36 GPa, which pertains to melts ranging from pure SiO2 to SiO2-poor melts, results from a common structural denominator. This inference would be misleading, however, for similar Gx values of the order of 1010 Pa apply to all kinds of glass-forming liquids in spite of the major composition and bonding differences that they represent. This is the reason why these liquids share the common feature that their viscosity is about 1012 Pa s when they pass through the

45

Figure 2.12 - Decoupling of viscosity and Na hopping in Na2Si2O7 melt as evidenced by increasing differences between the characteristic times xn and TNa of these processes [George and Stebbins, 1998].

glass transition with a cooling rate of a few degrees per minute, i.e., with experimental timescales of the order of 100 s. Although silicate melts are made up of a variety of structural entities, there is a single glass transition, not different points at which mobility would successively set in for different kinds of atoms or atomic groups. This feature reflects the cooperative nature of the glass transition. As described in more detail in Chapter 4, the bulk dynamics of silicate liquids are controlled by the strong Si-0 bonds of the anionic framework [Farnan and Stebbins, 1994; Stebbins et al., 1995], Structural, enthalpy, and volume relaxations are determined by the rate of exchange of these bonds. This does not mean, however, that atomic mobility completely vanishes below the glass transition. Measurements of electrical conductivity or element diffusivity indicate that matter is still transported, although it does so at too slow a rate for the bulk properties of the glass to be affected. It is possible to determine the characteristic times for various relaxation mechanisms. In a Nuclear Magnetic Resonance (NMR) study of a sodium silicate (Fig. 2.12), George and Stebbins [1998] observed that, with decreasing temperatures, the correlation time for Na site hopping (rNa) derived from 23Na spin-lattice relaxation data becomes much shorter than the viscosity relaxation time (T ) determined from the Maxwell relation (2.10). Similar results have been obtained for three different processes in calcium aluminosilicates over wider temperature intervals extending to below the standard glass transition (Fig. 2.13). In their study, Gruener et al. [2001] determined the rate of exchange of Al-0 bonds from 27 Al spin-lattice NMR experiments, the characteristic time for calcium hopping from electrical conductivity measurements, and structural relaxation times from viscosity and Figure 2.13 - Decoupling of calcium mobility from network relaxation [Gruener et al., 2001]. Characteristic times as determined from measurements of viscosity (T^), electrical conductivity (ra) and, at high temperature, from 27A1 spin-lattice relaxation (TC). The effect of the glass transition (T ) on TCT is shown as the difference between the measurements and the curve fitted to the high-temperature data.

46

Chapter 2

Figure 2.14- Self diffusion of oxygen, calcium and sodium in a soda (16 wt%)-lime (12 wt%) silica melt down to the glass transition. Data from Johnson et al. [1951] for 22Na, Wakabayashi [1977] for 45Ca at high temperature, and Terai and Oishi [1977] for 18O and 45Ca at lower temperatures. The standard glass transition is indicated by the arrow.

Maxwell model (Fig. 2.13). Whereas all three times are similar above 1600 K, decoupling between structural relaxation and calcium hopping becomes considerable at lower temperatures. At the standard T , the relaxation times for these processes differ by seven orders of magnitude. The glass transition itself has little effect on the calcium hopping frequency, for Fig. 2.13 merely shows a slight change in slope between the data for the liquid above T and the "isostructural" data at lower temperatures. Decoupling between alkali mobility and network relaxation was also observed near T through lineshape analyses in a Brillouin scattering study of alkali silicates [Kieffer et al., 1995]. Likewise, in neutron scattering experiments the dynamical timescale was still found 100 times shorter for Na diffusion than for network relaxation at 1300°C [Meyer et al., 2002], For a soda-lime silicate melt (Fig. 2.14), decoupling is also attested by a change in diffusion regime occurring near the glass transition for oxygen, but not for calcium and sodium. These and other observations on simple silicates [e.g., Yinnon and Cooper, 1980; Braedt and Frischat, 1988] indicate that the mechanisms of diffusion differ for networkmodifying cations and for oxygen (and silicon as well). For oxygen, there exist at least two different mechanisms. As shown in section 4.4b, the high-temperature process is closely related to viscous flow. Accordingly, oxygen diffusion varies as strongly as viscosity with the silicate composition. For network-modifying cations, a single mechanism might instead operate from low to high temperature. Because they are not controlled by the bulk of the structure, the diffusivities of these cations tend to vary less strongly with composition. Decoupling of bulk and local relaxation has many important implications. As a single example, the fact that element diffusivities differ much less at high temperature, where they tend to converge, than near and below the glass transition, where considerable differences are observed, implies that the mechanisms of redox reactions vary with temperature (see Chapter 10). Besides, this high-temperature convergence points to a linear correlation between the activation enthalpies for diffusion and the pre-exponential terms of Arrhenius laws. Empirically, this relationship is known as a compensation law [see Winchell, 1969; see also Chakraborty, 1995].

Glass Versus Melt

47

Figure 2.15 - Schematic representation of potential energy in a glass as a function of interatomic distance. Also shown is the manner in which potential energy is related to vibrational energy levels and to the configurational parts of heat capacity and thermal expansion coefficient. The zero-point energy is neglected. [From Richet, 2001].

2.2. Glass Transition Equilibrium phase transitions have a thermodynamic origin because they allow the Gibbs free energy of the system to decrease in response to pressure or temperature changes. Kinetic phase transitions are quite different because they result from the fact that, under given circumstances, the system has not enough time to minimize its Gibbs free energy through adjustments of its configuration. When the system is trapped in such a state of high Gibbs free energy, which does not correspond to the equilibrium configuration, it ceases to be in internal equilibrium and its properties depend on its previous history. This is one of the main consequences of the glass transition. 2.2a. A Microscopic Picture In this section, we will describe how the changes in second-order thermodynamic properties through the glass transition are related to atomic mobility in the liquid. Referring to early [Davies and Jones, 1953] or recent [Richet, 2001] reviews of the thermodynamics of glasses, we will restrict ourselves to a schematic one-dimensional picture of interatomic potentials (Fig. 2.15). Contrary to crystals, where these potentials have a long-range symmetry, glasses have essentially a short-range order because the bond angles and distances between next-nearest neighbor atoms are not constant but spread over a range of values. As described by Goldstein [1969], the minima of potential energy, which determine the glass configuration, are separated by barriers with varying heights and shapes. When thermal energy is delivered to the glass, the subsequent temperature rise is associated only with increasing amplitudes of vibration of atoms within their potential energy wells. Like for any solid, the heat capacity of the glass is, therefore, only vibrational in nature. At sufficiently high temperature, thermal energy increases to the point that atoms can overcome the barriers that separate their own from the neighboring potential energy wells (Fig. 2.15). This onset of atomic mobility signals structural relaxation. If, however, the relaxation time is longer than the experimental timescale, only the vibrational heat capacity is measured. If the temperature is increased further, or if time is sufficient for the

48

Chapter 2

Figure 2.16 - Enthalpy variations through the glass transition and associated changes in heat capacity. The glass transition is cycled with two different heating and cooling rates qY and q2 [Moynihan et al., 1976]. Note the higher enthalpy of the glass quenched with the fastest cooling rate, and the hysteresis observed for H and Cp at the transition.

new equilibrium configuration to be attained during the measurement, then the configurational heat capacity is also measured. When integrated over all atoms, the configurational heat capacity represents the energy differences between the minima of the potential energy wells that are explored as temperature increases (Fig. 2.15). Hence, the glass transition can be viewed as the point from which atoms begin to explore positions characterized by higher potential energies. Regardless of the complexity of this process at a microscopic level, this spreading of configurations over states of higher and higher potential energy is the main feature of atomic mobility. As a consequence, configurational heat capacities are positive. This, in turn, is consistent with the fact that any configurational change must cause an entropy rise when the temperature increases. As for relaxation times, they decrease with rising temperatures because large thermal energies allow potential energy barriers to be overcome more easily. 2.2b. Rate Dependence of the Glass Transition If enthalpy is measured, not as a function of time at constant temperature but as a function of temperature at constant cooling rate, configurational changes gradually vanish because of the continuous increase of relaxation times. Both the enthalpy and its derivative, the heat capacity, also decrease smoothly (Fig. 2.16). At the same (absolute) rate, however, a different pathway is followed on heating and on cooling. Relaxation does resume at the temperature at which it vanished on cooling, but the first effect of heating is to lower the enthalpy of the glass and bring it closer to the equilibrium values of the supercooled liquid. At higher temperatures, the enthalpy curve of the material has already crossed that of the supercooled liquid when relaxation becomes almost complete at the timescale of the experiment. The heat capacity then increases rapidly (Fig. 2.16) in a way that depends on thermal history. The rise is highest for samples initially cooled down at the slowest rates or for samples heated at the highest rates. For all substances, the glass transition occurs when the viscosity is about 1012 Pa s for cooling rates of 1-10 K/min. In accordance with the Maxwell model, such a viscosity holds for macroscopic measurements whose timescale of 102 -103 s is typical of calorimetry

Glass Versus Melt

49

Figure 2.17 - Relaxation effects on the longitudinal sound velocity, v , of sodium disilicate melt as determined by ultrasonic measurements made at the frequencies indicated [Nikonov et al., 1982]. The dashed lines VM and v 0 indicate the unrelaxed velocity in the glass and the relaxed, equilibrium velocity in the liquid, respectively. By comparison, the standard glass transition is 450°C.

or dilatometry experiments. This is why we term standard T the temperature at which the viscosity is 1012 Pa s. Consistent with this close link between viscosity and glass transition, the variation of T with the heating or cooling rate, q, is described by the empirical relation proposed by Moynihan et al. [1974]: d In \q\/d(VTg) = - AHJR,

(2.12)

where R is the gas constant, and AH^ = R d In r\ld{\IT) the activation enthalpy for viscous flow, which also characterizes the temperature dependence of relaxation times over restricted temperature intervals. For a typical £Hn of 500 kJ/mol and a standard glass transition temperature of 1000 K, equation (2.12) indicates that T increases by only 30 K when the cooling rate varies from 0.01 to 100 K/s. Such a width is small. Nonetheless, it allows structural studies made on glasses quenched at different rates to yield valuable information on configurational changes induced by larger temperature variations [Geissberger and Galeener, 1983]. In turn, this intimate connection between dT/dq and viscosity allows AH to be estimated from the observed width of the glass transition [Moynihan, 1993]. Like faster heating or cooling rates, shorter experimental timescales shift the glass transition to higher temperatures (Fig. 2.2). The rate dependence of the glass transition temperature is seen most clearly in measurements of the adiabatic compressibility ()3S) by sound velocity experiments. This compressibility is obtained from Ps=Upvp\

(2.13),

where p is the density and v the compressional (or longitudinal) sound velocity. Equilibrium values are measured only if the pressure changes induced by the acoustic wave are short with respect to the time needed by the fluid to adjust its structure in response to this perturbation. Ultrasonic velocities and compressibilities are then frequency independent [e.g., Rivers and Carmichael, 1987; Kress et al., 1989].

50

Chapter 2

Figure 2.18 - Compressional sound velocity in a calcium aluminosilicate as measured ultrasonically [Webb and Courtial, 1996] and by Brillouin scattering [Vo Thanh, unpub. results]. The arrow indicates the standard T . Because sound velocity in solids depends primarily on density, the break in Brillouin data around T is not due to the onset of configurational changes, but to the increase of thermal expansion at this temperature.

Ultrasonic measurements are made at MHz frequencies, i.e., with timescales of the order of 10"6 s. From the Maxwell relationship (2.10), the relaxation times of the liquid is shorter than such a value only if the viscosity is lower than 1 Pa s. The glass transition thus occurs at much higher temperatures than in calorimetry or dilatometry experiments as shown in Fig. 2.17 for sodium disilicate [Nikonov et al., 1982]. Below 700°C, relaxation times are so long that configurational changes do not take place during the passage of acoustic waves. The liquid behaves instead as a solid so that velocities are frequencyindependent. Configurational changes are revealed above 700°C by a temperature interval where v decreases markedly and becomes frequency-dependent. The onset of this v decrease is found at lower temperatures for lower frequencies (i.e., shorter timescales). Then, the equilibrium state is reached at higher temperatures when a single linear temperature dependence is finally observed for v , shown as v^ in Fig. 2.17. The effect of frequency is even more dramatic when hypersonic sound velocities are measured by Brillouin scattering with timescales of the order of 10"10 s [see Masnik et al., 1993 for details]. These timescales are so short that relaxed velocities are typically observed only above 2000 K for silicate melts [Vo Thanh et al., 1996]. At such high temperatures, the observed velocities are similar to the values determined by ultrasonic methods (Fig. 2.18). With decreasing temperatures, the loss of equilibrium is signaled by a progressive increase of the sound velocity. That Brillouin scattering begins to probe the acoustic properties of a material with a fixed configuration is also indicated by the possibility of measuring shear wave velocities (vs), which are zero in a relaxed liquid, well above the standard glass transition temperature [Askarpour et al., 1993]. The material is not really a "glass" because its configuration changes rapidly with temperature, but a "glass-like" material. Only the solid-like part of its acoustic properties is probed. Its adiabatic compressibility is not the equilibrium value, but that of an isotropic solid, &=l/p(v p 2 -4/3v s 2 ), which joins smoothly with that of the real glass at the glass transition.

(2.14)

51

Glass Versus Melt

2.2c. Fictive Temperature The rate dependence of T has the important consequence that the enthalpy, entropy or volume of a glass depend on thermal history and not only on pressure (P) and temperature (7). Ritland [1956] showed that all physical properties of a glass at given Tand P cannot be specified by a single additional parameter. A number of order parameters should be required instead for rigorous descriptions of the index of refraction or electrical conductivity. For thermodynamic properties, however, a simple empirical description is generally appropriate because the heat capacity or thermal expansion coefficient of silicate glasses are not very sensitive to thermal history. For instance, the enthalpy or volume curves of a glass formed with different cooling rates are practically parallel. Knowledge of the actual glass transition temperature thus enables the enthalpy or volume to be determined. For continuous cooling, this temperature is a third variable describing the state of a glass called the fictive temperature, T. As an example,_the enthalpy and entropy differences between two glasses having fictive temperatures T, and T 2 are given by AHa= |

(Cpl-Cpg)dT,

ASa= / (Cpl- Cpg)/TdT,

(2.15)

where C . is the heat capacity of the equilibrium liquid and C that of the glass. Analogous equations can be written in terms of thermal expansion coefficients for volume differences between glasses having differing thermal histories. The fictive temperature is well defined only for glasses cooled rapidly below the glass transition range. What happens if the glass is heated back up to the glass transition range, i.e., in a temperature interval where structural relaxation will resume? Like enthalpy and volume, the fictive temperature must vary to approach the equilibrium value, which is the actual temperature of the experiment. Hence, the fictive temperature is more precisely defined as the temperature at which the glass configuration would be the equilibrium configuration of the supercooled liquid. Although it cannot be measured directly, the fictive temperature is related to observable properties. The simplest way of doing so is to define it as that part of the given property (H, V, etc.) that relaxes, expressed in temperature units [Moynihan et al., 1976]. Accordingly, we write for enthalpy relaxation: H(T) = Hl(f)-

1 CpgdT,

(2.16)

where Ht{ T) is the equilibrium enthalpy at temperature T. Differentiation of equation (2.16) with respect to Tthen yields the variation of T with temperature under the particular conditions of the experiment: dfldT= (Cp - Cpg)\Tl (Cpl - C re )| f-

(2-17)

This derivative is the relaxational part of the heat capacity, whose instantaneous value is denoted by C . It is zero for the glass and unity for the liquid. At equilibrium, the fictive temperature is equal to the actual temperature, i.e., T(T) = T. For continuous cooling,

52

Chapter 2

Figure 2.19 - Standard glass transition temperature, T , and temperature of Kauzmann paradox, TK, for CaMgSi2O6. The entropy difference between the amorphous and crystalline phases, St - Sc, and the configurational entropy, Sc°"/, are also plotted. Calorimetric data as indicated by Richetef al. [1986].

equations (2.16) and (2.17) indicate that T tends to a limiting value T', which depends on the cooling rate and is equal to the previously defined glass transition temperature. 2.2d. Kauzmann Paradox When viscous liquids escape crystallization, why do they eventually vitrify instead of remaining in the supercooled liquid state? One answer to this question is purely kinetic and relies only on increasingly long relaxation times on cooling. If experiments could last forever, any glass would eventually relax to the equilibrium state. Then, the glass transition would result only from the limited timescale of feasible measurements. In fact, a simple thermodynamic argument proposed by Kauzmann [1948], known as Kauzmann's paradox, indicates that this answer is incorrect. The reason originates in the existence of a configurational contribution that causes the heat capacity of a liquid to be generally higher than that of a crystal of the same composition. As a consequence, the entropy of the liquid decreases faster than that of a crystal when the temperature is lowered (Fig. 2.19). If the entropy of the supercooled liquid is extrapolated to temperatures below the glass transition range, it will become lower than that of the crystal at a temperature TK which is high enough for such an extrapolation to remain reasonable. This situation is not thermodynamically forbidden, but it seems unlikely, indeed, that an amorphous phase could have a lower entropy than a crystalline material of the same composition. The conclusion is that an amorphous phase cannot exist below TK. The temperature of such an entropy catastrophe constitutes the lower bound to the metastability limit of the supercooled liquid. As internal equilibrium cannot be reached below TK, the liquid must undergo a phase transition before reaching it. This is, of course, the glass transition, and Kauzmann's paradox suggests that, although it is kinetic in nature, it anticipates a thermodynamic transition whose nature is still debated extensively [e.g., Donth, 2001]. In its original form, Kauzmann's paradox implicitly neglects possible differences in vibrational entropy between the amorphous and crystalline phases. This simplification is actually incorrect but it does not detract from the gist of the argument, for taking into

53

Glass Versus Melt

Figure 2.20 - Heat capacity of a variety of silicates glasses and melts. Data for WG (window glass) from Richet et al. [ 1997]. See Richet and Bottinga [ 1995] for other data sources. 900

1200

1500

1800

T, K

account such differences would only shift TK slightly. A more rigorous statement of the paradox is that the catastrophe would occur when the configurational entropy of the supercooled liquid vanishes. 2.3. Configurational Properties The configurational contributions to physical properties are a macroscopic consequence of atomic mobility. The second-order thermodynamic properties of liquids thus differ from those of glasses. Specifically, the configurational heat capacity and compressibility are necessarily positive. The reason is to be found in Le Chatelier's laws, which dictate that the temperature dependence of entropy and the pressure dependence of volume be greater for the liquid than for the glass phase of a substance. Although there is no such thermodynamic constraint on the configurational thermal expansion coefficient, experience shows that it is also generally positive. A practical difficulty to determine configurational properties stems from the so-called crystallization curtain which generally prevents observations in temperature intervals between T and the liquidus. When physical measurements can be performed accurately, however, the difficulty is not serious as long as experiments are made even over a narrow temperature range just above the glass transition and above the liquidus. As shown for the heat capacity [Richet and Bottinga, 1984] or the density [Bottinga et al., 1982; Lange, 1996], interpolations between the two ranges then yield reliable values because of the smooth variations of properties that prevail in the whole liquid range [Richet and Bottinga, 1980]. In particular, there is no singularity at the liquidus temperature since the properties of supercooled liquids cannot be influenced by the possible formation of a crystalline phase. 2.3a. Thermal Properties Whereas the heat capacity is an additive function of composition for silicate glasses [Richet, 1987], it varies in a complex way for melts (Fig. 2.20). In practical terms, the distinction between vibrational and configurational contributions is useful only if their relative importance can be evaluated. One can write

54

Chapter 2

Cp = Cpvib + Cpconf,

(2.18)

but determination of the configurational part requires knowledge of the baseline vibrational C . Strictly speaking, these contributions are not mutually independent. Configurations of higher energy tend to be associated with lower vibrational frequencies and, thus, with higher vibrational heat capacities and entropies. Fortunately, silicates exhibit a very useful simplifying feature, first pointed out by Haggerty et al. [1968]: with usual cooling rates, the glass transition occurs when the isobaric heat capacity of the glass is close to 3R/g atom (R = gas constant). This is the Dulong-and-Petit harmonic limit for the isochoric heat capacity (from which, as already noted, C differs little). As listed by Richet and Bottinga [1986] and illustrated in Fig. 2.20, subsequent measurements have confirmed this correlation although both the magnitude of the heat capacity change at Tg and the temperature dependence of the liquid heat capacity depend markedly on chemical composition. The only exceptions to this rule are some borosilicates and hydrous silicates [Richet et al., 1997; Bouhifd et al., unpub. results]. For reasons discussed by Richet et al. [1986], the vibrational C should not vary significantly with temperature above Tg. It follows that the configurational heat capacity (Cpconf) can be determined from the equation Cpco"f=Cpl-Cpg(Tg).

(2.19)

This expression also shows that most of the temperature dependence of Cp/, if any exists, can be ascribed to temperature-dependent configurational changes in the liquid. Likewise, the composition dependence of C t is the same as that of the configurational heat capacity. The existence of a configurational heat capacity implies that configurational parts can also be defined for the enthalpy and entropy. Their variations with temperature are given by: cconf =

(dffonf/dT)p

=

j (ftco*/^

( 2 2Q)

Between any two temperatures, Tx and T2, the variations of configurational enthalpy and entropy are Hconf=Hcmf(Tl)+

f CDconfdT,

(2.21)

I CpconfITdT.

(2.22)

and SC0nf=Sconf(Tl)+

2.3b. Volume Properties Another general feature of interatomic potentials is their anharmonic nature: displacements of the vibrating atoms from their equilibrium positions are not strictly proportional to the

Glass Versus Melt

55

Figure 2.21 - Permanent compaction of a glass that has been frozen in at temperature T p at the high pressure Pv and then brought back to room pressure (P2)- The difference between the isothermal compressibilities of the liquid (PTj) and the glass (j3r) phases originates in the existence of a configurational contribution in the former.

forces exerted on them. Because increasing vibrational amplitudes result in increasing interatomic distances (Fig. 2.15), the thermal expansion coefficient is generally positive for glasses. In the liquid, it increases markedly when even greater interatomic distances result from configurational changes. Melts being isotropic, their volume thermal expansion coefficient is three times the linear coefficient derived from dilatometry experiments. In such experiments, the increase of thermal expansion is revealed by the important variation of the slope of the length-temperature relationship (Fig. 2.1). Because measurements are generally made at a constant heating rate, relaxation is not complete when the length of the sample begins to decrease at the so-called softening point as a result of not so high a viscosity. It follows that the configurational thermal expansion coefficient ((fon^) differs from the observed change in thermal expansion coefficient (Aa) at T . Experimentally, the difficulties due to incomplete relaxation can be obviated in three different ways. First, one can take advantage of the equivalence of relaxation kinetics for enthalpy and volume so that calorimetric data can serve as templates for deriving a ; through extrapolation of the dilatometric measurements [Knoche et al., 1992]. Second, thermal expansion can be measured for a sample enclosed in an appropriate container in which softening does not affect the dilatometric experiment [Gottsmann et al., 1999]. Third, vibrational and configurational relaxation can be observed directly in highprecision dilatometric experiments made at constant temperature (Fig. 2.8), and the equilibrium thermal expansion coefficient (a;) be determined for the supercooled liquid [Toplis and Richet, 2000]. Like other physical properties discussed in this chapter, compressibility is also made up of vibrational and configurational contributions. Because the shape of interatomic potentials determines the vibrational energy levels, compression is termed vibrational for the elastic part of the deformation. As for the configurational contribution, it manifests itself when the applied pressure changes the potential energy wells and causes modifications in short-range order through shorter equilibrium distances and steeper slopes around the minima pictured in Fig. 2.15. These two contributions can be separated by a combination of experiments made at different timescales. As described in section 2.2b, ultrasonic measurements yield the equilibrium adiabatic compressibility, whereas Brillouin

56

Chapter 2

Figure 2.22 - Molar volume of a Fe-free hydrous "tephrite" glasses against water content for samples synthesized at the indicated pressures [Richet et al., 2000]. The 0.1 MPa (room pressure) data refer to glasses relaxed at this pressure.

scattering experiments probe only its vibrational part. The configurational compressibility is then given by the difference between these two results [Askarpour et al., 1993]. 2.3c. Permanent Compaction of Glass In the same way as glasses can have different fictive temperatures, glasses with different fictive pressures can be prepared (Fig. 2.21): the compact configuration achieved by a melt at high pressure is frozen in if the glass transition takes place at the pressure of the experiment [Tammann and Jenckel, 1929]. Because the melt is necessarily more compressible than the glass, permanent compaction arises from the fact that only the elastic part of compression is released when the glass is eventually decompressed to ambient pressure at room temperature. The density of a glass thus increases with the pressure at which the liquid is quenched. This feature is another indication that glasses are nonequilibrium substances. It offers an indirect way to estimate the compressibility of the liquid [Maurer, 1957]. As shown in Fig. 2.22 for a series of hydrous tephrite glasses, permanent compaction becomes significant for synthesis pressures of a few hundred MPa (i.e., a few kbar). Because the pressure dependence of T is small for amorphous silicates [Rosenhauer et al., 1979], the effect depends primarily on the pressure at which vitrification occurs and on the compressibility contrast between the liquid and glass. If the compacted glass is heated at room pressure, its density decreases to the value of the same glass formed at this pressure. Such a volume relaxation begins well below the standard T [Mackenzie, 1963a]. For compacted hydrous phonolite glasses (Fig. 2.23), it causes the thermal expansion coefficient to become anomalously high at temperatures at which the viscosity is about 1016 Pa s [Bouhifd et al, 2001]. On further heating after complete relaxation, a "normal" expansivity is, in contrast, observed (Fig. 2.23). Interestingly, glasses compressed at low temperature to pressures of a few GPa also undergo permanent compaction. This effect was discovered by Bridgman and Simon [1953] for SiO2 glass compressed beyond 10 GPa in minute-long experiments at room temperature. For example, an 18% compaction was observed for a peak pressure of

Glass Versus Melt

57

Figure 2.23 - Volume relaxation of a Fefree hydrous "phonolite" glass during dilatometric experiments [Bouhifd etal, 2001] with 1.6 wt % H2O synthesized at 0.3 GPa (3 kbar, compacted curve) and after relaxation to the room-pressure density (relaxed curve).

20 GPa. Especially under nonhydrostatic stresses [see Mackenzie, 1963b], high pressure can induce large irreversible configurational changes at temperatures at which the substance is said to be a glass. For given frequencies or experimental timescales, the kinetics of pressure- and temperature-induced configurational modifications are thus markedly different. This dissimilarity exists because potential energy wells vary much less with temperature than with pressure. At elevated temperatures, high kinetic energy simply allow states of higher potential energy to be explored. At sufficiently high pressure, the shape of the potential energy wells change, even at low temperature, in a way that gives rise to new configurations. 2.3d. Configurational Entropy and Viscosity Configurational properties have proven most useful for dealing with the temperature, composition, and pressure dependence of the viscosity of silicate melts [Richet, 1984]. To describe such a connection in this section, we first note that any process induced by a temperature decrease is necessarily accompanied by an entropy decrease. This is the simplest evidence for the importance of entropy in glass transition and, thus, in glass formation. Among the many statistical mechanical models that have attempted to account for the glass transition and solve Kauzmann's paradox, the early one proposed by Gibbs and Di Marzio [1958] is of special interest. This model predicts that the supercooled liquid would transform to an "ideal" glass through a second-order transition at the temperature To at which its configurational entropy would vanish. Since then, the existence and the nature of such a transformation have been much debated. This discussion notwithstanding, the important point for our discussion is the result subsequently derived by Adam and Gibbs [1965] on the basis of a lattice model of polymers. This result is a very simple relationship between relaxation times and the configurational entropy of the melt, viz

T(T)=Aexp(B/rSconf),

(2.23)

where A is a pre-exponential term and Be is approximately a constant proportional to the Gibbs free energy barriers hindering the cooperative rearrangements of the structure. Qualitatively, the idea behind this theory is that structural rearrangements would be

58

Chapter 2

Figure 2.24 - Viscosity of stable and supercooled CaAl2Si2Og liquid, (a) Against reciprocal temperature, (b) Against l/TS00^. Data from Urbain etal. [1982; open squares], Scarfe etal. [1983; solid circles], and Sipp et al. [2001; open circles],

impossible in a liquid with zero configurational entropy so that relaxation time would be infinite. If two configurations only were available for an entire liquid volume, mass transfer would require a simultaneous displacement of all structural entities. The probability for such a cooperative event would be extremely small, but not zero, and the relaxation times would be extremely high, but no longer infinite. When configurational entropy increases, the cooperative rearrangements of the structure required for mass transfer can take place independently in smaller and smaller regions of the liquid. As embodied in equation (2.23), relaxation times, thus, decrease when configurational entropy increases. As described by Goldstein [1969], such a relaxation model relying on potential energy barriers would apply to melts whose viscosity is higher than about 1 Pa s. Except for SiO2poor compositions, this is generally the case of silicate liquids. From a structural standpoint, nanoscale heterogeneities near the glass transition are a key ingredient of the model. Their existence has been established spectrocopically [e.g., Malinovsky and Sokolov, 1986]. Moynihan and Schroeder [1993] have shown that these heterogeneities can indeed be interpreted as configurational entropy fluctuations and, in addition, that they can account for the aforementioned non-exponentiality of the kinetics of structural relaxation. In a wide variety of contexts, the Adam-Gibbs theory of relaxation processes has received renewed interest in the last decade [see McKenna and Glotzer, 1997]. In this section, we will discuss briefly its application to the viscosity of silicate melts, refering to other papers for more detailed accounts [Richet, 1984; Richet and Bottinga, 1995; Toplis, 1998; Toplis, 2001] or for connections with TVF equations and Kauzmann paradox [Sipp et al., 2001]. In preamble, note that the two main parameters in equation (2.23), Be and Scmf, have to be dealt with separately. The former is related to bond strength whose influence on viscosity will be discussed in section 4.4a. Here, we will focus on the latter and examine how it accounts quantitatively for the temperature and composition dependences of viscosity over ranges which can cover more than 1013 orders of magnitude. Quantitative applications of Adam-Gibbs theory, however, have long suffered from the difficulty to evaluate configurational entropy. A common approximation is to take the entropy difference between a melt and a crystal of the same composition. The data of

59

Glass Versus Melt

Figure 2.25 - Comparison between the configurational entropies at the standard glass transition temperature determined from calorimetric (Scal) and viscosity (Svjs) measurements. See Richet and Bottinga [1995] for the sources of the data. Svis, J/mol K

Fig. 2.19 illustrates that this procedure is not warranted. In this respect, silicates have the important advantage that their configurational heat capacity can be determined readily, which makes reliable calorimetric determinations of S00"* possible. By combining the Maxwell relationship (2.10) and equation (2.23), one finds that log ri = Ae + BJTSconf,

(2.24)

where Ae is a constant. Richet [1984] thus pointed out that this equation could be checked quantitatively against experimental viscosity data if S00^ was evaluated with equation (2.22). According to equation (2.24), the manner in which log r] deviates from Arrhenius laws (Fig. 2.24a) as a function of composition is determined by the temperature dependence of 5 con/ (Fig. 2.24b) and, thus, by the magnitude of the configurational heat capacity. When calculating S""^ from equation (2.22), for reasons of consistency one generally takes the temperature Tl as the fictive temperature of the glass used in calorimetric measurements. If the residual entropy of the glass has been measured, then equation (2.24) is a two-parameter equation. If not, the configurational entropy at T can also be determined from the observed viscosity-temperature relationship. In fact, such a rheological approach has many advantages over calorimetric determinations of SCO"^(T ) whose principle is depicted in Fig. 2.19. The viscosity experiments are much less tedious to perform than the comprehensive calorimetric measurements required to evaluate Scon^(T ). Because the viscosity data do not represent 6

small differences between large numbers, as do the calorimetric values, they are also more accurate. But a most useful feature is that this procedure is not restricted to the few mineral compositions for which the whole set of calorimetric measurements can be performed. From a theoretical standpoint, therefore, equation (2.24) is important because it represents the only means to determine configurational entropies for solutions and to calculate the thermodynamically important entropies of mixing. A general feature of viscosity is that its composition dependence is much stronger at low than at high temperatures. That viscosities should actually converge at infinite

Chapter 2

60

temperature is borne out by the Maxwell relationship (2.10) because relaxation times would then become nearly independent of any structural feature and be determined instead only by similar periods of atomic vibrations. At low temperature, the composition dependence of viscosity is, in contrast, extremely large with differences of more than 1012 orders of magnitude [e.g., Richet, 1984]. According to the empirical TVF equation, (2.25)

\nr] = A + B/(T-T1),

the temperature Tx at which the viscosity would diverge is a strong function of composition. This temperature is similar to the Kauzmann temperature at which the configurational entropy would vanish [see Sipp et al., 2001 ]. Analytically, equation (2.25) might be derived from equation (2.24) under the assumption that C con^ is of the form a/T, where a is a constant Such a temperature dependence does not hold true for silicates. The numerical equivalence of equations (2.24) and (2.25) has nonetheless been demonstrated from highprecision viscosities measured to more than 1013 Pa s [Sipp et al., 2001]. At constant temperature, configurational entropy of course depends on chemical composition. This is why equation (2.24) can also account for the composition dependence of viscosity [Richet, 1984]. Many different factors contribute to Scon^. Their relative importance can vary markedly with temperature, with the result that the composition dependence of viscosity is generally much stronger near the glass transition than at superliquidus temperatures (Fig. 2.26). A case in point is the entropy due to mixing of network-forming cations {e.g., Si and Al) or of network-modifyer cations, such as alkali or alkaline earth cations, which can be assumed to mix ideally within a fixed silicate framework. For one mole of melt, Richet [1984] noted that the configurational entropy of mixing is ASm = -RXxilrvci,

(2.26)

where the x{ are the mol fractions of the cations that mix, for instance Na and K, or Ca and Mg as considered in Fig. 2.26. For a given mixed melt, we then write: Sconf = I, xi S*onf+ ASm,

(2.27)

where AS'mis given by equation (2.26). In CaSiO 3 -MgSiO 3 melts, the good fit to the experimental data indicates that the deep viscosity minimum at low temperatures results directly from mixing of the CaSiO3 and MgSiO3 endmembers. But the entropy of mixing as given by equation (2.25) does not vary with temperature. Its relative contribution to the total entropy, equation (2.27), thus decreases with increasing temperatures to the point that the viscosity

Figure 2.26 - Viscosity of mixed (Ca,Mg)SiO3 melts at the indicated temperatures [Neuville and Richet, 1991].

Glass Versus Melt

61

Figure 2.27 - Glass formation in the Na2O-SiO2 and K2O-SiO2 systems, (a) Critical cooling rate for vitrification (CCR) from Fang et al. [1983], referring to crystal volume fractions lower than 10'6. (b) Viscosity along the liquidus; data from Poole [1948], Bockris et al. [1955] and Urbain etal. [1982]. The arrows indicate the positions of the SiO2-Na2Si2O5 and K2Si205-K2Si409 eutectics (see Fig. 6.1).

becomes an almost linear function of composition (Fig. 2.26). Analogous trends are observed when structurally similar ions are exchanged. Examples include melts along the joins K2Si307 - Na2Si3O7 [Richet, 1984] or Ca3Al2Si3012 - Mg3Al2Si3012 [Neuville and Richet, 1991], and molten NaAlSi3O8 mixed with H2O and F [Dingwell and My sen, 1985]. Such trends do not hold true if mixing cannot be described with equation (2.26), for example because of differences in ionic radius or electrical charge. In such cases, mixing of two different silicate framework also contributes to the configurational entropy of mixing and equation (2.26) is no longer valid. 2.3e. Glass Formation Knowledge of composition ranges of glass formation is useful for a variety of practical reasons. In view of the rate dependence of the glass transition, the boundaries of such domains refer to specific conditions. These include not only the average cooling rate and size of the sample, but also the nature of the container or of the melting atmosphere because crystal nucleation is generally heterogeneous. Under well-defined conditions of homogeneous nucleation, a more precise approach consists of determining the critical cooling rate to be achieved for restricting the crystal volume fraction to a given value, generally taken as 10"6, which is the resolution limit of the optical microscope. Such data are scarce, but they nonetheless demonstrate that critical rates depend strongly on composition. In particular, it appears that glass formation tends to be markedly favored around eutectic compositions (Fig. 2.27a). The Maxwell relationship and the operational definition of the standard glass transition as the temperature at which viscosity is 1012 Pa s embody the intimate relationship between viscosity and vitrification. Any factor that causes a viscosity increase thus favors glass formation. Other things being equal, vitrification is easier near eutectics because freezingpoint depression enables lower temperatures and higher viscosities to be reached. But this explanation is just a starting point since the viscosity variations along the liquidus represent a complex interplay of temperature and composition changes as shown in Fig. 2.27b

62

Chapter 2

Figure 2.28 - Configurational entropy of Mg2SiO4 glass and liquid. The standard T of about 1000 K, estimated from data for magnesium aluminosilicate melts, is 130 K higher than the Kauzmann temperature. Data from Richet et al. [1993].

for alkali silicate melts. The viscosity first drops at high SiO2 contents because the effects of the breakup of the SiO2 structure predominate over those of rapidly decreasing liquidus temperatures (see Fig. 6.16). The converse holds true for alkali oxide contents higher than about 12 mol %. The viscosity increases to a maximum value and then eventually falls off. Correspondence between the eutectic composition and the viscosity maximum is observed only for the Na2O-SiO2 system. For K2O-SiO2 melts, this explanation accounts for only part of the observed composition dependence of vitrification. Deep freezing-point depressions at eutectic points are associated with negative enthalpies of mixing, i.e., with predominantly attractive interactions between the melt components. Because such negative values also result in compound formation, glass formation should take place in composition domains where compounds form within a given system. Such seemingly paradoxical correlations will indeed be observed repeatedly in the following chapters. Enthalpies of mixing must not be of too high a magnitude, however, otherwise compounds with high liquidus temperatures will form and the kinetics of crystal growth will be too rapid even slightly below the liquidus because of too low a viscosity. Glass formation is often discussed within the framework of crystal nucleation and growth. Unfortunately, not much information can be drawn in this respect, for the "classical" nucleation theory underestimates experimentally observed rates by tens of orders of magnitude [e.g., Fokin and Zanotto, 2000]. One reason for this failure is that, especially at high degrees of supercooling, crystallization tends to produce metastable phases whose composition differs markedly from that of the stable liquidus phases [Roskosz et al., 2005]. That kinetics takes over thermodynamics in the process is exemplified by supercooled Mg3Al2Si3O12 liquid which crystallizes congruently to aluminous enstatite instead of incongruently to the equilibrium assemblage forsterite + sapphirine + cordierite [Lejeune and Richet, 1995]. Since crystallization is in this case accompanied by a 20% density increase, the factor limiting nucleation is clearly element diffusion to form three different phases and not the large structural rearrangements required for congruent crystallization of aluminous enstatite. But the difficulty of incorporating kinetics in theories of glass formation is compounded by the fact that, owing to the decoupling between local and bulk relaxation (section 2.1e), the diffusivity of network-modifying cations does not

Glass Versus Melt

63

scale with viscosity. The consequence is that crystals are nonstoichiometric and enriched in the most mobile network-modifying cation [Roskosz et al., 2005]. A rigorous theory of glass formation has yet to be established. Owing to its close connection with viscosity, configurational entropy is a factor that must be considered in this respect. Of course, the important parameter is not viscosity at the liquidus temperature, where the driving force for crystallization is zero, but at large degrees of supercooling. Everything else being equal, melts lose entropy faster and, thus, vitrify less readily when thay have high (e.g., alkaline earth silicates) rather than low (e.g., alkali silicates) configurational heat capacities. As an example, glasses with the M 2 Si0 4 (orthosilicate) stoichiometry are extremely difficult to quench. For Mg 2 Si0 4 , the standard glass transition should be about 1000 K, as determined from extrapolations of data for joins in the MgOAl2O3-SiO2 system [Richet et al., 1993] or from a comparison with a molten peridotite [Dingwell et al., 2004]. At this temperature, however, configurational entropy has nearly vanished (Fig. 2.28). To obtain the significant configurational entropy of 2-3 J/g atom K typical of silicate glasses, the fictive temperature should be in the range 1200-1300 K. This, in turn, requires high cooling rates of at least 700 K/min [Tangeman et al., 2001]. Additional evidence supporting the importance of entropy in vitrification is provided by the so-called "invert" glasses [Hanlein, 1933; Trap and Stevels, I960]. These materials are SiO2-poor but bear a number of other oxides such that configurational entropy of mixing is high and predominates over the topological contribution. For silicates, these glasses illustrate what is informally termed the "principle of confusion" in the literature on chalcogenide and other exotic glasses [e.g., Lucas, 1999]. According to this rule, a more complicated chemical composition translates into a greater number of compounds that could nucleate and, thus, in mutual competition such that crystal nucleation and growth is frustrated and does not take place on sufficiently rapid cooling. In other words, the probability of forming viable nuclei through composition fluctuations of the melt is lower when several compounds can form than when a single crystal structure is available. 2.4. Summary Remarks 1. A glass is an amorphous solid whose disordered atomic configuration is that of the supercooled liquid that has been frozen in at the glass transition. The glass transition itself is a kinetic transformation that takes place at higher temperature for higher cooling rate and is signaled by rapid variations of second-order thermodynamic properties. The heat capacity and compressibility necessarily decrease when the liquid transforms to a glass. Although no constraint is placed on it, the thermal expansion coefficient also generally decreases. 2. Because glasses are nonequilibrium substances, their physical properties depend not only on temperature, pressure and chemical composition, but also on thermal history. By contrast, supercooled liquids are in internal thermodynamic equilibrium. For stable and supercooled silicate melts, physical properties can be split conveniently into

64

Chapter 2

vibrational and configurational parts, the latter accounting for the structural changes induced by temperature and pressure variations. 3. When heated in appropriate temperature ranges, glass properties relax to approach the equilibrium values of the supercooled liquid. Relaxation rates are the same for macroscopic properties such as enthalpy, volume or viscosity. Especially near the glass transition range, they can differ for bulk and local properties like element diffusivity. 4. As exemplified by Kauzmann's paradox, configurational entropy is a fundamental parameter to account for viscosity, the glass transition, and the compositional extent of glass formation. References Adam G. and Gibbs J. H. (1965) On the temperature dependence of cooperative relaxation properties in glass-forming liquids. J. Chem. Phys. 43, 139-146. Angell C. A., Ngai K. L., McKenna G. B., McMillan P. R, and Martin S. W. (2000) Relaxation in glassforming liquids and amorphous solids. J. Appl. Phys. 88, 3113-3157. Askarpour V., Manghnani M. H., and Richet P. (1993) Elastic properties of diopside, anorthite, and grossular glasses and liquids: A Brillouin scattering study up to 1400 K. J. Geophys. Res. 98, 17683-17689. Bockris J. O. M., Mackenzie J. D., and Kitchener J. A. (1955) Viscous flow in silica and binary liquid silicates. Trans. Farad. Soc. 51, 1734-1748. Boltzmann L. (1874) Zur Theorie der elastichen Nachwirkung. I. Aufsuchung des matematischen Ausdruckes fur die elastische Nachwirkung. Sitzber Kgl. Akad. Wiss. Wien., Math-Naturw. Klasse 70, 275-306. Bottinga Y. and Richet P. (1996) Silicate melt structural relaxation; rheology, kinetics, and AdamGibbs theory. Chem. Geol. 128, 129-141. Bottinga Y., Weill D., and Richet P. (1982) Density calculations for silicate liquids. I. Revised method for aluminosilicate compositions. Geochim. Cosmochim. Ada 46, 909-919. Bouhifd M. A., A. W., and Richet P. (2001) Partial molar volume of water in phonolitic glasses and liquids. Contrib. Mineral. Petrol. 142, 235-243. Braedt M. and Frischat G. (1988) Sodium self diffusion in glasses and melts of the system Na2ORb2O-SiO2. Phys. Chem. Glasses 29, 214-218. Bridgman P. W. and Simon I. (1953) Effects of very high pressures on glass. J. Appl. Phys. 24, 405-413. Chakraborty, S. (1995) Diffusion in silicate melts. In Structure, Dynamics and Properties of Silicate Melts, Reviews in Mineralogy, Vol. 32 (eds. J. R Stebbins, P. F. McMillan, and D. B. Dingwell) pp. 411-504. Davies R. O. and Jones G. O. (1953) Thermodynamic and kinetic properties of glasses. Adv. Phys. 2, 370-410. Debenedetti P. G. (1997) Metastable Liquids. Princeton University Press, Princeton. Dingwell D. B. (1995) Relaxation in silicate melts: Some applications. Rev. Mineral. 32, 21-66. Dingwell D. B. and My sen B. O. (1985) Effects of water and fluorine on the viscosity of albite melt at high pressure: A preliminary investigation. Earth Planet. Sci. Lett., 266-27'4. Dingwell D. B. and Webb S. L. (1989) Structural relaxation in silicate melts and non-Newtonian melt rheology in geologic processes. Phys. Chem. Minerals 16, 508-516. Dingwell D. B. and Webb S. L. (1990) Relaxation in silicate melts. Eur. J. Mineral. 2, 427-449.

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Dingwell D. B., Courtial P., Giordano D., and Nichols A. R. L. (2004) Viscosity of peridotite liquid. Earth Planet Sci. Lett. 226, 127-138. Donth E. (2001) The Glass Transition. Relaxation Dynamics in Liquids and Disordered Materials. Springer, Berlin. Fang C. Y., Yinnon H., and Uhlmann D. R. (1983) A kinetic treatment of glass formation. VIII: Critical cooling rates for Na2O-SiO2 and K2O-SiO2 glasses. J. Non-Cryst. Solids 57, 465-471. Faman I. and Stebbins J. (1994) The nature of the glass transition in a silica-rich oxide melt. Science 265, 1206-1209. Fokin V. M. and Zanotto E. D. (2000) Crystal nucleation in silicate glasses: The temperature and size dependence of crystal/liquid surface energy. J. Non-Cryst. Solids 265, 105-112. Geissberger A. E. and Galeener F. L. (1983) Raman studies of vitreous SiO2 versus fictive temperature. Phys. Rev. B 28, 3266-3271. George A. and Stebbins J. F. (1998) Structure and dynamics of magnesium in silicate melts: A hightemperature 25Mg NMR study. Amer. Mineral. 83, 1022-1029. Gibbs J. H. and Di Marzio E. (1958) Nature of the glass transition and the glassy state. J. Chem. Phys. 28, 373-383. Goldstein M. (1969) Viscous liquids and the glass transition: A potential energy barrier picture. J. Chem. Phys. 51, 3728-3739. Gottsmann J., Dingwell D. B., and Gennaro C. (1999) Thermal expansion of silicate liquids: Direct determination using container-based dilatometry. Amer. Mineral. 84, 1176-1180. Gruener G., Odier P., De Sousa Meneses D., Florian P., and Richet P. (2001) Bulk and local dynamics in glass-forming liquids: A viscosity, electrical conductivity and NMR study of aluminosilicate melts. Phys. Rev. B 64, 024206. Haggerty J. S., Cooper A. R., and Heasley J. H. (1968) Heat capacity of three inorganic glasses and supercooled liquids. Phys. Chem. Glasses 5, 130-136. Hanlein W. (1933) Die physikalischen Eigenschaften des Systems SiO2-Na2O-K2O-CaO. Z Techn. Phys. 14,418-424. Hessenkemper H. and Bruckner R. (1989) Relaxation behaviour, high-temperature tensile strength and brittleness of glass melts. Glastechn. Ber. 62, 399-409. Hessenkemper H. and Bruckner R. (1990) Some aspects of the workability of glass melts. Glastechn. Ber. 63, 19-23. Hodge I. M. (1994) Enthalpy relaxation and recovery in amorphous materials. J. Non-Cryst. Solids 169,211-266. Hooke R. (1678) Potentia Restitutiva, or Spring. John Martyn, London. Johnson J. R., Bristow R. H., and Blau H. H. (1951) Diffusion of ions in some simple glasses. J. Amer. Ceram. Soc. 34, 165-172. Kauzmann W. (1948) The nature of the glassy state and the behavior of liquids at low temperatures. Chem. Rev. 43, 219-256. Kieffer J., Masnik J. E., Reardon B. J., and Bass J. D. (1995) High-frequency relaxational spectroscopy in liquid borates and silicates. J. Non-Cryst. Solids 183, 51-60. Knoche R., Dingwell D. B., and Webb S. L. (1992) Temperature-dependent thermal expansivities of silicate melts: The system anorthite-diopside. Geochim. Cosmochim. Acta 56, 689-699. Kohlrausch F. W. (1863) Ueber die elastische Nachwirkung bei der Torsion. Ann. Phys. Chem. 119, 337-368. Kress V. C, Williams Q., and Carmichael I. S. E. (1989) When is silicate melt not a liquid? Geochim. Cosmochim. Acta 53, 1687-1692.

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Lange R. A. (1996) Temperature independent thermal expansivities of sodium aluminosilicate melts. Geochim. Cosmochim. Acta 60, 4989-4996. Lejeune A.-M. and Richet P. (1995) Rheology of crystal-bearing silicate melts: An experimental study at high viscosities. J. Geophys. Res. 100, 4215-4229. Lucas J. (1999) Les verres de fluorures. Actualite Chimique, 14-18. McKenna G. B. and Glotzer S. C. (1997) 40 years of entropy and the glass transition. J. Res. Nat. Inst. Stand. Technol. 102, 135-248. Mackenzie J. D. (1963a) High-pressure effects on oxide glasses: II. Subsequent heat treatment. J. Amer. Ceram. Soc. 46, 470-476. Mackenzie J. D. (1963b) High-pressure effects on oxide glasses. I. Densification in rigid state. J. Amer. Ceram. Soc. 46, 461-470. Malinovsky V. K. and Sokolov A. P. (1986) The nature of the boson peak in Raman scattering in glasses. Solid state Comm. 57, 757-761. Masnik J. E., Kieffer J., and Bass J. D. (1993) Structural relaxations in alkali silicate systems by Brillouin light scattering. J. Amer. Ceram. Soc. 76, 3073-3080. Maurer R. D. (1957) Pressure effects in the transformation range of glass. J. Amer. Ceram. Soc. 40,211-214. Maxwell J. C. (1868) On the dynamical theory of gases. Phil. Mag. 35, 129-145 and 185-217. Mazurin O. V., Startsev Y. K., and Potselueva L. N. (1979) Temperature dependences of the viscosity of some glasses at a constant structural temperature. Sov. J. Glass Phys. Chem. 5, 68-79. Meyer A., Schober H., and Dingwell D. B. (2002) Structure, structural relaxation and ion diffusion in sodium disilicate melts. Europhys. Lett. 59, 708-713. Moynihan C. T. (1993) Correlation between the width of the glass transition region and the temperature dependence of the viscosity of high-T glasses. J. Amer. Ceram. Soc. 76, 1081-1087. Moynihan C. T. (1995) Structural relaxation and the glass transition. Rev. Mineral. 32, 1-19. Moynihan C. T. and Schroeder J. (1993) Non-exponential structural relaxation, anomalous light scattering and nanoscale inhomogeneities in glass-forming liquids. J. Non-Cryst. Solids 160, 52-59. Moynihan C. T., Easteal A. J., Wilder J., and Tucker J. (1974) Dependence of the glass transition temperature on heating and cooling rate. J. Phys. Chem. 78, 2673-2677. Moynihan C. T., Macedo P. B., Montrose C. J., Gupta P. K., De Bolt M. A., Dill J. R, Dom B. E., Drake P. W., Easteal A. J., Elterman P. B., Moeller R. P., Sasabe M., and Wilder J. A. (1976) Structural relaxation in vitreous materials. Ann. N.Y. Acad. Sci. 279, 15-35. Neuville D. R. and Richet P. (1991) Viscosity and mixing in molten (Ca,Mg) pyroxenes and garnets. Geochim. Cosmochim. Acta 55, 1011-1020. Newton I. (1725) Philosophiae Naturalis Principia Philosophica, lib. II, cap. IX, 3'd ed. (transl. by A. Motte as Mathematical Principles of Natural Philosophy, 1729, rev. by F. Cajori, University of California Press, Berkeley, 1934). Nikonov A. M., Bogdanov V. N., Nemilov S. V., Shono A. A., and Mikhailov V. N. (1982) Structural relaxation in binary alkalisilicate melts. Fys. Khim. Stekla, 8, 694-703. Polian A., Vo-Thanh D., and Richet P. (2002) Elastic properties of a-SiO2 up to about 2300 K from Brillouin scattering measurements. Europhys. Lett. 57, 375-381. Poole J. P. (1948) Viscosite a basse temperature des verre alcalino-silicates. Verres Refract. 2, 222-228. Rekhson S. M., Bulaeva A.V., and O.V. M. (1971) Changes in the linear dimensions and viscosity of window glass during stabilization. Inorg. Mater. 7, 622-623.

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Richet P. (1984) Viscosity and configurational entropy of silicate melts. Geochim. Cosmochim. Acta 48, 471-483. Richet P. (1987) Heat capacity of silicate glasses. Chem. Geol. 62, 111 -124. Richet P. (2001) The Physical Basis of Thermodynamics. Plenum Publishing. Richet P. and Bottinga Y. (1980) Heat capacity of silicate liquids: New measurements on NaAlSi3O8 and K2Si409. Geochim. Cosmochim. Acta 44, 1535-1541. Richet P. and Bottinga Y. (1984) Anorthite, andesine, wollastonite, diopside, cordierite and pyrope: thermodynamics of melting, glass transitions, and properties of the amorphous phases. Earth Planet. Sci. Lett. 67, 415-432. Richet P. and Bottinga Y. (1986) Thermochemical properties of silicate glasses and liquids: A review. Rev. Geophys. 24, 1-25. Richet P. and Bottinga Y. (1995) Rheology and configurational entropy of silicate melts. In Structure, Dynamics and Properties of Silicate Melts, Reviews in Mineralogy, Vol. 32 (eds. J. F. Stebbins, P. F. McMillan, and D. B. Dingwell) pp. 67-93. Richet P., Bottinga Y., and Tequi C. (1984) Heat capacity of sodium silicate liquids. J. Amer. Ceram. Soc. 67, C6-C8. Richet P., Robie R. A., and Hemingway B. S. (1986) Low-temperature heat capacity of diopside glass: A calorimetric test of the configurational entropy theory as applied to the viscosity of liquid silicates. Geochim. Cosmochim. Acta, 50, 1521-1533. Richet P., Leclerc F., and Benoist L. (1993) Melting of forsterite and spinel, with implications for the glass transition of Mg2SiO4 liquid. Geophys. Res. Lett. 20, 1675-1678. Richet P., Bouhifd M. A., Courtial P., and Tequi C. (1997) Configurational heat capacity and entropy of borosilicate melts. J. Non-Cryst. Solids 211/3, 271-280. Richet P., Whittington A., Holtz F., Behrens H., Ohlhorst S., and Wilke M. (2000) Water and the density of silicate glasses. Contrib. Mineral. Petrol. 138, 337-347. Ritland H. N. (1956) Limitations of the fictive temperature concept. J. Amer. Ceram. Soc. 39, 403-406. Rivers M. and Carmichael I. S. E. (1987) Ultrasonic studies of silicate melts. J. Geophys. Res. 92, 9247-9270. Rosenhauer M., Scarfe C. M., and Virgo D. (1979) Pressure dependence of the glass transition temperature in glasses of diopside, albite, and sodium trisilicate composition. Carnegie Instn. Washington Year Book 78, 547-551. Roskosz M., Toplis M. J., Besson P., and Richet P. (2005) Nucleation mechanisms: A crystal chemical investigation of highly supercooled aluminosilicate liquids. J. Non-Cryst. Solids, in press. Scarfe C. M., Cronin D. J., Wenzel J. T., and Kauffmann D. A. (1983) Viscosity-temperature relationships at 1 atm. in the system diopside-anorthite. Amer. Mineral. 68, 1083-1089. Scherer G. W. (1986) Relaxation in Glasses and Composites. John Wiley & Sons, New York. Siewert R. and Rosenhauer M. (1997) Viscoelastic relaxation measurements in the system SiO2NaAlSiO4 by photon correlation spectroscopy. Amer. Mineral. 82, 1063-1072. Sipp A. and Richet P. (2002) Equivalence of volume, enthalpy and viscosity relaxation kinetics in glass-forming silicate liquids. J. Non-Cryst. Solids 298, 202-212. Sipp A., Neuville D. R., and Richet P. (1997) Viscosity, configurational entropy and structural relaxation of borosilicate melts. J. Non-Cryst. Solids 211/3, 281-293. Sipp A., Bottinga Y., and Richet P. (2001) New viscosity measurements for 3D network liquids and new correlations between old parameters. J. Non-Cryst. Solids 288, 166-174.

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Stebbins J. R, Sen S., and Farnan I. (1995) Silicate species exchange, viscosity, and crystallization in a low-silica melt: In situ high-temperature MAS NMR spectroscopy. Amer. Mineral. 80, 861-864. Stevenson R. J., Dingwell D. B., Webb S. L., and Bagdassarov N. S. (1995) The equivalence of enthalpy and shear stress relaxation in rhyolitic obsidians and quantification of the liquid-glass transition in volcanic processes. /. Vole. Geotherm. Res. 68, 297-306. Tammann G. and Jenckel E. (1929) Die Zunahme der Dichte von Glasern nach Erstarrung unter erhohtem Druck und die Wiederkehr der natiirlichen Dichte durch Temperatursteigerung. Z. Anorg. Allg. Chem. 184, 416-420. Tangeman J. A., Phillips B. L., Navrotsky A., Weber J. K. R., Hixson A. D., and Key T. S. (2001) Vitreous forsterite (Mg2Si04): Synthesis, structure, and thermochemistry. Geophys. Res. Lett. 28,2517-2520. Terai R. and Oishi Y. (1977) Self-diffusion of oxygen in soda-lime silicate glass. Glastechn. Ber. 50, 68-73. Toplis M. J. (1998) Energy barriers associated with viscous flow and the prediction of glass transition temperatures of molten silicates. Amer. Mineral. 83, 480-490. Toplis M. J. (2001) Quantitative links between microscopic properties and viscosity of liquids in the system SiO2-Na2O. Chem. Geol. 174, 321-331. Toplis M. J. and Richet P. (2000) Equilibrium expansivity of silicate liquids in the glass transition range. Contrib. Mineral. Petrol. 139, 672-683. Trap H. J. L. and Stevels J. M. (1960) Conventional and invert glasses containing titania. Part 1. Phys. Chem. Glasses 1, 107-118. Urbain G., Bottinga Y., and Richet P. (1982) Viscosity of liquid silica, silicates and aluminosilicates. Geochim. Cosmochim. Ada 46, 1061-1072. Vo-Thanh D., Polian A., and Richet P. (1996) Elastic properties of silicate melts up to 2350 K from Brillouin scattering. Geophys. Res. Lett 23, 423-426. Wakabayashi H. (1977) Self-diffusion coefficients of calcium in molten soda-lime-silica glass. J. Non-Cryst. Solids 24, 427-429. Webb S. L. (1992a) Shear, volume, enthalpy and structural relaxation in silicate melts. Chem. Geol. 96, 449-457. Webb S. L. (1992b) Low-frequency shear and structural relaxation in rhyolite melt. Phys. Chem. Glasses 19, 240-245. Webb S. L. and Courtial P. (1996) Compressibility of melts in the CaO-Al2O3-SiO2 system. Geochim. Cosmochim. Ada 60, 75-86. Webb S. L. and Knoche R. (1996) The glass transition, structural relaxation and shear viscosity of silicate melts. Chem. Geol. 128, 165-183. Winchell P. (1969) The compensation law for diffusion in silicates. High Temp. Sci. 1, 200-215. Yageman V. D. and Matveev G. M. (1982) Heat capacity of glasses in the system SiO2-Na2O.SiO2. Fiz. Khim. Stekla 8, 238-245. Yinnon H. and Cooper A. R. (1980) Oxygen diffusion in multicomponent glass forming silicates. Phys. Chem. Glasses 21, 204-211. Zanotto E. D. and Gupta P. K. (1999) Do cathedral glasses flow? Additional remarks. Amer. J. Phys. 67, 260-262.

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Glasses and Melts vs. Crystals Although much information has been directly gathered on glasses and melts, crystals are still useful references for discussing the structure and properties of these materials. If a property-composition-structure relationship is known for crystals, then comparisons with glasses or melts can provide valuable insights into structural features relevant to the same property of the amorphous phases. In this respect, an important simplifying feature is that the properties of glasses and melts tend to vary smoothly with composition, without the irregularities of crystal properties that originate in the specificity of each crystal structure. In other words, the conclusions drawn from a few amorphous compositions can in general be extended to a much wider composition range than for crystals. As glasses are solids, they share with crystals common features determined by atomic vibrations in a fixed configuration. At the atomic scale, the structure of both kinds of phases can be considered as a three-dimensional arrangement of the oxygen coordination polyhedra of cations. As a result of lack of long-range order, this arrangement is disordered in glasses but there nevertheless remain definite short-range order similarities with crystals. As will be seen, these manifest themselves in two important thermochemical properties, the low-temperature heat capacity and entropy. Because liquids undergo configurational changes, they differ from both glasses and crystals for all features related in some way to atomic mobility. As described in Chapter 2, glasses and liquids do join smoothly at the glass transition. It follows that any difference in structure and properties between melts and solids, whether vitreous or crystalline, are highest at the highest temperatures. Thermochemical data, for instance, demonstrate that structural differences between a glass and a melt at superliquidus temperatures can be as great as those between a glass and a crystal of the same composition. In view of such differences, the specificity of the liquid state must be understood. For this purpose, silicate crystals again represent a useful starting point. At temperatures that are not necessarily near the melting points, they show anomalous variations of physical properties that are also due to configurational changes. In the last part of this chapter, attention will thus be paid to cation disorder, a-|3 transitions and premelting effects, whose mechanisms give some insights on similar rearrangements that operate in melts. 3.1. Basics of Silicate Structure Because of the partially covalent nature of bonding, the actual ionic charges in silicates are much smaller than the formal charges of 2- for O, 4+ for Si, etc. For liquid SiO2, charges of 2.76 and -1.38 have for instance been derived from ab initio

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Figure 3.1 - Low-pressure SiO4 tetrahedra vs. high-pressure SiO6 octahedra. In the SiO2 polymorphs, they are exemplified by quartz and stishovite, respectively.

calculations for Si and O, respectively [Tangney and Scandolo, 2002]. Even for the archetypal ionic crystal MgO, charges of ±1.44 have been calculated in the same way for Mg and O [Tangney and Scandolo, 2003]. To a first approximation, silicates can, nonetheless, be considered as ionic substances in which a single anion, oxygen, bonds to a wide variety of cations of different sizes and electrical charges. Given that the actual charge of an ion depends on the overall composition and can vary from one structural position to another, this approximation represents the only way to rationalize simply the structure of silicates, be they crystalline or amorphous. Empirically, it is justified by the fact that the charge ratios between cations and oxygens remain close to the nominal values. The fundamental assumption thus made is that, with the exception of the constraints imposed by long-range order, the principles established for ionic crystals [Pauling, 1929] are applicable to amorphous phases [Zachariasen, 1932]. To begin this chapter, only those structural aspects relevant for comparisons between crystalline and amorphous silicates will be summarized along these lines. Following this elementary picture, more detailed descriptions will be given in following chapters. 3.1a. Oxygen Coordination Polyhedra Oxygen is the main constituent of silicates. Not only are there always more oxygens than atoms of any other elements, but the ionic radius of the O2" ion, which is about 1.30 A, is so large compared to the radii of most cations that oxygen atoms occupy for example 100 and 8 times more space than cations in pure SiO2 and olivines, respectively [all ionic radii taken from Whittaker and Muntus, 1970]. Hence, deciphering the structure of silicates is tantamount to describing how cations fit in-between oxygen anions. This is conveniently done in terms of polyhedra whose apices are the oxygens binding to a given cation (the ligand). Such oxygen coordination polyhedra are determined by a complex balance of electrostatic interactions. They are characterized by the number of ligands, the so-called coordination number, and by the various cation-oxygen distances. Both kinds of parameters are primarily determined by ionic radius ratios between O2" and cations.

Figure 3.2 - Connectivity between oxygen coordination tetrahedra of Si with the octahedron of another cation M through nonbridging oxygens.

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9 Bridging oxygen (BO) Nonbridging oxygen (NBO) • Tetrahedrally-coordinated cation (T) • Network-modifying cation (M)

Figure 3.3 - Schematic representation of interconnected silicate tetrahedra and larger metal oxide polyhedra in the various Q" structural units. In the Q4 sketch, the short lines indicate effectively infinite extension of the structure.

Everything else being equal, small and highly charged cations compete more effectively for bonding with oxygen. On this basis, cations can be compared in terms of their electrical charge Z and ionic radius r. Among major elements in silicates, silicon is the most efficient because it has the smallest radius and the highest formal charge (4+). At low pressure, its optimum coordination is achieved in the form of SiO4 tetrahedra in which r - 0.34 A and Si-O distances are near 1.60 A (Fig. 3.1). At high pressures, it forms instead SiO6 octahedra with r = 0.48 A and Si-0 distances near 1.90 A (Fig. 3.1). Such a transformation is abrupt in crystals, as exemplified by the coesite-stishovite transition near 10 GPa, but progressive in liquids in which it likely begins at lower pressures [Waff, 1975; Stolper and Ahrens, 1987]. By forming their own oxygen coordination polyhedra, other cations then share oxygens with SiO4 tetrahedra at low pressure (Fig. 3.2), or with SiO6 octahedra at high pressure. A dramatic illustration of the difference in bond strength between Si4+ and other cations is provided by Mg2Si04 glass. The structure of this material is made up of isolated, regular SiO4 tetrahedra, similar to those of the crytalline form (forsterite), which are randomly oriented and linked through a variety of highly distorted MgOn polyhedra, with 4 < n < 6 [Kohara et al., 2004]. This contrast between SiO4 and MgOn polyhedra illustrates the fact that, although Si4+ ions are twice less abundant than Mg2+, they keep controlling the structure and leave to Mg2+ ions a menial role of "space fillers". Even when Si4+ is not the most abundant cation, its oxygen polyhedra constitute an anionic framework whose connectivity depends on the Si/O ratio of the material (Fig. 3.3).

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For the SiO2 stoichiometry of pure silica, all low-pressure SiO4 tetrahedra necessarily polymerize to form an open, three-dimensional network in which each oxygen is bridging (BO), i.e., shared by two neighboring tetrahedra. At the other end, the M 2 Si0 4 stoichiometry of olivines gives rise to isolated SiO4 tetrahedra where all oxygens are nonbridging (NBO). Between these two extremes, the number of nonbridging oxygens per silicon atom increases from 0 to 4. This number is an average value that characterizes the degree of polymerization of the silicate framework. Since oxygens are either bridging or nonbridging, various kinds of SiO4 tetrahedra must be distinguished to describe the structure in more detail. Following Shramm et al. [1984], one designates in this way by a Qn-species an SiO4 tetrahedron in which n oxygens are bridging and 4-n are nonbridging (Fig. 3.3). The silicate chains of pyroxene (MSiO3) crystals are for example made up of only Q2 species, but there is, in contrast, a distribution of Q"-species around a mean value of 2 in amorphous phases of the same stoichiometry [Etchepare, 1972; Brawer and White, 1975]. Whereas tetrahedral coordination always holds for Si at low pressure, the coordination number of oxygen increases from 2, for pure SiO2, to higher values for depolymerized structures. These values depend on the manner in which other cations bond to nonbridging oxygens between SiO4 tetrahedra (Fig. 3.3). The latter cations will be referred to as Mcations. In olivine crystals, for instance, divalent metal cations are 6-fold coordinated by oxygens, which are themselves bound to 4 M-cations. Although the number of cations to which oxygen can be coordinated varies widely in oxide compounds, the ionic radius of O2 varies only from 1.27 to 1.34 A between 2-fold and 8-fold coordination. Such variations are very small compared to those experienced by cations when their coordination changes. This is illustrated by Si4+ (see above) or Na+ (r = 1.07 A and 1.40 A for 4- and 9 fold coordination, respectively). This sensitivity difference is the main reason why attention is paid to cation coordination by oxygen and not to oxygen coordination by cations. As already noted, the actual charges of cations and anions are not only lower than the formal charges that are usually assumed, but they are not constant for a given ion. According to ab initio calculations on sodium tetrasilicate, the charge of Si within Q4and Q3-species is on average 0.14 and 0.10 higher, respectively, than in Q2-species, whereas nonbridging oxygens are more negatively charged than bridging oxygens by 0.15 charge units [Ispas et al., 2001]. An important consequence of such charge distributions is that bonding of bridging oxygens with silicon leaves a residual charge which is used for bonding with other cations. The relative contribution of bridging and nonbridging oxygens to the oxygen coordination of these cations is known poorly. In molecular dynamics simulations of soda-lime silicates, this contribution is in a ratio varying from 1:5 to 1:10 for glasses quenched from the very high temperature of 6000 K [Cormack and Du, 2001]. Such calculations do not allow the actual ratio to be determined for the actual temperature ranges of interest, but this important feature should be kept in mind when discussing silicate structures. 3.1b. Network-Formers and Modifiers When an alkali or alkaline earth oxide is mixed with pure SiO2, the ensuing decrease of the Si/O ratio causes depolymerization of the silicate framework. According to a

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73

Figure 3.4 - Mean T-0 distances within T0 4 tetrahedra of aluminosilicates against Al/(A1+Si) [from Taylor and Brown, 1979].

terminology already used by Warren and Pincus [1940], silicon is a network-former and most other metal cations are network-modifiers. By substituting for Si, a few elements can be both network-modifiers and network-formers. Aluminum is the most important in this category. At low pressure, its ionic radius (r = 0.47 A) is comparable to the 0.34 A of Si 4+ , but its formal charge is only 3+ so that it can enter tetrahedral sites of the silicate framework only by associating with a neighboring charge-compensating cation to achieve the 4+ formal charge of Si. This role is generally played by an alkali (univalent) cation or by an alkaline earth (divalent) cation, which compensates for two different Al 3+ as illustrated in crystals by anorthite (CaAl 2 Si 2 0 8 ). Other cations achieve tetrahedral coordination when their ionic radii is not too different from that of Si4+ and their mismatch in electrical charge can be compensated. In crystalline silicates, this is the case of P5* (r - 0.25 A), at least at low pressures, and of Fe 3+ (r = 0.57 A) although ferric iron sometimes has more than 4 oxygen ligands. Boron may occur either in BO45" tetrahedra (r = 0.20 A) and in BO33" triangles (r = 0.10 A). With its somewhat higher ionic radius of 0.61 A, Ti 4+ is usually coordinated by more than 4 oxygens but there is evidence for 4-fold coordination. In both cases, however, the strength of the Ti-0 bond is such that Ti has to be considered as a network-former. By contrast, we have noted above (for Mg 2 Si0 4 glass) that being in part 4-fold coordinated does not confer to Mg 4+ a network former status. Hence, tetrahedral coordination and network-forming role are not to be used synonymously. For convenience, any network-forming, tetrahedrally coordinated cation will be denoted by T. Describing the anionic framework of amorphous silicates becomes more complicated when several of these cations are present in appreciable amounts. The T-0 distances between the central T-cation in a tetrahedron and an oxygen, whether bridging or nonbridging, are sensitive functions of the type of T-cation (Fig. 3.4). The same applies to the intratetrahedral (O-T-O) and intertetrahedral (T-O-T) angles, the latter also depending on the polymerization state of the silicate framework [see Furukawa et al., 1981]. The NBO/T atomic ratio represents the simplest way to characterize the degree of polymerization of the structure. As will be shown in following chapters, this parameter has proven useful for rationalizing glass and melts properties. It is necessarily approximate,

74

Chapter 3

Figure 3.5 - Relationships between average M-0 bond length and Pauling bond strength [after Gibbs et al, 2000].

however, for it does not take into account the nature of the network-forming and of the network-modifying metal cations. 3.1c. Bond Energies For obvious geometrical reasons, metal-oxygen bond distances are positive functions of the oxygen coordination number. In addition, stability reasons dictates that, everything else being equal, bond strength of purely ionic substances decreases when this number increases. This conclusion is embodied in Pauling's [1929] rules and has been justified by theoretical studies in which bond strength, or site potential, is a systematic function of bond distance (Fig. 3.5). These relationships become less clear, however, in crystals with mixed ionic and covalent bonding [e.g., Gibbs et al., 2000]. In other words, the simple relationship of Fig. 3.5 should be treated with some caution in silicate crystals where bonds often are significantly covalent. The same caution applies to glasses and melts. Within a given TO4 tetrahedron, the oxygen bond length can vary by about 10%. These variations are often governed by substitution of Si4+ by other tetrahedrallycoordinated cations, for instance by Al whose Al-0 length is ~ 1.71 A as compared with ~ 1.60 A for Si-0 [e.g., Navrotsky et al., 1985]. As discussed in more detail in the following chapter, shorter T-0 bond lengths are accommodated by increases of intertetrahedral angles because these angles can vary widely without large energy changes. For example, theroretical calculations made on H6Si207 clusters indicate that similar increases in bonding energy are caused by a 0.01 A increase of T-0 distances and by a decrease from 180° to 140° of T-O-T angles [Gibbs et al., 1981]. An important simplifying feature follows from these observations, namely that, regardless of the degree of polymerization of the structure, TO4 tetrahedra may be treated as near-rigid units [e.g., Hazen and Finger, 1982]. The energy differences between T-0 bonds also have important consequences for the way in which different tetrahedrally coordinated cations mix within the anionic framework. For two different cations T and T', the extreme cases are complete mixing with a random distribution of T-O-T' linkages, and complete ordering with distinct T-O-T and T'-O-T' linkages that would represent the coexistence of two separate, intermingling anionic

Glasses and Melts vs. Crystals

75

frameworks. Because mixing is determined by the balance of enthalpy and entropy factors in the Gibbs free energy, the distribution of network-forming cations is strongly temperature dependent, random mixing being favored by high temperatures. For Al-0 bonds, the energy difference with Si-0 bonds is small enough that the latter situation is not relevant. In such a case, a limiting situation could be complete ordering of Al and Si in the same anionic framework. A more likely limiting situation is pictured by the Loewenstein [1954] avoidance principle, which simply states that a given oxygen cannot be shared by two A1O4 tetrahedra. The subtle influence of bonding differences manifests itself in crystals by the fact that Si<=>Al ordering depends not only on temperature but also markedly on composition even within the single tectosilicate family [Dove etal, 1996]. Because of the lower energy of M-0 compared to T-0 bonds, it has often been assumed, at least implicitly, that network-modifier cations are simply fitting within holes of the silicate framework. That this assumption is incorrect is shown by marked variations in physical properties when an alkali or an alkaline earth cation is substituted for another (see Chapter 6). We leave to following chapters a description of the way in which the energetics of M-0 bonds affect the anionic structure. Here we merely point out that a clear signature of differences in bonding energy between M-O and T-O bonds is found in vibrational spectra. In fact, it is this feature that allows vibrational spectroscopy to be a structural probe. In any solid, the vibrational density of states, g(v), gives the number of vibrational modes with a frequency ranging from v to v + dv. Although g{v) is a complicated function of frequency, it can be conveniently split into two distinct ranges for silicates (Fig. 3.6). A simple justification for this distinction, which is particularly clear cut for disordered phases, is provided by the analogy between a spring and a chemical bond of same strength k. In both cases, the vibrational frequency is given by v = llln VA//I where jx is either the mass suspended at the end of the spring, or a given function of the mass of the atoms involved in the vibrational mode. The lattice vibrations involve a large number of atoms and represent a variety of stretching and bending of M-0 bonds in conjunction with displacements of TO4 tetrahedra, which are then Figure 3.6 - Raman spectra of considered as rigid units. With low k and high jx, anorthite and CaAl2Si20g liquid 1 they are typically found below about 500 cm' . In [Mysen, unpub.]. The spectrum of contrast, the internal vibrations within TO4 tetrahedra a disordered anorthite grown near take place within the averaged environment of the glass transition is included for network-modifier cations. With high k and low fi, comparison [Roskosz etal., 2005].

76

Chapter 3

these are primarily localized T-0 stretching modes, found in the frequency range 8001200 cm"1, and a broad envelope at 600 ± 100 cm"1 that represents mainly O-T-0 bending vibrations. Everything else being equal, the frequencies of internal modes depend on Qn-speciation. The stretching modes are found at higher frequencies in Q° than in Q4 species, whereas the converse is true for bending vibrations (see Chapter 7). Replacement of Si by another cation in tetrahedral sites or of an M-cation by another also affects the energy of T-0 and M-0 bonds. In all cases, the existence of a distribution of bond strength results in a distribution of vibrational frequencies and, thus, in a broadening of bands in vibrational spectra. This effect is apparent in the Raman spectrum of a highly disordered anorthite crystal (Fig. 3.6). Of course, broadening is still more important in glasses and melts where long-range order is lost and distribution of bond lengths and bond distances widens further (Fig. 3.6). 3.2. Thermodynamic Properties From a purely thermochemical standpoint, crystals are the necessary starting point for determinations of melt properties. This holds especially true for the entropy, whose "absolute" value can be determined only from a cycle that starts with the third-law zero value of the crystal (see Fig. 2.19). Hence, it is appropriate to review first a few aspects of heat capacities and entropies of crystals relevant to amorphous phases. In preamble, note that the difference between the isobaric and isochoric heat capacity is equal to TVo?lf5v where a is

Figure 3.7 - High-temperature enthalpy (a) and heat capacity (b) of diopside and glassy and liquid CaMgSi 2 O 6 , to which the subscripts c, g, and / refer, respectively. The enthalpy of the crystal at 298 K is taken as 0; that of the glass is plotted for the two different fictive temperatures indicated. The C hysteresis at the glass transition was actually not observed. The temperature and enthalpy of melting are denoted by 7^-and AHf From Richet and Bottinga [1986].

Glasses and Melts vs. Crystals

11

Figure 3.8 - Fusion of Na 2 Si0 3 and Li2SiO3 as observed in relative enthalpy experiments [Tequi et al., 1992]. Measurements plotted as mean heat capacities, Cm = (HT-H273)/(T- 273), to show at an expanded scale the enthalpy data on both sides of the melting point.

the thermal expansion coefficient and j3Tthe isothermal compressibility. For glasses, this difference is so small that it will be consistently neglected in the following discussion. 3.2a. High-Temperature Enthalpy and Entropy In solids, the isobaric heat capacity (C ) is the physical property most directly related to atomic vibrations.3'1 For silicates above room temperature, its value is already close to the Dulong-and-Petit limit of 3 R/g atom K. As this limit depends only on the number of atoms in the selected gram formula weight, it cannot depend sensitively on vibrational density of states and, thus, on structure. This is why glasses and crystals have similar heat capacity, except at low temperatures and in phase transition regions. As discussed in the previous chapter, there is an abrupt Cp increase at the glass transition caused by the onset of configurational changes in the liquid. For enthalpy, this implies that differences between crystals and melts increase markedly from T to superliquidus conditions (Fig. 3.7). The effect is similar to that already pictured in Fig. 2.19 for the entropy in connection to Kauzmann's paradox. For both enthalpy and entropy, the differences between glasses and crystals at T can be half those observed between liquids and crystals at the liquidus. These variations demonstrate unambiguously the importance of temperature-induced structural changes in liquids. When investigating the structure of glasses near room temperature, it should thus be kept in mind that differences between a glass at T and a liquid at high temperature can be as great as those between a crystal and a glass at room temperature. Application of equilibrium thermodynamics to glasses might seem unwarranted because the existence of a reversible pathway between any two temperatures is required to define the entropy of a phase. Now, the heat capacity hysteresis represented in Fig. 2.16 indicates that some entropy is created when CfT is integrated along a heating and cooling cycle through the glass transition range. This is, indeed, an intrinsic feature of the irreversibility of a nonequilibrium transformation. In practice, however, the entropy created is small relative to the vibrational entropy of the glass as given by equation (3.4) [Bestul and Chang, 1965]. Hence, the deviations of experimental pathways from reversible ones are not a significant problem in calorimetric measurements and do not prevent the entropy of a glass from being defined operationally.

78

Chapter 3

The enthalpy and entropy differences between crystals and melts — the enthalpies and entropies of fusion, for short — play a fundamental role in determining solid-liquid equilibria. These properties must be known accurately for thermodynamic calculations. As shown in Fig. 3.8 for lithium and sodium metasilicates, the simplest way would be to measure the enthalpy released by a melt when it crystallizes. The sluggish nature of crystallization in silicate systems usually makes such experiments impossible, however, because the melt vitrifies or undergoes only partial crystallization on cooling. The problem raised by glass-forming tendency may be circumvented through solution calorimetry. After complete dissolution in an appropriate solvent, the same final state (i.e., the same speciation) is obtained for initially amorphous and crystalline phases. The enthalpy differences between both phases (the enthalpy of vitrification) then is simply the difference, AHV(TV), between the negatives of the enthalpies of solution measured at temperature Tv. Experiments are made either in HF solutions near room temperature [e.g., Hovis et al., 1998], or in molten lead borate near 700°C [e.g., Navrotsky, 1997]. Denoting by C , C and C . the heat capacities of the crystal, glass and liquid, respectively, one calculates the enthalpy of fusion at any temperature Tfrom: AHf(T) = AHv (Tv) + ] (Cpg - Cpc) dT+ I (Cpl - Cpc) dT,

(3.1)

where T, the fictive temperature of the glass investigated in solution calorimetry, must be known as accurately as possible. The enthalpy plots of Fig. 3.7 illustrate the calculations made with Equation (3.1). A summary of enthalpies of fusion has been published by Richet and Bottinga [1986]. Since then, additional measurements have been made by Zigo etal, [1987] for gehlenite (Ca2Al2Si07: AHf= 172 ± 6 kJ/mol at Tf= 1863 K); by Richet et al. [1993a] for spinel (MgAl2O4: AHf= 107 ±11 kJ/mol at Tf= 2408 K) and forsterite (Mg2Si04: AHf= 142 ± 14 kJ/mol at Tf= 2174 K); by Sugawara and Akaogi [2003] for Ni2SiO4 (AHf= 221 ± 26 kJ/mol at 7}= 1923 K) and Co2SiO4 (AHf= 103 ± 15 kJ/mol at Tf= 1688 K), and by Sugawara and Akaogi [2004] for hematite (Fe2O3: AHf- 133 ± 10 kJ/mol at Tf= 1895 K) and acmite (NaFeSi2O6: AHf= 70.5 ± 9.4 kJ/mol at Tf= 1373 K). If melting is congruent, the entropy of fusion of a mineral is given by (3.2)

ASfT) = AHfT)ITf

where 7\is the equilibrium melting temperature. If not, only the temperature dependence of the entropy of fusion can be determined from calorimetric measurements with: ASfT) = ASfTr) + ] (Cpl - Cpc)ITdT, Tr

(3.3)

where Tr is an arbitrary reference temperature. With an equation analogous to (3.1), the calculation may be extended to below Tg if the fictive temperature of the glass is known. As described in section 2.3a, both enthalpy and entropy of liquids can be split into vibrational and configurational parts. In the absence of any phase transition, crystals

79

Glasses and Melts vs. Crystals

T, K Figure 3.9 - Entropy differences between amorphous and crystalline silicates [see Richet and Bottinga, 1986, for data sources]. The open arrows indicate the congruent melting temperatures, the solid arrows the calorimetric glass transition temperatures.

have only vibrational properties. This suggests that configurational enthalpy and entropy of liquids could be approximated by the enthalpy and entropy differences between liquids and crystals. Such an approximation is not correct, however, especially for entropy (Figs 2.19 and 3.9). First, small C differences between crystals and glasses can translate into significant enthalpy and entropy differences when integrated over wide temperature intervals. Second, these C differences can be large at the low temperatures from which integrations must be performed to derive entropies. This is illustrated by the large variations of the entropy differences shown in Fig. 3.9 below 300 K. For this and other reasons, low-temperature heat capacities must also be considered. 3.2b. Low-Temperature Heat Capacity and Vibrational Entropy The low-temperature heat capacity is needed to determine the standard entropy of a phase or, more precisely, its vibrational entropy, with

S29fi-S0=Tci/TdT,

(3.4)

Chapter 3

80

Figure 3.10 - Entropy against volume for SiO2 and GeO2 glasses and polymorphs. Co: coesite; GeO2Gl: GeO2 glass; Gl: SiO2 glass; h-GeO2: hexagonal GeO2; Qu: quartz; St: stishovite; t-GeO2: tetragonal GeO2; Tr: tridymite. Data for rutile (TiO2) also included. See Richet et al. [1993b, 2003b] for data sources.

where the residual entropy, So, cannot be omitted because it does not vanish for disordered substances such as glasses. For minerals, it has long been known that 529g - 5 0 depends on volume or, more precisely, on atomic packing, i.e., short-range order around cations, and especially on oxygen coordination of cations [Robinson and Haas, 1983; Holland, 1989]. These effects are nicely summarized by the entropies of the isostructural forms of SiO2 and GeO2 (Fig. 3.10). In both instances, the entropy is markedly lower for the tetragonal ("rutile") polymorphs, where Si and Ge are octahedrally coordinated, than for the hexagonal ("quartz") forms where both cations are in tetrahedral coordination. For the latter forms and the glass as well, the entropy is only a slightly positive function of molar volume. Qualitatively, these variations are readily accounted for. In a solid, the isochoric heat capacity of a single oscillator of frequency, v, is given by the Einstein function cv(T) = x2ex/(ex-l)2,

(3.5)

where x = hv/kT, and h and k are Planck and Boltzmann constants, respectively [see for example Kittel, 1996]. The only assumption made is that vibrations are harmonic, which is justified at low temperatures where vibrational amplitudes are small. If the vibrational density of states is known, the molar heat capacity of the material is calculated with CV(T)= J

cvg(v)dv,

(3.6)

where vm is the highest vibrational frequency in the solid and the integration made over a total of 3/V modes for a substance with N atoms in its gram formula weight. The Einstein function, equation (3.5), tends to 0 at 0 K and has k as a high-temperature limit. Hence, the Dulong and Petit high-temperature limit of Cv is 3 R if N is taken to be the Avogadro number. In general, g( v) is not sufficiently well known to predict accurately CV(T). At least qualitatively, the trends of Fig. 3.10 are nonetheless accounted for readily

Glasses and Melts vs. Crystals

81

Figure 3.11 - Vibrational entropy of aluminosilicate glasses (open symbols) and crystals (solid symbols). Ab (albite): NaAlSi3O8; An (anorthite): CaAl 2 Si 2 0 8 ; CaTs (calcium Tschermak molecule): CaAl 2 Si0 6 ; Jd (jadeite): NaAlSi2O6; Ne (nepheline) and Ca (camegieite): NaAlSiO4. The data for An and CaAl2Si20g glass plot at the same point. See Richet et al. [1993b] for data sources.

in terms of the variations of the vibrational density of states induced by the change from 4- to 6-fold coordination of either Si or Ge. At a given temperature, the heat capacity of an oscillator increases when its frequency (or bond distance), decreases. For SiO2 and GeO2 polymorphs, Si-0 and Ge-0 bond distances are longer in the tetragonal than in the hexagonal phases. Lengthening of Si-0 (and Ge-O) bonds thus leads to lower vibrational frequencies for Si-O stretching modes. However, the ensuing higher heat capacity of the internal modes of SiO4 and GeO4 tetrahedra are more than compensated by the C decreases of the lattice modes, which are due to shorter Si-Si and Ge-Ge distances between second-nearest neighbors in the more compact tetragonal structure of the high-coordination polymorphs. The net effect is a decrease of the heat capacity and entropy [Gillet et al., 1990]. In addition to be needed for thermodynamic calculations, heat capacity thus appears to be a structural probe. For silicates, this sensitivity on short-range order obtains below about 200 K. The S29g - 5 0 data plotted in Fig. 3.11 for sodium and calcium aluminosilicates show that the transformation from 4- to 6-fold coordination has similar effects for aluminum as for silicon [Richet et al, 1993b]. In both Na and Ca series, the glasses define smooth entropy trends. These are also consistent with the data for the low-pressure crystal phases in which Al is tetrahedrally coordinated. In contrast, the high-pressure crystalline phases jadeite (Jd, NaAlSi2O6) and Ca-Tschermak pyroxene (CaTs, CaAl2Si06), where all or some Al is 6-fold coordinated, have entropies departing negatively from these trends. Without any structural information for glasses, we could thus conclude that Al is essentially 4-fold coordinated for all glass samples of these series. This conclusion is valid at least for all peralkaline and peralkaline earth compositions [de Ligny et al., 1996]. Low-temperature heat capacities also provide information on the local environment of network-modifying cations, especially for binary SiO2-M2O systems for which

82

Chapter 3

Figure 3.12 - Low-temperature heat capacity of binary M 2 Si 2 0 5 glasses (solid curves) and crystals (dashed curves), with M = Li, Na and K. Data from Westrum et al. [1989].

measurements are the most extensive. The observations for M2Si205 glasses and crystals plotted in Fig. 3.12 illustrate two general trends. First, at a given temperature the heat capacity decreases regularly in the order K, Na, Li, which is a direct consequence of the increase in average bond strength in the same order due to the decrease of the ionic radius of the alkali. Second, the heat capacity of a glass is higher than that of its crystalline counterpart, which correlates with the lower density of the glass and the correlative decrease in bond strength within this phase. Again, there is a regular trend since these differences increase in the order K, Na, Li. If this volume effect is taken into account, then the small C differences, and particularly their systematic nature, rule out markedly differing coordination numbers for alkali ions in glasses and crystals of the same composition. Hence, especially for potassium silicates, the average number should not depart much from the value of about 5 which holds in the crystals. As made by Holland [1989], the entropy of silicate crystals may be approximated as the sum of entropy coefficients pertaining to each oxide in which the cation has the appropriate coordination number (Table 3.1). Owing to the continuous nature of glass solutions, an analogous procedure allows partial molar relative entropies of oxides in glasses to be determined from an analysis of available data [Richet et al, 1993b; de Ligny et al., 1996]. The additive nature of S298 - So suggested by the linear trends of Fig. 3.11 is borne out by an analysis of the data available for more than 30 different glasses. The experimental results are reproduced to better than 1% with a set of composition-independent partial molar entropies (Table 3.1). This is another way of stating that short-range order around cations does not depend strongly on composition in glass-forming silicates. A distinction must be made, however, in that two different values are found for Na2O and K2O depending on whether the alkali element is "free" or is associated as a charge compensator for tetrahedral Al (Table 3.1). The higher entropy derived in the latter case indicates that, when the alkali associates with Al, its coordination number increases from about 5 to a higher value similar to those determined for crystalline tectosilicates. This conclusion agrees with the analogous increase of the size of the oxygen shell around sodium determined by Isard [1959] from electrical conductivity measurements on aluminosilicates. In contrast, a single partial molar entropy obtains for the oxides of Ca and for Mg when these cations switch from a network-modifying to a charge-compensating

83

Glasses and Melts vs. Crystals Table 3.1. Partial molar relative entropies of oxides in silicate glasses, and entropy coefficients of oxides in crystals for the coordination numbers listed in Roman numbers Oxide

Glasses3

SiO2 A12O3 MgO CaO Li2O Na2O

43.4 69.1 30.7 42.8 49.0 85b 96.7° 108b 119.1° 56.1

K2O FeO

Crystals" 40.3 (IV) - 27.8 (VI)C 72.1 (IV)-43.8 (VI) 26.7 (VI) - 27.7 (VII) 39.6 (VI) - 38.7 (VIII) 38.5 (IV-V) 76 (IV-V) 97.3 (IX) 101 (V-VI) 114.3-120.4 43.2 (IV-VIII)

a

Data in J/mol K from Richetetal. [1993b] for glasses, and from Holland [1989] for crystals In Al-free silicates c For Al-charge compensating alkali cation

b

role. As will be seen in Chapter 8, this contrasting behavior of alkali and alkaline earth cations translates into different composition dependences of physical properties of melts at high temperatures. This is another way of stating that configurational properties are sensitive functions of cation coordination. 3.2c. Boson Peak Although the vibrational entropy of glasses is essentially a linear function of composition (see previous section), additivity does not necessarily hold true for heat capacity because data close to 0 K contribute little to entropy. As a matter of fact, additivity of heat capacity breaks down below about 50 K so that two different temperature ranges must be distinguished in low-temperature C analyses. Of course, these regimes have no sharp boundaries as illustrated in Fig. 3.13 by the C calculations made for SiO2 glass from a

Figure 3.13 - Heat capacity of SiO2 glass as determined from its vibrational density of states, g(v) [solid curve, from Galeener etal, 1983]. At each temperature indicated (in K), the heat capacity is given by the area under the g(v) cv(T) function, plotted as a dashed curve, where cv(7) is the Einstein function for a single oscillator [see deLigny etal, 1996].

84

Chapter 3

o

Figure 3.14 - Boson peak of SiO2 glass and polymorphs. See Richet et al. [2003] for data sources. The slight boson peak of stishovite likely results from small amounts of an amorphous SiO2 phase in the natural sample investigated by Holm et al. [1967].

CO

a.

o

in O

T, K

reported vibrational density of states. Graphical integration of the g(v)cv(T) functions indicates that only modes with frequencies lower than 200 cm"1 really contribute to C below 50 K. These low-frequency modes involve either weak bonds or motion of a large number of atoms. As such, they are probes of medium-range order. Indeed, it is only in this temperature range that a dependence of C on the thermal history of the glass has been detected: the heat capacity is higher for samples with higher fictive temperatures and lower densities [e.g., Westrum, 1956; Richet et al, 1986; Perez-Encisco era/., 1997]. Near 0 K, the heat capacity of crystals is generally proportional to r 3 . This feature is simply accounted for by the Debye model that considers a crystal as an isotropic continuum in which longitudinal and transversal acoustic waves propagate with constant velocities. The constancy of C7T3 predicted by the Debye model at very low temperature is not borne out by the experimental data, however, which show instead a sharp maximum at temperatures below 50 K. In other words, the heat capacity is much greater and the number of low-frequency modes much higher than indicated by the Debye model. At low frequencies, there indeed exists a broad feature known as the boson peak, observed by inelastic neutron scattering or Raman spectroscopy. Its extent depends on thermal history and correlates with the magnitude of excess heat capacities, being higher for quenched than for annealed glasses [e.g., Ahmad et al., 1986]. It is often assumed that such deviation from the Debye model is typical of glasses and other disordered materials [e.g., Pohl, 1981]. But deviations have also been observed for crystalline materials. For example, the data for SiO2 polymorphs (Fig. 3.14) clearly show that the anomaly can be still greater for a crystalline polymorph — cristobalite — than for SiO2 glass [Bilir etal., 1975]. The boson peak is almost nonexistent for stishovite and, among phases with 4-fold coordinated Si, it is smallest for coesite, the densest phase. Qualitatively, the explanation is the same as for the C decreases resulting from the change of Si (and Ge) from 4- to 6-fold coordination described in the previous section. Lengthening of Si-0 (and Ge-O) bonds leads to lower vibrational frequencies for Si-0 stretching modes, but this effect is overwhelmed by the increases of the frequencies of lattice modes such that the boson peak becomes much smaller. Similar trends are observed for other crystalline silicates. The magnitude of the boson peak decreases with decreasing degree of

Glasses and Melts vs. Crystals

85

Figure 3.15 - Boson peak of forsterite (Mg 2 Si0 4 ), enstatite (MgSiO3) and MgSiO3 glass. Similar results are observed for geikielite (MgTiO3). Data from Robie et al. [1982, 1989], Richet etal. [1993b] and Krupka et al. [1985].

polymerization as illustrated by the SiO2 polymorphs (Fig. 3.14) and enstatite and forsterite (Fig. 3.15). It is for such depolymerized structures that atomic disorder is required to cause boson anomalies as observed for MgSiO3 glass. Many general interpretations have been proposed for the boson peak. For SiO2 glass, Buchenau et al. [1986] concluded from neutron scattering and C measurements that it is essentially due to coupled librations of the corner-shared SiO4 tetrahedra (at 0.3 - 4 THz frequencies). This interpretation has been confirmed by hyper-Raman scattering measurements [Hehlen et al., 2000]. It agrees with the observation that the boson peak is most intense for three-dimensional open networks. It is less clear why disorder is needed to produce these low-frequency excitations for depolymerized structures like those of pyroxenes, apart from the general fact that a distribution of bond angles and distances and the existence of defect structures necessarily widen the vibrational density of states on the low-frequency side. Phenomenologically, however, the negligible C differences found between anorthite and CaAl2Si20g glass [Robie et al., 1978] indicate great structural similarity that extends to medium-range order. A similar conclusion probably holds true for cordierite and Mg2Al4Si5018 glass [de Ligny et al., 1996]. In contrast, there exists a large C difference between albite and NaAlSi3Og glass (Fig. 3.9) which also points to stronger association with Al for alkali than for alkaline earth cations and possibly to different topologies in albite and NaAlSi3O8 glass. This conclusion is consistent with the structural interpretation discussed in Chapter 9. 3.2d. Configurational Entropy The residual entropy of a glass, 5(0), is the configurational entropy frozen in at the glass transition. As apparent in Fig. 2.19, this entropy represents a small difference between the large variations of the melt and crystal entropies from the melting point to 0 K. As such, it is sensitive to the various structural features discussed in previous sections. But an important difficulty is that S(0) can be determined by calorimetric means only for a small number of compositions because the entropy cycle necessarily involves fusion of a congruently melting compound. Available data are summarized in Table 3.2 where results for other related glass-forming oxides are included.

86

Chapter 3 Table 3.2. Residual entropy of glasses, S (0), and entropy of Ca<=>Mg or Si<=>Al disordering, 5 / Sg(0)

J/mol K B2O3 GeO2 SiO2 CaSiO3 CaMgSi2O6 MgSiO3 NaAlSiO4 NaAlSi3O8 KAlSi3O8 CaAl2Si208 Mg3Al2Si3O12 Mg2Al4Si5O18

11.2(0.8) 6.6(1.1) 5.1(1.2) 8.8(2) 23.0(4) 11.2(5) 9.7(2) 36.7(6) 28.3(6) 36.8(4) 56.3(13) 94.0(13)

Sd

J/g atom K 2.24(0.16) 2.20(0.37) 1.70(0.4) 1.76(0.4) 2.30(0.4) 2.24(1.0) 1.38(0.3) 2.82(0.46) 2.18(0.46) 2.83(0.31) 2.81(0.65) 3.24(0.45)

J/g atom K

1.1 1.6 1.4 1.4 1.8 1.4 1.8

a

Calorimetric values as listed by Richet and Neuville [1992], de Ligny et al. [1996] and Richet et al. [2003] On a g atom basis, 5 (0) varies with composition by more than a factor of two. To examine these results, it is useful to split the configurational entropy in two parts [Richet and Neuville, 1992]. The first is topological and accounts for the distribution of bond angles and bond distances. It is specific to the amorphous state and varies in a complex manner with the melt composition. The second contribution to configurational entropy is termed chemical and is analogous to that of crystalline solid solutions where similar cations substitute for one another on sites of the structure. Even though such sites are less well defined in glasses than in crystals, at least to a first approximation one can assume that mixing is ideal and that the resulting entropy is given by ASm = -nR^xi\nxi,

(3.7)

where R is the gas constant and n the number of moles of atoms being mixed. As long as mixing is complete, this expression applies to mutual substitution of both networkmodifying cations, such as Na and K or Ca and Mg, and network-forming cations (Si, Al, B, Ti) within the anionic framework. When several substitutions take place simultaneously, an interesting feature is that, in analogy with the case of crystalline substitutions, equation (3.7) can be applied properly regardless of possible complexity of chemical composition [Weill et al, 1980]. The calorimetric data of Table 3.2 indicate that chemical and topological contributions are comparable in the glassy state. An interesting exception is NaAlSiO4 glass whose residual entropy is only 1.4 J/g atom K, a value lower than the 1.7 J/mol K found for pure SiO2 glass (Table 3.2). Now, the entropy of SiO2 glass represents a reference for that of other three-dimensional open networks because it is purely topological. Even if topological

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entropy were lower in NaAlSiO4 than in SiO2 glass, one concludes that these data leave little room for significant Si<=»Al disordering in the former [Richet et al, 1990]. As predicted by the Loewenstein avoidance principle, a 17O NMR study has indeed shown that the Si<=>Al distribution is highly ordered in NaAlSiO4 glass where there is less than 10% of Al-O-Al linkages [Lee and Stebbins, 2000]. In analogy with crystals, the ensuing question is how SioAl ordering in melts varies with temperature above the glass transition. Discussion of this question is postponed until the next section because another complexity must first be mentioned. It has to do with the fact that glasses and melts benefit from their disordered structures, which allow a variety of elements to coexist in a single phase over wide composition regions. Specifically, elements like boron and titanium likely mix with silicon only at high temperatures. Contrary to Al, they tend to form their own network at lower temperatures without, however, causing macroscopic phase separation. As a result, the distinction between chemical and topological entropy becomes blurred and their estimation still more difficult. The point to be stressed here is that topological entropy raises major difficulties in thermodynamic modeling. It cannot be estimated because only part of the structural entities that mix have been identified, and its evaluation would remain a very difficult theoretical problem even if the structure of the melt were known exactly. This problem is compounded by the fact that the relative importance of topological entropy increases with temperature whenever cation mixing is complete at the glass transition, in which case chemical entropy as given by equation (3.7) is constant. As described in section 2.3d, the possibility of determining configurational entropies from analyses of viscosity data thus represents a valuable source of thermochemical and structural information. 3.3. Liquid-Like Character of Crystals Crystals are often considered to be perfect up to their melting point. Of course, the existence of point defects or dislocations is acknowledged, but it is rightly held that, however important these defects may be for plasticity or atomic diffusion, they are of little relevance to phase equilibria and thermodynamic properties. What is less well known is that high temperatures generally confer a specific liquid-like character to a crystal. This feature is linked to some kind of atomic mobility and can have significant thermodynamic implications. As a complement to analyses of low-temperature properties, which bring information on static structural features, a review of high-temperature properties throw some light on the dynamics of phases and especially on the energetics of these processes. In this section our purpose is, therefore, to take advantage of the simplicity afforded by the existence of long-range order in crystals to derive some information on atomic mobility in melts. 3.3a. Glass-Like Transitions The most conspicuous effect is the actual glass transition observed in plastic, or glassy crystals, which are good examples of disordered systems with three-dimensional long-

88

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Figure 3.16- Temperature dependence of the degree of inversion, x, revealing the glass-like transition of hercynite (FeAl2O4). The arrow indicates the decrease of x caused by relaxation on annealing near 900 K. Data of Harrison etal. [1998].

range order. These crystals are characterized by a low entropy of fusion and a unusually high plasticity. They possess weakly bonded molecular groups whose orientation can change around the lattice points at higher temperatures, but become frozen in on cooling [Suga and Seki, 1974]. These transformations are phenomenologically similar to the glass transition. Instead of relating a liquid to a crystal, Kauzmann's paradox involves in this case metastable and stable crystals. The familiar ice I polymorph is probably the most common glassy crystal. Its residual entropy of 3.4 J/mol K [Haida et al., 1974] results from a random orientation of the hydrogen bonds linking different H2O molecules into H4O tetrahedra in the hexagonal lattice defined by the oxygen atoms. The large bond strength differences that allow some molecular groups to reorient freely do not generally exist in silicates. Although one cannot exclude that some hydrous minerals might behave as glassy crystals, the important point is that the common orderdisorder reactions involving cations should also follow the same phenomenology. The best documented transition concerns hercynite (FeAl2O4) spinel. It will be described in some detail as an example of observations that might be made for silicates. In spinels, the divalent cation, A (e.g., Fe, Mg), and trivalent cation, B (e.g., Al, Cr), distribute themselves over one tetrahedral site and two octahedral sites in an approximately cubic close-packed arrangement. Accordingly, the general formula A ^ B ^ A ^ B J .^2)2O4 can be written, where the parentheses indicate those cations that occupy octahedral sites. The degree of inversion, x, varies from 0 for ordered, "normal" spinels, to 2/3 for a random cation distribution, and even to 1 for "inverse", ordered spinels where all A cations occupy a tetrahedral site. For FeAl2O4, Harrison et al. [1998] found that x varies strongly with temperature (Fig. 3.16). The measurements were made on heating on a sample that had first been rapidly quenched to room temperature. On reheating, x remained constant at about 0.13 as long as the relaxation kinetics for the ordering reaction were slow. Relaxation set near 800 K when x began to decrease and approached the equilibrium value. Within the timescale of the experiment, equilibrium was reached from about 900 K, above which x increased steadily. Conversely, the data of Fig. 3.16 show that the partially disordered Fe/Al cation distribution over the two kinds of crystallographic sites was frozen in at about 980 K during the initial quench of the sample. For FeAl2O4, calorimetric measurements are lacking to evaluate the thermal effects of this transition. For MgAl2O4, in which

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Figure 3.17- Configurational heat capacity of MgAl2O4 spinel approximated by the difference between the heat capacity of the mineral and the values calculated from summation of the data for MgO and A12O3 [Richet and Fiquet, 1991]. similar changes in the degree of inversion take place [e.g., Maekawa et al., 1997], the data plotted in Fig. 3.17 suggest an excess C of only 6 and 8 J/mol K at 1100 and 2000 K, respectively. In silicates, cation order-disorder is a common kinetically controlled transformation. The reactions involving divalent cations in olivines and pyroxenes are cases in point which have long been investigated [e.g., Mueller, 1967; Virgo and Hafner, 1972]. Experimentally, the problem encountered here is that the kinetics of such process are generally either very fast or very slow because relaxation times vary strongly with temperature. In the latter case, the transition temperature does not change much with cooling rate. As a result, it is difficult to quench crystals with different structural states or to measure the rate of cation exchange among the crystallographic sites of the structure. Neutron and x-ray diffraction measurements have, nonetheless, revealed variations in site occupancies with temperature [Akamatsu and Kumazawa, 1993; Artioli et al., 1995; Henderson et al., 1996; Schlenz et al., 2001]. The important result is that the cation distributions measured under ambient conditions represent those frozen in on cooling and differ from the distributions prevailing at higher temperatures. If configurational heat capacities are small, then residual entropies of partially disordered crystals do not depend appreciably on thermal history. For ice, for instance, 5(0) varies by only 0.06 J/mol K between samples quenched rapidly and those equilibrated at 89 K [Haida et al., 1974]. By assuming ideal mixing, one finds that the effect would be more significant for hercynite, with residual entropies of 7.4 and 6.5 J/mol K for quenched (x - 0.134) and annealed samples (JC = 0.112), respectively. No such data are available for olivines or pyroxenes because the range of structural states that can be preserved on quenching is not well known. But it is tempting to conclude that, because of intrinsic atomic mobility in the liquid state, disordering should be effective in melts for network modifier cations whenever charge and ionic radius constraints are satisfied. As shown in previous chapter, the existence of mixed alkali and mixed alkaline earth effect on viscosity is consistent with this view. From an entropy standpoint, the other important case is that of order-disorder reactions involving network-forming cations. It is beyond our scope to review the important literature devoted to this subject, especially for Si<=>Al ordering in crystals whose kinetics can be neither too fast nor too slow in temperature ranges of present interest [e.g., Dove et al.,

90

Chapter 3 Table 3.3. Thermodynamics of cc-p transitions and of fusion of tectosilicates T, Quartzb Cristobalite Carnegieite

a b

847 525 966

a-P transition AH, AS, 0.65 1.32 8.10

0.76 2.50 8.38

Tf 1700 1999 1799

fusion AHf 9.4 8.9 21.7

ASf 5.5 4.5 12.1

Data in K, J/mol and J/mol K, from Richet et al. [1982] and Richet and Mysen [1999]. Small transition effects because of extensive premonitory effects.

1996]. What is relevant for this discussion is that variations of Si^^Al ordering are associated with large entropy and heat capacity changes. As already mentioned, the two limiting cases are complete order, at low temperature, and complete disorder at high temperature; the possible intermediate situation of obeyance to the Loewenstein avoidance principle lies in between. For albite (NaAlSi3O8), these three cases correspond to configurational entropies of 0,18.7 and 12.6 J/mol K, respectively, as calculated with the assumption of ideal mixing. The prevalence of order-disorder reactions in the crystalline state leaves no doubt as to their existence and to a likely larger extent in glasses and melts. Little is known, however, about the temperature and composition dependences of Sk=>Al ordering although information on the extent of Al-O-Si bonding (and B-O-Si bonding as well) is being obtained by NMR spectroscopy [Lee and Stebbins, 2003; Du and Stebbins, 2003]. A case in point is NaAlSiO4 glass whose residual entropy is lower than that of pure SiO2 glass, as mentioned in the previous section. Because SIAL disorder necessarily prevails at high temperature, the disordering process should contribute to the configurational C of the melt, and more specifically, to its strong temperature dependence [Richet et al., 1990]. 3.3b. CC—ft Transitions

Although a - p transitions occur in only a few tectosilicates such as SiO2 and NaAlSiO4 polymorphs, they deserve attention because they represent strong evidence for extensive oxygen dynamics in crystalline silicates. These transitions are reversible and their enthalpy changes seem modest but, since transition temperatures can be rather low, the entropy changes represent high fractions of entropies of fusion (Table 3.3). The importance of structural rearrangements occurring at the transition is borne out by the considerable broadening of bands in the Raman spectra (Fig. 3.18). This is especially the case for the spectral features near 400 cm"1, which involve extensive oxygen motion, whereas the changes observed for high frequency modes, representing mainly Si-0 stretching vibrations, can be assigned to rigid tetrahedra in a constant averaged environment. This dynamic nature of P-cristobalite is also borne out by the strong similarity of its low-frequency Raman spectra with that of SiO2 liquid close to its melting temperature [Richet and Mysen, 1999].

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Figure 3.18- Raman spectra of cristobalite and carnegieite on both sides of a - p transitions [Richet and My sen, 1999]

Cristobalite has been studied extensively. It has long been recognized that the structure of the (3-phase is a dynamic average. Averaging could be made over a-type domains [Hatch and Ghose, 1991], but the dynamics more likely result from free rotation of rigid SiO4 tetrahedra caused by precession of Si-0 bonds with respect to their average orientation [Swainson and Dove, 1995; Dove et al, 1997]. Once the dynamics has set in at the oc-|3 transition, little energy is required in view of the insensitivity of potential energy surfaces to changes in O-Si-O angles. This agrees with the calorimetric data that do not point to significant configurational heat capacity for cristobalite (Fig. 3.19). In other words, the important result is that the onset of atomic mobility at the a-|3 transition through movement of oxygen atoms entails similar entropy variations as disappearance of long-range order at the melting point.

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Figure 3.19 - Heat capacity of the Pphases of SiO2 and NaAlSiO4; see Richet and My sen [1999] for data sources. The Dulong and Petit limit of 3 R/g atom K is shown as a reference to reveal configurational heat capacities.

As indicated by molecular dynamics simulations, another interesting feature is that the dynamics can be related to the existence of three slightly different crystal structures between which P-cristobalite keeps switching [Bourova et al, 2000]. With its higher density, quartz has sharper interatomic potentials and has only two such structures for its P-phase. As for coesite, oxygen motion is less extensive and sets in without any a-P transition because there is only one possible structure for this dense polymorph [Bourova et al., 2004]. That the number of possible configurations is much reduced at high pressure is also shown by the fact that, in contrast to the situation at ambient pressure where several polymorphs are found, coesite is the only known high-pressure SiO2 polymorph with tetrahedral Si coordination. Owing to the structural similarities of cristobalite with SiO2 glass, the configurational entropy of amorphous SiO2 should thus decrease at high pressure. Structurally, carnegieite can be considered as a stuffed derivative of cristobalite. An interpretations similar to that presented for cristobalite should obtain for its a-P transition, with the difference that the heat capacity of P-carnegieite is anomalously high, being from 5 to 20% higher than the Dulong and Petit value (Fig. 3.19). Other configurational changes thus take place, which are superimposed on the dynamics of oxygen atoms. Consistent with the considerable broadening of the high-frequency features (Fig. 3.18) in the Raman spectra, which is not seen for cristobalite, these could be temperature-induced disordering of silicon and aluminum. Such disordering, which has been invoked in the previous section to account for the high temperature dependence of the heat capacity of NaAlSiO4 liquid [Richet et al, 1990], would take place to a lesser extent in nepheline, the other NaAlSiO4 polymorph (Fig. 3.19). 3.3c. Premelting Premelting represents perhaps the most conspicuous evidence for configurational changes in crystals. Macroscopically, premelting manifests itself as anomalous increases of the heat capacity when the melting temperature of a crystal is approached (Fig. 3.20). These begin from 80 to 250 K below the reported congruent melting points and are associated with enthalpy and entropy effects that represent from 7 to 22% of the enthalpies and

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Figure 3.20 - Premelting effects in calorimetric measurements. Mean heat capacity, Cm = (HT - H273)/(T - 273), of Na 2 Si0 3 (NS), CaMgGeO4 (CMG), diopside (Di, CaMgSi2O6), akermanite (Ak, Ca2MgSi07), pseudowollastonite (PsWo, CaSiO3), and anorthite (An, CaAl 2 Si 2 0 8 ). Data from Richet et al. [1994] and Courtial et al. [2000].

entropies of fusion [Courtial et al., 2000]. The reversible nature of the phenomenon as well as the lack of any microtextural differences between samples heated below and in the premelting range indicate that such anomalies are not due to partial melting of the crystal but to nonquenchable, temperature-induced configurational changes within a solid substance [Richet et al., 1994]. This is also consistent with the fact that premelting is not observed for minerals exhibiting oc-(3 transitions, for which such changes are activated at the transition temperature. At the scale of the unit-cell, x-ray diffraction experiments do not reveal anomalies in thermal expansion in the premelting range [Richet et al, 1996, 1998]. Since there is no evidence for anomalously high concentrations of crystal defects, which could affect molar volume, volume effects do not seem to contribute to the enthalpy anomalies shown by the calorimetric data. That these anomalies are associated with atomic disorder is clearly apparent in Raman spectra where considerable band broadening and loss of resolution are observed [Richet et al, 1996, 1998]. Anorthite is probably the mineral that has been subjected to the most thorough structural and calorimetric investigations after heat treatments at high temperatures. Samples show an increasing degree of Ak=>Si disorder when quenched from temperatures increasingly higher than 1670 K, whereas little effects are apparent after annealing below 1670 K where the disordering kinetics become very slow [Benna et al., 1985]. It is unlikely fortuitous that this temperature is the same as that of the onset of premelting [Richet et al, 1994]. Compared to completely ordered samples, anorthites quenched from 1800 K have an excess enthalpy of about 3 kJ/mol [Carpenter et al., 1990]. Including the premelting enthalpy, the total excess enthalpy at the melting point is about 13 kJ/mol. This number is smaller than the enthalpy differences of 15 kJ/mol which has been estimated between completely disordered and ordered samples [Carpenter et al, 1990]. Without the (unknown) entropy frozen in during quenches from 1800 K, the entropy of premelting represents 25% of the 23 J/mol K of complete, ideal Si<=>Al disordering. Hence, this process alone is more than sufficient to account for the observed calorimetric effects, which suggests that it should also contribute to the configurational heat capacity of aluminosilicate liquids.

Chapter 3

Figure 3.21 - Dynamics of silicate chains in the premeling range crystalline of Na2Si03 as indicated by 29 Si NMR spin echo spectra plotted for the indicated temperatures [George et al, 1998].

Disorder is also related to premelting of alkaline earth silicates or aluminosilicates. In this case, marked band broadening is observed only in the low-frequency part of Raman spectra, which involve mainly T-O-T bending and M-0 stretching and bending [Richet et al., 1998; Bouhifd etal., 2002]. Whereas the silicate framework is not affected much, the onset of premelting correlates with the temperature at which the self-diffusion of Ca begins to increase markedly in diopside [Dimanov and Ingrin, 1995], and that at which electrical conductivity rises sharply in pseudowollastonite and gehlenite [Bouhifd et al., 2002]. As discussed above, such cation mobility can give rise to glass-like transitions. And because premelting is even observed for compounds with a single or two different cations, it is likely that high-temperature disorder involves crystallographic sites that are not occupied at low temperature. The picture is somewhat different in the simple alkali silicates Na 2 Si0 3 and Li 2 Si0 3 [Richet et al, 1996], Changes in Raman spectra are strongest in the lowfrequency part where they are observed much below the premelting range. That Li, and especially Na are highly mobile is confirmed by "liquid-like" spin-lattice relaxation times determined by 7Li and 23Na NMR spectroscopy [George et ah, 1998]. Such high mobility involves exchange among many sites, without any disordering of silicon or oxygen positions, but it is not associated with any significant Cp anomaly. The onset of premelting correlates instead with structural rearrangements of the silicate chains, which, Figure 3.22 - Raman spectra of in turn, enhances alkali hopping and gives rise to a Na2Si03 solid and liquid near distribution of Q"-species in the crystal that prefigures the melting temperature of the melt structure. These structural changes manifest 1089°C. The individual bands themselves in NMR spectroscopy as variations in the that make up the high-frequency lineshapes of 29Si spin echo spectra, which become part of the spectra are shown in similar to those of a melt (Fig. 3.21). Likewise, the both cases [Richet et al, 1996].

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Raman spectra show an asymmetric broadening of the distribution of Si-O stretching mode frequencies. The similarity with the liquid is even such that the high-frequency Raman spectrum of Na 2 Si0 3 shows, in addition to the most intense band assigned to Q2-species, bands pertaining to the other Q"-species observed in the melt (Fig. 3.22). In this respect, the difference between Li 2 Si0 3 and Na 2 SiO 3 is that these configurational changes take place just before the congruent melting temperature and about 150 K below it for the former and the latter, respectively. Owing to the relatively small enthalpy cost of Na+ and Li+ diffusive motion in the solid state, most of the enthalpy of melting is associated with disruption of the silicate framework. Likewise, the configurational heat capacity of liquids should primarily correspond to further changes affecting the silicate entities, and thus should be associated with short-range siliconoxygen interactions in averaged alkali environments. At the end of this brief review, it may be useful to recall that the glimpses provided by high-temperature studies of crystals do not represent a comprehensive picture of atomic mobility in liquids and of the associated structural changes. Because of lack of longrange order, melts can sample a much wider configurational space than crystals. In particular, rare structural units in crystals could be common in melts. As a single example, temperature increases appear to induce a change to the unusual 5-fold coordination for a small fraction of the network-forming cations Si4+ and Al3+ [Stebbins, 1991; Stebbins and McMillan, 1993]. In spite of their usefulness, comparisons with crystals cannot be a substitute for direct structural investigations of glasses and melts. 3.4. Summary Remarks 1. In glasses and melts, it is often difficult to know in advance which structural features are relevant to a given physical property. When dealing with composition-property relationships, comparisons of glasses and melts with crystals thus provide useful information for either solid-like or liquid-like contributions. 2. Processes associated with important energy changes involve short-range order around cations. The standard vibrational entropy of glasses is mainly determined by the oxygen coordination polyhedra of the various cations of the structure. The composition dependence of S29g -So indicates that the oxygen coordination of alkaline earths does not change significantly when these cations become charge compensators for Al3+ in tetrahedral coordination, whereas that of alkali increases markedly. 3. Medium-range order involves subtler energy changes whose influence on heat capacity and entropy is observed only at very low temperatures. Medium-range order is less directly amenable to structural studies than short-range order. In this case, however, checks of calculated low-temperature heat capacities against the experimental data available for wide composition ranges represent one of the most stringent tests of the validity of structural models.

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4. Studies of crystals at high temperatures where these phases show a liquid-like character yield information on configurational changes in liquids. The great flexibility of Si-OSi bonds is attested by the dynamically average structures of the (3-polymorphs of SiO2. The prevalence of order-disorder reactions involving either network-forming or network-modifying cations is revealed by premelting effects. In melts, temperatureinduced S i o A l disordering should represent an important contribution to configurational heat capacity and entropy. References Ahmad N., Hutt K. W., and Phillips W. A. (1986) Low-frequency vibrational states in As2S3 glasses. J. Phys. C. Solid State Phys. 19, 3765-3773. Akamatsu T. and Kumazawa M. (1993) Kinetics of intracrystalline cation redistribution in olivine and its implication. Phys. Chem. Minerals 19, 423-430. Artioli G., Rinaldi R., Wilson C. C , and Zanazzi P. F. (1995) High-temperature Fe-Mg partitioning in olivine: In-situ single crystal neutron diffraction study. Amer. Mineral. 80, 197-200. Benna P., Zanini G., and Bruno E. (1985) Cell parameters of thermally treated anorthite. Al, Si configurations in the average structures of the high temperature calcic plagioclases. Contrib. Miner. Petrol. 90, 381-385. Bestul A. B. and Chang S. S. (1965) Calorimetric residual entropy of a glass. J. Chem. Phys. 40, 3731-3733. Bilir N. and Phillips W. A. (1975) Phonons in SiO2: The low-temperature heat capacity of cristobalite. Phil. Mag. 32, 113-122. Bouhifd M. A., Gruener G., Mysen B. O., and Richet P. (2002) Premelting and calcium mobility in gehlenite (Ca2Al2Si07). Phys. Chem. Minerals 29, 655-662. Bourova E., Parker S. C., and Richet P. (2000) Atomistic simulations of cristobalite at high temperatures. Phys. Rev. B62, 12052-12061. Bourova E., Parker S. C , and Richet P. (2004) High-temperature structure and dynamics of coesite (SiO2) from numerical simulations. Phys. Chem. Minerals 31, 569-579. Brawer S. A. and White W. B. (1975) Raman spectroscopic investigation of the structure of silicate glasses. I. The binary silicate glasses. J. Chem. Phys. 63, 2421-2432. Buchenau U., Prager M., Nucker N., Dianoux A. J., Ahmad N., and Phillips W. A. (1986) Lowfrequency modes in vitreous silica. Phys. Rev. B34, 5665-5673. Carpenter M. A., Angel R. J., and Finger L. W. (1990) Calibration of Al/Si order variations in anorthite. Contrib. Mineral. Petrol. 104, 471-480. Cormack A. N. andDu J. (2001) Molecular dynamics simulations of soda-lime-silicate structures. J. Non-Cryst. Solids 293-295, 283-289. Courtial P., Tequi C , and Richet P. (2000) Thermodynamics of diopside, anorthite, pseudowollastonite, CaMgGeO4 olivine and akermanite up to near the melting point. Phys. Chem. Minerals 27, 242-250. de Ligny D., Westrum E. F., Jr, and Richet P. (1996) Entropy of calcium and magnesium aluminosilicate glasses. Chem. Geol. 128, 113-128. Dimanov A. and Ingrin J. (1995) Premelting and high temperature diffusion of Ca in synthetic diopside: An increase of the cation mobility. Phys. Chem. Minerals 22, 437-442.

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Dove M. T., Keen D. A., Hannon A. C, and Swainson I. P. (1997) Direct measurements of the SiO bond length and orientational disorder in the high-temperature phase of cristobalite. Phys. Chem. Minerals 24, 311-317. Dove M. T., Thayaparam S., Heine V., and Hammonds K. D. (1996) The phenomenon of low AlSi ordering temperatures in aluminosilicate framework structures. Amer. Mineral. 81,349-362. Du L. S. and Stebbins J. F. (2003) Nature of silicon-boron mixing in sodium borosilicate glasses: A high-resolution "B and 17O NMR study. J. Phys. Chem. 107, 10063-10076. Etchepare J. (1972) Study by Raman spectroscopy of crystalline and glassy diopside. In Amorphous Materials (ed. R. W. Douglas and E. Ellis), pp. 337-346. Wiley-Interscience. FurukawaT., Fox K. E., and White W. B. (1981) Raman spectroscopic investigation of the structure of silicate glasses. III. Raman intensities and structural units in sodium silicate glasses. J. Chem. Phys. 153, 3226-3237. Galeener F. L., Leadbetter A. J., and Stringfellow M. W. (1983) Comparison of the neutron, Raman, and infrared vibrational spectra of vitreous SiO2, GeO2 and BeF r Phys. Rev. B27, 1052-1078. George A. M., Richet P., and Stebbins J. F. (1998) Cation dynamics and premelting in lithium metasilicate (Li2Si03) and sodium metasilicate (Na2Si03): A high-temperature NMR study. Amer. Mineral. 83, 1277-1284. Gibbs G. V., Boisen M. B., Hill F. C, and Tamada O. (2000) Search for a connection among bond strength, bond length, and electron-density distributions. In Physics Meets Mineralogy: Condensed-Matter Physics in Geoscinecs (eds. H. Aoki, Y. Syono, and R. J. Hemley), pp. 83123. Cambridge University Press. Gibbs G. V., Meagher E. P., Newton M. D., and Swanson D. K. (1981) A comparison of experimental and theoretical bond length and angle variations for minerals and inorganic solids, and molecules. In Structure and Bonding in Crystals (eds. M. O'Keefe and A. Navrotsky), pp. Ch. 9. Academic Press. Gillet P., Le Cleac'h A., and Madon M. (1990) High-temperature Raman spectroscopy of the SiO2 and GeO2 polymorphs: Anharmonicity and thermodynamic properties at high-temperature. J. Geophys. Res. 95, 21635-21655. Haida O., Matsuo T., Suga H., and Seki M. (1974) Calorimetric study of the glassy state. X. Enthalpy relaxation at the glass transition temperature of hexagonal ice. J. Chem. Therm. 6, 815-825. Harrison R. J., Redfern S. A. T., and O'Neill H. S. C. (1998) The temperature dependence of the cation distribution in synthetic hercynite (FeAl2O4) from in-situ neutron structure refinements. Amer. Mineral. 83, 1092-1099. Hatch D. M. and Ghose S. (1991) The a-(3 phase transition in cristobalite, SiO2. Phys. Chem. Minerals 17, 554-562. Hazen R. M. and Finger L. W. (1982) Comparative Crystal Chemistry: Temperature, Pressure, Composition, and the Variation of Crystal Structure. Wiley and Sons. Hehlen B., Courtens E., Vacher R., Yamanaka A., Kataoka M, and Inoue K. (2000) Hyper-Raman scattering observations of the boson peak in vitreous silica. Phys. Rev. Lett. 84, 5355-5358. Henderson C. M. B., Knight K. S., Redfern S. A. T., and Wood B. J. (1996) High-temperature study of octahedral cation exchange in olivine by neutron powder diffraction. Science 271, 1713-1715. Holland T. J. B. (1989) Dependence of entropy on volume for silicate and oxide minerals: A review and a predictive model. Amer. Mineral. 74, 5-13.

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Holm J. L., Kleppa O. J., and Westrum E. R, Jr (1967) Thermodynamics of polymorphic transformations in silica. Thermal properties from 5 to 1070°K and pressure-temperature stability fields for coesite and stishovite. Geochim. Cosmochim. Ada 31, 2289-2307. Hovis G. L., Roux J., and Richet P. (1998) A new era in hydrofluoric acid solution calorimetry; Reduction of required sample size below ten milligrams. Amer. Mineral. 83, 931-934. Isard J. O. (1959) Electrical conduction in the aluminosilicate glasses. J. Soc. Glass Technol. 43, 113-123. Ispas S., Benoit M., Jund P., and Jullien R. (2001) Structural and electronic properties of the sodium disilicate glass Na2Si4O9 from classical and ab initio molecular dynamics simulations. Phys. Rev. B64, 214206-1-9. Kittel C. (1996) Introduction to Solid State Physics. John Wiley & Sons. Kohara S., Suzuya K., Takeuchi K., Loong C. K., Grimsditch M., Weber J. K. R., Tangeman J. A., and Key T. S. (2004) Glass formation at the limit of insufficient network formers. Science 303, 1649-1652. Krupka K. M., Robie R. A., Hemingway B. S., Kerrick D. M., and Ito J. (1985) Low-temperature heat capacities and derived thermodynamic properties of antophyllite, diopside, enstatite, bronzite, and wollastonite. Amer. Mineral. 70, 249-260. Lee S. K. and Stebbins J. F. (2000) Al-O-Al and Si-O-Si sites in framework aluminosilicate glasses with Si/Al=l: Quantification of framework disorder. J. Non-Cryst. Solids 270, 260-264. Lee S. K. and Stebbins J. R (2002) Extent of intermixing among framework units in silicate glasses and melts. Geochim. Cosmochim. Ada 66, 303-309. Loewenstein W. (1954) The distribution of aluminum in the tetrahedra of silicates and aluminosilicates. Amer. Mineral. 39, 92-96. Maekawa H., Kato S., Kawamura K., and Yokokawa T. (1997) Cation mixing in natural MgAl2O4 spinel: A high-temperature 27A1 NMR study. Amer. Mineral. 82, 1125-1132. Mueller R. R (1967) Model for order-disorder kinetics in certain quasi-binary crystals of continuously variable composition. J. Phys. Chem. Solids 28, 2239-2243. Navrotsky A. (1997) Progress and new directions in high temperature calorimetry revisited. Phys. Chem. Minerals 24, 222-241. Navrotsky A., Geisinger K. L., McMillan P., and Gibbs G. V. (1985) The tetrahedral framework in glasses and melts — Inferences from molecular orbital calculations and implications for structure, thermodynamics, and physical properties. Phys. Chem. Minerals 11, 284-298. Pauling L. (1929) The principles determining the structure of complex ionic crystals. J. Amer. Chem. Soc. 51, 1010-1026. Perez-Encisco E., Ramos M. A., and Vieira S. (1997) Low-temperature specific heat of different B2O3 glasses. Phys. Rev. B56, 32-35. Pohl R. O. (1981) Low-temperature specific heats of glasses. In Topics in Current Physics, Vol. 24 (ed. W. A. Phillips), pp. 27-52. Springer Verlag. Richet P. and Bottinga Y. (1986) Thermochemical properties of silicate glasses and liquids: A review. Rev. Geophys. 24, 1-25. Richet P. and Fiquet G. (1991) High-temperature heat capacity and premelting of minerals in the system MgO-CaO-Al2O3-SiO2. J. Geophys. Res. B96, 445-456. Richet P. and Neuville D. R. (1992) Thermodynamics of silicate melts. Configurational properties. In Thermodynamic Data; Systematics and Estimation., Vol. 10 (ed. S. K. Saxena), pp. 132-161. Springer, New York. Richet P. and My sen B. O. (1999) High-temperature dynamics in cristobalite (SiO2) and carnegieite (NaAlSiO4): A Raman spectroscopy study. Geophys. Res. Lett. 26, 2283.

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Richet P., Robie R. A., and Hemingway B. S. (1986) Low-temperature heat capacity of diopside glass: A calorimetric test of the configurational entropy theory as applied to the viscosity of liquid silicates. Geochim. Cosmochim. Ada, 50, 1521-1533. Richet P., Robie R. A., Rogez J., Hemingway B. S., Courtial P., and Tequi C. (1990) Thermodynamics of open networks; ordering and entropy in NaAlSiO4 glass, liquid, and polymorphs. Phys. Chem. Minerals 17, 385-394. Richet P., Leclerc R, and Benoist L. (1993a) Melting of forsterite and spinel, with implications for the glass transition of Mg2SiO4 liquid. Geophys. Res. Lett. 20, 1675-1678. Richet P., Robie P. A., and Hemingway B. S. (1993b) Entropy and structure of silicate glasses and melts. Geochim. Cosmochim. Ada 57, 2751-2766. Richet P., Ingrin J., Mysen B. O., Courtial P., and Gillet P. (1994) Premelting effects in minerals: An experimental study. Earth Planet. Sci. Lett. 121, 589-600. Richet P., MysenB.O., and AndraultD. (1996) Melting and premelting of silicates: Raman spectroscopy and X-ray diffraction of Li2Si03 and Na2Si03. Phys. Chem. Minerals 23, 157-172. Richet P., de Ligny D., and Westrum E. F. J. (2003) Low-temperature heat capacity of vitreous GeO2 and B2O3: Thermophysical and structural implications. J. Non-Cryst. Solids 315, 20-30. Robie R. A., Haselton H. T., Jr, and Hemingway B. S. (1989) Heat capacities and entropies at 298.15 K of MgTiO3 (geikielite), ZnO (zincite) and ZnCO3 (smithsonite). J. Chem. Therm. 21, 743-749. Robie R. A., Hemingway B. S., and Takei H. (1982) Heat capacities and entropies of Mg2Si04, Mn2Si04, and Co2SiO4 between 5 and 380 K. Amer. Mineral. 67, 470-482. Robie R. A., Hemingway B. S., and Wilson W. H. (1978) Low-temperature heat capacities and entropies of feldspar glasses and of anorthite. Amer. Mineral. 63, 109-123. Robinson G. R. and Haas J. L., Jr. (1983) Heat capacity, relative enthalpy, and calorimetric entropy of silicate minerals: An empirical method of prediction. Amer. Mineral. 68, 541-553. Schlenz H., Kroll H., and Phillips M. W. (2001) Isothermal annealing and continuous cooling experiments on synthetic orthopyroxenes: Temperature and time evolution of Fe,Mg distribution. Eur. J. Mineral. 13, 715-726. Schramm C. M., DeJong B. H. W. S., and Parziale V. F. (1984) 29Si magic angle spinning NMR study of local silicon environments in-amorphous and crystalline lithium silicates. J. Amer. Chem. Soc. 106, 4396-4402. Sokolov A. P., Kisliuk A., Soltwisch M., and Quitmann D. (1993) Low-energy anomalies of vibrational spectra and medium range order in glasses. Physica A 201, 295-299. Stebbins J. F. (1991) Experimental confirmation of five-coordinated silicon on a silicate liquid structure: A multi-nuclear, high temperature NMR study. Science 255, 586-589. Stebbins J. F. and McMillan P. (1993) Compositional and temperature effects on five coordinated silicon in ambient pressure silicate glasses. J. Non-Cryst. Solids 160, 116-125. Stolper E. M. and Ahrens T. J. (1987) On the nature of pressure-induced coordination changes in silicate melts and glasses. Geophys. Res. Lett. 14, 1231-1233. Suga H. and Seki M. (1974) Thermodynamic investigation on glassy states of pure simple compounds. J. Non-Cryst. Solids 16, 171-194. Sugawara T. and Akaogi M. (2003) Calorimetric measurements of fusion enthalpies for Ni2Si04 and Co2SiO4 olivines and application to olivine-liquid partitioning. Geochim. Cosmochim. Ada 67, 2683-2693. Sugawara T. and Akaogi M. (2004) Calorimetry of liquids in the system Na2O-Fe2O3-SiO2. Amer. Mineral. 89, 1586-1596.

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Swainson I. P. and Dove M. T. (1995) Molecular simulation of a- and (3-cristobalite. J. Phys., Cond. Mat. 7, 1771-1778. Tangney P. and Scandolo S. (2002) An ab initio parametrized interatomic force field for silica. J. Chem. Phys. 117, 8898-9904. Tangney P. and Scandolo S. (2003) A many-body interatomic potential for ionic systems: Application to MgO. J. Chem. Phys. 119, 9673-9685. Taylor M. and Brown G. E. (1979) Structure of mineral glasses. II. The SiO2-NaAlSiO4 join. Geochim. Cosmochim. Acta 43, 1467-1475. Tequi C, Grinspan P., and Richet P. (1992) Thermodynamic properties of alkali silicates: Heat capacity of Li2Si03 and lithium-bearing melts. J. Amer. Ceram. Soc. 75, 2601-2604. Virgo D. and Finger L. W. (1972) Temperature-dependent Mg,Fe distribution in a lunar olivine. Earth Planet. Sci. Lett. 14, 305-312. Waff H. S. (1975) Pressure-induced coordination changes in magmatic liquids. Geophys. Res. Lett. 2, 193-196. Warren B. E. andPincus A. G. (1940) Atomic considerations of immiscibility in glass systems. J. Amer. Ceram. Soc. 23, 301-304. Weill D. F., Hon R., and Navrotsky A. (1980) The igneous system CaMgSi2O6-CaAl2Si2OgNaAlSi3Og: Variations on a classical theme by Bowen. In Physics of Magmatic Processes (ed. R. B. Hargraves). Princeton Universiy Press. Westrum E. F., Jr. (1956) The low-temperature heat capacity of neutron-irradiated quartz. Trav. 4ieme Congr. Int. Verre, Paris, 396-399. Westrum E. F, Jr, Barber S. W, and Labban A. K. (1989) Analysis and interpretation of morphology of heat capacity of silica and silicate glasses. In Proc. XVInt. Cong. Glass, Vol. la, Structure of Glass, Glass Formation, Glass Transition, Rheology. (ed. O. V. Mazurin). Nauka, Leningrad. Whittaker E. J. W. and Muntus R. (1970) Ionic radii for use in geochemistry. Geochim. Cosmochim. Acta 34, 945-957. Zachariasen W. H. (1932) The atomic arrangement in glass. J. Amer. Chem. Soc, 54, 3841-3851. Zigo O., Adamkovicova K., Kosa L., Nerad I., and Proks I. (1987) Determination of the heat of fusion of 2CaOAl203«Si02 (gehlenite). Chem. Papers 41, 171-181.

101

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Melt and Glass Structure Basic Concepts In this chapter, we will discuss in more detail bond lengths, bond angles, and bond strength common to all silicate melt and glass systems. We will also discuss how these parameters vary with chemical composition, and how properties of melts and glasses can be related to these variables. Data from specific chemical systems will be used to illustrate the general concepts. Details of property-structure relationships will be discussed in later chapters. 4.1. Bond Length, Bond Angle, and Bond Strength in Silicates The energetics of bonding are governed by the types of tetrahedra, their linkages, and the manner in which all polyhedra mix in the structure. These concepts, as well as some definitions and terms used here and elsewhere in the book, are discussed below. 4.1a. Basic Definitions and Concepts of Bonding A number of principles of bonding derived from crystal chemistry are also used in examination of properties and structure of melts and glasses. In crystal chemistry, one considers 4 basic types of bonds: ionic, covalent, van der Waals, and metallic. On the basis of our understanding of structure and energetics in melts and glasses, we will consider only ionic and covalent bonding. In a situation of pure ionic bonding one may consider that the individual cations have undeformable symmetry such that the interatomic distance, d, is simply the sum of the ionic radii of the two cations, r, and rf. (4.1)

d=ri + rJ.

The interaction between ions is purely coulombic with no shared electrons. Classic theory [Lewis, 1916] states that atoms are linked to form a molecule by sharing outer electrons in a purely covalent bond. In silicate systems, be they molten, glassy, or crystalline, - bonds are neither ionic nor covalent, but may be viewed as having a fractional ionic character where the fraction, / , depends on the structure and atoms involved. A number of definitions have been proposed. A common expression is that of Phillips [1970), f,= E?/(Ei

+

Ej),

(4.2)

102

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where £, and Ej are ionic energy gaps a n d / is the fractional ionic character. An earlier and commonly used definition is that of Pauling [I960]. He related the fractional ionic character to the electronegativity, Xt ar>d Xp °fthe two atoms in a bond: /i=l-exp[-l/4(x-^)]-

(4-3)

The electronegativity, %h is the tendency to attract electrons and has been defined in a number of ways [Mulliken, 1935; Gordy, 1946; Sanderson, I960]. A convenient operational definition is that of Sanderson [1960], X, = 35/4nrh

(4.4)

where S is the atomic number and r, is the covalent nonpolar radius. The concept of ionization potential is useful when describing melt and glass structure in terms of systematic relations to properties of the metal cations. In this book, we will use the definition, X{ = Z-Jr^

(4.5)

where Z, is formal electrical charge and r, is ionic radius. We must recognize, however, that this definition is one of convenience because it assumes that the bonding is fully ionic, - which it is not. Furthermore, because ionic radius depends on the number of ligands in a polyhedron of interest, ionization potential depends on the coordination number. 4.1b. Bond Strength, Bond Angle, and Composition A central feature of melt and crystal structure is bond strength, which is related ultimately to bond energy. Among the earliest to use this term, Pauling [1929] defined mean bond strength (S) as the ratio of the valence over coordination number. It is necessary, however, to consider the fact that most bonds have a partial covalent character. To this end, Donnay [1969] proposed the expression,

S =S r

{ r~j '

(4 6)

-

where S is the strength of a bond with length, /-,-, So is an ideal bond strength of length, r(-, and «j is a constant. A recent summary [Smyth and Bish, 1988] reveals that the electrostatic energy of metal-oxygen bonds - an expression of bond strength - tends to fall in reasonably welldefined ranges depending on the particular cation of interest and on the oxygen coordination number (Table 4.1). For a given coordination number, the site potential is

103

Melt and Glass Structure - Basic Concepts

Table 4.1. Site potential, oxygen coordination number, and cation types in minerals [data from Smyth and Bish, 1988]

a b

Cation

Coordination number

Al 3+ Al 3+ Al 3+ Ca 2+ Ca 2+ Ca 2+ Fe 2+ K+ K+ Mg 2+ Mg 2+ Na+ Na+ Na+ Si 4+

4 5 6 6 7 8 6 6 8 6 8 6 7 8 4

Ionic radius, Aa 0.47 0.56 0.61 1.08 1.15 1.20 0.69 1.46 1.59 0.80 0.97 1.10 1.21 1.24 0.34

Site potential energy range, eV b 105-166 111 92-117 33-50 37-83 38-51 46-107 8-19 7-12 47-77 49-50 4-17 14-34 14-18 145-207

From Wittaker and Muntus [1970] Site potential = electrostatic energy/electrical charge; eV = electron volt

positively correlated with the ionization potential of the metal cation. For a given metal cation, the site potential, or bond strength, decreases as the oxygen coordination number increases. Theoretical studies have shown that bond strength is a systematic function of bond distance (Fig. 3.1). The shorter a metal-oxygen bond, the greater is its strength [Pauling, I960]. For obvious geometrical reasons, metal-oxygen bond distances are a positive function of the oxygen coordination number. Everything else being equal, it follows that bond strength decreases when the oxygen coordination number increases. This simple view holds well for highly ionic crystals and led to Pauling's rules [Pauling, 1929], for example. These relationships become less clear in crystals with mixed ionic and covalent bonding [e.g., Gibbs et ah, 2000]. In other words, in silicate crystals where bonds often are significantly covalent, the relationship illustrated in Fig. 3.1 should be treated with some caution. The same caution likely applies to melts and glasses. The basic building block in silicate structure is the oxygen tetrahedron. This tetrahedron may be treated as a near-rigid unit regardless of the extent of polymerization of the tetrahedra [e.g., Hazen and Finger, 1982]. In crystalline silicate structures, bond length variation is accommodated by changes in intertetrahedral angle. Such relationships have been observed in naturally occurring minerals [e.g., Brown et ah, 1969] and shown in model calculations [e.g., Gibbs et ah, 1981; Poole et ah, 1995]. In the simulations in

104

Chapter 4

Fig. 4.1 bond length is negatively correlated with intertetrahedral angle [see also Gibbs et al, 1981; Poole et al, 1995]. This relationship is similar to that observed in the crystal structures of natural silicates and aluminosilicates (Fig. 4.2) and inferred for aluminosilicate glasses [Taylor and Brown, 1979a]. The relationship between bond distance and intertetrahedral angle is particularly well illustrated by numerical simulations of the potential energy surface for H 6 Si 2 0 7 clusters (Fig. 4.1). The minimum of this energy surface follows a broad line (shaded in Fig. 4.2) that correlates decreasing bond angle with increasing bond length in the silicate tetrahedra. An increase in pressure has a similar effect (Fig. 4.3). The energy surfaces derived from H 6 Si 2 0 7 clusters qualitatively resemble those at ambient pressur, but for a given T-0 bond distance, the intertetrahedral angle (T-O-T angle) is smaller. In other words, the bond distance is more sensitive to bond angle at high than at ambient pressure. The greater compressibility of molten and glassy silicates compared with their crystalline equivalents [e.g., Levien et al, 1980; Seifert et al, 1983] may result from greater flexibility of intertetrahedral, Si-O-Si, angle and, therefore, of Si-0 bond length [Seifert et al, 1983; Kubicki and Lasaga, 1987]. It should also be noted that in silicate structures that contain bridging oxygens, variations in intertetrahedral angles may also be driven by changes in the number of oxygen bridges, whether for silicate minerals [e.g., Liebau, 1981] or for silicate glasses and melts [e.g., Soules, 1979; Furukawa et al., 1981]. While the proportion of oxygen bridges decreases, the intertetrahedral angle becomes larger.

Figure 4.1 - Relationships between bond distance, Si-O, and intertetrahedral bond angle, Si-O-Si, calculated for H6Si207 clusters [Gibbs et al., 1981; Poole et al, 1995].

Melt and Glass Structure - Basic Concepts

105

Figure 4.2 - Relationships between bond distance, T-0 (T = Si,Al), and intertetrahedral bond angle, T-O-T, for natural silicate and aluminosilicate minerals [Brown etal, 1969].

4.2. Network-Formers At low pressure, silicates - whether crystalline, glassy, or molten - consist of a network of SiO 4 tetrahedra in which Si 4+ may be partially replaced by other cations that have a similar ionic radius, r, and a formal electrical charge, Z, of about 4. As described in the previous chapter, cations of this type are referred to as network-formers. Bond lengths and bond angles (and, therefore, bond strength) depend not only on pressure and temperature but also on the nature of the tetrahedrally coordinated cations, T. This bond length can vary perhaps by as much as 10%. This variation is often governed by substitution of Si 4+ by other tetrahedrally coordinated cations such as Al3+ whose ideal Al-0 length is -1.71 A as compared with -1.60 A for Si-0 [e.g., Navrotsky et al, 1985].

Figure 4.3 - Relationships between bond distance, Si-O, and intertetrahedral bond angle, Si-O-Si, calculated for HeSi2C>7 clusters at ambient pressure (dashed lines) and at 1 GPa (solid lines) [Meagher et al., 1980; Ross and Meagher, 1994].

106

Chapter 4

Figure 4.4 - Sodium-23 NMR spectra of Na2Si2O5 and NaAlSieOu glasses [Lee and Stebbins, 2003a].

Other cations potentially in 4-fold coordination with oxygen are Fe 3+ , B 3 + , and P 5+ . Substitution of these cations for Si 4+ , however, requires charge-balance (sometimes also termed "charge-compensation") via close association with other cations to obtain a formal charge near 4+ at the tetrahedral site. 4.2a. Charge-Balance of Network Formers The concept of charge-balance of certain tetrahedrally coordinated cations illustrates the dual structural roles played by alkali metals and alkaline earths. One role is to serve as network-modifiers. In this sense, these cations are linked to terminal oxygens in a tetrahedral network. The other role is to charge-compensate cations such as B 3+ , Al 3+ and possibly Fe 3+ in tetrahedral coordination. For trivalent cations (Al3+ and B 3+ ), this can be accomplished with alkalis or alkaline earths. For P 5+ the situation is more complex. In highly polymerized, silica-rich glasses and melts, one oxygen double-bonded to P may serve this purpose. Another common charge-compensation for tetrahedrally coordination P + is via Al-phosphate complexing. The most prevalent substitution is Al 3+ for Si4+. Simple charge-balance is obtained when the proportion of charge-balancing cation(s) is equal to, or in excess of, that required for this purpose. When there is an excess of alkali metal or alkaline earth over that required to provide a formal charge of 4+ for Al in tetrahedral coordination, the system is called

Figure 4.5 - Sodium-23 chemical shift of glasses along the SiCh-NaAlCh join against Al/(A1+Si) [Lee and Stebbins, 2003a].

Melt and Glass Structure - Basic Concepts

107

"peralkaline". When the proportion of alkali metal or alkaline earth is exactly equal to that required to provide a formal charge of 4+ for Al in tetrahedral coordination, the system is termed "meta-aluminous". When the proportion of Al exceeds that of available cations for charge-balance, the system is called "per-aluminous". Evidence exists for this dual structural role of alkali metals and alkaline earths in silicate glass and melt. Results from recent molecular orbital calculations suggest that the Na-NBO (NBO: nonbridging oxygen) bond is shorter than Na-BO (BO: bridging oxygen) distances and that Ca-NBO distances are shorter than Ca-BO distances [Uchino and Yoko, 1998; Cormack and Du, 2001; Ispas et al, 2002; Cormier et al, 2003]. For Na+, for example, such a difference in bond distance is likely to cause more electronic deshielding of the Na nucleus as the proportion of Na-NBO bonds increase. In Al-free glasses, the Na nucleus becomes more deshielded with increasing Na/Si, which is consistent with the Na-NBO distance increasing with increasing Na/Si [Xue and Stebbins, 1993; Lee and Stebbins, 2003a]. That prediction agrees with recent 23Na NMR data for binary Na2O-SiO2 glasses and ternary meta-aluminosilicate glasses along the SiO2-NaAlO2 join [Xue and Stebbins, 1993; Lee and Stebbins, 2003a] (Fig. 4.4). Lee and Stebbins [2003a] concluded from their 23Na NMR data that the Na-NBO distance might be as

108

Chapter 4

much as 10% longer than the Na-BO distance although the exact relationship to shielding of the Na nucleus also depends on Na/Si and Al/(A1+Si) of the glasses. For glasses with the same Na/Si ratio with Na+ serving to charge-balance A l + , the Na chemical shift increases (Na becomes more deshielded) with increasing Al/(A1+Si) (Fig. 4.5). As far as deshielding is concerned, however, there remains a distinct difference between Na as a charge-balancing cation and Na as a network-modifier. 4.2b. Aluminum Substitution X-ray radial distribution (XRDF) analysis is useful to determine T-O, T-T, and O-O bonds lengths (T = tetrahedrally coordinated cation) and may be used to map bond lengths to distances reaching several coordination spheres. Such features are well illustrated by xray radial distribution functions of meta-aluminosilicate glasses. The x-ray radial distribution functions of glasses along the SiO 2 -NaAlO 2 join do exhibit, for example, significant similarity to at least 3 A, which is the approximate distance between the central T-cations of 2 neighboring tetrahedra. This similarity may even extend to the 2 nd coordination sphere (Fig. 4.6). Taylor and Brown [1979a] concluded that the gradual evolution of the spectra of glasses along the SiO 2 - NaAlO 2 join was consistent with random substitution of Al3+ for Si 4+ in the structure. From these x-ray data, they extracted an average T-0 bond length that increases systematically with increasing Al/(A1+Si) (Fig. 4.7). This increase is consistent with the generally slightly longer Al-0 bond length compared with Si-0 bonds in the oxygen tetrahedra deduced from observations on natural

Figure 4.7 - Bridging oxygen distance (T-O T, T=Al,Si) along the SiO2-NaAlO2 join from analysis of the x-ray radial distribution functions of glasses [Taylor and Brown, 1979a, b].

Figure 4.8 - Full width at half height of ^ Si peak from 29Si MAS NMR spectra against Al/(A1+Si) of glasses along the joins SiO2NaA102 and SiO2-CaAl2O4, and for KAlSi3O8 [Murdoch etal., 1985].

Melt and Glass Structure - Basic Concepts

109

Figure 4.9 - X-ray radial distribution functions of CaAl2Si2Os and NaAlSiC>4 glass (solid lines) and of anorthite and nepheline (dashed lines) [Taylor and Brown, 1979a, b]. aluminosilicate crystals [Brown et al., 1969] and from theoretical considerations [Geisinger etal., 1985;Tossell, 1993]. The ionization potential [as defined by equation (4.5)] of the charge-balancing cation can affect the extent of Al<=>Si ordering in melts and glasses [Seifert et al., 1982; Lee and Stebbins, 1999]. For example, whereas they have similar ionic radii [Whittaker and Muntus, 1970], Ca2+ and Na + charge-balance 2 and 1 tetrahedrally coordinated A l + , respectively. This effect is seen quite clearly in the electron density around Al-O bonds in crystals like nepheline and anorthite [Tait et al., 2003; Angel, 1988]. In anorthite, at least one of the Al-O bonds is severely underbonded, presumably reflecting the steric problems associated with Ca2+ charge-compensation of Al + in the crystal structure. Similar structural restrictions likely exist in aluminosilicate glasses and melts as suggested, for example, the systematic relationship between 29Si NMR line width and ionization potential of the charge-balancing cation in glasses along the joins SiO2-NaAlO2, SiO 2 -KAlO 2 , and SiO 2 -CaAl 2 O 4 [Murdoch et al., 1985; Lee and Stebbins, 2003a]. Although this line width also depends on Al/(A1+Si), for a given Al/(A1+Si), it increases

no

Chapter 4

as the charge-balancing cation becomes more electronegative (K+, Na+, and Ca2+; see Fig. 4.8). These line width relationships are consistent with increasing Si<=>Al disorder with increasingly electronegative charge-balancing cations [see also Murdoch et al., 1985; Lee and Stebbins, 1999] As derived from x-ray radial distribution analysis, Al<=>Si ordering may also help explain why the structures of CaAl2Si208 and NaAlSiO4 glass differ. The T-0 radial distance of the first coordination sphere is approximately the same. However, the T-O radial distance to the second and third coordination spheres in the spectrum of CaAl2Si2Og glass is longer than for NaAlSiO4 (Fig. 4.9). The spectra in Fig. 4.9 suggest that there is longer-range order in CaAl2Si208 glass than in NaAlSiO4 glass [Taylor and Brown, 1979a, b]. Additional details of the structural behavior of Al3+ will be provided in Chapter 9. 4.2c. Other Tetrahedrally Coordinated Cations Ferric Iron: Ferric iron is frequently assumed to be tetrahedrally coordinated in silicate glasses and melts [Brown et ah, 1995], Tetrahedrally coordinated Fe3+ is consistent with the hyperfine parameters from Mossbauer spectroscopy of Fe3+-rich silicate glasses [Dingwell and Virgo, 1988]. Four-fold coordinated Fe3+ is also consistent with the x-ray radial distribution function of NaFeSi3O8 glass (Fig. 4.10). In the discussion of these data, however, Henderson et al. [1984] noted that the radial distribution function of NaFeSi3Og glass differs from that of the Al-bearing counterpart, NaAlSi3O8. They obtained a better fit by comparing the spectrum of NaFeSi3O8 with that of NaAlSiO4 glass (Fig. 4.10). In other words, the T-0 bond length in the ferrisilicate glass appears longer than that for an equivalent aluminosilicate glass. This observation is consistent with the likely longer bond distance found for H1Fe3+-0 than for [4]Al-0 [Redhammer, 1998; Okamura et al., 1974]. Considerable Si<=>Fe3+ ordering has been suggested, possibly with clusters of Fe + -0 tetrahedra in which there may not be any substitution of Si4+ for Fe + [Mysen et al., 1984; Alberto et al., 1996]. A detailed discussion of the role of iron in silicate glasses and melts is found in Chapter 11. Phosphorus: Phosphorus is a tetrahedrally coordinated cation in most Al-free silicate glasses or melts, even in the system SiO2-P2O5 where P=O bonding is observed in the

Figure 4.10 - X-ray radial distribution functions of NaFeSi3Os glass (solid line) and of nepheline (dashed line) [Henderson etal, 1984].

Melt and Glass Structure - Basic Concepts

111

Figure 4.11 - Phosphorus-31 MAS NMR spectra of glasses in the system Na2OAl 2 O 3 -SiO 2 + 3 mol % P2O5 for compositions indicated on individual spectra. Spinning sidebands marked with • [Cody etal, 2001].

phosphate tetrahedra [Shibata et al., 1981]. In alkali and alkaline earth silicate glasses and melts, phosphorus forms phosphate complexes with different degree of polymerization, NBO/P, where the value of NBO/P depends on P-content [Nelson and Tallant, 1984, 1986; Dupree, 1991; Kirkpatrick and Brow, 1995]. However, the very narrow bands associated with phosphorus in both the Raman and 31P NMR spectra of P-bearing alkali and alkaline earth silicate glasses suggest that these phosphate complexes form clusters in the structure. The behavior of phosphorus in aluminosilicate melts may differ from that in Al-free (or Al-poor) melts. The 31P NMR spectra of aluminosilicate glasses are quite broad and resemble those of Si in this respect (Fig. 4.11). It has been suggested that Al-phosphate complexes are distributed within the aluminosilicate melt structure [Cody et al., 2001]. These and other features of the role of phosphorus in melts and glasses are the subject of Chapter 13. Titanium: The structural information on Ti + in silicate glasses suggests that this cation may be in several different coordination states. Its complex structural behavior is such that systematic relationships between oxygen coordination and intensive and extensive variables have not as yet been developed. Available data do not suggest simple substitution for Si 4+ as discussed in Chapter 12. 4.2d. The NBO/T Parameter, Melt Structure, and Melt Composition The NBO/T (nonbridging oxygen, NBO, per tetrahedrally coordinated cation, T) can be calculated from melt composition, provided that the proportion of tetrahedrally coordinated cations is known from relevant structural information. A procedure for this purpose is given in Table 4.2. At present, this calculation can be conducted at comparatively low pressures for which the necessary information is available. At high pressures, such as in

112

Chapter 4 Table 4.2. Procedure for calculations of NBO/T from oxide composition at low pressures

Step 1

Convert chemical analyses (in wt %) to atomic proportions.

Step 2

T=Si+Al+Fe3+. Assign alkalis and alkaline earths to Al3+ and Fe3+ for chargebalance in tetrahedral coordination (relative stability of aluminate and ferrite complexes known from thermochemical data). The order of charge-balance is: K>Na>Ca>Fe2+>Mg and AlO2>FeO2".a

Step 3

Use formal charge of T-cations (4+) and oxygen (2-), which then gives NBO=(2O-4T) and NBO/T=(2O-4T)/T.

a

Note that Ti4+, P5+, and B3+ are not included in this calculation. See text for discussion of complex and variable structural role of these cations. the deeper portion of the Earth's upper mantle and below, this information is not necessarily available because both Si4+ and Al + may undergo partial or complete coordination transformation, under which circumstances the degree of melt polymerization changes [Xue et al., 1994; Yarger et al., 1995; Poe et al, 2001]. Thus, the NBO/T parameter as a structural monitor cannot be used with currently available data at high pressure. Knowledge of NBO/T is useful because a number of melt properties is correlated with NBO/T in a manner simple enough that predictions can be made. For example, in its simplest form, NBO/Si is positively correlated with high-temperature melt viscosity of simple binary metal oxide-SiO 2 melts [Mysen, 1995]. This is not surprising because in such compositionally simple melts, NBO/Si and alkali/silicon ratios are effectively equivalent, and melt viscosity is known to depend on the latter ratio [Bockris et al., 1955]. Relationships between NBO/T and melt viscosity may be extended to natural magmatic liquids at pressures and temperatures where the proportion of tetrahedrally coordinated cations can be calculated [Mysen, 1987]. Although there is considerable scatter in such relationships, the NBO/T can be a useful parameter in estimating semiquantitatively viscosity [Giordano and Dingwell, 2003]. Other parameters that seem related to degree of melt polymerization include activity-composition relations of major, minor, and trace elements in silicate melts [Mysen, 1995]. Therefore, the NBO/T can be used to express melt-composition dependence of mineral-melt element partitioning [Jana and Walker, 1997; Walter and Thibault, 1995; Toplis and Corgne, 2002]. 4.3. Network-Modifying Cations and Linkage between Structural Units Network-modifying cations link the silicate or aluminosilicate network units via bonding with nonbridging oxygen (Fig. 3.2). These cations are commonly referred to as networkmodifiers. For the most part, they are alkali metals or alkaline earths. It is also possible that Fe 2+ is in this category; but some uncertainty exists as to its exact role (see Chapter 11).

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113

Figure 4.12- -Sodium-23 NMR spectra of Na2Si2O5 and Na2SiO3 glasses [Lee and Stebbins, 2003a].

4.3a. The Nature of Nonbridging Oxygen Bonds For illustration purposes, the oxygen polyhedron is represented as an octahedron in Figs. 3.2 and 3.3. The number of ligands varies with the kind of network-modifying cations and generally increases with increasing ionic radius of the metal cation. In addition, the polyhedra may be significantly distorted as seen for CaO 6 polyhedra, for example, [Binsted et ah, 1985; Jones et ai, 2001]. It also appears that the metal-oxygen distances may differ depending on whether or not an alkali metal or alkaline earth is a network-modifier [Cormack and Du, 2001; Lee and Stebbins, 2003a]. Furthermore, low-temperature heat capacity data of alkali aluminosilicate glasses indicate that the oxygen coordination number around Na+, for example, depends on whether or not Al3+ is present in the structure [Richet etal, 1993]. Both the metal-nonbridging bonds and the Si-nonbridging oxygen bonds are likely affected by the electronic properties of the network-modifying metal cation. The structure of most melts and glasses consists of several different coexisting units, each with a different number of nonbridging oxygen to which metal cations are bonded (Qn-species). For a given metal cation, therefore, there may be an effect of melt and glass composition on metal-oxygen bonds. This effect has been documented for Na-0 bonding in Na 2 O-SiO 2 glass, for example [Lee and Stebbins, 2003a]. In the 23Na NMR spectrum of Na 2 SiO 3 glass, which contains about 60 mol % Q2 and 25-30 mol % Q 3 structural units [Maekawa et al., 1991; Buckermann et al., 1992], there is evidence for 2 peaks with different chemical shifts (Fig. 4.12). Because the Na nucleus is likely more deshielded the greater the Na/Si ratio [Maekawa etal., 1991; Xue and Stebbins, 1993; Lee and Stebbins, 2003a], the peak with the highest chemical shift in the 23Na spectrum can be assigned to Na-nonbridging oxygen bonds involving Q 2 units. The peak with the lower chemical shift is likely assigned to Na-nonbridging oxygen bonds from nonbridging oxygen in Q3 units. That suggestion is also consistent with the observation that the latter peak occurs at the same frequency as the main Na peak in Na 2 Si 2 O 5 glass where Q 3 structural units dominate. The Si-nonbridging oxygen bonds are also influenced by the type and proportion of network-modifying cation. Such effects are evident in Raman spectra of alkali and alkaline

114

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Figure 4.13 - Sodium-23 chemical shifts of peaks assigned to Q4, Q3, and Q2 in Na2O-SiO2 glasses against composition [Maekawa et al., 1991].

earth silicate glasses [Mysen and Frantz, 1994; Frantz and Mysen, 1995] indicating correlations between the force constants of Si-nonbridging oxygen bonds and ionization potential of the alkali metal or the alkaline earth. Similar conclusions were drawn by Jones et al. [2001] from 29Si NMR spectroscopy and by Ispas et al. [2002] from numerical simulation of Na 2 O-CaO-SiO 2 glass structure. This effect is shown more clearly in the 29 Si NMR chemical shift of Na 2 O-SiO 2 glasses (Fig. 4.13), which indicate that the Si nucleus in the Q4, Q 3 , and Q 2 units become more deshielded the higher the Na/Si [Lee and Stebbins, 2003a]. This relationship can also be inferred from the 29Si MAS NMR spectra of Li 2 O-SiO 2 , Na 2 O-SiO 2 , and K 2 O-SiO 2 glasses [Maekawa et al., 1991]. Interestingly, the Na/Si effect on the isomer shifts is greater for more polymerized Qn unit (Fig. 4.13). 4.3b. Ordering of Network-Modifying Cations Site preference is a common structural feature in silicate crystals. For example, in orthopyroxene and olivine, Fe 2+ and Mg 2+ are distinctly ordered between the Ml and M2 sites [Finger and Virgo, 1971; Hafner and Virgo, 1970]. If there exists energetically nonequivalent nonbridging oxygen in glasses and melts, one might likewise expect that distinct network-modifying cations exhibit a preference for specific nonbridging oxygens. The systematic relationship between ionization potential of metals and the width of liquid immiscibility gaps in metal oxide-SiO 2 melts [Hudon and Baker, 2002] may reflect such ordering phenomena. Among network-modifying cations, ordering would also influence activity-composition relations in silicate melts as inferred from liquidus phase relations, for example, [Kushiro, 1975;Ryerson, 1985] and configurational properties [Richetand Neuville, 1992] of metal oxide-SiO 2 systems. From a structural perspective, Jones et al. [2001] suggested that, in mixed Na 2 OCaO-SiO 2 glasses whose dominant Qn structural units are of Q and Q type, C a + shows

Melt and Glass Structure - Basic Concepts

115

a tendency to form Ca-oxygen bonds preferentially with nonbridging oxygen in the Q2 structural units, whereas Nanonbridging oxygen bonds are formed preferentially in Q3 structural units. This suggestion was further documented in triple quantum 17O NMR spectroscopy of glasses in the same system by Lee and Stebbins [2003b]. These experiments clearly distinguished oxygen associated only with Si4+ (bridging oxygen in Si-O-Si), with Na only (nonbridging Na-O), with Ca only (nonbridging Ca-O), and with a mixed (Na,Ca)-environment [nonbridging (Ca,Na)O] (Fig. 4.14). Although the 17O data do not offer information on where the various nonbridging oxygens exist in the silicate network, the data of Fig. 4.14 reflect ordering of Na+ and Ca2+ among different nonbridging oxygens in the glasses. In light of the similar ionic radius of Na+ and Ca2+, it is likely that this ordering results from different electrical charge. Analogous behavior has been observed for Mg2+ and Ba2+ in MgO-BaOSiO2 glasses and melts [Lee et al., 2002]. These structural interpretations suggest, therefore, that differences in ionic radius may also result in ordering of the networkmodifying cations among energetically nonequivalent nonbridging oxygens in the glasses and melts. 4.4. Bonding, Composition and Effects on Melt Properties Properties that are determined by bond strength depend on compositional variables such as Si/Al-ratio, for example. Substitution of Si4+ by cations such as Al3+ weakens the T-0 bond and, in turn, affects any property that depends on T-0 bond strength.

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Figure 4.15 - Activation enthalpy of viscous flow, AHA, as a function of Na2O content for high-temperature viscosity of melts in the system Na2O-SiO2 [Bockris et al., 1955],

4.4a. Viscous Flow Transport properties of silicate melts and glasses strongly depend on bond strength [e.g., Bockris and Reddy, 1970]. In particular, the energy required to break oxygen bonds in order to form melt entities that actually move finds its measure in activation energy of transport. Melt viscosity as a function of temperature and melt composition has been studied extensively. In early studies of high-temperature melt viscosity [e.g., Bockris etal., 1955], simple Arrhenius equations were fitted to the observations, viz • t) = r]oexp(AHJRT),

(4.7)

where f] is viscosity, r\0 a pre-exponential term, AH^ activation enthalpy, T temperature, and R the gas constant. This activation enthalpy is often a systematic function of silica content. For example, the high-temperature activation enthalpy of viscous flow for Na 2 OSiO 2 melts (Fig. 4.15) decreases rapidly from 600 kJ/mol near pure SiO 2 - similar to the Si-0 bond energy - to a nearly constant value for melts with Na 2 O contents higher than about 15 mol %. Similar relations hold - at least qualitatively - for other alkali and alkaline earth silicate melts [Bockris etal., 1955, 1956]. In binary alkali silicates, there is also an effect, albeit smaller, of the nature of the metal cation on AHV which decreases by 50 kJ/mol from K to Li. The relationships of Figs. 4.15 and 4.16 are consistent with breakage of bridging SiO-Si bonds as an important structural control of viscous flow at high temperature (i.e., well above the glass transition) with a lesser effect of alkali- or alkaline earth-oxygen bonding on the properties. In fact, this was the assumption made by Bockris and Reddy [ 1970], when deducing melt structure from physical properties. They built a melt-structure model based on bond strength considerations where they envisioned a small number of coexisting structural units with different Si/O-ratios. This concept is consistent with current views of the structure simple silicate glasses and melts.

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117

Figure 4.16 - Activation enthalpy of viscous flow, AH^, from hightemperature viscosity of M2Si03 melts (M = K, Na, Li) as a function of ionization potential, Z/r2, of metal cation [from Bockris et al., 1955]. Ionization potential calculated for M in 6-fold coordination with ionic radii from Whittaker and Muntus [1970].

The Al-0 bond strength in silicate crystals with tetrahedrally coordinated A13+ is, on average, between 50 and 75% of that of the Si-0 bond (see Table 4.1). The exact value of Al-O bond strength depends on details of the local charge compensation around the tetrahedrally coordinated Al 3+ . That notwithstanding, activation enthalpy of hightemperature viscous flow of meta-aluminosilicate melts is a negative function of the Al/ (Al+Si) of the melt [Riebling, 1964, 1966; Neuville, 1992; Toplis et al., 1997a]. This feature is illustrated in Fig. 4.17 for SiO2-NaAlO2 melts at ambient pressure. Hence, the AH^ decreases monotonously with increasing Al/(A1+Si). Note, however, that for peralkaline melts with constant M/[Si+(MAl)], the high-temperature activation enthalpy of viscous flow is not only less sensitive to Al/(Al+Si), but may actually have a parabolic form as a function of Al/(Al+Si). Further complexity in relationships between viscosity and melt composition is introduced when the ratio of alkalis or alkaline earths relative to

Figure 4.17 - Activation enthalpy of viscous flow, AH^, from hightemperature viscosity of melts along the join NaAlO2-SiO2 at TIT% = 1.7 (solid line and solid symbols - data from Toplis et al., [1997a]) and along the join Na2Si2O5-Na2(NaAl)2O5 at 1200°C as a function of Al/(A1+Si) of the melts (dashed line and open symbols - data from Dingwell [1986]).

118

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Al is varied for melts with constant total SiO2 content. In the system Na2O-Al2O3-SiO2, for example, this composition change can be expressed as Na/(Na+Al) at constant total SiO2 content. As melts along such joins become increasingly aluminous, they also become more viscous with a maximum near, but not necessarily exactly at, Na/(Na+Al) = 0.5. The 0.5-value corresponds to meta-aluminosilicate (Fig. 4.19). For highly peraluminous melts, the viscosity actually decreases with decreasing Na/(Na+Al). It appears, therefore, that if viscous flow of aluminosilicate melts reflects relative strength of Si-O and Al-0 bonds, the influence of Al3+ in aluminosilicate melts is considerably more complex than might be expected from simple substitution of Al + for Si +. These matters are discussed in more detail in Chapter 8. 4.4b. Interrelationships of Transport Properties There exist relatively simple functional relationships between viscosity and other transport properties, such as diffusivity and electrical conductivity. For example, the Nernst-Einstein equation may be used to relate conductivity of component, A,, to diffusivity, Dt [Nernst, 1888; Einstein, 1905; see also Mott and Gurney, 1940], (4.8)

X, = f-ZpjkT,

where F is Faraday's constant, Z, the electric charge of ion i, and k Boltzmann's constant. The diffusivity can be related to viscosity via the Stokes-Einstein equation [Einstein, 1905], (4.9)

rj = kT/6nriDh where r, is the radius of the moving particle. In practical terms, the Eyring equation [Eyring, 1935a, b],

Figure 4.18- Viscosity, r\, of melts in the system Na2O-Al2O3-SiO2 at constant SiO2 content (mol %) as a function of Na/ (Na+Al) at 1596°C [Toplis etal., 1997b].

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119

Figure 4.19- Relationship between viscosity, T], and oxygen diffusion coefficient, D, for NaAlSi2O6 and CaMgSi2O6 melts at 1 GPa. Solid line shows calculated relationship between viscosity and diffusion coefficient from the Eyring equation [eqn. (4.10)] with jump distance, A=2.8A (about twice the ionic radius of O 2 ) [Shimizu and Kushiro, 1984].

r\ = kTlaPi,

where a, is the jump distance, is more useful than the Stokes-Einstein equation for silicate melts [Magaritz and Hofmann, 1978; Watson, 1979; Shimizu and Kushiro, 1984, 1991]. Its utility is to relate oxygen and silicon diffusion to melt viscosity. This is shown in Fig. 4.20 with the calculation made with a jump distance twice the ionic radius of O " (2.8A) for compositions such as NaAlSi2O6 and CaMgSi2O6. Hence, a case may be made that oxygen motion is an integral part of viscous flow. Self-diffusion of Si in SiO2-rich melts also seems to follow the Eyring equation [Watson, 1982; Watson and Baker, 1991; Baker, 1990], which makes intuitive sense because silicon motion in a melt is likely linked to oxygen motion.

Figure 4.20 - Diffusion coefficients of Ca, Mg, and Si as a function of composition in melts along the join NaAlSi2C>6-CaMgSi2O6 at 1550°C and 1 GPa [Shimizu and Kushiro, 1991].

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4.4c Thermochemistry and Bond Strength In solution calorimetry, one measures the change in enthalpy when a material is dissolved under conditions such that its atomic constituents become infinitely diluted in the solvent. Enthalpies of solution in an appropriate solvent, thus, represent a rather direct measure of average bond strength within a glass or a melt. From HF solution calorimetry at 25°C, Tischer [1969] and Ho vis et al. [2004) observed that for Na2O-SiO2 glasses quenched from 1300°C, the enthalpy of solution decreases as a systematic function of Na2O content (Fig. 4.21). This decrease may reflect decreasing abundance of Si-0 bonds with large bond strength and increasing abundance of Na-0 bonds with considerably smaller bond strength. In terms of site potential in crystals, these values are about an order of magnitude greater for Si-0 compared with Na-0 bonds (Table 4.1). When alkali aluminate components (KA1O2, NaA102, and LiAlO2) are mixed with SiO2 in a glass, the enthalpy of solution at 700°C in molten lead borate is also a systematic function of both the Al/ (Al+Si) of the glasses and the electronic properties of the different alkali metals that act as charge-compensators for Al + which substitute for Si4+ in the glass structure (Figs. 4.22 and 4.23). 4.5 Mixing, Order, and Disorder A number of properties clearly show that silicate glasses and melts are not random mixtures of components, but may be viewed instead as mixtures of structural entities that - at least at a local scale - resemble those of crystalline phases existing at or near their liquidus. For example, in a study of compressibility of vitreous SiO2 (Fig. 4.24) Vuckevitch [1972] observed anomalous temperature and pressure relations that he rationalized by proposing that two three-dimensionally interconnected SiO2 structures coexist. He suggested that such structures (denoted a and (3) were similar to a- and P-polymorphs of crystalline cristobalite. Likewise, the composition dependence of other properties such as index of refraction and viscous behavior has been used to suggest that discrete structural units exist in silicate

Melt and Glass Structure - Basic Concepts

Figure 4.22 - Enthalpy of solution of glasses along the joins SiO2-KAlO2, SiO2-NaAlO2, and SiO2-LiAlO2 as a function of their Al/(A1+Si) [Navrotsky et al, 1982; Roy and Navrotsky, 1984; Navrotsky etal., 1985].

121

Figure 4.23 - Enthalpy of solution of glasses along the joins SiC^-MAlCh and Si02-Mo.5A102 (M = Ba, Sr, and Ca) at Al/(A1+Si) = 0.25 against ionization potential for M in 6-fold coordination. Same data as in Fig. 4.22, with ionic radii from Whittaker and Muntus [1970].

glasses and melts [e.g., Babcock, 1968; Bockris and Reddy, 1970]. This concept also found support in the early success of the so-called pseudocrystalline model of melt structure [e.g., Burnham, 1975; Bottinga and Richet, 1978; Nekvasil and Burnham, 1987], and in models of crystal nucleation that assumed entities in the melt with a structure that resemble - at least at a local seal - that of the nucleating phase [Kirkpatrick, 1983]. Mixing of two or more structural entities, whatever their structural characteristics may be, affects melt and glass properties. 4.5a Viscous Flow and Mixing in Silicate Glass and Melt Application of the Adam and Gibbs [1965] configurational entropy theory of relaxation processes to viscosity was discussed in section 2.3d where emphasis was put on the effects of temperature and composition through the relevant variations of configurational entropy. Here, we will focus on the connection between bond strength and the potential energy barriers opposing viscous flow. The starting point is the expression derived by Adam and Gibbs [1965], BJf^iTJ

= z(Ts)AiJ/k,

(4.11)

122

Chapter 4

Figure 4.24 - Compressibility of SiC)2 glass as a function of (a) temperature and (b) pressure [Vuckevitch, 1972]. Note that the compressibility decrease above about 3 GPa may be because of irreversible densitification during the high-pressure experiments. where Tg is the glass transition temperature, z is the size of the smallest rearranging units in the liquid at the glass transition temperature, and A^u is the Gibbs free energy barrier opposing configurational rearrangements. From the rheological data available for simple binary alkali silicate melts, Toplis [1998] observed that BJ^°n\T^) decreases rapidly with increasing alkali content and reaches a constant value for melts with ~ 30 mol % or more Na2O (Fig. 4.25). He suggested, therefore, that a unique 5 e /5° onf (r g )-value may be assigned to individual metal oxides. His results for alkali metals in alkali tetrasilicate (M 2 Si 4 0 9 ) melts are shown in Fig. 4.26. It follows from those data that either the Gibbs free energy barrier, A^, or the size of the smallest rearranging units, z*(Tg) are negatively correlated with alkali content for compositions less alkali-rich than about 30 mol % oxide [Fig. 4.26; see also equation (4.11)]. For fixed alkali content, either of these two variables [A^and z*(Tg)] is positively correlated with the ionic radius of the alkali cation. Most likely, the dominant factor between the two is the energy barrier [Toplis, 1998]. The lowering of A/i is consistent

Figure 4.25 - Relationship between Be/Sconf(Tg) and composition in the system Na2O-SiO2 [Toplis, 1998]. See Chapter 2 for configurational entropy theory.

Melt and Glass Structure - Basic Concepts

123

Figure 4.26 - Relationship of BJScmf(Tg) and ionic radius of alkali metal in the systems Li2O-SiO2, Na2O-SiO2, K2OSiO2, Rb2O-SiO2 [Toplis, 1998].

with the observation (Table 4.1) that alkali-oxygen bond strengths are only about 1020% of that of Si-O bonds. The relationships between BjtfOT£{J^ and ionic radius of the alkali metal (Fig. 4.27) may be the result of the larger size of the alkali cation, for which more energy is thus required to cross the energy barrier. In a similar study of NaAlO 2 -SiO 2 glasses and melts, Toplis et al. [1997a] found that BJS*0" (Tg) is negatively correlated with Al/(A1+Si). Therefore, in analogy with the analysis of the variations of Be/SlConf(Tg) in alkali silicate melts, one concludes that the height of the energy barrier, A^u, is lowered as the system becomes more aluminous. This effect is reasonable given the premise that, with Si and Al in 4-fold coordination, the bond strength of the Al-Obond is lower than that of the Si-O bond (Table 4.1). Thus, the energy barrier associated with cooperative motion during viscous flow will also be lowered. 4.6. Summary Remarks 1. The structure of the silicate network in silicate melts and glasses can be described in terms of network-forming cations (Si4+, Al3+, and Fe3+) that form oxygen tetrahedra. These tetrahedra can be linked across bridging oxygen, or linked to different groups of oxygen tetrahedra via nonbridging oxygen that are bonded to both a tetrahedrally coordinated, network-forming cation and a network-modifying cation. 2. The dominant network-forming cation in most silicate glass and melt systems is Si +. Al 3+ may substitute for Si4+ on these structural locations. Ferric iron may also play such a role; whereas, when in tetrahedral coordination, other cations such as P 5+ (and possibly Ti4+ and B3+) likely form separate tetrahedral clusters. 3. Al and Fe + in tetrahedral coordination in the silicate network require chargecompensation, generally by alkali metals or by alkaline earths. The type of chargecompensation may govern the extent of S i o A l and S i o F e + ordering. 4. Alkali metals and alkaline earths serving either as a network-modifying cations or to charge-balance Al3+ are structurally different. 5. The oxygen coordination number of the network-modifying cations depends on the electronic properties of the cation and tends to increase with ionic radius of metal cation. These polyhedra tend to become more deformed with increasing ionization potential.

124

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6. In mixed alkali, alkaline earth (or both) silicate glasses and melts, there is ordering of the metal cations among energetically non-equivalent nonbridging oxygens. The most electronegative network-modifying cation tends to form oxygen polyhedra with nonbridging oxygen in the most depolymerized among coexisting Qn structural units. 7. Properties that are related to breakage and formation of bonds in unary, binary, ternary, and, perhaps, even chemically more complex glasses and melts are functions of composition. In binary metal oxide-silica melts, the SiO2 content is critically important. This importance can be related to differences in Si-O versus metal-O bond strength (which can reach an order of magnitude). Substitution of Si4+ by Al + leads to reduction in bond strength. Thus, many properties of aluminosilicate melts are directly related to their Al/(A1+Si). 8. Properties that are related to mixing behavior of components (or perhaps discrete species) are systematic functions of ordering parameters. These observations lead to the conclusion that silicate glasses and melts become increasingly disordered with decreasing SiO 2 content, with increasing A12O3 content, and with increasing electronegativity of alkali metals and alkaline earths. References Adam G. and Gibbs J. H. (1965) On the temperature dependence of cooperative properties in glass-forming liquids. J. Chem. Phys. 43, 139-146. Alberto H. V., Pinto da Cunha J. L., Mysen B. O., Gil J. M., and de Campos N. A. (1996) Analysis of Mossbauer spectra of silicate glasses using a two-dimensional Gaussian distribution of hyperfine parameters. J. Non-Cryst. Solids 194, 48-57. Angel R. J. (1988) High-pressure structure of anorthite. Amer. Mineral. 73, 1114-1119. Babcock C. L. (1968) Substructures in silicate glasses. J. Amer. Ceram. Soc. 51, 163-169. Baker D. R. (1990) Chemical interdiffusion in dacite and rhyolite: Anhydrous measurememnts at 1 atm and 10 kbar, application of transition theory, and diffusion in zoned magma chambers. Contrib. Mineral. Petrol. 104, 407-423. Binsted N., Greaves G. N., and Henderson C. M. B. (1985) An EXAFS study of glassy and crystalline phases of compositions CaAl2Si2Os (anorthite) and CaMgSi2O6 (diopside). Contrib. Mineral. Petrol. 89, 103-109. Bockris J. and O'M.Reddy A. K. N. (1970) Modern Electrochemistry. Plenum Press. New York. Bockris J., O'M.Mackenzie J. O., and Kitchener J. A. (1955) Viscous flow in silica and binary liquid silicates. Trans. Faraday Soc. 51, 1734-1748. Bockris J. O. M., Tomlinson J. W., and White J. L. (1956) The structure of liquid silicates. Trans. Faraday Soc. 52,299-311. Bottinga Y. and Richet P. (1978) Thermodynamics of liquid silicates, a preliminary report. Earth Planet. Sci. Lett. 40, 382-400. Brown G. E., Gibbs G. V., and Ribbe P. H. (1969) The nature and variation in length of the Si-0 and Al-0 bonds in framework silicates. Amer. Mineral. 54, 1044-1061. Brown G., E., Farges F., and Calas G. (1995) X-ay scattering and x-ray spectroscopy studies of silicate melts. In Reviews in Mineralogy (ed. J. F. Stebbins, P. F. McMillan, and D. B. Dingwell), pp. 317-410. Mineralogical Society of America. Washington DC. Buckermann W.-A., Muller-Warmuth W., and Frischat G. H. (1992) A further 29Si MAS NMR study on binary alkali silicate glasses. Glasstechn. Ber. 65, 18-21.

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Burnham C. W. (1975) Thermodynamics of melting in experimental silicate-volatile systems. Geochim. Cosmochim. Ada39, 1077-1084. Cody B. O., Mysen B. O., Saghi-Szabo G., andTossell J. A. (2001) Silicate-phosphate interaction in silicate glasses and melts. I. A multinuclear (27A1,29Si, 31P) MAS NMR and ab initio chemical shielding (31P) study of phosphorus speciation in silicate glasses. Geochim. Cosmochim. Ada 65, 2395-2312. Cormack A. N. andDu J. (2001) Molecular dynamics simulations of soda-lime-silicate glasses. J. Non-Cryst. Solids 293, 283-289. Cormier L., Ghaleb D., Neuville D. R., Delaye J.-M., and Calas G. (2003) Chemical dependence of network topology of calcium aluminosilicate glasses: a computer simulation study. J. NonCryst. Solids 332, 255-270. Dingwell D. B. (1986) Viscosity-temperature relationships in the system Na2Si2O5-Na4Al2Os. Geochim. Cosmochim. Ada 50, 1261-1265. Dingwell D. B. and Virgo D. (1988) Viscosities of melts in the Na2O-FeO-Fe2O3-SiO2 systems and factors-controlling relative viscosities in fully polymerized melts. Geochim. Cosmochim. Ada 52, 395-404. Donnay G. (1969) Further use for the Pauling-bond concept. Carnegie Instn. Washington, Year Book 68, 292-295. Dupree R. (1991) MAS NMR as a structural probe of silicate glasses and minerals. Trans. Amer. Cryst. Soc. 27, 255-269. Einstein A. (1905) Uber die von der molekular-kinetischen Theorie der Warme geforderte Bewegung von in ruhenden Flilssigkeiten suspendierten Teilchen. Ann. Phys. 17, 549-560. Eyring H. (1935a) The activated complex in chemical reactions. J. Chem. Phys. 3, 107-115. Eyring H. (1935b) The activated complex and the absolute rate of chemical reactions. Chem. Rev. 17, 65-77. Finger L. W. and Virgo D. (1971) Confirmation of Fe/Mg Ordering in olivines. Carnegie Instn. Washington, Year Book 70, 221-225. Frantz J. D. and Mysen B. O. (1995) Raman spectra and structure of BaO-SiO2, SrO-SiO2, and CaO-SiO2 melts to 1600°C. Chem. Geol. I l l , 155-176. FurukawaT., Fox K. E., and White W. B. (1981) Raman spectroscopic investigation of the structure of silicate glasses. III. Raman intensities and structural units in sodium silicate glasses. J. Chem. Phys. 153, 3226-3237. Geisinger K. L., Gibbs G. V, and Navrotsky A. (1985) A molecular orbital study of bond length and bond angle variations in framework structures. Phys. Chem. Minerals. 11, 266-283. Gibbs G. V., Meagher E. P., Newton M. D., and Swanson D. K. (1981) Acomparison of experimental and theoretical bond length and angle variations for minerals and inorganic solids, and molecules. Ch. 9 In Structure and Bonding in Crystals (ed. M. O'Keefe and A. Navrotsky), Academic Press. New York. Gibbs G. V., Boisen M. B., Hill F. C, and Tamada O. (2000) Search for a connection among bond strength, bond length, and electron-density distributions. In Physics Meets Mineralogy: Condensed-Matter Physics in Geosciences (ed. H. Aoki, Y. Syono, and R. J. Hemley), pp. 83123. Cambridge University Press. Cambridge. Giordano D. and Dingwell D. B. (2003) Viscosity of Etna basalt: Implications for Plinian-style eruptions. Bull. Volcan. 65, 8-14. Gordy W. (1946) A new method for determining electronegativity from other atomic properties. Phys. Rev. 69, 604-607.

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Gruener G., De Sousa Meneses D., Odier P., and Loup J. P. (2001) Influence of network on conductivity in ternary CaO-A^Ch-SiCh glasses and melts. J. Non-Cryst. Solids 281, 117-124. Hafner S. S. and Virgo D. (1970) Temperature-dependent cation distribution in lunar and terrestrial pyroxenes. Proc. 3rd Lunar. Sci. Conf., 2183-2198. Hazen R. M. and Finger L. W. (1982) Comparative Crystal Chemistry: Temperature, Pressure, Composition, and the Variation of Crystal Structure. Wiley and Sons, New York. Henderson G. S., Fleet M. E., and Bancroft G. M. (1984) An X-ray scattering study of vitreous KFeSi3O8 and NaFeSisOs and reinvestigation of vitreous SiCh using quasicrystalline modelling. J. Non-Cryst. Solids 68, 333-349. Hovis G. L., Toplis M. J., and Richet P. (2004) Thermodynamic mixing properties of sodium silicate liquids and implications for liquid-liquid immiscibility. Chem. Geol. 213, 173-186. Hudon P. and Baker D. R. (2002) The nature of phase separation in binary oxide melts and glasses. I. Silicate systems. J. Non-Cryst. Solids 303, 299-345. Ispas S., Benoit M., Jund P., and Jullien R. (2002) Structural properties of glassy and liquid sodium tetrasilicate: comparison between ab initio and classical molecular dynamics simulations. J. Non-Cryst. Solids 307, 946-955. Jana D. and Walker D. (1997) The influence of silicate melt composition on distribution of siderophile elements among metal and silicate liquids. Earth Planet. Sci. Lett. 150, 463-472. Jones A. R., Winter R., Greaves G. N., and Smith I. H. (2001) MAS NMR study of soda-limesilicate glasses with variable degrees of polymerisation. J. Non-Cryst. Solids 293-295, 87-92. Kirkpatrick R. J. (1983) Theory of nucleation in silicate melts. Amer. Mineral. 68, 66-78. Kirkpatrick R. J. and Brow R. K. (1995) Nuclear magnetic resonance investigation of the structures of phosphate and phosphate containing glasses: A review. Solid State Nucl. Magn. Res. 5, 3-8. Kubicki J. D. and Lasaga A. C. (1987) Molecular dynamics simulation of Mg2Si04 and MgSiCh melts: Structural and diffusivity changes with pressure. EOS, Trans. Amer. Geophys. Union 68,436. Kushiro I. (1975) On the nature of silicate melt and its significance in magma genesis: Regularities in the shift of liquidus boundaries involving olivine pyroxene, and silica materials. Amer. J. Sci. 275, 411-431. Lee S. K. and Stebbins J. F. (1999) The degree of aluminum avoidance in aluminum silicate glasses. Amer. Mineral. 84, 937-945. Lee S. K. and Stebbins J. F. (2003a) The distribution of sodium ions in aluminosilicate glasses: A high-field Na-23 MAS and 3Q MAS NMR study. Geochim. Cosmochim. Ada 67, 1699-1710. Lee S. K. and Stebbins J. F. (2003b) Nature of cation mixing and ordering in Na-Ca silicate glasses and melts. J. Phys. Chem B. 107, 3141-3148. Lee S. K., Stebbins J. F., Mysen B. O., and Cody G. D. (2002) The nature of polymerization in silicate glasses and melts: Solid state NMR, modeling and quantum chemical calculations (abstr.). Eos Trans. AGU, 83, 47. Levien L., PrewittC. T., andWeidnerD. J. (1980) Structure and elastic properties of quartz at high pressure. Amer. Mineral. 65, 920-930. Lewis G. N. (1916) The atom and the molecule. J. Amer. Chem. Soc. 38, 762-785. Liebau F. (1981) The influence of cation properties on the conformation of silicate and phosphate anions. In Structure and Bonding in Crystals (ed. M. O'Keeffe, A. Navrotsky) pp. 197-232. Academic Press. New York. Maekawa H., MaekawaT., Kawamura K., and Yokokawa T. (1991) The structural groups of alkali silicate glasses determined from 29Si MAS-NMR. J. Non-Cryst. Solids 127, 53-64. Magaritz M. and Hofmann A. W. (1978) Diffusion of Sr, Ba, and Na in obsidian. Geochim. Cosmochim. Ada 42, 595-605.

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Toplis M. J. andCorgne A. (2002) An experimental study of element partitioning between magnetite, clinopyroxene and iron-bearing silicate liquids with particular emphasis on vanadium. Contrib. Mineral. Petrol. 144, 22-37. Toplis M. J., Dingwell D. B., Hess K.-U., and Lenci T. (1997a) Viscosity, fragility, and configuration entropy of melts along the join SiO2-NaAlO2. Amer. Mineral. 82, 979-990. Toplis M. J., Dingwell D. B., and Lenci T. (1997b) Peraluminous viscosity maxima in Na2OA^Ch-SiCh liquids: The role of triclusters in tectosilicate melts. Geochim. Cosmochim. Ada 61, 2605-2612. Tossell J. A. (1993) A theoretical study of the molecular basis of the Al avoidance rule and of the spectral characteristics of Al-O-Al linkages. Amer. Mineral. 78, 911-920. Uchino T. and Yoko T. (1998) Structure and vibrational properties of sodium disilicate glass from ab initio molecular orbital calculations. J. Phys. Chem. B 102, 8372-8378. Vuckevitch M. R. (1972) A new interpretation of the anomalous properties of vitreous silica. J. Non-Cryst. Solids 11, 25-63. Walter M. J. and Thibault Y. (1995) Partitioning of tungsten and molybdenum between metallic liquid and silicate melt. Science 270, 1186-1189. Watson E. B. (1979) Calcium diffusion in a simple silicate melt to 30 kbar. Geochim. Cosmochim. Ada 43, 313-323. Watson E. B. (1982) Basalt contamination by continental crust: Some experiments and models. Contrib. Mineral. Petrol. 80, 73-87. Watson E. B. and Baker D. R. (1991) Chemical diffusion in magmas: An overview of experimental results and geochemical implications. In Crystal Chemistry of Magmas (eds. L. L. Perchuk and I. Kushiro), pp. 120-151. Springer. New York NY. Whittaker E. J. W. and Muntus R. (1970) Ionic radii for use in geochemistry. Geochim. Cosmochim. Ada 34, 945-957. Xue X. and Stebbins J. F. (1993) 23Na NMR chemical shifts and local Na coordination environments in silicate crystals, melts and glasses. Phys. Chem. Minerals 20, 297-307. Xue X., Stebbins J. R, and Kanzaki M. (1994) Correlations between 17O parameters and local structure around oxygen in high-pressure silicates: Implications for the structure of silicate melts at high pressure. Amer. Mineral. 79, 31-42. Yarger J. L., Smith K. H., Nieman R. A., Diefenbacher J., Wolf G. H., Poe B. T., and McMillan P. F. (1995) Al coordination changes in high-pressure aluminosilicate liquids. Science 270,1964-1966. Zachariasen W. (1932) The atomic arrangement in glass. J. Amer. Chem. Soc. 54, 3841-3851.

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Silica — A Deceitful Simplicity Silica is the commonest oxide on Earth with a mean abundance of about 37 wt % [Allegre et al., 1995]. The silica content increases from 40-50 wt % for fresh magma forming at depth to about 75 wt % in the Earth's crust where magmatic differentiation ends. Quartz precipitates when silica saturation in magma is reached, at typical contents of about 65 wt % under low-pressure conditions. Eventually, quartz tends to separate from other minerals that are altered more readily through subsequent weathering of silicic rocks. In this manner quartz becomes the main source of silica for ceramics and glasses, either as pure SiO 2 or as a major component of chemically more complex materials [e.g., Beall, 1994]. Whether for geochemical or industrial purposes, silica is the natural starting point to the study of silicates. Except for its simple chemical formula, SiO 2 , however, complexity is its hallmark. To start with, the rigid SiO4 tetrahedra that form at low pressure can assemble in a great many ways to build an open three-dimensional network. About 20 crystalline phases of SiO 2 have been identified [e.g., Sosman, 1965] whose mutual relationships are often not clearly understood yet [see Heaney, 1994]. Fortunately, only a few SiO 2 polymorphs are relevant to investigations of the structure and properties of SiO 2 glass and melt (Fig. 5.1). At low pressure, the liquidus phases observed at progressively higher temperatures are (3-quartz, tridymite, and (3-cristobalite. Tridymite has a very small stability field and its actual existence as an SiO 2 polymorph is still uncertain because its structure might need stabilization by trace amounts of other metal oxides [see Heaney, 1994]. When

Figure 5.1 - High-temperature and highpressure phase relations of SiCh- Calculations of Swamy et al. [1994] reproducing the melting results of Jackson [1976] and Zhang et al. [1993]. Tridymite is not shown (see text). The dashed curves picture the metastable extensions of the melting curves of quartz and coesite. Because of their negative slopes, both minerals become unstable with respect to an amorphous phase at high pressure and room temperature.

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pressure increases, (3-quartz becomes the high-temperature liquidus phase. Coesite is then stable between about 4 and 10 GPa (i.e., 40 and 100 kbar), before being succeeded by the denser stishovite and post-stishovite phases at even higher pressures. Numerous attempts have been made at determining which crystalline silica polymorph is the most closely related to amorphous silica. In particular, anomalies in properties observed near the temperatures of the a-[3 transitions undergone by the low-pressure SiO2 polymorphs have long been taken as evidence for such similarities [see section 1.4a and Goodman, 1987]. The sometime doubtful reality of these anomalies notwithstanding, such claims are difficult to sustain because the properties of amorphous silica can depend markedly on the impurity content of the sample [see Fanderlik, 1990]. As for other exceptional properties of SiO2, this influence of impurities originates in the unusual strength of the Si-0 bond combined to the ease of deformation of Si-O-Si angles (see Chapter 4). 5.1. An Outstanding Oxide The unusual properties of pure silica have long made melting of quartz quite difficult (see section 1.3c). As a matter of fact, the first viscosity measurements made by Volarovich and Leontieva [1936] showed that SiO2 is the most viscous liquid known and, consequently, has the highest standard glass transition temperature. It follows that investigation of molten SiO 2 is technically challenging. The intrinsic difficulties due to high-temperature experiments on a highly viscous melt are compounded by strong reactivity with contaminants present within the experimental setup. Without proper care, Mazurin et al. [1975], for instance, noted that the kinetics of silica crystallization "depend more on the appropriate properties of the refractories and heater material than on the properties of the investigated glass". Amorphous SiO 2 is, in fact, especially sensitive to impurity content as a very small fraction of nonbridging oxygens or other defects can have disproportionate effects on silica properties through breaking up of a fully polymerized structure. Such effects, due to impurity content and method of fabrication, have been reviewed by Bruckner [1970] and Fanderlik [1990]. 5.1a. The Archetypal Strong Liquid A viscosity comparison with molten GeO 2 and B 2 O 3 , two other glass-forming oxides, illustrates the remarkable properties of SiO2 liquid (Fig. 5.2a). Not only is there a very large viscosity increase from B 2 O 3 to GeO 2 and SiO 2 , but the deviation of viscosity from Arrhenian variations decreases markedly in the same order. A result of this evolution is that the activation enthalpies for viscous flow {AH ) of these melts differ much less near the glass transition than at high temperatures. In the terminology introduced by Angell [1985], molten silica is the archetype of a strong liquid, whereas B 2 O 3 has a definite fragile character. To compare the viscosity of liquids having widely different standard glass transition temperatures (Tg), Laughlin and Uhlmann [1972] introduced plots of log rj against the

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Figure 5.2 - Viscosity of molten glass-forming oxides, alumina and Mg2SiC>4 (Fo). (a) Against reciprocal temperature; the crystallization temperatures are indicated by arrows, (b) Against T/Tg; the extreme fragility of AI 2 O 3 liquid is shown by the data plotted with the two arbitrary values Tg = 1000 K (left) and 1500 K (right) which, by definition, join with the other sets at Tg/T = 1. Data for SiO2 from Urbain et al. [1982]; for GeC>2 from Fontana and Plummer [1966]; for B 2 O 3 from Napolitano etal. [1965] and Macedo and Napolitano [1968]; for A^ C h from Urbain [1982]; for Fo from Urbain et al. [1982], with values near Tg extrapolated from binary joins in the system MgOAI2O3-S1O2 investigated by Neuville [1992].

reduced temperature 7yT (Fig. 5.2b). In such a representation, the fragility,/, is defined as the viscosity gradient at Tg: f = d log r)l(.d{TgIT).

(5.1)

Then, no liquid indeed is known to be stronger (or less fragile) than molten silica. The other common oxide components of silicate melts either decompose before melting (alkali oxides) or are extremely poor glass formers (e.g., MgO, CaO, A12O3). At best, their viscosity-temperature relationships are known over restricted temperature intervals above their liquidus. As an example, the data for molten alumina included in Fig. 5.2 illustrate that other molten metal oxides are much less viscous than SiO2 and have smaller activation energies for viscous flow. Above 2000 K, the AHn is, for instance, 110 (5) and 515 (3) kJ/mol for A12O3 and SiO 2 , respectively, whereas extrapolations of measurements made along the CaO-Al2O3 join yield a value of 90 (1) kJ/mol for molten CaO [Urbain, 1983]. In accordance with these results, one observes that, when mixed with pure SiO2, other oxides systematically cause viscosity to decrease and fragility to increase (see also section 5.2d and Chapters 6 and 8). This is illustrated in Fig. 5.2 with the data for molten Mg 2 SiO 4 , which represents an extreme case of fragility for silicates. For the glass-forming oxides of Fig. 5.2, the obvious correlation between viscosity and melting temperature of the liquidus polymorph is consistent with the influence of bond strength on both properties (see section 4.4a). Although B-0 bonds are very strong, they make up BO 3 triangles in B 2 O 3 between which bonding is weak [Mozzi and Warren,

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1970]. The three-dimensional network of GeO2 is, by contrast, closely related to that of SiO2 [e.g., Konnert et al., 1973]. The viscosity difference of GeO2 and SiO2 stems essentially from lower ionization potential of Ge + compared with Si +. The bond strength-viscosity correlation also holds for predominantly ionic molten oxides such as alumina. There is an apparent anomaly, however, in that, despite weaker bond strength, corundum, lime, and periclase all melt at much higher temperatures than cristobalite. The reason is that, in view of the strong ionic character of these oxides, bonding lacks directionality so that the configurational rearrangements that cause melting require breaking of M-0 bonds. In contrast, the partially covalent nature of Si-0 bonds gives rise to a strong directionality within the SiO4 tetrahedra. This directionality is associated with great flexibility of Si-O-Si angles. Because Si-0 bonds do not need to be severed for configurational rearrangements to occur (see section 3.3b), melting is made possible at lower temperatures. 5. 1b. A Short Classification Depending on synthesis procedure, the most common types of SiO2 glass can be grouped in four categories [Hetherington and Jack, 1962; Bruckner, 1970, 1971]. The main distinction is made on the basis of water content (usually expressed as OH) because of markedly different effects of water on optical absorption spectra compared with metal oxides, and because the influence of water on SiO2 properties is often stronger than that of metal oxides at the same low concentration. Type I glass is prepared through electric melting of very pure natural quartz under vacuum or an inert atmosphere. The main impurities are aluminum (typically less than 50 ppm) and alkali metals (a few ppm). The OH content is less than 1 ppm. As fusion is generally performed in graphite crucibles, the reducing atmosphere causes silica to be slightly deficient in oxygen with an actual SiO2.x formula, where x ranges from 10"4 to 10 5 [Bell et al, 1962]. Effects of such a nonstoichiometry on silica properties have been described by Leko and Meshcheryakova [1975]. In the following, more attention will paid to water dissolved in two other types of SiO2 glass. In type II, the starting material is also natural quartz but melting is done in a flame as originally made by Gaudin [1839]. With respect to type I, the main difference of type II is an OH content of a few hundred ppm. The aluminum, alkali metals, and other element contents of type I and II are too high for some applications. These concentrations can be limited to less than 0.1 ppm in type III glasses, which are prepared by vapor-phase hydrolysis or oxidation of SiCl4. With values of the order of 0.1 wt %, the OH content is still higher than for type II, whereas the Cl concentration is about 100 ppm. To limit water intake in type IV glass, SiCl4 is oxidized in a plasma flame free of water vapor. The OH content is less than 1 ppm, but the Cl concentration reaches 200 ppm.

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5.7c. Phase Transitions: Melting and Amorphization At room pressure, Greig [1927] reported that cristobalite melts at 1713°C on the Geophysical Laboratory temperature scale. This value, which has been confirmed by Wagstaff [1969], translates to 1726°C on later international temperature scales [see Richet et al, 1982]. Because of the sluggish kinetics of the quartz-cristobalite transition, melting of quartz can also be observed [Mackenzie, 1960; Ainslie et al, 1961]. From Gibbs-free energy data [Richet et al, 1982] and extrapolation of the high-pressure melting curve to ambient pressure [Jackson, 1976; Zhang et al., 1993], the metastable room-pressure melting temperature of quartz is found to be about 1400°C [Bourova and Richet, 1998]. Cristobalite and quartz are unusual compounds in that both can be significantly superheated. For polycrystalline cristobalite and single-crystal quartz, superheating has been observed over 40 and 300 degrees intervals, respectively, during a few tens of minutes [Ainslie et al., 1961]. Melting is heterogeneous and propagates inward from the surface [Wagstaff, 1969]. At the temperatures of fusion of cristobalite and quartz, the viscosity of type I molten SiO2 is 1062 and 1088 Pa s, respectively [Urbain et al, 1982]. Albite (NaAlSi3O8), which also has a fully polymerized structure, is the only other silicate known to superheat [Dietz et al., 1970]. This mineral has been observed 40°C above its melting point of 1118°C, at which the viscosity of the liquid is 1069 Pa s [Urbain et al, 1982], which confirms that superheating is related to unusually high melt viscosity. The connection between high viscosity and glass-forming ability has already been described in section 2.3e. Viscosity is not, however, the single parameter controlling fusion and crystallization. Whereas NaAlSi3O8 has been kept for five years at 100°C below its melting temperature without showing any trace of crystallization [Schairer and Bowen, 1956], cristobalite crystallizes readily above 1350°C. Less extensive configurational rearrangements probably account for faster crystallization of cristobalite. As has long been known by glassmakers, the kinetics of this process are strongly enhanced by impurities such as water or even finger marks on glass pieces [Dietzel and Wickert, 1956; Wagstaff and Richards, 1966; Mazurin et al 1975]. Quartz does not form from SiO2 melt at room pressure. Its growth has only been observed at the surface of quartz grains that had first been amorphized by ion bombardment [Devaud et al., 1991 ]. At first sight, the low temperature of 83O°C of the quartz-cristobalite transition [Richet et al, 1982] should indeed prevent quartz from crystallizing. Crystallization of a metastable polymorph is, however, a common feature of silicates, so that the lack of quartz crystallization does point to greater structural similarity of SiO2 melt with cristobalite than with quartz. The same conclusion can be drawn from the fact that transformation of quartz to cristobalite takes place via an intermediate melting stage [Mackenzie, I960]. The reverse should hold true within the stability field of quartz where cristobalite does not form, whereas nucleation and growth of quartz depend on the same factors as described above for cristobalite in its own stability field [Fratello etal, 1980].

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For the high-pressure crystalline SiO2 polymorphs, coesite and stishovite, the melting temperature increases with pressure (Fig. 5.1). Both forms can be easily quenched to ambient conditions from their field of stability. When heated at room pressure, these metastable phases do not transform directly to quartz, the stable polymorph, but first to an amorphous phase. Amorphization can begin below 930°C for coesite [Dachille et al., 1963; Gong et al, 1996] and between 300 and 650°C for stishovite, at temperatures that increase with the quality of the sample [Skinner, 1963; Xue et al., 1993; Grimsditch et al., 1994]. Thermochemical considerations indicate that coesite should melt at 600°C, i.e., well below the standard glass transition of SiO2, whereas stishovite is unstable at any temperature with respect to amorphous SiO2 [Richet, 1988]. Clearly, these polymorphs amorphize instead of transforming to quartz because thermal energy is insufficient at such temperatures to overcome the potential energy barriers opposing the cooperative rearrangements needed for a crystal-crystal phase transition. Alternatively, amorphization can be induced by compression at room temperature. This was first observed for quartz and coesite compressed at a few tens of GPa [Hemley et al., 1988] and subsequently for a number of other silicates [see Richet and Gillet, 1997, for a more detailed discussion]. Again, the basic mechanism is that the kinetics of reconstructive structural transitions are much too low for Si to change from the 4-fold Si coordination of quartz and coesite to the 6-fold coordination of stishovite. Progressive amorphization proceeds instead to phases in which some remnants of crystalline order can still be found. Because any pressure-induced transformation necessarily involves a volume decrease, the amorphous phase is denser than the crystal at the pressure of the experiment. If one assumes a continuity between the volume of the melt, at high temperature, and that of the amorphous phase, it follows that the volume of melting of both quartz and coesite becomes negative and that the melting curve passes through a maximum at some high pressure (Fig. 5.1). 5.2. Physical Properties The physical properties of molten silica are still debated in spite of their basic importance. There is, however, more information than often realized. From available information, we will try to clarify the situation for thermal and volume properties as well as for viscosity. This discussion is, in particular, relevant to polyamorphism, a topic that is arousing much theoretical interest [Poole et al., 1997]. For molten sulfur and other liquids, polyamorphism is revealed by a first-order liquid-liquid transition. It has not been observed for molten silicates, possibly because it might occur in the supercooled liquid. If so, the critical point at which the liquid-liquid univariant equilibrium curve ends would be located below the liquidus. An example of this situation is provided by water, which exhibits a sharp transition near 70 K between two different amorphous phases [Mishima, 1984]. Structural analogy between water and silica has long been pointed out [e.g., Angell and Kanno, 1976]. Along with this analogy, computer simulations do suggest that metastable polyamorphism could exist in silica [e.g., Roberts and Debenedetti,

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Figure 5.3 - Low-temperature heat capacity differences between glasses and crystals. Coes: coesite; Cr: cristobalite; GeCh-Tet and -Hex: tetragonal and hexagonal forms of GeCh; Qu: quartz; St: stishovite. See Richet et al. [2003] for data sources and a discussion of the Cp difference apparent for B2O3, which is due to the existence of boroxol rings in only the glass.

1996; Hemmati etal, 2001]. Anomalous variations of the heat capacity, thermal expansion coefficient, and compressibility of amorphous SiO 2 could be macroscopic evidence of such a transformation [Poole et al. 1997]. Attention will thus be paid to features suggestive of polyamorphism in this section. One should keep in mind, however, that an almost infinite diversity of quenched silica glasses can be prepared through different temperature and stress conditions. In other words, any difference in a given physical property between different silica glasses, as observed, for instance, in Brillouin scattering experiments [Grimsditch, 1984], does not constitute per se evidence for polyamorphism. 5.2a. Thermal Properties The high-temperature heat capacity (Cp) of silica glass is known accurately from many measurements [see review by Richet et al., 1982]. No anomaly is found up to the glass transition. As usually observed for solids, effects of impurities on Cp have not been detected. A possible exception could be the slight effect of water reported in measurements made on type I and III glasses [Casey et al., 1976]. Heat capacity data between 0 K and room temperature are scarce. Entropy assessments have generally relied on unpublished measurements made by E.F. Westrum, Jr, which have recently been confirmed by Yamashita et al. [2001]. Westrum [1956] also reported a marginally positive Cp difference between two samples annealed at 1340 and 1570 K. The sensitivity of Cp to short-range order around metal cations below 200 K has been discussed in section 3.2b. The Cp differences between glasses and crystals are small if Si (or Ge) is 4-fold coordinated by oxygen in both phases, and large if Si (or Ge) is 6-fold coordinated in the crystal (Fig. 5.3). In the immediate vicinity of 0 K, Cp depends strongly on thermal history and impurity content [e.g., Grosmaire-Vandorpe et al., 1983], but discussion of these effects is beyond our scope. Data on the heat capacity change at the glass transition have long been lacking because of the problems raised by accurate measurements at high temperature. At the rapid cooling rate of drop-calorimetry experiments, the glass transition of a type I SiO2 is 1480 K and the associated Cp increase is only 10% [Richet et al., 1982]. The similarity between SiO 2

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Figure 5.4 - Heat capacity changes at the glass transition for SiCh, GeCh and B2O3. Adiabatic measurements for B2O3 [Shmidt, 1966] and values derived from drop calorimetry experiments for GeCh [Richet, 1990] and SiO2 [Richet et al., 1982]. The Dulong-and-Petit harmonic limit of 3R/g atom K is shown for comparison.

and GeO 2 in Fig. 5.4 might suggest that the heat capacity of SiO 2 liquid increases slightly with temperature as does that of GeO 2 . This is unlikely, however, because other measurements yield a constant partial molar heat capacity for SiO2 that is equal to the 81.37 J/mol K of the heat capacity of pure SiO 2 liquid [Richet and Bottinga, 1985]. These measurements made for a variety of silicate systems include data obtained up to 1800 K, over about 1000 degrees for Na 2 O-SiO 2 liquids [Richet et al, 1984]. Hence, evidence is lacking for a significant minimum in heat capacity. The glass transition range of SiO 2 should depend as strongly as viscosity on impurity content (see below), but the effect has not been investigated in calorimetry experiments. There are, however, data for GeO 2 which indicate that the presence of 0.06 mol % Li2O lowers Tg by 200 degrees without influencing the heat capacity of the liquid [Richet, 1990]. Another unusual feature of silica is the low enthalpy of fusion (AHf) of quartz and cristobalite (Table 5.1). The small AHf of less than 10 kJ/mol confirms that bond breaking is not the essential feature of melting of quartz and cristobalite. More generally, the fusion data of Table 5.1 indicates that molten SiO2 and cristobalite have more similar ordering characteristics than any other silicate [see also Bourova et al, 2000].

Figure 5.5 - Entropy of fusion of crystals in the systems (a) Na2O-SiO2 and (b) SiO2-NaAlO2 as a function of composition. Data from Richet and Bottinga [1986].

139

Silica — A Deceitful Simplicity Table 5.1. Thermodynamic properties at the melting points of P-cristoba and P-quartz [Richet and Bottinga, 1986; Bourova and Richet, 1998]. Property 7}(K) V,(cmVmol) Vc(cnWmol) AVf(cm2/mo\) AS/J/molK) AHf(kJ/mo\) dT/dP (K/GPa)

P-cristobalite

P-quartz

1999 27.3 27.4 -0.1 4.61 8.92 -21.7

1673 27.3 23.5 3.8 6.06 9.10 625

The enthalpy or entropy of fusion of SiO2 polymorphs can also be compared with the values measured for simple binary silicates and aluminosilicates (Fig. 5.5). A large increase of the entropy of fusion results from either breakup of the silica network by a network modifier or substitution of Al 3+ for Si 4+ . Analogous relationships exist for other systems [e.g., Stebbins etal, 1983], and confirm that melting involves less structural rearrangement for SiO 2 than for any other silicates. Finally, a residual entropy of 1.7 J/g atom K is determined for SiO 2 glass at 0 K from the calorimetric cycle described in Fig. 2.19. Representing the configurational entropy of the liquid frozen at the glass transition, this value is one of the smallest for silicates (Table 3.2). Of course, the reason is that this entropy is made up of a single topological contribution, without any contribution of mixing of chemically similar elements. Curiously, configurational entropy is usually ignored in structural models of vitreous silica. An exception is the estimate derived by Bell and Dean [1968] within the framework of random network theory. Their upper bound of 1.9 J/g atom K is slightly higher than the experimental value, but their recommended range of 1.1-1.25 J/g atom K is too low. 5.2b. Ambient-Pressure Density Silica glass has a low density of 2.20 g/cm3 (molar volume: 27.3 cm 3 ). As might be expected from its low molecular weight, water dissolved in silica glass causes a density decrease. For trace amounts, however, this decrease is less than 0.001 g/cm3 for 0.1 wt % OH [Bruckner, 1970; Shackelford etal, 1970]. Silica glass distinguishes itself by its extremely small thermal expansion. In type III glass, dissolved water enhances dilation by about 5% from 0 to 100°C [Hetherington and Jack, 1962]. The effect extends to higher temperatures. The average of mean thermal expansion coefficient, measured between 0 and 1000°C, for various type I, II and III glasses is 45.5, 45.8 and 48.9 10"8 K 1 , respectively [Oishi and Kimura, 1969]. These values are from 10 to 100 times smaller than generally determined for silicate glasses. Because thermal expansion depends on the thermal history of the sample [Douglas and Isard, 1951], dilatometry experiments must be performed on glasses annealed at

Chapter 5 Figure 5.6 - Densities of quartz and cristobalite against temperature [Bourova and Richet, 1998] and 25°C density of SiO2 glass against quench temperature, with data from Bruckner [1970], for type I silica (solid squares), and Sen et al. [2004] for a type III SiO2 (solid circles) after complete density relaxation (1200°C density assumed to be 2.203 g/cm3). The data for quartz have been displaced downward by 0.345 g/cm3 to expand the scale as much as possible.

well-defined temperatures and be terminated before reaching temperatures at which relaxation becomes significant. Douglas and Isard [1951] showed that an equilibrium density is reached in 50 hours at 1080°C, but cannot be attained in more than 400 hours at 903°C. A density maximum was reported by Bruckner [1970] for samples quenched from 155O°C (Fig. 5.6), whereas a minimum has been found at 950°C for structurally relaxed samples [Sen et al., 2004]. The density of SiO 2 liquid is more controversial because derivation of melt properties from measurements on glasses is fraught with difficulties in view of possible uncontrolled effects during the quench. As an example, the existence of the density maximum reported by Bruckner [1970] has been questioned from observed Raman shifts of glasses with fictive temperatures up to 155O°C [Kakiuchida et al., 2003]. The only density measurements have been made between 1930° and 2170°C by Bacon etal. [I960]. These yield a molar volume of 28.87 cm /mol at 1730°C and a high thermal expansion coefficient of 10"4 K"1. If real, both properties would imply a dramatic dilation change somewhere below 1930°C to match the density data on quenched glasses. No data support this conclusion, however, which may reflect instead the technical difficulties of density measurements for very viscous liquids. The molar volume of molten SiO 2 can be determined more reliably from the melting curve of cristobalite, which has a very small slope [Jackson, 1976; Zhang et al., 1993]. From the Clausius-Clapeyron equation, it follows that the volume difference between molten SiO 2 and cristobalite is also very small. Hence, the volume of SiO 2 liquid is close to the 27.4 cm3/mol measured for cristobalite at its melting temperature (Fig. 5.6). Support for this value is provided by extrapolations of molar volumes of binary barium and sodium silicate melts to pure SiO 2 (Fig. 5.7). On the other hand, the partial molar volume of SiO 2 in silicate melts is 26.8 cm /mol, with a negligible thermal expansion coefficient at least up to 1950°C. This value has been derived consistently ever since Bottinga and Weill [1970] showed that the volume of liquid silicates is a linear function of composition. The slight 0.6 cm3/mol difference between the molar volume of pure SiO 2 liquid and the partial molar volume of SiO 2 in metal oxide-silica melts agrees with the suggestion that

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Figure 5.7 - High-temperature molar volumes: cristobalite at 1700°C [Bourova and Richet, 1998], Na2OSiO2 melts at 1400°C [[Bockris et al., 1956], and BaO-SiO2 melts at 1700°C [Tomlinson
bridging oxygens have a larger partial molar volume than nonbridging oxygens [Bottinga and Richet, 1995]. Contrary to the results of Bacon [1960], there are three different reasons why the thermal expansion coefficient of SiO2 liquid is also small. First, the volume of SiO2 melt varies by less than 0.1 cm3/mol between the glass transition and the melting point of cristobalite. This constrains the thermal expansion coefficient to be lower than 7 10"6 K"1, i.e., to be consistent with the low value of 10" K"1 drawn from extrapolations to pure SiO2 of measurements made for binary metal oxide systems (see section 6.3a). Second, the compressional sound velocity of amorphous SiO2 is a linear function of temperature from the glass transition to more than 2000°C (see below). In view of the strong sensitivity of sound velocity to density, this linear relationship rules out any significant increase of thermal expansion coefficient at a temperature below 2000°C. Third, SiO2 liquid has definite structural similarity with cristobalite [Bourova et al., 2000; Takada et al., 2004], whose thermal expansion coefficient is also very small near its melting point. In fact, cristobalite, and quartz as well, contract slightly before melting [Bourova

Figure 5.8 - Molar volume of SiO2 glass at 25°C against pressure as compiled by Hemley et al. [1994]. Solid line: fit to ultrasonic measurements, Brillouin scattering, and static compression data. Cross-hatched area: range in molar volume derived from shockcompression data.

Chapter 5

Figure 5.9 - Variations of the onset and extent of densification of SiCh glass with differing experimental conditions. Ambient densities measured after quenching from the temperature (°C) and pressure indicated. Strongly nonhydrostatic conditions: solid symbols; quasi-hydrostatic conditions: open symbols. Data of Mackenzie [1963].

and Richet, 1998], consistent with the aforementioned minimum density observed for SiO2 glasses quenched from 950°C [Sen et al., 2004]. 5.2c. Compressibility In contrast to its low thermal expansion, silica glass is highly compressible (Fig. 5.8). The high-pressure compression predicted from elastic data is lower than experimentally determined, however, because permanent compaction takes place above a few GPa. As an irreversible phenomenon, compaction depends strongly on the conditions of the experiment. Its onset is observed at lower pressure either when the temperature is increased or under increasingly nonhydrostatic conditions (Fig. 5.9). Owing to this sensitivity, it is not possible to predict accurately the density of SiO2 glass beyond the pressure range where it is mechanically elastic. Likewise, the adiabatic bulk and shear moduli are well defined only at low pressure (Fig. 5.10) where they first decrease linearly [Kondo et al., 1981; Suito et al., 1992; Zha et al., 1994]. After passing through a minimum near 2 GPa, both moduli increase as a result of the permanent compaction that begins to take place near this pressure. Interestingly, extrapolation of the low-pressure data indicates that both

Figure 5.10 - Bulk (Ks) and shear (G) moduli of silica glass against pressure at room temperature [Suito et al., 1992]. The roompressure values are 36.9 and 31.1 GPa for Ks and G, respectively. The dashed lines give the pressure dependence of the moduli in the elastic region (dK/dP = -5.12 and dG/dP = -3.34).

Table 5.2. Compressibility (/?, 1011 Pa1) and bulk modulus (K, GPa) of molten SiO2a j8

K

2.1 47 8.5 11.8 5.7 17.6 7.5(2) 13.0 6.9 14.5

Method Uniaxial compression, 1075°C Brillouin scattering, 1200-1700°C Brillouin scattering, 1100°C Ultrasonics, binary systems, 1400-1630°C Ultrasonics, multicomponent systems, HOOT

Ref Douglas and Isard [1951] Bucaro and Dardy [1973] Krol et al. [1986] See section 6.3b Kress and Carmichael [1991]

a

In view of the negligible thermal expansion coefficient of molten silica, the differences between the isothermal and adiabatic data are also negligible

moduli would vanish at a pressure of about 9 GPa. Hence, permanent compaction prevents such a mechanical instability from occurring. The high viscosity of liquid SiO 2 makes determination of its compressibility (/3) difficult. The available data are summarized in Table 5.2. An indirect method was used by Douglas and Isard [1951]. With the assumption that thermal expansion is not affected by densification, they derived the isothermal compressibility of the melt from roomtemperature density changes induced by application of a uniaxial stress at temperatures above the glass transition temperature. Their result seem too low, illustrating the aforementioned pitfalls that beset determination of melt properties from glass measurements. In Brillouin scattering experiments [Bucaro and Dardy, 1973; Krol et al., 1986], relaxation problems were circumvented through determination of the so-called Landau-Placzek ratio, the intensity ratio of the Rayleigh and Brillouin lines, from which the adiabatic compressibility is obtained. The differences between the two determinations made in this way (Table 5.2) are probably within the error margins of the technique. Likewise, the temperature dependence of the compressibility is too small to be determined. Finally, the equilibrium compressibility of molten silica cannot be determined by ultrasonic methods but extrapolation of the measurements performed on SiO2-rich melts may be used to check these results. The observations for binary metal-oxide systems (see section 6.3b) are in best agreement with the datum of Bucaro and Dardy [1973]. Interestingly, the partial molar compressibility of SiO 2 in multicomponent melts does not differ significantly from this value [Kress and Carmichael, 1991]. The 3:1 bulk modulus ratio between SiO 2 melt and glass illustrates the importance of configurational changes in high-temperature compressibility. Comparison of equilibrium and vibrational compressibility determined by Brillouin scattering enables a more detailed analysis (see section 2.2b). Between 1200 and 1700°C, Bucaro and Dardy [1973] reported a constant value of 2 10"11 Pa"1 for vibrational compressibility. This implies that 75% of the compression of molten SiO 2 originates in configurational changes, a conclusion confirmed by Polian et al. [2002]. Instead of being constant, however, the vibrational compressibility decreases with increasing temperature from 25 to 2000°C (Fig. 5.11). The unusual feature is the variation of its temperature dependence observed not at the

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Figure 5.11- Elastic properties of type I SiCh glass and liquid determined from Brillouin scattering [Polian et al, 2002]. (a) Vibrational compressibility against temperature; the two different linear fits to the data do not imply an abrupt change in the slope near 700°C but, simply, that the low- and high-temperature regimes differ. The glass transition is shown by an arrow, (b) Compressional and shear wave velocities, the latter being displaced upward by 2 km/s. glass transition, but at a lower temperature of 750°C. This change is attributable to the shear velocity, which decreases with rising temperatures above Tg, whereas the compressional velocity measured at the highest temperatures extrapolates smoothly down to the glass transition range. In the experiments by Polian et al. [2002], crystallization of the supercooled SiO 2 liquid prevented measurements from being made between 1100 and 1550°C and, thus, from checking the existence of the density maximum reported by Bruckner [1970]. With increasing pressure the compressibility of SiO 2 liquid necessarily decreases, but the effect cannot be determined from quench experiments because of permanent compaction. As high-pressure measurements are lacking, the compressibility of molten silica has been determined from thermodynamic analyses of the melting curve of SiO 2 polymorphs [e.g., Bottinga, 1991; Swamy et al., 1994]. Such determinations are useful starting points, but they suffer from the fact that pressure and temperature are not independent variables along a melting curve. In addition, the results thus obtained depend on the high-pressure melting properties of the polymorphs which are much less well known than their equations of state [e.g., Fabrichnaya et al, 2004]. 5.2d. Viscosity The general features of the viscosity of SiO 2 have already been described. The influence of impurities was already suspected by Volarovitch and Leontieva [1936]. Since then, it has been extensively studied near the glass transition range. The review by Leko [1979] provides a comprehensive summary of the work done until that time. Other comparisons have been made by Urbain and Auvray [1969] and Weiss [1984]. The effects of impurities are greater at lower concentrations (Fig. 5.12a). They also depend strongly on the nature of the impurity. For Al and Ga, the influence is moderate because it reflects the decrease of the strength of T-O-T bonds when Al3+ and Ga3+ substitute

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Figure 5.12- Effects of impurities on the viscosity of SiCh near the glass transition range, (a) Viscosity at 1200°C against Na2O, AI2O3, Ga2C>3, and OH contents. In the inset, data at higher sodium content for binary silicate melts [Bockris etal., 1955]. (b) Activation enthalpy of viscous flow in the glass transition range. Data from Leko et al. [ 1977] for type I SiCh, for all impurities, and from Hetherington^ a/. [1964] for OH (OHHal), with OH contents as given by Hetherington and Jack [1962], for Si 4+ on tetrahedral sites of the structure without charge-compensating cations. For Na, the results of Leko et al. [1977] join smoothly with measurements on binary silicates made up to 35 mol % Na 2 O [Bockris et al., 1955]. The viscosity decrease is very large as a result of the breakup of the three-dimensional SiO 2 framework by network-modifying cations. For OH, good agreement is found between the measurements of Hetherington et al. [1964] and Leko etal. [1977]. Both data sets indicate an effect of water intermediate between those of Na and Al. The influence of impurities on the activation enthalpy of viscous flow (AHfp is less well determined although it tends to parallel those on viscosity (Fig. 5.12b). The activation enthalpy drops upon addition of Na 2 O but increases by 80 kJ/mol for 6 mol % A12O3. For OH, the data of Hetherington et al. [1964] and Leko et al. [1977] differ significantly but both indicate a rapid decrease of AH^. Hetherington et al. [1964] noted that its main

Figure 5.13 - Combined effects of alumina and alkali oxides (ZM2O) on the viscosity and activation energy for viscous flow of type I SiO2 between 1160° and 1300°C [Bihuniak et al., 1983]. The highest impurity contents are 0.035 mol % for AI2O3 and 8 10'3 mol % for Na2O+Li2O.

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consequence is to make the data for various types of SiO2 merge near the softening point at 106 6 Pa s and 1590°C, offsetting the differences of 120°C that are observed at the strain point (10 135 Pas). The relative proportions of impurities must also be considered. In the presence of alkali oxides, both viscosity and activation energy increase when alumina is added and induce repolymerization of the network (Fig. 5.13). A plateau is reached for more than 0.01 mol % A12O3, indicating that addition of non charge-compensated Al + no longer affects these properties. Much less is known at temperatures 104/T, K-1 above the liquidus where control of Figure 5.14 - Viscosity of molten silica. Hal: experimental conditions and, in Hetherington etal. [1964]; V&L: Volarovich and particular of impurity content, is Leontieva [1936]; F&P: Fontana and Plummer difficult. It is a general rule that [1966]; Ual: Urbain et al. [1982], U m : Urbain viscosity is a considerably stronger [1990] for type III SiO2; Bal: Bacon etal. [I960]. function of composition near the glass transition than at high temperatures [see Richet, 1984]. For this reason, or also because of possible loss of volatile impurities, available data do show much less variations above than below 2000 K (Fig. 5.14). Among existing data, those of Urbain et al. [1982] are generally taken as a reference because they cover a wide temperature interval and are part of an extensive and accurate set of measurements performed over a large composition interval. Unfortunately, these data do not establish rigorously the actual Arrhenian nature of the viscosity of SiO2. At the lowest temperatures, their timescale of a few hours [see the procedure described by Urbain and Auvray, 1969] may have been insufficient to obtain equilibrium viscosities. In other words, the reported viscosity values might be too low. Attainment of equilibrium was checked in the experiments of Hetherington et al. [ 1964]. The fact that they join smoothly with those of Urbain et al. [1982] near 1350°C could, thus, point to the non-Arrhenian character that is apparent in Fig. 5.14 when both data sets are considered [see Richet, 1984]. Unfortunately, it difficult to check this conclusion because only fitted results were published by Hetherington et al. [1964]. 5.2e. Element Diffusion This survey will end with a summary of tracer diffusivity measured for a number of elements in amorphous SiO2 (Fig. 5.15). Although most results do not cover a very wide temperature range, there is no evidence for changes in diffusivity mechanisms at the

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Figure 5.15 - Diffusion in amorphous SiC>2. (a) Tracer diffusivity of various elements against reciprocal temperature. The glass transition of SiCh is shown as a dashed line, (b) Comparison of the silicon and oxygen tracer diffusivities of with the values predicted from Eyring relation (4.10) with a jump distance of 2.8 A and the viscosities of Hetherington et al. [1964, Hal] andUrbain et al. [1982, Ual]. In (a), 31Si measurements for a type I silica [Brebece/ al, 1980]; I8O data for a type II silica at 0.01 MPa O2 pressure [Muelenbachs and Schaeffer, 1977], and fitted results of Sucov [1963] for an "optical quality" sample heated at 0.1 MPa O2 pressure; "H2O" data for a type I glass in an H2 atmosphere [Bell et al., 1962]; Ar data for a SiCh thin film deposited on a porous Vycor substrate [Perkins and Begeal, 1971]; for Cl: Cl-free SiO2 under a low Cl pressure [Hermann et al, 1985]; 45Ca data from Zhabrev et al. [1976] for type III glass; 137Cs data for types I, II and III SiC>2 heated under Ar [Rothman et al, 1982]; for 22Na: type I silica, probably in air [Frischat, 1968]; for 20Ne: type I silica under 0.1 MPa Ne pressure [Frank et al, 1961]; for He: similar procedure by Swets et al [1961]. glass transition. This observation is consistent with the slight magnitude of temperatureinduced structural changes in liquid SiO 2 which is indicated by the small configurational heat capacity. The other important feature is the clear correlation between the diffusivity and structural role of the element and, particularly, the strength of its bonding within the silica network. For activation enthalpies, these effects have been discussed by Roselieb and Jambon [2002] to whom we refer for more details. As expected from its small size and chemical inertness, helium diffuses the fastest. It is closely followed by neon, which is bigger, and, rather surprisingly, by sodium which exhibits very small differences between various types of SiO 2 glasses [Frischat, 1968, 1970]. As already noted for viscosity, there is large difference between the diffusivities of Na and "water", the latter diffusing about four orders of magnitude slower than the former. In turn, "water" diffuses faster than Cl, which suggests that chlorine and hydroxyl ions do not interact in a similar way with bridging oxygens. For alkali elements, the influence of ionic radius is clearly shown by the difference between the diffusivities of Na and Cs, the latter being similar to that of the alkaline earth Ca. Measurements are not available for Al because of the lack of a suitable radioactive isotope. For 18 O, the two data sets plotted in Fig. 5.15 illustrate that agreement between existing diffusivity data is not excellent. This could be due to differing impurity content

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or heating atmosphere. That problem notwithstanding, the definite feature is that the diffusivity of oxygen is intermediate between those of Cl and Si. As might be expected, silicon is indeed the slowest diffusing element. Given the large difference between oxygen and silicon diffusivities, the question arises as to which one correlates better with the values calculated from viscosity through the Eyring relationship (4.10). The answer is unambiguous (Fig. 5.15b). There is close agreement with silicon diffusivity from either the viscosities of Hetherington et al. [1964] or those of Urbain et al. [1982]. The much higher diffusivity measured for 18O indicates that other mechanisms than viscous flow are operating for transporting oxygen. This conclusion suggests that the oxygen dynamics that prevail in SiO2 polymorphs at high temperatures [see section 3.3b and Bourova et al., 2004] could also operate in amorphous SiO2. 5.3. Structure of SiO2 Glass and Melt Structural models proposed for SiO2 glass and melt may be grouped into three types, (i) The earliest models assumed a random network structure, (ii) In contrast, some similarity with crystal structure is assumed in pseudocrystalline models, (iii) The coexistence of several, distinct structural entities forms the basis of the third kind of models 5.3a. Random Network Structure The random network model for the structure of vitreous SiO2 was suggested originally by Zachariasen [1932]. This model has four important premises, (i) The structural positions are energetically equivalent for all oxygen atoms as well as for all silicon atoms, (ii) There is no ordering among the SiO4 tetrahedra. (iii) Oxygen in the corners of SiO4 tetrahedra are shared between neighboring tetrahedra. (iv) The structure is 3-dimensionally interconnected. The random network model received support in spectroscopic studies by Bell and coworkers [Bell and Dean, 1970; Bell etai, 1980; Bell and Hibbins-Butler, 1976]. With some differences, this model allowed these workers to calculate important features of the vibrational and neutron spectra of vitreous SiO2. The differences between observed and calculated spectra are most notable in the low-frequency end. In this regime, Phillips [1984] noted, for example, that the Raman bands are unusually narrow, which suggests localized vibrations. Localized vibrations cannot easily be accommodated with the random network model where all O and all Si positions are energetically equivalent. 5.3b. Pseudocrystalline Structure Model Because the Si and O positions in vitreous SiO2 cannot be energetically equivalent [Phillips, 1984], the random network model has been refined such that, at least on the scale of several A, structural similarities between glass (and melt) and crystalline SiO2 polymorphs may exist. The pseudocrystalline structure model (see also section 1.4a), found early support in Randall et al. [1930] from an x-ray diffraction study of SiO2 glass and cristobalite.

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Radial distance, A Figure 5.16 - Pair distribution function from x-ray diffraction data of vitreous SiO2 at ambient pressure and 25°C. Dashed line: distribution function for cristobalite [Mozzi and Warren, 1969]. Structural similarity between these two materials also finds support in the exceptionally small values of enthalpy and entropy of fusion as well as the negligible heat capacity difference between vitreous SiO 2 and cristobalite compared with other silicates (Table 5.1; Fig. 5.5). Modeling of x-ray diffraction data of vitreous SiO2 by plausible crystalline models met with significant success [Mozzi and Warren, 1969; see also discussion by Taylor and Brown, 1979]. These x-ray data are best displayed in terms of pair distribution functions whereby the obtained Si-O, O-O, and Si-Si distances are compared with distances in appropriate models (Fig. 5.16). Mozzi and Warren [1969] originally stated that their x-ray data were best interpreted on the basis of the random network model, but that some similarities between the spectra of vitreous SiO2, tridymite, and cristobalite do exist. Konnert and Karle [1973] andKonnert et al. [ 1973] concluded that significant similarities persisted between the spectra of vitreous SiO2 and that of tridymite to distances of perhaps as much as 15-20 A. Bourova et al. [2000], from their numerical simulation, found considerable similarity between the structure of P-cristobalite and molten SiO2 to distances beyond the first Si-O, Si-Si, and 0 - 0 distances in these materials. Short- and medium-range structural similarity between molten SiO 2 and silica polymorphs is also consistent with results of numerical simulations and structural interpretations of neutron, x-ray, and NMR data [Geissberger and Bray, 1983; Grimley et al, 1990; Yuan and Cormack, 2003; Clark et al, 2004]. We note, however, that among

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Figure 5.17 - Angle distribution function for SiO2 glass at ambient pressure and 25°C obtained from xray diffraction data [Mozzi and Warren, 1969].

the possible crystalline SiO 2 model compounds, the P-cristobalite structure shows the greatest similarity to the structure of SiO2 glass and melt. Structural differences between glass and melt, on the one side, and P-cristobalite on the other, however, remain in the medium and long-range domains [Wright, 1994; Bourova et al., 2000]. 5.3c. Coexisting Structural Units As noted by Vuckevitch [1972], two or more average structures may coexist in glassy and molten SiO 2 . If SiO2 melt and glass have more than one average structure, this feature may be reflected in the distribution of average Si-O-Si angles because one of the differences between such units is their Si-O-Si angle [e.g., Galeener, 1982; Kubicki and Sykes, 1993; Uchino et al., 1998]. The Si-O-Si angle distribution drawn from the x-ray study of vitreous SiO 2 by Mozzi and Warren [1969] ranges between 120° and 180° and is asymmetric towards larger angles (Fig. 5.17). The maximum in the angle distribution

Figure 5.18 - Angle distribution function for SiO, glass at ambient pressure and 25°C from 29Si NMR spectra fitted to two different angle distribution functions, p(8) [Mauri et al, 2000].

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Figure 5.19 - Transmission electron micrographs of vitreous SiO2 [Gaskell and Mistry, 1979] and crystalline tridymite [Heaney, 1994]. function is near the Si-O-Si angle of crystalline quartz (144°, see, for example, Hazen et al. [1989]). Poulsen et al. [1995] reported similar asymmetric angle distribution from high-energy x-ray diffraction. Their calculated average Si-O-Si angle (147°) is within error the same as the 144° reported by Mozzi and Warren [1969]. This 147° angle, as well as the asymmetric angle distribution, is also near that obtained by numerical simulation of the vitreous SiO2 structure by Yuan and Cormack [2003]. The 17O and 29Si NMR chemical shifts from NMR spectroscopy depend on intertetrahedral angle [e.g., Geissberger and Bray, 1983; Engelhardt and Michel, 1987; Oestrike et al., 1987; Grandinetti et al., 1995; Xue and Kanzaki, 2000]. The 29Si chemical shift was used by Mauri et al. [2000] to derive Si-O-Si angle distributions in vitreous SiO2. They suggested two possible models (Fig. 5.18), which they obtained by fitting their 29Si NMR data to an angle distribution function, p(Q), of two different forms. In particular one of their models (model 1 in Fig. 5.18) shows a distinct asymmetry toward the higher angles, also with the total angle distribution between about 120° and 180°, as in the case of the angle distribution from the x-ray data (Fig. 5.17). Mauri et al. [2000] concluded, however, that the maximum in the angle-distribution function is somewhere between about 150° and 155°, a value slightly higher than that reported from the x-ray distribution function [Mozzi and Warren, 1969; Poulsen et al, 1995]. Interestingly, this value is quite similar to the maximum in the average Si-O-Si angle distribution from numerical simulation of P-cristobalite at temperatures near its melting point [Bourova et al., 2000]. This angle maximum is also similar to the 150°-153° range in vitreous SiO2 suggested by Henderson et al. [1984] and Mitra [1982]. Oxygen-17 NMR spectroscopy is sensitive to local structure near oxygen and has been used, therefore, to examine Si-O-Si angle distribution in vitreous SiO2. In what may

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have been the first study of I7O NMR spectra of vitreous SiO2, Geissberger and Bray [1983] found their data consistent with a 144° angle. In a recent 2-dimensional dynamic angle 17O NMR study, Clark et al. [2004] reported the angle maximum at 147°. They also noted a much narrower angle distribution than those in previous x-ray and NMR studies (including those of Mozzi and Warren [1969] shown in Fig. 5.17 and Mauri et al. [2000] in Fig. 5.19). Interestingly, all these studies are consistent with a maximum in the angle distribution similar to the Si-O-Si angle in silica polymorphs. Most recently, Clark et al. [2004] strongly point toward the structure of vitreous and molten silica consisting predominantly of 3dimensionally interconnected, 6-membered rings. A smaller number of tetrahedra yields Si-O-Si angles that are much too narrow compared with experimental and simulation data[Uchinoe?<3/., 1998]. The x-ray data and most of the interpretations of 29Si and 17O NMR information of vitreous SiO2 are consistent with an asymmetric Si-O-Si angle distribution. Asymmetric angle distribution, in turn, is consistent with proposals that the structure of vitreous SiO2 may consist of more than one structural unit or domain. Such a concept is also consistent with early TEM data (Fig. 5.20). Variation in Si-O-Si intertetrahedral angle or Si-0 bond length can be accomplished by altering the number of SiO4 tetrahedra in 3-dimensionally interconnected rings or by puckering of the rings [e.g., Zoltai and Buerger, 1960; Newton and Gibbs, 1980; Mammone et al., 1981; Galeener, 1982; Tossell and Lazzaretti, 1988; Kubicki and Sykes, 1993; Barrio et al., 1993; Sykes and Kubicki, 1996; Uchino et al., 1998]. The potential energy per tetrahedron depends on the number of tetrahedra in a ring (Fig. 5.20a) and the extent

Figure 5.20 - (a) Energy of formation per Si (eV) calculated as a function of the number of Si in planar rings [Galeener, 1982]. (b) Potential energy function of SiO2 glass as a function of intertetrahedral angle, Si-O-Si [Gibbs et al., 1981] with the potential energy of 4-membered rings puckered with intertetrahedral angle, 0, at 138°. For 4-membered planar ring, 6 = 160° [Sykes and Kubicki, 1996].

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Figure 5.21 - Unpolarized Raman spectrum of SiO2 glass at ambient pressure and 25°C [Seifert etal, 1983]. to which rings are puckered (Fig. 5.20b). For planar rings, the minimum energy is obtained with 4 tetrahedra (Fig. 5.20a). Puckering tends to decrease the energy of rings (Fig. 5.20b). The simple energy calculations summarized in Figs. 5.21 and 5.22 lead to the suggestion that 4-membered rings are particularly stable. In these calculations, the energy penalty associated with increasing the number of tetrahedra is quite small and could probably be eliminated by puckering of the rings. Interestingly, among silicate crystals with 3-dimensionally interconnected structure, only 4- and 6-membered rings have been documented [e.g., Zoltai and Buerger, I960]. The (3-cristobalite structure consists of 6membered rings. The Raman spectrum of vitreous and molten SiO2 has been used extensively in the discussion of ring distributions. The principal Raman spectral features relevant to the discussion of ring systematics are highlighted in Fig. 5.21. Following McMillan et al. [1994], the 450 cm1 band is a symmetric oxygen stretching motion of bent Si-O-Si linkages or a bending motion of these linkages. The 495 and 605 cm'1 bands are oxygen breathing vibrations. The 1060 and 1200 cm1 bands are antisymmetric Si-0 stretching modes, whereas the broad band near 800 cm1 may be a vibration of oxygen with a motion perpendicular to the Si-Si line. In analogy with silicate crystals, Mammone et al. [1981] and Sharma et al. [1981] suggested from the Raman spectra of vitreous SiO2 that there are, on average, two kinds of rings with either 4 or 6 Si. The Raman signals used to document their presence were the 495 and 605 cm1 bands. Seifert et al. [1982] examined the entire Raman spectrum and found that it could be deconvoluted into doublets (Fig. 5.22). By using a simple central force model [Sen and Thorpe, 1977; Galeener, 1979], Seifert et al. [1982] concluded that the band doublets reflect two coexisting, 3-dimensionally interconnected structures whose intertetrahedral angles, 6l and 92, differed, on average, by 5-10°. This view is in accord with the model of Vuckevitch [1972] who envisioned a structure analogous to that of the a- and P-polymorphs of cristobalite with an Si-O-Si angle

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Figure 5.22 - Raman spectrum of SiO2 glass at ambient pressure and 25°C with curve-fitted bands as conducted by Seifert et al. [1983]. The schematic Si-O-Si bridges with intertetrahedra angles, 0x and 92, corresponding to those obtained via the use of the central force model of Sen and Thorpe [1977].

difference of 8°. A simple cristobalite-like model is also appealing in that it accounts for the very small or negligible AHf, AVf, and ASfof silica polymorphs (Table 5.1). If the two rings contain the same number of Si, this relatively small angle difference (5-10°) requires different extents of puckering. If these two ring structures comprise different number of SiO4 tetrahedra, there must also be differences in puckering between the two. Otherwise, the Si-O-Si angle difference would be greater than 5-10°. Most studies of the ring geometry in vitreous silica have focused on the low-frequency bands (450, 495, and 605 cm 1 ) of the Raman spectrum (Fig. 5.23). Galeener [1982] and Revesz and Walrafen [1983] originally assigned the last two bands to 3- and 4-membered ring structures. These bands have subsequently attracted considerable attention in part because they are unusually narrow. This sharpness implies localized motions in the SiO2 glass [e. g., Phillips, 1984] and perhaps vibrational decoupling from the rest of the spectrum [Barrio et ah, 1993]. A detailed theoretical study led to the conclusion that the 490 and 605 cnr 1 modes are indeed essentially decoupled and that these most likely reflect the presence of 4- and 3-membered rings, respectively [Barrio et al, 1993]. This interpretation is consistent with that of Sykes and Kubicki [1996], which was based on numerical simulations of silicate clusters. In this model, the 3-membered ring would be essentially planar with an intertetrahedral angle near 130°. However, with the general consensus from spectroscopy and simulation studies that the angle maximum is near 150°, rings with such a small number of tetrahedra seems unrealistic (see also recent discussion by Clark et al. [2004]). The structure model of multiple rings in SiO2 may be used to explain the anomalous properties of SiO 2 glass and melt. One may rationalize them by assigning different compressibilities [see Vuckekvitch, 1972], thermal expansion [see Bruckner, 1970], and elastic properties [see Zha et ah, 1994; Polian and Grimsditch, 1993] to individual ring structures. For the most part such information is not available, however, so relationships between ring geometries and physical properties remain to be quantified. Multiple ring structures with different number of SiO4-tetrahedra do represent an intuitive problem when considering the thermodynamics of melting of cristobalite or any other SiO 2 polymorphs [Richet et ah, 1982; Stebbins et ah, 1983; Bourova and Richet,

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Figure 5.23 - Molar volume of SiO2 glass quenched from 900°C at high pressure as a function of pressure of quenching [from Seifert etal, 1983].

1998; see also Chapter 2]. These data suggest quite small structural differences between SiO 2 melt and its liquidus phase, cristobalite (or, for that matter, tridymite, and quartz). The cristobalite structure can be viewed as consisting of 6-membered, 3-dimensionally interconnected rings [Downs and Palmer, 1994]. Thus, the thermochemical data would suggest that SiO 2 melt consists predominantly of ring structures resembling those of cristobalite (6 Si atoms per ring) and not rings with a smaller number of SiO4 tetrahedra. If SiO2 melt contains a different number of SiO4 tetrahedra than the crystalline form of SiO 2 , melting which most likely would result in significant differences in thermodynamic properties of molten and crystalline SiO 2 , which is not the case (Table 5.1). This apparent contradiction between some of the interpretations of the spectroscopic data on SiO2 glass and thermodynamics of melting is not easily reconciled. It may be that the ring systematics depends on temperature leading to more and more structurally open 6-membered rings as SiO 2 liquid is heated up or that the abundance of 4- and 3-membered rings is small compared with the abundance of 6-membered rings. The simplest way to reconcile thermodynamic and structural data is that, even though multiple average ring structures probably exist in SiO2 glass and melt, the small difference in intertetrahedral angle (5-10°; see Vuckevitch [ 1972]; Seifert et al. [ 1982]) simply reflects ring structures with the same number of tetrahedra (6), but that the extent of puckering of these rings differs. A structural model based on 6-membered, 3-dimensionally interconnected rings of SiO4 tetrahedra is consistent with most experimental and theoretical structural data. This model is also consistent with physical properties of vitreous and molten SiO 2 . Structures of rings with less than 6 tetrahedra as the dominant feature are difficult to reconcile with these data. 5.4. Effects of Pressure and Temperature From the preceding discussion, it is tempting to conclude that the properties of pure SiO 2 glass and melt are simply those expected from structural flexibility of a 3-dimensional open network of SiO 4 tetrahedra. Effects of temperature and pressure on properties of

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Figure 5.24 - Relationship between variation of intertetrahedral angle, Si-O-Si, and compression, V/VQ, of quartz and SiO2 glass at25°C[Levien^a/., 1980].

vitreous SiO 2 may, thus, offer information on the response of Si-O bond length and Si-O-Si bond angles to changes in these parameters. 5.4a. Pressure The Si-O distance in the SiO 4 tetrahedra in crystalline and vitreous SiO 2 is nearly the same [Wright, 1994; Dove et al., 1997; Clark et al, 2004]. The Si-O bonds in crystalline quartz are nearly incompressible [Hazen and Finger, 1982]. By assuming that this also holds true for SiO 4 tetrahedra in vitreous SiO2, Seifert et al. [1983] suggested that the pressure effects on the density of vitreous SiO 2 unlikely result from changes in Si-O bond distances. Furthermore, they noted that shortening of bond distances is reversible, whereas the density effects of glasses compressed both at 25° and 900°C (Fig. 5.8 and 5.23) are quenchable. These relationships point to rearrangement of the tetrahedra in the glass structure and not to compression of the Si-O bonds. Such rearrangement is not simply a change in Si-O-Si angles, however, because a comparison between quartz and vitreous SiO 2 reveals that the compression, V/Vo, is much less sensitive to changes in Si-O-Si angles for SiO 2 glass than for quartz (Fig. 5.24). Seifert etal. [1983] suggested, instead, that multiple compression mechanisms might operate in SiO 2 glass. The fastest relaxation occurs near 200°C with an activation energy

Figure 5.25 - Compression of intertetrahedral angle, Si-O-Si, as a function of pressure in SiO2 glass quenched from 900°C [Seifert et al., 1983].

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Figure 5.26 - Raman spectra of SiO2 glass at 25°C at the indicated pressures [Hemley etal, 1986].

in the 4-40 kJ/mol range. However, compressed SiO2 glass heated even to 700°C at ambient pressure retains the pressure-induced reduction of Si-O-Si angles. At this temperature, however, the activation energy of relaxation is so high (130-300 kJ/mol) that it likely reflects more than just angle relaxation and rotation of silicate tetrahedra [Kimmel and Uhlmann, 1969]. This relaxation may instead (or in addition to) also involve breakage of bonds in the structure, perhaps through the formation of an activated state [Angell and Torell, 1983]. High-pressure Raman and x-ray data of vitreous SiO2 are consistent with the idea that Si-O-Si angles govern at least some aspects of pressure-dependent properties [Seifert etal., 1983; Hemley etal., 1986; Meade etal, 1992]. Between ambient pressure and 2 GPa, for example, there is about a 1.5° decrease in the average Si-O-Si angle (Fig. 5.25). Higher-pressure Raman spectra (Fig. 5.26) suggest a further Si-O-Si angle decrease at least to about 8 GPa [Hemley et al., 1986, 1994]. Whether these changes in average Si-O-Si angle are similar for all structural entities in SiO2 glass or whether the proportion of coexisting, 3-dimensionally interconnected rings of SiO4 rings also depends on pressure, is not known. One might suggest intuitively that puckered rings are not favored by pressure. Instead, the ring structures would likely become less puckered with increasing pressure thus leading to increased Si-O-Si angle. One might also surmise that increasing pressure would tend to favor rings with smaller number of SiO4 tetrahedra because the larger the number of tetrahedra in a ring, the more open the structure. Regardless of the details, it is likely that the ring geometry it is affected by pressure. In a review of high-pressure response of the structure of vitreous SiO2, McMillan and Wolf [1995] proposed that the 3-dimensionally interconnected open network of glassy and molten SiO2 would encounter a deformation limit when the volume reaches about 17 cm3/mol. At or near this value, the material would reach a state where oxygen is in or near a cubic body-centered packing [see also Hazen et al., 1989], with Si-O-Si angles near 120°, and where the Si atoms would be in or near non-bonding contact. According to the equation-of-state of vitreous SiO2, the 17 cmVmol volume is reached at a pressure of

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Figure 5.27 - Unpolarized Raman spectra of SiO2 glass and supercooled melt at temperatures indicated on individual spectra. Tg indicates the glass transition temperature of SiO2 [Richet etal, 1982]. Arrow indicates approximate position of 440 cm1 band discussed in text [McMillan et al, 1994]. about 15 GPa at 25°C (see Fig. 5.23). From this reasoning, one may conclude, therefore, that a further pressure increase will cause a disruption of the SiO 2 network resulting from coordination changes of Si4+. Experimental data support this view. For example, the Raman spectrum of vitreous SiO2 undergoes dramatic changes between about 8 and 27 GPa (Fig. 5.26). At high pressure, the main peak is a broad band with a maximum near 600 cm 1 . Hemley et al. [1986] suggested that this spectrum reflects at least a portion of the Si4+ in oxygen coordination polyhedra with more than 4 oxygens. The infrared spectrum of vitreous SiO 2 above 20 GPa is also consistent with at least a partial coordination transformation of Si4+ [Williams et al, 1993]. Results from x-ray diffraction studies of SiO2 glass to 42 GPa point to a significant lengthening of the Si-0 bond [Meade et al, 1992]. Meade et al. [ 1992] concluded that the Si-0 bond length increases from 1.59 to 1.64 A between ambient pressure and 28 GPa and then to 1.66 A at 42 GPa. In stishovite, where Si4+ in 6-fold coordination, the Si-O bond length is 1.69 A at 42 GPa [Meade et al, 1992]. Thus, the xray data are consistent with at least a partial coordination transformation of Si4+ at pressures higher than about 15 GPa. These data also agree with the Raman and infrared information [Hemley et al, 1986, 1994; Williams et al, 1993]. 5.4b. Temperature The unusual temperature-dependence of many physical properties of SiO2 glass and melt suggests that temperature may cause unusual structural changes in these materials. One must determine, therefore, to what extent the structure of the melt differs from that of its glass.

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Figure 5.28 - Unpolarized Raman spectra recorded at 1677°C for supercooled SiO2 melt [McMillan et al, 1994] and at 1700°C for cristobalite [Richet and My sen, 1999].

The extent to which silicate structures change with increasing temperatures above the glass transition has been addressed by means of high-temperature Raman spectroscopy. Broadly speaking, the Raman spectra of SiO2 glass and supercooled liquid resemble one another on both sides of the glass transition (Fig. 5.27). Thus, to a first approximation, the structures of SiO2 melt above Tg and that of SiO2 glass below Tg appear similar. Interestingly, when cristobalite is heated to temperatures near its melting point, its Raman spectrum becomes more similar to that of SiO2 melt (Fig. 5.28). This observation is also consistent with the numerical simulation results of Bourova et al. [2000]. As discussed in sections 3.3b and 5.2, these similarities are also in agreement with the concept that the structure of SiO2 melt shares common traits with that of its liquidus phase, (3-cristobalite. Even though the Raman spectra of SiO2 glass and melt resemble one another (Fig. 5.29), there are subtle but important features that may reflect temperature-induced structural changes as SiO2 liquid is heated up. For example, the frequency of the 440 cm 1 band in the spectra of SiO2 (marked with an arrow in Fig. 5.27) exhibits a distinct change of slope at a temperature in the glass transition range (Fig. 5.29; see also McMillan et al. [1994]). None of the other bands in the Raman spectrum shows a similar temperaturedependent frequency. McMillan et al. [1994] suggested that the variation of the 440 cm1 band reflects the response to temperature of Si-O-Si angles in the network. The break in the slope of the Raman frequency-temperature relationship in the glass transition range was

Figure 5.29 - Shift of 440 cm1 band in Raman spectrum of SiO2 glass and melt as a function of temperature [McMillan etai, 1994].

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taken to suggest that there exist entities with small Si-O-Si angles in relaxed SiO2 melt but that these entities are less evident in SiO2 glass. This conclusion, consistent with other structural data [Geissberger and Galeener, 1983], indicates that the intertetrahedral angle in molten SiO2 decreases at a rate of about 1° per 100 K temperature increase. McMillan et al. [1994] proposed that the anomalous thermal expansion of SiO2 can be explained via this structural interpretation of their Raman spectra. In their view, the lowtemperature anharmonic narrowing of the Si-O-Si angles would tend to displace the Si atoms towards each other. This process would tend to move the silicate tetrahedra into free volumes in the structure and, in the process, to oppose the "normal" thermal expansion of the SiO2 melt structure. These competing effects may lead to the unusual behavior of properties of silica. 5.5. Summary Remarks 1. Silica is an exceptional oxide in many respects. One unusual feature is its many polymorphs of which five are liquidus phases. Transitions between crystalline and amorphous phases can also be unusual, with the occurrence of superheating and pressure-induced amorphization at room temperature. 2. Molten SiO2 is the archetype of the strong liquid with an almost Arrhenian variation of viscosity and a small configurational heat capacity. The physical properties of SiO2 glass and liquid are markedly affected by impurity content such as trace amounts of water. 3. Thermal expansion is small, but compressibility is large and mostly configurational in origin. In both cases, the temperature-dependence is slight and little difference is found between the properties of pure silica liquid and the partial molar properties of SiO2 in binary metal oxide-silica melts. The same applies to the configurational heat capacity. 4. At least to about 15 GPa, the structure of amorphous SiO2 has a 3-dimensionally interconnected structure of SiO4 tetrahedra. The average Si-O-Si angle is 144°-153° at ambient pressure. Most recent data suggest a 147° angle. 5. The average Si-O-Si angle decreases by about 1° per 100 K at temperatures above the glass transition range at ambient pressure. At least at room temperature, the angle decreases to about 120° at pressures near 15 GPa. At higher pressures, there is a gradual transformation of Si4+ from 4-fold to higher coordination with oxygen. 6. The structure of SiO2 glass and melt may consist of coexisting rings. Coexisting 6membered rings with different average intertetrahedral angles (5°-10°) are consistent with thermodynamic and property data.

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Binary Metal Oxide-Silica Systems I. Physical Properties There are many practical and fundamental reasons why the physical properties of molten silicates have been most extensively investigated for binary systems with either alkali or alkaline-earth oxides. For instance, low liquidus temperatures and ease of vitrification make a large variety of experiments feasible for alkali silicates over large temperature intervals that span both the stable and metastable states. Besides, such simple melts represent obvious model systems for industrially important materials as thousand of factories worldwide produce flat or container glass whose composition is approximately 70 mol % SiO2,15% Na2O and 15% CaO + MgO. Although alumina is a major component of magma, alkali and alkaline earth silicates also represent important starting points in geochemistry because the very high temperatures at which SiO2-Al2O3 melts must be studied raise considerable experimental difficulties. Hence, it is much easier to determine the effect of added alumina on the properties of metal oxide-silica systems than that of metal oxides on the properties of SiO2-Al2O3 melts. The main goal of this chapter is to present some general conclusions that can be drawn from macroscopic properties and to set the frame for the structural discussion that follows in the next chapter. In passing, we will also give a few glimpses into experimental accuracy and constraints. Because dealing with all important physical properties is beyond our scope, index of refraction, surface tension or internal friction will not be addressed. A wealth of references on these and other subjects can be found in available compilations [Mazurin etal, 1987; Bansal and Doremus, 1986]. Also note that ferrous iron is a divalent cation that exerts an influence on melt properties which, in some respect, is analogous to that of alkaline earths. In view of the complications raised by the existence of two valence states, however, the properties of iron-bearing melts will be dealt separately in Chapter 10. In the following, we will denote by M^O both alkali and alkaline-earth oxides, with x = 1 and 2 for the former and latter, respectively. 6.1. Phase Relationships Phase diagrams indicate the pressure and temperature conditions under which thermodynamic equilibrium between different phases is reached as a function of composition. They are a prerequisite to any practical use of amorphous silicates as liquidus and solidus relations indicate the temperatures at which the first crystal should form and that at which the last droplet of liquid should crystallize, respectively. From a fundamental

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Figure 6 . 1 - Phase diagrams of binary alkali (left) and alkaline earth (right) systems. Data of Kracek [1930a] and Haller [1974] for Li2O; Kracek [1930b], Williamson and Glasser [1965] and Haller et al. [1974] for Na2O; Kracek [1929, 1937] and Charles [1967] for K2O; Bowen and Andersen [1914] and Hageman et al. [1986] for MgO; Rankin and Wright [1915] and Tewey and Hess [1979] for CaO; and Eskola [1922] and Seward et al. [1968] for BaO. See Levin [1970], Mazurin et al. [ 1984] and Hudon and Baker [2002a] for other determinations or assessments of miscibility gaps.

Binary Metal Oxide-Silica Systems I. Physical Properties standpoint, phase diagrams represent an integrated balance of crystal and melt properties that can be subjected to quantitative thermodynamic analyses. These relations also point to significant structural similarity between amorphous and crystalline phases and, thus, give useful information on mixing in both. 6.1 a. Phase Diagrams: Liquidus and Solvus Relations Solid-liquid phase relations in silicate systems are usually determined from quenching experiments because, except for transformations involving very fluid Si02-poor melts, melting and crystallization near equilibrium are sluggish reactions. For simple systems, these experiments have been performed during the first half of the 20th century with an unsurpassed care. At the highest reported temperatures, slight adjustments of up to 20 degrees may be needed from the original temperature scale to the current International Practical Temperature Scale [e.g., Sosman, 1952]. Of more serious concern is the fact that, owing to the lack of microanalytical methods at that time, the petrographic microscope was the main tool used for mineral characterization. With the exception of well-known continuous solid solutions, minerals were thus generally assumed to have the nominal stoichiometry and phase diagrams to be eutectic when they actually could have shown narrow solid solutions. These limitations should be kept in mind when examining silicate phase diagrams determined in this manner. At least in the SiO2-rich parts of phase diagrams, however, solid solutions are unlikely significant in binary metal oxide-silica systems with alkali and alkaline earth elements (Fig. 6.1). For the sake of comparison, the experimental data have been plotted in these diagrams on a mol % basis. A common topology is observed for all systems. The main features are the occurrence of liquid immiscibility at high silica contents and the existence of eutectic-type equilibria at high metal oxide concentrations. In both instances, the equilibrium temperatures and compositions depend systematically on the cation size and charge, such that the trend defined by alkaline cations is extended by alkaline earth cations (Table 6.1). Concerning the critical temperature of the miscibility gap, an important distinction must first be made depending on whether liquid unmixing takes place at temperatures higher or lower than the liquidus. In the former case (e.g., Ca, Mg), liquid immiscibility is stable and precedes crystallization because of very rapid kinetics at the high temperatures at which it takes place. In the latter case (e.g., Ba, Li, Na, K), phase separation is metastable and can proceed only if crystallization is bypassed. In view of the low temperatures at which it develops, the process is time dependent and its kinetics practically vanish below the glass transition. As a result, in M2O-SiO2 systems the solvus is still controversial for K2O, whereas its existence for Rb2O and Cs2O cannot be observed because the critical temperature, if any, is likely lower than the standard glass transition. 6.1 b. The Difficult Match with Q3 Species A general trend apparent in Fig. 6.1 is that the composition of the most silica-rich compound shifts toward the metal oxide when the ionization potential of the cation decreases. Whereas potassium fits in a tetrasilicate crystal (80 mol % SiO2), calcium and magnesium are

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Table 6.1. Binary systems: composition of the most silica-rich liquidus phase, temperature of the deepest eutectic, and critical temperature and width at the monotectic of the solvus (mol % ) b First compound mol%SiO 2 NBO/T K2O Na2Oa Li2O BaO SrO CaO MgO a b

80 73 67 67 50 50 50

3.5 3.25 3 3 2 2 2

^«,(°C) ?380 800 1000 1370 1358 1460 1543

Solvus Tc (°C) Width 350 820 1000 1460 1642 1890 1960

19 28 39

Na 6 Si 8 0 19 (N3S8): incongruently melting compound [Williamson and Glasser, 1976]. See Fig. 6.1 for references. Data for SrO from Hageman and Oonk [1986].

incorporated only in crystals with at most 50 mol % SiO2. On the SiO2-poor side of the diagrams, in contrast, there can be a variety of compounds with M / ) contents higher than the 50 mol % of metasilicates. This difference in mixing between the two sides of metal oxide-silica systems also holds for liquids. A single solution exists for SiO2-poor compositions, but the difficulty of mixing pure SiO2 with metal oxides is indicated by the prevalence of liquid-liquid unmixing. In all systems, a very SiO2-rich melt coexists with another phase whose composition becomes more M^O-rich at lower temperatures and tends to that of the first existing silicate compound (Fig. 6.1). For the silica-rich phase, structural mismatch is reduced only near the critical point where the width of the solvus becomes narrower because the possibility of incorporating some metal oxide becomes effective. As was already described by Warren and Pincus [1940] for miscibility gaps, phase diagrams provide valuable information about the competition between silicon and other metal cations for bonding with oxygen. In either a crystalline or in an amorphous phase, it is clearly difficult to form the coordination polyhedra of the network-modifying cations with the oxygens of a silica-rich framework. Optimization of coordination polyhedra of metal cations requires a number of nonbridging oxygens. As discussed further in section 7.4d, the first nonbridging oxygens formed belong to Q3 species when the continuous three-dimensional network of pure SiO2 melt begins to depolymerize. But bonding to the nonbridging oxygen of a number of Q3 species meets with serious steric hindrance, and thus energetic difficulties. Nonbridging oxygens belonging to smaller entities, to which metal cations can bond more readily, are provided by disproportion reactions of the form 2 Q3 <s=> Q2 + Q . The need for a metal cation to bond to several nonbridging oxygens causes segregation of Q and Q species and eventually formation of two different phases, which both have a narrow Q"-distribution. As nonbridging oxygens are scarce, the Q -rich phase generally remains close in composition to pure SiO2, whereas greater flexibility in the more

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173

depolymerized phase allows its composition to vary with temperature. Beyond the metasilicate stoichiometry, Q1 and Q° species become common [Mysen et al., 1982]. They represent an abundant resource of nonbridging oxygens to which metal cations can bond readily. In the system MgO-SiO2, bonding is optimized in the single forsterite (Mg2Si04) structure. For the lower field strength cations Ca and Ba, by contrast, the existence of a series of compounds points to greater possibilities of combining metal oxide and silicon coordination polyhedra. Such a description is only a starting point, however, as other factors must be invoked for a more realist description [see Charles, 1969; Levin, 1970; Hudon and Baker, 2002a,b]. In particular, the nominal number of nonbridging oxygens is not sufficient to account for metal cation content along the SiO2-rich branch of the solvus. The effective electrical charge of bridging oxygens, which is not zero (section 3.1a), should also be considered. As such, it allows these oxygens to contribute to the coordination polyhedra of metal cations, a feature observed in molecular dynamics simulations [Cormak and Du, 2001]. Everything else being equal, large miscibility gaps are produced by small cations with a high ionization potential which compete the most effectively with silicon for oxygen. For large cations with a low ionization potential, the steric hindrance and energetic problems are less severe so that the solubility of the metal oxide in SiO2 is more extensive. This interpretation agrees with the observation that, in crystal structures, the more silicarich the mineral, the greater the steric hindrance associated with bonding of alkali and alkaline earth to oxygen. In other words, the availability of electron donors diminishes with greater SiO2 content, thus restricting the types of crystal structures that may form. In crystal structures with silicate chains, for example, the chains become less stretched (more buckled) the greater the ionization potential of the metal [Liebau and Pallas, 1981]. 6.1c. Energetics and Phase Stability The differences in ionization potential or bond strength discussed in Chapter 4 also manifest themselves in the phase diagrams of Fig. 6.1. The stable or metastable nature of the solvus reflects directly the differing strength of interactions of oxygens with alkaline earth and alkali cations in the SiO2-rich parts of the diagrams. Likewise, melting is associated with configurational rearrangements which require lower thermal energy when bonding is weak. Liquidus temperatures thus are systematically lower for alkali than for alkaline earth systems and vary systematically in both series (Fig. 6.1). The differences are especially large at the eutectic points, which are as low as 800°C for alkali but higher than 1300°C for alkaline earth systems. The contrast between alkali and alkaline earth silicate systems extends dramatically toward the pure metal oxide endmembers. Liquidus temperatures rise very steeply toward CaO or MgO, which are among the most refractory compounds known. In this respect, it might seem paradoxical that CaO and MgO melt at a much higher temperature than SiO2 polymorphs given the lower strength of M-0 compared to Si-0 bonds. This apparent anomaly is due to the ready configurational changes in molten SiO2 that are made

174

Chapter 6

possible, without severing of Si-0 bonds, by the great flexibility of Si-O-Si angles (see section 5.1). Solid-liquid phase diagrams do not picture glass-forming regions because vitrification is not an equilibrium but a kinetic process (see section 2.3e). As already pointed out, the glass-forming ability of alkaline earth silicate melts is severely limited to a narrow range near eutectic points. On the SiO2-rich side, formation of homogeneous glasses is prevented by stable liquid immiscibility. At high M/) contents, rapid crystallization takes place, probably because too much configurational entropy is lost on cooling: ultrafast quenching techniques are, then, required to make glasses which have fictive temperatures much higher than the standard T . As for alkali-rich crystalline silicates, they do not give rise to glasses because they decompose increasingly readily, in the order of increasing alkali mass, on moderate heating well before melting (Fig. 6.1). An analogous trend is observed for the hygroscopicity of alkali-silicate glasses and crystals, which indicates that protons compete successfully with alkali, but not with alkaline earth cations, to bind with oxygen. Hygroscopicity is in fact such a problem that physical or structural information is very scarce for binary Rb2O- and Cs2O-SiO2 systems. 6.2. Thermodynamics of Mixing In multicomponent systems, phase relationships at a given pressure and temperature are determined by the composition dependence of Gibbs free energies of mixing, AGm, which are themselves made up of enthalpy and entropy contributions. When dealing with silicate melts, the basic difficulty is that information on the latter is virtually nonexistent. Although, as described in section 2.3d, entropies of mixing could be obtained from analysis of viscosity data, little use has been made of such results in thermodynamic modeling. In this section we will thus begin with a review of only enthalpies of mixing. 6.2a. Enthalpy of Mixing Thermodynamically, two phases unmix if phase separation causes a decrease of the Gibbs free energy of the system. In other words, the Gibbs free energy of mixing must be positive: AGm = AHm-TASm>0,

(6.1)

where AHm and A5m denote the enthalpy and entropy of mixing. Because ASm is positive, phase separation requires a positive enthalpy of mixing of magnitude greater than TASm (Fig. 6.2). Unmixing in silicate melts usually tends to disappear at higher temperatures, however, because of the increasing contribution of TASm to AGm. In other words, the width of the solvus decreases with increasing temperature and vanishes at the critical point when the entropy term, which favors mixing, takes over the enthalpy term of steric hindrance in the Gibbs free energy of mixing of the system. Enthalpies of mixing should correlate with critical temperature and extent of liquid immiscibility in the SiO2-rich parts of the binary systems of Fig. 6.1, and, thus, with the ionization potential of the cation. Although AHm could be determined from solution

175

Binary Metal Oxide-Silica Systems I. Physical Properties

0 A

0.2

0.4

0.6 X

Figure 6.2 - Gibbs free energy in a phase-separating binary system A-B. (a) Gibbs free energy of mixing, AGm, as given by the difference between the Gibbs free energy of the solution (solid curve) and that of a mechanical mixture of the components A and B (dashed line). In silicate melts, unmixing is a very sensitive probe of the energetics as the associated AGm is only a few hundred joules [see Tewhey and Hess, 1979]. In the central part of the diagram, the solution is unstable because any composition fluctuation causes a decrease of G. In the metastable range [Cahn and Charles, 1965], unmixing takes place through nucleation and growth as separation in two phases first causes an increase of G. At both ends the solution is stable. The compositions N and N' of the coexisting liquids are determined by the two points at which the G curve has a common tangent such that the criterion (6.5), see below, is satisfied; the chemical potentials of both components are then given by the intercepts of this tangent on the A and B axes, (b) Variation with temperature (in K) of AGm for a symmetric AHm - Wx (1 - x), with W= 20 kJ/mol (dashed curve), and an ideal entropy of mixing ASm = - R Ex In x (R = gas constant). In this case, the critical point is Tc = W/2R = 1200 K as determined from the criterion (d^Gldxy)PT = 0. calorimetry experiments, such data are lacking. For alkaline earth systems, homogeneous amorphous samples cannot be obtained over sufficiently large composition intervals. For alkali silicates, reliable data are limited to sodium silicates from pure SiO2 to the metasilicate composition (Fig. 6.3). The data define two distinct composition ranges when referred to isothermal values with equation (2.15). From 100 to about 70 mol % SiO2, an excess enthalpy is clearly observed. Within the field of metastable liquid immiscibility, it translates to a positive enthalpy of mixing of about 4 kJ/mol near 10 mol % Na2O. The Figure 6.3 - Enthalpy of solution of ', glasses in HF solutions at 50°C [Hovis et al., 2004]. All data are referred to 1000 K; a comparison with the raw data of Fig. 4.21 shows the effect of this adjustment. The straight lines represent ideal mixing within the two subsystems that join near 30 mol % Na2O. Enthalpies of mixing do not depend on temperature because of the linear variation of C with composition for the liquids (see Fig. 6.4).

176

Chapter 6

asymmetry of the AHm curve indicates that partial molar enthalpies of mixing are much greater near the SiO2 endmember than on the other side of the solvus of the system. This observation agrees with the fact that the composition of the SiO2-rich unmixed phase varies much less with temperature than that of the second phase. From about 70 to 50 mol % SiO2, enthalpies vary linearly with composition, which shows that mixing of silicate entities becomes almost ideal when the amount of Q4 species vanishes. 6.2b. Heat Capacity The heat capacity determines the temperature dependences of the Gibbs free energy and other thermodynamic functions. Its basic importance for igneous petrology was stressed by Carmichael et al. [1977] who performed the first systematic measurements on compositions of geochemical interest. To give a specific example, enthalpy of mixing as derived in previous section from solution calorimetry relies on appropriate C data for glasses and liquids. The heat capacity must also be known in solid-liquid phase equilibria calculations. Given the differences between crystal and melt properties illustrated by Fig. 3.7, the freezing point depressions that can reach 1000 K in binary alkali silicates cannot be modeled correctly without the required heat capacity data. Because the heat capacity can be split into vibrational and configurational parts, the latter can also provide basic information on atomic interactions. A summary of available C measurements for binary metal oxide-silicate melts is given in Fig. 6.4. In most systems, the heat capacity does not depend on temperature and is a linear function of composition from pure SiO2 to the highest metal oxide content investigated. Hence, when writing Cp = lXiCPi=lXiCp;

(6.2)

where x, is the mol fraction of oxide i, CPi, the partial molar heat capacity of i does not depend on composition (and also on temperature) and thus is equal to a constant value C p°. The conclusion is best established for sodium silicates where measurements have been made on temperature intervals reaching 1000 K for the stable and supercooled liquid states. It is more circumstantial for CaO and MgO, in which cases the conclusion has to be drawn from analyses of data for more complicated melts because liquid immiscibility restricts measurements in binary systems to too narrow composition intervals. The only exceptions to these simple trends are provided by potassium silicates for which C increases with temperature and does not vary linearly with composition (Fig. 6.4). Similar variations for the binary systems involving the heavier alkali elements Rb and Cs could be expected, but measurements are lacking for both alkalis to check this assumption. An important practical consequence of the lack of excess heat capacity embodied in the linear trends of Fig. 6.4 is that both enthalpy and entropy of mixing are independent of temperature. In addition, from the thermodynamic relationship: G, = Cp; - 2 RT(3ln y/dT)Pnj - RT1 0 2 In y/dT2)^,

(6.3)

Binary Metal Oxide-Silica Systems I. Physical Properties

177

Figure 6.4 - Heat capacity of binary silicate liquids. All C data are temperature independent, except for the K2O-SiO2 system for which C is shown at 1200 and 1800 K. Data from from Stebbins et al. [1984] for 66 mol % BaO, and from Richet et al. [1984], RichetandBottinga [1985],Tequi et al. [1992] for other melts.

one concludes that the activity coefficient of any oxide i varies with temperature as InYi=kt/r+kj2

(6.4)

whenever the partial molar heat capacities of oxide components are independent of the composition of the melt. The configurational heat capacity is approximated by the difference between the measured C and the vibrational value of 3/?/g atom K (see section 2.3a). Its magnitude is higher for alkali than for alkaline earth elements. As noted by Stebbins et al. [1984], it actually increases with the ionization potential of the cation and, thus, correlates with the extent of liquid immiscibility. In this respect, an important conclusion is that the partial molar heat capacities of SiO2 and metal oxides do not generally depend on composition even though the melt structure varies widely between pure SiO2 and the metasilicate stoichiometry, i.e., from predominantly Q4- to Q2-species and with NBO/T varying from 0 to 2. This feature indicates that temperature-induced structural changes in melts depend mainly on the basic structural units that do not change much with composition, and not on the details of the structure. Hence, most of the configurational heat capacity is associated with short-range oxygen-cation interactions, which are also at the roots of liquid immiscibility, and with coordination changes of network-forming cations as observed for Si [Stebbins, 1991; Stebbins and McMillan, 1993]. This view does not mean that mediumrange order is not affected but, rather, that the energetics involved in such changes are small, as already stated in section 3.2c from an analysis of low-temperature heat capacities. 6.2c. Activity ofSiO2 in Binary Melts A review of phase diagram calculations is beyond the scope of this chapter. We will limit ourselves to the observed regularities in liquidus branches of the SiO2-rich parts of the diagrams and to the main factors that determine variations of SiO2 and M^O activities. In a system in thermodynamic equilibrium, the temperature and pressure are constant and the chemical potential (/i) of any component i is the same in all coexisting phases. Equilibrium between two phases a and (3 (either solid and liquid, or both liquid) thus requires that:

178 tf= H?

Chapter 6 (6-5)

for each independent component of the system. By expressing the chemical composition of the relevant solid or liquid solution in terms of mol fraction, xt, one writes for the chemical potential of component i in this phase: /i,. = n° + RTIn a,. = n° + RTInxt + RTIn y;,

(6.6)

where R is the gas constant, fi° the standard potential, a, the activity, and yt the activity coefficient of component i. Alternatively, the chemical potential of i can be expressed as ^,. = /V + A7L - rA
(6.7)

where AHmi and AS™ are the partial molar enthalpies and entropies of mixing of i in the relevant solid or liquid solutions. In both cases, the standard state is usually taken as pure / in the crystalline state at the temperature and pressure of interest. In the absence of solid solution, the chemical potential of the crystalline phase then reduces to ^ = H°c + RT\na'=nr

(6-8)

because the activity of i is unity in the crystal. Phase relations could be calculated if either the activity-composition relationships or the enthalpies and entropies of mixing were known independently over the relevant temperature and composition ranges. These data are now available for major solid solutions [see Geiger, 2001; Fabrichnaya et al., 2004]. By contrast, only activity data are available for binary metal oxide-silica melts. For more complicated systems, these are generally lacking for a variety of reasons, such as difficulties of high-temperature experiments or the almost infinite diversity of chemical composition to be dealt with. Hence, phase diagrams still represent the main and most abundant source of thermodynamic information, for equations of the form (6.1) can be written for two or more phases along any coexistence curve. The phase diagram information is available in the form of extensive compilations [Levin et al., 1975], but it is incomplete since temperature and composition are not independent variables along a liquidus or a solvus. The limitation is no longer serious, however, because the availability of heat capacity data now allows the temperature dependence of thermodynamic functions to be calculated properly. In this respect, the thermodynamic significance of the regular evolution of the liquidus branches of Fig. 6.1 near pure SiO2 was pointed out by Kracek [1930c]. Along related lines, Ryerson [1985] noted that cristobalite can be considered a pure phase in binary metal oxide-silica systems. When cristobalite is in equilibrium with a melt, equations (6.5) and (6.8) state that the activity of SiO2 in the liquid (aSio2me") is buffered to the unity value of the SiO2 activity in the crystal. From the known SiO2 mol fraction of the melt in equilibrium with cristobalite, it is possible to calculate tfsiCh""*w i t n equations * (6.5)-(6.6) and to determine how the activity coefficient of SiO2 in the melt

179

Binary Metal Oxide-Silica Systems I. Physical Properties

100

Figure 6.5 - (a) Liquidus branches in the SiO2-rich part of binary silicate melts, (b) Derived activity coefficient of SiO2 in the meltatl550°C [Ryerson, 1985].

varies with the network-modifier metal cation. By assuming that the partial molar enthalpy of SiO2 in a given system is constant, Ryerson [1985] derived the activity coefficients of the form (6.4) plotted in Fig. 6.5 along with the input liquidus information. There is a clear hierarchy in these data since /sick"1*" *s positively correlated with the ionization potential of alkali metal and alkaline earth. This trend is, of course, consistent with the inferences drawn from liquid immiscibility relations in the same systems. In other words, the increase in steric hindrance as the Z/r2 of the metal cation increases is reflected by increased activity coefficients of SiO2. 6.2d. Oxygen Activity and Acid-Base Reactions We now turn to the more important variations of the SiO2 activity induced by large changes in the NBO/T of the melt. Such determinations can be made through measurements of vapor pressures [e.g., Frohberg et al., 1973; Plante, 1978] and electromotive forces [e.g., Kohsaka et al., 1979], or through studies of equilibration of the melt with another phase for which the activity-composition relationship of the component of interest is known [e.g., Rao and Gaskell, 1981; Chamberlin et al., 1994]. For alkali silicates, the activity of metal oxides has also been determined from ionic conductivity measurements with the assumption that the number of M+ carriers is determined by the dissociation equilibrium of metal oxide into M+ and OM" ions [Ravaine and Souquet, 1977]. Often, the experiments cannot be performed from 0 to 100 mol % SiO2 with the same method or the activity of only one component can be measured, in which case that of the second can be determined through integration of the Gibbs-Duhem equation. In all instances, the silica activity decreases from values higher or lower than unity near pure SiO2 (Fig. 6.5) to become close to zero at a low M^O concentration which depends on the M-cation (Fig. 6.6). Such variations are intimately related to the acid-base character of the oxygen speciation reactions. In this respect, we may recall first that, in the 19th century, it became widely believed that all silicates derived from silicic acid, H 4 Si0 4 . A reminder of these ideas is the use of the terms acid and basic applied to igneous rocks to designate what today is more properly denoted by silicic and mafic (from Mg and Fe) rocks, respectively. Ironically, more recent ideas could be invoked to justify this old nomenclature. The success of the ionic theories developed by Arrhenius and Bronsted for aqueous solutions have resulted in attempts at transposing analogous concepts to reactions in other

Chapter 6

180

Figure 6.6 - Activity of SiO 2 in binary systems. Values determined from electrochemical experiments for Na 2 O-SiO 2 at 1200°C and K 2 O-SiO 2 melts at 1100°C [Frohberg et al., 1973], and from the equilibrium constant of the reaction SiO 2 + 3 C <=> SiC + 2 CO measured for CaO-SiO 2 melts at 1550°C [Kay and Taylor, I960].

kinds of solvents. Adopting Lewis' [1923] definition of acids and bases as acceptors and donors of an electron doublet, respectively, Lux [1939] and Flood and Forland [1947] for instance considered that acid-base reactions take place in molten oxides via exchange of "free" O2~ ions. According to this definition, SiO2 is an acid whereas metal oxides are bases, in accordance with the basic character long attributed to an oxide like CaO. To account for such acid-base reactions, Toop and Sammis [1962] started from the equilibrium between the three different kinds of oxygens first considered by Fincham and Richardson [1954]: O° (bridging oxygen) + O2" (free oxygen) <=> 2 O" (nonbridging oxygen).

(6.9)

Of course, equation (6.9) is just a shorthand notation for the various reactions that involve more complex entities with various proportions of bridging and nonbridging oxygens. The equilibrium constant of this reaction is related to the oxygen ion activities by: K=ao2/(ao0aO2-).

(6.10)

Finally, the Gibbs free energy of mixing is given by AGm = 0.5No .RT\nK,

(6.11)

because NOJ2 oxygens react for one mole of melt. By definition, AGm is independent of composition and is proportional to the degree of depolymerization. With the assumption of ideal mixing, activities are replaced by mol fractions in equation (6.10). In addition, there are two equations accounting for the tetrahedral coordination of Si and the total number of free oxygen ions: 2N& + No. = 4NSi,

(6-12)

NO2-= l-NSi-NoJ2,

(6.13)

where NSi is the number of moles of SiO2. Various oxygen distributions for differing values of K are readily calculated from this set of three equations (Fig. 6.7). The two extreme situations are K = 0 and K = °°. In the former, only free and bridging oxygens

Binary Metal Oxide-Silica Systems I. Physical Properties

181

exist, which is tantamount to a mixing of SiO2 and M^O units. In the latter, nonbridging oxygens coexist with either free oxygens below 33 mol % SiO2, or with bridging oxygens at higher SiO2 contents. In the intermediate case of K = 17 in Fig. 6.7, all three species coexist. Their concentrations vary smoothly with SiO2 content: that of nonbridging oxygens peaks near the orthosilicate stoichiometry, whereas those of free and bridging oxygens decrease or increase continuously. Because individual ion activities cannot be determined, the next step is to derive the activities of oxides which are actually measured (e.g., Fig. 6.6). For this purpose, one can use Temkin's [1945] model, which assumes that anions and cations mix separately in different sublattices. For the metal oxide component of a melt, the activity is written as the product of the activities of the anionic and cationic r.nnstitnents as follows«M 2 O

= (aM"*f12 aoi-

(6.14)

From activity data available for various binary systems, Toop and Sammis [1962] determined values of Pranging from 0.35 for Cu2O at 1100°C to 0.0017 for CaO at 1600°C. Besides, an interesting implication of this formalism is that the activity of free oxygen ions is a measure of melt basicity through the relation aoi- = a0.aGo).

(6.15)

To a first approximation, the oxygen ion activity is also a measure of the melt depolymerization or, more precisely, of the ratio between nonbridging and bridging oxygens. Through the very simple Toop and Sammis [1962] model, the considerable variations of asio2melt are related in this manner to changes in the concentrations of the three kinds of oxygen ions. Because it distinguishes only three different species, the model could in principle be generalized to multicomponent systems. Agreement with experimental activity data is not excellent, however, because the four basic assumptions are not really valid even for binary systems: (i) The equilibrium constant K does depend on composition and, thus, on the degree of polymerization of the melt and, in particular, on Q"-speciation for a given composition [Dron,

Figure 6.7 - Distribution of oxygen ions in metal oxygen-silica melts from equations (6.12-6.15) for the indicated values of the equilibrium constant K [from Hess, 1980].

182

Chapter 6

1982]. As described in Chapter 10, such a simple formalism fails when applied to iron redox reactions because the activity coefficients of the three kinds of oxygens involved depend on the composition of the system. (ii) The three types of oxygens do not mix ideally, as indicated by the prevalence of stable or metastable miscibility gaps in binary metal oxide-silica systems and by the existence of positive enthalpies of mixing (Fig. 6.3). Thus, the oxygen activities in equation (6.10) are average values. (iii) The assumption that the metal oxide M^O dissociates entirely is difficult to ascertain, for this would require characterization of all sorts of M-O bonds. However, no significant "free" oxygen ions have, for instance, been observed in silicates with more than 50 mol % SiO2 through electrical conductivity measurements (see section 6.3c). (iv) The Gibbs free energy of mixing is not entirely due to mixing of the three kinds of oxygen ions, because their distribution within the Q"-units and mixing of larger anionic units should also contribute to entropy of mixing. Such features have been taken into account in different ways to achieve agreement with experimental activity data [e.g., Ravaine and Souquet, 1978; Rego et al., 1985]. Another approach was inspired by polymer theory to describe progressive condensation of the silicate network [Masson, 1968,1977]. Such models have already been reviewed [Hess, 1980, Bottinga et al, 1981]. They will not be discussed further because they have not been generalized to multicomponent systems or because they do not lend themselves to ready structural interpretations. We also refer to Blander and Pelton [1987] or Pelton and Wu [1999] for a formal discussion of phase diagram calculations in relation to activity modeling. In passing, we also add that, as originally used by Richardson [1956], the Temkin model is most appropriate to calculate activities in ternary melts when similar M-cations are exchanged. The success of acid-base theories in aqueous solutions rests primarily on the welldefined nature and extremely small concentration of solutes. It is this fact that allows activities to be either approximated by mol fractions, or readily calculated from the DebyeHiickel theory of electrolytes for solute concentration of up to about 1 mol %. Although a Debye-Hiickel formalism has been used to model liquid immiscibility in binary metal oxide-silica systems [Tomozawa et al, 1990], no further application has been made. As a matter of fact, a general theory of aqueous solutions valid for concentrations of solutes similar to those of M^O oxides in silicate melts remains to be worked out. Hence, formalisms established for concentrated aqueous solutions are unlikely to be transposable to silicate melts where MOn complexes are not discrete, independent entities dispersed throughout the solvent but essential components of the structure. These differences notwithstanding, there remain definite similarities between the optical spectra of ions in silicate glasses and in aqueous solutions [see Duffy and Ingram, 2002]. The similar colors conferred by dissolved ions in both cases are the most obvious manifestation of this kinship. For this reason, Duffy and Ingram [1971] assumed that spectroscopic measurement could provide a measure of the electron donor power of oxygen as a function of the nature of the cation. Such a general scale of optical basicity relies on ultraviolet spectroscopic measurements made on dissolved ions, such as Tl+ and Pb2+, whose

183

Binary Metal Oxide-Silica Systems I. Physical Properties

Figure 6.8 - Molar volumes of Na2O-SiO2 glasses and melts for the Na2O mol fractions indicated. Dilatometric data of Shermer [1956] up to the glass transition and Archimedean measurements of Bockris et al. [1956] above the liquidus.

electron densities are very sensitive probes of the extent to which these ions receive negative charge from oxygen atoms. Duffy and Ingram [1971] thus defined the optical basicity as: A

= (vfree ion "

glassV(vfree ion " V Ca O -'

(6.

16

)

where V is the s-p frequency of the probe ion in a free, uncomplexed state (e.g., 60 700 cm"1 for Pb 2+ ), in the glass, and in crystalline CaO (e.g., 29 700 cm"1 for Pb 2+ ) which is taken as a convenient reference state. This parameter ranges from 0.33 (P5+) to 1.7 (Cs + ), with values of 0.48 (Si 4+ ), 0.60 (Al 3+ ), 1.0 (Fe 2+ ), 1.15 (Na+) and 1.3 (Mg 2+ ). It can be used for phosphate and other oxidic glass. Hence, it allows basicity to be determined directly for a variety of complex materials and to be related to other measures of basicity such as carbonate or sulphide solubility [e.g., Moretti and Ottonello, 2003]. Further work has lead to its empirical determination as a function of composition [Duffy, 1993; Mills, 1993], 6.3. Volume and Transport Properties In industry or in the earth sciences, few physical properties of silicate melts match in practical importance volume (or density) and viscosity. Both properties also are of fundamental interest. Whereas volume is a direct measure of ionic radii and atomic packing, the fact that viscosity is a very strong function of composition has been used to derive the first realistic structural models of melts [Bockris et al., 1956]. In addition to volume and viscosity, electrical conductance must be mentioned because this transport property has provided the most demonstrative evidence for the partially ionic nature of silicate melts [Bockris etal, 1952b]. 6.3a. Volume and Thermal Expansion The limitations of glasses as model substances for liquids are particularly clear when one considers the volume-composition relationship of sodium silicates (Fig. 6.8). Not only is the thermal expansion coefficient much smaller for glasses than for liquids, but the voTumecomposition relationships are markedly different in both kinds of phases. Because the thermal expansion coefficient of liquids increases strongly with increasing NajO content, the density

184

Chapter 6

mol % SiO

mol % SiO

Figure 6.9 - Molar volumes of binary metal oxide-silica melts at 1400°C. (a) Alkali silicates [Bockris et al, 1956]; (b) Alkaline earth silicates [Tomlinson et al, 1958].

decreases sympathetically for high-temperature liquids, whereas it increases for glasses and liquids below about 1300 K. The effect, of course, reflects the increasingly important configurational changes that take place in the liquid as a result of increasing depolymerization. For glasses, the density and thermal expansion are readily measured through Archimedean and dilatometric experiments, respectively. As apparent in Fig. 2.1, however, softening of the sample in the glass transition range and then too high viscosities, often associated with partial crystallization, prevent dilatometric measurements at higher temperatures. For melts, several methods can be used when the viscosity has become sufficiently low above the liquidus. The most precise is high-temperature Archimedean measurements [see data comparisons by Bottinga et al., 1983]. By combining such data with volumes determined by dilatometry at the glass transition, one can determine an average thermal expansion coefficient for the liquid, a=\IV{dV/&T)p,

(6.17)

as shown in Fig. 6.8 for sodium silicates [Richet and Bottinga, 1983]. In this case, the differences in the density-composition relationships between the glass and hightemperature liquid illustrate the importance of knowing the changes in thermal expansion coefficient at the glass transition as accurately as possible. For binary metal oxide-silica systems, the most precise and extensive measurements remain those of Bockris et al. [1956] for alkalis and Tomlinson et al. [1958] for alkaline earths. In all cases (Fig. 6.9), the volume-composition relationships are linear within experimental error. As emphasized by Bottinga and Weill [1970], the partial molar volumes of oxides thus are essentially independent of composition from 40 to 80 mol % SiO2. For the SiO2 component, the partial molar volume of about 26.8 cm3/mol is, in addition, almost temperature independent. If volume is an additive function of composition at any temperature, then additivity also holds true for (dV/dT)p with the consequence that the thermal expansion coefficient, as given by equation (6.17), cannot be exact linear functions of composition. But the effect is small so that, in the high-temperature range investigated

Binary Metal Oxide-Silica Systems I. Physical Properties

185

Figure 6.10 - Thermal expansion coefficient of binary metal oxide-silica melts at 1400°C. (a) Alkali silicates [Bockris et al., 1956]; (b) Alkaline earth silicates, for which the scatter in the data is relatively high [Tomlinson et ah, 1958].

by Archimedean methods, a is also an additive function of composition within experimental errors (Fig. 6.10). The continuous decrease of thermal expansion down to pure SiO2 is, in particular, borne out by the data for binary systems. Such linear variations seem to leave little room for detailed structural interpretations except for the fact that, as expected, partial molar volumes of oxides vary with the ionic radius of the network-modifying cation [see Lange and Carmichael, 1990], and that changes in Q"-speciation does not have significant effects on the partial molar volume of SiO2 and metal oxides. The measurements for homogeneous BaO- and Na2O-bearing melts suggest, however, a breakdown of linearity near pure SiO2 (Fig. 5.7). The partial molar volume of SiO2 apparently increases from 26.8 cm3/mol for 80 mol % SiO2, to 27.3 cm3/mol for 90 mol% SiO2. This effect has been attributed to a greater volume for bridging than for nonbridging oxygens [Bottinga and Richet, 1995]. Since volume is the pressure derivative of the Gibbs free energy, it follows that high pressure should promote depolymerization of the silicate framework, a conclusion consistent with the decreases of viscosity with pressure observed for silicates with a low NBO/T (see section 7.4c). Finally, it is often overlooked that density, along with chemical composition, remains a basic parameter for characterizing a glass. As given by the analog of equation (2.15) for enthalpy, the density of a glass varies with the fictive temperature, T, as follows dp=p(a,-a)dT,

(6.18)

where at and ag are the thermal expansion coefficients of the liquid and glass, respectively. For a given composition, the effects are small because the range of fictive temperatures that can be achieved with usual laboratory cooling rates is generally a few tens of degrees (section 2.2b). In contrast, the effects of fictive temperature differences are not necessarily negligible when dealing with different glasses belonging to the same system. The extreme case is that of binary alkali silicates whose fictive temperatures can be lower than that of pure SiO2 by 700 K or even more.

186

Chapter 6

Figure 6.11 - Structural relaxation in sound velocity measurements made at the indicated frequencies for two potassium silicates [Laberge et ah, 1973]. For both melts, equilibrium values are observed above 1300°C, where the viscosity is about 20 Pa s [Bockrisera/., 1955].

With typical values for silicates p = 3 g/cm3, a, = 8 10~5 and av = 10"5 K"1, equation (6.17) indicates that a fictive temperature difference of 100 K translates into a density change of 0.02 g/cm3. This figure, in fact, represents the magnitude of density changes induced by variations in medium-range order. Hence, such simple calculations could be used to constrain models of glass structure. Conversely, slight apparent breaks found near eutectic compositions in density-composition relationships determined for glasses at room temperature have been interpreted in terms of varying substructure [Robinson, 1969; Doweidar, 1996]. To be warranted, however, such interpretations should first rule out any bias due to differing thermal histories. 6.3b. Compressibility High-pressure volumes can be calculated from the isothermal compressibility, PT=-l/V{dV/dP)r

(6.19)

Figure 6.12 - Elastic properties of binary silicate liquids, (a) Sound velocity at 1900 K for Ca, at 1670 K for K, and at 1670 and 2070 K for SiO2-poor and SiO2-rich Li melts, respectively (both sets join smoothly because of a slight temperature dependence in this system). Data of Baidov and Kunin [1968], with measurements of Laberge etal. [1973, open squares] and Rivers and Carmichael [1987, open cicles] near 1700 K for potassium silicates, (b) Adiabatic compressibility derived from the data shown in (a) and the densities of Bottinga and Weill [ 1970]. The Brillouin results of Bucaro and Dardy [1973, B&D] and Krol et al. [1986, Kal] are plotted for pure SiO2 (see section 5.2b).

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Figure 6.13 - Influence of compressibility mechanisms on phase equilibria in the system MgSiO3-SiO2: stable liquid immiscibility at room pressure and eutectic relation at 5 GPa [Dalton and Presnall, 1997].

but experimental determination of (5T is fraught with considerable difficulties for liquids. With ultrasonic or Brillouin scattering methods, it is in principle much less difficult to measure compressional sound velocities, v , which yield the adiabatic compressibility from the where p is the density. : Ps =

-l/V(dV/dP)s=l/pvp2,

(6.20)

But few studies have been made because of the high temperatures required to overcome relaxation problems (Fig. 6.11 and section 2.2b) that clearly beset earlier work [e.g., Bockris and Kojonen, I960]. For alkali silicates, an added difficulty lies in the risk of composition changes caused by sample vaporization during the experiments at such high temperatures. Results for binary metal oxide-silica melts are plotted in Fig. 6.12. They indicate linear variations of both sound velocity and adiabatic compressibility with composition at least to 90 mol% SiO 2 . Relaxation is a problem for the SiO2-rich melts investigated. This is shown in Fig. 6.12a by the sound velocities measured at 2070 K for lithium silicates, which become increasingly too high at SiO2 contents higher than 88 mol %. For relaxed data, the effects of metal oxides depend on the nature of the metal cation. The contrast between the influence of K2O, on the one hand, and that of CaO and Li2 O, on the other, shows that the compressibility is increased or decreased by addition of metal oxides depending on whether the ionization potential is low or high. For the three binary systems of Fig. 6.12, the adiabatic compressibility converges toward a common value of about 7.5 10"11 Pa"1 for 100 mol % SiO2, which appears to depend little on temperature in view of the differing temperatures of the experimental data. This figure is consistent with Brillouin scattering measurements on molten SiO 2 (see section 5.2c) and with extrapolations made in section 8.3b for calcium aluminosilicate melts. The precision of these data is insufficient, however, to check whether there could exist a compressibility difference between bridging and nonbridging oxygens analogous to that discussed for molar volume in the previous section. To illustrate the importance of configurational changes in compressibility mechanisms, we compare in Fig. 6.13 phase relations in the system MgSiO3-SiO2 at low and high pressure. At 5 GPa, the shape of the liquidus branch of coesite suggests that liquid unmixing has become metastable, as observed for alkali silicates at room pressure (Fig. 6.1). Bonding of Mg 2+ to oxygen becomes clearly easier at high pressure. Whether due to partial change of Si from 4-

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Figure 6.14 - Electrical resistivity of alkali silicate melts, (a) Against reciprocal temperature; (b) Against metal oxide content at 1200°C. Data from Tickle [1967]. Compositions abbreviated as K: K2O; L: Li2O; N: Na2O and S: SiO2. to 6-fold coordination or to rearrangement of the tetrahedral network, this feature agrees with the 29Si NMR observations of Kanzaki et al. [ 1998] for alkali silicates which point to stronger interactions between oxygens and network-modifier cations at high pressure.

6.3c. Electrical Conductivity Until the mid-19th century, molten silicates were generally considered to be made up of molecular entities. Following the discovery of ionic dissociation in solutions, the question remained unclear until the classic high-temperature experiments by Bockris et al. [ 1952a,b] eventually demonstrated the ionic nature of a variety of binary metal oxide-silica systems. First, Bockris et al. [1952b] found that the electrical resistivity of these melts is lower, but of the same order of magnitude, than that of chlorides of the same metals. Second, the resistivity decreases with the proportion of metal oxide and is lowest with oxides of univalent metals with small ionic radii. Over the temperature intervals investigated, the resistivity follows an Arrhenius law: pe = p 0 exp (-AH/RT).

(6.21)

The activation enthalpy AH increases slightly with increasing metal-oxide content, whereas the pre-exponential parameter p 0 decreases or increases with increasing metaloxide content in alkaline earth and alkali systems, respectively. Through electrolysis experiments, Bockris et al. [1952a] further showed that electrical current is carried wholly by network-modifying cations. They found no evidence for either "free" oxygen ions O2" or free Si4+, the concentration of the former having later been found to be of the order of 10"5 [Semkow and Haskin, 1985]. These observations demonstrated that silicate melts are only partially ionic and that anions must be large in size compared to the cations. Bockris et al. [1952b] also made the important observation

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that the activation energy is from 2 to 4 times smaller for electrical conduction than for viscous flow, indicating that the two properties are governed by different processes with different energy barriers. This point has already been mentioned in section 2.1e with respect to decoupling between bulk structural relaxation and mobility of network-forming cations. Although it has often been assumed that electrical resistivity follows Arrhenian laws, measurements made over sufficiently large temperature intervals show that this is generally not the case (Fig. 6.14a). As for viscosity, the observations can be reproduced by TVF equations, logp e = A + B / ( r - r , ) ,

(6.22) Figure. 6.15 - Mixed alkali

where A, B and Tx are fit parameters. In alkali silicates, effect on electrical resistivity. electrical conductivity is due to the mobility of alkali Data for(Na,K)2Si4O9 liquids ions. Because alkali ions remain mobile when viscous at the temperatures indicated flow become vanishingly small, the temperature Tl of [Tickle, 1967]. such equations are lower for electrical resistivity than for viscosity. For instance (see the next section for viscosity data), the Tl values are 318 (35) and 427 (11) for K2Si9019, and 88 (173) and 420 (3) for NajSijOj, for electrical resistivity and viscosity, respectively. The electrical resistivity is a regular function of ionic potential, the order being Li, Na, K (Fig. 6.14b), except at high SiO2 content where, for reasons that are yet unclear, the order is Na, Li, K [Tickle, 1967]. Another significant feature is the marked nonlinear variation of resistivity when two different alkali cations are mixed and the M2O/SiO2 ratio is kept constant (Fig. 6.15). The effect is more pronounced the lower the temperature. It parallels the viscosity extremum described in section 2.3d for an alkaline earth system, with the important feature that the viscosity minimum is associated with a resistivity maximum. These are two manifestations of the so-called mixed alkali effect, which is also observed in internal friction, electrical conductivity or alkali diffusion experiments. Although numerous theories have been proposed to account for its various aspects [e.g., Day, 1976; Ngai et al, 2002], no general explanation has been agreed upon. Similar effects are observed when alkaline earth cations are mixed [Hasegawa, 1980; Neuville and Richet, 1991]. 6.3d. Viscosity Viscosity is of particular importance because it controls the rate of transport of matter and, thus, of energy. For silicate melts, it is usually measured either above the liquidus, in the range 1-105 Pa s, or near the glass transition in the interval 1013-109 Pa s. Crystallization generally prevents measurements from being made at intermediate viscosities, which is not problematic bacause reliable interpolations can be made empirically with TVF or

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Figure 6.16 - Viscosity of binary Na2O-SiO2 melts at 1200°C. Data of Bockris e; a/. [1955] and Leko et al. [1977] for high and low Na2O contents, respectively.

configurational entropy equations. As reviewed by Bottinga and Weill [1972] and Ryan and Blevins [1987], a great many measurements have been made by glassmakers and metallurgists on binary metal oxide-silica melts. Those by Bockris and Lowe [1954] and Bockris et al. [1955] still constitute the most extensive data set and remain the most reliable at high temperature. Owing to the problems raised by poor glass formation, hygroscopicity at low SiO2 concentration, or liquid immiscibility at high SiO2 content, measurements are scarce, in contrast, near the glass transition where they are restricted to alkali silicates [e.g., Poole, 1948]. The most conspicuous feature is the tremendous variations of viscosity with both composition and temperature. Probably there is no other property of silicate melts that can vary by 11 orders of magnitude at constant temperature along a binary join (Fig. 6.16). This much larger variation than observed for electrical conductivity (Fig. 6.14b) indicates that the kinetics of structural relaxation vary much more with temperature than that of the mobility of the network-modifier cations which carry electrical current. In other words, it is another manifestation of the decoupling between bulk and local relaxation discussed in section 2.1e. Likewise, the viscosity varies by more than 10 orders of magnitude between the glass transition and superliquidus conditions (Fig. 6.17a). In an Arrhenius diagram, it also appears that both viscosity and its temperature dependence depend markedly on composition. The departure from an Arrhenian variation increases with decreasing SiO2 content and is larger for alkaline earth than for alkali silicates. For a given stoichiometry, the viscosity varies relatively little within both series. Practically, an important consequence of non-Arrhenian viscosity is the crossover observed at around 1200 K (Fig. 6.17a) when alkali silicates, least viscous at low temperatures, become more viscous than alkaline earth melts. As described in section 2.3d, these variations are quantitatively connected to the melt configurational heat capacities through the Adam and Gibbs [1965] theory of relaxation processes [Richet, 1984]. In contrast to the many orders of magnitude differences that prevail near the glass transition, the viscosity of silicate melts depends relatively weakly on composition at high temperature (Figs. 6.17b). As already shown in Fig. 6.16, the largest changes are found when metal oxides begin to be added to pure SiO2. The associated variations of activation energies follow similar trends. These changes are much greater than the

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Figure 6.17 - Viscosity of binary metal oxide-silica melts, (a) Against reciprocal temperature, (b) Against SiO2 content for alkali and alkaline earth melts at 1400 and 1700°C, respectively. At these temperatures, the log viscosity (Pa s) of SiO2 liquid is 8.9 and 6.4 [Urbain et al., 1982]. Abbreviations used in (a): Ba (BaO), C (CaO), K (K2O), L (Li2O), M (MgO), N (Na2O), S(SiO2), Sr (SrO). Data from Fontana and Plummer [1979] for NS2; Bockris et al. [1955], Poole [1948] and Sipp and Richet [2002] for other alkali silicate; Bockris et al. [1955] and Neuville [unpub.] for BaS2; Neuville [2005] for Sr4S6; Bockris et al. [1955] and Neuville and Richet [1991] for MS and CS. In (b), all data from Bockris and Lowe [1954] and Bockris et al. [1955].

differences observed within both the alkali and alkaline earth series where the viscosity varies by less than a factor of 5 at constant temperature for a given stroichiometry. Again the viscosity varies as the ionization potential of the cation, except for Li melts at high SiO2 content. When observed by Bockris et al. [1955], such variations provided strong support for the concepts of network-former and network-modifier cations, and for the idea that ionic groups of smaller size progressively form when metal cations are introduced and cause depolymerization of the silicate framework. In the "iceberg" model [see Bockris and Reddy, 1970], network modifier cations and nonbridging oxygens concentrate in parts of the melt to optimize mutual coordination. As the metal oxide content increases, the microheterogenous structure transforms gradually to large, discrete polyanions, and finally to isolated SiO44" ions. When liquid immiscibility occurs, the silica-rich phase constitute "islets" or "icebergs", with a structure similar to that of pure SiO2 liquid, within the polyanions of the other phase. It is remarkable that this picture still represents a qualitatively valid description of melt structure. The fact that activation enthalpies of viscous flow depend on temperature (Fig. 6.18) has been taken as evidence for significant structural reorganization such as decreases in the degree of melt polymerization with rising temperatures [e.g., Scarfe et al., 1983]. As described in section 2.3d, however, the Adam and Gibbs [1965] theory of relaxation processes provides a much simpler explanation in terms of increases of configurational entropy, the energy barriers hindering the cooperative rearrangements of the structure

Chapter 6

192

Figure 6.18- Actual, temperature dependent activation enthalpies for viscous flow of sodium silicate liquids at the temperatures indicated. Values derived by Richet et al. [1986] from the data of Poole [1948] above the glass transition, and Bockris et al. [1956] above the liquidus. For comparison, the mean activation enthalpies determined from Arrhenius laws for each range of temperatures are plotted as open symbols.

remaining the same at all temperatures [Richet et al., 1986]. Specifically, one derives from equation (2.24): AHn = 2.303 RBe (Sconf + Cnconf)/(Sconf)2,

(6.23)

an equation that accounts quantitatively for the observed variations of activation energies. In addition, alkali silicate liquids illustrate an important pitfall that can affect activation energies. Viscosity is measured either above the liquidus or close to the glass transition. There is generally a gap at intermediate temperatures because of incipient crystallization. In both temperature intervals, viscosity may appear Arrhenian if the data cover restricted temperature intervals or experimental accuracy is not high. The comparisons made in Fig. 6.18 for sodium silicate melts between such isothermal activation energies and average "Arrhenian" values show that the latter can be biased to the point that their composition dependence is the opposite of the actual trend. The origin of the bias is that the temperature intervals investigated vary systematically with composition because they are determined by various conditions (glass transition and liquidus temperatures, high-temperature volatility, etc.), which also vary strongly with composition. Identification of breaks in activation energies at eutectic or other fixed points of phase diagrams, thus, is not warranted unless actual isothermal values have been derived from non-Arrhenian fits made to the experimental data. 6.3e. Element Diffusivity Although there is a wealth of tracer diffusion data for simple metal oxide-silica systems, few measurements have been made for the same composition. Some of these results have already been mentioned in section 2.1e to show the great difference between the diffusivities and associated activation enthalpies that is observed between network-forming cations and oxygen. Measurements made for several elements along a given compositional series are still more limited. Interesting exceptions are the data gathered at 1600°C for CaO-SiO2 melts

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Figure 6.19 - Tracer diffusivities of 45Ca, I8O and 31Si against SiO2 content in binary CaOSiO2 melts at 1600°C [Keller and Schwerdtfeger, 1979; Keller et al., 1979, 1982]. The dashed line represents diffusivities calculated from the Eyring relation and the viscosities of Bockris and Lowe [1954] and Urbainefa/. [1982].

(Fig. 6.19). Consistent with the trends already discussed, no difference is found between oxygen and silicon diffusivities which are both lower than that of Ca by less than an order of magnitude. All diffusivities are linear functions of composition in the investigated intervals. Interestingly, however, their difference decreases sufficiently rapidly with increasing SiO2 content that an extrapolation of these trends would point to faster diffusion for Si and O than for Ca at SiO2 contents higher than 80 mol %. In view of the data shown in Fig. 5.15, this situation is unlikely. This indicates that, before such a concentration is reached, the linear relationships should break down to match the higher diffusivity of O compared to Si in pure SiO2. One might expect that information could be derived in this respect from the Eyring relationship (4.10) as it relates diffusivities to viscosities which are known up to 100 mol % SiO2. The Eyring diffusivities are of little help, however, because they match curiously the Ca data at low SiO2 content before tending to the Si diffusivities as described for pure SiO2 in section 5.2e. 6.4. Summary Remarks 1. Liquid immiscibility is prevalent in the SiO2-rich parts of the M^O-SiO2 systems and results from competition between Si4+ and M-cations for bonding with oxygen. Reflecting differences between ionization potential of the metal cation, unmixing is metastable in alkali silicates and stable in alkaline earth systems. 2. The existence of miscibility gaps attests to the thermodynamically nonideal nature of M/)-SiO 2 solutions. Qualitatively, the activity-composition relationships can be related to equilibria between free, nonbridging and bridging oxygens. Despite actual analogies between aqueous and silicate solutions , mixing of M^O and SiO2 cannot be treated as simple acid-base reactions, but a basicity scale can nonetheless be established from spectroscopic measurements. 3. Physical properties of binary metal oxide-silica systems vary considerably from pure SiO2 to the most SiO2-poor melts. The progressive breakup of the three-dimensional structure of SiO2 is accompanied by increasingly important configurational contributions to the thermodynamic and volume properties of the melt. The magnitude of these effects is generally higher the higher the ionization potential of the metal cation.

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Hudon P. and Baker D. R. (2002b) The nature of phase separation in binary oxide melts and glasses. II. Selective solution mechanisms. J. Non-Cryst. Solids 303, 346-353. Kanzaki, M, Xue, X., and Stebbins, J.F. (1998) Phase relations in Na2O-SiO2 and K2Si4O9 systems up to 14 GPa and 29Si study of the new high-pressure phases: Implications to the structure of high-pressure silicate glasses. Phys. Earth Planet. Int., 107, 9-21. Kay D. A. R. and Taylor J. (1960) Activities of silica in the lime + alumina + silica system. Trans. Farad. Soc. 56, 1372-1386. Keller H. and Schwerdtfeger K. (1979) Tracer diffusivity of 31Si in CaO-SiO2 melts at 1600°C. Metal. Trans. B10, 551-554. Keller H., Schwerdtfeger K., and Hennesen K. (1979) Tracer diffusivity of 45Ca and electrical conductivity in calcium oxide-silica melts. Metal. Trans. B10, 67-70. Keller H., Schwerdtfeger K., Petri H., Holzle R., and Hennesen K. (1982) Tracer diffusivity of 18O in CaO-SiO2 melts at 1600°C. Metal. Trans. B13, 237-240. Kohsaka S., Sato S., and Yokokawa T. (1979) E.m.f. measurements of molten oxide mixtures. III. Sodium oxide + silicon dioxide. J. Chem. Therm. 11, 547-551. Kracek F. C. (1930a) The binary system Li2O-SiO2. J. Phys. Chem. 34, 2641-2650. Kracek F. C. (1930b) The system sodium oxide-silica. J. Phys. Chem. 34, 1583-1598. Kracek F. C. (1930c) The cristobalite liquidus in the alkali-oxide systems and the heat of fusion of cristobalite. J. Amer. Chem. Soc. 52, 1436-1442. Kracek F. C , Bowen N. L., and Morey G. W. (1929) The system potassium metasilicate-silica. J. Phys. Chem. 33, 1857-1879. Kracek F. C, Bowen N. L., and Morey G. W. (1937) Equilibrium relations and factors influencing their determination in the system K2SiO3-SiO2. /. Phys. Chem. 41, 1183-1193. Krol D. M., Lyons K. B., Brawer S. A., and Kurkjian C. R. (1986) High-temperature light scattering and the glass transition in vitreous silica. Phys. Rev. B33, 4196-4201. Laberge N. L., Vasilescu V. V., Montrose C. J., and Macedo P. B. (1973) Equilibrium compressibility and density fluctuations in K2O-SiO2 glasses. J. Amer. Ceram. Soc. 56, 506-509. Lange R. L. and Carmichael I. S. E. (1990) Thermodynamic properties of silicate liquids with emphasis on density, thermal expansion and compressibility. In Modern Methods of Igneous Petrology: Understanding magmatic Processes, Vol. 24 (eds. J. Nicholls and J. K. Russell), pp. 25-64. Mineralogical Society of America, Washington D.C. Leko V. K., Gusakova N. K., Meshcheryakova E. V., and Prokhorova T. I. (1977) The effect of impurity alkali oxides, hydroxyl groups, A12O3, and Ga2O3 on the viscosity of vitreous silica. Sov. J. Glass Phys. Chem. 3, 204-210. Levin E. M. (1970) Liquid immiscibility in oxide systems. In Phase Diagrams, Materials Science and Technology., Vol. Ill, pp. 143-236. Academic Press, New York. Levin E. M., Robbins C. R., and McMurdie H. F. (1975) Phase Diagrams for Ceramists. 2nd ed. Amer. Ceram. Soc, Columbus. Lewis G. N. (1923) Valence and the Structure of Atoms and Molecules. Chemical Catalog Company, New York. Liebau F. and Pallas I. (1981) The influence of cation properties on the shape of silicate chains. Z Kristall. 155, 139-153. Lux H. (1939) "Saiiren" und "Basen" im Schmelzfluss: Die Bestimmung des SauerstoffionenKonzentration. Z. Elektrochem. 45, 305-309. Masson C. R. (1968) Ionic equilibria in liquid silicates. J. Amer. Ceram. Soc. 51, 134-143. Masson C. R. (1977) Anionic constitution of glass-forming melts. J. Non-Cryst. Solids 1, 1-42.

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Mazurin O. V., Roskova G. P., and Porai-Koshits E. A. (1984) Immiscibility diagrams of oxide glass-forming systems. In Phase Separation in Glass, (eds. O. V. Mazurin and E. A. PoraiKoshits), pp. 103-142. North Holland, Amsterdam. Mazurin O. V., Streltsina M. V., and Shvaiko-Shvaikovskaya T. P. (1987) Handbook of Glass Data. Part A. Silica Glass and Binary Silicate Glasses. Elsevier, Amsterdam. Mills K. C. (1993) The influence of structure on the physico-chemical properties of slags. ISIJ Int 33, 148-155. Moretti R. and Ottonello G. (2003) A polymeric approach to the sulfide capacity of silicate slags and melts. Met. Mat. Trans. B34, 399-410. Mysen B. O., Virgo D., and Seifert F. A. (1982) The structure of silicate melts: Implications for chemical and physical properties of natural magma. Rev. Geophys. 20, 353-383. Neuville D. R. (2005) Structure and properties in (Sr, Na) silicate glasses and melts. Phys. Chem. Glasses, in press. Neuville D. R. and Richet P. (1991) Viscosity and mixing in molten (Ca,Mg) pyroxenes and garnets. Geochim. Cosmochim. Acta 55, 1011-1020. Ngai K. L., Wang Y., and Moynihan C. T. (2002) The mixed alkali effect revisited: The importance of ion-ion interaction. J. Non-Cryst. Solids 307-310, 999-1011. Pelton A. D. and Wu P. (1999) Thermodynamic modeling in glass-forming melts. J. Non-Cryst. Solids 253, 178-191. Plante E. R. (1978) Vapor pressure measurements of potassium over K2O-SiO2 solutions by a Knudsen effusion, mass spectrometric method. NBS Spec. Pub. 561, 265-281. Poole J. P. (1948) Viscosite a basse temperature des verre alcalino-silicates. Verres Refract. 2, 222-228. Rankin G. A. and Wright F. E. (1915) The ternary system CaO-Al2O3-SiO2. Amer. J. Sci. 39, 1-79. Rao K. D. P. and Gaskell D. R. (1981) The thermodynamic properties of melts in the system MnOSiO2. Metal. Trans. B12, 311-317. Ravaine D. and Souquet J. L. (1977) A thermodynamic approach to ionic conductvity in oxide glasses. Part 1. Correlation of the ionic conductivity with the chemical potential of alkali oxide in oxide glasses. Phys. Chem. Glasses 18, 27-31. Ravaine D. and Souquet J. L. (1978) A thermodynamic approach to ionic conductvity in oxide glasses. Part 2. A statistical model for the variations of the chemical potential of the constituents in binary alkali oxide glasses. Phys. Chem. Glasses 19, 115-120. Rego D. N., Sigworth G. K., and Philbrook W. O. (1985) Thermodynamic study of Na2O-SiO2 melts at 1300° and 1400°C. Metal. Trans. B16, 313-323. Richardson F. D. (1956) Activities in ternary silicate melts. Trans. Farad. Soc. 52, 1312-1324. Richet P. (1984) Viscosity and configurational entropy of silicate melts. Geochim. Cosmochim. Acta 48, 471-483. Richet P. (2001) The Physical Basis of Thermodynamics. Kluwer/Plenum Publishing, New York. Richet P. and Bottinga Y. (1983) Verres, liquides et transition vitreuse. Bull. Mineral. 106, 147-168. Richet P. and Bottinga Y. (1985) Heat capacity of aluminum-free liquid silicates. Geochim. Cosmochim. Acta 49, 471-486. Richet P., Bottinga Y, and Tequi C. (1984) Heat capacity of sodium silicate liquids. J. Amer. Ceram. Soc. 67, C6-C8. Richet P., Robie R. A., and Hemingway B. S. (1986) Low-temperature heat capacity of diopside glass: A calorimetric test of the configurational entropy theory as applied to the viscosity of liquid silicates. Geochim. Cosmochim. Acta, 50, 1521-1533.

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Rivers M. and Carmichael I. S. E. (1987) Ultrasonic studies of silicate melts. J. Geophys. Res. 92, 9247-9270. Robinson H. A. (1969) Physical properties and structure of silicate glasses: I. Additive relations in alkali binary glasses. J. Amer. Ceram. Soc. 52(392-399). Ryan M. P. and Blevins J. Y. K. (1987) The Viscosity of Synthetic and Natural Silicate Melts and Glasses at High Temperatures and 1 bar (10s Pascals) Pressure and at Higher Pressures. U.S. Geological Survey, Washington D.C. Ryerson F. J. (1985) Oxide solution mechanisms in silicate melts: Systematic variations in the activity coefficient of SiO2. Geochim. Cosmochim. Acta 49, 637-651. Scarfe C. M., Cronin D. J., Wenzel J. T., and Kauffmann D. A. (1983) Viscosity-temperature relationships at 1 atm in the system diopside-anorthite. Amer. Mineral. 68, 1083-1088. Scarfe C. M., Mysen B. O., and Virgo D. (1987) Pressure dependence of the viscosity of silicate melts. In Magmatic Processes: Physicochemical Principles (ed. B. O. Mysen), pp. 59-68. Geochemical Society, University Park, PA. Semkow K. W. and Haskin L. A. (1985) Concentrations and behavior of oxygen and oxide ion in melts of composition CaOMgOxSi0 2 . Geochim. Cosmochim. Acta 49, 1897-1908. Seward T. P., Ill, Uhlmann D. R., and Turnbull D. (1968) Phase separation in the system BaOSiO2. J. Amer. Ceram. Soc. 51, 278-285. Shermer H. F. (1956) Thermal expansion of binary alkali silicate glasses. J. Nat. Bureau Stand 57,97-101. Sipp A. and Richet P. (2002) Equivalence of volume, enthalpy and viscosity relaxation kinetics in glass-forming silicate liquids. J. Non-Cryst. Solids 298, 202-212. Sosman R. B. (1952) Temperature scales and silicate research. Amer. J. Sci. 250A., 517-528. Stebbins J. F. (1991) Experimental confirmation of five-coordinated silicon on a silicate liquid structure: A multi-nuclear, high temperature NMR study. Science 255, 586-589. Stebbins J. F. and McMillan P. (1993) Compositional and temperature effects on five coordinated silicon in ambient pressure silicate glasses. J. Non-Cryst. Solids 160, 116-125. Stebbins J. F., Carmichael I. S. E., and Moret L. K. (1984) Heat capacities and entropies of silicate liquids and glasses. Contrib. Mineral. Petrol. 86, 131-148. Temkin M. (1945) Mixtures of fused salts as ionic solutions. Acta Physicochim. USSR 20,411-420. Tequi C, Grinspan P., and Richet P. (1992) Thermodynamic properties of alkali silicates: Heat capacity of Li2Si03 and lithium-bearing silicate melts. J. Amer. Ceram. Soc. 75, 2601-2604. Tewhey J. D. and Hess P. C. (1979) The two-phase region in the CaO-SiO2 system: Experimental data and thermodynamic analysis. Phys. Chem. Glasses 20, 41-53. Tickle R. E. (1967) The electrical conductance of molten alkali silicates. Part I. Experiments and results. Phys. Chem. Glasses 8, 101-112. Tomlinson J. W., Heynes M. S. R., and Bockris J. O. M. (1958) The structure of liquid silicates. Part 2. Molar volume and expansivities. Trans. Farad. Soc. 54, 1822-1834. Tomozawa M., McGahay V., and Hyde J. M. (1990) Phase separation of glasses. J. Non-Cryst. Solids 123, 197-207. Toop G. W. and Sammis C. S. (1962) Activities of ions in silicate melts. Trans. Met. Soc. AIME 224, 878-887. Urbain G., Bottinga Y., and Richet P. (1982) Viscosity of liquid silica, silicates and aluminosilicates. Geochim. Cosmochim. Acta 46, 1061-1072. Warren B. E. andPincus A. G. (1940) Atomic considerations of immiscibility in glass systems. J. Amer. Ceram. Soc. 23, 301-304. Williamson J. and Glasser F. P. (1965) Phase relations in the system Na2Si205-Si02. Science 148, 1589-1591.

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Binary Metal Oxide-Silica Systems II. Structure In this chapter, we will discuss the structure of binary alkali and alkaline earth silicate glasses and melts. A number of structure models have been proposed. These fall in four categories as they rely on (i) pseudocrystalline analogies, (ii) thermodynamic considerations, (iii) numerical simulations, or (iv) direct structure observations. Pseudocrystalline models rely on the assumption that there exist in melts (and glasses) structural entities that resemble, at least on a local scale, those of crystals on or near the liquidus for the same system. Models based on assumptions of how physicochemical properties are governed by structure also use crystal chemical analogies. In thermodynamic modeling, one assumes a specific set of components, which should, ideally, resemble those in the melts. This is not a requirement, however, although the models that do so tend to be the more successful. Numerical simulation is based on energy-minimization techniques to calculate bond angles, bond distances, bond strengths, and coordination numbers. Models derived from direct structural information are based on measurements of bond angles, bond distances, and coordination numbers. Such models often also identify specific structural units in the melts and how these may be connected to one another. The ultimate goal is understanding of how structure governs the physical and chemical properties of melt and glass. Ideally, all data, be they structural or physicochemical, should be integrated into internally consistent models. In this chapter, we will illustrate how current knowledge of metal oxide-silica melt structure approaches this goal. However, before doing so, the most important features of the individual models will be summarized. 7.1. Pseudocrystalline Models of Melt Structure Pseudocrystalline structure models rely on the assumption that, at least on a local scale (several A), there exist in melts and glasses silicate species resembling those found in crystalline materials. In one group of models, structural similarity of minerals on the liquidus and the melt is assumed [Morey and Bowen, 1924; Burnham, 1975; Bottinga and Richet, 1978; Burnham and Nekvasil, 1986]. Melt structure modeled on this basis has been used, for example, to derive liquidus phase relations [Burnham, 1975; Bottinga and Richet, 1978; Bottinga et al., 1981; Burnham and Nekvasil, 1986]. Such models also have been used, with some success, to explain nucleation in metal oxide silicate systems [Kirkpatrick, 1983; Davis and Ihinger, 1999; 2002; Zotov and Delaplane, 2000]. Many of these structural ideas are also incorporated in models that were also used in early

200

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attempts to compute transport and volume properties of silicate melts [Bottinga and Weill, 1970, 1972; Bottinga et al, 1982]. Bottinga and Richet [1978] pointed out that the constraints imposed by liquidus phase equilibria and the Gibbs-Duhem equation are not sufficient to calculate the chemical potential of a liquidus phase in multicomponent systems because all possible structural entities in the melt must be identified and their mixing properties ascertained. In light of of the paucity of such information, they assumed that the structural entities present in a multicomponent melt are produced by melting of the known crystalline materials in the system. For example, in the system MgO-SiO2, liquidus phases are periclase (MgO), forsterite (Mg2SiO4), clinoenstatite (MgSiO3), and silica polymorphs [Bowen and Andersen, 1914; Greig, 1927]. In other systems (e.g., alkali silicates), the number of liquidus phases sometimes is greater [Kracek, 1930a, b, 1932; Morey et al., 1930], and the number of assumed species in the liquid must increase correspondingly. Another group of models that relies on structural similarities of local melt and crystal structure is based on inferences from measurements of physical properties. Although such assumptions may seem intuitively attractive, we emphasize that the linkage between structure and properties of silicate melts is not always clear. This notwithstanding, several models have met with significant success and some have arrived at conclusions surprisingly similar to those derived from spectroscopic measurements. This includes the model by Bockris and Reddy [1970], which was based on an assumed relationship between activation energy of viscous flow and Si-0 bond strength. Another example is the substructure model proposed by Babcock [1968] from refractive index and molar volume data of glasses. 7.2. Thermodynamic Modeling and Melt Structure Structure inferred from modeling of thermodynamic properties share a common trait that the thermodynamic data can be described in terms of components that are not necessarily equivalent to actual structural entities in the melt. That notwithstanding, models of this type have been developed to such a level of refinement that these can reproduce properties of the system with considerable accuracy [Ghiorso and Sack, 1994]. The use of such models for compositions, temperature, or pressures outside the range where the modeling was carried out is, however, fraught with danger. A better approach to modeling thermodynamic behavior is to incorporate presumed melt species that may resemble, at least in a compositional sense, those of relevant crystalline silicates [Bottinga and Richet, 1978; Pelton and Wu, 1999]. 7.2a. Polymer Modeling In polymer models, the formation of silicate melt is considered as chemical interaction between metal oxide (e.g., MO) and silica. There are various versions of this model [e.g., Masson, 1968, 1977]. One may view this as a gradually evolving polymerization of silicate complexes:

Binary Metal Oxide-Silica Systems II. Structure SiO:- + S i

n

O ^ «Sin+10?+n4+2h+02-.

201 (7.1)

This model received experimental support in several experimental studies of structure with the aid of analysis of TMS (trimethylsilyl) derivatives of the silicate glass network. These include those of Smart and Glasser [1978] for the system PbO-SiO2 and Lentz [1969] for the system Na2O-SiO2. Distributions of silicate polymer calculated with this approach [Hess, 1971,1980] correspond fairly well with the measurements of Smart and Glasser [1978] using TMS derivatives. There are, however, important problems with TMS-method, which make the results unreliable. First, it involves formation of a solution from the glass. This solution does not produce 100% yield. Presumably, the residue contains highly polymerized units that cannot be broken down so that chromatographic analysis of solutions of TMS-derivatives provides incomplete results. Second, in the data reported by Smart and Glasser [1978] for a PbOSiO2 glass, for example, the bulk melt polymerization, NBO/Si, obtained by adding up the proportions of the various reported structural units (monomers, dimers, trimers etc.) results in NBO/Si=2.4, whereas the bulk composition yields a nominal value of 2.79. In the study by Lentz [1969] on glasses in the system Na2O-SiO2, the bulk NBO/Si from the measurements of TMS-derivatives was 2.84, yet the bulk composition had a nominal NBO/Si-value of 1.0. Third, as will become more evident from the discussion of glass and melt structure (section 7.4), the results of this type of modeling are inconsistent with actual spectroscopic data. 7.2b. Quasichemical Modeling of Melt Structure Quasichemical models can incorporate structural information in the formulations of equilibria used for free energy minimizations. For example, Bottinga and Richet [1978] modeled successfully the liquidus phase relations in the MgO - SiO2 system. Their model comprises elements of this approach. Blander and Pelton [1987] suggested, however, that this model is difficult to extend to chemically more complex multicomponent systems. Pelton and coworkers [Blander and Pelton, 1984, 1987; Pelton and Wu, 1999] developed a model driven in part by the observation that there is a pronounced free energy minima near orthosilicate compositions in binary metal oxide-silica systems (see, Navrotsky et al. [1985], for compilation of these data). In binary metal oxide (M) silicate (Si) melts, the model considers the formation to M-Si bonds from M-M and Si-Si bonds [Pelton and Wu, 1999] as follows: (M-M)+(Si-Si) <=> 2(M-Si).

(7.2)

To minimize the energy change of reactions formalized in this equation, equilibria among species in the melts of interest are considered. For example, for the system MgOSiO2, Blander and Pelton [1987] wrote: MgOliquid + SiO2"quid <=* MgSiO3liquid,

(7.3)

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Figure 7.1 - Comparison of radial distribution function for a simulated glass with 30 mol % and 70 mol % SiO2 [Huang and Cormack, 1990] with experimental distribution function from neutron diffraction of a glass with 33.9 mol% Na2O and 66.1 mol % SiO2 [Misawa et al, 1980]. Insert shows details of the topology of the structure of the Si-0 bond distance as a function of Na2O content in simulated Na2O-SiO2 glass [Huang and Cormack, 1990].

and 2MgO liquid + SiO2'iquid <=> Mg 2 Si0 4 liquid .

(7.4)

Other reactions could also be written, but these were obviously chosen in part so that the most reliable thermodynamic data can be brought to bear on the question. By choosing melt components resembling structural species otherwise determined for the melts and glasses of interest, this treatment brings thermodynamic modeling closer to the melt structure.

203

Binary Metal Oxide-Silica Systems II. Structure

Table 7.1. Comparison of bond distance (A) and coordination number (CN) for Na2Si4C>9 glass via MD numerical simulation [Ispas et al., 2002] and from experimental distances from neutron diffraction [Zotov and Keppler, 1998] Simulation Bond Si-O Si-Si O-O Na-0

Distance, A 1.63 2.06 2.66 2.28

Neutron diffraction CN 4.0 3.5 5.5 5.4

Distance, A 1.63 3.06 2.61 2.45

CN 4 3.6 5.5 4.3

7.3. Numerical Simulation of Melt Structure Thanks to rapid advances in computational power in recent years, numerical simulations can yield significant insight into the structure and dynamics of amorphous materials [see Tossell and Vaughn, 1992]. Early successful modeling includes the studies of Soules and coworkers [Soules, 1979, 1982], Gibbs and coworkers [Gibbs et al., 1972, 1981; Tossell and Gibbs, 1978; Gibbs, 1982; Geisinger et al, 1985], Angell and coworkers [Woodcock et al., 1976; Angell and Kanno, 1976; Angell et al, 1982, 1983; Angell and Torell, 1983; Angell, 1985; Scamehorn and Angell, 1991], and Matsui and coworkers [Matsui et al, 1982; Matsui and Kawamura, 1980]. The structural ideas brought forth by those and other authors have provided the basis for more recent modeling work. For alkali and alkaline earth silicate melts, recent theoretical work has focused on calculating bond angles, bond distances, and angle and distance distributions. For example, Huang and Cormack [1990] simulated radial distribution functions for melts in the system Na2O-SiO2 and derived Si-O, Si-Si, O-O, and Na-0 bond distances as functions of composition. Results obtained in this way are shown in Fig. 7.1 for an Na2O-SiO2 melt with 30 mol % Na2O. There is good agreement between radial distribution functions from both numerical simulation and neutron diffraction. Another comparison of simulated structure and that obtained by neutron diffraction for an Na2O-SiO2 glass with 20 mol % Na2O is shown in Table 7.1. The radial distribution function simulated for the Na2O - SiO2 glass with 30 mol % Na2O (Fig. 7.1) closely resembles, at least up to about 4 A, that derived from an experimental neutron diffraction study [Misawa et al, 1980]. The first three distances, Si-O-, O-O, and Si-Si, are clearly identified. Another important feature is the fact that the Si-O peak broadens when the Na2O content increases (see insert) and eventually evolves into two distinct components. One Si-O peak is near or slightly below 1.6 A and the other near 1.65 A. This broadening likely results from overlapping of Si-NBO and Si-BO distances (between Si and nonbridging and bridging oxygen, respectively), as shown more clearly in Fig. 7.3 for a simulated Na2Si409 melt [Ispas et al, 2002]. These simulations (Figs. 7.2 and 7.3) are consistent with NMR data, which also indicate that

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Figure 7.2 - Details of the first peak Si-0 distance simulated for Na2Si4C>9 glass [Ispas et al, 2002].

bond distances are different for Si-NBO and Si-BO [Lee and Stebbins, 2003a]. The Si-NBO bond distance is several percent shorter than the Si-BO bond. This difference is understandable given the much weaker Na-0 bond in the nonbridging Si-O-Na linkages compared with the Si-0 bond in the bridging Si-O-Si linkages (Table 4.1). The weaker Na-O bond results in the nonbridging oxygen in Si-O-Na linkage moving closer to the Si atom. In an early examination of distributions of intertetrahedral (Si-O-Si) and intratetrahedral (O-Si-O) angles, Soules [1979] concluded that the Si-O-Si angle distributions of Na2O-SiO2 melts with 32 and 22 mol % Na2O exhibit two maxima, one near 160° and another near 110°. More recent and more sophisticated models of similar melts do not show such two maxima [Huang and Cormack, 1990; Ispas et al., 2002]. It is clear, however, from these two latter structure models that both Si-O-Si and O-Si-0 angle

Figure 7.3 - Si-O-Si and O-Si-O angle distribution functions from molecular dyanamics simulations of Na2O-SiO2 glass with 72 mol % Na2O [Huang and Cormack, 1990].

Binary Metal Oxide-Silica Systems II. Structure

205

Figure 7.4 - Si-O-Na angle distribution function distance simulated glass [Ispase?a/.,2002].

distributions are distinctly asymmetric toward smaller angles (Fig. 7.3). The maxima occur at values close to those found for vitreous SiO2 (Figs. 5.23 and 5.34). Ispas et al. [2002] suggested that the asymmetry in Si-O-Si angle distribution (Fig. 7.3) reflects the presence of more than one structural unit in the materials, possibly resembling, for example, SiO2 and SiO3 groups (3-dimensionally interconnected and chain-like structures, respectively). That conclusion is also consistent with significant asymmetry or even with the two distinct peaks of the Si-O-Si angle distribution simulated for Na2Si4O9 melt (Fig. 7.4). In a simulation of Na2Si3O7, Newell et al. [1989] inferred that its melt structure consists of 2 structural units having, on average, 1 and 0 nonbridging oxygens, along with smaller proportions of structural entities that are characterized by NBO/Sivalues of 2 and 1. 7.4. Structure from Direct Measurements Direct structural examination of metal oxide-silica glasses has been carried out since the early 1970s when vibrational spectroscopy and neutron and x-ray diffraction techniques began to be applied extensively. Among these methods, neutron and x-ray diffraction probe bond distances and bond angles relevant to short- and mediaum-range order, whereas vibrational and nuclear magnetic resonance (NMR) spectroscopy probe local structure in and near individual SiO4 tetrahedra as well as the extent to which these form extended, more polymerized silicate structures. More recently, vibrational spectroscopy and, to a lesser extent, NMR and diffraction techniques have also been applied to probe temperatureinduced structural changes in liquids. Details of these methods can be found in Brown et al. [1995], McMillan and Wolf [1995], and Stebbins [1995]. 7.4a. Structure Determinations Vibrational spectroscopy was originally used to probe the anionic structure of silicate glasses through the so-called "fingerprinting" technique. With this method, the main features of the spectra of a glass are compared with those of relevant crystals. As an

206

Chapter 7

Figure 7.5 - Raman spectra of crystalline and glassy K^O'SiCh (left diagram) and K.2O»2SiO2 (right diagram). Shaded regions represent frequency ranges of antisymmetric Si-NBO stretch and Si-BO bending vibrations [Brawer and White, 1975]. example, Etchepare [1972] was among the first to suggest that the main anionic entities of CaMgSi 2 O 6 glass resemble those of diopside because the main Raman peaks in both spectra occur at approximately the same frequency. A comparison of the Raman frequencies in spectra of CaMgSi 2 O 6 melt and diopside recorded at the diopside liquidus temperature (1392°C; see Kushiro [1969]) have revealed even greater similarity between spectra of diopside and CaMgSi 2 O 6 melt [Richet et al, 1994]. Brawer and White [1975, 1977] greatly expanded the fingerprinting technique in their Raman spectroscopic study of binary M 2 O-SiO 2 (M = Li, Na and K) glasses and for ternary and even quaternary systems in which alkaline-earth elements were present. They assigned the main peaks in the Raman spectra of these glasses to antisymmetric stretching of Si-NBO bonds and to Si-BO-Si bending modes, and observed that these peaks occur in isochemical glasses and crystals at nearly the same frequency (shaded region in Fig. 7.5). As documented further via modeling [Lazarev, 1972; Furukawa et al, 1981], the bands assigned to antisymmetric stretching of Si-NBO and Si-BO bonds 7 1 occur in the 850-1200 cm"1 region, whereas Si-BO-Si bending modes are found between about 500

7

'The Si-NBO and Si-BO bonds of interest are those that exist in SiO4 tetrahedra of the various anionic silicate groups with different number of nonbridging and bridging oxygen.

Binary Metal Oxide-Silica Systems II. Structure

207

and 700 cm"'. The frequencies of the stretching modes increase with decreasing degree of polymerization of the glass {i.e., increasing NBO/Si). The frequencies of the Si-NBO-Si bending modes vary both with degree of polymerization and intertetrahedral angle, Si-O-Si [Furukawaefa/., 1981]. Brawer and White [1975, 1977] also observed that the maximum intensity of the Raman bands assigned to antisymmetric Si-NBO stretching in SiO3 and Si2O5 groups in crystalline alkali silicates are found in glass spectra of M 2 Si0 3 and M2Si2O5 (M = alkali metal) composition. These features were referred to as SiO3 "chain-like" and Si2O5 "sheetlike" structures in alkali silicate glasses. Intermediate compositions resulted in Raman spectra with intermediate intensity. In a further extension of the structural concepts originally advanced by Etchepare [1972] and Brawer and White [1975, 1977], Virgo et al. [1980], Mysen et al. [1980, 1982], and McMillan [1984a] investigated glasses ranging from pure SiO2 to nearly as depolymerized compositions as orthosilicate. Not only do SiO3- and Si2O5-like structures exist, but there are additional types of units such as SiO2, Si2O7, and SiO4 groups. Virgo et al., [1980] suggested that disportionation reactions such as, Si2O5 <=>SiO3+SiO2,

(7.5)

can be used to describe their mutual equilibria. Starting with Schramm et al. [ 1984] in their study of 29Si NMR spectra of Li2O-SiO2 glasses, the stoichiometric notations (SiO2, Si2O5, SiO3, Si2O7, and SiO4) were replaced by the so-called Qn concept in the subsequent literature (see also Figs. 3.1 to 3.3). In this notation, SiO2 unit is equivalent to Q4, Si2O5 to 2Q3, SiO3 to Q2, Si2O7 to 2Q1, and SiO4 to Q°. Stebbins [1987] described equilibria among these Qn-species as follows: 2Qn <=* Q nl +Q n+1 .

(7.6)

A striking feature of alkali and alkaline earth glass Raman spectra is that, regardless of the metal/silicon ratio, the frequencies assigned to antisymmetric Si-NBO and Si-BO stretch vibrations in the various Qn-species are nearly independent of glass composition (Fig. 7.6). This observation strongly supports the idea that the structure cannot be described by gradually increasing degree of polymerization of individual structural species in the glasses with decreasing metal/silicon-ratio. In other words, data such as those in Fig.7.6 indicate that polymerization models (section 7.2) are not a faithful representation of metal oxide -silica glass structure. The Qn-concept does have, however, many similarities with pseudocrystalline glass structure models (section 7.1). These concepts developed from Raman spectra of metal oxide-silica glasses are also consistent with results from numerical simulation of structure (section 7.3). Although interpretation of vibrational spectra lends strong support to a model with a few coexisting structural units in silicate glasses, vibrational spectroscopy suffers from two limitations [McMillan, 1984b; McMillan and Wolf, 1995]. First, it does not probe

208

Chapter 7

Figure 7.6 - Frequency of Raman bands in spectra of metal oxide glasses assigned to Si-NBO and Si-BO in Q4, Q3, Q2, Q1, and Q° structural units as a function of nominal NBO/Si of glass for compositions identified on the figure [Mysen etal, 1982].

the immediate and local structural environment near specific elements. Instead, the vibrational spectra provide information on bond strength and bond angles within regions that could contain numerous silicate tetrahedra [McMillan and Wolf, 1995]. Second, the intensity of Raman bands does not depend only on concentration of specific structural units, but also varies as a function of other variables such as (i) the nature of next-nearest neighbors, (ii) the type of cations in tetrahedral coordination, (iii) the number of nonbridging oxygen in the Qn-species of interest, and (iv) the temperature at which a Raman spectrum is recorded. Many of these limitations can be overcome through nuclear magnetic resonance spectroscopy (NMR) as a probe of glass structure [Mysen and Cody, 2001, 2003; Mysen et ah, 2003]. Nuclear magnetic resonance is nucleus (or element) specific [Stebbins, 1995] and, therefore, probes the immediate structural environment around an element of interest {e.g., Si). In addition, the relative areas of the NMR bands is a measure of the abundance of the Qn-species or structural units, provided that the dwell time exceeds the relaxation time of the nucleus of interest (i.e., 29Si for silicates) and that the integrated areas of individual bands can be determined with the necessary precision. In a comprehensive 29Si MAS NMR (MAS: magic angle spinning) study of glass structure in the systems K2O-SiO2, Na2O-SiO2, and Li2O-SiO2, Maekawa et al. [1991] observed that individual peaks remain at nearly constant frequency but change their relative intensity as a function of the alkali/silicon ratio (Fig. 7.7). These frequencies, indicated by thick lines in Fig.7.7, are similar to those observed in 29Si NMR spectra of crystalline alkali silicates (see also Engelhardt and Michel [1987]). As the number of bridging oxygens in a structural entity decreases (the value of n in the Qn-species decreases), the Si nucleus becomes progressively deshielded resulting in decreasing values of the chemical shifts. The Si MAS NMR data plotted in Fig. 7.7 offer conclusive support, therefore, to the concepts that a small number of Qn-species exist in silicate glasses (see Fig. 3.3), and that equation (7.7), indeed, expresses the equilibria among these structural units.

Binary Metal Oxide-Silica Systems II. Structure

209

Figure 7.7 - Silicon-19 MAS NMR spectra of glasses in the system Na2O-SiO2 for Na2O content indicated on individual spectra. See text for discussion of assignments and thick lines [Maekawae/a/., 1991].

The chemical shift of bands assigned to individual Qn-species varies lightly because there is a small deshielding effect even for the individual Qn-species (Fig. 7.7). This effect results from the fact that the extent of deshielding of 29Si nucleus is also dependent on Si-O bond length, Si-O-Si bridging bond angles, and on changes in 2 nd - and 3rd-nearest neighbor environments [Murdoch et al., 1985; Oestrike et al., 1987; Schneider et al, 1987; Engelhardt and Michel, 1987;Xueefa/., 1994; Stebbins, 1995; Mauri ef al, 2000]. Silicon-29 NMR spectra of glass have been used to determine the abundance of structural units as a function of metal/silicon ratio. Abundance data, shown for K 2 O-SiO 2 and Na 2 O glasses in Fig. 7.8, are consistent with the idea that the principal structural variations in metal oxide silicate glasses are in the abundance of the individual structural units, as observed by Schramm et al. [1984], Stebbins [1987], and Buckermann et al. [1992]. In pure SiO2 glass, only Q4 species are detected (with the possible exception of some bond defects, see also Chapter 5). Addition of metal oxide to SiO 2 causes a decrease of Q abundance and an increase of Q 3 abundance. The abundance of Q reaches a maximum near the disilicate stoichiometry (Si2O5), and then that of Q2 near the metasilicate stoichiometry (SiO3). In other words, the ideas originally proposed by Etchepare [1972] and Brawer and White [1975,1977] from Raman spectroscopy are fully supported by the 29 Si MAS NMR spectra. The NMR data in Fig.7.8 offer a hint that the abundances of Qn-species also depend on the type of metal cation in the alkali silicate glass. This dependence has been further documented by 29Si MAS NMR data of M 2 Si 2 0 5 glasses (M = K, Na, and Li) shown in

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Figure 7.8 - Abundance (mol %) of Q , Q , Q , and Q species in K2O-SiO2 and Na2O-SiO2 glasses against composition [Maekawa et al., 1991]. Fig.7.9. For a glass with fixed M/Si-ratio, the abundance of Q3 species decreases with increasing ionization potential of the alkali metal, whereas those of Q2 and Q4 increase. These relationships suggest that equation (7.6) shifts to the right, at least with n = 3, with increasing ionization potential of the metal cation. We infer from these observations (Figs. 7.8 and 7.9) that the nonbridging oxygens in the various Qn-species are not energetically equivalent. This inference has been substantiated via 29Si MAS NMR and 17 O triple quantum NMR spectroscopy of glasses in the systems Na2O-CaO-SiO2 [Jones et al., 2001; Lee and Stebbins, 2003b] and BaO-MgO-SiO2 [Lee et al., 2003a]. The more electronegative the metal cation, the stronger is its tendency to bond with nonbridging oxygen in the least polymerized Qn-species available. This steric hindrance is also seen in the effect of cation size on O-Si-0 angles in SiO3 chains in glasses. The chain becomes

211

Binary Metal Oxide-Silica Systems II. Structure

Figure 7.9 - Abundance of Q 4 , Q 3 , and Q2 species in Na2Si2Os and Li2Si2Os glass relative to their abundance in K2Si2Os glass [Mysen, 1997].

increasingly buckled the smaller the cation (Table 7.2), although Li-silicate may deviate some from this relationship as the small Li+ cation actually may form mixed bonding with bridging and nonbridging oxygens [Yasui et al., 1983]. Similar structural effects have been observed in crystalline metasilicate structures [Liebau and Pallas, 1981]. Energetically non-equivalent nonbridging oxygens in the different Qn-species in metal oxide-silica glass implies that there is also some ordering of the metal cations. This idea accords with neutron diffraction data of Li2Si205 glass [Zhao et al., 1998], which yield Li-Li interatomic distances near or slightly below 2 A. This distance is considerably smaller than that which would be expected if Li+ were randomly distributed in the glass. Lee and Stebbins [2003a] reported 23Na MAS NMR chemical shifts in spectra of Na2O-SiO2 that could be related to different Na-NBO bonding characteristics in the different Qn-species. Calas et al. [2002] concluded that similar structural features are found in other metal silicate glasses, both for alkali and alkaline earth metals and for transition metals. 7.4b. High-Temperature Structure at Ambient Pressure The glass transition range reflects relaxation of the structure to its equilibrium state on the timescale of a property measurement [Dingwell and Webb, 1990]. This transition is observed as rapid variations of heat capacity and other 2nd-order thermodynamic properties (see Chapter 2). Table 7.2. Alkali-oxygen distance and O-Si-0 angles in alkali metasilicate glasses [Yasui etal, 1983] Alkali metal(M) M-NBO distance, A M-BO distance, A Li 2.221 2.929 Na 3.322 2.278 K 3.342 2.820 Cs 3.288 3.691

O-Si-O angle 0-8 20 9 3

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Figure 7.10 - Comparison of curve-fitted 29Si MAS NMR [Mysen and Cody, 2003] and roomtemperature Raman spectra of Na2Si2Os glass [Mysen, 1997].

In view of the lack of discontinuities, changes in bond angles and bond distances do not take place abruptly at the glass transition temperature, but develop progressively in the supercooled liquid. This has been observed in neutron diffraction experiments [Zotov and Keppler, 1998; Majerus et al., 2004] and in simulation of Na 2 Si 2 0 5 structure [Ispas et al, 2002]. For the same reason, the glass transition cannot be detected in exchange frequencies of Si and O between coexisting Qn-species [Farnan and Stebbins, 1990a, b; Maekawa and Yokokawa, 1997]. The glass transition, however, has been seen as an abrupt decrease in 2 Si spin relaxation time from NMR spectroscopy of K 2 Si 2 0 5 glass and melt [Farnan and Stebbins, 1990a,b]. Although NMR spectroscopy is a precise method to determine glass structure at ambient temperature, interpretation of high-temperature NMR spectra is difficult because the frequencies of oxygen and silicon exchange among structural units are such that multiple oxygen exchanges occur over the signal acquisition time [Farnan and Stebbins, 1990b; McMillan et al., 1992]. When this happens, the NMR spectra collapse to a single Lorentzian line. In contrast, Raman spectroscopy can be used at high temperature because its probe frequency is many orders of magnitude greater than the oxygen and silicon exchange frequencies [McMillan et al., 1992]. Although interpretation of earlier Raman data was somewhat empirical, recent complementary use of NMR and Raman spectroscopy of glasses has led to more precise analysis of the Raman data [Mysen and Cody, 2001, 2003; Mysen et al, 2003]. A comparison of 29Si MAS NMR and Raman spectra of Na 2 Si 2 O 5 glass is shown in Fig. 7.10. The band assignments and structural interpretations of Raman spectra of glass can then be used to interpret Raman spectra of high-temperature melts (including Qn-species abundance) with methods described by McMillan et al. [1992], Mysen and Frantz [1993], and Daniel et al [1995].

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Figure 7.11- Abundance of Qn-species in Na2Si2C>5 and K2Si2Os below and above the glass transition against temperature from in-situ Raman spectroscopy [Mysen and Frantz, 1994; Mysen, 1997]. Glass transition temperatures, Tg, are marked as gray lines [compiled by Richet and Bottinga, 1986].

The structural relaxation associated with the glass transition in metal oxide-silica glasses is manifested by a distinct change in the slope of the temperature versus Qn abundance relationship (Fig. 7.11). Below the glass transition, the abundance of Qn-species does not vary with temperature, whereas that of Q3 decreases and those of Q4 and Q2 increase with temperature above Tg. Qualitatively similar variations of the Qn-species can be found in other alkali silicate glasses and melts [Mysen, 1997; Mysen et ah, 2003]. The temperature-dependent Qn abundance also demonstrates that the electronic properties of the metal cation are important variables not only below Tg (see also Fig. 7.10), but also in the melts at temperatures above T% (Fig. 7.11). The structural information in Fig.7.11 is consistent with the proposal of Stebbins [1988] and Brandriss and Stebbins [1988], subsequently documented by in-situ, hightemperature studies in a variety of metal oxide silicate melt systems [McMillan et al, 1992; Mysen and Frantz, 1992], that equilibrium (7.6) with n = 3, shifts to the right with increasing temperature. This shift has been examined in terms of the effect of temperature on the constant, K, for this equilibrium,

(r T '

(7 7)

-

where it is assumed that the mol fraction of the individual Qn-species, JC2«, is equal to activity. Below Tg, the equilibrium constant does not vary with temperature (Fig. 7.12). Above the glass transition range, where structural relaxation develops, In AT is a linear function of reciproval temperature and is a positive function of the ionization potential of

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Figure 7.12 - Relationship between equilibrium constant, In K, for equilibrium, 2Q3 <=> Q4 + Q2 [equivalent to equation (7.6) with n = 3] and reciprocal temperature below and above the glass transition temperature, Tg, and melt for Na 2 Si 2 0 5 [Mysen, 1997; Tg from the compilation by Richet and Bottinga, 1986].

the metal cation (Fig. 7.13). Thus, steric hindrance, governed by the electronic properties of the cation, remains in the melt. The enthalpy (AH) of reaction (7.6) can be estimated from the slope of the In K versus IIT relationship. For Na-disilicate melts, the AH was originally suggested to be near -30 kJ/mol [Stebbins, 1988; Brandriss and Stebbins, 1988] from analysis of Si NMR spectra of glasses with different fictive temperatures. This A//-value is close to the -27±5 kJ/mol found for Na 2 Si 2 0 5 melt by Maekawa and Yokokawa [1997] from hightemperature 29Si NMR spectroscopy. From calibrated, high-temperature Raman spectra of Na 2 Si 2 0 5 melt, Mysen [1997] reported AH near -20 kJ/mol and noted that the AH of reaction (7.6) for n = 3 is positively correlated with the ionization potential of the metal cation (Fig. 7.14). The enthalpy also increases as the melt becomes more polymerized (Fig. 7.14). Thus, the details of the equilibria among Qn-species in metal oxide silicate

Figure 7.13 - Relationship between equilibrium constant, In K, for equilibrium, 2Q3 <=> Q4+Q2 and Z/r2 (Z = electrical charge and r = ionic radius, A, for alkali metal in 6-fold coordination with oxygen from Whittaker and Muntus [1970] for disilicate melts, K.2Si2Os, Na2Si2Os, and Li2Si205 at 1050°C [Mysen, 1997].

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Figure 7.14 - Relationship between the enthalpy of reaction, 2Q 3 <=> Q 4 +Q 2 , AH and Zlr2 with ionic radius, r, for alkali metal in 6-fold coordination with oxygen from Whittaker and Muntus, 1970] for disilicate melts, K 2 Si 2 0 5 , Na 2 Si 2 0 5 , and Li 2 Si 2 0 5 (nominal NBO/Si = 1) and tetrasilicate melts, K2Si4O9, Na2Si4O9, and Li2Si4O9 (nominal NBO/Si=0.5), at 1050°C [Mysen, 1997].

melts depend on both the properties of the metal cation and on the degree of polymerization, NBO/Si, of the melt. 7.4c. Effect of Pressure on Metal Oxide Silicate Glass and Melt Structure The way in which pressure affects metal oxide silicate glass and melt structure depends on the sign of volume change associated with reaction (7.6). Pressure effects also depend on the extent to which there may be pressure-induced coordination changes of cations in the materials. The sign of AV of equilibrium (7.6) depends primarily on the partial molar volumes of bridging (BO) and nonbridging (NBO) oxygens, on the compressibility of the metaloxygen polyhedra, and on the compressibility of the 3-dimensionally interconnected Q4 structural units. Bottinga and Richet [1995] inferred from molar volume relations that the partial molar volume of bridging oxygen is greater than that of nonbridging oxygen. Increasing pressure might, therefore, favor depolymerization of silicate melts. Whether or not volume relations of BO and NBO can be applied to predict the pressure-dependence of reaction (7.6) is not clear because that reaction does not involve a change in proportion of bridging and nonbridging oxygens. One might reason, however, that the partial molar volume of nonbridging oxygen (NBO) in different Qn-species could also be different because the extent of Si-NBO bond contraction may depend on the number of nonbridging oxygen in the Qn-species of interest. The Na-0 bond distance change with Na/Si in Na2O-SiO2 glasses [Lee and Stebbins, 2003a] is consistent with this proposal as these variations imply that the Si - NBO bond strength and bond distance depend on the number of nonbridging oxygen in a Qn-species. As the number of nonbridging oxygen increases, it is reasonable to surmise, therefore, that the partial molar volume of the nonbridging oxygen decreases. If so, one would expect that, even in the absence of oxygen coordination changes in a melt, reaction (7.6) would shift to the right with increasing pressure.

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Figure 7.15 - Raman spectra of K.2Si4O9 glass, temperature-quenched at ambient pressure and at 2.1 GPa. Grayed area in left panel is expanded in the right panel [Dickinson et al., 1990].

The compressibility of Q units is likely to resemble that of pure SiO2 (Table 5.2). The Q and Q units are likely less compressible. The compressibility of metal-oxygen polyhedra is not well known, but given the much weaker metal-oxygen bonds compared with Si-0 bonds (Table 4.1), bonds in metal-oxygen polyhedra are likely more compressible than Si-0 bonds. The increase in the Griineisen parameter, which is inversely correlated with compressibility, with increasing metal/silicon-ratio of alkali silicate glasses [Ferraro et al., 1973], suggests that the compressibility of individual Qn-species depends on the type of Qn-species. It could be argued, therefore, that because of the higher metal/Si-ratio in Q compared with Q structural units (2 versus 1), the compressibility of Q2-units is greater than Q3. This idea would also lead to equilibrium (7.6) shifting to the right with increasing pressure whether or not pressure also results in coordination transformations in the melt and glass. Ideally, structural studies should be conducted in-situ at high temperature and high pressure. Such data are not, as yet, available. Only data for glasses formed by temperaturequenching at pressure have been reported (Fig. 7.15). Dickinson et al. [1990] suggested that the Raman spectra of K2Si409 glass quenched at 2.1 GPa (Fig. 7.15), are consistent with a slight increase in Q4 and Q2 abundance in K2Si409 melt with pressure, a conclusion similar to that of Mysen [1990] for Na2Si205 quenched at 2 GPa. Those conclusions accord with 29Si NMR data by Xue et al [1989]. These results are consistent, therefore, with equilibrium (7.6) shifting to the right with pressure possibly because of the volume and compressibility effects described in the previous paragraph. In analogy with the structural behavior of crystalline silicates, pressure may also cause changes in oxygen coordination numbers. Raman spectroscopy is not particularly sensitive to coordination transformation, be it of the metals or of silicon, although 6-fold

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Figure 7.16 - Silicon-29 MAS NMR spectra of K2Si
Figure 7.17 - Oxygen-17 Triple quantum NMR spectra of Na2Si3C>7 glass quenched at ambient pressure (0.001 GPa - left panel) and at 10 GPa (right panel). [41Si denotes Si4+ in 4-fold coordination with oxygen, whereas [5'6]Si notes 5- and 6-fold coordined Si4+ [Lee et al., 2003b],

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also suggested that the proportion of Q4-species in the 1.9 GPa glass was lower than that in glass quenched at ambient pressure. Whether or not this decrease also implies a decrease in Q4 abundance relative to the Q3 and Q2 species is not clear. There is incontrovertible evidence, however, from 17O triple quantum NMR that at 10 GPa, glass of Na2Si307 contains both [4}Si-O-[5>61Si and Na-O-[5'61Si bonds (Fig. 7.17). This conclusion [Lee and Stebbins, 2003b] was also supported by Xue et al. [1994] from static and MAS NMR studies of other high-pressure Na-silicate glasses. The extent to which Si-coordination changes occurs with pressure appears dependent on the availability of nonbridging oxygen in the starting materials [Lee et al, 2003b]. 7.5. Structure and Melt Properties The variations with composition of properties of silicate melts and glasses, in general, and binary metal oxide, in particular, reflect structural changes. As discussed above, structural models were derived on the basis of assumed relationships between structure and properties before structure data became available. Some of these models are consistent with the structural data obtained by direct measurements, thus lending credence to the assumptions in some of the property-based structure models [e.g., Babcock, 1968; Bockris and Reddy, 1970]. In other cases, current understanding of melt structure can be used to decide which among competing property-based structure models are consistent with structural data. 7.5a. Liquidus Phase Relations The minimum M/Si-ratios of stable crystalline phases in various metal oxide silicate crystals reflect the extent steric hindrance is associated with accommodation of cations in a crystalline silicate network (Table 6.1). In silicate glasses and melts, many of the same structural restrictions can be applied by considering relative stability of Qn-species. The fact that the equilibrium constant for equation (7.6) is positively correlated with the ionization potential of the metal cation is a direct consequence of steric restrictions associated with bonding the metal cations to nonbridging oxygen in Q3-species a shown in Figs. 7.9 and 7.13. In simple binary metal oxide-silica systems, the compositions of liquidus phases are commonly simple and their thermodynamic properties sometimes are known. Thus, relations between liquidus surfaces and ionization potential of metal cations reflect melt structure, which is itself governed by M/O ratio (or NBO/Si), nature of the metal cation, temperature, and pressure. In terms of melt structure, the activity of SiO2 as deduced from the cristobalite/ tridymite liquidus trajectory (section 6.2c) is particularly interesting as it is related to the abundance of Q species in the melt. The expansion of the cristobalite/tridymite liquidus volume toward decreasing silica content with increasing ionization potential of the metal cation (Fig. 7.18) follows naturally from the observation that the disproportionation reaction among Qn-species [equation (7.6)] shifts to the right with increasing ionization

Binary Metal Oxide-Silica Systems II. Structure

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Figure 7.18 - Activity of SiO2, tfsio2, in Li2O-SiO2, Na2O-SiO2, and K2O-SiO2 melts at their liquidii relative to Q4 abundance in the liquid (from compilation of Ryerson [1985] together with melt structure data for these systems from Mysen and Frantz, [1994]).

potential of the metal cation (Fig. 7.13). Thus, even if the mixing properties between Qn species were not affected by the properties of the metal cations, the relationships in Fig. 7.13 are consistent with the liquidus phase relations in Fig. 7.18. In other words, an increase in activity coefficient of the component, SiO2, as derived from liquidus relations [see also Ryerson, 1985], at least in part, is the result of increasing concentration of fully polymerized Q species in the melt. From liquidus phase relations, enthalpy of fusion data for appropriate liquidus minerals, and the structural data on abundance of Qn-species in individual metal oxide melts, some information on the mixing behavior of the individual Qn-species in the melt can be derived with the aid of the Van't Hoff equation, using Qn components in lieu of oxide components. The stoichiometry of the Qn-species is similar to that of liquidus phases

Figure 7.19 - Logarithmic relationships between activity coefficients, YQ4, 7Q3> a n d mol fractions of Q 4 and Q 3 species, XQ4, and XQ3~ respectively, at liquidus of silicate polymorphs (for Q 4 relations) and alkali disilicate crystals (for Q 3 relations) [Mysen and Frantz, 1994].

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that often occur over wide compositional ranges. The activity of such species can be defined as equal to 1 at the composition and liquidus temperature of the crystalline phase with similar stoichiometry. For example, aQ4 = 1 at the liquidus of pure SiO2, aQ3 = 1 at the liquidus of disilicate crystals and so forth. Examples of such calculations for melts in alkali oxide-silica systems are summarized in Fig. 7.19. Expressed in terms of the logarithms of the activity coefficients and the mol fractions of the species, these are linearly correlated. Notably, the compositional differences between the systems do not affect these relationships. It would appear, therefore, that the activity coefficient of a structural unit in a metal oxide-silica melt can be estimated if its abundance is known. 7.5b. Mixing Behavior As discussed in section (6.2), the Gibbs free energy of mixing depends on the temperaturedependence of enthalpy and entropy of mixing. From a melt structural perspective, the entropy of mixing ASm may be approximated by mixing Qn-species, the compositionand temperature-dependence of which are available from high-temperature structural data. By using mol fractions of Qn-species for x-t in equation (2.25), the effects of composition and temperature on the entropy of mixing can be determined provided that the topology of the indvidual Qn-species does not vary with temperature. Mixing parameters such as configurational heat capacity, Cpconf, can also be derived from Qn-speciation provided that Cpconf can be obtained for each Qn-species. This can be accomplished by combining, for example, the thermodynamic data summarized by Richet and Neuville [1992] for Na 2 O-SiO 2 melts with Qn-speciation information from the same system [Mysen, 1997]. For Q4, Q3, and Q2 species, the individual C/ on/ (Q n )-values can be obtained from a set of linear equations of the type: n4

i xonycp^(Qn)=cc;nf.

n=0

(7.1D

Figure 7.20 - Comparison of measured configurational heat capacity, Cpco"\obs), and calculated, C/°"^(calc) of the systems K2O-SiO2 (at 1200°C), Na2O-SiO2, and Li2O-SiO2.

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We can apply the Cpconf(Qn) data from Na2O-SiO2 melts to other systems by adding a mixing term in which the temperature-dependence of Qn-speciation and glass transition temperature for the composition of interest are known [Mysen, 1995,1997]. A comparison of configurational heat capacities calculated in this manner for melts in the systems K2OSiO2 (at 1200°C), Na2O-SiO2, and Li2O-SiO2 shows a close match with the observed values (Fig. 7.20). This Cpconf information can then be used in conjunction with, for example, the configuration entropy model for melt transport to estimate melt viscosity and, perhaps, diffusion. 7.5c. The Mixed Alkali Effect Addition of a second oxide to binary metal oxide silicate glasses and melts often cause deviation from linearity of properties by up to several orders of magnitude. This effect is referred to commonly as the mixed alkali effect [e.g., Day, 1976; see also section 6.3c]. Recent theoretical and experimental examination of this effect is based on the observation that there often is substantial ordering of network-modifying cations among energetically non-equivalent sites in the structure [Zotov et al., 1995; Yap and Elliott, 1995; Park and Cormack, 1999; Cormack and Du, 2001; Lee and Stebbins, 2003b]. In this treatment, the availability of specific sites in the structure is diminished by the introduction of a second cation with substantially different ionization potential (different ionic size or electrical charge). Thus, the probability of any one of the other cations being able to move to an energetically equivalent site decreases. This change, in turn, can be reflected in, for example, transport properties of silicate melts and glasses, and, therefore, the mixed alkali effect. 7.5d. Transport Properties Viscosity, diffusivity, and electrical conductivity are most often related to melt structure via the activation enthalpy of the property of interest. High-temperature activation enthalpy of viscous flow has long been thought closely related to the energy of oxygen bonds, and more specifically to bonding between oxygen and tetrahedrally coordination cations (see section 4.4). In fact, it was the systematic relationships between metal/silicon ratio of a metal oxide silicate melt and the high-temperature activation enthalpy of viscous flow that led Bockris et al. [1956] to propose melt structural models based on the concept of discrete anionic structural units (see also Bockris and Reddy [1970]). In this data set, the activation energy function shows rapid changes at compositions near disilicate (NBO/Si near 1) and metasilicate (NBO/Si near 2). These changes are at or near compositions where the abundance of Q3 and Q2 species are at their maximum values (disilicate and metasilicate respectively). These observations lead to the suggestion that the abundance of bridging oxygen bonds in specific structural units contributes significantly to the activation enthalpy of viscous flow (but by no means the only contribution). This concept also has direct bearing on diffusion of atoms that form the anionic structure of the silicate network (oxygen and tetrahedrally coordinated cations). One would expect, therefore, that the activation enthalpy of Si and O self-diffusion would resemble

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that of viscous flow. It does [Shimizu and Kushiro, 1984, 1991; Reid et al, 2001, 2003]. Diffusivity and activation enthalpy of network-modifiers do not [Shimizu and Kushiro, 1991; Watson and Baker, 1991]. The activation enthalpy typically is 20-40 % of those of oxygen and silicon. Interestingly, the activation enthalpy of electrical conductivity (section 6.3b) resembles those of network-modifiers. Given the premise that, at least in simple binary metal oxide melt, the metal cation is the charge-carrier for the electrical current (section 6.3b), the relationship between activation energy of diffusion of networkmodifying cations and electrical conductivity can be understood. An understanding of transport behavior at high pressure is of particular importance in the earth sciences. Considerable effort has been devoted to characterize the response to pressure of the properties and structure SiO2 glass (see section 5.3). In contrast, similar information is considerably less abundant for metal oxide-silica melts and glasses. Little is known, aside from the study by Scarfe et al. [1987], suggesting that nominal NBO/Sivalue of a melt is an important factor in determining whether viscosity increases or decreases with increasing pressure from ambient to 2 GPa. A change from negative to positive pressure dependence of melt viscosity occurs at nominal NBO/Si near 1 [Scarfe et al., 1987]. This suggests that the abundance of Q4 units, and their response to pressure may be important in this regard. With NBO/Si > 1, the abundance of Q units in metal oxide silicate melts is negligible [Maekawa et al, 1991; Mysen, 1999]. Bottinga and Richet [1995] asserted that negative pressure-dependence of melt viscosity may be explained by an increase in configurational entropy caused by pressureinduced melt depolymerization. This depolymerization is governed by the volume difference between bridging and nonbridging oxygens. Although it is not well known how much depolymerization is needed to cause the melt viscosity to decrease, suffice it to say that, at least to about 2 GPa, the proportion of Si in high coordination is on the order of 1-2 % only. Thus, other factors, such as compression of Si-O-Si bond angles in Q4 species and changes in Qn-abundance, may be more important. Bond angle compression results in weakening of T-O bonds and, thus, in decreasing activation energy of viscous flow. Another question revolves around possibilities to increase the configurational entropy of the melt without resorting to changes in abundance of bridging and nonbridging oxygen. This is indeed possible if the volume change of reaction (7.6) (n = 3) is negative so that this reaction shifts to the right with pressure. Such a change would increase the entropy of mixing. Therefore, within the context of the configurational entropy model it would lead to a decrease in viscosity. In order to accomplish this, one has to suggest that the metal-nonbridging oxygen distances differ in Q3 and Q2 species. Structural data [Lee and Stebbins, 2003a] are consistent with this idea. A shift of reaction (7.6) to the right with pressure, even in the absence of silicon coordination changes, have also been proposed on the basis of Raman spectra of metal oxide glasses quenched at pressures to 2.4 GPa [Mysen, 1990; Dickinson et al., 1990]. Thus, a decrease of viscosity with increasing pressure can be understood without resorting to coordination changes.

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In light of the relationships between viscosity and self-diffusion of oxygen and tetrahedrally coordinated cations (the network-forming components) it is likely that pressure-dependent activation energy of diffusion of these components has the same structural explanation as melt viscosity. This suggestion does not apply to diffusion of network-modifying cations whose pressure dependence often has the opposite sign as those of network-forming cations [Watson, 1981]. This effect is consistent with the decoupling described in section 2.1e between the mobility of network-forming and network-modifying cations. Similarly, one would expect that electrical conductivity will decrease with increasing pressure. 7.6. Summary Remarks 1. Results from numerical simulation, x-ray, and neutron diffraction of metal oxide silicate glasses and melts point to a distribution of intertetrahedral angles that is consistent with multiple coexisting structural units. The intratetrahedral angles indicate increasing distortion within the silicate network the smaller the metal cation. 2. X-ray and neutron diffraction data indicate that the metal cation in these materials are in 4-8-fold coordination with oxygen, with a larger coordination number the larger the ionic radius of the metal. 3. The silicate tetrahedra in glasses and melts can be described in terms of 5 different types defined in by their number of bridging oxygen. These are referred to as Qnspecies. 4. In both glasses and melts, the nonbridging oxygens in Qn-species are energetically non-equivalent as shown by the ordering of metal cations among them. The more electronegative the metal cation, the stronger is its tendency to form bonds with nonbridging oxygen in the least polymerized of the Qn-species. 5. The Qn-speciation in metal oxide silicate glasses is independent of temperature below the glass transition temperature range. Above this temperature range, the Qn-speciation in metal oxide-silica melts is a systematic function of temperature. 6. Qn-speciation systematics can be related to activity-composition relations in the melts. Their mixing behavior can also be used to model configurational and transport properties of metal oxide silicate melts. References Angell C. A. (1985) Strong and fragile liquids. In Relaxation in Complex Systems (eds. K. L. Ngai and G. B. Wright), pp. 3-11. U. S. Department of Commerce Technical Information Service. Washington DC. Angell C. A. and Kanno H. (1976) Density maxima in high-pressure supercooled water and liquid silicon dioxide. Science 193, 1121-1122. Angell C. A. and Torell L. M. (1983) Short term structural relaxation processes in liquids: Comparison of experimental and computer simulation glass transitions on picosecond timescales. J. Chem. Phys. 78, 937-945.

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Aluminosilicate Systems I. Physical Properties The presence of alumina in glass usually results in increased chemical durability, hardness, tensile and compressive strengths, and thermal endurance. It also reduces devitrification tendency and lowers thermal expansion. This influence is, therefore, of considerable practical interest. Besides, approximately 95% of magma composition can be expressed within the system metal oxide-alumina-silica [Mysen, 1987]. In fact, the alumina content can be as high as 15 mol % in magma and still higher in some melts of industrial interest such as SiO2-poor slags. To describe composition effects on aluminosilicate properties, we will take as a starting point the binary metal oxide silicates discussed in previous chapters. Leaving aside for the moment iron oxides, we will deal mainly with addition of alumina at constant SiC^/M^O ratio, with substitution of A12O3 for M^O at constant SiO2 content, or with substitution of Al for Si at constant nominal NBO/T, where M designates an alkali or an alkaline earth cation. In view of the possible dual role of aluminum as a network-former or network-modifier, an important distinction pertaining to charge compensation of Al 3+ must first be recalled. Depending on whether or not there are sufficient metal cations to charge-compensate Al 3+ in tetrahedral coordination, aluminosilicates are said to be peralkaline (even in alkaline earth systems) or peraluminous (see also Chapter 4). The boundary between these two fields is represented by meta-aluminosilicates in which metal cations reach the appropriate proportion needed for charge-compensation of all Al 3+ . It has long been reckoned that a change of aluminum from network former to network modifier should affect physical properties. Hence, an important issue is how physical properties actually when the meta-aluminous join is crossed. The question is not at all new. Since the early 1960s, such variations, when observed, have been associated with either coordination changes of aluminum, generally from tetrahedral to octahedral [Day and Rindone, 1962; Riebling, 1964, 1966], or to incorporation of Al in triclusters, i.e., in groups of three (Si,Al)O4 tetrahedra sharing a common bridging oxygen [Lacy, 1963; Osaka et al., 1987]. 8.1. Phase Relationships Introduction of aluminum in binary silicate melts has definite effects on glass formation, on liquidus and solidus temperatures, and on the extent of liquid-liquid immiscibility. This influence is stronger in alkali than in alkaline-earth systems. As a result, the marked

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Figure 8.1- Effect of alumina addition on immiscibility temperatures of sodium aluminosilicate melts for the constant SiO2 content indicated [Topping and Murthy, 1973]. Similar effects have been described by Hager et al. [1967] for even smaller alumina additions.

contrast in physical properties between alkali and alkaline-earth Al-free systems tends to disappear in aluminosilicate melts when the meta-aluminous join is approached. 8.1a. Immiscibility Fields In alkali silicate melts, the metastable miscibility gaps disappear rapidly when aluminum is introduced. For the sodium system (Fig. 8.1), addition of less than 2 wt % A12O3 displaces the solvus below the glass transition range where the kinetics of unmixing are vanishingly slow [Topping and Murthy, 1973]. Consistent with the relative extent of miscibility gaps in Al-free melts (Fig. 6.1), a similar effect has been observed for lithium aluminosilicates with the slightly higher alumina addition of 5 mol % [Savva and Newns, 1971]. As already described by Greig [1927], a large reduction in solvus temperatures near the M^O-SiOj join is also observed for alkaline earth compositions (Fig. 8.2). The solvus crosses the liquidus surface and becomes metastable with more than about 3 mol % A12O3 in the Mg system, and at still lower contents in the other aluminosilicates of Fig. 8.2. An important feature is that the aluminum oxide does not affect the relative extent of unmixing in the alkaline earth series compared to that in Al-free systems. In both cases, phase separation is favored by high ionization potential of the metal cation. In a qualitative manner, these trends are readily accounted for. When Al3+ substitutes for Si4+, it causes the anionic framework to polymerize through association with the other metal cations which are no longer network-modifiers. As a consequence, the steric hindrance problems discussed in previous chapters for bonding of "free" metal cations with nonbridging oxygens diminishes. Interestingly, however, unmixing vanishes well before the meta-aluminosilicate join is reached (Fig. 8.2). This feature provides further evidence for bonding between metal cations and bridging oxygens. Because Al-0 bonds are not as strong as Si-0 bonds (see Table 4.1), one can surmise that the proportion of bridging oxygens in the coordination sphere of M-cations not involved in charge compensation for Al3+ is higher in Al-bearing than in Al-free systems. Likewise, this proportion is probably higher in alkali than in alkaline-earth aluminosilicates at comparable temperatures and overall stroichiometry or nominal NBO/T. Other things being equal, the influence of Al3+ on immiscibility is the least important in the magnesium system (Fig. 8.2). This indicates that Mg2+ is the alkaline earth cation

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Figure 8.2 - Liquid-liquid immiscibility in ternary alkaline-earth aluminosilicates as summarized by Galakhov et al. [1985]. Temperatures of the isotherms indicated in K.

that associates the least strongly with Al3+. The strength of this association increases in order of increasing ionic radius for other cations of the series. Another metastable miscibility gap exists near the SiO2-Al2O3 join. Its critical temperature and composition have been found at 1630°C and 73 mol % SiO2 by MacDowell and Beall [1969], but the 1300°C and 80 mol % of Galakhov et al. [1976a] are likely more reliable [Mazurin et al, 1984]. According to the diagrams of Fig. 8.2, alkaline earth cations exert the same influence on this gap as on phase separation in the Al2O3-poor sides of the systems. Stronger association between Al and metal cation favors mixing of silicate and aluminate entities, with the consequence that unmixing near the SiO2-Al2O3 join is marginal for Sr, small for both Ba and Ca, but significant for Mg. As a result, immiscibility is prevalent throughout the silica-rich part of the Mg aluminosilicate system. One could then wonder how homogeneous glasses can be prepared in that case. From a practical standpoint, this very wide field of unmixing is not necessarily problematic. Supercooling is intrinsically difficult for Mg compositions, so that crystallization would begin before the onset of phase separation. This is the reason why determination of the SiO2-Al2O3 miscibility gap has proven so difficult. But both processes are bypassed with the high cooling rates needed to quench the melt in the composition range where homogeneous vitrification is possible.

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Figure 8.3 - Liquidus surfaces of ternary aluminosilicates redrawn on a mol % oxide basis from Levin et al. [1964]. The compounds crystallizing from the melts are shown as solid points, stable miscibility gaps as hachured areas, the domains of glass formation under usual cooling rate conditions as gray areas [data from Bowen and Schairer, 1955,1956, and from the authors' own observations]. Abbreviations: A: A12O3; K: K 2 O; N: NajO; S: SiO2; Ab: albite (NaAlSi3O8); AE: aluminous enstatite (Mg 3 Al 2 Si 3 0 12 ); An: anorthite (CaAl 2 Si 2 0 8 ); Co: cordierite (Mg2Al4Si5O20); En: enstatite (MgSiO3); Fo: forsterite (Mg 2 Si0 4 ); Geh: gehlenite (Ca 2 Al 2 Si0 7 ); Kals: kalsilite (KAlSiO 4 ); KF: K feldspar (KAlSi3O8); La: larnite (Ca 2 Si0 4 ); Leu: Leueite (KAlSi2O6); Mu: mullite (Si 2 Al 6 O 13 ); Ne: nepheline (NaAlSiO4); PsWo: pseudowollastonite (CaSiO3); Sa: sapphirine (Mg 4 Al 10 Si 2 O 23 ); Yo: yoshiokaite (wide solid solution around the composition CaAl 2 Si0 6 ). Aluminous enstatite and yoshiokaite form metastably at high degree of supercooling [see Lejeune and Richet, 1995; Roskosz et al. 2005]. Other such metastable compounds could exist.

8. lb. Liquidus Relations Liquidus phase relations are represented on a mol % basis for the Na, K, Ca, and Mg aluminosilicate systems in Fig. 8.3. Most diagrams share a common feature, namely, the

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presence of only two ternary compounds on the liquidus. In the Na, K, and Ca systems, the less silica-rich compound has the same MjtO#Al2O3«2SiO2 stoichiometry, from which the magnesian mineral cordierite (MgOAl 2 0 3 *2.5Si0 2 ) does not depart significantly. Just above the glass transition, a greater number of disordered, nonstoichiometric crystalline phases can nucleate and grow metastably [Longhi and Hays, 1979; Roskosz et al, 2005], but they eventually transform to the stable phases on moderate heating. Even for potassium aluminosilicates, for which four such compounds exist, only a few aluminosilicate configurations are stabilized at high temperature in the crystalline state despite the wide ranges of composition and stoichiometry presented by the ternary systems. The differing topological complexity of the ternary diagrams of Fig. 8.3 is essentially due to differences in the number of compounds stable on the liquidus in the limiting binary M^O-SiOj and M^O-A12O3 systems, because there is a single compound, mullite (Al2O3»2SiO2), along the common Al2O3-SiO2 join shared by the ternary diagrams. In the limiting binary M x O-SiO 2 systems, there are two compounds for Mg, three for K, and four for both Na and Ca. But the largest difference is found along the M^O-AljOj joins where the calcium system stands apart with its five different compounds. Such a variety signals a remarkable match between the ionic radius of O2" with those of Ca 2+ and also of Si4+ and of Al 3+ in both 4- and 6-fold coordination. Another important feature of the diagrams of Fig. 8.3 is the markedly differing manner in which liquidus temperatures vary with composition in alkali and alkaline earth systems.

Figure 8.4 - Influence of alumina on liquidus phase relations at constant or near constant M^ in alkaline and alkaline earth systems, (a) Phase diagrams of the systems CaSiO3-CaAl2Si2O8 [Osborn, 1942] and CaSiO 3 -Ca 2 Al 2 SiO 7 [Osborn and Schairer, 1941]: An: anorthite (CaAl 2 Si 2 0 8 ); Ge: gehlenite (CaAl 2 Si0 7 ); L: liquid; PsWo: pseudowollastonite (CaSiO3). Analogous diagrams are not available for MgSiO 3 because of the incongruent melting of enstatite at ambient pressure, (b) Phase diagrams of the systems K 2Si2O5-KAlSiO 4 [Schairer and Bowen, 1955] and Na 2 Si 2 0 5 -NaAlSi0 4 [Tilley, 1933]: Cam: carnegieite (NaAlSiO4); Kals: kalsilite (KAlSiO4); Ne: nepheline (NaAlSiO4).

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The effect is evident when A12O3 is added at constant Ni/Si ratio, as shown in Fig. 8.4 for pseudobinary joins M;cO»2SiO2-MA.O»2SiO2»Al2O3. In the alkaline earth systems (Fig. 8.4a), the differences between the melting temperatures of the endmembers are marginal. In contrast, they are considerable in alkali systems (Fig. 8.4b): liquidus temperatures increase by about 600 degrees when the A12O3 content increases from 0 to 25 mol % and eventually become comparable to, or even higher than, those of the alkaline earth melts. This trend correlates with the increase in coordination number described in section 3.2b for chargecompensating alkali cations. In other words, the average bond strength in alkali and alkaline earth systems becomes at least similar with increasing alumina content. Not only are weak M - 0 bonds replaced by stronger Al-0 bonds when the melt polymerizes, but the order of liquidus temperatures near the meta-aluminous join confirms that the strength of the association of Al with metal cations increases in the order Mg, Ca, Na, K. Interestingly, the same trend holds in complex melts as concluded from phase equilibria experiments on immiscible melts of the system MgO-CaO-TiO2-Al2O3-SiO2 [Hess and Wood, 1982]. Beyond the meta-aluminous join, the influence of individual M-cations becomes blurred for SiO2-rich compositions because liquidus temperatures obviously tend to be governed by the SiO 2 and A12O3 components. Likewise, near the M^O endmember the properties of each oxide predominate. As discussed in section 6.1c, the high-temperature instability of alkali oxides contrasts markedly with the extremely high temperatures that prevail close to the CaO and MgO endmembers. In both cases, the effect is that glass formation is prevented. In alkali systems, however, the strong association of Al with alkali cations also manifests itself by the fact that alkali-rich glasses are stabilized by losing their very high hygroscopic character as soon as a few mol % A12O3 are added. The last factor affecting liquidus temperatures to be mentioned is Si<=>Al substitution. The effect is most clearly observed between pure SiO2 and ternary compounds on the meta-aluminous join (Fig. 8.5). For reasons of clarity, phase diagrams are shown only for Ca, Ba, and K aluminosilicates although a similar contrast would be observed in the analogous Na- and Mg-systems (see Fig. 8.3). The lowest temperature is that of a eutectic point located in the SiO2-rich part of both diagrams of Fig. 8.5, but this freezing-point depression is considerably greater for alkali than for alkaline earth systems. As will be discussed below from a calorimetric standpoint, this contrast reflects a difference between the affinities of SiO 2 and M^/2A1O2 groups, which are stronger for alkali than for alkaline earth M-cations. 8.1c. Glass Formation With usual cooling rates of tens of degrees per second, the composition range where vitrification of aluminosilicates is possible also depends on the metal cation (Fig. 8.3). As expected from the trends in the Al-free binary melts, glass formation occurs over a wider compositional range in the K and Na than in the Mg system and also in the Cs system [Bollin, 1972]. Clearly, the Ca system does not fit with this trend because its glass-forming region is anomalously large and even extends to Si-free materials along the join CaOA12O3. This exceptionally wide glass-forming region makes calcium aluminosilicates

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Figure 8.5 - Influence of Ak=>Si substitution on aluminosilicate melting equilibria, (a) Phase diagram of the systems SiO 2 -CaAl 2 Si 2 O 8 [Schairer and Bowen, 1947] and SiO 2 -BaAl 2 Si 2 O g [Foster and Lin, 1969]: An: anorthite (CaAl 2 Si 2 O 8 ); Ce and HCe: celsian and hexacelsian (BaAl 2 Si 2 O g ); L: liquid; SiO2: cristobalite and tridymite. (b) Phase diagram of the system SiO2-KAlSiO4 [Schairer and Bowen, 1955]: Kals: kalsilite (KAlSiO4); K-Fel: KAlSi 3 O 8 ; Leu: leucite (KAlSi2O6).

particularly well suited for investigating glass and melt properties not only over a wide range of composition, but also over large temperature intervals owing to the possibility of performing measurements down to the glass transition. Calcium aluminosilicates are, therefore, valuable model systems for other alkaline earth aluminosilicates. As a network-forming cation, aluminum generally improves glass formation because the viscosity increases caused by polymerization of the anionic framework ensures slower crystallization kinetics. This effect is particularly clear along the joins MSiO3-Al2SiO5 (M = Mg, Ca) where, contrary to MSiO3 metasilicates, compositions close to the metaaluminous joins vitrify readily. As described in section 2.3e, glass formation is easier near eutectic compositions because lower liquidus temperatures also result in higher viscosity. Regardless of the structural role of Al, consistently high liquidus temperatures can account for the poor vitrification ability of peraluminous compositions. However, the very wide glass-forming region of calcium aluminosilicates cannot be explained in terms of viscosity changes. For instance, the SiO2-free melts that vitrify along the join CaO-Al2O3 are extremely fluid [Urbain, 1983] at liquidus temperature that can exceed 1600°C (Fig. 8.3). Hence, other factors must be considered. Compared to Na, K or Mg compositions, Ca aluminosilicates have an important peculiarity: as a result of the aforementioned match between the ionic radii of Ca2+ and other ions, a greater number of compounds are stable on the liquidus of the two limiting CaO-SiO2 and CaO-Al2O3 binaries. As described in section 2.3e, it is tempting to relate their strong glass-forming ability to this feature. In Fig. 8.3, a correlation is indeed observed between the extent of glass formation and the abundance of compounds stable on the liquidus.

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8.2. Thermodynamics of Mixing Thermodynamically, the reduction of the size of miscibility gaps is a clear evidence for decreasing deviations from ideality upon addition of alumina to binary metal oxide-silica systems. But there remain important differences between alkaline and alkaline earth aluminosilicate systems. This is especially so for the influence of "free" and chargecompensating metal cations on melt properties. 8.2a. Heat Capacity In liquids, the heat capacity (C') is made up of vibrational and configurational contributions. The former has been extensively discussed in section 3.2b in relation to short-range order and oxygen coordination of cations in glasses. It suffices here to recall that the vibrational density of states is a sensitive function of oxygen coordination of every cation. In particular, low-temperature heat capacity conveys information on the environment of cations whether free or acting as charge compensators. At least for peralkaline compositions, analysis of the available C data indicates that association with aluminum entails major changes in short-range order around alkali cations whose oxygen coordination number increases from about 5 to the higher values found in tectosilicate crystals. In contrast, the oxygen environment of alkaline earth cations does not change significantly. It follows that networkmodifying and charge-compensating alkali cations must be distinguished when evaluating the vibrational entropy of silicate glasses, whereas such a distinction is unnecessary for alkaline earth cations. Unfortunately, no information can be drawn for compositions beyond the meta-aluminous join as low-temperature C measurements require large glass samples that cannot be prepared for peraluminous glasses. We must also recall that the heat capacity of glasses is additive with respect to chemical composition and that it is close to the Dulong-and-Petit limit of 3 Rig atom K at the standard glass transition. The configurational heat capacity (C con^), then, is approximated by the difference between the measured heat capacity of the liquid (C ,) and this limit. Because the Dulong-and-Petit limit is determined by the number of atoms in the formula unit, the composition dependences of Cpl and Cpconfare the same. These are strong as apparent in Fig. 8.6 which illustrates, on a g atom basis, the effects of substitution of A12O3 for M^O at constant SiO 2 content for three different M-cations. For analogous melt compositions, these and other data indicate that Cpconf increases in the order Mg, Ca, Na, K. Another noteworthy feature of Fig. 8.6 is that, when significant, the temperature dependence of Cpconf increases in the opposite order. As the temperature derivative of configurational entropy (S001^), C con^is a measure of temperature-induced structural changes. More precisely, C con^mainly reflects short-range interactions as discussed in section 6.2b. Hence, its variations are consistent with the increasingly strong association between Al and M-cation with decreasing ionization potential of the charge-compensating cation. From Mg to K, this association restricts the number of configurations available to alkali compared to alkaline earth melts. On the

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Figure 8.6 - Heat capacity comparison between fully polymerized aluminosilicates liquids and their Al-free counterparts with the same SiO2 content. Because the value of 3 R is approximately 25 J/mol K, the manifold dependence of Cpmnf (= Cpl - 3R) on composition is clear in this plot; Wo: CaSiO3; An: CaAl2Si208; K-Fel: KAlSi3O8; KS3: K2Si3O7; Ne: NaAlSiO4; NS: Na2Si03. Data from Richet and Bottinga [1984a,b, 1985] and Richet et al [1984].

other hand, the rate at which new configurations become accessible increases faster with temperature in alkali than in alkaline earth systems because, due to increasing thermal energy, high enthalpy barriers can be overcome to maximize the entropy. Along with formation of highly coordinate Si and Al species, as discussed in the next chapter, Si<=>Al disordering should be one of such factors that contribute to the higher dC con^/dT of alkali aluminosilicates. In Fig. 8.6, the C con^contrasts between Al-free melts and their fully polymerized Albearing counterparts are small except for the two potassium-bearing compositions. On average, such differences might seem insignificant over wide temperature intervals. This slight effect could be misleading, however, if one were not heeding the large differences in polymerization between the various series of melts of Fig. 8.6. As discussed in section 6.2b for binary M^O-SiO2 systems, Ccon^ decreases with increasing degree of polymerization and reaches a minimum value for pure SiO2. For a given NBO/T, the data of Fig. 8.6 thus point to a marked increase of C ""^when Al substitutes for Si. As a network forming cation, Al3+ causes C con^to increase to the value of the Al-free melt with a much higher NBO/T. A more detailed examination indicates that these effects depend on the nature of the M-cation. For the system MgO-Al2O3-SiO2, the C measurements are summarized in Fig. 8.7. At constant Mg/Al along two different joins (Fig. 8.7a), C varies linearly with composition at all temperatures. Interpolated at constant SiO2 content (Fig. 8.7b), these trends again show a linear variation with composition. When extrapolated to the MgOA12O3 join, the trends for different temperatures converge to the temperature-independent partial molar heat capacity of MgO derived for Al-free silicates (Fig. 8.7c). These trends also extrapolate to values consistent with the heat capacity measured for pure A12O3 liquid. In agreement with the interpretations presented above, this observation implies that the temperature dependence of C is entirely attributable to the partial molar heat capacity of the A12O3 component in Mg aluminosilicate melts.

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Figure 8.7 - Heat capacity of magnesium aluminosilicate melts at 1200 (open symbols) and 1800 K (solid symbols): (a) When the SiO 2 content varies at constant Mg/Al. (b) When MgO substitutes for A12O3 at constant SiO2 content, (c) When data are extrapolated along the join MgO-Al 2 O 3 . Data from Courtial and Richet [1993] with the value derived for pure MgO in Al-free melts [Richet and Bottinga, 1985] and that reported for pure A12O3 liquid [Barkhatov et ah, 1973]. The solid lines are calculated with composition-independent partial molar heat capacities.

Even though Mg aluminosilicates are thermodynamically strongly nonideal solutions, they do not show excess heat capacity at least up to the meta-aluminous join. As far as C co"fis concerned, there is no need to distinguish between free and charge-compensating Mg. Denoting the mol fraction of oxide i by xp one writes: n — Zj X-

L*pi,

\O.LJ

and finds that the partial molar heat capacity of oxide i, CPi, is independent of composition and varies with temperature only for A12O3. Again, no inference can be made for compositions lying beyond meta-aluminous join because high liquidus temperatures and problems with quenching crystal-free glasses have prevented measurements from being made. This simplicity is lost if the coordination of the M-cation changes through Al charge compensation. For sodium aluminosilicates, the heat capacity is not a linear function of either SiO2 content at constant Na/Al (Fig. 8.8a) or of Na/(Na+Al) at constant SiO2 content (Fig. 8.8b). The temperature dependence of C is also a complex function of composition. It is significant only near the meta-aluminous join and causes the Cp vs. composition relationships to become linear at high temperature along the meta-aluminous join (Fig. 8.8a). Conversely, at constant SiO2 content this relationship becomes increasingly nonlinear with increasing temperatures (Fig. 8.8b). To rationalize such complicated variations, one needs to distinguish in equation (8.1) partial molar heat capacities of sodium oxides with either free or charge-compensating Na, such that only the latter depends on temperature. Finally, it appears that C varies smoothly when the meta-aluminous join is crossed (Fig. 8.8b). Owing to the sensitivity of configurational properties on short-range

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Figure 8.8 - Heat capacity of sodium aluminosilicate liquids, (a) Against SiO 2 content at constant Na/Al ratio, (b) Against Al/(Al+Na) at 75 mol % SiO2. For Al-free and Al-poor melts, the temperature dependence of C is too small to be detected even when the calorimetric measurements span intervals of almost 1000 degrees. Data from Richet and Bottinga [1984b] and Richet [unpub].

order around cations, this feature suggests that Al remains essentially in tetrahedral coordination when present in excess of charge-compensating Na. Heat capacity data for other systems are less comprehensive. From Mg to K systems they do conform to the trends already described in this chapter. Along the meta-aluminous join, calcium aluminosilicates have slight excess heat capacities [Richet and Neuville, 1992]. Hence, they depart slightly from the ideal solution of the Mg system although such deviations are much less marked than for sodium aluminosilicates. Finally, the heat capacity of potassium aluminosilicates shows a stronger temperature dependence than that of their sodium counterparts [Richet and Bottinga, 1984b]. The reason is that, among Al-free melts, only potassium silicate liquids have a temperature-dependent C (see Chapter 6), which enhances this feature in K-bearing aluminosilicates. 8.2b. Enthalpy of Mixing Configurational heat capacity characterizes the temperature dependence of configurational enthalpy and entropy. The former data can be determined from solution calorimetry, but these measurements are, unfortunately, scarce. Most data address Si<=>Al substitution for a number of alkali and alkaline earth cations [e.g., Navrotsky et al., 1982]. As summarized by Roy and Navrotsky [1984], these results are plotted in Fig. 8.9 in the form of negative of enthalpies of solution because this representation allows the enthalpy scale to be visualized directly. Depending on whether the standard glass transition temperature is lower or higher than 700°C, the temperature of solution calorimetry, the measurements refer to glasses or to relaxed supercooled liquids. In the former case, samples have different fictive temperatures so that proper isothermal adjustment of the data should be made with equation (2.15). Such adjustments typically can amount to 5 kJ/mol or more [Richet and Bottinga,

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Figure 8.9 - Energetics of Si<=>Al substitution in aluminosilicate glasses or supercooled liquids: enthalpy of solution in molten lead borate at 700°C along the joins SiO2-M^/2AlO2, where M is an alkali or alkaline earth element [Roy and Navrotsky, 1984].

1984a; Hovis et al., 2004]. Because of the slight curvature of the enthalpies plotted in Fig. 8.9, these adjustments would be necessary to determine accurately enthalpies of mixing between SiO 2 and the most SiO2-poor composition investigated for a given system. For our purpose of comparing the effects of different M-cations, however, these adjustments are unnecessary in view of the large differences between the enthalpy trends for each system. From K to Mg, all enthalpy-composition relationships succeed each other in the order of ionization potential of the metal cation (Fig. 8.9). Only a single measurement exists for Rb and Cs, but both data conform to this order although they suggest some leveling off of the systematics beyond potassium. Of special interest is the fact that there is no sharp boundary between the alkaline and alkaline earth series, as the data for the Li and Ba compositions fall practically on the same curve. For all systems, the most evident feature is the negative enthalpy of mixing between SiO 2 and M;(/2A1O2 which indicates strong affinity between these components. When the composition range investigated allows its determination, the enthalpy minimum is found near 50 mol % SiO2. Its magnitude varies strongly with the nature of the M-cation, occurring near 10 kJ/mol for Mg- and below -20 kJ/mol for K-aluminosilicates. The depths of these minima correlate with the relative extent of freezing-point depressions at eutectic points (Fig. 8.5). In contrast, the compositions of the eutectics do not match that of the enthalpy minima of Fig. 8.9. The reason is, of course, that enthalpy is not the only factor determining phase equilibria. We finally note that only Mg-aluminosilicates unmix at very high SiO 2 content along the meta-aluminous join (Fig. 8.1). Consistent with this observation, the Mg meta-aluminate join is the only one for which the enthalpy-composition relationship in Fig. 8.9 shows an initial maximum, i.e., the positive enthalpy of mixing that is generally associated with phase separation.

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Figure 8.10 - Effects of a variety of oxides and aluminates: (a) On freezing-point depressions near the SiO2 endmember on meta-aluminous joins; (b) On the activity coefficient of SiO2 in the same melts [Ryerson, 1985].

8.2c. Activity The systematics in liquidus relations along meta-aluminosilicate joins have been used by Ryerson [ 1985] to determine the composition dependence of SiO2 activity in melts at high silica content. The method has already been described in section 6.2c for binary metal oxide-silica systems. The results are plotted in Fig. 8.10. The activity-composition relationship is nearly ideal for the Na system, whereas negative and positive deviations from ideality are found for the K and Ca systems, respectively. These results are consistent with the enthalpies of mixing determined along the same joins (Fig. 8.9). This indicates that departures from ideality mainly results from the enthalpy, and not from the entropy, contribution to the Gibbs free energy. Activity measurements for ternary aluminosilicate melts are scarce for alkali aluminosilicates. Owing to the experimental difficulties due to high liquidus temperatures, the data are sketchy for magnesium aluminosilicates [Henderson and Taylor, 1966]. They have long been more extensive for the CaO-MgO-A^Oa-SiCh system [e.g., Rein and Chipman, 1965], and particularly for calcium aluminosilicates because of the importance of these melts in desulfurization and dephosphorization of steel through metal-slag equilibria [see Zaitsev et al, 1997]. As expected, marked nonideality prevails in both instances but these results do not warrant lengthy comments because they lend themselves more readily to thermodynamic calculations than to structural interpretations. Of more relevance here is the approach recently followed by Beckett [2002] who has shown that the formal activity model of Berman and Brown [1984] for Ca and Mg aluminosilicate melts can be rationalized in terms of degree of polymerization (as given by the simple NBO/T parameter) and optical basicity (as estimated from the empirical model of Mills [1993]). In this way, not only is the number of fitting parameters reduced in thermodynamic modeling, but quantitative modeling of redox reactions or sulfur solubility can be made consistently with the same formalism.

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Figure 8.11 - Room-temperature molar volume of Al2O3-bearing Na 2 OCaOnSi0 2 glasses against alumina content for the three values of n indicated. Data from Safford and Silverman [1947], referred to a total of one mol of oxides. The partial molar volumes of A12O3 derived from these linear trends are 40.0, 40.2, and 40.1 cm3/mol for n = 4, 5, and 6, respectively.

8.3. Volume and Viscosity Due to their considerable practical importance, the volume and viscosity of aluminosilicates have been investigated extensively. As will also be apparent, however, these properties have also long been studied to elucidate the structural role of Al because both are sensitive function of structure. 8.3a. Volume and thermal expansion As a direct measure of atomic packing, volume and related properties are a sensitive probe of oxygen coordination around cations. This was demonstrated long ago by the density and refractivity measured by Safford and Silverman [1947] for several series of Na2OCaO-SiO2 glasses to which A12O3 was added (Fig. 8.11). Decades before NMR demonstrated the point at a microscopic scale, these data indicated, without ambiguity, that most Al is in tetrahedral coordination because the partial molar volume of 40 cm3/mol found for A12O3 is much greater than that the 25 cm3 of the molar volume of corundum. Thermal expansion will not be mentioned explicitly in this section because, as found in section 6.3a for Al-free melts, it has the same composition dependence as volume. This was shown in the study of Bottinga and Weill [1970] which established that both partial molar volume and expansivities of aluminosilicate melts could be considered as additive functions of composition. Since then, empirical models have been improved to predict density with greater accuracy or over wider temperature and composition ranges [Bottinga et al, 1982, 1983; Lange and Carmichael, 1987; Knoche et al, 1995; Lange, 1997]. For this purpose, new measurements have been made on compositions scattered throughout a variety of systems [e.g., Stein et al., 1986; Lange and Carmichael, 1987; Lange, 1996]. Since it is difficult to draw structural inferences from multiparameter analyses of measurements, we will consider instead data along well-defined joins. Particular attention will be paid to the circumstances under which the additive nature of molar volume could break down and to aluminum environment in peraluminous melts. Among existing models, only that of Bottinga et al. [1982] dealt with peraluminous melts and the departure from volume additivity in these melts caused by the fact that the molar volume of liquid alumina (about 33 cm3/mol above 2000°C) is lower than the 38-39 cm3/mol derived for the partial molar volume of A12O3 in peralkaline melts

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Figure 8.12 - Molar volume of binary SiO 2 -Al 2 O 3 melts at the temperatures indicated. Data of Aksay et al. [1979] for binary compositions, Mitin and Nagibin [1970] and Shpil'rain et al. [1973] for pure A12O3 and Bottinga and Richet [1995] for SiO 2 (see also Chapter 5). The dashed curve BW70 shows the 1800°C model values of Bottinga and Weill [1970].

(Fig. 8.12). Subsequent models have not addressed this question, however, probably because nonlinear effects remain small within the composition range of geochemical interest. In spite of technical difficulties caused by very high temperatures, reliable measurements are available for binary SiO 2 -Al 2 O 3 liquids [Aksay et al., 1979]. They join smoothly with the data for pure A12O3 and SiO2 (Fig. 8.12). Although the thermal expansion coefficients of liquid A12O3 and of the most Al2O3-rich melt are not well constrained, a definite nonlinearity is observed beyond about 60 mol % A12O3 at 1900-2000°C, the interval where A12O3 and all binary compositions could be investigated. The manner in which the density of binary Al2O3-SiO2 melts is approached from ternary metal aluminosilicate systems should depend on the nature of the M-cation. For Na and Mg, this hypothesis can be checked with the measurements made by Riebling [1964, 1966]

Figure 8.13 - Molar volume of alumosilicate melts at 1800°C at constant SiO 2 content, (a) Sodium aluminosilicates for the SiO2 mol fractions indicated [Riebling, 1966]. (b) Magnesium aluminosilicates at 50 mol % SiO 2 ; data from Riebling [1964] andTomlinson etal. [1958] for the Al-free endmember. Note the scale difference between both diagrams, where the data for SiO 2 -Al 2 O 3 melts are the interpolated values of Aksay et al. [1979] in Fig. 8.12.

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Figure 8.14- Compressional sound velocity in calcium aluminosilicate melts at 2000 K. (a) Against SiO2 content at constant Ca/AI. (b) Against A12O3 content at constant Si/Ca; the arrows indicate the position of the meta-aluminous join. Data from Sokolov et al. [1970]. for a series of joins at constant SiO2 content. For the sodium system, additivity of molar volume with respect to chemical composition breaks down as soon as the meta-aluminous join is crossed (Fig. 8.13a). The extent of nonlinearity increases with decreasing SiO 2 content, i.e., with increasing A12O3 concentration. For 50 mol % SiO 2 , there is even a clear maximum in molar volume that probably lies between Al/(A1+Na) values of 0.6 and 0.8, i.e., between 30 and 40 mol % A12O3. With a same SiO2 content of 50 mol %, the single join investigated in the Mg system shows less deviation from linearity (Fig. 8.13b). The data extrapolate to a volume of 31 cm3/mol for pure A12O3 (compared with 32.5 cm3/mol for the analogous Na join), which is only 3% higher than the volume of A12O3 liquid. In summary, additive models of prediction of density breaks down for peraluminous melts because the partial molar volume of alumina then depends on composition. As might be expected, the density of peralkaline melts also bears witness to the less strong association of Al with Mg than with Na. Clearly, Al is present in a denser state in peraluminous than in peralkaline melts. But volume data cannot help discriminate between various structural models in which Al has a coordination higher than tetrahedral or achieves a dense arrangement through the existence of oxygen triclusters. 8.3b. Compressibility With ultrasonic methods, the adiabatic compressibility (/3S) is determined from the density (p) and the longitudinal sound velocity (v ) by equation (6.19), /3S = 1/pv 2 . For aluminosilicates, whose high viscosity can translate into long relaxation times, determination of Ps is made difficult by the high temperatures at which measurements must be performed to achieve complete relaxation (see section 2.2b). At such high temperatures, composition changes induced by partial volatilization are a serious concern. For alkali systems, this is why measurements are available for few compositions over narrow temperature intervals [Rivers and Carmichael, 1987; Kress et al., 1988]. From an analysis of their measurements

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Figure 8.15 - Adiabatic bulk modulus, Ks = l/f5s, of calcium aluminosilicates at constant Ca/Al and 1600°C. From Webb and Courtial [1996], with data of Sokolov et al. [1970], Rivers and Carmichael, 1987] and, for SiO 2 , the result of Table 5.1.

for sodium aluminosilicates, Kress et al. [1988] did, nevertheless, conclude that sound velocity is insensitive to Na/Si and increases linearly with A12O3 content in peralkaline compositions, from 2450 m/s for molten sodium metasilicate to 2900 m/s for a melt with 20 mol % A12O3. These trends are not followed in calcium aluminosilicates which have been comprehensively studied by Sokolov et al. [1970]. Their results are generally consistent with the less extensive observations of Rivers and Carmichael [1987] and Webb and Courtial [1996]. More attention will be paid in this section to velocities than to adiabatic compressibilities because it is not possible to determine accurately densities over the whole composition range investigated, which extends to peraluminous melts. A continuous decrease in sound velocity is observed when Al is substituted for Si along two different joins (Fig. 8.14a). As might be expected from weaker Al-0 compared to Si-0 bonds, in both cases these variations are offset by those of density so that the adiabatic bulk modulus (Ks = 1/PS) derived by Webb and Courtial [1996] actually increases with decreasing SiO2 concentration (and increasing Ca0 5 A1O2 content) as seen in Fig. 8.15. The variations are not as simple when A12O3 is added at constant Si/Ca (Fig. 8.14b). For Si/Ca = 2, little attention should be paid to the complex variation of sound velocity, which is due to the stable miscibility gap existing close to the limiting binary SiO2-Al2O3 (see Fig. 8.2). No such bias affects the measurements for the join at constant Si/Ca = 1. There, the speed of sound decreases continuously with increasing A12O3 content from the metasilicate composition to beyond the meta-aluminous join. This trend should not be followed at higher alumina content, however, because the speed of sound must increase markedly to match that of pure alumina, which is about 3000 m/s [Slagle and Nelson, 1970]. Actually, such an increase is suggested by the results for the most Al2O3-rich melts along the join Si/Ca = 2 (Fig. 8.14b). Combined with another marked rise in density, which is indicated by the plots of Figs 8.12-8.13, this increase will result in a strong decrease in compressibility when the alumina endmember is approached. This effect conforms to the general trend according to which compressibility decreases with increasing density and, thus, with more compact atomic arrangement.

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Figure 8.16 - Viscosity of silicate and aluminosilicate melts against reciprocal temperature. Ab: NaAlSi 3 O 8 [Urbain et al, 1982; Taylor and Rindone, 1970]; An: CaAl 2 Si 2 0 8 [Urbain etal., 1982;Neuville, 1992]; Ca0.39: (CaO) 0 3 9 .(Al 2 O 3 ) 0 5 1 [Urbain, 1983; Sipp and Richet, 2002]; Py: Mg3Al2Si3O12 and CS: CaSiO3 [Neuville and Richet, 1991]; NAS: Ab«NS 2 [Riebling, 1966] and Taylor and Rindone [1970]; NS 4 ( N a ^ O g ) [Bockris et al, 1955; Sipp and Richet, 2002].

Like the heat capacity, the compressibility of liquids is made up of vibrational and configurational contributions. A more detailed analysis of compressibility must deal separately with both aspects. When made with Brillouin scattering, the timescale of sound velocity measurements is so short that, even above 2000 K, only the solid-like response of the liquid is probed (see section 2.2b). The relative importance of vibrational and configurational compressibility thus can be ascertained through a combination of unrelaxed and fully relaxed measurements of sound velocity. The information obtained in this way is still very sketchy [Askarpour et al., 1993]. For calcium aluminosilicates, both contributions to compressibility vary strongly with composition. The total compressibility is 4.83 1011 and 3.84 10 u Pa"1 for molten CaAl 2 Si 2 0 g and Ca 3 Al 2 Si 3 0 12 , of which the configurational part represents 58 and 32%, respectively. Clearly, compression and rotation of bonds represent only a fraction of the compressibility of the open, three-dimensional network of CaAl 2 Si 2 0 8 . In this case, configurational changes give rise to additional compression mechanisms that are more restricted in the less polymerized structure of Ca 3 Al 2 Si 3 O 12 . 8.3c. Viscosity The influence of composition on the viscosity of aluminosilicate melts is summarized in Fig. 8.16. Of particular interest are the meta-aluminous compositions whose viscosities, which are similar near glass transition, diverge at higher temperatures before converging again in the high-temperature limit. Like the other aspects of viscosity, this effect is readily accounted for quantitatively with equation (2.24) in terms of differences in configurational heat capacities [Richet, 1984]. The data for NajS^Og and CaSiO3 are included as a reminder of the differences between Al-free alkali and alkaline earth melts. Consistent with the effects described in previous sections, these differences reduce gradually when Al is introduced. From Al-free compositions to the meta-aluminous join or beyond, these changes will be described in more detail below. They are, in fact, so large that comparisons of isothermal values require unwarranted extrapolation of the data when these have been gathered only at high or low

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Figure 8.17- Composition dependence of viscosity near the glass transition as given by the temperature of the 10 12 Pa s isokom. (a) Against mol % alumina along the joins NajSijCyA^Oj (Na), MgSiO 3 A12O3 (Mg), and CaSiO 3 -Al 2 O 3 (Ca). The arrows indicate the position of the meta-aluminous join. (b) Effect of Si<=>Al substitution along the Li, Na, Mg and Ca meta-aluminous joins. Data from Shelby [1978], Taylor and Rindone [1970], and Neuville [1992].

viscosities for a given composition. To avoid these problems, it is preferable to compare the temperature of a given isokom {i.e., of isoviscosity values). This will mainly be made near the glass transition because of the sensitivity of viscosity to composition and structure is much greater in this temperature range than above the liquidus where the data tend to converge [Figs. 6.17a, 8.16]. The effects of addition of alumina at constant M/Si ratio are shown in this way in Fig. 8.17a along only three binary joins, but are also observed for other M/Si atomic ratios. Once more, the differences between alkali and alkaline earth systems are borne out by the temperature of the 1012 Pa s isokom. This temperature does not vary much for Mg liquids, rises gently for Ca melts, and increases by nearly 400 degrees for the Na system before decreasing beyond the meta-aluminous join. For alkali systems, a practical consequence of such extremely steep variations is that small departure from nominal stroichiometry can cause large errors in viscosity and standard glass transition temperature. Differences of more than 100 K have, for instance, been found between the Tg reported for NaAlSi3Og (albite) composition [Richet and Bottinga, 1984b]. The trend of Fig. 8.17a indicates that the higher values are the most reliable. For charge-compensating cations, the viscosities of Fig. 8.17a illustrate the more general fact that the strength of the association with aluminum decreases in the familiar order Na, Ca, Mg. Liquidus temperatures and melt viscosity depend on bond strength. Hence, there is similarity between the variations of both kinds of properties as shown in Fig. 8.4 and 8.17a. The main difference, of course, deals with the existence of minima at eutectic points for liquidus temperatures which cannot have any counterpart in viscosity. This difference accounts for the basic unreliability of the various empirical relationships, such as the rule

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Figure 8.18 - Effects of the chargecompensating cation of Al 3+ on viscosity along the meta-aluminous join at 2000 K. Data from Riebling [1964, 1966] for Mg and Na systems and from Arrhenian fits made to the measurements of Urbain ef al. [1982] and Boiret and Urbain [1987] for the other joins.

TJTl = 2/3 (Tl = liquidus temperature) proposed by Kauzmann [ 1948], which aim at relating liquidus and standard glass transition temperatures. Regarding Si<=>Al substitution, the difference in Si-0 and Al-0 bond strength is evident in the temperature Tl2 of the 1012 Pa s isokom (Fig. 8.17b) and in plots of the hightemperature viscosity along the meta-aluminous join (Fig. 8.18). From pure SiO2, the decrease amounts to more than 300 K for Tn and to more than 4 orders of magnitude for viscosity. Because association of Al with the charge-compensating cation is weaker in Mg than in Ca melts (Fig. 8.17b), viscosity is lower within the former than the latter system such that the order of increasing viscosity becomes Mg, Ca, Na, Li. This is confirmed and complemented by high-temperature viscosities, which are extensive along the meta-aluminous join (Fig. 8.18). These viscosity data indicate that Sr and Ba fit in between Ca and Na in this trend and that K succeeds Na. As to the less viscous melts investigated by Urbain et al. [1982], they contain the transition metal cation Mn. Recognition of such a systematic relationship among charge-compensating cations was, in fact, the basis of the successful model of prediction of high-temperature viscosity proposed by Bottinga and Weill [ 1972], which relied on correct identification of the metal cation-aluminate species present in the melt. The systematics in viscosity (Fig. 8.18) and enthalpy (Fig. 8.9) are remarkably similar, with the single important exception of LiA102 which plots along with BaQ5A102 in enthalpy and with Mg05AlO2 in viscosity [Boiret and Urbain, 1987], at values much lower than could have been expected. In detail, indeed, departures from the above systematics can be observed. This is also indicated by the dilatometric glass transition temperatures measured by Hasegawa [1986] for Mg, Ca, Sr, and Ba aluminosilicates, which define trends that may depend on M^O content. The viscosity-composition relationships are markedly nonlinear at high temperature and especially near the glass transition. Because they originate from the same datum for

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Figure 8.19 - Effect of Na-Al association on viscosity at constant SiO2 content, (a) Temperatures oftheisokomslog?7(Pas) = 9, 10, 11, and 12 for 75 mol % SiO2 [Taylor and Rindone, 1970]. (b) Viscosity at 1800 K for the four SiO2 mol % indicated [Riebling, 1966, with data of Bockris et al., 1955 for the Al-free endmembers].

SiO2 liquid, from Mn to K their order is that of increasing deviations from Arrhenian laws or of increasing fragility. This order is also that of increasing configurational heat capacity (see Fig. 8.6). As described in section 2.3d for mixed alkaline earth melts, these features are readily interpreted within the framework of configurational entropy theory according to which the temperature dependence of viscosity is inversely related to that of configurational entropy [Adam and Gibbs, 1965; Richet, 1984]. Consistent with the contribution of Si<=>Al mixing to chemical entropy, the viscosity-composition relationship is still more nonlinear near the glass transition than at high temperatures (Fig. 8.18). For the Na system, a detailed analysis of these variations in terms of mixing between silicate and aluminate entities has been made on this basis by Toplis et al. [1997a]. Finally, the extreme sensitivity of viscosity to structure has long been used to examine whether or not structural changes occur across the meta-aluminous join, over narrow composition intervals where they are difficult to observe in the other measurements reviewed in this chapter. For sodium aluminosilicates, the observations made at constant SiO2 content close to the glass transition range [Taylor and Rindone, 1970] and at high temperature

Figure 8.20 - Viscosity variations across the meta-aluminous join for Ca and Mg aluminosilicates with 50 mol % SiO2 at 1150 K (a) and 1800 K (b). Data of Toplis and Dingwell [2004].

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Figure 8.21 - Tracer diffusivity in amorphous NaAlSi3Og against reciprocal temperature. Data from Roselieb et al. [1992] for He and Ar; Jambon and Semet [1976] for Li; Jambon and Carron [1976] for Na, K, Rb and Cs; Roselieb and Jambon [2002] for Mg, Sr and Ba; Jambon and Delbove [1977] for Ca; and Baker [1995] for Si and Ga.

[Riebling, 1966] have long shown either a plateau or a decrease in viscosity when the Na/Al atomic ratio is close to unity (Fig. 8.19). In both studies, this feature was assigned to a change of Al from tetrahedral network-former to octahedral network-modifier. The effects of such a change were also observed in electrochemical measurements performed on the same series of sodium-bearing glasses [Graham and Rindone, 1964]. More recent observations by Toplis et al. [ 1997b] agree with Riebling's [ 1966] results, although they do not locate the viscosity maximum on the meta-aluminous join but at values of Na/(Na+Al) slightly lower than 0.5. The deviation from this value varies with SiO 2 content and increases with decreasing temperatures. These features have been interpreted in terms of triclusters by Toplis et al. [1997b]. A similar plateau has been observed in the dilatometric glass transition temperatures of lithium aluminosilicates at Li/(Li+Al) of about 0.48 [Shelby, 1978]. In view of the differing effects of alkaline and alkaline earth elements on viscosity, the existence and position of this maximum should indeed depend on the nature of the M-cation. For Ca and Mg aluminosilicates, the results subsequently obtained at low and high temperature by Toplis and Dingwell [2004] do show important differences since a viscosity maximum is observed only for the former. This is seen in Fig. 8.20 for melts with 50 mol % SiO2. 8.3d. Element Diffusivity The geochemical importance of aluminosilicates has motivated numerous diffusion studies [for a review, see Freer, 1981]. In particular, the extensive data available for NaAlSi 3 O 8 throw interesting light on the factors that determine atomic mobility, at least along the meta-aluminous join (Fig. 8.21). As already noted for SiO2 in section 5.2e, weakly bonded noble gases diffuse the fastest, with a diffusivity that decreases in the order of increasing atomic size. Tracer diffusion is in general faster for alkali than for alkali earth cations and is slowest for Si and Ga, another network-forming cation which was investigated by Baker [1995] as a proxy for Al. In these three series, the activation enthalpy for diffusion increases

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Figure 8.22 - Influence of ionic radius on diffusivity in amorphous NaAlSi 3 O 8 . (a) Tracer diffusivity at 1000°C from the data of Fig. 8.21. (b) Activation enthalpy for diffusion. Ionic radii of Whittaker and Muntus [1970]. In a similar way, alkali diffusion in amorphous KAlSi3O8 is fastest for K [Jambon andCarron, 1976].

when the diffusivity decreases so that the linear relationships of Fig. 8.21 tend to converge at very high temperature. For network-modifier cations, diffusivity is not affected by the glass transition. This is consistent with the observation made in Fig. 5.15 for SiO 2 for which the small configurational changes exhibited by its liquid phase do not leave much room for abrupt changes in diffusion mechanisms at Tg. As reviewed by Roselieb and Jambon [2002], there is a clear control of both tracer diffusivity and activation enthalpy for diffusion by the ionic radius and charge of the cation (Fig. 8.22). The simple influence of size is illustrated by noble gases, for which electrical charge does not need to be considered. For other elements, an optimum is reached for a certain ionic radius for a given charge. In a structure tailored for Na, the larger ionic radius of heavier alkali elements or the 2+ charge of alkaline earths lowers diffusion considerably through steric hindrance or electrostatic interactions. Because the relevant parameters are the size and especially the charge differences with Na, diffusivities and activation energies do not vary monotonously with the ionization potential of the cation. Given the existence of the plagioclase solid solution, it is not fortuitous that Ca is the alkaline earth with the highest diffusivity and lowest activation energy for diffusion. As for Ga, it is probably fortuitous that its data plot in Fig. 8.22 on the alkaline earth trends. 8.4. Summary Remarks 1. The composition dependences of transport and thermodynamic properties differ markedly in alkali and in alkaline earth aluminosilicate melts. Consistent with the inferences drawn in Chapter 3 from low-temperature heat capacity and entropy, this difference stems from the manner in which M-cations act as charge compensators for aluminum. Whereas short-range order around alkaline earths is not significantly affected, the oxygen coordination number of alkalis increases markedly when these cations transform from network-modifiers to charge compensators for Al 3+ .

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2. Correlatively, the strength of association with aluminum increases in the order Mg, Ca, Na, and K. The other alkaline earth cations Sr and Ba fit in this order between Ca and Na in this series. The data for Rb and Cs are too sketchy to determine whether they are positioned according to their size in this trend or they have effects similar to those of K. The enthalpy and viscosity data point to differing effects for Li. This illustrates the fact that the real nature of the association between Al and its charge compensators is not well understood. 3. The existence of marked changes across the meta-aluminous join depends on the thermodynamic or transport property considered. For a given property, the effect varies with the nature of the M cation. Especially for Al-rich peraluminous melts, the existence of more compact configurations is revealed by density increases and compressibility decreases. References Adam G. and Gibbs J. H. (1965) On the temperature dependence of cooperative relaxation properties in glass-forming liquids. J. Chem. Phys. 43, 139-146. Aksay I. A., Pask J. A., and Davis R. F. (1979) Densities of SiO2-Al2O3 melts. J. Amer. Ceram. Soc. 62, 332-336. Askarpour V., Manghnani M. H., and Richet P. (1993) Elastic properties of diopside, anorthite, and grossular glasses and liquids: A Brillouin scattering study up to 1400 K. J. Geophys. Res. 98, 17683-17689. Baker D. R. (1995) Diffusion of silicon and gallium (as an analogue for aluminium) networkforming cations and their relationship to viscosity in albite melt. Geochim. Cosmochim. Ada 59,3561-3571. Barkhatov L. S., Kagan D. N., Tsytsarkin A. R, Shpil'rain E. E., and Yakimovich K. A. (1973) Investigation of the thermodynamic properties of molten aluminum oxide. Teplofiz. Vys. Temper. 11, 1188-1191. Beckett J. R. (2002) Role of basicity and tetrahedral speciation in controlling the thermodynamic properties of silicate liquids, part 1: The system CaO-MgO-Al2O3-SiO2. Geochim. Cosmochim. Ada 66, 93-107. Berman R. G. and Brown T. H. (1984) A thermodynamic model for multicomponent melts, with application to the system CaO-MgO-Al2O3-SiO2. Geochim. Cosmochim. Ada 48, 661-668. Bockris J. O. M., Mackenzie J. D., and Kitchener J. A. (1955) Viscous flow in silica and binary liquid silicates. Trans. Farad. Soc. 51, 1734-1748. Boiret M. and Urbain G. (1987) Mesures de viscosites d'aluminosilicates de lithium. C.R. Acad. Sci., II, 305, 167-169. Bollin P. L. (1972) Glass formation in the system Cs2O-Al2O3-SiO2. J. Amer. Ceram. Soc. 55,483. Bottinga Y. and Richet P. (1995) Silicate melts: The "anomalous" pressure dependence of the viscosity. Geochim. Cosmochim. Ada 59, 2725-2731. Bottinga Y. and Weill D. F. (1970) Densities of liquid silicate systems calculated from partial molar volumes of oxide components. Amer. J. Sci. 269, 169-182. Bottinga Y. and Weill D. F. (1972) The viscosity of magmatic silicate liquids: A model for calculation. Amer. J. Sci. 272, 438-475. Bottinga Y., Weill D. F., and Richet P. (1982) Density calculations for silicate liquids. I Revised method for aluminosilicate compositions. Geochim. Cosmochim. Ada 46, 909-919.

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Lacy E. D. (1963) Aluminium in glasses and melts. Phys. Chem. Glasses 4, 234-238. Lange R. A. (1996) Temperature independent thermal expansivities of sodium aluminosilicate melts. Geochim. Cosmochim. Acta 60, 4989-4996. Lange R. A. (1997) A revised model for the density and thermal expansivity of K2O-Na2O-CaOMgO-Al2O3-SiO2 liquids from 700 to 1900 K: extension to crustal magmatic temperatures. Contrib. Mineral. Petrol. 130, 1-11. Lange R. A. and Carmichael I. S. E. (1987) Densities of Na2O-K2O-CaO-MgO-Fe2O3-Al2O3-TiO2SiO2 liquids: New-measurements and derived partial molar properties. Geochim. Cosmochim. Acta 51, 2931-2946. Lejeune, A.-M. and Richet P. (1995). Rheology of crystal-bearing silicate melts: An experimental study at high viscosities. J. Geophys. Res. 100, 4215-4229. Levin E. M, Robbins C. R., and McMurdie H. F. (1964) Phase Diagrams for Ceramists. 2nd ed. Amer. Ceram. Soc, Columbus. Longhi J. and Hays J. F. (1979) Phase equilibria and solid solution along the join CaAl2Si2O8-SiO2. Amer. J. Sci. 279, 876-890. MacDowell J. F. and Beall G. H. (1969) Immiscibility and crystallization in Al2O3-SiO2 glasses. J. Amer. Ceram. Soc. 52, 17-25. Mazurin O. V., Roskova G. P., and Porai-Koshits E. A. (1984) Immiscibility diagrams of oxide glass-forming systems. In Phase Separation in Glass, (eds. O. V. Mazurin and E. A. PoraiKoshits), pp. 103-142. North Holland. Mills K. C. (1993) The influence of structure on the physico-chemical properties of slags. ISIJ Int 33, 148-155. Mitin B. S. and Nagibin Y. A. (1970) Density of molten aluminum oxide. Russ. J. Phys. Chem. 44, 741-742. Navrotsky A., Peraudeau G., McMillan P., and Coutures J. P. (1982) A thermochemical study of glasses and crystals along the joins silica-calcium aluminate and silica-sodium aluminate. Geochim. Cosmochim. Acta 46, 2039-2047. Neuville D. R. (1992) Etude des proprietes thermodynamiques et rheologiques des silicates fondus, Ph D Thesis, Universite Paris 7. Neuville D. R. and Richet P. (1991) Viscosity and mixing in molten (Ca,Mg) pyroxenes and garnets. Geochim. Cosmochim. Acta SB, 1011-1020. Osaka A., Ono M., and Takahashi K. (1987) Aluminum oxide anomaly and structure model of alkali aluminosilicate glasses. J. Amer. Ceram. Soc. 70, 242-245. Osborn E. F. (1942) The system CaSiO3-diopside-anorthite. Amer. J. Sci. 240, 751-788. Osborn E. F. and Schairer J. F. (1941) The ternary system pseudo-wollastonite-akermanite-gehlenite. Amer. J. Sci. 239, 715-763. Rankin G. A. and Wright F. E. (1915) The ternary system CaO-AL,O3-SiOr Amer. J. Sci. 39, 1-79. Rein R. H. and Chipman J. (1965) Activities in the liquid solution SiO2-CaO-MgO-Al2O3 at 1600°C. Trans. A1ME 233, 415-425. Richet P. (1984) Viscosity and configurational entropy of silicate melts. Geochim. Cosmochim. Acta 48, 471-483. Richet P. and Bottinga Y. (1984a) Anorthite, andesine, wollastonite, diopside, cordierite and pyrope: Thermodynamics of melting, glass transitions, and properties of the amorphous phases. Earth Planet. Sci. Lett. 67, 415-432. Richet P. and Bottinga Y. (1984b) Glass transitions and thermodynamic properties of amorphous SiO,, NaAISi O, , and KAISi A - Geochim. Cosmochim. Acta 48, 453-470. 2'

n

2n+2

3

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Richet P. and Bottinga Y. (1985) Heat capacity of aluminum-free liquid silicates. Geochim. Cosmochim. Ada 49, 471-486. Richet P. and Neuville D. R. (1992) Thermodynamics of silicate melts; configurational properties. In Thermodynamic Data; Systematics and Estimation., Vol. 10 (ed. S. K. Saxena), pp. 132-161, Springer, New York. Richet P., Bottinga Y., and Tequi C. (1984) Heat capacity of sodium silicate liquids. J. Amer. Ceram. Soc. 67, C6-C8. Richet P., Robie R. A., and Hemingway B. S. (1986) Low-temperature heat capacity of diopside glass: A calorimetric test of the configurational entropy theory as applied to the viscosity of liquid silicates. Geochim. Cosmochim. Ada, 50, 1521-1533. Riebling E. F. (1964) Structure of magnesium aluminosilicate liquids at 1700°C. Can. J. Chem. 42,2811-2821. Riebling E. F. (1966) Structure of sodium aluminosilicate melts containing at least 50 mole % SiO2 at 1500°C. J. Chem. Phys. 44, 2857-2865. Rivers M. and Carmichael I. S. E. (1987) Ultrasonic studies of silicate melts. J. Geophys. Res. 92, 9247-9270. Roselieb K. and Jambon A. (2002) Tracer diffusion of Mg, Ca, Sr, and Ba in Na-aluminosilicate melts. Geochim. Cosmochim. Ada 66, 109-123. Roselieb K., Rammensee W., Buttner H., and Rosenhauer M. (1992) Solubility and diffusion of noble gases in vitreous albite. Chem. Geol. 96, 241-266. Roskosz M., Toplis M. J., Besson P., and Richet P. (2005) Nucleation mechanisms: A crystal chemical investigation of highly supercooled aluminosilicate liquids. J. Non-Cryst. Solids, in press. Roy B. N. and Navrotsky A. (1984) Thermochemistry of charge-coupled substitutions in silicate glasses: The systems M1/n"+AlO2-SiO2 (M = Li, Na, K, Rb, Cs, Mg, Ca, Sr, Ba, Pb). J. Amer. Ceram. Soc. 67, 606-610." Ryerson F. J. (1985) Oxide solution mechanisms in silicate melts: Systematic variations in the activity coefficient of SiO r Geochim. Cosmochim. Ada 49, 637-651. Safford H. W. and Silverman A. (1947) Alumina-silica relationship in glass. J. Amer. Ceram. Soc. 30,203-211. Savva M. A. and Newns G. R. (1971) Metastable liquid-liquid immiscibility in the lithium aluminium silicate system. IXth International Congress on Glass, 419-424, Institut du verre, Paris. Schairer J. F. and Bowen N. L. (1947) The system anorthite-leucite-silica. Bull. Comm. Geol. Finl. 20, 67-87. Schairer J. F. and Bowen N. L. (1955) The system K2O-Al2O3-SiO2. Amer. J. Sci. 253, 681-746. Schairer J. F. and Bowen N. L. (1956) The system Na2O-Al2O3-SiO2. Amer. J. Sci. 254, 129-195. Shelby J. E. (1978) Viscosity and thermal expansion of lithium aluminosilicate glasses. J. Appl. Phys. 49, 5885-5891. Shpil'rain E. E., Yakimovich K. A., and Tsitsarkin A. F. (1973) Experimental study of the density of liquid alumina up to 2750°C. High Temp. High Press. 5, 191-198. Sipp A. and Richet P. (2002) Equivalence of volume, enthalpy and viscosity relaxation kinetics in glass-forming silicate liquids. J. Non-Cryst. Solids 298, 202-212. Slagle O. D. and Nelson R. P. (1970) Adiabatic compressibility of molten alumina. J. Amer. Ceram. Soc. 53, 637-638. Sokolov L. N., Baidov V. V, and Kunin L. L. (1970) Ultrasonic study of melts of the calcium oxide - aluminum oxide - silicon dioxide ternary system. Svoista Strukt. Shlakovykh Rasplatov, 94-100.

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Stein D. J., Stebbins J. R, and Carmichael I. S. E. (1986) Density of molten aluminosilicates. J. Amer. Ceram. Soc. 69, 396-399. Taylor T. D. and Rindone G. E. (1970) Properties of soda aluminosilicate glasses: V, Lowtemperature viscosities. J. Amer. Ceram. Soc. 53, 692-695. Tilley C. E. (1933) The ternary system Na2Si03-Na2Si2O5-NaAlSiO4. Mineral. Petr. Mitt. 43,406421. Tomlinson J. W., Heynes M. S. R., and Bockris J. O. M. (1958) The structure of liquid silicates. Part 2. Molar volume and expansivities. Trans. Farad. Soc. 54, 1822-1834. Toplis M. J. and Dingwell D. B. (2004) Shear viscosities of CaO-Al2O3-SiO2 and MgO-Al2O3SiO2 liquids: Implications for the structural role of aluminium and the degree of polymerisation of synthetic and natural aluminosilicate melts. Geochim. Cosmochim. Acta 68, 5169-5188. Toplis M. J., Dingwell D. B., and Lenci T. (1997a) Peraluminous viscosity maxima in Na 2 OAl2O3-SiO2 liquids: The role of triclusters in tectosilicate melts. Geochim. Cosmochim. Acta 61, 2605-2612. Toplis M. J., Dingwell D. B., Hess K.-U., and Lenci T. (1997b) Viscosity, fragility, and configurational entropy of melts along the join SiO2-NaAlO2. Amer. Mineral. 82, 979-990. Topping J. A. and Murthy M. K. (1973) Effect of small additions of A12O3 and Ga 2 O 3 on the immiscibility temperature of Na2O-SiO2 glasses. J. Amer. Ceram. Soc. 56, 270-275. Urbain G. (1983) Viscosite de liquides du systeme CaO-Al2O3. Rev. Int. Hautes Temp. Refract. 20, 135-139. Urbain G., Bottinga Y., and Richet P. (1982) Viscosity of liquid silica, silicates and aluminosilicates. Geochim. Cosmochim. Acta 46, 1061-1072. Webb S. and Courtial P. (1996) Compressibility of melts in the CaO-Al2O3-SiO2 system. Geochim. Cosmochim. Acta 60, 75-86. Whittaker E. J. W. and Muntus R. (1970) Ionic radii for use in geochemistry. Geochim. Cosmochim. Acta 34, 945-957. Zaitsev A. I., Litvina A. D., Lyakishev N. P., and Mogutnov B. M. (1997) Thermodynamics of CaO-Al2O3-SiO2 and CaF 2 -Ca0-Al 2 0 3 -Si0 2 melts. J. Chem. Soc, Farad. Trans. 93,3089-3098.

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Aluminosilicate Systems II. Structure Most of the property-composition relationships necessary to understand magmatic processes depend on the concentration of alumina. The relationships between properties and Al-content (see Chapter 8) also provide the basis for industrial use of aluminosilicate glasses. Characterization of the structure of aluminosilicate melts is central to our understanding structure-property relationships of both natural magmatic liquids and industrial melts and glasses. In natural magmatic liquids, for example, alumina is the second-most important component (after SiO2) [e.g., Chayes, 1975]. More than 95 % of their components can be described by the components SiO2, A12O3, and metal oxide (Fig. 9.1). As discussed in Chapter 8, many of their properties of aluminosilicate melts and glasses depend on whether there is excess or deficiency of metal cations of charge-balance of Al3+.The stuctuural consequences of the extent of charge-balance sometimes can be observed by the changing degree of polymerization (NBO/T) with A12O3 conent of melts with constant SiO2 content (Fig. 9.2). In general, the NBO/T approaches a minimum near the meta-aluminosilicate join [Mysen and Cody, 2001]. The structure of peralkaline, meta-aluminous, and peraluminous compositions will be discussed separately in this chapter. The limiting binary Al2O3-bearing glasses and melts will be reviewed first.

Figure 9.1- Compositional relations between peralkaline, peraluminous, and metaaluminous compositions in the pseudoternary system Mn+On/2-Al2O3-SiO2 where M is an alkali and alkaline earth oxide. Fe2+ has been considered to be an M-cation for plotting the range of natural igneous rocks as the hachured area in this diagram [data from Chayes, 1975].

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Figure 9.2 - Relationship between measured NBO/T and AI2O3 content of glasses with 90 mol % SiO2 in the system Na2O-Al2O3-SiO2 [Mysen and Cody, 2001].

9.1. Binary AI2O3-Bearing Glasses and Melts Binary SiO 2 -Al 2 O 3 melts are important because they offer information on the structural role of Al 3+ when there is no metal cation for charge-compensation. Other important limiting systems are A12O3-M/AA1O2 and M^O-M iA AlO 2 , where M is a metal cation different from both Si4+ and Al3+. 9.1a. SiO2-Al2O3 Much less information is available for pure A12O3 than for SiO2 because A12O3, which is an extremely poor glass-former, has to be investigated above 2071 °C, the melting point of corundum. See Chapter 5 for a review of the structure of SiO2 glass and melt. In an x-ray diffraction study, Nukui et al. [1978] compared the Al-0 bond lengths in molten A12O3 near 2100°C with those in various crystalline A12O3 polymorphs and concluded that the local structure of molten A12O3 resembles that of corundum. Results of 27A1NMR spectroscopy of molten A12O3 to temperatures near 2450°C are also consistent with high-coordinated Al3+, but perhaps mostly in 5-fold coordination [Florian et al., 1995; Bessada et al., 1999]. The latter conclusion also accords with more recent x-ray studies of liquid A12O3 at similar temperature, where 4- and 5-fold coordination of Al 3+ was found to dominate the structure [Ansell et al., 1997; Landron et al., 2001]. For SiO 2 -Al 2 O 3 glasses with up to 6 wt % A12O3, Kato [1976] found that the Raman spectra are quite similar to the spectrum of pure SiO2 glass and concluded that, at least to this amount of A12O3, the dissolved A12O3 does not disrupt the SiO 2 glass structure significantly. These early data formed the basis for a more comprehensive Raman spectroscopic study of SiO2-Al2O3 glass with up to 59 mol % A12O3 [McMillan and Piriou, 1982]. Even though rapid splat cooling was used (~106 - 107 °C/s), phase separation or

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Figure 9.3 - Aluminum coordination in the system SiCh-AhCh as a function of A12O3 content, (a) 27A1 MAS NMR isotropic chemical shift from spectra recorded above 2000°C. (b) Average oxygen coordination number around Al3+ from numerical simulation of melt structure [Poe et al., 1992].

crystal nucleation developed in many of the glasses [McMillan and Piriou, 1982; Sato et al., 1991]. That problem notwithstanding, McMillan and Piriou [1982] concluded that the structure of silica-rich (>70 mol % SiO2) glasses along the SiO2-Al2O3 join resembles that of pure SiO2 with, however, a small number of nonbridging oxygens in addition to some Si-O-Al linkages between oxygen tetrahedra in the structure. For higher alumina contents, McMillan and Piriou [1982] suggested that a significant portion of the Al3+ occurs in some form of aluminate clusters. More detailed information has been derived from 27A1 MAS NMR spectra. For SiO2-A12O3 glasses that also suffered from incipient phase separation, Risbud et al. [1987] concluded that Al + exists in 4-, 5-, and 6-fold coordination with oxygen. Investigating the same series of samples as McMillan and Piriou [1982], Sato et al. [1991] confirmed this conclusion and added that the proportions of these Al-complexes vary with A12O3 content and also, interestingly, with the rate at which the glasses had been quenched. This conclusion accords with recent multinuclear NMR spectroscopy of SiO2-Al2O3 glasses [Sen and Youngman, 2004]. The difficulties associated with quenching of melts to homogeneous glass and the observation that Al-speciation in SiO2-Al2O3 glasses may depend on quenching rate make structural interpretation difficult and prevent ready application of glass structure data to the melts. Quenching problems were avoided, however, by Poe et al. [1992] who coupled hightemperature 27A1 NMR spectroscopy with molecular dynamics simulation of SiO2-Al2O3 melts above 2000°C. In the NMR spectra, the 27A1 isotropic shift is broadly correlated with the A12O3 content (Fig. 9.3a). In the numerical simulations, the average coordination number of Al with oxygen increases with increasing A12O3 content (Fig. 9.3b). This increase

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Figure 9.4 - Schematic representation of an Al-tricluster in Al-coordination number might be consistent with the increasing 27 Al isotropic chemical shift [Poeetal., 1992; Bessada etal., 1999]. Further, the average Al-coordination number was thought to reflect the presence of Al3+ in several different aluminate complexes whose coordination numbers range between 4 and 6. The results of Poe et al. [1992], thus, indicate that high-coordination Al-0 polyhedra become more abundant when the A12O3 content of the melt increases. This observation is at least qualitatively in accord with the earlier interpretation of Raman and NMR spectra of SiO2-Al2O3 glasses [McMillan and Piriou, 1982; Risbud etal, 1987; Sato etal., 1991].

Figure 9.5 - Signature of Al tricluster in nuclear magnetic resonance spectra of CaAUC^ crystals (a) 17O MAS NMR and (b) 27A1 MAS NMR [Stebbins et al, 2001].

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Figure 9.6 - (a) Aluminum-27 MAS NMR isotropic chemical shift from spectra of AhCh-CaAhC^ melts recorded near 2300°C. (b) Average oxygen coordination number around Al3+ from numerical simulation of melt structure [Poe et al, 1994].

Interestingly, though, there is a significant fraction of 4-fold coordinated Al3+ even in the most aluminous SiO2-Al2O3 glasses and melts, including pure A12O3. This observation implies that some of the Al4+ may be in 4-fold coordination with oxygen without metal cations for charge-compensation. Lacy [ 1963] proposed aluminum triclusters as a means to accomplish electrical neutrality under such circumstances (Fig. 9.4). The tricluster concept was used subsequently to rationalize a number of features of Alcontaining silicate melts that do not contain metal cations in sufficient quantity to provide formal charge-compensation of Al3+ in tetrahedral coordination. The details of the tricluster structures remains uncertain, however [e.g., Stebbins and Xue, 1997; Stebbins et al, 2001; Kubicki and Toplis, 2002]. 9.1b.

A12O3-M1/XAIO2

Aluminum triclusters could also exist in glasses and melts along the peraluminous join, A12O3-M/AA1O2. Supporting evidence was reported by Stebbins et al. [1999, 2001] in combined 27A1 and 17O MAS NMR studies of CaAl2O4 and CaAl4O7 glasses (Fig. 9.5). The 17O and 27A1 NMR peaks marked "triclusters" in Fig. 9.5a,b were assigned with the aid of spectra of crystalline compounds [see also Skibsted et al., 1993; Gervais et al., 2001]. Triclusters would also be consistent with the presence of nonbridging oxygens in the 17O 3Q MAS NMR spectrum of nominally fully polymerized CaAl2O4 [Stebbins et al., 2001]. This information notwithstanding, alternative structural interpretations of the 17 O 3Q MAS NMR data have been advanced [Kubicki and Toplis, 2002 Neuville et al, 2004] in part because the peaks assigned to triclusters cannot easily be distnguished from those of other (Si,Al)-O-(Si,Al) linkages [Kubicki and Toplis, 2002; Gervais et al, 2004].

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Poe et al. [1993, 1994] examined the structure of melts along the Al2O3-CaAl2O4 and Al2O3-MgAl2O4 joins at high temperature in a manner similar to that used for SiO 2 -A1 2 O 3 melts (Fig. 9.6; see also Fig. 9.3). The 27A1 isotropic chemical shift in spectra of Al 2 O 3 -CaAl 2 O 4 melts, recorded near 2300°C, decreases systematically with increasing A12O3 content (Fig. 9.6a). From molecular dynamics simulations, Poe et al. [1993, 1994] suggested that an increase in A12O3 content is correlated with a higher average oxygen coordination around Al3+. In their analysis, the 27A1 isotropic chemical shift was ascribed to an increase in average Al-coordination number. They added that the average coordination number of Al 3+ is slightly higher in Al 2 O 3 -MgAl 2 O 4 melts than in melts along the join Al 2 O 3 -CaAl 2 O 4 . As concluded for the SiO2-Al2O3 melt structure [Poe et al, 1992], the increased number of oxygens coordinated to Al3+ was assigned to composition-dependent changes in the proportions of 4-, 5, and 6-fold coordinated Al3+ in both CaO-CaAl 2 O 4 and MgO-MgAl 2 O 4 melts, the proportion of Al3+ with the highest coordination number increasing with the A12O3 content of the melt. This may be an oversimplification of the structure, though, because there was no consideration of other parameters that could affect the 27A1 shifts. For instance, McMillan et al. [1996] noted that, in crystalline Ca-aluminates, Al-0 bond lengths, which are affected by Al - coordination changes, do not correlate well with 27A1 chemical shift [Engelhardt and Michel, 1987; Skibsted et al, 1993]. On balance, we nevertheless conclude that some high-coordination Al3+ exists in these melts, as does, most likely, some form of Al-triclusters. The structural data are not, however, sufficiently clear to determine systematic relations between melt composition, temperature, and the various proposed A l - 0 structural species in A12O3-M//VA1O2 peraluminous glasses and melts. 9.1c. MXO-MI/XAIO2 Compositions along M/)-M y/x AlO 2 joins have excess metal cations over those needed to charge-balance Al 3+ in tetrahedral coordination. Here, only the join CaO-CaAl 2 O 4 will be dealt with because little is known about structure of glasses and melts along other

Figure 9.7 - Ca-BO and Ca-NBO distances in melts along the join AhCb-CaAhC^ with nominal NB0/A1 near 0.7 obtained in numerical simulations [Cormier et al, 2003].

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Figure 9.8 - Oxygen-17 MAS NMR spectrum of a glass along the join AUOa-CaAhCU with nominal NBO/Al near 0.6 [Allwardt et al, 2003].

metal oxide-alumina joins. This paucity of data for other compositions is in part because of practical difficulties. Not only are these melts notoriously poor glass-formers but, for alkali systems, they are, in addition, prone to metal loss during high-temperature experiments. From numerical simulation of high-temperature melts along the CaO-CaAl2O4 join, Cormier et al. [2003] distinguished Ca-BO and Ca-NBO bond distances (Fig. 9.7), thus separating Ca2+ serving to charge-compensate Al3+ in tetrahedral coordination from network-modifying Ca2+. The Ca-NBO distance is the shortest, an observation similar to that made for Na-BO and Na-NBO bond lengths inferred from 23Na MAS NMR of alkali aluminosilicate glasses [Lee and Stebbins, 2003] and from numerical simulations of Na2OCaO-Al2O3-SiO2 glasses [Cormier and Neuville, 2004]. Structural information has also been derived from Raman and NMR spectroscopy. The 17O MAS NMR spectrum of a CaO-CaAl2O4 glass with nominal NBO/Al = 0.62 (Fig. 9.8) shows clear evidence of nonbridging oxygen [Allwardt et al, 2003a]. The a NBO/Al calculated from the relative integrated area of the peak assigned to nonbridging

Figure 9.9 - Al-BO and Al-NBO distances in a melt along the join AhCh-CaAhC^ with nominal NBO/Al near 0.7 obtained with numerical simulation [Cormier et al, 2003].

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Figure 9.10 - Distribution of Qn species obtained in a numerical simulation of a melt with nominal NBO/A1 near 0.7 along the join Al2O3-CaAl2O4 [Cormier etal., 2003].

oxygen in the spectrum in Fig. 9.8 is 0.6, thus suggesting that the nominal and actual NBO/Al-values are identical. Hence, at least for such a peralkaline composition, all the oxygens in the glass are either bridging or nonbndging and there is no need for exotic aluminate structures. The I7O NMR results in Fig. 9.8 also agree with a molecular dynamics simulation made for a composition with nominal NBO/A1 = 0.7 by Cormier et al.

Figure 9.11- Aluminum-27 isotropic chemical shift from MAS NMR spectra along the join CaO-AhCh for glasses (closed symbols) [McMillan et al., 1996] and melts near 2300°C (open symbols) [Poe etal., 1994],

Figure 9.12 - Average coordination number of oxygen around Al 3+ obtained by numerical simulation of melts along the join CaO-Al2O3[Poeefa/., 1994].

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[2003] in which all Al-O bonds involved only bridging and nonbridging oxygens (Fig. 9.9). The Al-NBO bonds are shorter than the Al-BO bonds, just as observed in metal oxide-silica systems where Si-NBO bonds are shorter than Si-BO bonds [Ispas et al., 2002]. In these calculations, the bridging and nonbridging oxygen are distributed between Qn-species as illustrated in Fig. 9.10. The results shown in Figs. 9.8-9.10 also accord with the interpretation of Raman spectra of glasses [McMillan and Piriou, 1982] and subsequently by McMillan et al. [1996]. They cannot, however, be easily integrated into the CaO-CaAl2O4 melt structure model of Poe etal. [1994]. McMillan etal. [1996] (closed symbols in Fig. 9.11) concluded that their 27A1 MAS NMR data for glasses are consistent with a structural model similar to that subsequently proposed by Cormier et al. [2003] (Fig. 9.10) where Al3+ is in 4-fold coordination. Poe et al. [1994], on the other hand, concluded from molecular dynamics simulations that the 27A1 isotropic chemical shifts reflect changes in the proportion of 4-, 5-, and 6-fold coordination of Al3+ with oxygen. These changes, in turn, would cause the variations of the average Al-coordination numbers shown in Fig. 9.12. With a value of 4.3, the average coordination number of oxygen around Al3+ in CaAl2O4 melt above its liquidus temperature (Fig. 9.12) is higher than the value of 4.0 derived from the models of glass structure in Figs. 9.8 to 9.10. This difference might point to temperature-induced structural changes. This explanation is inconsistent, however, with the observation that the 27A1 isotropic chemical shifts of CaO-CaAl2O4 glasses do not differ significantly from those of the melts (Fig. 9.11). Although this point should be clarified, the important result of these studies is that glass and melt structure along the CaO-CaAl2O4 join can be described in terms of only 4-fold coordination of Al3+ bonded to nonbridging and bridging oxygen. For lack of data, it is tempting to conclude that the same conclusion holds for melts along other MXO-M/AA1O2 joins. 9.2. Meta-Aluminosilicate Glasses and Melts (SiO2-Mi/cAlO2) Existing data on the structure of melt and glass along meta-aluminosilicate joins, SiO2-M;/l.AlO2, are considerably more comprehensive, detailed, and systematic than for compositions along the binary aluminate joins discussed in the previous section. This is probably due to the direct relevance of compositions along SiO2-M1/xAlO2 joins to both industry and igneous processes, and also to the fact that experiments are often technically more tractable (lower temperatures, better glass-formers, and so forth). 9.2a. Charge-compensation of Al + and (SidAl)-Ordering Charge-compensation of Al3+ in tetrahedral coordination is accomplished with either alkali or with alkaline earth metals. The nature of the charge-balancing cation itself also affects the structural behavior of Al3+ because, in analogy with crystalline aluminosilicates such as anorthite, albite, and sanidine, Al-0 bond properties depend on the metal cation [Phillips and Ribbe, 1973; Prewitt et al, 1976; Angel etal., 1991]. Differences in Al-0 bonds determined by the ionization potential of the charge-compensating metal cation are

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Figure 9.13 - Numerical simulation of the distribution of the intertetrahedral angle, (Si,Al)O-(Si,Al) in Mgo.5AlSi04, Ca0.5AlSiO4, and NaAlSiO4 melt [Scamehorn and Angell, 1991].

manifest in the rheological, mixing, or volume relations of meta-aluminosilicate melts [see Chapter 8 and Riebling, 1964, 1966; Seifert et al, 1982; Navrotsky et al, 1985; Neuville, 1992]. Furthermore, there is evidence from NMR spectroscopy that the structure of Ca and Mg meta-aluminosilicate glasses is not completely polymerized as would be expected if all Al + were in tetrahedral coordination and be charge-compensated with the alkaline earths (nominal NBO/T = 0). Instead, several percent of nonbridging oxygen has been inferred for CaAl 2 Si 2 0 8 glass from 17O 3Q MAS NMR spectroscopy [Stebbins and Xue, 1997]. Along the join SiO2-MgAl2O4, Toplis et al. [2000] concluded from 27A1 MAS NMR spectra of glasses that up to 6 % of the Al3+ is in 5-fold coordination with oxygen. If so, one would also expect a small proportion of nonbridging oxygens in SiO2MgAl 2 O 4 glasses. There is considerably more disorder in the glass (and melt) than in the crystal structure. The extent of disorder in a glass depends on both Al/Si and charge-compensating metal

Figure 9.14- Relationship between Al/(A1+Si) and intertetrahedral angle, T-O-T (T=Al,Si) for SiO2NaA102 glasses [Taylor and Brown, 1979b].

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Figure 9.15 - Integrated line width in 29Si MAS NMR spectra of glasses along the joins SiChNaA102 (NAS) and SiO2-CaAl2O4 (CAS) as a function of Al/(A1+Si) [Lee and Stebbins, 1999].

cation [e.g., Taylor and Brown, 1979a; Navrotsky et al, 1985; Murdoch et al, 1985; Scamehorn and Angell, 1991; Stebbins et al, 1999; Lee and Stebbins, 1999]. One expression of how disorder depends on the metal cation is the distribution of intertetrahedral angles, T-O-T as illustrated in Fig. 9.13 for Mg-, Ca-, and Na-metaaluminosilicate melts with Al/Si= 1 [Scamehorn and Angel, 1991]. For all three materials, the T-O-T angles range between about 120° and 180°. However, both the maximum in the angle distribution function and the distribution around this maximum depend on the type of metal cation. The maximum shifts to lower values and the distribution becomes broader as the ionization potential of the metal increases (Mg2+>Ca2+>Na+) (Fig. 9.13). The T-O-T angle decrease is also consistent with results from numerical simulation of Na2O-CaO-Al2O3-SiO2 melt structure [Angeli et al., 2000]. For any given metal cation such as, for example, Na+ in the system SiO2-NaAlO2 [Taylor and Brown, 1979a,b], the maximum in the angle distribution is negatively correlated with the Al/(A1+Si) of the glass (Fig. 9.14). As expected [Brown et al, 1969; Gibbs etal, 1981; Ross and Meagher, 1984], that angle decrease is also negatively correlated with the T-O distance. Relationships between T-O-T angle distribution, cation properties, and extent of glass and melt disorder are evident in 29Si MAS NMR spectra of meta-aluminosilicate glasses [Murdoch et al, 1985; Engelhardt and Michel, 1987; Oestrike et al, 1987; Lee and Stebbins, 1999]. The line width of 29Si NMR spectra can be viewed as an expression of disorder [Engelhardt and Michel, 1987; Oestrike et al, 1987; Lee and Stebbins, 1999]. In the Si MAS NMR spectra of meta-aluminosilicate glass, the line width decreases with increasing Al/(A1+Si), whereas, for a given Al/(A1+Si), it increases with the ionization potential of the metal cation that charge-compensate Al3+ in tetrahedral coordination (Fig. 9.15). Thus, one might infer that the extent of disorder decreases with increasing Al/(A1+Si) and with increasing ionization potential of the cation that serves to chargecompensate tetrahedrally coordinated Al3+.

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Figure 9.16 - Shift of Raman bands assigned to (Si,Al)-BO stretching of glasses on the join SiO2-NaAlO2 as a function of Al/(A1+Si) [Seifertefa/., 1982].

9.2b. Systematics ofSiO2-M1/xAlO2 Glass and Melt Structure In SiO2-M1/xAlO2 systems, structural data for SiO2-NaAlO2 glasses and melts are considerably more comprehensive than for melt with metal cations other than Na+. Some structural data have been reported for K- and Li systems and to a lesser extent, SiO2CaAl2O4 and SiO2-MgAl2O4 glass and melt. In a radial distribution analysis of SiO2-NaAlO2 glasses (see Fig. 4.7), Taylor and Brown [1979b] found that there are only subtle structural variations with Al/(A1+Si), pointing to a simple network structure smoothly varying between pure SiO2 to at least NaAlSiO4 composition. This systematic and gradual evolution in the radial distribution functions with Al/(A1+Si) suggests that glasses along the SiO2-NaAlO2 join have considerable structural resemblance with pure SiO2. In both glassy and molten forms, the structure of SiO2 is likely made up of distribution of a small number of 3-dimensionally interconnected rings of SiO4 tetrahedra (see chapter 5). Although there are many differences

Figure 9.17 - Structure model of Seifert et al. [1982] for glasses and melts along the join SiCh-NaAlCh. The mol fraction refers to 3-dimensionally interconnected structural entities. Numbers represent the Al/(A1+Si) in the structural units shown as solid symbols.

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Figure 9.18- Shift of Raman bands assigned to (Si,Al)-BO stretching of glasses on the join SiO2-CaAl2O4 as a function of Al/(A1+Si) [Seifert et al., 1982]. The band near 900 cm"1 may be assigned to (Si,Al)-NBO.

in detail, results of molecular dynamics simulation are also consistent with this view [Zirl and Garofalini, 1990]. The Raman spectra of SiO2-NaAlO2 glasses and melts have also been interpreted in terms of ring distributions. Seifert et al. [1982] found that the spectra of SiO2-NaAlO2 glasses could be deconvoluted into doublets analogous to those of vitreous SiO2 (Fig. 5.21). The frequencies of the Raman bands, in particular those assigned to (Si,Al)-0 stretching in the 900 1200 cm"1 range [see also McMillan and Wolf, 1995], decrease in simple a systematic manner with increasing Al/(A1+Si) of the glass (Fig. 9.16). Seifert et al. [1982] suggested that this decrease, reflecting decreasing force constants, at least in part, was due to decreasing bond strength as Al3+ is substituted for Si4+. By using a simple central force model [Sen and Thorpe, 1977; Galeener, 1979], similar to that employed to interpret the Raman spectrum of vitreous SiO2 (see Chapter 5), Seifert et al. [1982] concluded that the band doublets in the Raman spectra of SiO2-NaAlO2 glasses reflect, on average, coexisting, 3-dimensionally interconnected structures whose intertetrahedral angles differ by 5°-10°. The actual values of these angles are difficult to determine with precision, but the average T-O-T angle decreases by about 6°-7° from SiO2 to NaAlSiO4 glass. The ring with the smaller angle probably is the most aluminous of the two structures. In the Seifert et al. [1982] model of SiO2-NaAlO2 glass and melt, the abundance of this structural unit increases with increasing Al/(A1+Si) (Fig. 9.17). The Al/(A1+Si) of this unit (unit 1 in Fig. 9.17) also increases with Al/(A1+Si). From this analysis, one cannot determine whether the two ring structures differ in the number of (Si,Al)O4 tetrahedra. The angle difference could also be due to differing extent of puckering (see Kubicki and Sykes [1993] for discussion of energy minimization modeling and its relationship to intertetrahedral angle variations). A variation of intertetrahedral angle of 5°-10° could also result from differences in Al/(A1+Si) as increasing Al + in tetrahedral coordination induces a decrease of intertetrahedral angle, at least in crystalline aluminosilicates [Brown et al., 1969]. Details of the structure of tetrahedrally coordinated Al3+ may depend on the nature of the metal cations that serve to charge-compensate Al3+ in tetrahedral coordination. For example, the frequency of Raman bands in the spectra of SiO2-CaAl2O4 glass assigned to (Si,Al)-BO (bridging oxygen) stretch vibrations do not vary with Al/(A1+Si) (Fig. 9.18), whereas

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Figure 9.19 - Structure model of Seifert et al. [1982] for glasses and melts along the join SiO2-CaAl2O4.

those of the Raman spectra of SiO2-NaAlO2 glasses do (Figs. 9.16 and 9.17). From their Raman data, Seifert et al. [ 1982] suggested that in contrast with the SiO 2 -NaAlO 2 glasses, three distinct structural entities coexist in SiO2-CaAl2O4 glasses. Each with a constant composition, they resemble A1O2, Al 05 Si 05 O2, and Al-free SiO2-like structures. Their abundance varies with Al/(A1+Si) (Fig. 9.19). Seifert et al. [1982] added that similar entities exist in SiO 2 -MgAl 2 O 4 glasses, but that their proportions depend on Al/(A1+Si) in a slightly different way. An interesting detail in the Raman spectra of SiO2-CaAl2O4 glasses is the weak band near 900 cm"1 (Fig. 9.18), whose relative intensity is less than 5 % in the frequency region of (Si,Al)-0 stretching. This band can be assigned to an (Si,Al)-0 vibration involving a nonbridging oxygen. This interpretation is consistent with the conclusions drawn from the 17O 3Q MAS NMR spectrum of CaAl 2 Si 2 0 8 glass [Stebbins and Xue,

Figure 9.20 - Silicon-29 MAS NMR spectra of glasses along the joins SiCh-CaAhCU (CAS) and SiO2-NaAlO2 (NAS) [Lee and Stebbins, 2002].

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Figure 9.21 - Silicon-29 spin lattice relaxation time from spectra of NaAlSijOs glass and melt as a function of temperature [Liu et al., 1987].

1997] as well as from x-ray diffraction data of glasses along the SiO2-CaAl2O4 join [Petkov etal, 1998,2000]. The maximum abundance of the Al0 5Sio.502 entity at the CaAl2Si2O8 (anorthite) stoichiometry is another notable feature of Fig. 9.19. That it represents about 85% of the structure is consistent with the aforementioned x-ray data that point to similar shortrange order in anorthite and CaAlSi2O8 glass (see also Fig. 4.10) and is also consistent with the low-temperature heat capacity data (section 3.2c). Another interesting feature derived by Seifert et al [1982] from the Raman spectrum of CaAl2Si208 glass is a small abundance of SiO2 and A1O2 entities. In other words, there is incomplete Al-avoidance, a conclusion subsequently substantiated by Al, Si and 17O NMR data for similar compositions [Merzbacher et al, 1990; Stebbins and Xue, 1997; Stebbins et al., 1999]. In fact, Stebbins and Xue [1997] reported NMR evidence for both Si-O-Si and Al-O-Al linkages in CaAlSi2O8 glass, which agrees with the interpretation of the Raman data in Fig. 9.19. The line widths of 29Si MAS NMR spectra have been correlated with the extent of (Al<=>Si)-ordering [Engelhardt and Michel, 1987; Oestrike et al, 1987; Lee and Stebbins, 1999]. This feature is evident in 29Si MAS NMR spectra which are broader for SiO 2 CaAl2O4 than for SiO2-NaAlO2 glass compositions at the same Al/(A1+Si) (Figs. 9.15 and 9.20). It follows that the (Al<=>Si)-disorder in alkaline earth meta-aluminosilicate glasses is greater than in alkali meta-aluminosilicate glasses. Recent refinements based on 29Si MAS NMR spectroscopy are consistent with this conclusion [Lee and Stebbins, 1999]. 9.2c. Temperature-Induced Transformations Along SiO2-Ml/xAlO2 Joins The structural data hitherto discussed have been obtained at ambient temperature and, thus, deal with the structure of the melts frozen in at the glass transition. Structural changes take place when the temperature is increased above the glass transition. For instance,

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Figure 9.22 - X-ray radial distribution functions of CaAl2Si2O8 and NaAlSisOs glasses and melts [Taylor and Brown, 1979a; Marumo and Okuno, 1984].

relaxation of melt structure in the glass transition range manifests itself by changes in the 29 Si spin lattice relaxation time of NaAlSi3Og (Fig. 9.21). In addition, (Al<=>Si)-ordering likely is temperature-dependent as in crystalline aluminosilicates (see chapter 3). Temperature-controlled changes could also affect bond lengths, bond angles, and ring statistics [McMillan etal., 1994]. Despite the observations above, the x-ray radial distribution functions of molten NaAlSi3O8 at 1200°C and CaAl2Si208 at 1600°C [Marumo and Okuno, 1984] resemble those of the glasses at ambient temperature (Fig. 9.22) although, at least for NaAlSi3O8, the first (Si,Al)-0 radial distance near 1.6-1.7 A (marked with an arrow in Fig. 9.22) might be slightly shorter in the glass than in the melt. This effect could follow from a temperature-driven opening of the structure. Larger angles at higher temperature could cause a shortening of the (Si,Al)-O bridging bond distance [Brown et al., 1969; Gibbs et al., 1981]. Such a structural effect cannot be discerned, however, in the x-ray radialdistribution functions of CaAl2Si208 glass and melt. This conclusion accords with that derived from in-situ, high-temperature Raman spectroscopic data of CaAl2Si208 glass and melt [Daniel et al., 1995]. In other words, despite the tentative suggestion based on

Figure 9.23 - Proportion of 3-dimensionally interconnected unit 1, with the largest Al/(A1+Si), as given by the structure model of Seifert et al. [1982] along the join SiO2-NaAlO2 for glasses and melts with two different bulk Al/(A1+Si) as a function of temperature [Neuville and Mysen, 1996].

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Figure 9.24 - Probability of forming an SiO4-tetrahedron of Q4-type with 2, 3, and 4 next-nearest Al3+ neighbors in a calcium aluminosilicate [Merzbacher et al, 1990].

the x-ray data (Fig. 9.22), Daniel et al. [1995] concluded that temperature does not affect intertetrahedral angles and, thus, presumably, (Si,Al)-0 bond lengths. Despite the suggested slight differences regarding (Si,Al)-0 bond length changes with temperature in NaAlSi3O8 melt [Marumo and Okuno, 1984], it seems that, at least for the CaAl2Si208 and NaAlSi3O8 feldspar compositions, glasses and melts have similar structures. Whether or not there may be effects of temperature on the structure of other meta-aluminosilicates has been examined along the join SiO2-NaAlO2 in the Al/(A1+Si) range between 0.05 and 0.5. Neuville and Mysen [1996] concluded that there is a small temperature effect on the proportion of the two coexisting, 3-dimentionally connected structural units (Fig. 9.23), and that this temperature-dependence also varies with Al/(A1+Si). From this analysis, the abundance of the unit with the highest Al/( Al+Si) (denoted unit" 1" in Figs. 9.17 and 9.23) decreases slightly with increasing temperature. Mass-balance considerations require a change in Al-distribution between the two structural units with temperature for this decrease to be possible. The distribution of Al3+among the coexisting, fully polymerized (Si,Al)O4 tetrahedra in SiO2-NaAlO2 melts appears, therefore, to be temperature-dependent. 9.3. Peralkaline Aluminosilicate Glasses and Melts Aluminum-bearing compositions to the left of the SiO2-M1/xAlO2 join in Fig. 9.1 are peralkaline. Strictly speaking, compositions on the join MXO-M1/XA1O2, described in section 9.1c, are also peralkaline, but will not addressed further here. 9.3a. Systematics ofSiO2-MxO-M,/xAlO2 Glass and Melt Structure Merzbacher et al. [1990] concluded that Al3+ is dominantly in Q4 units in peralkaline glasses, at least for compositions with less than about 15 mol % SiO2 along a join with nominal NBO/T = 0.5 in the CaO-Al2O3-SiO2 system (Fig. 9.24). This conclusion is consistent with results from 29Si and 27A1 MAS NMR as well as molecular dynamics

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Figure 9.25 - Concentration of Q 4 , Q 3 , and Q 2 species in glasses along the join Na2Si3O7Na2(NaAl)3O7 as a function of bulk melt Al/(A1+Si). The Qn-species abundance is calculated with Si 4+ and Al3+ incorporated in the individual Qn-species as described by Mysen et al. [2003].

simulations of peralkaline, low-Si glasses and melts in this system [Engelhardt et al., 1985; Cormier et al., 2003]. Similar behavior has been reported from NMR and Raman data of peralkaline glasses and melts in the system Na2O-Al2O3-SiO2 [Allwardt et al.., 2003a; Mysen et al., 2003]. An implication of Al-preference for fully polymerized structural units, Q , in peralkaline aluminosilicate melts and glasses is that the equilibrium originally proposed for Al-free alkali silicate glasses and melts [Schramm et al., 1984; Stebbins, 1987]: 2Q 3 o Q 4 + Q 2 ,

(9.1)

depends on Al/(A1+Si). Systematic relationships between Al/(A1+Si) and Qn-speciation have been determined for glasses and melts in Li2-Al2O3-SiO2, Na2O-Al2O3-SiO2, and K 2 O-Al 2 O 3 -SiO 2 systems [Maekawa et al, 1991; Mysen, 1999]. Some data are also available for CaO-Al 2 O 3 -SiO 2 and MgO-Al 2 O 3 -SiO 2 glasses [Mysen et al, 1981; Merzbacher and White, 1991]. The structural role of Al + in alkaline earth aluminosilicates is not as well known as in alkali aluminosilicate because liquid immiscibility limits the compositional range that can be examined [Osborn and Muan, 1960a, b]. Further, rapid nucleation at the time scale of spectroscopic measurements on supercooled melts tends to restrict the temperature range over which the structure of peralkaline melts can be studied in these systems (see also Chapter 8). Solution of A12O3 in alkali silicate glasses and melts results in equilibrium (9.1) shifting to the right (Fig. 9.25). Thus, as Al/(A1+Si) increases in systems where the nominal NBO/T (T = Si+Al) is constant, the abundance of Q 2 and Q 4 structural units increases whereas Q3 units become less abundant. Further, because Al + substitutes for Si4+ preferentially

Aluminosilicate Systems II. Structure in Q units, their Al/(A1+Si) increases rapidly with Ay(Al+Si) of the melt (Fig. 9.25). The relationships between Qn-abundance and temperature in peralkaline aluminosilicates qualitatively resemble those observed for the Al-free alkali silicate endmember compositions [McMillan et al., 1992; Mysen and Frantz, 1992,1994; Mysen, 1995, 1997, 1999]. The concentration of Q2, Q3, and Q4 species initially remain insensitive to temperature over several hundred degrees (Fig. 9.26). At temperatures above the glass transition, the abundances of Q4 and Q2 species then increase and that of Q decreases [Mysen et al, 2003]. Although the temperature-dependent Qnspeciation resembles that of Al-free alkali silicate melts, the speciation is somewhat more sensitive to temperature than in the absence of alumina (Fig. 9.26). The enthalpy, AH, of equilibrium (9.1) (obtained as discussed in section 7.4b) generally is also a positive function of the bulk Al/(A1+Si) (Fig. 9.27a) and a negative function of nominal NBO/T of the melt [Mysen, 1999]. This enthalpy also depends on the nature of the alkali metal as it is higher the more electronegative the alkali metal (Fig. 9.27b).

Figure 9.26 - Concentration of Q4, Q3, and Q2 species in glasses and melts along the join Na2Si3O7Na2(NaAl)3C>7 as a function of temperature. Species abundance shown for melts and glasses with Al/(Al+Si)=0 (open symbols) and Al/ (Al+Si)=0.2 (closed symbols) [Mysen etal, 2003].

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Figure 9.27 - Enthalpy of reaction (9.1) calculated from the abundance of Q4, Q 3 , and Q 2 structural units at temperatures above the glass transition range for tetrasilicate melts [after My sen, 1999]. (a) AH for melts along the join Na2Si4O9-Na2(NaAl)4O9 as a function of bulk melt Al/(A1+Si), (b) Mi for melts along the joins K^CVK^KAl^Ocj, Na2Si4O9-Na2(NaAl)4O9, and Li2Si4O9-Li2(LiAl)4O9 at bulk melt Al/(A1+Si) = 0.2 as a function of ionization potential, ZJr1, where Z is the formal electrical charge and r the ionic radius for cation in 6-fold coordination with oxygen [Whittaker and Muntus, 1970].

9.4. Pressure and the Structure of Aluminosilicate Melts At subsolidus temperatures, the P, T curve of the univariant equilibrium: albite <=> jadeite + quartz,

(9.2)

crosses the albite liquidus curve near 1450°C and 3 GPa [Johannes et al., 1971]. This observation led Waff [1975] to suggest that Al3+ might transform from 4- to 6-fold coordination in NaAlSi3O8 melts near 3 GPa. Early measurements showing a decrease of the viscosity of NaAlSi2O6 melt at high pressure were also thought to result from such an Al-coordination change [Kushiro, 1976]. In a Raman spectroscopic study of NaAlSi2O6 melt quenched from high temperature at several GPa pressure, Sharma et al. [1979] did not, however, observe any evidence for Al-coordination transformation in this pressure regime. In a more comprehensive study of quenched melts along the joins SiO2-NaAlO2 and SiO2-CaAl2O4, Mysen et al. [1983] arrived at a similar conclusion. They did find, however, that the average intertetrahedral angle decreases with pressure at least to ~3 GPa (Fig. 9.28). The extent of compression of the intertetrahedral angle depends on both Al/(A1+Si) and ionization potential of the charge-balancing cation. This angle is more sensitive to pressure in SiO2-NaAlO2 than in SiO2-CaAl2O4 melts (Fig. 9.28). It increases with Al/(A1+Si) in SiO2-NaAlO2 melts and decreases with pressure in SiO2-CaAl2O4 melts

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Figure 9.28 - Relative change in average intertetrahedral angle (% relative to angle at ambient pressure) as a function of pressure for glasses along the joins (a) SiCh-NaAlCh and (b) SiO2CaAl2O4 whose bulk melt Al/(A1+Si) is indicated [Mysen et al, 1983].

(Fig. 9.28). The explanation of this different response to pressure lies in the dependence of structural role of Al + on the charge-compensating metal cation (Figs. 9.17, 9.19). In the SiO2-NaAlO2 system, substitution of Al3+ for Si4+ results in increasing Al/Si-ratio in the 3-dimensionally interconnected rings. Because replacement of Si4+ with Al3+ results in weakening of the (Si,Al)-0 bonds (Table 4.1), these bonds become more flexible and the (Si,Al)-O-(Si,Al) angles more compressible with increasing Al/(A1+Si). In SiO 2 CaAl2O4 melts, on the other hand, the Si/Al-ratios in the 3-dimensionally interconnected units in the melts do not vary with Al/(A1+Si). Only their proportions do. Therefore, the changes in average intertetrahedral angles merely reflect variations of these proportions and the compressibility of these units. Among these, the more open SiO2 unit is likely the most compressible. In the SiO2 structural entity, the Si-O-Si angle is likely near 150° in analogy with the average Si-O-Si angle in vitreous SiO2 (see section 5.3b). In the Al0 5Si0.5O2 entity, the average (Si,Al)-O-(Si,Al) angle is near 135°-140° in analogy with the angle in CaAl2Si208 melt [Scamehorn and Angell, 1991]. As the abundance of Alfree SiO2 units decreases with increasing Al/(A1+Si), bulk compressibility is also likely to decrease. This structural effect is evident in the decreasing sensitivity to pressure of the intertetrahedral angle as Al/(A1+Si) of SiO2-CaAl2O4 melts increases (Fig. 9.28). Structural examination of aluminosilicate quenched melts to ~ 3 GPa suggest at most less than 1 % of the Al3+ coordination states higher than 4 [Stebbins et al., 2000; Alwardt et al., 2003b]. A further pressure increase does, however, cause significant coordination changes. Yarger et al. [1995] reported 27A1 MAS NMR evidence for partial coordination transformation of Al3+ in a (NaAlSi3O8)50(Na2Si4O9)50 melt quenched from high

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Figure 9.29 - Aluminum-27 MAS NMR spectra of (NaAlSi308)5o(Na2Si409)5o glass quenched from above the liquidus temperature at pressures indicated. Positions of Al3+ in 4, 5, and 6-fold coordination with oxygen marked on individual spectra [Yarger et al, 1995].

temperature at > 6 GPa (fig. 9.29). Lee et al. [2003] reported 27A1 and 17O 3Q-MAS NMR spectra for pure NaAlSi 3 O 8 and a peralkaline composition between NaAlSi 3 O 8 and Na 2 Si 3 0 7 [(Na2O)0 75(Ai203)o.25#3Si02] quenched from pressures up to 8 GPa (Fig. 9.30). Five- and 6-fold coordinated Al3+ are evident in the NMR data of the high-pressure glasses from both studies (Figs. 9.29 and 9.30). It is also clear (Fig. 9.29) that the proportion of 6-fold coordinated Al 3+ is positively correlated with pressure. It is also noteworthy that the pressure at which higher oxygen-coordination numbers for Al 3+ can be detected is considerably higher than that where Al3+ in minerals with 6-fold coordination become stable. Furthermore, in contrast to minarals where this transformation is abrupt, the coordination transformation in aluminosilicate melts is a gradual function of increasing

Figure 9.30 - Aluminum-27 3Q MAS NMR spectra of glass quenched from melt above the liquidus temperature at 8 GPa for (a) NaAlSi3O8 and (b) (Na20)o.75(Al203)o.75»3Si02 [Lee et al, 2003].

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pressure. It also appears that Al3+-coordination transformation is enhanced by the presence of nonbridging oxygens in the lowe-pressure aluminosiloicate melt (Fig. 9.30). 9.5. Structure and Properties of Aluminosilicate Melts The extent to which Al3+ is charge-compensated in silicate melts affects both melt structure and properties. Furthermore, the ionization potential of the charge-compensating cation also affects the structural role of Al3+ and the properties of the aluminosilicate melts. Finally, structural behavior of Al3+ and melt properties depend on whether a melt is fully or nearly fully polymerized or whether both fully polymerized and depolymerized Qnspecies coexist in the melt. 9.5a. Peraluminous Melts Physical properties such as viscosity and volume are sensitive to the melt structure. In Na-aluminosilicate melts, isothermal viscosity reaches a maximum value near the SiO2NaA102 join (Chapter 8), a feature that led Riebling [1966] to suggest that as Naaluminosilicate melts enters the peraluminous field, there may be a partial coordination transformation of the Al3+ that is not charge-compensated by Na+. That simple model is consistent with the structural data in Fig. 9.2, which indicate that an increase in Al content from peralkaline to peraluminous is associated with a minimum in degree of polymerization (NBO/T) near the meta-aluminosilicate join. Whether the increase in NBO/T on the peraluminous side of the SiO2-NaAlO2 join reflects a change in the coordination number of oxygen around Al3+ or whether there may be other structural changes of Al3+ remains, however, a matter of discussion. At least for peraluminous compositions near the meta-aluminosilicate join, most recent models have invoked Al-triclusters (see Fig. 9.4) where Al3+ remains in tetrahedral coordination but with a local structural environment differing significantly from that of tetrahedrally coordinated when Al3+ is charge-compensated with alkali metals or alkaline earths. Although it is unclear whether Al3+ in peraluminous melts near the metaaluminosilicate join undergoes coordination transformation with increasing peraluminosity, transformation does take place as the melt compositions approach the SiO2-Al2O3 join. It is not surprising, therefore, that the partial molar volume of A12O3, for example, in peralkaline aluminosilicate melts differs substantially from the molar volume of liquid A12O3 (see Fig. 8.11 and discussion of these differences in Chapter 8). 9.5b. Meta-aluminous Melts The structure of melts along meta-aluminosilicate joins, where nominally all Al3+ is chargecompensated with either alkali metals or alkaline earths, is nearly fully polymerized. Many properties reflect, therefore, simply the effect on melt structure of Al/(A1+Si) variations and the ionization potential of the charge-compensating metal cation. Substitution of Al3+ for Si4+ results in weakening of the (Si,Al)-0 bridging oxygen bonds (Table 4.1). This means that any property that depends on (Si,Al)-0 bond

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Figure 9.31 - Liquidus phase relations, at ambient pressure, along the join Na2Si2O5Na2(NaAl)2O5 [Osborn and Muan, 1960c].

strength reflects this substitution. That effect is, for example, evident in decreasing viscosity and activation energy of viscous flow of meta-aluminosilicate melts with increasing Al/(A1+Si). The magnitude of this relationship does, however, depend on the metal cation [Neuville, 1992; Toplis et al, 1997]. This is in part because the strength of bridging Al-0 bonds is likely negatively correlated with the ionization potential of the charge-compensating metal cation. Such relationships between bond strength and ionization potential of the charge-compensating metal cation may also be one of the reasons why heat of solution of glasses along meta-aluminosilicate joins diminishes as the metal cation becomes more electronegative (see, for example, Fig. 8.9) and why the molar volume of meta-aluminosilicate melts show different functional relationships to Al/(A1+Si) depending on whether Al3+ is charge-compensated by Na+ or Ca2+ [Navrotsky et al, 1982].

Figure 9.32 - Activity coefficient of SiCh in melts in the Na2O-Al2O3-SiO2 and K2OAl 2 O 3 -SiO 2 systems, ySi02me", for compositions along the metaaluminosilicate joins, SiO2-NaAlO2 and SiO2-KAlO2 (solid lines), and along joins of peralkaline compositions, Na2Si4C>9Na2(NaAl)4O9 and K2Si4O9-K2(KAl)4O9 (dashed lines) from the temperaturecomposition trajectories of silica polymorphs on the liquidus. Calculations are based on ambient-pressure liquidus phase equilibrium data by Osborn and Muan [1960c, d].

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The latter structural differences may also account for the much greater compressibility of Si0 r NaA10 2 compared with SiO2-CaAl2O4 melts [Kushiro, 1980, 1981] and explain why the pressure-dependence of viscosity of SiO2-NaAlO2 melts differs from that of SiO 2 -CaAl 2 O 4 melts. For SiO2-NaAlO2 melts, there is a negative pressure effect that increases with increasing Al/(A1+Si) [Kushiro, 1976, 1978, 1980], whereas along the join SiO2-CaAl2O4, the melt viscosity becomes less dependent on pressure the higher the Al/(A1+Si) of the melt [Kushiro, 1981]. Mysen et al. [1983] suggested that this effect is related to differences in the flexibility of (Si,Al)-O-(Si,Al) angles depending on the nature of the charge-compensating cation. 9.5c. Peralkaline Aluminosilicate Melts Structure-property relationships in peralkaline aluminosilicate melts are affected by the fact that Al3+ tends to partition into Q4 units compared with depolymerized structural units such as Q 3 and Q 2 and by the fact that increasing Al/(A1+Si) tends, therefore, to drive equilibrium (9.1) to the right. This effect is reflected, for example, in changes in liquidus phase relations along composition joins with constant nominal NBO/T but varying Al/(A1+Si). An example is the join Na 2 Si 2 O 5 -Na 2 (NaAl) 2 O 5 (Fig. 9.31). Increasing Al/(A1+Si) results in rapid disappearance of Na 2 Si 2 0 5 as the liquidus phase. However, instead of an aluminous liquidus phase, Na-metasilicate (Na 2 SiO 3 ) is on the liquidus over a wide Al/(Al+Si)-range (Fig. 9.31). Although liquidus phase relations obviously depend on the properties of both melts and solids, this change is certainly consistent with increasing abundance of Q2 units in the melts as the Al/(A1+Si) increases. In aluminosilicate systems, the tridymite liquidus surface can be used to calculate the activity of SiO2 in the melts (see section 6.2d). The trajectory of the SiO2 activity coefficient, ysiO2meU> differs significantly depending on whether we consider metaaluminosilicate compositions with nearly all Q 4 species in the melt, and peralkaline, depolymerized aluminosilicate melts where Q4-species coexist with Q3 and Q species (Fig. 9.32). In the latter systems, the activity coefficient of SiO2 is profoundly dependent on the fact that the Al3+ is not randomly distributed among the Qn-species, but substitutes for Si4+ predominantly in Q4 units. In meta-aluminosilicate melts, in comparison, which comprise essentially only Q 4 units, ySi02melt is o n ly marginally affected by Al/(A1+Si) (Fig. 9.32). It has been suggested that the viscosity minima of melts along Na 2 Si 2 0 5 Na 2 (NaAl) 2 O 5 [Dingwell, 1986] may also find an explanation in the Al3+-distribution between Qn-species [Mysen and Frantz, 1994]. The observation that the abundance of Qn-species as well as their temperaturedependence vary with Al/(A1+Si) can also affect configurational properties. This is because the solution of A12O3 affects the entropy of mixing via an expression such as equation (3.7) (Chapter 3). Furthermore, because the temperature-dependence of equilibrium (9.1) is a function of Al/(A1+Si) of peralkaline aluminosilicate melts, the temperature-dependence of entropy of mixing will also vary with Al/(A1+Si). In fact, Mysen [1999] pointed out that even if one assumes that the partial molar heat capacities of Q 4 , Q 3 , and Q 2 units do not vary with

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Al/(A1+Si), the negative correlation between configurational heat capacity and temperature of peralkaline aluminosilicate melts observed for Na2Si205-Al203 [Tangeman and Lange, 1998] can be rationalized with a temperature-dependent entropy of mixing term. 9.6. Summary Remarks l.The structure of aluminosilicate melts and glass is sensitive to composition. The proportions of Al3+ relative to alkali metals or alkaline earths is of particular importance because this controls how Al3+ in tetrahedral coordination is charge-balanced. 2. For compositions where Al3+ exceeds the charge-compensating capacity of alkalis or alkaline earths, the excess Al3+ may exist in the form of aluminum triclusters as well as in 5- and 6-fold coordination with oxygen. For compositions near the metaaluminosilicate joins, triclusters appear to be the principal structural form, whereas for glasses and melts on or near the SiO2-Al2O3 join, 5- and 6-fold coordinate Al + exist. 3. Meta-aluminosilicate glasses and melts are nearly fully polymerized although a few percent nonbridging oxygen appear present in alkaline earth meta-aluminosilicate glasses. Nonbridging oxygen appears more abundant in alkalin earth than in alkali aluminosilicate melts and glasses. 4. In meta-aluminosilicate glasses and melts, the extent of (Si<=>Al) ordering varies with the nature of the metal cation required to charge-compensate Al3+ in tetrahedral coordination. The extent of ordering is correlated with the ionization potential of the charge-balancing cation. 5. In peralkaline aluminosilicate glasses and melts, Al3+ exists preferentially in Q4-type structural units. Thus, the Al/Si-ratio of a melt governs equilibria among coexisting Qn-species so that increasing almina content is correlated with a shift of the equilibrium, 2 Q3 <=» Q4 + Q2 to the right. 6. The temperature-dependence of the equilibrium constant of the reaction 2 Q3 <=> Q4 + Q2 is similar in Al-free and peralkaline aluminosilicate melts. The enthalpy of this reaction is, however, positively correlated with the bulk melt Al/(A1+Si) and with the ionization potential of the metal cation. 7. High pressures exerted on aluminosilicate melts induce both compression of intertetrahedral angle and, at P > 6 GPa, partial coordination transformation of Al3+ from 4-fold to 5- and 6-fold coordination with oxygen. Coordination changes in aluminosilicate melts occur at lower pressure for of Al3+ than for Si4+. This pressure is also lower for depolymerized than for highly polymerized aluminosilicate melts.

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Risbud S. H., Kirkpatrick R. J., Taglialavore A. P., and Montez B. (1987) Solid-state NMR evidence of 4-, 5-, and 6-fold aluminum sites in roller-quenched SiO2-Al2O3 glasses. J. Amer. Ceram. Soc. 70, C10-C12. Ross N. L. and Meagher E. P. (1984) A molecular orbital study of HeSi2O7 under simulated compression. Amer. Mineral. 69, 1145-1149. Sato R. K., McMillan P. R, Dennison P., and Dupree R. (1991) A structural investigation of high alumina glasses in the CaO-Al2O3-SiO2 system via Raman and magic angle spinning nuclear magnetic resonance spectroscopy. Phys. Chem. Glasses 32, 149-160. Scamehorn C. A. and Angell C. A. (1991) Viscosity-temperature relations and structure in fully polymerized aluminosilicate melts from ion dynamics simulations. Geochim. Cosmochim. Ada 55, 721-730. Schramm C. M., DeJong B. H. W. S., and Parziale V. F. (1984) 29Si magic angle spinning NMR study of local silicon environments in-amorphous and crystalline lithium silicates. J. Amer. Chem. Soc. 106, 4396-4402. Seifert F. A., Mysen B. O., and Virgo D. (1982) Three-dimensional network structure in the systems SiO2-NaAlO2, SiO2-CaAl2O4 and SiO2-MgAl2O4. Amer. Mineral. 67, 696-711. Sen N. and Thorpe M. F. (1977) Phonons in AX2 glasses: From molecular to band-like modes. Phys. Rev. Lett. B 15, 4030-4038. Sen S. and Youngman R. E. (2004) High-resolution multinuclear NMR structural study of binary aluminosilicate and other related glasses. J. Phys. Chem. B 108, 7557-7564. Sharma S. K., Virgo D., and Mysen B. O. (1979) Raman study of the coordination of aluminum in jadeite melts as a function of pressure. Amer. Mineral 64, 779-788. Skibsted J., Henderson E., and Jakobsen H. J. (1993) Characterization of calcium aluminate phases in cements by high-performance 27A1 MAS NMR spectroscopy. Inorganic Chem. 32,1013-1027. Stebbins J. F. (1987) Identification of multiple structural species in silicate glasses by 29Si NMR. Nature 330, 465-467. Stebbins J. F. and Xue X. (1997) NMR evidence for excess non-bridging oxygen in an aluminosilicate glass. Nature 390, 60-62. Stebbins J. E, Lee S. K., and Oglesby J. V. (1999) Al-O-Al oxygen sites in crystalline aluminates and aluminosilicate glasses: High-resolution oxygen-17 NMR results. Amer. Mineral. 84, 983-986. Stebbins J. E, Kroeker S., Lee S. K., and Kiczenski T. J. (2000) Quantification of five- and sixcoordinated aluminum ions in aluminosilicate and fluoride-containing glasses by high-field. high-resolution 27A1 NMR. J. Non-Cryst. Solids 275, 1-6. Stebbins J. E, Oglesby J. V, and Kroeker S. (2001) Oxygen triclusters in crystalline CaAUO7 (grossite) and in calcium aluminosilicate glasses: 17O NMR. Amer. Mineral. 86, 1307-1311. Tangeman J. A. and Lange R. A. (1998) The effect of Al3+, Fe3+, and Ti4+ on the configurational heat capacities of sodium silicate liquids. Phys. Chem. Minerals 26, 83-99. Taylor M. and Brown G. E. (1979a) Structure of mineral glasses. I. The feldspar glasses NaAlSisOs, KAlSi3O8, CaAl2Si208. Geochim. Cosmochim. Ada 43, 61-77. Taylor M. and Brown G. E. (1979b) Structure of mineral glasses. II. The SiO2-NaAlSiO4 join. Geochim. Cosmochim. Ada 43, 1467-1475. Toplis M. J., Dingwell D. B., and Lenci T. (1997) Peraluminous viscosity maxima in Na2O-Al2O3SiO2 liquids: The role of triclusters in tectosilicate melts. Geochim. Cosmochim. Ada 61, 2605-2612.

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291

Chapter 10

Iron-bearing Melts I. Physical Properties Iron is ubiquitous in igneous rocks. Its abundance generally decreases with magmatic differentiation and increasing SiO2 content, but it remains present in amounts that have significant effects on physical properties. Even at low concentration, iron signals in fact its presence by the dark hue it confers to minerals and glasses. As a result, clear, transparent glass requires less than 0.1 wt % iron oxides in the raw materials, which has long made work difficult for glassmakers. Optical transitions in the visible part of the electromagnetic spectrum are a common feature of transition metals, of which iron is by far the most abundant naturally. Another characteristic feature of transition metals, of greater importance, is the existence of several oxidation states. For iron, the metal (Fe°) can coexist with the ferric (Fe2+) and ferrous (Fe3+) states. The latter two valences affect melt structure and properties in a specific and often complex way because their relative abundances vary with temperature, pressure, and chemical composition, with a strong dependence on oxygen fugacity. These complexities clearly set iron apart from aluminum or alkali and alkaline earth elements which have been dealt with in the previous chapters. They make it useful to distinguish the compositions in which Fe2+ and Fe3+ predominate by the terms ferro- and ferrisilicates, respectively. The first studies of iron redox reactions were made by glass scientists as early as in the 1930s. In petrology, interest in the redox state of iron came later. It was raised by Kennedy [1948] who showed that the iron redox ratio could be used as an indicator of total volatile pressure. Then, following Fudali [1965], it became clear that the iron redox ratio of igneous rocks is a probe of redox conditions within the Earth. As a result, understanding how Fe3+/Fe2+ ratio is determined by intensive thermodynamic parameters has motivated numerous experimental studies. These have complemented determinations of the influence of iron content and redox state on density, viscosity, and other physical properties of melts. Before reviewing these features, a basic difference between oxidation and reduction reactions must be pointed out. When changes in an intensive property induce reduction, the reaction cannot be prevented because oxygen can eventually be released and form bubbles which separates from the melt. In contrast, oxidation cannot proceed without a source of oxygen. It follows that experimental control is easier for oxidation than for reduction reactions. This is why the kinetics and mechanisms of redox reactions have been mainly investigated for oxidation.

292

Chapter 10 Table 10.1. Ionic radii (A) for iron in 4- and 6-fold oxygen coordination IV Fe 2+ Fe 3+

0.71 0.57

VI (high spin) 0.69 0.63

VI (low spin) 0.86 0.73

10. Ferrous and Ferric Iron In this chapter, we will deal mostly with redox reactions between ferrous and ferric iron. Metallic iron will be paid little attention because its solubility in silicate melts is quite low. Under sufficiently reducing conditions, it precipitates and forms solid solutions of its own. Then, its main effect is to induce changes in the melt composition. As usually made, we will denote by XFe the total atomic Fe 2 + + Fe 3 + or the total wt % FeO + Fe 2 O 3 . In the literature, the iron redox ratio is expressed either as Fe 2+ /£Fe or Fe 3+ /£Fe. On an atomic or weight % basis, the latter definition will be used consistently in the following. Besides, we will use the notations "FeO" or "Fe 2 O 3 " to report total iron contents in the form of either Fe 2+ or Fe 3+ . 10.1a. Redox States In the metallic state, the 3d electronic shell of iron is partially filled so that the electronic configuration is As2 3d6. Without the two electrons of the outer 4s shell of Fe°, the configurations of Fe 2+ and Fe 3+ are 3d6 and 3d5, respectively. Because they are generally present in a high-spin state, both ions have a magnetic moment which make them very sensitive to their local environment in solid solutions [see Harrison and Becker, 2001]. The differing electronic configurations of Fe 2+ and Fe 3+ are associated with relatively small differences in ionic radii [Whittaker and Muntus, 1970, see Table 10.1]. Of special interest is the fact that the spin configuration and the oxygen coordination number itself exert a comparable influence on the ionic radius of both ions. It is this narrow range of radii that results in multiple structural states and makes diverse coupled substitutions with di, tri- and tetravalent cations possible. As a starting point to an analysis of redox reactions, consider the solid-state formation of wiistite (FeO) and hematite (Fe2O3) from metallic iron: Fe + 1/2 O 2 <=> FeO

(10.1)

2 Fe + 3/2 O 2 o Fe 2 O 3

(10.2)

From the mass action law and the reported Gibbs free energies of formation of the oxides [Robie et al, 1979], the oxygen fugacities (fo ) are readily calculated as a function of temperature for both equilibria (Fig. 10.1). One finds that high temperature induces iron reduction. This trend is a direct consequence of Le Chatelier's principle in that reduction

Iron-bearing Melts — I. Physical Properties

293

Figure 10.1 - Oxygen buffers: oxygen fugacity (in bar, as usually reported) for iron and nickel oxidation equilibria. Metals are stable at high temperature and low oxygen fugacity, oxides at low temperature and high oxygen fugacity. Calculations made with the data of Robie etal. [1979]. Data for nonstoichiometric wiistite.

implies production of gaseous oxygen, which causes a large entropy increase and, correlatively, a decrease of the Gibbs free energy of the Fe-0 system. In contrast to other major elements, for which a single valence has to be considered, iron has the peculiarity that two of its valence states are energetically similar. This similarity is evident in Fig. 10.1 when one compares the positions of the two oxidation reactions of Fe to that of Ni whose 2+ state is closely related to Fe 2+ (with which it forms a continuous solid solution). Hence, another important feature apparent in Fig. 10.1 is that slight variations of temperature or oxygen fugacity can induce definite changes in the iron redox ratio. A noteworthy consequence of the similar energetics of Fe 2+ and Fe 3+ in oxides is the nonstoichiometry of wiistite, a mineral whose actual formula is Fer_XO. As a matter of fact, wiistite has a defect rocksalt structure in which 1 - 3x Fe 2+ ions fit with vacancies and 2x Fe 3+ ions, the value of x (0.04 < x < 0.12) depending on synthesis conditions [see Hazen and Jeanloz, 1984]. Not only is the stoichiometric x - 1 value not reached below 10 GPa, but Fe 2+ occupies either octahedral sites or tetrahedral interstices of the structure. Wiistite, the simplest iron-bearing oxide compound, thus summarizes the complex structural and physical problems raised by the commonest transition element. 10.1b. Iron Coordination and Melt Polymerization Owing to the lack of long-range order, the relative proportions of Fe 2+ and Fe 3+ may vary to a much greater extent in melts than in crystals. According to the classic study of Darken and Gurry [1946], the redox ratio of pure molten iron oxide for instance varies from 0.08 to 0.75 around 1550°C between oxygen fugacities of 10"8 and 1 bar. Because of their diversity of chemical composition, silicate melts offer still greater possibilities for complex interactions of iron with either network-forming or network-modifying cations. The dual structural role of ferric iron will be described in the next chapter. As a network former, Fe 3+ is likely coordinated tetrahedrally with oxygen. Here, the important point is that it is produced in melts via the dissolution reaction Fe 2 O 3 + 02~ 2 FeO2".

(10.3)

294

Chapter 10

Figure 10.2 - Shift of the liquidus boundary of calcium silicates against the NBO/T of the melt whose variations result from changes in the proportions of Fe2+ and Fe3+. Plot drawn by My sen [1988] from the CaO-"Fe 2 O 3 "-SiO 2 phase diagram (see Fig. 10.7).

In contrast to its SiO2 counterpart, FeO2" bears a negative charge, due to the 3+ valence of iron, which must be compensated by another cation. As made by Al3+ in this role, Fe 3+ induces polymerization by consuming an oxygen ion. It differs from Al3+, however, in that it can also be, on its own, an octahedral network modifier, even when other cations could provide charge compensation for tetrahedral coordination. When produced by the reaction Fe 2 O 3 «=> 2 Fe 3+ + 3 O 2 \

(10.4)

Fe 3+ then induces depolymerization of the silicate network with the "free" oxygen that is released. In the acid-base terminology, Fe 2 O 3 is, therefore, an amphoteric oxide because it either releases oxygen ions (base) or reacts with them (acid). Although ferrous iron can also be in tetrahedral coordination under certain circumstances (see section 11.2a), only its more common role of network modifier will be considered in this section to write the dissociation reaction of FeO as FeO <=> Fe 2+ + O2~.

(10.5)

Depending on the structural state of Fe 3+ and total iron content, the iron redox reaction can thus affect melt polymerization to a large extent. In turn, all properties that depend on extent of polymerization are sensitive to the redox state of the melt. An example of how liquidus boundaries are affected by changes of the NBO/T due to iron redox variations is shown in Fig. 10.2. Upon addition of Fe 2+ , the liquidus boundary between larnite (CajSiO^ NBO/T = 4) and pseudowollastonite (CaSiO3, NBO/T = 2) shifts toward less polymerized compositions. Because the chemical composition of iron-bearing glasses and melts is intrinsically variable, an adequate characterization of the iron redox ratio is a necessity during phase-equilibria and physical-property experiments as well as a prerequisite to interpretations of these results. 10.1c Oxygen Fugacity For any melt, the temperature dependence of the redox reaction causes Fe 3+ /Fe 2+ to be the highest near the glass transition and the lowest at superliquidus temperatures. The changes in the relative abundances of ferrous and ferric iron are simply described by the reaction:

Iron-bearing Melts — I. Physical Properties 2 FeO + 1/2 O2 <=> Fe2O3.

295 (10.6)

At constant temperature and pressure, the equilibrium constant of this reaction depends on the activities of FeO and Fe2O3 in the melt, which are both complex functions of composition, and especially of oxygen fugacity. In experimental studies, care is thus taken to achieve equilibrium under well-defined redox conditions. In general, oxygen fugacities are controlled with buffers [see Huebner, 1971; Myers and Eugster, 1983; O'Neill and Pownceby, 1993]. In a system where Ni and NiO coexist (NNO buffer), for example, the/ 0 is fixed and given by the value shown in Fig. 10.1 for the temperature of interest. The same applies to the coexistence of iron and wiistite (IW buffer), of magnetite (Fe3O4) and hematite (MH buffer), or of quartz, fayalite (Fe2Si04) and magnetite (QFM buffer). At low pressure, however, there is no need for these solid phases to be physically present in the system. The oxygen fugacities of a given buffer can be reproduced through equilibration, at the temperature of the experiment, of the right proportions of gases (CO and CO2, or H2 and H2O) that make up the experimental atmosphere. In this case, redox conditions nevertheless remain frequently referred to such buffers. Because the/ 0 -temperature relationships of different buffers have similar slopes (Fig. 10.1), this is a simple means of using a relative redox scale that depends little on temperature. In iron redox studies, particular attention must be paid to possible interactions between the melt and its container. An oxygen buffer approaching iron-wiistite conditions is realized when an iron crucible is used [Bowen and Schairer, 1932; Thornber and Huebner, 1982]. The oxygen fugacity is not determined only by temperature, however, because the activity of FeO in the melt depends on chemical composition and also because that of Fe in the metal can be affected by impurity content. Platinum is the most inert material for containing liquid silicates, but it has long been known that it forms a continuous solid solution with Fe under reducing conditions [Isaac and Tamman, 1907]. Alloying between these two metals causes equilibrium (10.1) in the melt to be displaced to the left and oxygen to be lost. The resulting changes in chemical composition can be significant [Bowen and Schairer, 1932]. They can be minimized through saturation of Pt with iron in preliminary experiments [e.g., Darken and Gurry, 1946] or the use of FePt alloys instead of pure platinum [Presnall and Brenner, 1974; Grove, 1981]. Alternatively, platinum can exert an oxidizing influence on iron. The effect has been described for alkali silicates with more than 70 mol % SiO2 by Paul and Douglas [1965] who assigned it to the reaction 1/4 Pt4+ + Fe2+ <=> 1/4 Pt + Fe3+,

(10.7)

which invokes initial formation of platinum oxide (PtO2). Finally, note that the concept of oxygen fugacity takes a different meaning in experimental studies, on the one hand, and in natural or industrial processes on the other.

296

Chapter 10

In the latter cases, equilibrium between a melt and a gaseous phase is generally irrelevant. Either heterogeneous redox reactions are too sluggish or, more simply, a gaseous phase is lacking. Then, the redox state of a system is entirely determined by its own chemical composition and the temperature and pressure of interest. An oxygen fugacity can nonetheless be defined. Without making reference to an actual gaseous phase, it just represents a convenient parameter to specify the redox state of the system. As noted by Fudali [1965], this is why the term "fugacity" is to be preferred over "partial pressure" although both are numerically equivalent at the low values appropriate for redox reactions of practical interest. An important example is that of industrial glasses whose oxygen fugacity is determined by the starting materials and added fining agents like sulphates, but not by the furnace atmosphere with which equilibration would be much too slow. 10. Id Analysis of Redox Ratio Description of experimental methods is beyond the scope of this book, but some details are in order for iron redox analyses because proper interpretation of the results reviewed in this chapter depend directly on accurate determination of ferrous and ferric iron contents. Wet chemical analysis has been the only available method for a long time. With the standard procedure reported by Wilson [1960], the concentrations of total iron and Fe2+ are derived from titrations made with a potassium dichromate solution after about 500 mg of glass has been dissolved in HF and in HF + H2SO4 solutions, respectively. Uncertainties of ± 0.02 on Fe3+/£Fe are usually reported. Since the Fe3+ concentration is given by the difference between these two figures, the relative errors are higher for oxidized samples. Alternatively, iron redox ratios can be determined by Mossbauer spectroscopy because glass structure is sufficiently rigid to allow recoiless absorption of gamma photons by 57Fe nuclei [see Kurkjian, 1970; Bancroft, 1973]. As resonant absorption takes place at different energies for Fe2+ and Fe3+, the relative abundances of the two cations are determined from the areas of the two peaks that form a broad doublet in the spectra (see Chapter 11). These areas are strictly proportional to concentrations only at cryogenic temperatures, but proper calibration allows measurements to be performed under ambient conditions [see Alberto et al., 1996]. The method has several advantages over wet chemical methods. It is nondestructive, less time consuming, requires smaller samples of about 50-100 mg with standard techniques, and can sometimes be used at the scale of 100 \im [McCammon, 1994]. In addition, Mossbauer spectroscopy provides direct structural information because the hyperfine parameters of both ferrous and ferric iron depend on oxygen coordination and geometry of coordination polyhedra. Comparisons made by Mysen et al. [1985a] and Dingwell [1991] between Mossbauer and wet chemical analyses performed on the same samples do not reveal systematic differences (Fig. 10.3). The precision of redox ratios derived from both methods is similar. This is especially true when new fitting procedures are applied to Mossbauer spectra which, furthermore, yield more detailed structural information [Alberto et al., 1996]. According to Lange and Carmichael [1989] and Ottonello et al. [2001], Mossbauer spectroscopy would underestimate Fe3+/Fe2+ for total iron oxide content higher than 14 wt %. Such an

Iron-bearing Melts — I. Physical Properties

297

Figure 10.3 - Comparison between redox ratios determined from Mossbauer spectroscopy experiments and wet chemical analyses; open circles: Mysen et al. [1985a]; solid circles: Dingwell [1991], The combined error margins of the measurements are shown as ovals around the data points.

effect is not demonstrated by the results of both techniques when their differences are plotted against XFe (Fig. 10.4). More important, the existence of systematic bias has not been confirmed by further analyses [Partzch et al., 2004], in accordance with the fact that there is no practical or theoretical reasons why Mossbauer analyses would be become unreliable at high iron contents [see also Jayasuriya et al., 2004]. Redox ratios can be determined on still smaller samples from the pre-edge feature of x-ray absorption spectra, which is sensitive to the redox state and local environment of iron [Waychunas et al, 1983]. The errors of about ± 0.05 on Fe 3+ /Fe 2+ are a little higher than with other methods. These x-ray absorption near edge structure (XANES) experiments have the important advantages of being very rapid and feasible at high temperatures so as to make in situ kinetic studies possible [Berry et al., 2003; Magnien et al, 2004]. A related technique is electron energy-loss spectroscopy (EELS), which is practiced in a transmission electron microscope at room temperature. This method used for minerals [e.g., Garvie and Buseck, 1994] could be also applied to glasses. Electron microprobe analyses must also be mentioned in view of their widespread use. Only total iron is usually reported in the form of FeO. For minerals, the iron redox state of minerals is determined from stoichiometry considerations [Droop, 1987], but such methods are not valid for glasses. Recent work has largely overcome the analytical

Figure 10.4 - Difference between redox ratios determined from Mossbauer and wet chemical analyses against total iron, expressed as Fe2O3. Same symbols and data sources as in Fig. 10.2.

298

Chapter 10

problems caused by very small differences in the x-ray wavelengths of the La peaks of Fe2+ and Fe3+, and also by rapid iron redox changes under the electron beam. As a result, the abundances of both valences can be determined directly with errors of about 5% [Fi&lin et al., 2004]. Finally, a few words must be devoted to electrochemical methods. High-temperature linear- and square-wave voltammetry are the most common, differing by the shape of the current pulse used [see Sasahira and Yokokawa, 1984; Gerlach et al., 1998; Medlin et al, 1998]. With reference to an oxygen electrode, the reduction potential of an element is determined from the observed current vs. tension relationship. These measurements can be made difficult by electrode corrosion and background corrections. They do not give redox ratios directly, but yield the enthalpy and entropy of the redox reaction when standard potentials are measured as a function of temperature. In addition, the potentials of the various valences can be measured in the same experiment for a multivalent element. Another advantage is that ion diffusion coefficients can also be estimated from the peak height of the current signal [Clausen et al, 1999; Wiedenroth and Riissel, 2003]. 10.2. Phase Equilibria 10.2a. Ferrosilicate Phase Relations The "FeO"-SiO2 phase diagram illustrates the actual ternary nature of binary iron-bearing melts (Fig. 10.5). The increase of the redox ratio with increasing iron content is a purely chemical effect: everything being equal, the opposite variation would be produced by the concomitant rise of liquidus temperatures. At temperatures sufficiently high for iron to be essentially ferrous, a large stable miscibility gap is observed in the SiO2-rich part of the FeO-SiO2 diagram. This gap is similar to those observed for binary alkaline earth silicates (compare with Fig. 6.1). Likewise, a eutectic is observed at a higher SiO2 content, which is similar to those of alkaline earth systems. As to the deeper freezing-point depression apparent in Fig. 10.5, it simply results from the much lower melting point of FeO (1339°C) compared to those of CaO or MgO, which are both higher than 2500°C.

Figure 10.5 - Phase diagram of the "FeO"SiO2 system [Greig, 1927a; Bowen and Schairer, 1932]. (a) Atomic redox ratio of charges quenched from the liquidus in the experiments made on Fe-rich melts, (b) Liquidus relationships determined for melts heated in iron crucibles under a nitrogen atmosphere. Cr: cristobalite and Tr: tridymite (SiO2); Fa: fayalite (Fe2SiO4); L: liquid; Wu: wustite.

Iron-bearing Melts — I. Physical Properties

299

Figure 10.6. Phase diagrams of ternary ferrosilicates redrawn on a mol % oxide basis. Fields of liquid immiscibility and glass formation (from the reported isofracts) indicated by hachured and grey areas, respectively. Abbreviations: A: A12O3; F: FeO; K: K2O; S: SiO2; Fa: Fayalite (Fe2Si04); Fo: Forsterite (Mg2Si04); Fs: Ferrosillite (Fe2Si03); En: Enstatite (MgSiO3); He: Hercynite (FeAl2O4); La: larnite (Ca2Si04); Mu: mullite (3Al2O3«2SiO2). Data from Schairer et al. [1954] for the system NFS, Roedder [1952] for KFS, Levin et al. [1964] for CFS and MFS, and Schairer andYagi [1952] for AFS. This kinship of Fe 2+ with alkaline earth cations is borne out by the phase diagrams of ternary system (Fig. 10.6). As indicated by the continuous (Fe,Mg) solid solutions of magnesiowiistite, olivine and pyroxene, the similarity is greatest with Mg 2+ . In the "FeO"MgO-SiO 2 system, the only liquidus phases are these three mineral solutions. The liquidus temperatures are generally high except in theFeO-rich part of the system. Along with the incongruent melting of ferrosillite (FeSiO 3 ), this trend points to weaker bonding in structures that could also be weakened by the presence of some Fe 3+ . The glass-forming ability is poor throughout most of the Mg system.

300

Chapter 10

The CaO-"FeO"-SiO 2 phase diagram is more complicated (Fig. 10.6). The inadequate match between the ionic radii of Ca 2+ and Fe 2+ is exemplified by the lack of continuous solid Ca,Fe solutions in the pyroxene and olivine structures [e.g., Bowen et al., 1933]. Liquidus temperatures remain high, however, with the exception of the valley that runs from CaSiO 3 to FeSiO 3 . Like for Mg, there is no new ternary compound. When liquidus temperatures are low, glasses can be prepared only via rapid quenching of small charges. Liquidus temperatures are markedly lower for alkali than for alkaline earth ferrosilicates. The phase relations are known for the "FeO"-K 2 O-SiO 2 system [Roedder, 1952] where two ternary compounds exist and vitrification takes place over a wide composition range. Phase relations are less well known for the "FeO"-Na 2 O-SiO 2 system. According to Schairer et al. [1954], the Fe 2 O 3 contents of melts on the liquidus are less than 2.5 wt %. The existence of at least one ternary compound was described by these authors. No phase was identified, however, and the stability field of this (these) phases does not encompass the composition Na 2 FeSi0 4 of the compound reported by Carter and Ibrahim [1952]. In both Na and K systems, vitrification is not too difficult as judged by the rather wide composition ranges where the index of refraction of glasses were measured. Schairer et al. [1954] pointed out that there are clear analogies between the topologies of the MgO-Na 2 O-SiO 2 and "FeO"-Na 2 O-SiO 2 phase diagrams. This similarity, which also exist with the "FeO"-K 2 O-SiO 2 diagram, applies in particular to liquid unmixing, which rapidly becomes metastable when Na 2 O and K2O are added to FeO-SiO 2 melts. Another similarity exists between the "FeO"-Al 2 O 3 -SiO 2 and MgO-Al 2 O 3 -SiO 2 phase relations (compare Fig. 10.6 with Fig. 8.3). In the former, the single ternary compound, Fe 2 Al 4 Si 5 O lg , has the same stoichiometry as cordierite with which it forms a solid solution. These observations thus confirm the conclusion drawn at the beginning of this section from the "FeO"-MgO-SiO 2 system, namely, that Fe 2+ is a weak analog of Mg 2+ . 10.2b. Ferrisilicate Phase Relations Phase relations under oxidizing condition have been less extensively studied (Fig. 10.7). In view of the wealth of information gathered for aluminosilicates (Chapters 8-9), an important question is the relative kinship of Fe 3+ and Al 3+ . With respect to physical properties, attention must, in particular, be paid to the influence of possible association of iron with a charge-compensating cation. In analogy with aluminosilicates, the metaferric join will designate the SiO 2 -M 2/x FeO 2 compositions where the metal cation M might charge compensate all Fe 3+ in tetrahedral coordination. If bond strength were dependent only on charge and ionic radius, one would expect bonding with oxygen to be weaker for Fe 3+ (r = 0.57 A) than for Al 3+ (r = 0.47 A). Actually, weaker bonding in Fe 2 O 3 compared to A12O3 manifests itself by the fact that, when heated in air, hematite decomposes to oxygen and an Fe 2 O 3 -Fe 3 O 4 solid solution well before reaching its congruent melting point which should be about 1895 K [see Muan and Osborn, 1965]. This feature translates into ternary systems. The phase diagrams of Fig. 10.7 indeed share the common trait that liquidus temperatures are systematically lower for ferri- than for aluminosilicates.

Iron-bearing Melts — I. Physical Properties

301

Figure 10.7 - Phase diagrams of ternary ferrisilicates redrawn on a mol % oxide basis. The fields of liquid immiscibility and glass formation (from the reported isofracts) are indicated by the hachured and grey areas, respectively. Abbreviations: F: Fe2O3; K: K2O; N: Na2O; S: SiO2; Acm: acmite (NaFeSi2O6); La: larnite (Ca2Si04); PsWo: pseudowollastonite (CaSiO3). Data from Bowen etal [1930] for the system NFS, Faust [1936] and Faust and Peck [1938] for KFS, and Levin et al. [1964] for CFS. The system "Fe 2 O 3 "-SiO 2 would be an obvious starting point but its melting relations cannot be investigated because significant iron reduction cannot be prevented at high temperatures. From extrapolation of data in ternary systems, Bowen et al. [1930] could nevertheless assert that binary SiO 2 -Fe 2 O 3 compounds do not exist. From these and other results by Greig [1927], they also concluded that the SiO 2 -Fe 2 O 3 eutectic should be very close to SiO 2 because of the existence of a large stable miscibility gap between the two molten oxides. It appears, therefore, that Fe 3+ substitutes much less readily for Si4+ than Al3+. For calcium systems, another difference with aluminosilicates is the number of mixed compounds. There are three along the join CaO-Fe 2 O 3 , compared to five along the CaOA12O3 join, and no ternary compound against the two calcium aluminosilicates anorthite and gehlenite (Fig. 8.3). Although there is definite affinity between CaO and Fe 2 O 3 , no clear specific association is induced by the presence of SiO 2 . Another significant feature is the similar trends seen in the FeO-poor parts of the Ca diagrams of Figs. 10.5 and 10.6. This could reflect the fact that, at temperatures of about 1400°C, the actual iron redox ratios in ferro- and ferrisilicates differ less than indicated by the nominal melt compositions. The difference with aluminosilicates is even clearer for sodium ferrisilicates. Four compounds have been described by Bowen et al. [1930], although only two, acmite (NaFeSi 2 O 6 , also named aegirine) and (Na2O)5«F2O3»(SiO2)8, have been adequately

302

Chapter 10

Figure 10.8. Silica-rich part of the phase diagram of the system Na 04 Si 08 Oj 8 -"Fe 2 O 3 " [Bowen and Schairer, 1929]. Acm: acmite (NaFeSi2O6); Hem: hematite (Fe3O4); L: liquid; Q: quartz and Tr: tridymite (SiO2). Similar liquidus relationships are observed for the sodium disilicate-acmite system, with a eutectic point at 810°C and 4.2 mol % Fe2O3 [Bowen etal., 1930].

identified. None of these compounds suggests an association between Na + and Fe 3+ of a strength comparable to that of Na+ with Al 3+ . Acmite, in particular, has a pyroxene structure with Fe in octahedral coordination. In this respect, the variations of liquidus temperatures between acmite and the Na 2 Si 4 0 9 composition (Fig. 10.8) differ considerably from those of the analogous aluminosilicate systems (Fig. 8.4). Although the eutectic compositions and temperatures are similar in both kinds of systems, acmite itself melts incongruently to hematite plus liquid at the low temperature of 1000°C. The available information is incomplete for potassium ferrisilicates. The important feature of the "Fe 2 O 3 "-K 2 O-SiO 2 system is the existence of three compounds that have the same stoichiometry as K-feldspar, leucite, and kalsilite [Faust, 1936] and, thus, lie on the meta-ferric join. Here, clear evidence for alkali charge compensation is provided by the existence of these compounds along with the limited solid solutions they form with their aluminosilicate counterparts. Finally, Na and K ferrisilicates share two common points. Owing to low liquidus temperatures, melts heated in air just above the liquidus have very low Fe 2+ contents in both systems. In addition, the area of glass formation is rather large. As pointed out in previous chapters, these areas correlate with the compositions of the compounds that crystallize from the melt. From this brief review of solid-liquid equilibria, it appears that the strength of the association with network-modifying cations varies in the same order for Fe 3+ and Al 3+ . Although association is strongest with potassium, lower liquidus temperatures and decomposition or incongruent melting indicate that Fe 3+ is at most a weak analog of Al 3+ . 10.2c. Phase Relations in Complex Systems As described for alkaline earth silicate systems in section 8.1a, the high-temperature miscibility gaps of iron-bearing systems (Fig. 10.5-10.7) disappear rapidly upon addition of alumina or alkali oxides. Following Greig's [1927b] work, it was widely thought, for this reason, that liquid immiscibility could not be relevant to the composition range of igneous rocks. That liquid unmixing is nevertheless of interest was pointed out by Roedder

Iron-bearing Melts — I. Physical Properties

303

Figure 10.9 - Schematic liquid unmixing (in grey) and phase boundaries in the system leucite (KAlSi2O6) - fayalite (Fe2SiO4) silica [Roedder, 1951, 1978]. The solid line within the ternary miscibility gap represents the 1180°C isotherm. Melts heated in iron crucible under an N2 pressure of 1 atm.

[1951] who discovered a rather large field of liquid unmixing in the system Fe2Si04KAlSi2O6-SiO2, i.e., in the high-silica corner of the "FeO"-K2O-Al2O3-SiO2 system (Fig. 10.9). Under reducing conditions, the gap occurs at temperatures between 1100 and 1270°C for compositions whose alkali content is higher than 16 wt %. This gap owes its importance to the fact that it subsists in more complex chemical compositions such as tholeiitic basalts [Roeder, 1978; Philpotts and Doyle, 1983]. The size of the miscibility gap shrinks with increasing pressure and could vanish near 1.5 GPa [Nakamura, 1974], an effect of pressure well described for the MgO-SiO2 system [Dalton and Presnall, 1997]. Conversely, the gap expands with increasing total iron content and oxygen fugacity [Naslund, 1983]. In these situations, Fe3+ thus enhances liquid immiscibility. Unmixing also develops upon addition of TiO2 and P2O5, two oxides which generally foster phase separation in silicate melts (see Chapters 12 and 13). According to the discussion of section 6. lb, miscibility gaps originate in steric hindrance problems experienced by network-modifying cations when bonding to nonbridging oxygens in strongly polymerized melts. Through its association with network-modifiers and the ensuing network polymerization, Al3+ causes unmixing to disappear. That Fe3+ does not is a clear evidence for a different structural role. Contrary to what might be assumed, however, the presence of iron is not a prerequisite for liquid unmixing to occur in complex systems. An analogous effect has, for instance, been described by Kingery et al. [1983] for the system CaO-K2O-Al2O3-SiO2. The main difference is that unmixing is metastable, and not stable as observed for the gap of Fig. 10.9. In these systems, iron ions thus seem more effective than Ca2+ to induce phase separation. The strong influence of the iron redox state on ternary phase equilibria translates to more complex systems. Osborn [1959], for instance, emphasized that crystallization paths depend markedly on whether or not iron participates in olivine, pyroxene and magnetite solid solutions. Although crystallization and melting paths can be complicated in multicomponent systems, they can be determined from equilibrium phase relations. By contrast, the effects of iron redox on the kinetics of crystal nucleation and growth in melts are less predictable.

304

Chapter 10

Regardless of the chemical complexity of a melt, crystallization is enhanced under oxidizing conditions. Rogers and Williamson [1969] found that Fe3+ acts as a nucleating agent in CaO-MgO-Al2O3-SiO2 glasses. This observation was also made by Cukierman and Uhlmann [1974] for an Fe-rich lunar composition. Beall and Rittler [1976] even claimed that oxidation of iron is the main factor controlling crystallization of basalt. Crystallization is fast only for oxidized samples, magnetite forming first between 650 and 700°C, followed by pyroxene which nucleates on magnetite nuclei and grows between 750 and 900°C. Similar results have been reported by Karamanov and Pelino [2001] for various glasses with SiO2 contents ranging from 4 to 72 wt %, and by Bouhifd et al. [2004] for another basalt. The effect might be related to weakening of the silicate network by tetrahedral Fe3+. Surprisingly, however, the Fe 3+ concentration can be much lower in the nucleating spinel than in the melt itself [Rogers and Williamson, 1969; Bouhifd etal., 2004]. Interestingly, Jurado-Egea etal. [1987] related magnetite crystallization to electronic conduction, but more work is needed to picture consistently nucleation and growth in ironbearing systems along with the mechanisms of redox reactions described below. 10.3. Iron Redox Reactions The basic features of redox reactions have been deciphered in the 1960s through experiments made mostly on alkali silicate melts. With proper adjustment for differing valence states, the phenomenology described below for iron applies to other multivalent elements that are important for practical applications (Mn, Ti, Cr, As, etc.) or for tracing geochemical processes (Eu, Ce, etc.). More recently, systematic measurements on a variety of model melts have aimed at determining the variations of the iron redox ratio over wide ranges of temperature, pressure, oxygen fugacity and chemical composition. 10.3a. Effects of Temperature and Oxygen Fugacity When written as equation (10.6), the iron redox reaction does not lend itself to ready thermodynamic or structural interpretations because the activities of both FeO and Fe2O3 are generally known only for limited composition ranges. In terms of ionic species, a more detailed representation of the redox reaction is provided by the equations Fe 2+ + 1/4 O2 <=> Fe 3+ + 1/2 O 2 \

(10.8)

Km = (aFei+/a¥e2+) (aO2-)y2/fO2l'\

(10.9)

where K3/2, the equilibrium constant of the reaction, is determined by oxygen fugacity and the activities (a) of iron and oxygen ions. The activities are replaced by concentrations if the silicate solution is assumed thermodynamically ideal. If the activity of the oxygen ion can further be assumed not to depend on the iron redox state, then a plot of log Fe /Fe against -log/ o at constant temperature should have a slope 1/4. For iron at small concentration in sodium disilicate melt (Fig. 10.10), the existing data refer to a wide range of oxygen fugacities achieved with air, CO-CO2, and H2-H2O

Iron-bearing Melts — I. Physical Properties

305

Figure 10.10 - Iron redox equilibrium at 1100°C for Na 2 Si 2 0 5 (NS 2 ) with 2.5 wt % Fe 2 O 3 [Johnston, 1964]. The slope of the solid line is 0.239 (2); the open circles indicate the conditions for metallic iron saturation at the temperatures indicated. For comparison, a slope of 0.245 (4) is shown at 1409°C for the diopside-anorthite eutectic composition (DiAn) with 1 wt % Fe2O3 [Jayasuriya et ai, 2004].

atmospheres [Johnston, 1964]. Between l o g / o = -0.7 (air) and -13, the experimental slope differs little from the expected 0.25 value. Similar results are shown in Fig. 10.10 for an aluminosilicate melt. In both cases, the assumed constancy of the oxygen ion activity is justified by the dilute nature of the iron solution, whereas the ratio of the activity coefficients of iron ions should differ less from unity than the individual coefficients. The errors due to both assumptions cannot be separated, but the differences of the slopes of Fig. 10.10 with the 0.25 nominal value are insignificant. For concentrated iron solutions, a mean value of 0.207 (7) has in contrast been reported [e.g., Kress and Carmichael, 1988]. Such a value represents an apparently simple means to account for the actual nonideality of the melt. As will mentioned below, however, this procedure refers to specific iron contents and other particular experimental conditions. As such, it is problematic because it prevents the limiting case of dilute iron concentrations, for which a slope of 0.25 does obtain, from being correctly accounted for. Another important point shown by the NS 2 data in Fig. 10.10 is the constancy of Fe 3+ /Fe 2+ at very l o w / o . This feature signals precipitation of iron metal [Johnston, 1964]. Saturation is attained at higher oxygen fugacity and lower redox ratio when the temperature increases. It can be described in terms of dismutation of ferrous iron according to: 3 Fe 2+ o Fe° + 2 Fe 3+ , 9

^2/03

=

•>

(aFe3+) A«Fe2+) •

(10.10) (10.11)

When the oxygen fugacity has become sufficiently low for iron to precipitate, the simplest manner for K2/03 to remain constant is that the redox ratio of the melt also remains constant. This constancy is borne out by the iron saturation data, which provide another justification for the use of concentration ratios in place of activity ratios for iron ions in equations (10.5) and (10.7). The Fe 3+ /Fe 2+ ratio at which Fe° precipitates is low, near 0.1 in Fig. 10.10, but such that the concentration of Fe 3+ remains significant. It is, in fact, a general observation that the three redox states of iron coexist in a system under highly reduced conditions (e.g., Fig. 10.5a). Another conclusion drawn from Fig. 10.10 is that solubility in the melt is lower for Fe 2+ than for Fe 3+ . This feature is also general and points to association of alkali cations with Fe 3+ , but not with Fe 2+ .

306

Chapter 10

Figure 10.11 - Temperature dependence of the iron redox ratio in air. Data of Johnston [1964] for the sodium disilicate of Fig. 10.4 in either platinum (open circles) or alumina (solid circles) crucibles, with more than 15 wt % A12O3 contamination in the latter case. NAS [Mysen and Virgo, 1989] and CAS [Mysen et ai, 1985c] are Na and Ca aluminosilicates with 5 wt % Fe2O3. The results of Baak and Hornyak [1961] for 2.9 wt % Fe2O3 in NS2 (B&H) illustrate departure from equilibrium at lower temperatures when run duration is too short.

Over temperature intervals of a few hundred degrees, the Fe 3+ /Fe 2+ ratio varies linearly with reciprocal temperature (Fig. 10.11). The enthalpy of the iron redox reaction is readily determined from these plots with the Van't Hoff relation. It is exothermic, as expected for an oxidation reaction, and varies with composition. In Fig. 10.11, the slope of the linear relationship is for example twice as high for CAS than for NAS. Other results for calcium and sodium aluminosilicate melts [Mysen etal., 1985c; Mysen and Virgo, 1989] indicate that such differences are systematic. 10.3b. Oxygen Activity and Glass Basicity Measurements on binary alkali melts have long been made to determine the influence of melt basicity on redox ratios of multivalent elements. For low values of XFe, one observes that log Fe 3+ /Fe 2+ is a linear function of SiO 2 content (Fig. 10.12). At the same silica content, iron is more oxidized in the order K, Na, Li. Because the linear relationships converge toward pure SiO 2 , they become less steep in the same order K, Na, Li. The redox reaction (10.8) should provide a simple means to interpret these effects of chemical composition on the redox state of a multivalent element. With the assumption of an ideal solution, Paul and Douglas [1965] wrote the equilibrium condition for reaction (10.9) as log (Fe3+/Fe2+) = log Km + 1/4 log fo - 1/2 log aQ2- = A - 1/2 log aoi-,

(10.12)

where A is a constant if the oxygen fugacity is constant. Other things being equal, this equation indicates that the redox ratio should decrease with increasing oxygen activity and, thus, with increasing melt basicity and alkali oxide content (see section 6.2d). For a given alkali element, the experimental results clearly contradict this prediction (Fig. 10.12). According to equation (10.12), the trends of Fig. 10.12 would then suggest that melt basicity increases in the order K, Na, Li for a given SiO 2 content. This prediction has been checked against experimental data. The basicity can be

Iron-bearing Melts — I. Physical Properties

307

Figure 10.12. Iron redox ratio of alkali silicate melts at 1400°C in air against SiO2 concentration [Paul and Douglas, 1965]. Total iron content of 0.41 wt %.

determined by various methods such as e.m.f. measurements or determinations of CO 2 solubility (from the equilibrium constant of the solution reaction CO 2 + O2" <=> CO32"). The results obtained in these different ways are not necessarily in quantitative agreement, but the trends are mutually consistent [Douglas et al., 1965]. For alkali systems, they indicate that melt basicity increases in the order Li, Na, K, a trend which is opposite to that expected from the redox data. Douglas et al. [1965] invoked variations of aO2- with composition to account for this failure. More specifically, Holmquist [1966] pointed out that the amphoteric nature of Fe 2 O 3 prevented the change in the activity of the oxygen ion from being estimated if the coordination of Fe 3+ were not known, see equations (10.3)-(10.5). In addition, Jeddeloh [1984] noted that equation (10.12) suffers from loosely defined standard states for the ionic species involved. When writing equation (10.9), the two kinds of oxygen ions that bond with Fe 2+ and Fe 3+ are implicitly assumed to be the same. But their standard states cannot be considered identical because pure FeO and Fe 2 O 3 liquids are of course not equivalent either structurally or energetically. When this assumption is denied explicitly, the equilibrium constant KV2 is written as: Ky2 = (a Fe3+ /a Fe 2 + ) [(aOn2-)/(aOm2.)m]fo2m,

(10.13)

where the indices II and III refer to oxygen ions bonding to Fe 2+ and Fe 3+ , respectively. Hence, relating redox ratio to average melt basicity is much less straightforward than suggested by equation (10.12). As an additional practical difficulty, standard state thermochemical calculations involving Fe 2 O 3 suffer from the high-temperature decomposition of hematite which hampers direct determinations of the melting properties of this oxide. The enthalpy and entropy of fusion of hematite recently estimated by Sugawara and Akaogi [2004] should thus prove useful in this respect. 10.3c. Composition Dependence of Iron Redox State Relative variations of the proportions of all oxides can induce changes in redox ratio at constant temperature, pressure and oxygen fugacity. Because analyses have been made on glasses, the redox state should depend on fictive temperature and, thus, on quenching rate. Significant effects of quenching rate have not been detected either on redox ratio or structural

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Figure 10.13 - Effect of total iron content on redox ratio, (a) In air, for a window glass (WG: 75 wt% SiO2, 10 CaO, 15 Na2O) melted in air at 1400°C in Pt crucibles [Densem and Turner, 1938] and for calcium metasilicate (CS) heated at 1725°C in a Pt loop [Mysen et al. 1984]. In the inset, data of Densem and Turner [1938] at very low iron content, (b) For the eutectic composition of the system CaAl2Si2O8-CaMgSi2O6 heated at the log / Oi indicated [Jayasuriya et al, 2004]. state of iron ions [Dyar and Birnie, 1984;Dyaretal., 1987].The range of fictive temperatures experimentally accessible was likely too narrow and the kinetics of the redox reaction too sluggish for changes in the redox ratio to occur during the quench. In experimental studies, a practical problem is that the redox ratio of a glass can differ markedly from that of its parent melt if partial crystallization takes place during the quench [Bowen and Schairer, 1932]. Along with decreasing precision of the analyses, an apparent decrease from 6 to 2 wt % of the Fe 2+ content of a calcium ferrosilicate glass was observed by Kress and Carmichael [1989]. Both effects were perhaps due to preferential partitioning of Fe 2+ into the quench crystals and, then, to lack of dissolution of these crystals during the wet chemical analyses. In other words, determinations of redox ratios have been restricted to liquids that could be quenched, often in small amounts, which introduces bias as to the composition ranges investigated. For example, data are more extensive for the system CaO-"FeO"-SiO 2 [Mysen et al, 1984; Kress and Carmichael, 1989] than for MgO-"FeO"-SiO 2 compositions [Mysen and Virgo, 1989]. The first composition effect to be examined is that of total iron content. In the "FeO"SiO 2 system, a 5-fold increase of Fe 3+ /ZFe ratio has been observed by Bowen and Schairer [1932] between 60 and 100 mol % "FeO" (see Fig. 10.5). According to other early experiments by Densem and Turner [1938] on a window glass composition, the redox ratio is a complex function of total iron at very low iron concentration before levelling off to a constant value above 2 wt % Fe 2 O 3 (Fig. 10.13a). Curiously, however, this effect does not seem to have been reinvestigated for any melt composition. For higher iron contents, an initial increase of the Fe 3+ /Fe 2+ ratio has also been observed for sodium disilicate [Larson and Chipman, 1953], Li, Na and K silicates with 70 mol % SiO 2 [Paul and Douglas, 1965], sodium borosilicates [Dunne? al, 1978], sodium silicates [Lange and Carmichael, 1989], and calcium silicates [Mysen et al, 1984]. For potassium

Iron-bearing Melts — I. Physical Properties

309

Figure 10.14 - Iron redox ratio against the ionization potential of the cation in alkali trisilicates with 0.4 wt % in air at 1400°C [Paul and Douglas, 1965] and in alkaline earth metasilicate melts with 5 wt % Fe2O3 heated in air at 1550°C [Mysen et al, 1984]. For Mg, the sample composition is slightly off the MgSiO3 stoichiometry.

silicates, in contrast, the redox ratio generally decreases [Tangeman et al., 2001], whereas Goldman [1983] did not observe any dependence on £Fe for two industrial borosilicate compositions to which from 0.09 to 0.5 wt % Fe 2 O 3 was added. The effect of iron content should also depend on oxygen fugacity, as shown by the data of Jayasuriya et al. [2004] for an aluminosilicate melt (Fig. 10.13b). In this case, the stronger dependence of the redox ratio on total iron content observed under reducing conditions points to the asymmetric nature of the interaction between Fe 3+ and Fe 2+ . Because of the aforementioned constraint of glass formation, available measurements in binary systems are the most abundant for alkali silicates. They indicate that the Fe3+/Fe2+ ratio decreases with increasing SiO 2 content (Fig. 10.12). As already concluded in section 10.2c from liquid immiscibility data, this transformation of ferric into ferrous iron does not conform to the trend expected if Fe 3+ were substituting for Si 4+ . In this were the case, the opposite transformation would represent a simple way to solve the steric hindrance problems raised by bonding of metal cations with non-bridging oxygens. For sodium silicates, the linear relationship of Fig. 10.12 has been doubted by Schreiber et al. [1994] who reported instead a maximum of log Fe 3+ /Fe 2+ near 45 mol % NajO. But the data for ternary systems mentioned below do support the linear trends established by Paul and Douglas [1965]. For a given stoichiometry, these results indicate that the redox ratio increases in the order Li, Na, K. There is, in fact, a clear correlation between the redox state and the ionization potential of the metal cation (Fig. 10.14). Interestingly, available data for alkaline earth obey the same relationship. The unicity of the correlation is probably coincidental in view of differing temperature and total iron contents in both series of experiments. Everything else being equal, it remains that the presence of cations with a low ionization potential favors the ferric state of iron. From the results discussed for Al in previous chapters, one can account for this effect in terms of more efficient charge compensation of Fe 3+ in tetrahedral sites by such cations. This disimilarity between alkalis and alkaline earths is reflected in the lines of constant redox ratios determined by Kress and Carmichael [1989] and Lange and Carmichael [1989] for the calcium and sodium systems, respectively (Fig. 10.15). In the former, the redox state is essentially determined by the Ca/Si ratio, with little influence of total iron content (except, as shown in Fig. 10.12, at very low Fe concentration). In the latter, increasing the Fe content at constant Na/Si results in a more oxidized state. Extensive measurements

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Figure 10.15. Contours of equal Fe3+/Fe2+ ratios in the systems CaO-"FeO"-SiO2 and Na2O-"FeO"-SiO2 as drawn by Kress and Carmichael [1989] from their data and those of Lange and Carmichael [1989]. These trends are consistent with the results of My sen et al. [1985c] for Ca and those of My sen and Virgo [1989] for Na systems. have also been made for the K 2 O-"Fe 2 O 3 "-SiO 2 system [Tangeman et al, 2001]. A more complex composition dependence is observed in that increasing K2O content causes the redox ratio to decrease in peralkaline melts. These effects determined in simple compositions are also observed in more complicated systems. In basaltic and other complex melts, the oxidizing power of cations increases in the order Ca, Na, K [Thornber et al, 1980; Kilinc et al, 1983; Dickenson and Hess, 1986a]. Likewise, the redox ratio systematically increases with melt depolymerization as expressed by the parameter NBO/T. In this respect, the influences of Al and Si are analogous in the quaternary system CaO-MgO-Al 2 O 3 -SiO 2 [Mysen et a/., 1985c] as well as in natural melts [Sack et al, 1980; Kilinc et al., 1983]. As indicated by phase equilibria data, the association of tetrahedral Fe 3+ with chargecompensating cations is strongest for K+. Attention has thus been paid to the competition between Fe 3+ and Al 3+ to associate with this cation. In potassium aluminosilicates, the variations of the iron redox state observed as a function of A1/(A1+K) show two different regimes (Fig. 10.16). The redox ratio first increases weakly in the peralkaline domain, and then decreases markedly after the meta-aluminous join has been crossed. Dickenson and Hess [1981] thus concluded that K+ does associate with Al 3+ in peralkaline melts, but not in peraluminous compositions where it partly reduces to Fe + which can in turn serves as a charge compensator for the remaining Fe 3+ . On the other hand, the weaker association of Ca 2+ with Fe 3+ is attested by the insensitivity of the redox ratio with respect to substitution of Ca 2+ for K+ in peralkaline melts, and its decreases in peraluminous melts [Dickenson and Hess, 1986a]. Comparing the effectiveness of tetrahedral ions to associate with the same charge-compensating cations, Dickenson and Hess [1986b] also found that Fe 3+ is not a good competitor to Ga as this cation induces iron reduction. Finally, another important question pertains to possible effects of water on iron redox reactions. No evidence for interference of water with the iron state was found in experiments on water-saturated peralkaline rhyolite, andesite and augite minette melts [Moore et al., 1995] as well as in hydrous haplogranite liquids [Wilke et al, 2002]. More complicated results have been obtained by Baker and Rutherford [1996] who concluded that the effects of water are similar to those of alkali metal oxides. For peraluminous rhyolites, Baker and Rutherford [1996] found that Fe 3+ /Fe 2+ decreases greatly, in a linear way, with hydroxyl content at high temperature for redox conditions near the nickel-nickel

Iron-bearing Melts — I. Physical Properties

311

Figure 10.16 - Iron redox ratio against K/(K+A1) for potassium aluminosilicates at constant 78 mol % SiO2 [Dickenson and Hess, 1981]. Experiments made in air at 1400°C with a total of2wt%FeO. oxide (NNO) buffer. For peralkaline rhyolites, a decrease was observed under NNO and MnO-Mn 3 O 4 oxygen buffer conditions. A similar conclusion has been arrived at by Gaillard et al. [2001] for other silicic meta-aluminous melts. The apparent disagreement between these studies suggests that the influence of water on iron redox state depends on silicate composition and oxygen fugacity. Indeed, Gaillard et al. [2003] have concluded that this influence is smallest for peralkaline compositions and oxidizing conditions. But the complex nature of the compositions investigated have prevented the main factors that determine these variations from being indentified. In agreement with the trends seen for dry systems in Fig. 10.15, Gaillard et al. [2003] did find that substitution of Ca for Na causes a decrease of the redox ratio in hydrous melts. 10.3d. Prediction of Iron Redox Ratios Ever since the first experiments of Kennedy [1948] and Fudali [1965], the importance of knowing iron redox ratio has motivated efforts to predict it as a function of temperature and composition. The first model seems to be that of Lauer [1977] and Lauer and Morris [1977] not only for Fe, but also for Ce and Cr whose redox states were measured by electron paramagnetic resonance. The composition depence of the activity coefficient of oxygen ions in simple silicate liquids was related empirically to the ionization potential of network-modifying cations. However, no attempt has been made to extend such a formalism to more complex compositions. A purely empirical approach was followed by Sack et al. [1980] who assumed that the effects of oxygen fugacity and temperature on the redox ratio do not depend on composition and that, at constant Tand/ O , the redox ratio is an additive function of oxide concentration. The expression they fitted to available and new redox data for melts of geochemical interest ranging from mafic to felsic was thus In (*Fe,o3/*Feo) = a \nf0

+ b/T + c + Y dtxt,

(10.14)

where x designates an oxide mol fraction, a, b and c are constants, and the dt are specific parameters for SiO 2 , A12O3, "FeO", MgO, CaO, Na 2 O and K 2 O. Because of the rather high Fe contents considered, a low stoichiometry coefficient a = 0.218 was derived by Sack et al. [1980]. With the same formalism, similar values were found by Kilinc et al.

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[1983] who complemented the data base with new redox ratios determined in air. There are, however, objections to the assumptions made in these models. These assumptions are, for example, inconsistent with the nonlinear dependence of redox ratio on total iron content (Fig. 10.13). Besides, network formers and modifiers should influence the redox state in differing ways. When the "FeO" content is not small, variations of the redox state are in addition synonymous with changes in melt polymerization, oxygen activity, and energetics of the redox reaction. All such factors make it difficult to neglect the influence of composition on the variation of redox state with temperature and oxygen fugacity which is indicated by other data for higher temperatures or lower oxygen fugacities. Such an influence is also shown by the wide 2.1-7.7 kJ/mol range of values determined by Mysen et al. [1985c] for the Gibbs free energy of the iron redox reaction in Ca,Mg aluminosilicates. To distinguish the effects of network-forming and modifying cations, Mysen [1987] modified equation (10.14) as follows In (jcFe3+/*Fe2+) = a ln/o 2 + b/T + c +
(10.15)

where JC. designates the NBO/T value pertaining to the network-modifying cation i. Although a better fit to the input data base of Kilinc et al. [1983] was obtained in this way by Mysen [1987], this model has not been extensively used in the petrological literature. Probable reasons are the need for structural information and the iterative nature of the calculation due to the fact that the model is function of both FeO and Fe 2 O 3 contents. More practical formalisms have been proposed. Borisov and Shapkin [1989] simply considered that the a, b and c parameters depend on composition when fitting equation (10.14) to redox data. A less empirical method was adopted by Kress and Carmichael [1988]. As described in section 10.3a, deviations from the nominal 0.25 value of the stoichiometry coefficient of the redox reaction are a measure of nonideal mixing of Fe 2+ and Fe 3+ . Conversely, one may try to cope with thermodynamic nonideality via the choice of components such that the stoichiometry coefficient remains close to 0.25. Kress and Carmichael [1988] used in this fashion FeO and FeO 1 4 6 4 components, the latter being thought to reflect a fundamental aspect of the structure of natural melts. The equation In (x FeOi JxFeO)

= 0.232 ln/o 2 - (AH+Z W^/RT

+ AS/R,

(10.16)

was then fitted by Kress and Carmichael [1988] to a data set complemented by new measurements made at very low oxygen fugacities. In this equation, note that the actual enthalpy of the redox reaction differs from the fit parameter AH because it depends on composition via the term involving the adjustable Wt variables. Subsequently, the effects of pressure on redox ratio were incorporated by Kress and Carmichael [1991] as part of a study of the compressibility of Fe-bearing melts. They reanalyzed some of their previous results and, abandoning equation (10.16), reverted to equation (10.14) to which they added pressure-dependent terms, viz

Iron-bearing Melts — I. Physical Properties m

(*Fe2o3/*Feo) = « ln/o 2 + b/T + c + X 4*, + e [ 1 - 7 / T - In 77T0] + fP/T + g (T-T0)P/T + hP2/T,

313

(10.17)

where e,/, g and h are fit parameters and To (1673 K) a reference temperature. These various models have been tested by Nikolaev et al. [1996]. In spite of their differences, they were found to give similar results, which typical deviations of 0.03-0.05 from the measured redox ratios. The less reliable predictions were for felsic melts of the andesiterhyolite series. To improve predictions, Nikolaev et al. [1996] finally split the available data base in four different domains of temperature, oxygen fugacity and redox ratio, for which they fitted distinct set of equation-(10.14) parameters. As tested by Partzsch et al. [2004] with new measurements, the latest models of Kress and Carmichael [1991] and Nikolaev etal. [1996] generally reproduce the observed Fe 3+ /Fe 2+ ratios to within 0.05. Deviations of up to 0.1 are nonetheless observed, particularly for felsic compositions or strongly oxidizing conditions. Interestingly, the models can also be extrapolated to subliquidus temperatures, where they are most useful, although they were necessarily calibrated with superliquidus data. The fact that composition effects are averaged out in complex systems ensures the interest of the predictions, but at the same time prevent them from being made outside the composition range on which they rely. The paradox is that further progress will require better understanding of basic mechanisms to be achieved from the study of simple systems to which current models cannot be applied. The Mossbauer study of an aluminosilicate melt by Jarasuriya et al. [2004] illustrates this point. In agreement with ealier results of Virgo and Mysen [1985], a definite interaction was detected between Fe 2+ and Fe 3+ (Fig. 10.13b) whose neglect is the reason why available models do not work well at low iron content. Jarasuriya et al. [2004] also pointed out that deviations from the nominal 0.25 stoichiometry coefficient of the redox reaction at low Fe concentration are indeed negligible if, consistent with equation (10.8), FeOj 5 , instead of Fe,O 3 , is chosen along with FeO as a component. Hence, the proper way to account for Fe + -Fe 3+ interactions is not to adjust the stoichiometry coefficient of the reaction, but to add a specific term in the expression of the redox ratio. In a development of In (;tFe0 /xFeO) of the form (10.14), Jarasuriya et al. [2004] thus included a regular-like interaction term derived from their results. In this very simple way, they showed how models could account for the dependence of redox ratio on total iron content. But the differing effects of £Fe observed in Fig. 10.13 indicate that such a term should vary with composition. Along different lines, the acid-base approach followed by Ottonello et al. [2001] is also of interest. The starting point is the model of Toop and Samis [1962] for the oxygen speciation reactions (6.10) whose equilibrium constants are determined from optical basicity data (see section 6.2d). The activities of iron oxides are then obtained from the Temkin model, with proper allowance for the network-forming or network-modifying character of Fe and other cations. In this respect, the main difference between iron oxides is the amphoteric character of Fe 2 O 3 that gives rise to two dissociation reactions instead of the single one that applies to FeO, see equations (10.3-10.5).

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As alluded to in the previous section, the fact that oxygen ions can appear either as reactants or products in the redox reaction explains why addition of metal oxides at constant oxygen fugacity can cause either oxidation or reduction. Although Ottonello et al. [2001] assumed that Fe + and Fe + mix ideally over the cation sublattice, the ratio of the activity coefficients of FeOj 5 and FeO differs from unity as a result of the contribution of these dissociation reactions to mixing in the anionic matrix. Making use of relevant thermochemical data, Ottonello etal. [2001] proceeded to calculate the activity of FeO as a function of composition and, finally, equilibrium redox ratios for the same data base as used by Kilinc et al. [1983]. The advantage of such a thermodynamically based approach is obvious if one considers that a precision similar to that of the model of Kilinc et al. [1983] was achieved with half less adjustable parameters. 10.3e. Mechanisms of Redox Reactions Thermodynamic measurements are of little help to understand the mechanisms of redox reactions. Insights have been gained instead from kinetic studies because these allow the rate-limiting parameters of the reactions to be determined. Most studies have been devoted to oxidation reactions, however, with the result that it is not clear whether oxidation and reduction reactions have the same kinetics and obey the same mechanisms. The simplest assumption is that the redox rate is controlled by diffusion of oxygen in either molecular or ionic form. In both cases, the relevant half reactions would be: O 2 + 4 e" <=> 2 O 2 \

(10.18)

4 Fe 2+ <=> 4 Fe 3+ + 4 e\

(10.19)

With diffusion of physically dissolved molecular oxygen, the redox and diffusion fronts coincide; starting from the surface, they move together inside the melt (Fig. 10.16). With (chemical) diffusion of O 2 \ the oxidation mechanism is more complicated because the oxygen ionization reaction (10.18) occurs at the melt-atmosphere interface, whereas the iron oxidation reaction (10.19) takes place at progressively greater depths within the melt so that a counterflux of electrons is needed to ensure local electroneutrality. Without distinguishing physical and chemical diffusion, Goldman and Gupta [1983] calculated the effective oxygen diffusivity needed to account for the rate of change of the redox ratio measured in air for a Ca-Al borosilicate. By assuming instantaneous local equilibrium between iron and oxygen ions, they derived from their kinetic measurements an oxygen diffusivity of 3.7 10"11 m2/s at 1260°C that is similar to tracer diffusivities measured for other silicate melts [Oishi et al, 1975; Yinnon and Cooper, 1980; Dunn, 1983] or calculated with the Eyring relation (4.10) from the melt viscosity. Goldman and Gupta [1983] thus concluded that oxygen diffusion is controlling the redox kinetics, whereas Goldman [1983] found that the reaction rate is slower for reduction than for oxidation. Schreiber et al. [1986] reached a similar conclusion from a more detailed analysis. They stated that, under a chemical gradient, the chemical diffusion of oxygen determined

Iron-bearing Melts — I. Physical Properties

315

Figure 10.17 - Reactions at the moving redox front and at the fixed melt-atmosphere interface, along with the associated fluxes of species, for rate-controlled oxidation by diffusion of molecular oxygen (a), oxygen ions (b), and divalent cations (c). In (c), crystallization at the surface can be more complicated when several divalent cations are present (see text). In a ionic medium, an electron and the surrounding region in which it induces strong polarization are called a polaron. Small polarons are of atomic size, have an effective mass much higher than that of the electron, and hop from one site to another with the assistance of phonons. It is often stated that they ensure electrical conductivity in glasses [e.g., Jurado-Egea et al., 1987]. Alternatively, electrical conduction in crystals indicates that electroneutrality can be achieved through a counterflux of electron holes in the valence band. These are also designated as small polarons because of the structural distortion they induce. In Fe-bearing olivines, electrical conductivity indeed results from small polaron hopping of holes from Fe3+ to Fe2+ on the Mg sublattice, which is a faster mechanism than electron hopping [Hirsch et al., 1993]. Because of their more familiar nature, electron fluxes are shown above but they could be readily replaced by opposite fluxes of electron holes. In (b), it follows that the electrical conductivity of the melt could be the rate-limiting factor. in redox studies is several orders of magnitude faster than the diffusion of oxygen belonging to the silicate framework which is measured in tracer studies (Fig. 10.18). For the latter process, activation enthalpies are, in addition, twice as great as for the former. Schreiber et al. [ 1986] also stressed that only oxygen ions, in equilibrium with dissolved O 2 (whose concentration is related to oxygen partial pressure via Henry's law), participate in the redox reaction. An intriguing fact is that both diffusivities and activation enthalpies for chemical diffusion of oxygen seem similar to the values determined for tracer diffusion of divalent networkmodifying cations [Dunn, 1982; Dunn and Scarfe, 1986]. This led Cook et al. [1990] to determine whether the redox reaction was controlled instead by diffusion of Ca2+ or Mg2+. The origin for this idea is the internal oxidation mechanism extensively studied for solidstate reactions [e.g., Schmalzried, 1983]. In a variety of ionic solids, including oxides and silicates such as magniesowiistites and (Mg,Fe) 2 Si0 4 olivines [Luecke and Kohlstedt, 1988; Wu and Kohlstedt, 1988], oxidation occurs via the removal of divalent cations rather than by addition of oxygen. With this mechanism, oxygen is not transported at all. At the redox front, it is released by alkaline earth cations which migrate toward the vapor-melt interface where they react with gaseous oxygen to form a thin oxide layer. Electroneutrality could be achieved through a simultaneous flux of electrons or a counterflux of electron holes from the surface to the redox front (Fig. 10.17). The fact that Fe ions are involved in these processes make the kinetics of the reaction dependent on total iron concentration.

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Figure 10.18 - Tracer diffusivities in tholeiitic basalt melts. Data for divalent cations from Magaritz and Hofmann [ 1977]; for silicon and oxygen (Lai) from Lesher et al. [1996]; for oxygen (CM) from Canil and Muelenbachs [1990] (same results under an O2 or a CO atmosphere); for oxygen (D-HP) from Dunn [1993] at 1.2 GPa (with a pressure effect of about -0.3 log units compared to room-pressure values). For oxygen (O/Chem), the chemical diffusivity of Wendlandt [1991] has been included.

Extensive study of this mechanism was made by Cook et al. [1990] for an Fe-bearing Mg aluminosilicate oxidized at 700-800°C in air. With transmission electron microscopy, the presence of a crystalline layer made up of MgO and (Mg,Fe) 3 O 4 was detected at the glass surface. With Rutherford backscattering spectroscopy, Cook etal.[\990] correlatively observed a depletion of divalent cations near the glass surface that followed a parabolic law characteristic of a diffusive process. These experiments have been complemented by observations made on a reduced nepheline normative olivine basalt glass heated in air at 550-600°C [Cooper et al., 1996a]. At the surface, precipitation of CaO and MgO was observed. As a result, Mg and Ca were depleted near the surface where Na was, in contrast, enriched because it charge-compensated Fe 3 + and, doing so, prevented spinel from crystallizing. Consistent results have been described for a tholeiitic basalt by Burkhard [2001] heated in air and in argon between 850 and 940°C. Internal oxidation does not necessarily yield the lowest energy state. It takes place when it dissipates the gradient of oxygen chemical potential between the melt and the external atmosphere faster than oxygen diffusion. Because what matters is the product of the concentration and diffusivity of mobile species {i.e., their flux), this mechanism is generally the most efficient near, or even below, the glass transition as decoupling between bulk and local relaxation makes diffusion much faster for network-modifying cations than for oxygen (see section 2.1e). For an Fe-bearing pyroxene composition, this has been confirmed by in situ XANES measurements made just above the glass transition range where the observed oxidation kinetics was orders of magnitude too fast to have been caused by oxygen diffusion [Magnien et al., 2004]. The mechanisms of internal oxidation depend on the silicate composition. In fact, this process had first been invoked to account for oxidation at 570°C of a Cu+-doped sodalime glass through diffusion of Na+ and surface precipitation of sodium carbonate [Barton and de Billy, 1980]. In another study of Na aluminosilicate melt [Barton et al, 1992;

Iron-bearing Melts — I. Physical Properties

317

Barton and Caurant, 1993], iron oxidation at 800°C again took place through diffusion of Na + . No crystalline precipitate was observed at the surface, however, whereas there was some evidence for back-diffusion of Na within the glass. In the other glasses investigated by Cooper and coworkers, crystalline precipitates formed at the surface. For Mg aluminosilicate glasses with Fe contents lower than 0.54 at% heated at 700-850°C in air, oxidation occurred via diffusion of Fe 2+ and a counterflux of electron holes [Cook and Cooper, 2000]. Interestingly, this mechanism did not operate below 800°C in glasses with less than 0.19 at% because the Fe concentration was then too low to ensure a sufficient conductive flux. Transport of oxygen species was assumed to have taken place instead. In another study, part of Mg 2+ ions were replaced by bigger Ca2+ ions to determine whether expansion of the structure would affect the oxidation mechanisms [Smith and Cooper, 2000]. The reaction remained dominated by diffusion of divalent cations, but the rate of the reaction was 100 times faster in the presence of Ca 2+ . Although the nature of crystalline precipitates differed in air and in argon, in both cases the morphology was suggestive of cation diffusion through the interconnected channels of the structure assumed in the modified random network model of Greaves [1985]. The question arises whether internal oxidation remains the dominant mechanism at high temperature where element diffusivities tend to converge. A positive answer has been given by observations made on droplets of molten basalt levitated in air at 1400°C [Cooper et al., 1996b]. Although quench reactions could have complicated the situation, precipitation of magnetite was observed at the redox front, and precipitation of hematite and pseudowollastonite near the sample surface. In this case, oxidation clearly caused an increase of liquidus temperature that made crystallization of these phases possible. Conversely, the very fact that crystallization cannot be observed under superliquidus conditions suggests that internal oxidation could no longer be the dominant mechanism at sufficiently high temperatures. When superliquidus conditions prevent crystallite precipitation at the surface, a possibility of lowering the Gibbs free energy of the melt disappears and, thus, a driving force for cation diffusion. As asserted by Goldman and Gupta [1983], oxygen diffusion could then be the dominant mechanism. As a matter of fact, differences in high-temperature diffusivities could be not as clear cut as has been concluded from measurements made on different melt compositions. This is suggested by the data available for molten tholeiitic basalts, which are the most extensive (Fig. 10.18). Only the diffusivity of iron [Dunn and Ratliffe, 1990] is several orders of magnitude lower than those of the elements considered in this figure. For hydrous melts, note finally that Gaillard et al. [2002] have described a two-step reaction mechanism whereby very fast hydrogen diffusion is followed by slow reorganization around iron ions. Support for this view is provided by a similar contrast in reduction mechanism. In a study of reduction of an Mg aluminosilicate between 1300 and 1400°C, Everman and Cooper [2003] observed the formation of nanometer-scale iron metal precipitates at an internal surface, which they assigned to flux of electron holes and Mg 2+ with a diffusivity of 10"1 m /s. Simultaneously, ionic oxygen was released at the surface where it transformed to molecular oxygen. It is common experience, however, that oxygen bubbles rapidly out

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Figure 10.19. Density of "FeO" at 1500°C against the atomic redox ratio of the melt in experiments made under varying CO-CO2 atmospheres [Mori and Suzuki, 1968]. The data shown for pure FeO are for a nearly stoichiometric FeO melt contained at 1410°C in iron crucibles, with argon as a bubbling gas.

of oxidized melts heated in air at sufficiently high temperatures. In this case, there is no evidence for precipitates when oxygen is released within the melt. Instead, oxygen bubbles nucleate very rapidly and grow while moving to the surface. 10.4. Physical Properties Measurements of physical properties of iron-bearing melts are made difficult by the intrinsic variations of the redox ratio with temperature, pressure and bulk chemical composition. Attainment of redox equilibrium must not only be checked, but the sample has to be quenched for analysis since it is usually not possible to determine simultaneously its redox state. In data analysis, proper allowance must then be made for the variations of the redox ratio with temperature. This represents a serious hindrance as inferences about the composition dependence of properties cannot be made from direct representations of the experimental data along simple joins. They have to be drawn from multivariate analyses of the data, which often do not yield unequivocal solutions. And although slags have been investigated extensively, use of these measurements can be made difficult by the need to disentangle the specific influence of FeO and Fe 2 O 3 from those of SiO2-poor contents, and resulting melt depolymerization. 10.4a. Density Volume properties exemplify the difficulties raised by measurements on iron-bearing melts. Although density can be measured irrespectively of the actual redox state, determination of molar volume and subsequent analysis in terms of partial molar volumes cannot. For molten "FeO", the large range of redox ratio induced by changes in oxygen fugacity yields a density decrease from 4.6 to 3.8 g/cm3 under increasingly oxidizing conditions (Fig. 10.19). Under the most reducing conditions, the density of 4.57 g/cm3 measured by Gaskell and Ward [1967] gives a molar volume of 15.8 cm3/mol for pure "FeO". For the pseudobinary "FeO"-SiO 2 system, measurements have been made by various methods [see Henderson, 1964; Shiraishi et al., 1978]. Under reducing conditions, the molar volume is a linear function of SiO 2 content (Fig. 10.20). A partial molar volume of 23.6 cm 3 /mol is obtained for SiO 2 , which is lower than the 26.8 cm3/mol derived in section 6.3a from measurements on binary alkali and alkaline earth systems. These two volumes are not directly comparable, however, because they refer to markedly different

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Figure 10.20 - Molar volume of "FeO"-SiO2 melts at 1410°C [solid squares: Gaskell and Ward, 1967] or 1400°C [open circles: Shirashi et al., 1978]. The dashed wavy curve represents the volumes calculated from the ternary compositions reported by Shiraishi et al. [1978] with the partial molar volumes of Bottinga and Weill [1970].

ranges of SiO2 contents. In accordance with the positive difference between the volumes of bridging and nonbridging oxygens noted in section 6. la, the lower partial molar volume found for the SiO2-poor melts of Fig. 10.20 could simply reflect a lower volume for SiO2 in Q°- than in Q"-species with a smaller number of nonbridging oxygens. The partial molar volume of FeO also depends on composition. The linear relationship of Fig. 10.20 yields a value of 15.8 cm3/mol, which is higher than the volumes ranging from 12.8 to 13.8 cm3/mol derived at 1400°C from measurements made on iron-bearing SiO2-rich melts [Bottinga and Weill, 1970; Mo etal, 1982; Bottinga et al, 1983;Dingwell et al, 1988; Lange and Carmichael, 1989]. That these models do not apply to slags and other Fe-rich melts is illustrated in Fig. 10.20 by the differences between their predictions and the experimental data for the "FeO"-SiO2 system, even when actual Fe2O3 contents are accounted for. Likewise, the agreement is not good between such model values and the volumes measured for ternary CaO-FeO-SiO2 melts by Henderson [1964] and Lee and Gaskell [1974]. In their study of SiO2-poor calcium ferrosilicate melts in equilibrium with iron, Lee and Gaskell [1974] reported that the partial molar volumes of both FeO and CaO depend on composition. They assigned these variations to preferred association of Ca2+ with the silicate anionic framework, and of Fe2+ with "free" oxygen ions. At higher silica contents, however, the partial molar volumes of these oxides are not a strong function of composition. Hence, possible changes in the structural state of Fe2+ seem to affect the density only at low SiO2 contents. In contrast, the 12.8-13.8 cm3/mol partial molar volume of FeO quoted above in silica-rich melts is closer to that of MgO (11.6 cm3/mol) than to that of CaO (16.5 cnrVmol), and is similar to the molar volume of wiistite (12.8 cm3 at 1400°C). These figures indicate essentially octahedral coordination for ferrous iron. They are, in addition, consistent with the greater similarity of Fe2+ with Mg2+ than with Ca2+ noted in previous sections. The variations of the partial molar volume of Fe2O3 with composition could be more problematic. For pure Fe2O3, the densities measured for molten ferrites (Fig. 10.21) converge at 1400-1500°C to a value of 4.7 g/cm3, which is similar to the density of FeO melt (Fig. 10.19). The resulting molar volume of 34.0 cm3 is marginally higher than that of hematite (32.8 cm3) at the same temperature, which suggests that Fe3+ would be

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Figure 10.21 - Molar volume of molten ferrites against Fe2O3 content. Data from Sumita et al. [1983] at 1400°C for Na 2 OFe 2 0 3 , and at 1500°C for the alkaline earth systems.

primarily in octahedral coordination in pure metastable Fe 2 O 3 melt. On the other hand, the presence of ferric iron lowers markedly the density of molten "FeO" (Fig. 10.19). That this effect could be due to tetrahedral coordination is indicated by the high partial molar volume of about 41 cnvVmol consistently determined for Fe 2 O 3 in silicate melts (see below). Hence, the question arises as to how the partial molar volume of Fe 2 O 3 varies between such low and high values when other oxides are introduced. In simple systems, two cases must be distinguished depending on the strength of the association between tetrahedral Fe 3+ and its charge-compensating cation. For sodium ferrisilicates, the existence of slight excess volumes asserted by Dingwell et al. [1988] has been denied by Lange and Carmichael [1989] on the basis of alledged systematic bias affecting redox analyses by Mossbauer spectroscopy (see section 10.1c). This disagreement is minor, however, compared to the main conclusion reached in both studies that Na+ clearly stabilizes Fe 3+ in tetrahedral coordination in the investigated peralkaline compositions. At 1400°C, for instance, the partial molar volume of Fe 2 O 3 is 40.7 and 41.8 cnrVmol according to Dingwell et al. [1988] and Lange and Carmichael [1989], respectively. For calcium ferrisilicates, composition-independent partial molar volumes were found inadequate by Dingwell and Brearley [1988]. These authors dealt with excess volumes primarily in terms of a large positive interaction between Ca and Fe,3+ in tetrahedral coordination. The nonlinear variations of molar volume was then assigned to the coexistence of octahedral and tetrahedral Fe 3+ whose proportions would vary with temperature and melt composition. Finally, Dingwell and Brearley [1988] suggested that the partial molar volume of FeO might also depend on composition in calcium systems. 10.4b. Pressure-Dependence of Iron Redox State Experiments on a variety of Fe-bearing melts show that increasing pressure induces iron reduction [e.g., Mysen and Virgo, 1978, 1985]. Efforts to determine the partial molar volume of Fe 2 O 3 have also been motivated by the close connection of this volume with the pressure dependence of the iron redox ratio. At constant temperature, the condition for univariant thermodynamic equilibrium boils down to AG = AV dP = 0. In view of the relationship

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(10.20)

RTd\nfo2=VOldP,

where Vo is the partial molar volume of O2 dissolved in the melt, Mo et al. [1982] pointed out that the variation of the oxygen fugacity for Fe3+-Fe2+ equilibrium is related to the partial molar volumes of Fe2O3 and FeO by: RTI

Po

rfln/o2=f

Po

(2V F 2 o3 -4VPtO)dP=l

Po

AV dP.

(10.21)

Integration of equation (10.21) from the reference pressure Po is straightforward if Av is assumed to be constant. With the partial molar volumes they determined from measurements made on a series of complex Fe-bearing melts, Mo et al. [1982] concluded that a 1-GPa pressure increase would affect the redox ratio in the same way as a 10-fold decrease of/o . Although further work has not confirmed the partial molar volumes derived by Mo et al. [1982], the important point is that A V is indeed positive and, thus, that Fe2+ is stabilized at high pressure at the expense of Fe 3+ as observed experimentally. The compressibility difference between Fe2+ and Fe3+ should be known for more detailed analyses of pressure effects. For both valences, transformation from tetrahedral to octahedral coordination ensures greater density increases than compression of FeO 6 octahedra. The coordination contrast between Fe2+ and Fe3+ at low pressure should thus result in a higher compressibility for Fe2O3 than for FeO. This prediction is borne out by available ultrasonic measurements on Fe-bearing melts. Although the data are too scarce to allow detection of possible effects of melt composition, the analysis made by Kress and Carmichael [1991] indicates that the average compressibility is about twice as great for the Fe 2 O 3 than for the FeO component. Curiously, however, compressibility appears to be 50% higher for FeO than for either MgO or CaO, whereas it is similar for Fe2O3 and A12O3. In fact, ultrasonic data indicate that the presence of Fe2O3 may even increase the stiffness of glasses [Burkhard, 2000]. As noted by Kress and Carmichael [1991], the difference in compressibility between Fe2O3 and FeO in melts is too small to change the sign of the volume difference in equation (10.21) below pressures of at least 3 GPa. In other words, the Fe3+/Fe2+ ratio of melts should decrease continuously in this interval with increasing pressure. For the opposite trend to occur at still higher pressure, the pressure derivative of the bulk modulus (Ks) should be much higher for the FeO than for the Fe2O3 component. Such a contrast is unlikely in view of the "normal" value dK^dP =10.1 determined for molten Fe2SiO4 from compression experiments up to 55 GPa [Agee, 1992]. 10.4c. Thermal Properties The activity measurements made for iron-bearing melts are too numerous to be reviewed (see, for instance, Doyle and Naldrett, 1986]. Here, the salient point to be emphasized is that, in accordance with Richardson's [1956] proposition and the kinship of Fe 2+ and Mg2+ noted in this chapter, mixing of FeO and MgO can be considered as ideal in simple as well as in complex mafic systems [Doyle and Naldrett, 1986; Doyle, 1988]. At the other end of

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Figure 10.22 - Viscosity of FeO-SiO 2 melts at 1400°C in equilibrium with iron. Solid circles: Shiraishi et al. [1978]; open circles: Urbain et al. [1982]. In the experiments of Shiraishi et al. [1978], the Fe 2 O 3 content decreased from 12 to 0.7 wt% from 100 to 61 wt % "FeO".

the composition range of geochemical interest, it is also of note that the effects of water on the activities of FeO and Fe 2 O 3 have been determined for hydrous silicic melts [Gaillard et al., 2003]. Under reducing conditions, water increases the activity of FeO and decreases that of Fe 2 O 3 , and both of them increase with oxygen fugacity. Calorimetric measurememts on iron-bearing glasses and melts are scarce. From literature data, Stebbins et al. [ 1984] calculated partial molar heat capacities of 79 (5) and 229 (18) J/mol K for FeO and Fe 2 O 3 , respectively. The results derived by Richet and Bottinga [1985] in a similar way were 79 and 200 J/mol K for FeO and Fe 2 O 3 . They compare with the values of 86 J/mol K for both MgO and CaO, and with an average value of 187 J/mol K at 1700 K for the partial molar C of A12O3, which is actually temperature and composition dependent. On a g atom basis, the values for FeO and Fe 2 O 3 are thus the same. They suggest configurational heat capacities that are similar for both oxides and higher than for A12O3. The first heat capacity measurements specifically devoted to Fe2O3-bearing melts were made between 1000 and 1400°C in air on a series of molten lavas and Na and Ca ferrisilicates [Lange and Navrotsky, 1992]. With a constant value of 241 ± 8 J/mol K, no composition dependence was found for the partial molar C of Fe 2 O 3 . For sodium ferrisilicates, other measurements have been made by differential scanning calorimetry just above the glass transition [Tangeman and Lange, 1998]. These results have revealed a decrease of C with increasing temperature similar to that observed for titanosilicates (see section 12.2a). Agreement with the high-temperature data of Lange and Navrostky [1992] was generally poor, however, with the result that the influence of Fe 3+ on heat capacity remains to be determined as a function of temperature and composition. 10.4d. Viscosity For obvious metallurgical reasons, the viscosity of SiO2 -poor ferrosilicate melts has long been investigated [see Bottinga and Weill, 1972]. As for the density, assessment of the specific effects of FeO are made difficult by the lower ranges of SiO 2 content investigated compared to those reviewed in previous chapters for other metal oxides. In addition, viscosity data are generally lacking near the glass transition because of the difficulties of

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Figure 10.23. Viscosity of "FeO"-SiO2 melts against oxygen fugacity. Results from Toguri et al. [ 1976] for three series whose Fe/Si atomic ratios is indicated. For each series (same symbols), the lower data refer to 1250°C and the upper data to 1350°C. The steeper slope of the results for Fe/Si = 1.95 at low/ o signals the Fe2Si04 anomaly. The iron redox ratios were not determined.

quenching iron-rich glasses in simple systems. Hence, viscosity-temperature relationships are generally known over only restricted intervals and the connections made in other chapters between rheological and thermodynamic properties remain to be established for Fe-bearing melts. Under reducing conditions, it appears that iron, in the form of FeO, does not induce any peculiar anomaly. Analogies between the effects of FeO, MgO and BaO on viscosity were for instance noted by Bills [1963]. Accordingly, Bottinga and Weill [1972], assumed in their empirical model of prediction of high-temperature viscosities that, like those of other metal oxides, the effects of FeO are a monotonous function of concentration. Good agreement with exprimental data on FeO-rich melts has been achieved in this way [e.g., Cukierman et al., 1972; Cukierman etal, 1974]. Even though Fe 2+ may also be in tetrahedral coordination (see section 11.2a), data are in fact lacking to document the influence that this coordination state might have on viscosity. In this section, this is why attention will be paid instead to changes in iron redox ratio and in coordination state of Fe 3+ whose effects have been more extensively investigated. In the binary "FeO"-SiO 2 system, the only anomalous feature is the intriguing viscosity maximum that has been repeatedly observed near the fayalite composition (Fig. 10.22).

Figure 10.24. Viscosity of molten binary ferrites against Fe2O3 content [from Sumita et al., 1983]. Data at 1400°C for sodium and 1500°C for alkaline earth ferrites.

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Figure 10.25 - Iron redox state and viscosity of melts with the stoichiometry M^FeSijOg (nominal). Results from Dingwell and Virgo [1987] for Na and Na2, another Na melt with a high Fe 2 O 3 content of 34 wt % (1430°C); Dingwell and Virgo [1988b] for Ca (1400°C, two data for reduced compositions discarded), and Dingwell [1991] for K (1380°C), Rb (1470°C), Ba (1345°C) and Sr (1350°C).

Although its magnitude differs from one study to another, this maximum has been interpreted as indicating some kind of clustering at the orthosilicate composition [see Shiraishi et al, 1978]. Unfortunately, data are lacking to check whether an analogous maximum would also be found for other binary metal oxide-silica melts. Of interest is also the slight influence of the iron redox state on the viscosity of "FeO"-SiO2 melts (Fig. 10.23). At these high temperatures and low SiO 2 contents, Fe 2 O 3 causes the viscosity to decrease. This influence is much lower than that of decreasing silica concentration, however, as also indicated by the measurements of Fig. 10.23 where the Fe 2 O 3 content becomes significant near pure "FeO". Without any complication from Si 4+ , molten ferrites represent a natural starting point to investigate the effects of changing Fe 3+ coordination on viscosity. In all systems of Fig. 10.24, the viscosity increases with increasing metal oxide content. A sharp maximum is observed near the equimolar M;cO/Fe2O3 ratio for Na, and at a slightly higher value for Ba, whereas the increase is continuous for both Ca and Sr. These variations clearly correlate with the specific affinity of Fe 3+ with the various charge-compensating cations. Most Na and a high fraction of Ba probably associate with Fe3+, but only part of Ca and Sr. It follows that the proportion of tetrahedral Fe 3+ seems to pass through a clear maximum for Na and Ba, but to increase almost continuously for Ca and Sr. Compared to those described in Chapter 8 for Al 3+ , these viscosity increases due to coordination changes of Fe 3+ are extremely small. In particular, they are not much greater for Na+ than for alkaline earth cations. Such extensive viscosity data cannot be gathered for Fe-bearing silicates. For these melts, the investigated changes in Fe 3+ coordination have resulted from variations of the iron redox ratio. This restriction notwithstanding, the measurements available for a variety of systems indicate that viscosity consistently increases upon iron oxidation (Fig. 10.25). The variations are larger with increasing iron content [Dingwell and Virgo, 1987]. Consistent with the relative strength of association with Fe 3+ , they are greater in alkali than in alkaline earth systems [Dingwell, 1991]. From primarily Fe 2+ to essentially Fe 3+ , however, the increase is less than one order of magnitude at high temperature. Likewise, viscosity increases have been observed near the glass transition. They increase with iron content,

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325

Figure 10. 26 - Comparison between the viscosity of sodium alumino- and ferri silicates, (a) Along the meta-aluminous and meta-ferric joins SiO 2 -NaRO 2 (R = Al, Fe) at 1400°C, the numbers near the data points indicating the redox ratios of the samples, (b) Along the joins Na 2 Si 4 O 9 -Na 2 (NaR) 4 O 9 at 1150°C. Data from Dingwell and Virgo [1988a].

reaching more than order of magnitude for about 10 wt% FeO in sodium aluminosilicates [Klein et al, 1983] as well as for a molten basalt [Bouhifd et al, 2004], At high temperature, the influence of redox ratio on the viscosity of silicate melts is of the same magnitude as the intrinsic effects of iron, whether ferrous or ferric. For Ca ferrisilicates, Mysen et al. [1985b] showed that substitution of Fe3+ for Si4+ lowers the viscosity by less than one order of magnitude. For Na systems, interesting comparisons have been made by Dingwell and Virgo [1988a] with aluminosilicates of the same stoichiometry (Fig. 10.26). In agreement with all the information reviewed in preceding sections, the bonding contrast between Fe3+ and Al3+ manifests itself in the systematically lower viscosities of ferrisilicates compared to aluminosilicates. As pointed out by Dingwell and Virgo [1988a], the viscosities of ferrisilicates are, in fact, similar to those of borosilicates. The depressing effect of iron should be much greater near the glass transition but, as already noted, data are unfortunately lacking.

Figure 10.27 - Viscosity of ferrisilicates with 67 mol % SiO 2 along the meta-ferric join against reciprocal temperature. Data from Dingwell and Virgo [1988a] for Na and from Dingwell [1989] for the other systems. Similar trends are observed for melts with 50 and 75 mol % SiO,.

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A final comparison with aluminosilicates can be made through the systematic measurements made by Dingwell [1989] for alkali and alkaline earth melts along the silicateferrite join SiO2-M2/AFeO4 (M = alkali or alkaline earth). The trends determined for 50,67 and 75 mol % SiO 2 are similar. They are shown in Fig. 10.27 for the single series with 67 mol % SiO 2 . At constant SiO 2 , the viscosity decreases in the order Cs, Rb, K, Na, Ba, Sr, Ca, Mg Li. The order is the same as determined for aluminosilicates (see Fig. 8.18). There are some bias because of the systematic variations of the actual redox ratio from a system to another. In view of the rather weak influence of the iron redox state on viscosity, the effect is sufficiently small that it does not affect the reported trend. From Li to Rb, the variation is about one order of magnitude, and thus is similar to the effects shown in Fig. 8.18 for the high-temperature viscosity of aluminosilicates. 10.5. Summary Remarks 1. Because of similar energetics, the Fe 2+ and Fe 3+ redox states of iron generally coexist in silicate melts. Under reducing conditions, reduction to metallic iron in addition takes place. At constant composition, the Fe 3+ / Fe 2+ ratio increases with oxygen fugacity and decreases with increasing temperature and pressure. In view of the differing effects of the valence states on phase equilibria and physical properties, adequate characterization of the redox state is a necessity in any investigation of iron-bearing glasses and melts. 2. The iron redox state has important consequences on solid-liquid phase equilibria. Thanks to its same charge and similar ionic radius, Fe 2+ substitute for Mg 2+ under reducing conditions in olivine, pyroxene and magnesiowiistite solid solutions. Under oxidizing conditions, the kinship of Fe 3+ with Al 3+ is in contrast much less marked; whereas Na+ and, especially, K+, may serve for charge compensation, there is no strong interaction with alkaline earth cations. Another feature of petrological importance is the existence of stable liquid immiscibility in complex iron-bearing systems. 3. The ferrous state is also favored by high SiO2 contents and the presence of cations with a high ionization potential. As expected from the reaction Fe 2+ + 1/4 O 2 <=> Fe 3+ + 1/2 O 2 \ the slope of the log Fe 3+ / Fe 2+ vs. f0 relationship is 0.25 for low iron concentrations. The dependence of the redox state on total iron concentration indicates that Fe 3+ and Fe 2+ ions do not mix ideally, however, a feature that should be taken into acount in models of predictions of the iron redox ratio as a function of temperature, pressure and melt chemical composition. Because of the amphoteric nature of Fe 2 O 3 , the connection between redox state and melt basicity is not straightforward. At lower temperatures, the mechanisms of redox reactions involve liberation of oxygen by divalent or monovalent cations which diffuse from the inside to the melt surface. The situation is less clear above the liquidus where oxygen diffusion could predominate. 4. The effects of Fe 2+ and Fe 3+ on the density, thermal properties and viscosity of silicate melts are not markedly different. These differences depend primarily on the structural

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state of ferric iron. They are greater when Fe 3+ is tetrahedrally coordinated, although ferric iron is this case a weak analog of Al 3+ . References Agee C. B. (1992) Isothermal compression of molten Fe2SiO4. Geophys. Res. Lett. 19, 1169-1172. Alberto H. V., Pinto da Cunha J. L., Mysen B. O., Gil J. M., and de Campos N. A. (1996) Analysis of Mossbauer spectra of silicate glasses using a two-dimensional Gaussian distribution of hyperfine parameters. J. Non-Cryst. Solids 194, 48-57. Baak T. and Hornyak E. J., Jr. (1961) The iron-oxygen equilibrium in glass: Effect of platinum on Fe27Fe3+ equilibrium. J. Amer. Ceram. Soc. 44, 541-544. Baker L. L. and Rutherford M. J. (1996) The effect of dissolved water on the oxidation state of silicic melts. Geochim. Cosmochim. Ada 60, 2179-2187. Bancroft G. M. (1973) Mossbauer Spectroscopy: An Introduction for Inorganic Chemists and Geochemists. McGraw Hill, New York. Barton J. L. and de Billy M. (1980) Diffusion and oxidation of Cu+ in glass. J. Non-Cryst. Solids 38-39, 523-526. Barton J. L. and Caurant D. (1993) The oxidation of ferrous iron in glass at high temperatures. Riv. Staz. Sperim. Vetro 23, 193-198. Barton J. L., Banner D., Caurant D., and Pincemin F. (1992) The oxidation of ferrous iron in glass at high temperature. Bull. Soc. Esp. Ceram. Vid. 31C-6, 215-220. Beall G. H. and Rittler H. L. (1976) Basalt glass ceramics. Ceram. Bull. 55, 579-582. Berry A. J., Shelley J. M. G., Foran G. J., O'Neill H. S. C, and Scott D. R. (2003) A furnace design for XANES spectroscopy of silicate melts under controlled oxygen fugacities and temperatures to 1773 K. J. Synchrotron Rad. 10, 332-336. Bills P. (1963) Viscosities in silicate slags systems. J. Iron Steel Inst. 201, 133-140. Borisov A. A. and Shapkin A. I. (1989) A new empirical equation rating Fe3+/Fe2+ in magmas to their composition, oxygen fugacity, and temperature. Geochem. Int. 27, 111-116. Bottinga Y. and Weill D. F. (1970) Densities of liquid silicate systems calculated from partial molar volumes of oxide components. Amer. J. Sci. 269, 169-182. Bottinga Y. and Weill D. F. (1972) The viscosity of magmatic silicate liquids: A model for calculation. Amer. J. Sci. 272, 438-475. Bottinga Y., Richet P., and Weill D. F. (1983) Calculation of the density and thermal expansion coefficient of silicate liquids. Bull. Mineral. 106, 129-138. Bouhifd M. A., Richet P., Besson P., Roskosz M., and Ingrin J. (2004) Redox state, microstructure and viscosity of partially crystallized basalt. Earth Planet. Sci. Lett. 218, 31-44. Bowen N. L. and Schairer J. F. (1929) The fusion relations of acmite. Amer. J. Sci. 18, 365-374. Bowen N. L. and Schairer J. F. (1932) The system, SiO2-FeO. Amer. J. Sci. 24, 177-213. Bowen N. L., Schairer J. F., and Posnjak E. (1933) The system, Ca2SiO4-Fe2SiO4. Amer. J. Sci. 25, 273-297. Bowen N. L., Schairer J. F., and Willems H. W V. (1930) The ternary system Na2SiO3-Fe2O3-SiO2. Amer. J. Sci. 20, 405-455. Burkhard D. J. M. (2000) Iron-bearing silicate glasses at ambient conditions. J. Non-Cryst. Solids 275, 175-188. Burkhard D. J. M. (2001) Crystallization and oxidation of Kilauea basalt glass: Processes during reheating experiments. J. Petrol. 42, 507-527.

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Canil D. and Muelenbachs K. (1990) Oxygen diffusion in an Fe-rich basalt melt. Geochim. Cosmochim. Acta 54, 2947-2951. Carter P. T. and Ibrahim M. (1952) The ternary system Na2O-FeO-SiO2. J. Soc. Glass Technol. 36,156. Clausen O., Gerlach S., and Rtissel C. (1999) Self-diffusivity of polyvalent ions in silicate liquids. J. Non-Cryst. Solids 253, 76-83. Cook G. B. and Cooper R. F. (2000) Iron concentration and the physical processes of dynamic oxidation in an alkaline earth aluminosilicate glasses. Amer. Mineral. 85, 397-406. Cook G. B., Cooper R. F., and Wu T. (1990) Chemical diffusion and crystalline nucleation during oxidation of ferrous iron-bearing magnesium aluminosilicate glass. J. Non-Cryst. Solids 120, 207-222. Cooper R. F, Fanselow J. B., and Poker D. B. (1996a) The mechanism of oxidation of a basaltic glass: Chemical diffusion of network-modifying cations. Geochim. Cosmochim. Acta 60, 3253-3265. Cooper R. R, Fanselow J. B., Weber J. K. R., Merkley D. R., and Poker D. B. (1996b) Dynamics of oxidation of a Fe2+-bearing aluminosilicate (basaltic) melt. Science 274, 1173-1176. Cukierman M. and Uhlmann D. R. (1974) Effects of iron oxidation on viscosity, Lunar composition 15555. J. Geophys. Res. 79, 1594-1598. Cukierman M., Tutts P. M, and Uhlmann D. R. (1972) Viscous flow behavior of lunar composition 14259 and 14310. Geochim. Cosmochim. Acta, Supplt 3, 2619-2625. Dalton J. A. and Presnall D. C. (1997) No liquid immiscibility in the system MgSiO3-SiO2 at 5.0 GPa. Geochim. Cosmochim. Acta 61, 2367-2373. Darken L. S. and Gurry R. W. (1946) The system iron-oxygen. II. Equilibrium and thermodynamics of liquid oxide. J. Amer. Chem. Soc. 68, 798-816. Densem N. E. and Turner W. E. S. (1938) The equilibrium between ferrous and ferric oxides in glasses. J. Soc. Glass Technol. 22, 372-389. Dickinson M. P. and Hess P. C. (1981) Redox equilibria and the structural role of iron in aluminosilicate melts. Contrib. Mineral. Petrol. 78, 352-357. Dickenson M. P. and Hess P. C. (1986a) The structural role and homogeneous redox equilibria of iron in peraluminous, metaluminous and peralkaline silicate melts. Contrib. Mineral. Petrol. 92, 202-217. Dickenson M. P. and Hess P. C. (1986b) The structural role of Fe3+, Ga3+, Al3+ and homogeneous iron redox equilibria in K2O-Al2O3-Ga2O3-SiO2-Fe2O3-FeO melts. J. Non-Cryst. Solids 86,303-310. Dingwell D. B. (1989) Shear viscosities of ferrosilicate liquids. Amer. Mineral. 74, 1038-1044. Dingwell D. B. (1991) Redox viscometry of some Fe-bearing silicate melts. Amer. Mineral. 76, 1560-1562. Dingwell D. B. and Virgo D. (1987) The effect of oxidation state on the viscosity of melts in the system Na2O-FeO-Fe2O3-SiO2. Geochim. Cosmochim. Acta 51, 195-205. Dingwell D. B. and Brearley M. (1988) Melt densities in the CaO-FeO-Fe2O3-SiO2 system and the compositional dependence of the partial molar volume of ferric iron in silicate melts. Geochim. Cosmochim. Acta 52, 2815-2825. Dingwell D. B. and Virgo D. (1988a) Viscosities of melts in the Na2O-FeO-Fe2O3-SiO2 systems and factors controlling relative viscosities of fully polymerized silicate melts. Geochim. Cosmochim. Acta 52, 395-403. Dingwell D. B. and Virgo D. (1988b) Viscosity-oxidation state relationship for hedenbergitic melt. Carnegie Instn. Washington Year Book 87, 48-53.

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Kingery W. D., Vandiver P. B., Huang I. W., and Chiang Y. M. (1983) Liquid-liquid immiscibility and phase separation in the quaternary systems K2O-Al2O3-CaO-SiO2 and Na2O-Al2O3-CaOSiO2. J. Non-Cryst. Solids 54, 163-171. Klein L. C , Fasano B. V., and Wu J. M. (1983) Viscous flow behavior of four iron-containing silicates with alumina: Effects of composition and oxidation condition. J. Geophys. Res. 88, A880-A886. Kblhler W. and Frischat G. (1978) Iron and sodium self diffusion in silicate glasses. Phys. Chem. Glasses 19, 103-107. Kress V. C. and Carmichael I. S. E. (1988) Stoichiometry of the iron oxidation reaction in silicate melts. Amen Mineral. 73, 1267-1274. Kress V. C. and Carmichael I. S. E. (1989) The lime-iron-silicate system: Redox and volume systematics. Geochim. Cosmochim. Ada 53, 2883-2892. Kress V. C. and Carmichael I. S. E. (1991) The compressibility of silicate liquids containing Fe2O3 and the effect of composition, temperature, oxygen fugacity and pressure on their redox states. Contrib. Mineral. Petrol. 108, 82-92. Kurkjian C. R. (1970) Mossbauer spectroscopy in inorganic glasses. J. Non-Cryst. Solids 3,157-194. Lange R. A. and Carmichael I. S. E. (1989) Ferric-ferrous equilibria in Na2O-FeO-Fe2O3-SiO2 melts: Effects of analytical techniques on derived partial molar volumes. Geochim. Cosmochim. Ada 53, 2195-2204. Lange R. A. and Navrotsky A. (1992) Heat capacities of Fe2O3-bearing silicate liquids. Contrib. Mineral. Petrol. 110, 311-320. Larson H. and Chipman J. (1953) Oxygen activity in iron oxide slags. Trans. AIME196, 1089-1096. Lauer H. V. J. (1977) Effect of glass composition on major element redox equilibria: Fe2+-Fe3+. Phys. Chem. Glasses 18, 49-52. Lauer H. V. J. and Morris R. V. (1977) Redox equilibria of multivalent ions in silicate glasses. J. Amer. Ceram. Soc. 60, 443-451. Lee Y. E. and Gaskell D. R. (1974) The densities and structures of melts in the system CaO"FeO"-SiO2. Met. Trans. 5, 853-860. Lesher C. E., Hervig R. L., and Tinker D. (1996) Self diffusion of network formers (silicon and oxygen) in naturally occurring basaltic liquids. J. Geophys. Res. 60, 405-413. Levin E. M., Robbins C. R., and McMurdie H. F. (1964) Phase Diagrams for Ceramists. 2nd ed. Amer. Ceram. Soc, Columbus. Luecke W. and Kohlstedt D. L. (1988) Kinetics of the internal oxidation of (Mg,Fe)O solid solutions. J. Amer. Ceram. Soc. 71, 189-196. McCammon C. A. (1994) A Mossbauer microprobe: Practical considerations. Hyperpne Interactions 92, 1235-1239. Magnien V., Neuville D. R., Cormier L., O. M., Pinet O., Briois V., Belin S., and Richet P. (2004) Kinetics of iron oxidation in silicate melts: A preliminary XANES study. Chem. Geol. 213, 253-263. Medlin M. W., Sienerth K. D., and Schreiber H. D. (1998) Electrochemical determination of reduction potentials in glass-forming liquids. J. Non-Cryst. Solids 240, 193-201. Mo X., Carmichael I. S. E., Rivers M., and Stebbins J. (1982) The partial molar volume of Fe2O3 in multicomponent silicate liquids and the pressure dependence of oxygen fugacity in magmas. Mineral. Mag. 45, 237-245. Moore G., Righter K., and Carmichael I. S. E. (1995) The effect of dissolved water on the oxidation state of iron in natural silicate liquids. Contrib. Mineral. Petrol. 120, 170-179.

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Sumita S., Morinaga K. J., and Yanagase T. (1983) Physical properties and structure of binary ferrite melts. Trans. Japan Inst. Metals 24, 35-41. Tangeman J. A. and Lange R. A. (1998) The effect of Al3+, Fe3+, and Ti4+ on the configurational heat capacities of sodium silicate liquids. Phys. Chem. Minerals 26, 83-99. Tangeman J. A., Lange R. A., and Forman L. (2001) Ferric-ferrous equilibria in K20-Fe0-Fe203SiO2 melts. Geochim. Cosmochim. Ada 65, 1809-1819. Thornber C. R. and Huebner J. S. (1982) Techniques for using iron crucibles in experimental igneous petrology. Amer. Mineral. 67, 1144-1154. Thornber C. R., Roeder P. L., and Foster J. R. (1980) The effect of composition on the ferricferrous ratio in basaltic liquids at atmospheric pressure. Geochim. Cosmochim. Acta 44, 525-532. Toguri J. M, Kaiura G. H., and Marchant G. (1976) The viscosity of the molten FeO-Fe2O3-SiO2 system. In Extraction Metallurgy of Copper. Vol. 1. Physical Chemistry of Copper Smelting, pp. 259-273. Met. Soc. AIME, New York. Toop G. W. and Sammis C. S. (1962) Activities of ions in silicate melts. Trans. Met. Soc. AIME 224, 878-887. Urbain G., Bottinga Y., and Richet P. (1982) Viscosity of liquid silica, silicates and aluminosilicates. Geochim. Cosmochim. Acta 46, 1061-1072. Virgo D. and Mysen B. O. (1985) The structural state of iron in oxidized vs. reduced glasses at 1 atm: A 57Fe Mossbauer study. Phys. Chem. Minerals 12, 65-76. Waychunas G. A., Apted M. J., and Brown G. E. (1983) X-ray K-edge absorption spectra of Fe minerals and model compounds: Near-edge structure. Phys. Chem. Minerals 10, 1-9. Wendlandt R. F. (1991) Oxygen diffusion in basalt and andesite melts: Experimental results and discussion of chemical versus tracer diffusion."Contrib. Mineral. Petrol. 108, 463-471. Whittaker E. J. W. and Muntus R. (1970) Ionic radii for use in geochemistry. Geochim. Cosmochim. Acta 34, 945-957. Wiedenroth A. and Rilssel C. (2003) The effect of mixed akaline earths on the diffusivity and the incorporation of iron in 5Na.,OxMgO(15-x)CaOyAl203«(80-y)Si02 melts. J. Non-Cryst. Solids 330, 90-98. Wilke M., Behrens H., Burkhardt D., and Rossano S. (2002) The oxidation state of iron in silicic melt at 500 MPa water pressure. Chem. Geol. 189, 55-67. Wilson A. D. (1960) The microdetermination of ferrous iron in silicate minerals by volumetric and colorimetric method. Analyst 85, 823-827. Wu T. and Kohlstedt D. L. (1988) Rutherford backscattering spectroscopy study of the kinetics of oxidation of (Mg,Fe)2Si04. J. Amer. Ceram. Soc. 71, 540-545. Yinnon H. and Cooper A. R. (1980) Oxygen diffusion in multicomponent glass forming silicates. Phys. Chem. Glasses 21, 204-211.

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Iron-bearing Melts II. Structure Iron oxides are major components in natural and industrial silicate melts and glasses. It is the only major component existing in both di- and trivalent form under most conditions. Despite their importance and abundance, however, our knowledge of the structural behavior of iron oxides is less complete than for other major components in silicate melts and glasses such as Al2O3. The equilibria between Fe3+ and Fe2+ involve interaction with oxygen. Redox relations of iron and the structural behavior of Fe3+ and Fe2+ in silicate melts do, therefore, depend on the structure. Conversely, variations in redox behavior affect the silicate melt structure. In this Chapter, we will first discuss existing structural data relevant to the oxygen coordination polyhedra of Fe3+ and Fe2+ before integrating that information with our understanding of silicate melt structure. 11.1. Ferric Iron The similar electric charge and ionic radii of Fe3+ and Al3+ [Whittaker and Muntus, 1970] have led to the suggestion that the structural position of these two cations is similar in silicate melts and glasses [Waff, 1977; Mysen and Virgo, 1978]. This analogy is not, however, borne out by the roles of Fe3+ and Al3+ in silicate crystals. Here, tetrahedrally coordinated Al3+ is common. However, tetrahedrally coordinated Fe3+ in crystals is rare. In fact, alumino- and ferrisilicate glasses are not structurally similar either. X-ray radial distribution functions of analogous glasses such as NaAlSi3O8 and NaFeSi3O8 [Henderson etal, 1984] reveal differences in average bond distances (Fig. 4.11; Table 11.1). The T-0 bond lengths (T=Al,Si) in the aluminosilicate glasses [Taylor and Brown, 1979] are shorter than those (T=Fe3+,Si) in ferrisilicate glasses [Henderson et al., 1984]. Bond lengths in NaAlSiO 4 glass, however, are similar to those in NaFeSi3O8 and KFeSi3Og glass (Table 11.1). In other words, with similar T-0 distances the proportion of Al in aluminosilicates is greater than the proportion of Fe3+ in ferrisilicates . 11.1a. Bond Length The Fe 3+ -0 bond lengths in NaFeSi3Og and KFeSi3Og glasses are, nevertheless, consistent with Fe3+ in tetrahedral coordination because a 1.60 A Si-0 bond length and a 1.91 A [41 3+ Fe -O bond length [Brese and O'Keefe, 1991] yield an average bond length of 1.68 A.

Chapter 11

336

Table 11.1 Bonding characteristics of glasses from radial distribution functions [Henderson et al., 1984] Composition

T-O, A

T-T, A

SiO,

1.60

3.10

151

NaAlSi3O8" NaAlSi,O6» NaAlSiO/

1.63 1.64 1.67

3.12 3.13 3.17

146 145 143

NaFeSi3O8 KFeSi,Oa

1.70 1.70

3.20 3.30

140 152

a

T-O-T angle, degree

From Taylor and Brown [1979]

This distance is, within error, identical to the measured T-O distances (T=Fe,Si) for NaFeSi3O8 and KFeSi3Og glasses [Henderson et al, 1984]. Additional information on Si-0 and Fe 3+ -0 bond distances in ferrisilicate glasses has been obtained with neutron diffraction measurements and molecular dynamics simulations along the join (Na2O)03»(SiO2)07-(Na2O)03«(Fe2O3)07 (Figs. 11.1 and 11.2). In Fig. 11.1, the correlation function for a glass with 13 mol % of the(Na 2 O) 03 »(Fe 2 O 3 ) 07 component is compared with a simulated acmite glass spectrum with Fe3+ constrained to 6-fold oxygen coordination. The Fe-0 distance in the glass is considerably shorter (—1.91 A) than in the simulated acmite glass spectrum (2.05 A) and is consistent with Fe3+ in 4-fold coordination with oxygen [Holland et al., 1999].

Figure 11.1 - Correlation functions from neutron diffraction spectrum of (Na2O)03.(Fe2O3)? 13.(SiO2)057 glass and from simulated acmite with Fe3+ in 6-fold coordination with oxygen [Holland et al., 1999; Johnson et al., 1999].

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Figure 11.2 - Si-O, Na-O, and Fe-0 distances in glasses along the join (Na2O)0 3 .(SiO 2 ) 0 7-(Na2O)0 3 .(Fe 2 O 3 ) 0 7 as a function of (Na 2 O) 0 3 «(Fe,O 3 ) 07 content [Holland et al.', 1999].

The Fe-0 distance in glasses along the (Na2O)03»(SiO2)07-(Na2O)03»(Fe2O3)07join does, however, decrease with increasing ferric iron content (Fig. 11.2). Extrapolation of these bond distances to lower Fe3+ concentrations suggests that the Fe 3+ -0 distance may, in fact, approach that of Fe3+ in coordination polyhedra with more than 4 oxygen. In other words, the structural position of Fe3+ may depend on the iron content of silicate glasses and melts.

Figure 11.3 - Isomer shift of Fe3+, 7SFe3+, relative of Fe metal at 298 K, from Mbssbauer spectra of glasses along the nominal joins Na,Si,O5-Fe,O3 (open symbols) and Si6 7 -NaFe6, (closed symbols) as a function of iron oxide (Fe,O3) added. Numbers on individual points denote the Fe3+/EFe of these glasses from Mossbauer spectroscopy [Virgo et al., 1983; Dingwell and Virgo, 1988].

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Figure 11.4 - lsomer shift of Fe3+ (closed symbols) and Fe2+ (open symbols) for Fe-bearing silicate crystals [Burns, 1994].

11.1b. Oxygen Coordination

The structural interpretation of neutron and x-ray diffraction data of Fe3+-rich alkali silicate and aluminosilicate glasses (Figs, 4.11, 11.1, and 11.2) is supported by results from 57Fe Mossbauer resonant absorption spectroscopy. U 1 For example, for quenched melts (glasses) along the nominal joins SiO2-NaFeO2 [Dingwell and Virgo, 1988] and Na 2 Si 2 0 5 -Fe 2 0 3 [Virgo et al., 1983], the isomer shift of Fe3+ (relative to Fe metal), /SFe3+, ranges from about 0.32 to about 0.21 mm/s (Fig. 11.3). 112 From the relationships between /SFe3+ and oxygen coordination in crystalline materials (Fig. 11.4), this range is consistent with Fe3+ in 4-fold coordination. As illustrated in Fig. 11.5, there is, however, a distribution of isomer shift and quadrupole splitting in silicate glasses [Wivel and Morup, 1981; Alberto etal., 1996; Rossano etal, 1999; Galoisy etal., 2000; Wilke etal, 2002]. This distribution indicates that there is a range in Fe3+-O bond distances and 0-Fe 3+ -0 bond angles in silicate glasses and melts. Variable Fe3+-O bond distance can also be inferred from changes in /SFe3+ [Jackson et al., 1993; Johnson et al., 1999]. The isomer shifts of Fe3+ are, for example, negatively correlated with the iron content of highly oxidized glasses (Fig. 11.3) and can be used to "•'The hyperfine parameters (isomer shift and quadrupole splitting) from Mossbauer spectra depend on the temperature at which a spectrum is obtained [e.g.,Bancroft, 1973; Mitra, 1992]. For the isomer shift of Fe3+, this dependence is approximately 5• 10"4 mm/s K [Alberto, 1995; Johnson et al., 1999]. Unless otherwise stated in this Chapter, we will refer to hyperfine parameters recorded at room temperature (298 K). 112 These joins are referred to as "nominal" because, even though the glasses were formed by quenching melts equilibrated with air, there is a small fraction of iron as Fe2+ in these samples (see numbers on individual symbols in Fig. 11.3).

Iron-bearing Melts II. Structure

339

Figure 11.5 - Example of isomer shift and quadrupole splitting distribution in Fe-bearing CaOSiO, glass [Alberto et al., 1996].

relate iron content to Fe 3+ -0 distance. This can be accomplished by combining neutron diffraction data of glasses to obtain Fe 3+ -0 bond length and 57Fe resonant absorption spectroscopy for isomer shift. An approximately linear relationship between bond length, dFei+ 0 , and /S Fe3+ is obtained as follows [Johnson et al., 1999]: <W-O = 1 - 5 8 + 1 - 3 0 / S F =3 + -

(11.1)

From this relationship, the isomer shift range in Fig. 11.3 corresponds to d¥e3+ 0 -values ranging from 1.99 A, for the lowest iron oxide content (2.2 mol % as Fe2O3) in Na2Si2O5 glass, to 1.89 A for the Na2Si2O5 sample with the highest iron oxide content (13.4 mol %). For glasses along the nominal SiO2-NaFeO2 join (closed symbols in Fig. 11.3), the average bond distance ranges between 1.99 and 1.86 A. In agreement with x-ray and neutron diffraction

Figure 11.6- Isomer shift of Fe3+ (relative to Fe metal at 298 K) from Mossbauer spectra of glasses containg 5 wt % iron oxide as Fe,O3 in the systems Na2OAl,O3-SiO, (NAS) and CaO-Al,O3-SiO, (CAS). The nominal NBO/T~of each Fe-free series is 0.65. Melts were equilibrated with air at 1550°C [Mysen et al., 1985; Mysen and Virgo, 1989].

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Figure 11.7 - Luminescence spectra of glasses (excited with the 21,839 cm1 line of violet laser) in the systsem Na,O-SiO, with 0.5 mol % iron oxide added as Fe,O3 and equilibrated with air at 1375°-HOOT. Lower spectrum: Na/Si =1.22; upper spectrum: Na/Si = 5.67 [Fox et al, 1982].

data (Figs. 11.1 and 11.2), the Mossbauer data are thus consistent with a dependence of the geometry of Fe3+-O polyhedra on iron content. Aluminum content is another variable affecting melt structure (see Chapter 9) and potentially, therefore, the local structure near Fe3+. This has been observed in alkali aluminosilicate glasses where there is a negative correlation of Al/(A1+Si) with the isomer shift of Fe3+ (Fig. 11.6). For Na2O-Al2O3-SiO2-Fe-O glasses in Fig. 11.6, for example, the dFe3+0, calculated with equation (11.1), varies between 1.93 A and 1.88 A as Al/(A1+Si) increases from -0.1 to -0.4. This decrease may be related to the diminishing T-0 bond

Figure 11.8- Difference Raman spectrum (heavy line) between Na,,O»1.5SiO, glass (dashed line) and N,O» 1.5SiO2 glass with 6.3 mol % iron oxide added as Fe 2 O 3 formed after equilibration with air at 1375°-1400°C [Fox et al., 1982].

Iron-bearing Melts II. Structure

341

Figure 11.9- (a) Isomer shift and (b) quadrupole splitting of Fe3+ (relative to Fe metal at 298 K) from Mossbauer spectra of several glasses. Each sample contains 5 wt % iron oxide as Fe2O3. Glasses formed by quenching of melts equilibrated with air at 1550-1625°C [Mysen et al., 1984]. strength with increasing Al/(A1+Si) (Table 4.1) and possibly also to the fact that the Q n -speciation in peralkaline aluminosilicate melts is affected by Al/(A1+Si) [Mysen et al., 2003]. Note, however, that there is no correlation between /SFe3+ and Al/(A1+Si) for equivalent melt compositions in the system CaO-Al2O3-SiO2 (Fig. 11.6). Furthermore, the isomer shifts of Fe3+ are higher in the CAS than in the NAS system, a difference similar to that in Al-free melt and glass systems. This relationship indicates, therefore, that geometric differences (bond length and angle distortions) between FeO4-tetrahedra in Al-free systems remains in Al-bearing glasses and melts. Variable Fe 3+ -0 distances in FeO 4 tetrahedra may, in fact, be because there exist more than one type of tetrahedron in silicate melts and glasses. Different tetrahedra have been documented in silicate glasses and melts. In simple Na2O-SiO2-Fe2O3 glasses, Fox et al. [ 1982] found that Fe3+ is in tetrahedral coordination from Raman and luminescence spectroscopic data. Ferric iron may exist in more than one type of tetrahedron because there are bands near 14,200 and 16,200 cm 1 in the luminescence spectra (Fig. 11.7) and bands near 890 and 980 cm 1 in the Raman spectra, the intensities of which are correlated with Fe3+ content. (Fig. 11.8). The relative abundance of these tetrahedra appears to be a function of the Na/Si-ratio [Fox et al., 1982]. The existence of two different FeO4-tetrahedra is also consistent with interpretations of the 57Fe Mossbauer spectra of glasses in the same system [Burkhard, 2000]. The structural role of ferric iron in metal oxide ferrisilicate glasses depends not only on total ferric iron content, but also on the metal cation. In 57Fe Mossbauer spectroscopy, both the isomer shift and the quadrupole splitting values of Fe3+ are positively correlated with the ionization potential of the metal cation, Zlr2 (Fig. 11.9). For the alkaline earth metasilicate compositions in Fig. 11.9, the IS¥ti+ of less than -0.3 mm/s (at 298K) for

342

Chapter 11

Figure 11.10 - Relationship between the proportion of 4- and 6-fold coordinated Fe3+ and temperature of equilibration for a (CaO) 04 .(SiO 2 ) 04 .(Fe 2 O 3 ) 02 (nominal) glass after melt equlibration with air at the temperatures indicated [Nagata and Hayashi, 2001].

BaSiO 3 , SrSiO3, and CaSiO 3 are consistent with Fe3+ in 4-fold coordination with oxygen, whereas the /SFe3+ (at 298 K) of Fe-bearing MgSiO 3 glass is near the lower end of the range observed in minerals with octahedral Fe3+ [Burns, 1994]. Another interpretation of the isomer shift trends in Fig. 11.9a is that Fe3+ exists in both 4-fold and 6-fold coordination in all the melts. The increase of /SFc3+ with Z/f of the metal cation could reflect increasing fraction of Fe3+ in 6-fold coordination, a concept consistent with results from other iron-bearing alkaline earth and mixed alkali/alkaline earth silicate melts [Dingwell and Brearley, 1988; Hannoyer et al., 1992; Nagata and Hayashi, 2001; Burkhard, 2000]. That there may be more than one coordination state of Fe3+ has also been proposed, for example, for mixed alkali/alkaline earth silicate glasses [Levy et al., 1976; Nagata and Hayashi, 2001]. By using Mossbauer spectroscopy to characterize a (CaO) 04 »(SiO 2) 04 »(Fe2O 3) 02 glass formed from a melt equilibrated with air between 1608

Figure 11.11 - Isomer shift of Fe3+ (relative to Fe metal at 298 K) from Mossbauer spectra as a function of the Fe3+/EFe of Na,O-Al,O 3 -SiO, glasses containing 5 wt % iron oxide as Fe,O3. Melts were equilibrated at 1550 ; C with air and CO-CO, gas mixtures between 10"0-68 and 10~9 bar. The Fe-free nominal NBO/T of each series is 0.65 [Mysen and Virgo, 1989].

Iron-bearing Melts II. Structure

343

and 1858 K, Nagata and Hayashi [2001] found that the [4)Fe3+/[61Fe3+ ratio is negatively correlated with temperature (Fig. 11.10). The temperature-dependence yields an enthalpy of 68 kJ/mol for this coordination change, but it is not clear whether this transformation is actually governed by temperature, or whether the data of Fig. 11.10 result from the effect of temperature on the iron redox ratio. This interpretation of 57Fe Mossbauer data is also consistent with oxygen coordination numbers inferred from Fe3+-0 bond length information. If we assume that equation (11.1), derived for alkali silicate glasses, can also be applied to alkaline earth compositions, the /5Fe3+ interval in Fig. 11.9a corresponds to i/Fe3+ 0 ranging from about 1.96 = for Fe3+ in BaSiO3 melt to 2.03 A for Fe3+ in MgSiO 3 melt. From bond-valence calculations [Brese and O'Keefe, 1991], ^Fe3+o= 2-03 A would be consistent with Fe3+ dominantly in 6-fold coordination, whereas the 1.96 ~ value is near or slightly above that expected for Fe3+ in 4-fold coordination. A mixture of 4- and 6-fold coordinated Fe3+ might yield average rfFe3+0-values in between. In analogy with other transition metals [e.g.,Calas etal., 2002], one might also surmise that a 5-fold coordination could exist, but no data currently available appear consistent with such an intermediate coordination state of Fe3+ in silicate melts and glasses [Tangeman and Lange, 1998]. As a matter of fact, a relationship between /SFe3+ and Fe3+/XFe shown in Fig. 11.11 suggests that the redox ratio may be an important factor controlling the coordination state of Fe3+ [Virgo and Mysen, 1985]. For a sodium aluminosilicate, the ISFe3+ increases from about 0.25 mm/s to about 0.58 mm/s in the Fe3+/£Fe-range between 0.79 and 0.2 (isomer shift data from 298K Figure 11.12- Pre-edge from x-ray absoprtion spectra of staurolite, fayalite, and a Fe-bearing Mossbauer spectra). This led Virgo and glass [Calas and Petiau, 1983]. Mysen [1985] to propose that iron-

344

Chapter 11

Figure 11.13- Pair distribution function for FeO in a CaFeSi,O6 glass, quenched from a melt equilibrated at/ 0 , = 107 bar at 1075 K, from molecular dynamics (MD) simulation and EXAFS analysis [Rossano etal., 2000].

complexes locally resembling an inverted spinel structure form in these melts and that the relative stability of such complexes is governed by the Fe3+/SFe of the melt. This structural model is also consistent with magnetic [O'Horo and Levy, 1978] and thermodynamic [Kress and Carmichael, 1988] data. 11.2. Ferrous Iron In analogy with the crystal chemistry of ferromagnesian silicate crystals, it is often assumed that Fe2+ occupies structural positions similar to Mg in silicate melts and glasses. From this reasoning Fe2+ is a network-modifying cation perhaps in octahedral coordination with oxygen. That assumption, however, is not always supported by experimental data. For example, in an x-ray absorption study of a 2 F e O 4 M g O 4 C a 0 « S i 0 2 glass, Calas and Petiau [1983] concluded that the oxygen coordination number around Fe2+ might be closer to 4 than to 6. They suggested that similar x-ray absorption spectra of staurolite, which has 4-fold coordinated Fe2+ [Smith, 1968], and that of the 2 F e O 4 M g O 4 C a O S i 0 2

Figure 11.14- Optical absorption spectra of Fe2+ in an NaAlSi3O8 glass containing 3.08 wt % FeO and in an (NaAlSi3O8)05(CaMgSi2O6)05 glass containing 1.98 wt % FeO. Glasses quenched from melts equilibrated at 1200-1500°C with CO,-H, gas mixture [Keppler, 1992].

Iron-bearing Melts II. Structure

345

glass (Fig. 11.12) are consistent with at least a large fraction of Fe2+ in 4-fold coordination with oxygen. The energy overlap with the spectrum of fayalite, Fe 2 Si0 4 (Fig. 11.12), which has Fe2+ in 6-fold coordination [Smyth, 1975], was rationalized as a crystal field effect in the fayalite spectrum. Whether or not there are crystal field effects in the glass is not known. 11.2a. Oxygen Coordination A suggestion by Calas and Petiau [1983] of 4-fold coordinated Fe2+ in an alkaline earth silicate glass has recently gained support from a study that combined x-ray absorption (EXAFS) and molecular dynamics simulation (MD) of a CaFeSi2O6 glass (Fig. 11.13). Here, Rossano et al. [2000] concluded that there are 2 different oxygen-coordination spheres around Fe2+. One is a distorted tetrahedron (4-fold coordination) and the other a trigonal bipyramid (5-fold coordination). Optical absorption spectroscopy is another method suited to examine the structural role of transition metals in silicate melts [e.g., Wong and Angell, 1976]. In Fig. 11.14 are shown the spectra obtained by Keppler [1992] for Fe2+-bearing glasses of NaAlSi3O8+3 wt % FeO and (NaAlSi 3 O 8 ) 05 (CaMgSi 2 O 6 ) 05 +2 wt % FeO composition. Both spectra are dominated by a broad peak with a maximum near 1100 nm, which can be assigned to Fe2+ in 6-fold coordination, as deduced from comparisons with optical absorption spectra of Fe2+-bearing minerals. Similar assignments of Fe2+ from optical spectra of other Fe2+-rich glasses have been made by Bell and Mao [1974] and Nolet et al. [1979]. There are, however, two bands in the absorption spectra. The weaker band near 1900 nm in the spectrum of (NaAlSi3O8)05(CaMgSi2O6)05+ 2 wt % FeO glass (Fig. 11.14) could result from transitions in a distorted octahedron or, alternatively, to tetrahedrally coordinated Fe2+. Keppler [1992] suggested that the former assignment is the most likely. Calas and Petiau [1983], however, assigned the band near 1900 nm in absorption spectra of other Fe2+-bearing glasses to Fe2+ in tetrahedral coordination because the halfwidth of this band is much smaller than that of the 1100 nm band. That notwithstanding, Keppler [1992] concluded that the argument based on halfwidth differences of the 1100 and 1900 cm 1 bands is not necessarily correct because different iron-oxygen bonds exist in strongly distorted polyhedra. Thus, there is no reason why the amplitudes of their vibrations should be similar. The hyperfine parameters (isomer shift and quadrupole splitting) of Fe2+ from 57Fe Mossbauer resonant absorption spectroscopy have also been be used to distinguish between the possible 4, 5, and 6 oxygen coordination numbers. In crystalline ferromagnesian silicates there is, however, some overlap in the isomer shift values for [41Fe2+ and [6iFe2+ (Fig. 11.4). The interpretation of the isomer shift becomes even more difficult when the possibility of Fe2+ in 5-fold coordination is included [Waychunas et al., 1988]. The variations in hyperfine parameters for 4- and 5-fold coordination of Fe2+ are not necessarily large. The uncertainties associated with interpretation of the Mossbauer spectra are compounded by the possibility that the values of hyperfine parameters derived from the

346

Chapter 11

Figure 11.15- Example of 2-doublet fit of Lorentzian lines to "Fe resonant absorption Mossbauer spectrum of a glass in the system CaO-MgO-FeO-AL,O3-SiO, formed by quenching a melt equilibrated at MOOT at/ 0 , = 106 bar. In this fit, the component peaks of the two doublets, AA'and BB', were constrained to have equal area and equal full width at half height [Mossbauer spectrum from Mysen and Dubinsky, 2004].

absorption envelope may depend on the method used to deconvolute the spectra. Broadened Lorentzian curves are often fitted to the spectra of glasses. Furthermore, when dealing with the Fe2+ absorption doublet of reduced Fe-bearing silicate glasses (Fig. 11.15), the asymmetry of the Fe2+ absorption doublet can result in a fit that is statistically better with two Fe2+ doublets than with a single one [e.g., Mysen et al., 1985; Dyar et al., 1987; Wang et al., 1993]. Two absorption doublets may imply 2 different Fe2+-O polyhedra in the glasses. In the example in Fig. 11.15, the isomer shifts of 1.1 and 1.25 mm/s from Mossbauer spectra recorded at 298 K point to Fe2+ in 6-fold coordination with oxygen in both polyhedra. Such a solution is not at all unique, however, as other fits could be made consistent with a splitting of Fe2+ between tetrahedral and octahedral coordination. In the latter case, the high-velocity component would fit at lower velocity for the AA' than for the BB'doublet in Fig. 11.15 [Dyar et al, 1987]. The underlying problem in Mossbauer spectroscopy of glasses is that rather than modeling the line shape of the absorption envelope, we should model the distribution of the hyperfine field because its distribution is in direct response to the structure around the Fe nucleus. Fitting of the hyperfine parameter distribution is, therefore, a more appropriate approach to the deconvolution of the Mossbauer absorption envelope [Alberto, 1995; Rossano et al., 1999; Galoisy et al, 2000; Wilke et al, 2002]. In reduced Fe-bearing Casilicate glasses, fitting the Fe2+ hyperfine parameter distribution (Fig. 11.16) yields maximum /SFe2+between 1.1 and 1.2 mm/s (marked "l6|Fe2+". 11.16). There is also a smaller intensity maximum near 0.9 mm/s (marked " |4| Fe 2+ ". 11.16). Alberto et al. [1996] interpreted the results of Fig. 11.16 (and those obtained for other Ca-silicate glasses) in

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347

Figure 11.16 - Example of 2dimensional fit to hyperfine parameter distribution (isomer shift and quadrupole splitting) of a CaOSiO, glass (Ca/Si=0.7) with 5 wt % FeO formed by quenching of melt equilibrated at 1550°C at/ 02 = 10" bar. The positions markedL4|Fe2+ and |6|Fe2+ indicate the location of maximum in distribution for 4- and 6-fold coordinated ferrous iron [Alberto, 1995].

terms of Fe2+ predominantly in 6-fold coordination along with less than 10 % of total Fe2+ in 4-fold coordination. In summary, the experimental data on the structural role of Fe2+ in silicate glasses are not always conclusive. Interpretations of optical absorption spectra favor Fe2+ in 6-fold coordination, whereas x-ray absorption techniques commonly have been interpreted in terms of a smaller number of oxygens in the Fe 2+ -0 polyhedra. In general, Mossbauer spectra have been found consistent with predominantly 6-fold coordination of Fe2+, but even this interpretation is not universal. The difficulty is compounded by the fact that different structural probes have been used to characterize the structural position of Fe2+ in the same sample in only a few studies . 11.3. Ferric and Ferrous Iron in Silicate Melts at High Temperature Application of glass structure data to Fe-bearing melts relies on the assumption that quenching does not significantly affect the structural position of Fe3+ or Fe2+. Resolution of this question requires examination of relations between quenching rate and redox relations or, even better, structural studies of melts at high temperature. There exist some data on redox and structural relations of iron oxides in glass as a function of temperature and quenching rate [Dyar and Birnie, 1984; Dyar et al., 1987]. From superliquidus temperatures to the glass transition, quenching at rates of the order of hundreds of degrees per second do not the affect redox ratio of the original melt. Dyar et al. [ 1987] did suggest, however, that the isomer shift of Fe2+ from Mossbauer spectroscopy

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Chapter 11

Figure 11.17 - Unpolarized Raman spectra of glass (25°C) and supercooled melt (771T)ofNa,O»3SiO,«0.5Fe,O3[Wangef al, 1993].

may depend on quenching rate although these were not quantified. If so, oxygen coordination polyhedra of Fe might differ in molten and glassy silicates. Diffraction techniques and vibrational spectroscopy have been used to examine the structure of Fe-bearing melts at high temperature, but only for a relatively small number of compositions. An oxidized and a reduced sample of a Fe-bearing sodium trisilicate were investigated by Wang et al. [1993]. From Mossbauer analysis of an Na2O»3SiO2»0.5Fe2O3 glass formed from melt equilibrated in air at 771°C, all iron was found to be oxidized. The Raman spectra of this glass at 25 °C and of the supercooled liquid at 771°C show considerable similarity (Fig. 11.17). Wang et al. [1993] concluded that Fe3+ is in 4-fold coordination in both the glass and the melt. They also observed, however, an intensity growth near 1060-1070 cm 1 in the high-temperature Raman spectrum, but could not determine whether this was due to some changes in Qn-abundance as the temperature was increased across the glass transition or, more simply, to temperaturedependent Raman cross-sections.

Figure 11.18 - Unpolarized Raman spectra of glass (25°C) and supercooled melt (676°C) of Na,O»3SiO,»FeO [Wang et al, 1993].

Iron-bearing Melts II. Structure

349

Figure 11.19 - Si-0 and Fe-0 distances in FeO-SiO, melts at 1250°-HOOT from x-ray diffraction [Waseda and Toguri, 1978].

By annealing the same material under a hydrogen atmosphere, Wang et al. [1993] obtained a glass of composition Na2O«3SiO2»FeO with all the iron as FeO. Its NBO/Si would be 1.3 with the assumption that all Fe2+ is a network-modifier. The Raman spectra at room temperature (glass) and at 676°C (supercooled liquid under a hydrogen atmosphere) are plotted in Fig. 11.18. Both spectra are nearly identical to that of Fe-free Na 2 O1.5Si0 2 glass, a glass whose NBO/Si is also 1.3 [Furukawa et al, 1981]. Hence, Wang et al. [1993] concluded that the Raman spectra of the reduced glass and melt are consistent with Fe2+ serving in a network-modifying role. Unfortunately, the structural interpretation by Wang etal. [1993] conflicts with those of near-edge x-ray absorption (XANES) spectra of glass and melt of a nearly identical composition [Waychunas et al., 1988]. Even though the Mossbauer spectra of glasses in the latter study are similar to those reported by Wang et al. [1993], Waychunas et al. [1988] concluded that the XANES spectra of melts at 850°C are best interpreted in terms of Fe2+ in 4-fold coordination. This conclusion would agree with that of Waseda and Toguri [1978] and Waseda et al. [1980] who found, from x-ray absorption studies of FeO-SiO 2 and FeO-Fe2O3-SiO2 melts, that the Fe-0 bond lengths (between 2.04 and 2.08 A) are those expected for Fe2+ in 4-fold coordination (Fig. 11.19). From the bond valence treatment, of Breseand O'Keefe [1991], Fe-0 bond lengths in this range could, however, be considered consistent with those expected for Fe2+ in a coordination state higher than 4. Thus, the conclusion that Fe2+ is in 4-fold coordination with oxygen might not be as firm as originally suggested by Waseda and Toguri [1978] and Waseda et al. [1980]. In summary, (i) the Raman data for Na2O«3SiO2«0.5Fe2O3 and Na2O»3SiO2«FeO glasses and melts indicate significantly different roles of Fe3+ and Fe2+ in the silicate melt structure (Figs. 11.17 and 11.18). (ii) The Raman spectra of Na2O«3SiO2»FeO glass and melts are similar to Raman spectra of Na2O»1.5SiO2 glass, which suggest that Fe2+ is indeed, a network-modifying cation, (iii) The Fe2+-O bond lengths from the hightemperature FeO-SiO 2 melt x-ray data (Fig. 11.19) are consistent with 6-fold coordinated Fe2+. (iv) In contrast, Fe3+ is in 4-fold coordination in oxidized melts and glasses.

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Chapter 11

11.4. Iron in Silicate Melts and Glasses at High Pressure

Figure 11.20 - (a) Redox ratio of iron, (b) quadrupole splitting, and (c) and isomer shift of Fe3+ from Mossbauer spectra (relative to Fe metal at 298 K) of Na,Si2O5 + 7.5 mol % (nominal) Fe,O3 quenched from 1400°C at the pressures indicated [Mysen and Virgo, 1985].

The similar ionic radii of Fe3+ and Al3+ and their similar formal electrical charge have led to suggestions in early studies that Fe3+ might be used as a proxy for Al3+ to investigate the effect of pressure on the structural role of Al3+ in silicate melts [Waff, 1977]. On this basis, Mysen and Virgo [1978] examined the influence of pressure on melts along the (nominal) join NaAlSi2O6-NaFe23+Si2O6 with the aid of Mossbauer spectroscopy. They found, however, that the main effect of pressure to several GPa pressure was to reduce Fe3+ to Fe2+. The redox ration of iron likely depends on pressure because the mollar volumes of FeO and Fe2O3 differ (see section 10.4b). This effect was investigated further by Mysen and Virgo [1985] with melts along the nominal join Na 2 Si 2 0 5 -Fe 2 0 r They reported 57Fe Mossbauer spectroscopic data of glasses formed by temperaturequenching melts in equilibrium with air at pressures of up to 4 GPa. They not only observed that Fe3+/£Fe decreases with increasing pressure (Fig. 11.20a), but also that the hyperfine parameters of Fe3+ are pressure sensitive (Fig. 11.20b and c). The rapid increase in isomer shift from about 0.3 mm/s, at ambient pressure and 298 K, to slightly less than 0.6 mm/s for glasses formed at 3 and 4 GPa points to a transformation of Fe3+ from tetrahedral to perhaps octahedral coordination. It was suggested that this coordination change was in response to decreasing Fe3+/£Fe as the

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351

pressure increased. There is no evidence in the Mossbauer spectra of these glasses to suggest that the structural role of Fe2+ varies with pressure. 11.5. Redox Relations and Melt Polymerization Reduction of network-forming Fe3+ to network-modifying Fe2+ may be expressed with the equation [Holmquist, 1966]: 4 FeO 2 ' <=> 4 Fe2+ + O2 + 6 O 2 \

(11.2)

In this equation, the oxygen anion, O2~, is the link between the redox reaction and the silicate network via a schematic reaction of the type: 2 Q4 + O2- <^> 2 Q3.

(11.3)

In equation (11.2), the NBO/Si of Q4 structural units equals 0, and that of Q3 equals 1. Reduction of tetrahedral Fe3+ to octahedral Fe2+ does, therefore, result in depolymerization of the melt: 4 FeO 2 ' + 12 Q4 <=> 12 Q3 + 4 Fe2+ + O2.

(11.4)

It follows from equation (11.4) that parameters affecting the iron redox ratio also influence melt polymerization and NBO/T (Fig. 11.21). By increasing the abundance of Fe2O3 in a silicate melt at ambient pressure, for example, silicate polymerization increases (Fig. 11.21a). The Fe3+/ZFe ratio can also control the silicate polymerization. This ratio, in turn, varies with temperature, pressure, oxygen fugacity, and melt composition. These parameters will, therefore, also affect polymerization of Fe-bearing silicate melts. At constant iron content and oxygen fugacity, increasing temperature results in decreasing Fe3+/XFe (see Chapter 10). Increasing temperature will, therefore, cause equilibria (11.3) and (11.5) to shift to the right thus depolymerizing Fe 3+ -containing silicate melts (Fig. 11.21b). Two trends are shown, however, in Fig. 11.21a. 113 The dashed line is NBO/T trajectory with Fe3+ in 4-fold coordination at all temperatures ([41Fe3+). The "actual" trend depicts gradual transformation o f [41Fe3+ to i6'Fe3+ due to increasing temperature and decrease in Fe3+/XFe, which, in turn, induces the coordination change of ferric iron [Mysen and Virgo, 1989]. As a result of the coordination transformation of Fe 3+ ,

113

The melt in Fig. 11.21B is a peralkaline Na,O-Al^-SiO,melt with Al/(A1+Si) = 0.334 and Na/(Al+Si)=0.65.

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Figure 11.21 - Relationships between degree of polymerization of silicate network, NBO/T, and structure and redox relations of iron, (a) Na,Si,O5+Fe,O3 (nominal mol % as indicated) glass quenched from melt equilibrated at 1400°C with air [Mysen and Virgo, 1985]. (b) Sodium aluminosilicateglass with Al/(A1+Si) = 0.334, Na/(Na+Al) = 0.65 and 5 wt % iron oxide added as Fe,O3 quenched from melt equilibrated with air at the temperatures indicated [Mysen and Virgo, 1989]. (c) Glass of nominal composition Na,Si,O5+7.5 mol % Fe,O3, quenched from 1400°C at the pressure indicated [Mysen and Virgo, 1985]. (d) Same glass as in (b) quenched from melt equilibrated with CO-CO, gas mixture to control fQl at 1550°C [Mysen and Virgo, 1989]. depolymerization of the melt occurs. This depolymerization can be described by the reaction: [41

FeO,- + 2 Q 4 <=> |61Fe3+ + 2 Q3.

(11.5)

Iron-bearing Melts II. Structure

353

Pressure increases also cause reduction of Fe 3+ to Fe 2+ and, therefore, depolymerization of the melt structure. For Na2Si2O5 melt with 7.5 mol % iron oxide added (Fig. 11.21c), the NBO/T is more sensitive to pressure ("actual" curve) than expected if the coordination state of Fe3+ were not affected by pressure (dashed line in Fig. 11.21c). In the latter case, pressure-induced melt depolymerization is that described by equation (11.4) only. However, as pressure can also induce coordination transformation of Fe3+ from 4-fold to 6-fold, equations (11.4) and (11.5) describe the circumstances. The resulting NBO/T trajectory is marked "actual" in Fig. 11.21c. Decreasing oxygen fugacity affects the degree of polymerization in the same manner as pressure and temperature (Fig. 11.21d). For the melt composition in Fig. 11.21d, the two depolymerization curves ("actual" and "|41Fe3+") meet at 1550°C at an oxygen fugacity between 10 8 and 10~9 bar, where all iron is Fe2+ [Mysen and Virgo, 1989]. Changes in melt polymerization, NBO/T, obviously also affect Qn speciation, but experimental data are lacking to determine the relationships between iron content, redox ratio of iron, structural roles of Fe2+ and Fe3+, and Qn speciation. These relationships will depend on whether tetrahedrally coordinated Fe3+ substitutes for Si4+ in the structure or if it forms isolated complexes. In the former case, partitioning of Fe3+ between individual Q"-species may affect speciation in a manner conceptually similar to that observed for Al3+ in peralkaline aluminosilicate melts (Fig. 9.25), thus, possibly driving the general Qn-speciation reaction (Stebbins, 1987), 2 Q" <=> Qn+1 + Q n l ,

(11.6)

to the right. The situation is, however, likely more complicated because Fe2+, with its large ionization potential, tends to favor bonding with oxygen in the least polymerized of available Q n -species [Q""1 in equation (11.6)]. This tendency would tend to drive equilibrium to the right with increasing pressure for Fe-bearing silicate melts. 11.5. Summary Remarks 1. The structural role of ferric iron in Fe3+-rich silicate melts and glasses is mainly that of a network-former. It depends, however, on the redox ratio of iron so that Fe3+ may be a network-modifying cation in melts with low Fe 3 7£Fe. 2. The oxygen coordination number around Fe2+ in melts is less clear. All evidence taken together indicates, however, that ferrous iron is dominantly a network-modifier, but it is possible that the structural role of Fe 2+ depends on silicate composition. 3. Given the above premises, increasing ferric iron content of a silicate melt induces melt polymerization, whereas increasing Fe2+ probably causes depolymerization. Thus, any variable affecting the redox state of iron (pressure, temperature, bulk composition, total iron content, and oxygen fugacity) will also affect polymerization and Qn-speciation of the melt.

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References Alberto H. V. (1995) Structural characterization of CaO-SiO,-TiO,-Fe-O glasses by Raman and Mossbauer spectroscopy. Ph. D., Univ. Coimbra. Alberto H. V., Pinto da Cunha J. L., Mysen B. O., Gil J. M., and de Campos N. A. (1996) Analysis of Mossbauer spectra of silicate glasses using a two-dimensional Gaussian distribution of hyperfine parameters. J. Non-Cryst. Solids 194, 48-57. Bancroft G. M. (1973) Mossbauer Spectroscopy: An Introduction for Inorganic Chemists and Geochemists. McGraw Hill. New York. Bell P. M. and Mao H. K. (1974) Crystal-field spectra of Fe2+ and Fe3+ in synthetic basalt glass as a function of oxygen fugacity. Carnegie Instn. Wash. Year Book 73, 496-497. Brese N. E. and O'Keefe M. (1991) Bond-valence parameters for solids. Ada Cryst. B 47, 192-197. Burkhard D. J. M. (2000) Iron-bearing silicate glasses at ambient conditions. J. Non-Cryst. Solids 275, 175-188. Burns R. G. (1994) Mineral Mossbauer spectroscopy: Correlations between chemical shift and quadrupole splitting parameters. Hyperfine Interact. 91, 739-745. Calas G. and Petiau J. (1983) Coordination state of iron in oxide glasses through high-resolution K-edge spectra: Information from pre-edge. Solid State Comm. 48, 625-629. Calas G., Cormier L., Galoisy L., and Jollivet P. (2002) Structure-property relationships in multicomponent oxide glasses. C. R. Chimie 5, 831-843. Dingwell D. B. and Brearley M. (1988) Melt densities in the CaO-FeO-Fe,O3-SiO, system and the compositional dependence of the partial molar volume of ferric iron in silicate melts. Geochim. Cosmochim. Ada 52, 2815-2825. Dingwell D. B. and Virgo D. (1988) Viscosities of melts in the Na,O-FeO-Fe,O3-SiO, systems and factors controlling relative viscosities in fully polymerized melts. Geochim. Cosmochim. Ada 52, 395-404. Dyar M. D. and Birnie D. P. (1984) Quench media effects on iron partitioning in a lunar glass. J. Non-Cryst. Solids 67, 397-411. Dyar M. D., Naney M. T., and Swanson S. E. (1987) Effect of quench methods on Fe3+/Fe2+ ratios: A Mossbauer and wet chemical study. Amer. Mineral. 72, 792-800. Fox K. E., Furukawa Y, and White W. B. (1982) Transition metal ions in silicate melts. Part 2. Iron in sodium silicate glasses. Phys. Chem. Glasses 23, 169-178. Furukawa T., Fox K. E., and White W. B. (1981) Raman spectroscopic investigation of the structure of silicate glasses. III. Raman intensities and structural units in sodium silicate glasses. J. Chem. Phys. 153, 3226-3237. Galoisy L., Cormier L., Rossano S., Ramos A., Calas G., Gaskell P., and Le Grand M. (2000) Cationic ordering in oxide glasses: The example of transition elements. Mineral. Mag. 64,409-424. Hannoyer B., Lenglet M., Diirr J., and Cortes J. (1992) Spectroscopic evidence of octahedral iron (III) in soda-lime silicate glasses and crystals. J. Non-Cryst. Solids 151, 209-216. Henderson G. S., Fleet M. E., and Bancroft G. M. (1984) An X-ray scattering study of vitreous KFeSi3O8 and NaFeSi3O8 and reinvestigation of vitreous SiO, using quasicrystalline modeling. J. Non-Cryst. Solids 68, 333-349. Holland D., Mekki A., Gee I. A., McConville C. F., Johnson J. A., Johnson C. E., Appleyard P., and Thomas M. (1999) The structure of sodium iron silicate glass - a multi-technique approach. J. Non-Cryst. Solids 253, 192-202. Holmquist S. (1966) Ionic formulation of redox equilibria in glass melts. J. Amer. Ceram. Soc. 49, 228-229.

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Jackson W. E., Mustre de Leon J., Brown G. E., Waychunas G. A., Conradson S. D., and Combes J.-M. (1993) High-temperature XAS study of Fe,SiO4 liquid: Reduced coordination of ferrous iron. Science 262, 229-232. Johnson J. A., Johnson C. E., Holland D., Mekki A., Appleyard P., and Thomas M. F. (1999) Transition metal ions in ternary sodium silicate glasses: A Mossbauer and neutron study. J. Non-Cryst. Solids 246, 104-114. Keppler H. (1992) Crystal field spectra and geochemistry of transition metal ions in silicate melts and glasses. Amer. Mineral. 11, 62-75. Kress V. C. and Carmichael I. S. E. (1988) Stoichiometry of the iron oxidation reaction in silicate melts. Amer. Mineral. 73, 1267-1274. Levy R. A., Lupis C. H., and Flinn P. A. (1976) Mossbauer analysis of the valence and coordination of iron cations in SiQ,-Na,O-CaO glasses. Phys. Chem. Glasses 17, 94-103. Mitra A. (1992) Applied Mossbauer Spectroscopy. Theory and Practice for Geochemists and Archaeologists, Pergamon Press. New York. Mysen B. O. and Virgo D. (1978) Influence of pressure, temperature, and bulk composition on melt structures in the system NaAlSLO -NaFe3+Si,O\. Amer. J. Sci. 278, 1307-1322. •*

2

o

2

6

Mysen B. O. and Virgo D. (1985) Iron-bearing silicate melts: relations between pressure and redox equilibria. Phys. Chem. Minerals 12, 191-200. Mysen B. O. and Virgo D. (1989) Redox equilibria, structure, and properties of Fe-bearing aluminosilicate melts: Relationships between temperature, composition, and oxygen fugacity in the system Na20-Al203-Si0,-Fe-0. Amer. Mineral. 74, 58-76. Mysen B. O. and Dubinsky E. (2004) Mineral/melt element partitioning and melt structure. Geochim. Cosmochim. Ada 68, 1617-1634. Mysen B. O., Virgo D., and Seifert F. A. (1984) Redox equilibria of iron in alkaline earth silicate melts: Relationships between melt structure, oxygen fugacity, temperature and properties of iron-bearing silicate liquids. Amer. Mineral. 69, 834-848. Mysen B. O., Virgo D., Neumann E. R., and Seifert F. A. (1985) Redox equilibria and the structural states of ferric and ferrous iron in melts in the system CaO-MgO-ALO3-SiO,: Relations between redox equilibria, melt structure and liquidus phase equilibria. Amer. Mineral. 70, 317-322. Mysen B. O., Lucier A., and Cody G. D. (2003) The structural behavior of Al+ in peralkaline melts and glasses in the system Na,O-Al,O3-SiO,. Amer. Mineral. 88, 1668-1678. Nagata K. and Hayashi M. (2001) Structural relaxation of silicate melts containing iron oxide. J. Non-Cryst. Solids 282, 1-6. Nolet D. A., Burns R. G., Flamm S. L., and Besancon J. R. (1979) Spectra of Fe-Ti silicate glasses: Implications to remote-sensing of planetary surfaces. Proc. 10th bun. Planet. Sci. Conf, 1775-1786. O'Horo M. P. and Levy R. A. (1978) Effect of melt atmosphere on the magnetic properties of a [(SiO,)45 (CaO)55]6, [Fe,O3]35 glass. J. Appl. Phys. 49, 1635-1637. Rossano S., Balan E., Morin G., Bauer J.-R, Calas G., and Brouder C. (1999) 57Fe Mossbauer spectroscopy of tektites. Phys. Chem. Mineral. 26, 530-538. Rossano S., Ramos A. Y., and Delaye J. M. (2000) Environment of ferrous iron in CaFeSi,O5 glass: Contributions of EXAFS and molecular dynamics. J. Non-Cryst. Solids 273, 48-52. Smith J. V. (1968) The crystal structure of staurolite. Amer. Mineral. 53, 1139-1155. SmythJ.R. (1975) High temperature crystal chemistry of fayalite. Amer Mineral. 60,1092-1097. Stebbins J. F. (1987) Identification of multiple structural species in silicate glasses by 29Si NMR. Nature 330, 465-467. Tangeman J. A. and Lange R. A. (1998) The effect of Al3+, Fe3+, and Ti4+ on the configurational heat capacities of sodium silicate liquids. Phys. Chem. Minerals 26, 83-99.

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Taylor M. and Brown G. E. (1979) Structure of mineral glasses. II. The SiO,-NaAlSiO4 join. Geochim. Cosmochim. Ada 43, 1467-1475. Virgo D. and Mysen B. O. (1985) The structural state of iron in oxidized vs. reduced glasses at 1 atm: A 57Fe Mossbauer study. Phys. Chem. Minerals 12, 65-76. Virgo D., Mysen B. O., and Danckwerth P. D. (1983) The coordination of Fe3+ in oxidized versus reduced sodium aluminosilicate glasses: A 57Fe Mossbauer study. Carnegie lnstn. Washington Year Book 82, 309-313. Waff H. S. (1977) The structural role of ferric iron in silicate melts. Can. Mineral. 15, 198-199. Wang Z., Cooney T. F., and Sharma S. K. (1993) High temperature structural investigation of Na,O»0.5Fe2O3»3SiO, and Na,OFe03SiO, melts and glasses. Contrib. Mineral. Petrol. 115, 112-122. Waseda Y. andToguri J. M. (1978) The structure of the molten FeO-SiO, system. Metall. Trans. B. 9, 595-601. Waseda Y, Shiraishi Y, and Toguri J. M. (1980) The structure of the molten FeO-Fe,,O3-SiO, system by X-ray diffraction. Trans. Jap. Inst. Metall. 21, 51-62. Waychunas G. A., Brown G. E., Ponader C. W., and Jackson W. E. (1988) Evidence from x-ray absorption for network-forming Fe2+ in molten alkali silicates. Nature 332, 251-253. Whittaker E. J. W. and Muntus R. (1970) Ionic radii for use in geochemistry. Geochim. Cosmochim. Acta 34, 945-957. Wilke M, Behrens H., Burkhard D. J. M., and Rossano S. (2002) The oxidation state of iron in silicic melt at 500 MPa water pressure. Earth Planet. Sci. Lett. 189, 55-67. Wivel C. and Morup S. (1981) Improved computational procedure for evaluation of overlapping hyperfine parameter distributions in Mossbauer spectra. J. Phys. E. Sci. Instr. 14, 605-610. Wong J. and Angell C. A. (1976) Glass Structure by Spectroscopy. Marcel Dekker, New York.

357

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The Titanium Anomalies Under oxidizing conditions, titanium has the same 4+ electrical charge as silicon. Its ionic radius (0.61 A) is about twice that of Si4+, so that Ti4+ might appear unfit to substitute for Si4+, at least at low pressure. With its preferred 6-fold coordination with oxygen in crystalline materials, exemplified by rutile (TiO2), Ti4+ could, instead, be considered essentially as a network-modifying cation in silicate glasses and melts. But the reality is not that simple. Titanium may not only be a network former on its own. It also seems to engage in exchange with Si. As a result, physical properties of glasses and melts can be complex functions of temperature and chemical composition. These complex relationships have a direct bearing on magma generation in the Earth because TiO2 is ubiquitous in igneous rocks with a typical abundance up to 2-3 wt %. Even at such contents, the presence of Ti affects important features such as liquidus phase relations [DeVries et al., 1954; Kushiro, 1975] or liquid immiscibility [Visser and van Groos, 1979]. Of course, the influence of TiO2 is still stronger when its abundance reaches 10 wt % as observed in some lunar glasses [Reid et al., 1973] or alkali-rich, silica-poor igneous rocks [Chayes, 1975; Mitchell, 1991]. A need to understand better the structure and properties of Ti-bearing silicates also stems from various practical applications of these materials. For instance, TiO2 has long been used as a nucleating agent in glass ceramics [e.g., Strnad, 1986], where crystallization often develops after liquid unmixing induced by small amounts of Ti has produced a poor glass-forming melt [Maurer, 1962]. Titanosilicate glasses are also of interest because of their unusual physical and chemical properties. A striking example is provided by Ti-bearing silica glasses whose thermal expansion is still lower than that of pure SiO2 [Nordberg, 1943; Schultz, 1976]. Other glass properties that can be controlled by TiO2 include tensile strength, refractive index, and resistance to corrosion [Evans, 1982; Morsi and El-Shennawi, 1984]. 12.1. Phase Relations and Glass Formation Solid-liquid phase equilibria illustrates the complex structural role of Ti in silicate melts. Before this information is reviewed, however, the redox state of titanium must be discussed briefly as the presence of Ti3+ would obviously affect phase relationships. 12.1a. Titanium Redox Reactions It is customary to deal solely with Ti4+ although titanium is a transition element whose 3+ valence is stabilized under moderately reducing conditions. This neglect of Ti3+ is reflected

358

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Figure 12.1 - Redox equilibrium of titanium against oxygen fugacity at the indicated temperatures in sodium disilicate [Johnston, 1965] and in two aluminosilicate melts [Schreiber, 1977]. In the latter case 1.3 wt % was added to FAD (54.2 SiO2, 9.9 A12O3, 5.6 CaO and 30.3 wt % MgO) and to FAC (51.6 SiO2, 2.3 A12O3, 19.2 CaO and 26.9 wt % MgO ).

in the scarcity of studies that have been devoted to determining the temperature, composition, and pressure dependences of Ti3+/Ti4+ ratios. This redox reaction is similar to that of iron (Chapter 10), and can be written as: 4 Ti4+ + 2 O2- <=> 4 Ti3+ + O r

(12.1)

The few experimental studies of this equilibrium have indeed shown a linear relationship between log Ti 3+ /Ti 4+ and log fo (fo = oxygen fugacity) with a slope of about 4 (i.e., near 0.25 for a plot of log Ti4+/Ti3+ vs. log/ o ) at constant temperature and silicate composition [Johnston, 1965; Schreiber, 1977; Schreiber et al., 1978; Iwamoto etal., 1983]. The strong composition and temperature dependences of the equilibrium constant of reaction (12.1) is apparent in Fig. 12.1. The Ti3+/Ti4+ ratio increases by nearly a factor of 10 for a temperature rise of 50°C. Under the same conditions, the equilibrium constant differs by nearly two orders of magnitude for the two Ca,Mg aluminosilicate melts considered. As for any redox reaction, the most reduced valence is favored by higher temperatures with the result that the abundance of Ti 3+ could become significant in air above about 2000°C at ambient pressure. In their investigation of the phase relations in the SiO 2 -TiO 2 system, DeVries et al. [1954] indeed noticed weight losses that could have been due to formation of 5 wt % Ti 2 O 3 , which would have been present in solid solution with TiO 2 . All experimental work mentioned in the rest of this chapter has been performed in air at temperatures that were not extremely high. This will justify the assumption that

The Titanium Anomalies

359

Figure 12.2 - The SiO2-TiO2 phase diagram. Solid-liquid equilibrium data from DeVries et al. [1954], which are consistent with the observations of McTaggart and Andrews [1957], and solvus from Kirsten et al. [1999], with an estimated critical temperature of 2612 ± 25 K. Crist: cristobalite; L: liquid; Rut: rutile.

titanium was essentially in the form of Ti 4+ ions. As a matter of fact, Ti 3+ gives a glass a purple color that is readily observed if this valence state is present in significant amounts. Possible effects of Ti 3+ can be important, however, when dealing with titanosilicates under oxygen fugacities lower than 10~5-10~6 atm. 12.1b. SiO2-TiO2 Phase Relations Simplicity is the hallmark of the SiO 2 -TiO 2 phase diagram (Fig. 12.2). There is not a single compound between the two endmembers. In the liquid state, miscibility is restricted to narrow composition intervals at both ends of the diagram. As noted by DeVries et al. [1954], liquid immiscibility is not only stable but is such that "two liquids separate almost immediately owing to the difference in physical properties". From their own experiments and thermodynamic modeling of the miscibility gap, Kirschen etal. [1999] have suggested that the critical point of the solvus is near 2600 K. These dramatic features of liquidus phase relations should not conceal less obvious aspects that are more directly relevant to the SiO2-rich silicates of natural or industrial interest. A freezing point depression of 170°C is found for cristobalite at the eutectic point near 1550°C and 10 mol % TiO2. This decrease contrasts with the less impressive 50°C freezing-point depression of rutile at the other end of the system. For binary silicate systems, the solvus has accordingly the peculiarity of being displaced away from SiO 2 instead of being located near SiO 2 . However, it is within the 0-15 mol % TiO2 composition range that homogenous glasses can be quenched. The particularly low thermal expansion of SiO2-TiO2 glasses was tentatively assigned by Dietzel [1943] to contraction of Ti-O-Si bridges. Solution of TiO 2 in SiO 2 glass tends to be unstable, however, on long annealing times. This is indicated by the unusual occurrence of structural relaxation 200°C below the standard glass transition temperature, T , at a viscosity of about 10 1 5 3 Pa s. This relaxation precedes partial precipitation of TiO 2 within the SiO 2 glassy matrix [Schultz, 1976]. An analogous contrast exists for the solid phases of SiO 2 and TiO2. There is no significant solid solution of SiO 2 in rutile, which is isostructural with stishovite (the high-

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Chapter 12

pressure structural form of silica). In contrast, up to about 10 mol % TiO2 can enter the cristobalite unit-cell when SiO2-TiO2 glasses crystallize at 1450°C. The lattice parameters of this cristobalite increase linearly with TiO2 content [Evans, 1970]. In spite of its strong preference for octahedral coordination, Ti4+ can thus enter in significant amounts in the open three-dimensional tetrahedral networks of the solid and liquid phases of SiO2. Under which disguise Ti4+ does so cannot be determined from this information, however, as other mechanisms can be envisioned in addition to Si4+<=>Ti4+ substitution on tetrahedral sites of the structure. 12.1c. Ternary Phase Relations: Alkali and Alkaline Earth Titanosilicates If substituting for Si4+ in tetrahedral coordination, Ti4+ would differ markedly from Al3+ because it does not need to associate with a charge compensating cation. Hence, no analogies are to be drawn between the properties of alkali or alkaline earth titanosilicate melts and their aluminosilicate counterparts, save for regular variations induced by differences in the ionization potential of the M-cation. Like for Al3+ in aluminosilicates, however, one does observe that Ti4+ has greater affinity for alkali than for alkaline earth cations. Marked contrasts in liquidus temperatures, ternary compounds, and extent of glass formation between alkali and alkaline earth systems are evident in the ternary phase diagrams of Fig. 12.3. There is less of an effect of metal cation on miscibility gaps because the single, shared feature is the field of liquid immiscibility that develops near the TiO2 end-member. The width of the miscibility gap increases only marginally in the order Na, Ca, Mg. The real differences in the extent of liquid immiscibility seen in Fig. 12.3 originate in unmixing in the silica-rich parts of the diagrams which have already been examined in Chapter 6. For alkaline earth titanosilicates, liquidus temperatures are higher in the Mg than in the Ca system, but their slight variations point to a dearth of specific association between the oxide components throughout the diagrams. There is a single ternary compound in the Ca system (titanite, CaTiSiO5) and none in the Mg system. Only along the binaries do we find two Ca titanates — perovskite (CaTiO3) and Ca3Ti207 —, and three Mg titanates (MgTi2O5, MgTiO3, and Mg2TiO4) whose melting temperatures range from 1550 to 1970°C. Solid solutions are lacking. The only known exception is the solubility of a few wt % of CaTiO3 in CaSiO3 which has been curiously observed, not in the liquidus phase, pseudowollastonite, but in the subliquidus phase wollastonite [De Vries et al., 1955]. Consistent with the relationship noted in Chapter 2 between difficulty of vitrification and scarcity of compounds, glass formation requires unusally rapid quenching, particularly for the Mg system. Glass formation is restricted to the eutectic valleys that runs from the metal oxide-silica systems toward the center of the diagrams (Fig. 12.3), a feature that is also observed for barium titanosilicates [Cleek and Hamilton, 1956]. Under similar quenching conditions, the compositional extent of vitrification increases in the order Mg, Ca, Ba.

The Titanium Anomalies

361

Figure 12.3 - Phase diagrams of ternary titanosilicate systems, including stable miscibility gaps (as hachured areas) and glass formation (as grey areas). Data sources: Glasser and Marr [1979] and Hamilton and Cleek [1958] for the Na system; Rao [1963] for K; Massazza and Sirchia [1958] for Mg; and De Vries et al. [1955] for Ca. The latter two diagrams have been redrawn in mol %. Less information is available for the alkali titanosilicates. Liquidus data seem to be lacking for the potassium system. Potassium-bearing titanosilicate glasses can, nonetheless, be quenched from 1100°C in a large composition range [Rao, 1963]. This suggests that liquidus temperatures should not be higher than those determined by Glasser and Marr [1979] for the sodium system outside of the miscibility gap (Fig. 12.3) where liquidus temperatures do not vary much with Ti content. The important difference with alkaline earth systems lies in a large number of binary and ternary compounds in alkali titanosilicate systems. There are four sodium titanates (Na 2 TiO 3 , Na g Ti 5 0 14 , Na 2 Ti 3 O 7 , and Na 2 Ti 6 0 | 3 ) with known melting points between 1030° and 1300°C. There are also four ternary compounds (Na 2 TiSi0 5 , Na 2 TiSi 2 0 7 , Na 2 Ti 2 Si 2 0 9 , and Na 2 TiSi 4 0 n ), which begin to melt, incongruently for three of them, at

362

Chapter 12

Fig. 12.4 - Phase diagram of the SiO2TiO2-Al2O3 system [Kirschen et al, 1999]. The TiAl2O5 binary compound melts at 2127 K. Its eutectic withTiO2 is at 1971 K and 82 mol % TiO2. Stable liquid unmixing near the SiO2-TiO2 join where isotherms are narrowly spaced. Glass formation in the grey area [Kajiwara, 1988] temperatures lower than 965°C. Therefore, the affinity between TiO 2 and alkali oxides in crystalline materials likely is not coupled with very strong bonding. Finally, vitrification is easy for not only for the K but also for the Na system and takes place throughout most of the composition ranges where melts can be prepared [Glasser and Marr, 1979; Rao, 1963]. Glass formation even extends to the binary K 2 O-TiO 2 join near the 1:1 oxide ratio. This suggests that Ti has a dual structural role. It cannot be only a network-modifier but, as stressed by Rao [1963], its glass-forming ability suggests that Ti can also be a network-former in the sense discussed in section 4.2. 12. Id. Phase Relations in Chemically More Complex Systems Titanosilicates are good model systems to determine whether information gathered on simple melts can be applied to more complicated compositions. In preamble, however, the effects of Al on the SiO2-TiO2 system must be summarized. No complete phase diagram of the system SiO 2 -TiO 2 -Al 2 O 3 has been published, but the melting relationships should be represented correctly by the calculations of Kirschen et al. [1999] shown in Fig. 12.4. As there is not a single ternary compound, the phase diagram is extremely simple. In contrast to the wide miscibility gap along the SiO 2 -TiO 2 join (Fig. 12.3), there is a mixed compound and two eutectics points along both limiting Al2O3-bearing binary joins (Fig. 12.4). This observation suggests that Al can act as a "middleman" between Si and Ti. Accordingly, A12O3 causes the miscibility gap to shrink. The ternary miscibility gap is, in fact, slightly asymmetric, such that A12O3 partitions preferentially into the TiO2-rich melt (or, conversely, such that Ti partitions preferentially into the Al-rich phase). This observation is consistent with a stronger affinity of Al for Ti than for Si, at least in the SiO 2 -TiO 2 -Al 2 O 3 system where metals are lacking for charge compensation of Al 3+ in tetrahedral coordination with oxygen. This preference is also suggested by larger freezing-point depressions in the TiO2-A12O3 than in the SiO2-A12O3 system. The major effect, however, is the shrinkage of the miscibility gap upon addition of A12O3. With 2.5 mol %, the critical temperature decreases from 2600 to 1800 K and the gap eventually disappears at a slightly higher A12O3 content.

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Figure 12.5 - Variation of the extent of miscibility gap with TiO 2 content in the system KAlSi 2 O & Fe 2 SiO 4 -SiO 2 -TiO 2 : composition of SiO2-rich (open circles) and mafic (solid circles) liquids, the numbers denoting wt % TiO 2 [Visser and van Groos, 1979].

In chemically more complex melts, the presence of TiO2 also causes an expansion of liquid miscibility gaps [Hudon and Baker, 2002]. This is observed in the K 2 0-Fe0-Al 2 0 3 SiO2 system [Visser and van Groos, 1979], where TiO2 partitions preferentially into the less SiO2-rich melt (Fig. 12.5). Conversely, Al very effectively supresses liquid immiscibility in quaternary titanosilicates. In the SiO2-TiO2-CaO-MgO system, Ti also partitions into the SiO2-poor melt but it does so less efficiently than the other cations [Wood and Hess, 1980]. The result is that TiO2 is the most abundant oxide, after SiO2, in the SiO2-rich phase. As for the network-forming character of Ti, it also manifests itself by the presence of 2 wt % TiO2 in cristobalite on the liquidus. Rutile solubility determinations have been used to investigate the competition of Ti and Al for association with K and Ca in aluminosilicate melts [Dickinson and Hess, 1985]. The saturation concentration of TiO2 varies little with the CaO/(CaO+Al2O3) ratio (Fig. 12.6a), which illustrates the non-specificity of the interaction between Ti and Ca whether Al is present or not. In contrast, the TiO2 saturation concentration increases markedly with K2O/(K2O+A12O3), but it does so only after the meta-aluminous join has been crossed (Fig. 12.6a). Hence, there appears to be a definite affinity of Ti for K in the melt, but only when some K is left after the strong charge-balancing needs of Al3+ have been satisfied. The enthalpy of solution of rutile measured in Al-free melts by Gan et al. [1996] complements these results (Fig. 12.6b). The enthalpy of solution of rutile is slightly exothermic and increases continuously with TiO2 content in two potassium silicates. It is more exothermic, but independent of TiO2 content, in calcium silicate. Some light can be shed on the network-forming role of a cation through examination of the shift of liquidus phase boundaries. Kushiro [1975] observed that liquidus boundaries between silicates of contrasting degree of polymerization (e.g., enstatite and forsterite in the MgO-SiO2 system, and pseudowollastonite and silica in CaO-SiO2 system) shift toward increasingly SiO2-rich compositions with increasing content of the network-modifier

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Chapter 12

Figure 12.6 - Interaction of Ti with K and Ca. (a) Solubility of rutile in M-aluminosilicates against M2O/(M2O+A12O3) at 1475°C [Dickinson and Hess, 1985]. (b) Enthalpy of solution of rutile in K 2 Si 2 0 5 and CaSi2O5 melts against TiO2 concentration; data from Gan et al., [1996] who also reported a constant enthalpy of -45 ± 6 kJ/mol in CaQ 5 KSi 2 0 5 melt up to 27 mol % TiO2. cations Na + and K+ (Fig. 12.7). In contrast, Ti 4+ causes these boundaries to shift in the opposite direction. Kushiro [1975], thus, concluded that, at least in depolymerized melts, Ti 4+ serves primarily as a network-former. Finally, as already discussed in previous chapters, analysis of liquidus surfaces yields information on the thermodynamic activity of a given melt component. In the system SiO 2 -TiO 2 , Ryerson [1985] found values higher than unity for the activity coefficient of SiO2, y Si0 , determined from an analysis of the silica liquidus branch (see Fig. 8.10). An increase of the activity coefficient of TiO 2 with SiO 2 content has been deduced from the saturation surface of TiO 2 in high-silica alkaline aluminosilicate melts [Ellison and Hess, 1986]. This positive deviation from ideality is consistent with the unmixing observed at slightly higher TiO 2 content. From the enstatite/forsterite liquidus boundary in the system MgO-SiO 2 -TiO 2 , Ryerson [1985] also concluded that solution of TiO 2 leads to an increase in ySiO2 (Fig. 8.10). The trend opposes that found for K2O and NaAlO 2 . Deviations from ideality remain markedly negative, however, in accordance with the exothermic nature of the enthalpy of solution of rutile.

12.2. Physical Properties Volume is an obvious macroscopic expression of structure and, thus, of the interactions exerted at a microscopic level between the components of a system. The distinct systematics for the volume properties of alkali and alkaline earth titanosilicates expected

The Titanium Anomalies

365

Figure 12.7 - Variation of the phase boundary between pseudowollastonite (a-CaSiO3) and cristobalite (or tridymite) along the join CaO-SiO2 as a function of oxide added (as marked on individual curves). Mole number: wt %/molecular weight of oxide [Kushiro, 1975].

on this ground are borne out by experimental evidence. A less predictable feature is that thermodynamic and rheologic properties of titanosilicates, in addition, present unusual temperature dependences compared with Ti-free silicate glasses and melts. 12.2a. The Heat Capacity Anomaly The influence of TiO2 on heat capacity (Cp) was investigated by Richet and Bottinga [1985] to model the Cp of silicate melts as a function of temperature and composition. Two alkali titanosilicates (M2TiSi2O7, M = Na, K) were selected because of the wide temperature intervals over which they could be studied. For both melts, the heat capacity decreases markedly with increasing temperature after an unusually large jump of about 50 % at the glass transition (Fig. 12.8). At the highest temperatures investigated, the heat capacity of these melts tends to the values of their Ti-free counterparts. These variations are due only to the presence of TiO2, as borne out by the fact that the same temperaturedependent partial molar heat capacity derived for TiO2 can account for the experimental results. This applies not only to the two titanosilicates studied by Richet and Bottinga

Figure 12.8 - Configurational heat capacity of alkali titanosilicates and some of their Ti-free counterparts. For comparison, the heat capacity at the glass transition is 25 J/g atom K. Data from Richet and Bottinga [1985] and Bouhifd et al. [1999]. Compositions abbreviated with N: ; K: K2O; T: TiO2; S: SiO r

366

Chapter 12

Figure 12.9 - Viscosity-temperature relationships for the alkali titanosilicates of Fig. 12.8. The solid lines are fits made to the experimental data with equation (12.2) and the configurational heat capacities of Fig. 12.8. Data from Bouhifd etal. [1999] for titanosilicates and from Fontana and Plummer [1979] for sodium disilicate (NS2) whose viscosity has a "normal" temperature dependence.

[1985], but also to the heat capacity of liquid CaTiSiO5 [King etal., 1954]. The anomalous temperature dependence of Cp, thus, appears independent of the nature of the M-cation. Further experiments have confirmed not only the negative temperature dependence of Cp for titanosilicate melts [Lange and Navrotsky, 1993; Tangeman and Lange, 1998; Bouhifd et al, 1999], but also the lack of composition dependence for the partial molar heat capacity of TiO2, at least for alkali systems [Bouhifd et al., 1999]. Investigation of alkaline earth compositions in more detail would be interesting, but measurements of such compositions are made difficult by high liquidus temperatures and the mediocre glass-forming ability of alkaline earth titanosilicates. It is possible, however, to study the effect of TiO2 in aluminosilicate liquids [Roskosz et al., 2004]. Similar decreases of Cp with increasing temperatures were observed for several series of Ti-bearing sodium aluminosilicates. The Cp anomaly remains proportional to TiO2 content. As for other silicates, the glass transition of titanosilicates occurs when the glass heat capacity is near 3 R/g atom K [Lange and Navrotsky, 1993; Tangeman and Lange, 1998; Bouhifd et al., 1999; Roskosz et al, 2004]. The entire Cp anomaly, thus, is clearly configurational in origin. This anomaly depends only on TiO2 content in both Al-free and Al-bearing titanosilicates, even when all alkali cations serve as charge compensators for Al3+. As noted in Chapters 6 and 8 for Ti-free melts, this observation implies that the configurational heat capacity originates in interactions between structural entities that exist throughout the whole composition range of interest. Consistent with the fact that energy lies in short-range interactions, not in medium-range order (see section 3.2), we, thus, conclude that the Cp anomaly of titanosilicates is due to short-range interactions of Ti with oxygen, and that the anomaly is affected little by possible changes of Ti4+ coordination with composition.

The Titanium Anomalies

367

Figure 12.10 - Configurational entropy of alkali titanosilicates and some of their Ti-free counterparts. Data from Bouhifd etal. [1999]. Same compositions as in Figs 12.8 and 12.9.

12.2b. Configurational Entropy and Viscosity Titanosilicate melts provide a dramatic illustration of the quantitative link between configurational entropy, Sconf, and viscosity, rj. Lange and Navrotsky [1993] pointed out that alkali titanosilicate melts undergo extensive structural rearrangements when the glass transition is approached in view of the anomalously high rate at which these liquids lose configurational entropy. It follows that the activation enthalpy for viscous flow must increase markedly at high viscosity, as predicted from the equation log t] = Ae + BJTSconf,

(12.2)

where Ae and Be are constants, which is derived from the Adam and Gibbs [1965] theory of relaxation processes in viscous liquids [see Richet, 1984 and section 2.3d]. The viscosities measured by Bouhifd et al. [1999] for a series of alkali titanosilicate melts (Fig. 12.9) conform quantitatively to equation (12.2), where the temperature dependence of configurational entropy is calculated from the experimental Cpco"f data (Fig. 12.8). The unusually steep increases in the viscosity of titanosilicate melts when the glass transition is approached are underscored by the comparison made in Fig. 12.9 with sodium disilicate melt. Whereas the viscosity of the Ti-free and Ti-bearing liquids are similar near 1600 K, they differ by more than 6 orders of magnitude at 800 K. What remains to be determined is whether titanosilicate melts have higher entropy than their Ti-free counterparts at high temperatures, or a lower entropy at low temperatures. Inspection of the configurational entropies derived with equation (12.2) from the viscosity data indicates that the second alternative is correct (Fig. 12.10). Hence, the presence of TiO2 in a melt gives rise to additional mixing mechanisms compared to Ti-free melts. Without considering the oxygen environment of Ti, we conclude that this temperaturepromoted process likely involves mixing of Ti with other network-forming cations.

368

Chapter 12

Figure 12.11 - Contrasting effects of Ti on the viscosity of sodium silicates at high and low temperatures, (a) At constant SiO2 content, (b) At constant 17 mol % Na2O content, Data from Poole [1948], Bockris et al. [1955], Liska et al. [1996] and Bouhifd et al. [1999]. The viscosity and its temperature derivative are also quite sensitive to TiO2 content. At high temperature, addition of up to 0.5 mol of TiO2 to an melt leads to a 10-fold viscosity decrease [Dingwell, 1992a], whereas substitution of TiO 2 for Na 2 O in melts with 75 mol % SiO 2 does not have significant effects (Fig. 12.11a). The substitution of TiO 2 for SiO 2 results in slight viscosity changes at high temperature (Fig. 12.1 lb). Hence, the viscosity increases with decreasing temperature caused by the heat capacity anomalies are so sharp that the composition dependence differs considerably at low and high temperatures. Near the glass transition, substituting Ti for Si causes the viscosity to decrease by more than four orders of magnitude (Fig. 12.11b). Overall, however, the viscosity variations suggest that Ti plays predominantly a role of network former. Finally, measurements by Dingwell [1992a] illustrate how the high-temperature viscosity of titanosilicate liquids vary with the nature of the alkali or alkaline earth cation for the same M^SiTiOj stoichiometry (Fig. 12.12). For the alkali series, the variation conforms to the trends observed in binary metal-oxide (Chapter 6) or in aluminosilicate melts (Chapter 8). For the alkaline earth, in contrast, the differences between the Ba, Sr and Ca melts are negligible.

Fig. 12.12 - Effects of different alkali and alkaline earth cation on the high-temperature viscosity of M^SiTiOj melts. Data from Dingwell [1992a; tabulation errors for Cs corrected].

369

The Titanium Anomalies

Figure 12.13 - Partial molar volume of TiO2 in the NajSiOj-TiOj (NTS) and CaSiO3TiO 2 (CTS) systems, as given by the intercept of linear relationships with the 100 mol % TiO 2 axis at the temperatures indicated [Dingwell, 1992b].

72.2c. Volume-Composition Relationships The volumes measured by Nelson and Carmichael [1979] on 21 different titanosilicate melts with 2 to 8 components indicated a constant value of 24.9 cm3/mol at 1500°C for —melt

the partial molar volume of TiO2, Vj-'O • Lange and Carmichael [1987] found this value too low to account for their own observations on sodium titanosilicates, which instead yielded a volume of 28.3 cm3/mol at 1500°C. That this volume difference is real is shown in Fig. 12.13 by measurements on melts along the joins Na2Si03-Ti02 and CaSiO3TiO2 [Dingwell, 1992b]. If thermal expansion were accounted for, the difference between the values of 27.6 and 24.3 cm3/mol found at 1150 and 1600°C for the Na and Ca systems, respectively, would be even greater. As a matter of fact, the value of 24.3 cm3/mol fits very well with the volume of pure TiO2 measured at higher temperatures [Dingwell, 1991]. It also agrees with the volumes measured for the whole series of MTiSiO5 alkaline earth melts [Dingwell, 1992b]. These observations are consistent with a constant average coordination state of Ti4+ along the CaSiO3-TiO2 join. At room temperature, the molar volume of rutile is 18.9 cm3/mol, that of anatase (the other TiO2 form with 6-fold coordinated Ti) is 20.5 cm3/mol, whereas the entropy-volume relationships of Fig. 3.10 suggest a volume of about 25 cm3/mol for hypothetical TiO2 glass with 4-fold coordinated Ti. Even if one considers thermal expansion, it seems difficult to account for the TiO2 melt volume of 24.3 cm3/mol in

Figure 12.14 - Apparent partial molar volume of TiO2 in K 2 O-SiO 2 -TiO 2 melts against K2O concentration [Liu and Lange, 2001].

370

Chapter 12

Figure 12.15 - Room-temperature molar volume of TiO2-Na2O»nSiO2 against TiO2 content for the three values of n indicated. The derived partial molar volume of TiO2 is 22.13 cm3/mol for n = 2, and 21.37 cmVmol for n = 3 and 4. Data from Turnbull and Lawrence [1952], referred to a total of one mol of oxides (three data corrected for typos).

terms of only 6-fold coordinated Ti. The density data, thus, suggest an average coordination lower than 6 in alkaline earth titanosilicates. The situation could be more complicated, however, as suggested by data published only in a graphical form which indicate a composition dependent VriO m c a l c i u m titanosilicate melts [Morinaga et ai, 1974]. A complicated volume dependence on chemical composition is well established for alkali titanosilicate glasses and melts. The values of Vrfd r a n 8 e fr°m 25.8 ± 0.5 (for Cs) to 31.3 ± 0.5 (for K) cm3/mol, and do not vary with the ionization potential or other simple parameters of the cation [Dingwell, 1992b]. From other measurements on Na and K titanosilicates, Liu and Lange [2001] found that both Vrfo an<^ * ts temperature derivative depend on alkali content, with about a 15 % decrease of VriO f° r a 1^% decrease in M 2 O content (Fig. 12.14). Such a range of values reflects large structural differences between the manner in which Ti interacts with the various alkali cations. On the basis of available structural information (see below), these data were interpreted by Liu and Lange [2001] in terms of temperature- and composition-dependent oxygen coordination numbers of Ti. The more extensive density data sets available for glasses indicate that the actual picture should be more complex. For Na titanosilicate glasses, the density and refractive index were measured by Turnbull and Lawrence [1952] for the very purpose of determining the coordination state of Ti. The partial molar volume of TiO 2 does not vary with TiO 2 content along the three joins investigated between sodium silicates (Na 2 O«2SiO 2 , Na 2 O»3SiO 2 , and Na2O»4SiO2) and TiO 2 (Fig. 12.15), but it seems to increase with the Na/Si ratio. 121 The density and refractive index data were thought by Turnbull and Lawrence [1952] to be consistent with a coordination number close to 6 for Ti. 121

It might be suggested that the volumes of Figs 12.14 and 12.15 are biased because the fictive temperatures of the glasses were not the same. From available thermal expansion data [e.g., Liu and Lange, 2001], however, one finds that these effects are much too small to affect our conclusions. This also holds along joins at constant TiO2 content, along which variations of 150 K at most observed for the softening point [Glasser and Marr, 1979] would translate into volume effects of less than 0.07 cm3/mol (see section 6.3a).

The Titanium Anomalies

371

Figure 12.16 - Room-temperature molar volume of alkali titanosilicate glasses against (a) N a ^ and (b) K2O content. The mol % TiO2 indicated are constant for sodium glasses [Hamilton and Cleek, 1958] and vary by 1.5 mol % for potassium glasses [Rao, 1963]. In a study of the density changes induced by replacement of Na 2 O by TiO 2 at constant TiO 2 content, Hamilton and Cleek [1958] found the volume-composition relationships to become increasingly nonlinear as the TiO 2 content increases (Fig. 12.16a). Hence, the partial molar volume of both Na 2 O and SiO 2 become increasingly composition dependent. Ironically, that of TiO 2 varies little, being consistent with the determinations made from the measurements of Tumbull and Lawrence [1952]. An analogous conclusion is drawn from the density for potassium titanosilicate glasses [Rao, 1963]. Although they do not refer to really constant TiO 2 contents, the molar volumes also show strong curvature when K2O replaces SiO 2 (Fig. 12.16b). In this case, however, the partial molar volume of K 2 O does not vary significantly, whereas that of SiO 2 does. From the Gibbs-Duhem equation, £ n^dV'i - 0, it follows that the partial molar volume of TiO 2 must also depend on composition. In summary, the densities of Fig. 12.16 are relevant to the structure of melts at the glass transition. They indicate that specific association exists not only between Ti and a given alkali cation, but also that their nature and their effect on density varies with composition within a single ternary system. Hence, the volume-composition relationships of titanosilicates cannot be unraveled through studies of the environment of Ti alone. It follows that the reported variations of the partial molar volume of TiO 2 in melts might be too large because they implicitly account for the more important variations of the partial molar volumes of Na 2 O and SiO 2 .

372

Chapter 12

Fig. 12.17 - Effects of different alkali and alkaline earth cation on the hightemperature bulk modulus of M^SiTiC^ melts [Webb and Dingwell, 1994]

The composition ranges investigated in elastic studies [e.g., Manghnani, 1972] are too restricted to determine whether the compressibility of glasses are as sensitive to composition as to density. For melts, Webb and Dingwell [1994] complemented with ultrasonic measurements their investigation of alkali and alkaline earth M^SiTiC^ titanosilicates (Fig. 12.17). No clear systematics are apparent for the temperature dependence of the bulk modulus of alkali-bearing melts, which makes it difficult to draw inferences on possible connections with the heat-capacity anomaly. In contrast, the influence wrought by the various cations on compressibility follows nicely the order of ionization potential in both alkali and alkaline earth series. Curiously, compressibility appears more sensitive to composition than viscosity (Fig. 12.11). This is another peculiar feature of molten titanosilicates. 12.3. Structure of Titanosilicate Glasses and Melts The properties reviewed above indicate that the solution mechanisms of TiO2 in silicate melts depend on composition. Both the nature of the metal cations and the TiO2 content of the melt are important. To unravel the structural role of Ti4+ and determine structureproperty relationships, isolating individual composition effects on the Ti4+ solution mechanisms has been the main goal of studies made on series of compositionally simple systems. 12.3a. The System SiO2-TiO2 The Raman spectra of SiO2-TiO, homogeneous glasses shown in Fig. 12.18 [Henderson and Fleet, 1995] are similar to those reported previously [Chakraborty and Condrate 1985; Kusabiraki, 1986; Knight et al, 1989; Bihuniak and Condrate, 1981]. Two bands, near 945 and 1100 cm 1 , are of special interest because their intensity grows with increasing TiO2 concentration. Henderson and Fleet [1995] suggested that they are Si-O vibrations and reflect depolymerization of the silicate network caused by dissolution of Ti4+. Alternatively, these two bands could be assigned to Ti-0 vibrations [Tobin and Baak, 1968; Bihuniak and Condrate, 1981; Knight et al, 1989]. The latter interpretation is

The Titanium Anomalies

373

Figure 12.18 - (a) Raman and (b) Si K-edge x-ray absorption spectra of glasses in the system SiO2-TiO2 for the TiO2 concentration indicated on individual spectra [Henderson and Fleet, 1995, 1997]. more likely because the titanium near-edge in XANES experiments on SiO 2 -TiO 2 glasses (Fig. 12.18b) does not vary with increasing Ti 4+ content [Henderson and Fleet, 1997], whereas experiments on Na 2 O-SiO 2 glasses, for example (Fig. 7.3), show that depolymerization through formation of nonbridging oxygen causes decreases of K-edge energies [Li et al, 1995]. Whether incorporation of Ti 4+ in the structure of vitreous SiO 2 takes place via substitution for Si 4+ or via formation of Ti-0 clusters is not clear. Henderson and Fleet [1995] concluded that SiO 2 vibrational bands shift to lower frequency with increasing Ti-content, which is consistent with Ti 4+ -substitution for Si 4+ . The energy of the xray K-edge of titanium, however, does not vary with TiO 2 content. The K-edge data of SiO 2 -TiO 2 glasses seem difficult to reconcile with a Ti4+<=>Si4+ substitution model because spectra of minerals do show a clear dependence of the Si K-edge energy on substitution of Si 4+ by other tetrahedrally coordinated cations [Li et al., 1995]. More detailed structural information has been derived from XANES spectra made at the L near-edge of titanium. From comparisons between minerals and glasses (Fig. 12.19), Henderson et al. [2002] concluded that, at low TiO 2 contents (<2.8 mol % TiO 2 ), the Ti L-edge spectrum of SiO2-TiO2 glass most closely resembles that of fresnoite (Ba 2 TiSi 2 0 8 ), where Ti 4+ is in 5-fold coordination with oxygen ( l5i Ti). At higher TiO 2 concentration, the Ti L-edge spectrum is similar to that of Ba 2 Ti0 4 , where Ti 4+ is in 4-fold coordination. Such a coordination change is consistent with earlier x-ray absorption studies of SiO2-TiO2 glasses [e.g., Sandstrom etal, 1980; Greegor etal, 1983], although Greegor etal. [1983] favored Ti 4+ in 6-fold coordination at low TiO, content.

374

Chapter 12

12.3b. Titanium in Metal Oxide-Silicate and Aluminosilicate Glass and Melt As reviewed above, a number of glass and melt properties suggest a variety of structural environments around Ti4+ whose nature seem dependent on composition, Ti content, and temperature. In a XANES study Dingwell et al. [1994] used an empirical relationship between the intensity of the titanium K pre-edge peak (IP) and the coordination number (CN) of Ti in minerals as follows: IP (intensity, %) = - 28.6 CN (coordination number) + 194.9. (12.3) They concluded that the oxygen coordination number of Ti4+ is higher for alkaline earth than for alkali titanosilicates, with values varying from slightly above 4.5 to nearly 6 (Fig. 12.20). These differences are consistent with the volume data Figure 12.19 - Titanium L-edge described in section 12.2c. spectra of crystalline fresnoite and The presence of Ti 4+ in five-fold Ba2TiO4 and of SiO2 - TiO2 coordination as a titanyl group, i.e., a tetragonal glasses as a function of TiO2 pyramid with one double Ti = O bond, was content [Henderson et al., 2002]. established by Varshal et al. [1974] from comparisons between alkaline earth titanosilicate glasses and crystals made with quadruple resonance spectroscopy, and confirmed by Loshmanov et al. [1975] from neutron diffraction experiments. Varshal et al. [1975] concluded that octahedral Ti4+ promotes liquid immiscibility whereas titanyl groups favor chemical homogeneity thanks to the possibility of cross-linking with the silicate network through the four Ti-O bonds. In another Ti XANES study, Farges et al. [1996a] and Farges [1997] concluded that titanyl groups predominate in Ca and K silicate and aluminosilicate glasses (Fig. 12.20b), with minor proportions of 4- and 6-fold coordination, and that the proportion of '4'Ti is slightly higher in alkaline earth than in alkali systems. From a Ti L-near edge XANES study of Na, K and Ca titanosilicate glasses, Henderson et al. [2002] found instead that (i) the Ti4+ coordination number in the Ca-system is lower, on average, than in the K- and Na- systems, (ii) the average coordination numbers differs even in the Na- and K-systems, and (iii) the Ti coordination numbers in all three systems depend on TiO2 content. In both Na and K systems, Henderson et al. [2002] asserted that low-Ti glasses are dominated with 4-fold coordinated Ti4+ and that the proportion of Ti4+ in 5-fold coordination increases with increasing TiO2 content, a conclusion that is in qualitative accord with a neutron diffraction study [Yarker et al., 1986; Cormier et al., 2001] and the early Raman

The Titanium Anomalies

375

Figure 12.20 - Relationship between Ti pre-edge intensity and coordination number of Ti4+ in crystalline titanites as given by Dingwell et al. [1994] (a) and Farges et al. [1996a] (b). Thick line marked "glasses" in diagram (a) represents the range in pre-edge intensity and interpreted Ti coordination in glasses [Dingwell et al, 1994]. spectroscopic investigation of Bobovich [1962]. From an 17O NMR examination of CaTiSiO 5 glass, Kroeker et al. [2002] concluded that the NMR data are consistent with all of the structural environments suggested above. Raman spectroscopy frequently has been employed rather extensively to address the structure of titanosilicate glasses and melts [e.g., Iwamoto et al, 1975; Kato, 1976; Furukawa and White, 1979; Mysen et al., 1980; Markgraf et al, 1992; Henderson and Fleet, 1995; Alberto et al, 1995; Mysen and Neuville, 1995; Reynard and Webb, 1998]. In addition to the Si-0 vibrational bands, the Raman spectra characteristically show one or more strong bands between 800 and 900 cm"1 whose relative intensities depend on the TiO 2 content of the glass (Fig. 12.21). These bands have sometimes been assigned to Ti 4+ in some form of 4- or 5-fold fold coordination with oxygen [Mysen and Neuville, 1995; Reynard and Webb, 1998]. Higher coordination numbers have also been proposed by analogy with the Raman spectra of titanate crystals [e.g., Sdkkzetal, 1989]. Other Raman bands between 850 and 1200 c m 1 are assignable to Si-0 stretch vibrations in SiO 4 polyhedra as found in Ti-free glasses and melts (Figs. 7.6 and 7.7). As illustrated in Fig. 12.21, the relative intensity of these bands is sensitive to TiO 2 content [Furukawa and White, 1979; Henderson and Fleet, 1995; Alberto et al, 1995; Mysen and Neuville, 1995], hereby suggesting that the Q n speciation depends on TiO 2 content. In fact, many of the interpretations of Raman data do not depend directly on assignments of Ti-0 vibrational modes, but rather on the response to dissolved TiO 2 of the silicate network structure whose Raman signals are well established (see chapter 7). In this respect, Raman spectroscopy carries less uncertainty than x-ray absorption studies,

376

Chapter 12

whose results are not internally consistent. In particular, Mysen and Neuville [1995] determined the degree of silicate polymerization, NBO/T, from the abundance of the individual Qnunits in Na2Si2O5-Na2Ti2O5 glasses (Fig. 12.22). They derived the effect of dissolved TiO2 on the degree of silicate polymerization, NBO/T, from the expression: 71 = 3

NBO/T = X (4-n)Qn .

(12.4)

71 = 0

The strongly nonlinear relationship between the NBO/T and TiO2 content of glasses indicates variations of Ti coordination. At low TiO2 content, Mysen and Neuville [1995] noted that the rapid increase in NBO/T indicates that Ti4+ serves predominantly as a network-modifier, whereas Ti4+ may be predominantly a networkFigure 12.21 - Raman spectra of glasses former at high TiO2 content where NBO/T is along the join Na2Si2O5-Na2Ti2O5 for much less variable, an interpretation that is in various mol % TiO2 [Mysen and accord with that of Rao [1963] for Ktitanosilicate glasses. Although Mysen and Neuville, 1995]. Neuville [1995] discussed the solution mechanism in terms of 6-fold (at low TiO2 concentration) and 4-fold (at high TiO2 concentration) for Ti4+, the same evolution in NBO/T could be accomplished with 5- and 4-fold coordination. From the Raman spectra of Na2TiSi207, Reynard and Webb [1998] suggested that the high-intensity band slightly below 900 cm"1 (Fig. 12.23) is indeed due to Ti-0 vibrations in a TiO5 polyhedron. This interpretation agrees with x-ray absorption information [DingweWetaL, 1994;Fargese?a/., 1996a; Henderson etal, 2002] although there remain inconsistencies between the suggested proportion of [4|Ti and [5]Ti as a function of TiO2 content. This interpretation of Reynard and Webb [1998] is also consistent with neutron scattering results on K titanosilicate glasses [Cormier et al, 1998]. In comparison, information on the structural role of Ti4+ in aluminosilicates is rare. In a XANES study of potassium aluminosilicates, Romano et al. [2000] found that the Ti-coordination number decreases when the Al content increases. As the aluminum and silicon K-edge spectra show little or no effects of dissolved Ti4+, this cation has no significant influence on the local environment of Al3+ and Si4+. This conclusion agrees with the marginal effect of Al content on the rutile solubility in similar melt compositions [Dickinson and Hess, 1985].

The Titanium Anomalies

377

Figure 12.22 - Change in melt polymerization, NBO/T, as a function of TiO2 concentration in glasses along the join Na 2 Si 2 O 5 -Na 2 Ti 2 O 5 [Mysen and Neuville, 1995].

In summary, the Raman spectroscopy, neutron diffraction, 17O NMR spectroscopy, and x-ray absorption data are consistent with (i) Ti 4+ coordination varying with TiO 2 content; (ii) Ti 4+ coordination depending on metal cation; and (iii) slight effects of Al 3+ with, perhaps, only a small decrease in Ti-coordination number compared with Al-free melts. 12.4. High-Temperature Studies When examining K, Na, and Ca titanosilicate melts to 1650 K by x-ray absorption fine structure (XAFS) spectroscopy, Farges et al. [1996b] did not see any temperature effects on the titanium K-edge. Thus, they concluded that the anomalous heat capacity and thermal expansivity of titanosilicate melts are related to medium-range structure of the melt and not the local environment of Ti. As already noted, this is inconsistent with the fact that large energy effects have their origin in short- and not in medium-range order. Hence, the XAFS observations of Farges et al. [1996b] were likely not sufficiently sensitive to detect changes of melt structure with temperature. Paris et al. [1993] investigated by x-ray absorption the same melts studied for density by Dingwell [1992b]. Interestingly, their structural interpretations are consistent with local structural changes. In contrast, Cormier et al. [2001] detected relative changes in bond distances with temperature in a neutron scattering study of Ti-bearing potassium silicate melts to 1360 K. Without finding evidence for temperature-induced changes in Ti coordination, they observed variations of bond distances in the dominant TiO5 polyhedra. Four Ti-0 bond lengths are near 1.96 A, whereas there is also one much shorter Ti-0 bond at 1.68 A (Fig. 12.24). This latter bond distance becomes less important as these melts are heated above T . In their Raman study of Na2TiSi2O7 glass and melt, Reynard and Webb [1998] did not find evidence for changes in Ti coordination with temperature (Fig. 12.23). The spectra showed, however, a distinct intensity decrease near 700 cm"1 which was attributed to temperature-induced breakage of Si-O-Si and Ti-O-Ti bonds. Curiously, Reynard and Webb [1998] suggested that there is no polymerization change, a suggestion that is inconsistent

378

Chapter 12

Figure 12.23 - Raman spectra of N^TiS^Qj glass and melt (temperature and background corrected). The arrow indicates the position of the hightemperature intensity decrease. Glass transition near 650°C [Reynard and Webb, 1998].

with the asserted disruption of bridging Si-O-Si bonds at high temperature. From a massbalance point of view, changes in the abundance of Si-O-Si bonds should affect TiOn polyhedra as well unless disruption induces formation of defects. Mysen and Neuville [1995] have also monitored the evolution of the Qn-species by Raman spectroscopy. The deduced NBO/T of Na 2 Si 2 0 5 -Na 2 Ti 2 0 5 melts remains constant at low temperature, but varies slightly above temperatures that are close to the glass transition (Fig. 12.25). The effect is greater the higher the TiO2 content of the melt and reflects, most likely, small but distinct changes in the structure governed by temperaturedependent environment of Ti4+. Such structural variations have also been proposed by Liu and Lange [2001] from volume data on alkali titanosilicate melts, and they might also explain the anomalous temperature dependence of C con! of titanosilicate melts discussed above. 12.5. Structure and Properties of Ti-bearing Melts The structural and property data point to multiple solution mechanisms of Ti 4+ in silicate glasses and melts. Although some details need clarification, Ti 4+ can (i) be in 4-fold coordination and substitute for Si 4+ in Q n structural units, (ii) be in 4-fold coordination, but may form separate clusters of TiO 4 tetrahedra, and (iii) exists in oxygen polyhedra with a number of oxygens in excess of 4. Solution mechanism (i), proposed, for example, for SiO 2 -TiO 2 melts [Henderson and Fleet, 1995], does not affect the overall polymerization of the silicate network. This mechanism may, therefore, account for the observation that the activity coefficient of SiO 2 (y siO2 ) m silica-rich portions of the SiO 2 - TiO 2 system is not very sensitive to TiO 2 content [Ryerson, 1985]. In depolymerized melt systems, on the other hand, the ySiO2 increases rapidly with increasing TiO 2 content (Fig. 8.10). This suggests that, under these circumstances, the melt becomes increasingly polymerized as TiO 2 content increases.

379

The Titanium Anomalies c g o •4—

C

o o o

Figure 12.24 - Differential correlation function of K 2 0«2Si0 2 «Ti0 2 glass and melt at several temperatures, obtained after subtracting contributions from Si-O, O-O, and K-0 [Cormier era/., 2001].

CD

Q 1.5

2.0

2.5

Radial distance, A That suggestion also agrees with the shift of the pseudowollastonite/silica polymorph liquidus boundary in Fig. 12.7. This interpretation is also in agreement with Si XANES spectra of T-bearing alkali and alkaline earth metasilicate glasses ([Henderson and StAmour, 2004]. One explanation for this evolution can be an equilibrium between Ti- and Sicomplexes with both Ti 4+ and Si 4+ in 4-fold coordination: Q4(Ti) + Q 3 <=» Q3(Ti) + Q 4 .

(12.5)

In this equation, Q4(Ti) and Q3(Ti) denote Qn-species with Ti 4+ in the tetrahedra, whereas Q 4 and Q 3 denote Qn-complexes with Si 4+ . The partitioning of Ti between coexisting immiscible liquids (Fig. 12.5) and the solubility of rutile in depolymerized melts (Fig. 12.6) suggest that Ti 4+ tends to favor structural species that contain nonbridging oxygen and, therefore, that equation (12.5) is shifted to the right. Given that the abundance of 4-fold coordinated Ti 4+ is higher the more electronegative the alkali or alkaline earth metal, the y siO2 in depolymeri/ed silicate melts is likely correlated positively with the ionization potential of the metal cation. In alkaline earth systems, the partial molar volume of TiO 2 ( V'TIV ) *s relatively insensitive to the nature of the cation (Table 12.1). This indicates that the coordination state of Ti 4+ in alkaline earth titanosilicate melts does not vary significantly with the ionization potential of the cation. In alkali systems, on the other hand, Vrfo is sensitive to the type and proportion of the alkali metal (Table 12.1, Fig. 12.14). Both x-ray diffraction and vibrational spectroscopic data indicate that the coordination state of Ti 4+ in such melts is sensitive to the same parameters. Coordination states higher than 4 implies that solution of TiO 2 results in silicate depolymerization, a feature that can be illustrated with a schematic expression of the form: Q4(Ti) + 2Q 4 <=> Ti(*) + 2Q 3 ,

(12.6)

380

Chapter 12

Figure 12.25 - Change in melt polymerization, NBO/T, as a function of temperature as calculated with equation (12.4) along the join Na2Si205-Na2Ti205 for various TiO2 contents [Mysen and Neuville, 1995].

where Ti(*) denotes Ti 4+ in a higher coordination state (whether 5 or 6). The v'nd increases with decreasing ionization potential of alkali metals (Table 12.1), as likely does the proportion of Ti(*) compared with Ti 4+ in 4-fold coordination. Thus, one may suggest that the Vrfd *s g r e a t er for Ti(*) than for [4]Ti and that the shift in equation (12.6) with metal cation governs the variations of Vrfo • Because the d(NBO/T)/dXTiO decreases with increasing XTiO (concentration of TiO2) at least in alkali silicate melts, one may propose that v'rfd m s u c n m e l t s should decrease with increasing TiO 2 content. This Table 12.1 Partial molar volume of TiO2 in MJSiO3 melt with 5 mol % TiO2 as a function of metal cation type, M [from Dingwell, 1991, 1992b] Partial molar volume, cm3/mol

M-cation Na K Rb Cs

1000T 29.1±0.5 31.3±0.5 27.6+0.5 25.8±0.5 1600°C Li Ca Sr Ba

26.9±0.5 24.8±0.5 24.210.5 24.210.5

The Titanium Anomalies

381

relationship between different Ti-coordination states and TiO 2 content may also explain the positive correlation between the enthalpy of solution and the TiO 2 content of alkali silicate melts. A number of structural explanations have been proposed to rationalize the anomalous temperature dependence of configurational properties of Ti-bearing silicate melts. Farges et al. [ 1996b] suggested that it is due to changes in medium-range order because they did not detect any changes in the Ti-O polyhedra as their glasses transformed to a melt. Because temperature-dependent changes in configurational properties are governed by local variations in cation and anion ordering and/or other local topological changes [e.g., Richet and Neuville, 1992; Lee and Stebbins, 1999; Roskosz et al, 2004], such changes in medium-range order should rather be a consequence of short-distance reorganization around Ti. This interpretation is consistent with high-temperature neutron diffraction data [Cormier et al, 2001]. It is also consistent with the observation that NBO/T of Ti-bearing alkali silicate melts is slightly temperature-dependent above the glass transition range [Mysen and Neuville, 1995]. 12.6. Summary Remarks 1. Titanosilicates exhibit an anomalous large heat capacity change at the glass transition, beyond which the heat capacity and configurational heat capacity decrease with increasing temperature. These anomalies are related to short-range order rearrangements around Ti. 2. The molar volume is a strongly nonlinear variation of composition not only in melts, but also in glasses where measurements are more extensive. The markedly composition dependent partial molar volumes for all oxides illustrate the great diversity of coordination polyhedra for cations induced by the presence of titanium, whose relative abundances depend on Ti content. 3. Among major elements, titanium competes successfully with silicon for bonding with oxygen, which gives rise to a variety of Ti-O polyhedra whose relative abundance depends on TiO 2 content, temperature, and the nature of the metal cations. Because Ti 4+ does not require charge compensation to substitute for S 4+ , its effects differ widely from those of Al 3+ . 4. Ti 4+ can occur in 4-fold coordination either as isolated clusters or in substitution for Si 4+ , and it can also be coordinated with more than 4 oxygens. It tends to have higher coordination numbers with oxygen the more electropositive the metal cation. References Adam G. and Gibbs J. H. (1965) On the temperature dependence of cooperative relaxation properties in glass-forming liquids. J. Chem. Phys. 43, 139-146. Alberto H. V., Mysen B. O., and DeCampos N. A. (1995) The structural role of titanium in silicate glasses: A Raman spectroscopic study of the system CaO-SiO2-TiO2. Phys. Chem. Glasses 36, 114-122.

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BihuniakP. P. and Condrate R. A. (1981) Structures, spectra and related properties of group IV Bdoped vitreous silica. J. Non-Cryst. Solids 44, 331-344. Bobovich Y. S. (1962) An investigation of the structure of glassy phosphates using Raman spectra. Opt. Spectry. (Engl. transl.) 13, 274-277. Bockris J. O. M., Mackenzie J. D., and Kitchener J. A. (1955) Viscous flow in silica and binary liquid silicates. Trans. Farad. Soc. 51, 1734-1748. Bouhifd M. A., Sipp A., and Richet P. (1999) Heat capacity, viscosity, and configurational entropy of alkali titanosilicate melts. Geochim. Cosmochim. Ada 63, 2429-2438. Chakraborty I. N. and Condrate R. A. (1985) The vibrational spectra of glasses in the NajO-SiOjP2O5 system with a 1:1 SiOo:P,O5 molar ratio. Phys. Chem. Glasses 26, 68-74. Chayes F. (1975) Average composition of the commoner Cenozoic volcanic rocks. Carnegie Instn. Wash. Year Book 74, 547-549. Cleek G. W. and Hamilton E. H. (1956) Properties of barium titanium silicates. J. Res. N.B.S. 57, 317-323. Cormier L., Calas G., Neuville D. R., and Bellisent R. (2001) A high temperature neutron diffraction study of a titanosilicate glass. J. Non-Cryst. Solids 293-295, 510-516. Cormier L., Gaskell P. H., Calas G., Zhao J., and Soper A. K. (1998) The titanium environments in potassium silicate glass measured by neutron scattering with isotopic substitution. Physica B 234, 393-395. DeVries E. E, Roy R., and Osborn E. F. (1954) The system TiO2-SiOr Trans. Brit. Ceram. Soc. 53, 525-540. De Vries R. C , Roy R., and Osborn E. F. (1955) Phase equilibria in the system CaO-TiCy SiO2. J. Amer. Ceram. Soc. 38, 158-171. Dickinson J. E. and Hess P. C. (1985) Rutile solubility and titanium coordination in silicate melts. Geochim. Cosmochim. Ada 49, 2289-2296. Dietzel A. (1943) Deutung auffalliger Ausdehnungsercheinungen an Kieselglas und Sonderglasern. Naturwiss. 31, 22-23. Dingwell D. B. (1991) The density of titanium(IV) oxide liquid. J. Amer. Ceram. Soc. 74,2718-2719. Dingwell D. B. (1992a) Shear viscosity of alkali and alkaline earth titanium silicate liquids. Amer. Mineral. 77, 270-274. Dingwell D. B. (1992b) Density of some titanium-bearing silicate liquids and the compositionaldependence of the partial molar volume of TiO2. Geochim. Cosmochim. Ada 56, 3403-3408. Dingwell D. B., Paris E., Seifert F., Mottana A., and Romano C. (1994) X-ray absorption study of Ti-bearing silicate glasses. Phys. Chem. Minerals 21, 501-509. Ellison A. J. and Hess P. C. (1986) Solution behavior of+4 cations in high silica melts: Petrologic and geochemical consequences. Contrib. Mineral. Petrol. 94, 343-351. Evans D. L. (1970) Solid solution of TiO2 in SiO r J. Amer. Ceram. Soc. 53; 418-419. Evans D. L. (1982) Glass structure: The bridge between the molten and crystalline states. J. NonCryst. Solids 52, 115-128. Farges D. (1997) Coordination of Ti4+ in silicate glasses: A high-resolution XANES spectroscopy study at the Ti K edge. Amer. Mineral. 82, 36-43. Farges E, Brown G. E., Navrotsky A., Gan H., and Rehr J. J. (1996a) Coordination chemistry of Ti(IV) in silicate glasses and melts. II. Glasses at ambient temperature and pressure. Geochim. Cosmochim. Ada 60, 3039-3054.

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Farges R, Brown G. E., Navrotsky A., H. G., and Rehr J. J. (1996b) Coordination chemistry of Ti(IV) in glasses and melts. III. Glasses and melts from ambient to high temperatures. Geochim. Cosmochim. Acta 60, 3055-3066 Fontana E. H. and Plummer W. A. (1979) A viscosity-temperature relation for glass. J. Am. Ceram. Soc. 62, 367-369. Furukawa T. and White W. B. (1979) Structure and crystallization of glasses in the Li 2 Si 2 0 5 -Ti0 2 system determined by Raman spectroscopy. Phys. Chem. Glasses 20, 69-80. Gan H., Wilding M. C, and Navrotsky A. (1996) Ti4+ in silicate melts: Energetics from high temperature calorimetric studies and implications for melt structure. Geochim. Cosmochim. Ada 60, 4123-4131. Glasser F. P. and Marr J. (1979) Phase relations in the system Na2O-TiO2-SiOr /. Amer. Ceram. Soc. 62, 42-47. Greegor R. B., Lytle W. B., Sandstrom D. R., Wong J., and Schultz P. (1983) Investigation of TiO2-SiO2 glasses by X-ray absorption spectroscopy. J. Non-Cryst. Solids 55, 27-43. Hamilton E. H. and Cleek G. W. (1958) Properties of sodium-titanium silicate glasses. J. Res. N.B.S. 61, 89-94. Henderson G. S. and Fleet M. E. (1995) The structure of Ti-silicate glasses by microRaman spectrocopy. Can. Mineral. 33, 399-408. Henderson G. S. and Fleet M. E. (1997) The structure of titanium glasses investigated by K-edge X-ray absorption spectroscopy. J. Non-Cryst. Solids 211, 214-221. Henderson G. S. and St-Amour J. C. (2004) A Si K-edge XANES study of Ti-containing alkali/ alkaline-earth silicate glasses. Chem. Geol. 213, 31-40. Henderson G. S., Liu X., and Fleet M. E. (2002) A Ti-L-edge x-ray absorption study of Ti-silicate glasses. Phys. Chem. Mineral. 29, 32-42. Hudon P. and Baker D. R. (2002) The nature of phase separation in binary oxide melts and glasses. I. Silicate systems. J. Non-Cryst. Solids 303, 299-345. Iwamoto N., Hidaka H., and Makino Y. (1983) State of Ti3t ion and Ti3+-Ti4+ redox reaction in reduced sodium silicate glasses. J. Non-Cryst. Solids 58, 131-141. Iwamoto N., Tsunawaki Y., Fuji M., and Hatfori T. (1975) Raman spectra of K2O-SiO2 and K2OSiO2-TiO2 glasses. J. Non-Cryst. Solids 18, 303-306. Johnston W. D. (1965) Oxidation-reduction equilibria in molten Na2O»SiO2 glass. J. Amer. Ceram. Soc. 48, 184-190. Kajiwara M. (1988) Formation and crystallization of Al2O3-SiO2-TiO2 glasses. Glass Ind. 29, 188-192. Kato D. (1976) Raman spectrometric determination of additive concentration in high-silica-content glasses. J. Appl. Phys. 47, 2050-2055. King E. G., Orr R. L., and Bonnickson K. R. (1954) Low-temperature heat capacity, entropy at 298.16 K and high temperature heat content of sphene (CaTiSiO5). J. Amer. Chem. Soc. 76, 4320-4321. Kirschen M., DeCapitani C, Millot R, Riflet J. C, and Coutures J. P. (1999) Immiscible liquids in the system SiO2-TiO2-Al2O3. Eur. J. Mineral. 11, 427-440. Knight D. S., Pantano C. G., and White W. B. (1989) Raman spectra of gel-prepared titania-silica glasses. Mater. Sci. Lett. 8, 156-160. Kroeker S., Rice D., and Stebbins J. R (2002) Disorder during melting: An l7O NMR study of crystalline and glassy CaTiSiO5. Amer. Mineral. 87, 572-579.

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Kusabiraki K. (1986) Infrared and Raman spectra of vitreous silica and sodium silicates containing titanium. J. Non-Cryst. Solids 79, 208-212. Kushiro I. (1975) On the nature of silicate melt and its significance in magma genesis: Regularities in the shift of liquidus boundaries involving olivine pyroxene, and silica materials. Amer. J. Set 275, 411-431. Lange R. A. and Carmichael I. S. E. (1987) Densities of Na2O-K2O-CaO-MgO-Fe2O3-Al2O3TiO2-SiO2 liquids: New measurements and derived partial molar properties. Geochim. Cosmochim. Acta 51, 2931-2946. Lange R. A. and Navrotsky A. (1993) Heat capacities of TiO,-bearing silicate liquids: Evidence for anomalous changes in configurational entropy with temperature. Geochim. Cosmochim. Acta 57, 3001-3012. Lee S. K. and Stebbins J. F. (1999) The degree of aluminum avoidance in aluminum silicate glasses. Amer. Mineral. 84, 937-945. Li D., Bancroft G. M., Fleet M. E., and Feng X. H. (1995) Silicon K-edge XANES spectra of silicate minerals. Phys. Chem. Mineral. 22, 115-122. Liska M., Simurka P., Antalik J., and Perichta P. (1996) Viscosity of titania-bearing sodium silicate melts. Chem. Geol. 128, 199-206. Liu Q. L. and Lange R. A. (2001) The partial molar volume and thermal expansivity of TiO2 in alkali silicate melts: Systematic variation with Ti coordination. Geochim. Cosmochim. Acta 65, 2379-2393. Loshmanov A. A., Sigaev V. N., Khodakovskaya R. Y, Pavlushkin N. M., Yamzin I. I., and Lyubimtsev V. A. (1974) A neutron-diffraction study of the structure of sodium titanium silicate glasses. Sov. J. Glass Phys. Chem. 1, 30-34. Manghnani M. H. (1972) Pressure and temperature dependence of the elastic moduli of NaoOTiO2-SiO2 glasses. J. Amer. Ceram. Soc. 55, 360-365. Markgraf S. A., Sharma S. K., and Bhalla A. S. (1992) Raman study of glasses of Ba2TiSi2Og and Ba^/TiGe^g. J. Amer. Ceram. Soc. 75, 2630-2632. Massazza F. and Sirchia E. (1958) II sistema MgO-SiO2-TiO2, II. Gli equilibri allo stato solido e alia fusione. Chim. Ind. (Milan) 40, 460-467. Maurer R. D. (1962) Crystal nucleation in a glass containing titania. J. Appl. Phys. 33, 2132-2135. McTaggart G. D. and Andrews A. I. (1957) Immiscibility area in the system TiO2-ZrO2-SiO2. J. Amer. Ceram. Soc. 40, 167-170. Mitchell R. H. (1991) Coexisting glasses occurring as inclusions in leucite from lamproites: Examples of silicate liquid immiscibility in ultrapotassic magmas. Mineral. Mag. 55,197-202. Morinaga K., Ito T., Suginohara Y, and Yanagase T. (1974) Density of the molten CaO-SiO2-TiO2 system and infrared absorption spectra of its glasses. J. Jap. Inst. Met. 38, 1065-1070. Morsi M. M. and El-Shennawi A. W. A. (1984) Some physical properties of silicate glasses containing TiO2 in relation to their structure. Phys. Chem. Glasses 25, 64-68. Mysen B. O. and Neuville D. (1995) Effect of temperature and TiO2 content on the structure of Na2Si205-Na2Ti205 melts and glasses. Geochim. Cosmochim. Acta 59, 325-342. Mysen B. O., Ryerson F. J., and Virgo D. (1980) The influence of TiO2 on structure and derivative properties of silicate melts. Amer. Mineral. 65, 1150-1165. Nelson S. A. and Carmichael I. S. E. (1979) Partial molar volume of oxide components in silicate liquids. Contrib. Mineral. Petrol. 71, 117-124. Nordberg N. E. (1943) Glass having an expansion lower than silica. US Patent No. 2,326,059.

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Paris E., Dingwell D. B., Seifert R, Mottana A., and Davoli I. (1993) An X-ray absorption study of Ti in Ti-rich silicate melts; correlations with melt properties. Terra Abstracts 5, Suppl. 1,521. Poole J. P. (1948) Viscosite abasse temperature des verres alcalino-silicates. Verres Refract. 2,222-228. Rao B. V. J. (1963) The dual role of titanium in the system K 2 O S i 0 2 » T i 0 2 . Phys, Chem. Glasses 4, 22-34. Reid A. M., Ridley W. I., Donaldson C , and Brown R. W. (1973) Glass compositions in the orange and gray soils from Shorty Crater, Apollo 17. EOS 54, 607-609. Reynard B. and Webb S. L. (1998) High-temperature Raman spectroscopy of Na 2 TiSi 2 0 7 glass and melt: Coordination of Ti4+ and nature of the configurational changes in the liquid. Eur. J. Mineral. 10, 49-58. Richet P. (1984) Viscosity and configurational entropy of silicate melts. Geochim. Cosmochim. Acta 48, 471-483. Richet P. and Bottinga Y. (1985) Heat capacity of aluminum-free liquid silicates. Geochim. Cosmochim. Acta 49, 471-486. Richet P. and Neuville D. R. (1992) Thermodynamics of silicate melts; configurational properties. In Thermodynamic Data; Systematics and Estimation (ed. S. K. Saxena), pp. 132-161. Springer. New York Romano C , Paris E., Poe B. T., Giuli G., Dingwell D. B., and Mottana A. (2000) Effect of aluminum on Ti-coordination in silicate glasses: A XANES study. Amer Mineral. 85, 108-117. Roskosz M., Toplis M. J., and Richet P. (2004) The structural role of Ti in aluminosilicate liquids in the glass transition range: Insights from heat capacity and shear viscosity measurements. Geochim. Cosmochim. Acta 68, 591-606. Ryerson F. J. (1985) Oxide solution mechanisms in silicate melts: Systematic variations in the activity coefficient of SiO 2 . Geochim. Cosmochim. Acta 49, 637-651. Sakka S., Miyaji R, and Fukumi K. (1989) Structure of binary K 2 O-TiO 2 and Cs 2 O-TiO 2 glasses. J. Non-Cryst. Solids 112, 64-68. Sandstrom D. R., Lytle F. W., Wei P., Greegor R. B., Wong J., and Schultz P. (1980) Coordination of Ti in TiO2-SiO2 glasses by X-ray absorption spectroscopy. J. Non-Cryst. Solids 41, 201-207. Schreiber H. D. (1977) Redox states of Ti, Zr, Hf, Cr and Eu in basaltic magmas: An experimental study. Eighth Lunar Science Conference, 1785-1809. Schreiber H. D., Thanyashiri T., Lach J. J., and Legere R. A. (1978) Redox equilibria of Ti, Cr and Eu in silicate melts: Reduction potentials and mutual interactions. Phys. Chem. Glasses 19, 126-140. Schultz P. C. (1976) Binary titania-silica glasses containing 10 to 20 wt % TiO 2 . J. Amer. Ceram. Soc. 59, 214-219.

Strnad Z. (1986) Glass-Ceramic Materials. Liquid Phase Separation, Nucleation, and Crystallization in Glasses. Elsevier. New York.

Tangeman J. A. and Lange R. A. (1998) The effect of Al3+, Fe3+, and Ti4+ on the configurational heat capacities of sodium silicate liquids. Phys. Chem. Minerals 26, 83-99. Tobin M. C. andBaakT. (1968) Raman spectra of some low-expansion glasses. J. Amer. Opt. Soc. 58, 1459-1460. Turnbull R. C. and Lawrence W. G. (1952) The role of titania in silica glasses. J. Amer. Ceram. Soc. 35, 48-53. Varshal B. G., Bobrov A. V., Mavrin B. N., Ilyukhin V. V., and Belov N. V. (1974) Coordination of titanium in titanium-containing systems. Dokl. Akad. Nauk. SSSR 216, 374-377.

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Varshal B. G., Ilyukhin V. V., and Belov N. V. (1975) Crystal-chemical aspects of liquation phenomena in three-component titanium-silicate glasses. Sov. J. Glass Phys. Chem. 1,103-106. Visser W. and Koster Van Groos A. F. (1979) Effects of P 2 O 5 and TiO 2 on liquid-liquid equilibria in the system K 2 O-FeO-Al 2 O 3 -SiO 2 . Amer. J. Sci. 279, 970-983. Webb S. L. and Dingwell D. B. (1994) Compressibility of titanosilicate melts. Contrib. Mineral. Petrol. 118, 157-168. Wood M. and Hess P. C. (1980) The structural role of A12O3 and TiO 2 in immiscible silicate liquids in the system SiO2-MgO-CaO-FeO-TiO2-Al2O3. Contrib. Mineral. Petrol. 72, 319-328. Yarker C. A., Johnson P. A. V., Wright A. C , Wong J., Greegor R. B., Lytle F. W., and Sinclair R.N. (1986) Neutron diffraction and EXAFS evidence forTiO 5 units in vitreous K 2 0«Ti0 2 »2Si0 2 . J. Non-Cryst. Solids 79, 7-136.

387

Chapter 13

Phosphorus In natural silicate melts, P2O5 can reach concentrations near 1 wt% [Pichavant et al, 1987; London et al., 1993]. Even at this comparatively low concentration P2O5 can have profound effects on liquidus phase relations and transport properties [Wyllie and Tuttle, 1964; Kushiro, 1975; Toplis etal, 1994; Dingwell et al, 1993; Wolf and London, 1994]. Crystallization of apatite may affect trace element evolution of magmatic systems [Watson and Capobianco, 1981; Montel, 1986]. The tendency of P2O5 to promote liquid immiscibility in silicate systems could induce unusual magmatic processes [Visser and van Groos, 1979]. Phosphurus-bearing silicate glasses also have a range of commercial applications and are used, for example, in optical communications systems [Li et al., 1995; Brow, 2000]. Phosphorus also plays a role in the development of ceramics and glasses [Kosinski et al, 1988; Chakraborty and Condrate, 1985] and particularly in bioceramics and bioglass technology [Grussaute et al, 2000]. 13.1. Properties of Phosphorus-bearing Glasses and Melts 13.1a. Solution Thermodynamics Phosphorus solubility in melts depends on silicate composition. This is evident in the widths of liquid immiscibility gaps [Tien and Hummel, 1962; Visser and van Groos,

Figure 13.1 - Relationships between liquid miscibility gap and P-content in the system Fe2Si04-KAlSi206SiO2. Open symbols: silica-rich melts; closed symbols: silica-poor melt. Numbers next to individual symbols are P,O5 contents (wt %) of melts [Visser and van Groos", 1979].

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Figure 13.2 - Phosphorus partition coefficient, Dp^'dtllelmelt = P2O5aPatlte/ P2O5melt (wt %), for coexisting silicate melt and F-apatite as a function temperature for the SiO2 contents indicated [Harrison and Watson, 1984].

1979] shown, for example, in the system K 2 O-FeO-Al 2 O 3 -SiO 2 -P 2 O 5 where the gap expands systematically with increasing phosphorus content (Fig. 13.1). That solution of P5+ in silica-rich melts is energetically unfavorable is also indicated by the fact that nearly all phosphorus is dissolved in the silica-poor melt of the miscibility gap. A pronounced dependence of phosphorus solubility on silica content and, therefore, melt polymerization, is evident in P-partitioning beeween F-apatite and magmatic liquids (Fig. 13.2). Harrison and Watson [1984] found that the partition coefficient, DpaPatite/melt (=P2O5 in apatite/P2O5 in melt), increases with increasing SiO2 content and is a linear function of reciprocal temperature (Fig. 13.2). In fact, they proposed that, for natural melts, apatite solubility is a negative function of SiO2 content, at least between about 45 and 75 wt%, and a positive function of temperature. In addition to these two factors, the A12O3 content of melts also affects P2O5 solubility as well as P-diffusion [Montel, 1986; Pichavant et al., 1992; Wolf and London, 1994]. This effect is particularly clear in the rapidly increasing P 2 O, solubility with Al content in peraluminous silicate melts (Figs. 13.2 and 13.3). '

Figure 13.3 - P2O5 content of peraluminous silicate melts in equilibrium with apatite as a function of per-aluminosity, A12O3/ (Na2O+K2O+CaO), of the melt [Wolf and London, 1994].

Phosphorus

389

Figure 13.4 - Activity coefficient of SiO2, ysio2, as a function of proportion of P2O5 calculated from the position of the forsterite/enstatite liquidus boundary in the system MgO-SiO2-P2O5 and compared with y si0 , calculated in the same manner in the system K2O-MgO-SiO2 [Ryerson, 1985].

As illustrated by equation (6.8), the activity of SiO2 as a function of the P-content of the melt can be determined from the cristobalite/tridymite liquidus [Ryerson, 1985]. Interestingly, the activity coefficient of SiO2, 7siO2' deduced in this way for the system SiO2-P2O5 decreases with increasing P2O5 content much faster than, on an equimolar basis, when adding a network-modifying oxide such as K2O (Fig. 8.10). On the other hand, the activity coefficient of silica increases with increasing phosphorus content in less silica-rich melts such as compositions corresponding to the olivine/protoenstatite liquidus boundary in the system MgO-SiO2-P2O5 (Fig. 13.4). In this system, the effect of P2O5 on ysiO2 is opposite to those of K2O and other alkali and alkaline earth oxides (Fig. 13.4). The complex activity-composition relations of P2O5 suggests that phosphorus is not simply either a network former or a network modifier in silicate melts. Depending on composition, P2O5 may instead play both roles and polymerize or break up the structure. 13.1b. Phosphorus and Viscosity Complicated structural interactions between dissolved phosphorus and silicate components in melts are also evident in the composition dependence of viscosity. In haplogranite, a highly polymerized KAlSi3O8-NaAlSi3Og-SiO2 melt with nominal NBO/T = 0, Dingwell et al. [1993] observed that increasing P2O content results in decreasing melt viscosity, whereas Toplis et al. [1994] reported an opposite effect on viscosity of a depolymerized natural ferrobasalt melt with P-free NBO/T = 0.75 (Fig. 13.5). Thus, both melt viscosity and activity coefficient of SiO2 appear to depend in a similar way on phosphorous content. In other words, P2O5 could be a network modifier in highly polymerized melts and, in contrast, a network former in depolymerized melts.

390

Chapter 13

Figure 13.5 - Viscosity of (a) haplogranite melt at 1000°C and (b) basalt melt at 1250°C as a function of the P2O5 content of the melt (mol %) [Dingwell et ai, 1993; Toplis et al., 1994].

To understand better the relationships between melt viscosity and composition, Toplis and Dingwell [1996] studied a series of compositions in the system xNa2O-(l-x)Al2O32SiO2 with P2OS contents ranging from 0 to about 7 mol % (Fig. 13.6). For the most alkaline series, NAPS70, both viscosity and high-temperature activation enthalpy of viscous flow increase systematically with increasing P2O5. In this series (Na/Al ~ 2.37), Na+ was in excess of that needed to charge-balance Al3+ in 4-fold coordination so that formation of Na-phosphate complexes was possible in the entire P2O5 concentration range investigated. In contrast, for meta-aluminosilicate melts with nominal NBO/T = 0, both viscosity and high-temperature activation enthalpy decrease whereas the series with Na/Al between 2.3 and 1.0, show an initial viscosity increase followed by a decrease at higher phosphorus content. Hence, it appears that the metal/alumina ratio plays a central role in the control of melt viscosity. According to Toplis and Dingwell [1996], the viscosities of Fig. 13.6 reflect interaction between phosphorus, metal cations and alumina. For a depolymerized, peralkaline aluminosilicate melt such as NPS70, the effect is described by a simple polymerization reaction, 2Si-O-Na + P-O-P <=> 2P-O-Na + Si-O-Si,

(13.1)

which would also take place in the ferrobasalt series of Fig. 13.5. The reason for the viscosity trend of meta-aluminosilicate melts is less clear. Toplis and Dingwell [1996] suggested that the viscosity decrease of NAPS50 melt with P2O5 results from formation of alkali and aluminum phosphate complexes through interaction between P2O5 and charge-balanced NaAlO2 [see also Gan and Hess, 1992]: NaA10 2 + P2OS<=> A1PO4+ NaPO 3 .

(13.2)

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391

Figure 13.6 - Viscosity relations at high temperature in the system Na2O-Al2O3-SiO2-P2O5 as a function of P2O5 concentration, (a) Change in melt viscosity with P2O5 content relative to that of Pfree melt at 1446°C. (b) Change in high-temperature activation energy of viscous flow with P2O5 content relative to that of P-free melts. NAPS50: meta-aluminosilicate melt with 50 mol % SiO2 and Na/Al~l (open circles); NAPS70: peralkaline aluminosilicate melt with 70 mol % SiO2 and Na/Al~2.3 (closed circles); NAPS55: peralkaline aluminosilicate melt with 55 mol % SiO2 and Na/Al~l .2. See also text for further discussion of these compositions [Toplis and Dingwell, 1996]. In melts of the series NAPS55, with intermediate Na/Al, some of the dissolved P2O5 might first interact with Na as described by equation (13.1). After exhaustion of the Na left by Al-charge balance, the mechanism of equation (13.2) might then operate.

13.1c. Properties and Phosphate Complexes A number of properties of P-bearing melts are consistent with formation of variety of different phosphate complexes. Addition of P2O5 to peralkaline melts causes them to become increasingly compressible than expected from simple polymerization of the silicate network [Webb and Courtial, 1996]. However, P2O5 addition to Al-bearing melts causes these to become stiffer and their density to increase. These observations suggest complicated interaction between dissolved phosphorus, alkali metals and aluminum. Watson [1976] observed that rare earth elements exhibit a pronounced tendency to partition into P-rich, depolymerized melts coexisting with immiscible P-deficient and highly polymerized melts. Rare earth phosphate complexes could thus govern partitioning of such minor and trace elements. A correlation between the P2O5 content and Fe37Fe2+-ratio of silicate melts was noted by Gwinn and Hess [1993] and Toplis et al. [1994]. However, both studies were carried out with chemically complex magma compositions which makes it difficult to ascertain how the various possible phosphate complexes govern the redox ratio of iron.

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Figure 13.7 - Effect of P2O5 on the H2Osaturated solidus of albite (NaAlSi3O8) [Wyllie and Turtle, 1964].

Phosphate complex formation could also be relevant in hydrous aluminosilicate melts. Although Harrison and Watson [1984] concluded that H2O content does not affect Ppartitioning between apatite and magmatic liquids, other properties seem to reveal an interplay between H2O and phosphorus. For example, the pressure-temperature trajectory of the albite-H2O-P2O5 solidus depends on P 2 O, content (Fig. 13.7). Holtz et al. [1993] found that addition of P,O, to KAlSLOa-NaAlSi,O.-H,O melts lowers H . 0 solubility in such felsic aluminosilicates (Fig. 13.8). It is not clear, however, whether the relations in Figs. 13.7 and 13.8 reflect interaction between dissolved P2O5 and dissolved H2O or whether solution of P2O5 affects the aluminosilicate network structure and, therefore, H2O solubility. A clue to these effects might be found in the liquidus phase relations of the system NaAlSi 3 O 8 -KAlSi 3 O 8 -SiO 2 -P 2 O 5 [London et al., 1993] where the so-called granite minimum [Turtle and Bowen, 1958] shifts away from the SiO2 apex toward the NaAlSi3Og-

Figure 13.8 - Effect of P 2 O 5 on the H 2 Osolubility in a haplogranite melt [Holtz et al, 1993].

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Figure 13.9 - Effect of P2O5 on composition of "granite minimum" (melt coexisting of with feldspar and quartz) in the system NaAlSiO4KAlSiO4-SiO2-H2O. Numbers next to data point represent P2O5 content of melt [London et al., 1993].

KAlSi3O8 join with increasing P2O5 content (Fig. 13.9). This shift is consistent with the formation of some form of Al-phosphate complex in the melt which would thereby expand the liquidus field of quartz relative to that of feldspar [London et al., 1993]. These effects on liquidus phase relations indicate that the SiO2 activity increases with the P2O5 content in hydrous melts. These changes in activity of SiO2 in hydrous, P-bearing melts may also account for the effect of P2O5 on solidus temperatures (Fig. 13.8) and H2O-solubility of aluminosilicate melts (Fig. 13.9). 13.2. Structure of Phosphorus-bearing Silicate Melts and Glasses The relationships between phosphorus content and properties of silicate melts and glasses suggest a variety of solution mechanisms for p 5+ . In all cases P5+ is in tetrahedral coordination. 13.2a. Charge-Compensation Mechanisms As phosphorus has a formal charge of 5+, some form of charge-compensation is to obtain a formal charge of 4+. In crystalline posphosilicates, this is accomplished by coupled substitutions such as, Si4+Si4+<=>P5+Al3+ (berlinite) Si4+Al3+<=>P5+Mg2+(ellenbergerite) Si 4+ AP + oP 5+ Be 2+ (hurlbutite) Si4+Fe2+<=>P5+Li (triphyllite) Si4+Mg2+0 5<^>P5+O (sarcopside) Si4+(Fe2+)2«=>P5+Fe3+(heterosite), where • denotes a vacancy. In addition, in crystalline P 2 O 5 , charge-compensation is accomlished via one oxygen double-bonded to phosphorus. Similar mechanisms may be envisioned for tetrahedrally coordinated P 5 + in silicate glasses and melts. The property data summarized above have often be explained, for

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Figure 13.10 - Correlation function from neutron diffraction of P,O5 glass. P-OT and P-OB denote phosphorus-oxygen distances for terminal and bridging oxygen, respectively, and OB-OT and OB-OT oxygen-oxygen distances from bridging to terminal and bridging to bridging oxygen, respectively [Uoppeetal., 1998].

example, with the aid of AlP and MxP charge-compensation. Double-bonded oxygen has also been proposed. To unravel the details the phosphorus solution mechanisms in glasses and melts, we will address first compositionally simple systems and then chemically more complicated melt compositions. The obvious starting point is P2O5, one of the rare oxides that itself is a good glass former.

Figure 13.11 - Comparison of Raman spectra of P,O 5 , SiO,, and SiO,+ 14 mol % P,O 5 . Arrows denote bands assigned to stretching of double bonded O near 1380 cm 1 and P-O bonds near 1150 cm 1 [Shibata et al., 1981; Meyer, 1997].

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13.2b. SiO2-P2Os

According to neutron diffraction data [Hoppe et al., 1998], there are two P-0 and two 0-0 bond distances in P2O5 glass (Fig. 13.10). The longer distance (-1.58 A), yielded by fits of Gaussian lines to the neutron diffraction spectrum, is a bridging P-O-P oxygen bond, denoted P-0 B . This bridging oxygen bond distance is nearly identical (-1.6 A) to the bridging oxygen bond distance in SiO4 tetrahedra (see Chapter 5). The shorter distance of 1.43 A, P-0 T , is that to a terminal oxygen,OT, double-bonded to P5+ in a 3-dimensionally interconnected structure with P5+ in tetrahedral coordination with oxygen. The existence of a double bond is consistent with interpretation of Raman spectra of P2O, glass, where a strong band near 1380 - 1390 cm1 (Fig. 13.11) has been assigned to stretch vibrations ofP=O bonds [Galeener and Mikkelsen, 1979; Shibata etal., 1981; Meyer, 1997].Thus, in fully polymerized, P-bearing silica glass and melts, charge-compensation is accomplished with the double-bonded P-OT, where OT is a terminal oxygen. Raman spectra of SiO2-P2O5 glasses suggest that many of the structural features of the P2O5 and SiO2 endmembers remain in mixed SiO2-P2O5 glasses (Fig. 13.11). Additional spectral features near 1100 cm1 in these glasses have been assigned to the presence of Si-O-P bridges. Phosphorus in this configuration might be referred to as a Q3(P) structural entity [Meyer, 1997]. Silicon K- and L-edge and phosphorus L-edge x-ray absorption spectra of SiO2-P2O5 glass with less than about 30 mol % P2O5 are also consistent with this interpretation [Li et al., 1995]. For higher phosphorus contents, Li et al. [1995] suggested that there is evidence for coordination transformation of some of the Si4+ from 4- to 6-fold coordination through, perhaps, formation of complexes with a structure resembling that of crystalline SiP2O7 [Li et al., 1994]. 13.2c. Phosphate-containing Metal Oxide-Silica Glass and Melt Phosphate complexes may polymerize to form entities conceptually similar to the Qn-species described for silicates (Fig. 3.3). There are, however, necessarily some differences between phosphate and silicate complexes because of the formal 5+ electric charge of phosphorus. One could imagine that any one of the oxygens in the phosphate species forms a double bond with P5+. Existing Raman and 31P MAS NMR data for alkali phosphate glasses indicate, however, that P=O bonds exist only in Q3(P) species which are characterized by three bridging oxygens and one oxygen forming a double bond with phosphorus. Less polymerized phosphate species [Q2(P), Q'(P)> and Q°(P)] have only bridging and nonbridging oxygens [Kirkpatrick and Brow, 1995]. In these less polymerized phosphate species, the nonbridging oxygens form bonding with other metal cations. In these cases, charge-compensation of P5+ is accomplished with a neighboring metal cation. Solution of P2O5 in binary metal oxide-silica melt and glass occurs through formation of phosphate species [Nelson and Tallant, 1984, 1986; Yang et al., 1986; Dupree et al., 1989;Lie?a/., 1995;Mysen, 1998; Toplis and Reynard, 2000; Toplis and Schaller, 1998]. There are systematic relationships between 31P NMR shift and phosphate polymerization, as well as between Raman shifts and phosphate speciation [Dupree, 1991; Nelson and Tallant, 1984,1986; Yamashita etal., 2000]. Increasing phosphate polymerization results

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Figure 13.12 - Summary of (a) 3IP MAS NMR shifts and (b) P-O Raman shifts for different Q°-species in phosphate systems. The n represents number of bridging oxygen in the phosphate species [Dupree, 1991]. in increasingly negative 31P shift (Fig. 13.12a) and in increasing frequencies of P-0 stretch vibrations (Fig. 13.12b). These spectroscopic trends resemble the relationships described for silicates between degree of polymerization and either Raman frequencies or 29Si NMR chemical shifts (Figs. 7.7 and 7.8). Nelson and Tallant [1984, 1986] first pointed out that the extent of phosphate polymerization in the silicate melts and glasses increases with phosphorus content. This is evident in the 31P MAS NMR spectra of Na 2 Si 2 0 5 +P 2 0 5 glasses (Fig. 13.13), and is also consistent with PL-edge x-ray absorption spectra [Li etal., 1995]. There appears, however, to be a maximum P2O content above which additional phosphorus may form a

Figure 13.13 - Example of 31P MAS NMR spectra of P-bearing Na-silicate glasses with the different P-content indicated, illustrating the position of the 31P resonances as a function of phosphate polymerization where n represents the number of bridging oxygens in the phosphate species [Dupree etal., 1989].

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Figure 13.14 - X-ray absorption K-near edge (XANES) of Na2O-SiO2-P2O5 glass as a function of P2O5 content [Li et al., 1995].

silicophosphate complex with Si4+ in 6-fold rather than 4-fold coordination. This structural phenomenon has been observed in Raman spectra [Chakraborty and Condrate, 1985; Yamashita et al., 2000] and in both 31P and 29Si MAS NMR spectra of P-rich alkali silicate glasses [Dupree et al., 1987, 1989]. The extent to which PO4-groups are interconnected with the silicate network has been studied by x-ray absorption and NMR spectroscopy. For glasses in the system Na2OSiO2-P2O5, Li et al. [1995] observed that increasing phosphorus contents results in increased energy of the K-edge (Fig. 13.14). As this shift was higher than the energy of the K-edge in fully polymerized SiO 2 glass, they concluded that it results from interconnectivity between SiO4 and PO 4 groups. In other words, Si-O-P bridges were inferred to exist in these materials.

Figure 13.15 - Calculated 31P MAS NMR shift as a function of number of P-O-Si bridges [Cody et al., 2001].

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Figure 13.16 - Phosphorus-31 MAS NMR spectrum (a) and Raman spectrum (a) of Na,0»9Si0, glass with 2 mol % P,05. Spinning side bands marked with • [Mysen and Cody, 2001]. If P-O-Si bridges exist in the glass and melt structure, an implication of the preceding observation is that the number of such bridges should also correlate with the isomer shift from 31P NMR spectroscopy. The effect is similar to the shielding of Si nucleus by nextnearest Al3+ in aluminosilicates [Engelhardt and Michel, 1987; see also Fig. 9.20]. Cody et al. [2001] employed ab initio shielding calculations to estimate how the number of P-O-Si bridges affect the chemical shift of 31P (Fig. 13.15). In the NMR spectrum of an Na 2 O9Si0 2 glass with 2 mol % P2O5, the chemical shift of a species with one Si-O-P bridge, Q'(P), is similar to that of a phosphate dimer, P2O7 (Fig. 13.16a). In the Raman spectrum of the same sample (Fig. 13.16b), however, Raman bands assigned to P-0 stretch vibrations are distinct because of mass differences between Si and P and also because the P-O force constant depends on the next nearest cation Si or P [Mysen and Cody, 2001]. Thus, taken together, the data from x-ray absorption, 31P NMR spectroscopy, Raman spectroscopy and numerical simulation indicate that phosphate species are connected to the silicate network via oxygen bridges as illustrated schematically in Fig. 13.17. Formation of PO4-complexes upon solution of P2O5 in metal oxide-silica melts is associated with an increase in silicate polymerization [Ryerson and Hess, 1980; Mysen et al, 1981; Nelson and Tallant, 1984; Dupree et al, 1989; Li et al., 1995; Toplis and Schaller, 1998; Mysen, 1998; Cody etal, 2001; Toplis and Reynard, 2000]. This is evident in the relative abundance of Q3 and Q4 structural units from 29Si MAS NMR spectra of quenched melts in systems such as Na2O-SiO2-P2O5 [Dupree et al., 1988, 1989; Toplis and Schaller, 1998], and K2O-SiO2-P2O5 [Lockeyer et al., 1991] as well as in other Pbearing alkali silicate and alkaline earth silicate glasses and melts [Yang et al, 1986; Grussaute et al., 2000]. Silicon-29 MAS NMR spectra of glasses demonstrating this structural effect are shown in Fig. 13.18.

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(?) Phosphorus (4-fold) © Network-former (not P) #

9

Network-modifying cation Bridging oxygen Nonbridging oxygen

Figure 13.17 - Schematic representation of Q°(P) species where n represents the number of P-O-T bridges (T=Si or Al) [Mysen and Cody, 2001].

The principal solution mechanism of P2O5 in binary metal oxide silicate glass and melts is described by equation (13.1). However, the actual process is more complicated than scavenging of metal oxide from the silicate to form metal phosphate complexes.

Figure 13.18 - (a) Evolution of 29Si MAS NMR spectra of Na,Si,O 5 glass as a function of P,O5 content and (b) molar ratio of QVQ3 from the 29Si MAS NMR spectra. Bands marked with dots represent spinning side bands [Dupree et al., 1988].

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Figure 13.19 - Phosphorus-31 MAS NMR spectra of Na,,09Si0 2 +Al,0 3 glasses with 2 mol % P2O5 as a function of A12O3 content (mol %, shown as NA0, NA2 etc, where number denotes mol % A12O3). Compositions with less 5 mol % A1,O3 are peralkaline, that with 5 mol % A12O3 is meta-aluminous, and those with more than 5 mol % A1,O3 peraluminous. Dots denote spinning side bands [Cody etal., 2001].

Even in compositionally simple systems, there exist at least three different phosphate complexes, namely, PO 4 , P2O7, and Q'(P)- Thus, one may express solution of P 2 O, in these melts with 3 equations that involve interactions between the silicate network and the phosphate complexes,

6Q 3 +P 2 O 5 <^6Q 4 +2PO 4 ,

(13.3)

4Q3 + P 2 O 5 <^4Q 4 +P 2 O 7 ,

(13.4)

and 10Q 3 +P,O,<=>8Q 4 +2Q'(P).

(13.5)

All three solution mechanisms describe polymerization of the silicate network. However, the production of PO4 groups is a more efficient process than production of P2O7 groups. The reaction (13.5) forming Q'(P) is even less efficient than either reaction (13.2) or (13.4).

13.2d. Phosphate in Metal Oxide-Alumina-Silica Systems A property such as viscosity (Fig. 13.6) is a strong function of the polymerization and Al/Si of P-bearing melts [Toplis and Dingwell, 1996]. In NMR studies, Toplis and Schaller [1998] and Schaller et al. [1999] examined structural interaction between P and Na and between P and Al in the same Na2O-Al2O3-SiO2-P2O5 glasses as investigated by viscometry. The 31P resonances assigned to PO4 and P2O7 indicate that these groups are indeed coupled to Na. Additional 3IP resonances are found in the NMR spectra of P-bearing aluminosilicate glasses, however, as illustrated in Fig. 13.19 by the MAS NMR spectra of a few Na 2 O-

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Figure 13.20 - Calculated 31P MAS NMR shift as a function of number of P-O-Al bridges [Cody et al, 2001].

Al2O3-SiO2 glasses where systematic variations of the spinning side bands are also observed. Both features have been dealt with by Cody et al. [2001] who made use of numerical simulations of shielding effects on the P nucleus by neighboring Si and/or Al (Fig. 13.20). By analogy with structural data from Na-aluminophosphate glasses [Inoue et al., 1995; Hartmann et al., 2000], they concluded that P-O-Al linkages become increasingly important when the Na/Al-ratio of peralkaline aluminosilicate melts decreases. This is in agreement with the structural interpretations of Schaller etal. [1999] and Toplis and Schaller [1998]. Therefore, in P-bearing aluminosilicate glasses and melts, chargebalance is via neighboring Al 3+ . Increasingly polymerized phosphate complexes linked to the aluminosilicate network dominate the structure as their Na/Al decreases (Fig. 13.21). Isolated PO 4 and P2O7 complexes can be detected only in peralkaline silicate and aluminosilicate melts. The most polymerized Al-phosphate species, Q 4 (P), with four P-O-Al bridges to the aluminosilicate network, appears for compositions slightly more aluminous than metaaluminosilicate. (For the join in Fig.13.21, 5 mol % A12O3 correspond to metaaluminosilicate composition, Na=Al.) The other species, Q'(P), Q2(P), and Q3(P), have 3, 2, and 1 nonbridging oxygen, respectively. These nonbridging oxygens are bonded to Na. As the PO 4 , P2O7, and Q'(P) species become less abundant when the Na/Al-ratio decreases (Fig. 13.21), solution of phosphorus via mechanisms analogous to reactions (13.3-13.5) become less important. The structural relationship between dissolved P2O5 and the aluminosilicate network can be generalized with the expression: 10Q3+ P2O5 <^> 2Qn(P) + (10-n)Q4.

(13.6)

Equation (13.6) cannot, however, completely describe solution of P2O5 in fully polymerized aluminosilicates such as melts along silica-meta-aluminate joins (SiO2NaA10 2 ). In these melts, Mysen et al. [1981] assumed that aluminosilicate depolymerization might also be involved because, if Al-phosphate speciation were the

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Chapter 13

Figure 13.21 - Evolution of phosphate species abundances for the same compositions as in Fig. 13.20 (also shown in insert) as a function of AL,O3 content [Cody etal, 2001].

principal solution mechanism, metal cations that originally served to charge-balance Al3+ might become network modifiers. No evidence for this depolymerization scheme has been found in subsequent Raman and NMR spectroscopy studies, however [Gan and Hess, 1992; Toplis and Schaller, 1998; Cody etal., 2001]. Gan and Hess [1992] suggested a mechanism that results in formation of both Al-phosphate and metal-metaphosphate complexes without aluminosilicate depolymerization. However, there is no evidence for the presence of metaphosphate (PO3) groups in the 31P MAS NMR spectra of such glasses [Toplis and Schaller, 1998; Cody et al., 2001]. Toplis and Schaller [1998] proposed, therefore, an alternative, whereby three of the oxygens in Q3(P) species bridge across either to Al3+ or to Si4+ in the aluminosilicate network. The fourth oxygen in the phosphate complexes could then be linked to metal cations. Although this kind of solution mechanism is difficult to check with available spectroscopic methods, the idea seems consistent with the structural data summarized in Fig. 13.21. Finally, Q4(P) groups dominate when P2O5 dissolves in peraluminous melts (>5 mol % A12O3 in Fig. 13.21). We surmise that the proportion of Qn(P) species with nonbridging oxygen bonded to metal cations [Q3(P) species] then decreases and that the dominant

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phosphate species is of Q4(P) type with its bridging oxygens linked to the aluminosilicate framework via Al3+ and Si4+. 13.2e. Temperature-Induced Transformations The structural information discussed above has been derived from glasses. Its application to the structure of P-bearing melts relies on the assumption that quenching of melts does not involve significant rearrangements of either the phosphate or the silicate portion of the structure. A few Raman spectroscopy studies carried out to temperatures above 1200°C have addressed the extent to which this hypothesis is justified [Mysen, 1996,1998; Toplis and Reynard, 2000; Mysen and Cody, 2001]. In Al-free, silica-rich melts (Na2O-SiO2-P2O5 compositions with nominal NBO/Si
(13.7)

and P 2 O 7 +5Q 4 «=>2Q'(P) + 3Q3.

(13.8)

The temperature dependence of the equilibrium constants of these two reactions, K B 7 and K13 g, indicate that P-bearing metal oxide silicates become slightly depolymerized as the temperature increases [Mysen, 1998; Mysen and Cody, 2001]. For Al-bearing melts, interaction between dissolved phosphorus and the aluminosilicate network involves not only reactions (13.7) and (13.8), but also complicated interactions between the Qn(P)-species themelves (Fig. 13.17) and the aluminosilicate network [Toplis and Reynard, 2000; Mysen and Cody, 2001]. In addition to equations (13.7) and (13.8), the two main equilibria are [Mysen and Cody, 2001]: 2Q3(P) o Q2(P) + Q4(P),

(13.9)

and Q4(P) + Q3 <=> Q3(P) + 2Q4.

(13.10)

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Figure 13.22 - Effect of temperature on phosphate (a) and silicate (b) species in Na,,O9Si0, glass and melt with 2 mol % P,6 5 [Mysen and Cody, 2001].

Equilibrium (13.9) is conceptually similar to equilibrium (7.9) for silicate species. It does not affect the silicate structure. The AH of reaction (13.9) is only slightly negative (-13 ± 11 kJ/mol, see Fig. 13.23) implying, therefore, that the equilibrium shifts slightly to the right at temperatures above the glass transition. Near the meta-aluminosilicate join, and for more aluminous melts, equilibrium (13.10) dominates in aluminosilicate melts [Mysen and Cody, 2001]. This equilibrium does affect the aluminosilicate structure. The K1310 is positively correlated with temperature, with an

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Figure 13.23 - Equilibrium constants for reactions (13.7-13.10), &"137and A"|3|o, at temperatures above the glass transition in the same system as in Figure 13.20 [Mysen and Cody, 2001]. enthalpy of reaction of about -23 kJ/mol. Thus, interactions between highly polymerized Q n (P)-species and highly polymerized Qn-species in aluminosilicate melts implies hightemperature depolymerization of the structure. 13.3 Structure and Properties of P-bearing Silicate Melts and Glasses The relationships between phosphate and silicate speciation [equations (13.3-13.6)] illustrate the sensitivity of the properties of P-bearing silicate melts to P-content. For example, the increase with P2O5 content of the activity coefficient of SiO2 in depolymerized melts (Fig. 13.4) is due to the higher abundance of Q4-species. It is perhaps less obvious, however, from the structural data why solution of P2O5 in SiO2 melt causes a decrease in 7sio2 (Fig- 8.10). Likely, this decrease is related to the linkage between Si4+ in Q4 species

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and P5+ on Q3(P) groups with one terminal P=O bond. This process effectively disrupts the 3-dimensionally interconnected silicate network structure, thus lowering the concentration of Q4-species in the melt. The negative correlation between phosphorus solubility and SiO2 contents of silicate melts (Fig. 13.2) is probably not related directly to the Qn-speciation relationships but instead to the associated changes in metal cation content of the silicate network. As the SiO2 content of a silicate melt decreases, the abundance of depolymerized Qn-species increases. The nonbridging oxygens in these Qn-species are linked via these metal cations. However, these same metal cations also form bonds with oxygen in depolymerized phosphate species such as PO4, P2O7 and more complicated phosphosilicate units [Schaller et al., 1999]. With decreasing SiO2 content, the melt becomes less polymerized and the activity of metal cations increases. Phosphate-forming reactions are then favored and, therefore, a negative correlation is found between phosphorus solubility and SiO2 content of melts. An analogous reasoning can explain the positive correlation between phosphorus solubility and alumina content of silicate melts (Fig. 13.3). In this case, the phosphate speciation is associated with formation of P-O-Al bridges in the melt structure as illustrated by reaction (13.6). Thus, as A12O3 contents of melts increase, the phosphorus solubility also increases. The complicated relationships between viscosity (and probably other transport properties), polymerization, and Na/Al content (Figs. 13.5 and 13.6) of P-bearing melts are probably related to at least three structural factors, (i) Solution of phosphorus in depolymerized silicate melts causes silicate polymerization, which qualitatively results in viscosity increases [e g., Urbain et al., 1982]. (ii) In highly polymerized silicate melts, the linkage between Si4+ in Q4 species and P5+ in Q3(P) groups with one terminal P=O bond effectively breaks up the silicate network. Thus, this mechanism should cause viscosity decreases as phosphorus is dissolved in highly polymerized silicate melts, (iii) In aluminosilicate melts, formation of Qn(P) complexes with P-O-Al bridging between phosphate and silicate structures causes depolymerization of the aluminosilicate. However, the more polymerized this aluminosilicate, the smaller is the effect of dissolved P2O5 on aluminosilicate polymerization. Thus, for depolymerized aluminosilicate melts, formation of Qn(P) species tends to drive the system toward greater aluminosilicate polymerization and, thus, higher melt viscosity. For highly polymerized aluminosilicate melts, this effect is greatly diminished or perhaps eliminated. 13.4 Summary Remarks 1. The physicochemical properties of P-bearing silicate and aluminosilicate melts are complicated functions of chemical composition. 2. The structure of P-bearing silicate and aluminosilicate melts is characterized by the existence of phosphate complexes that are either isolated or linked to the silicate network via P-O-Si and P-O-Al bridges.

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3. The polymerizing effect of dissolved phosphorus is greater when isolated phosphate complex are either abundant or more depolymerized. 4. The abundance of phosphate complexes incorporating P-O-Al and P-O-Si bridges increases with the degree of polymerization of the melt. Thus, the more polymerized a silicate melt, the less pronounced is the depolymerizing effect of dissolved phosphorus. 5. Equilibria between phosphate and silicate complexes slightly depend on temperature so that most silicate and aluminosilicate melts should become more depolymerized as the temperature is increased. 6. The complicated composition dependence of the physicochemical properties of Pbearing melts reflects the complicated relationships between phosphate and silicate complexes. References Brow R. K. (2000) Review: the structure of simple phosphate glasses. J. Non-Cryst. Solids 263 & 264, 1-28. Chakraborty I. N. and Condrate R. A. (1985) The vibrational spectra of glasses in the Na,O-SiO,P,O5 system with a 1:1 SiO,:P,O5 molar ratio. Phys. Chem. Glasses 26, 68-74. Cody B. O., Mysen B. O., Saghi-Szabo G., and Tossell J. A. (2001) Silicate-phosphate interaction in silicate glasses and melts. I. A multinuclear (27A1,29Si, 3IP) MAS NMR and ab initio chemical shielding (3IP) study of phosorus speciation in silicate glasses. Geochim. Cosmochim. Ada 65, 2395-2312. Dingwell D. B., Knoche R., and Webb S. L. (1993) The effect of P,O5 on the viscosity of haplogranitic liquid. Eur. J. Mineral. 5, 133-140. Dupree R. (1991) MAS NMR as a structural probe of silicate glasses and minerals. Trans. Amen Cryst. Soc. 27, 255-269. Dupree R., Holland D., and Mortuza M. G. (1987) Six-coordinated silicon in glasses. Nature 328, 416-417. Dupree R., Holland D., and Mortuza M. G. (1988) The role of small amounts of P,O5 in the structure of alkali disilicate glassses. Phys. Chem. Glasses 29, 18-21. Dupree R., Holland D., Mortuza J. A., Collins J. A., and Lockyer M. W. G. (1989) Magic angle spinning NMR of alkali phospho-alumino-silicate glasses. J. Non-Cryst. Solids 112, 111-119. Engelhardt G. and Michel D. (1987) High-re solution Solid-State NMR of Silicates and Zeolites. Wiley. New York. Galeener F. L. and Mikkelsen J. C. (1979) The Raman spectra and structure of pure vitreous P2O5. Solid State Comm. 20, 505-510. Gan H. and Hess P. C. (1992) Phosphate speciation in potassium aluminosilicate glasses. Amer. Mineral. 11, 495-506. Grussaute H., Montagne L., Palavit G., and Bernard J. L. (2000) Phosphate speciation in Na,OCaO-P2O5-SiO, and Na2O-TiO2-P,O5-SiO2 glasses. J. Non-Cryst. Solids 263 & 264, 312-317. Gwinn R. and Hess P. C. (1993) The role of phosphorus in rhyolitic liquids as determined from the homogeneous iron redox equilibrium. Contrib. Mineral. Petrol. 113, 424-435. Harrison T. M. and Watson E. B. (1984) The behavior of apatite during crustal anatexis; equilibrium and kinetic considerations. Geochim. Cosmochim. Acta 48, 1467-1477.

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Hartmann P., Vogel J., Friedrich U., and JagerC. (2000) Nuclear magnetic resonance investigations of aluminum containing phosphate glass-ceramics. J. Non-Cryst. Solids 263 & 264, 94-100. Holtz R, Dingwell D. B., and Behrens H. (1993) Effects of F, B,O3, and P9O5 on the solubility of water in haplogranitic melts compared to natural silicate melts. Contrib. Mineral. Petrol. 113, 492-501. Hoppe U., Walter G., Barz A., Stachel D., and Hannon A. C. (1998) The P-0 bond lengths in vitreous P,O5 probed by neutron diffraction with high real-space resolution. J. Phys.: Condensed Matter 10~ 261-270. Inoue H., Makishima A., Kanazawa T., Nanba T., and Yasui I. (1995) Structure of 50Na,O»xAl,O3»(50-x)PoO5 and (50-x/2)Na,O«xAl,O3»(50-x/2)PoO5 glasses. Phys. Chem. Glasses 36, 37-43. Kirkpatrick R. J. and Brow R. K. (1995) Nuclear magnetic resonance investigation of the structures of phosphate and phosphate containing glasses: a review. Solid State Nucl. Magn. Res. 5, 3-8. Kosinski S. G., Krol D. M., Duncan T. M., Douglass D. C, MacChesney J. B., and Simpson J. R. (1988) Raman and NMR spectroscopy of SiO, glasses co-doped with A1OO3 and POO5. J. NonCryst. Solids 105, 45-52. Kushiro I. (1975) On the nature of silicate melt and its significance in magma genesis: Regularities in the shift of liquidus boundaries involving olivine pyroxene, and silica materials. Amer. J. Sri. 275, 411-431. Li D., Bancroft G. M., Kasrai M., Fleet M. E., Feng X. H., and Tan K. H. (1994) High-resolution Si and O K- and Li-edge XANES spectra of crystalline SiP,O7 and amorphous SiO,-P,O5. Amer. Mineral. 79, 785-789. Li D., Fleet M. E., Bancroft G. M., Kasrai M., and Pan Y. (1995) Local structure of Si and P in SiO,-P,O5 and Na,O-SiO,-P,O.. glasses: a XANES study. J. Non-Cryst. Solids 188, 181-189. Lockeyer M. W. G., Dupree R., and Holland D. (1991) MAS NMR applied to potassium phosphosilicate glasses. Trans. Amer. Cryst. Soc. 27, 285-292. London D., Morgan G. B., Babb H. A., and Loomis J. L. (1993) Behavior and effects of phosphorus in the system Na,O-K,O-Al,O3-SiO,-P,O5-H,O at 200 MPa (H,O). Contrib. Mineral. Petrol. 113,450-465. Meyer K. (1997) Characterization of the structure of binary zinc ultraphosphate glasses by infrared and Raman spectroscopy. J. Non-Cryst. Solids 209, 227-239. Montel J.-M. (1986) Experimental determination of the solubility of Ce-monazite in SiO2-Al2O3K,O-Na,O melts at 800°C, 2 kbar, under H,-O-saturated conditions. Geology 14, 659-662. Mysen B. O. (1996) Phosphorous speciation changes across the glass transition in highly polymerized alkali silicate glasses and melts. Amer. Mineral. 81, 1531-1534. Mysen B. O. (1998) Phosphorus solubility mechanisms in haplogranitic aluminosilicate glass and melt: Effect of temperature and aluminum content. Contrib. Mineral. Petrol. 133, 38-50. Mysen B. O. and Cody G. D. (2001) Silicate-phosphate interaction in silicate glasses and melts. II Quantitative, high-temperature structure of P-bearing alkali aluminosilicate melts. Geochim. Cosmochim. Ada 65, 2413-2431. Mysen B. O., Ryerson F. J., and Virgo D. (1981) The structural role of phosphorous in silicate melts. Amer. Mineral. 66, 106-117. Nelson C. and Tallant D. R. (1984) Raman studies of sodium silicate glasses with low phosphate contents. Phys. Chem. Glasses 25, 31-39.

Phosphorus

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Nelson C. and Tallant D. R. (1986) Raman studies of sodium phosphates with low silica contents. Phys. Chem. Glasses 26, 119-122. PichavantM., Herrera J. V., Boulmier S., BrigueuL., Joron J.-L., Juteau L. M., MichardA., Sheppard S. M. R, Treuil M., and Vemet M. (1987) The Macusani glasses, SE Peru: Evidence of chemical fractionation of peraluminous magmas. In: Magmatic Processes: Physicochemical Principles (ed. B. O. Mysen), pp. 359-374. Geochemical Society. University Park, PA. Pichavant M., Montel J.-M., and Richard L. R. (1992) Apatite solubility in peraluminous liquids: Experimental data and an extension of the Harrison model. Geochim. Cosmochim. Ada 56, 3855-3861. Ryerson F. J. (1985) Oxide solution mechanisms in silicate melts: Systematic variations in the activity coefficient of SiOv Geochim. Cosmochim. Ada 49, 637-651. Ryerson F. J. and Hess P. C. (1980) The role of P,O5 in silicate melts. Geochim. Cosmochim. Ada 44,611-625. SchallerT., Ring C, Toplis M. J., and Cho H. (1999) TRAPDOR NMR investigations of phosphorusbearing aluminosilicate glasses. J. Non-Cryst. Solids 248, 19-27. Shibata N., Horigudhi M., and Edahiro T. (1981) Raman spectra of binary high-silica glasses and fibers containing GeO,, P,O5 and B,O3. J. Non-Cryst. Solids 45, 115-126. Tien T.-Y. and Hummel F~ A."(1962) The system SiO,-P,O5. J. Amer. Ceram. Soc. 45, 422-424. Toplis M. J. and Dingwell D. W. (1996) The variable influence of P,O5 on the visocosity of melts of differing alkali/aluminum ratio: Implications for the structural role of phosphorus in silicate melts. Geochim. Cosmochim. Ada 60, 4107-4121. Toplis M. J. and Reynard B. (2000) Temperature and time-dependent changes of structure in phosphorus containing aluminosilicate liquids and glasses: in situ Raman spectroscopy at high temperature. J. Non-Cryst. Solids 263 & 264, 123-131. Toplis M. J. and Schaller T. (1998) A31P MAS NMR study of glasses in the system xNa,O-(l-x)Al,O32SiO,-yPoO5. J. Non-Cryst. Solids 12A, 57-68.

Toplis M. J., Dingwell D. B., and Libourel G. (1994) The effect of phosphorus on the iron redox ratio, viscosity, and density of an evolved ferro-basalt. Contrib. Mineral. Petrol. 117, 293-304. Tuttle O. F. and Bowen N. L. (1958) Origin of granite in light of experimental studies in the system NaAlSLO -KA1SLO -SiO,-HoO. Geol. Soc. Amer. Mem. 74, 1-153. Urbain G., Bottinga Y., and Richet P. (1982) Viscosity of liquid silica, silicates and aluminosilicates. Geochim. Cosmochim. Ada 46, 1061-1072. Visser W. and Koster Van Groos A. F. (1979) Effects of P,O5 and TiO, on liquid-liquid equilibria in the system K,O-FeO-Al,O,-SiOo. Amer. J. Sci. 279, 970-983. Watson E. B. (1976) Two-liquid partition coefficients: Experimental data and geochemical implications. Contrib. Mineral. Petrol. 56, 119-134. Watson E. B. and Capobianco C. J. (1981) Phosphorous and rare earth elements in felsic magmas: An assessment of the role of apatite. Geochim. Cosmochim. Ada 45, 2349-2358. Webb S. L. and Courtial P. (1996) Compressibility of P,O5-Al,O3-Na,SiO3 melts. Phys. Chem. Mineral. 23,205-211. Wolf M. B. and London D. (1994) Apatite dissolution into peraluminous haplogranitic melts: An experimental study of solubilities and mechanisms. Geochim. Cosmochim. Ada 58, 4127-4145. Wyllie P. J. and Tuttle O. F. (1964) Experimental investigation of silicate systems containing two volatile components. III. The effects of SO3, P,O5, HC1, and Li,O in addition to HOO on the melting temperatures of albite and granite. Amer. J. Sci. 262, 930-939.

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Yamashita H., Yoshino H., Nagata K., Inoue H., Nakajin T., and Maekawa T. (2000) Nuclear magnetic resonance studies of alkaline earth phosphosilicate and aluminoborosilicate glasses. J. Non-Cryst. Solids 270, 48-59. Yang W.-H., Kirkpatrick R. J., and Turner G. (1986) 31P and 29Si magic-angle sample-spinning NMR investigation of the structural environment of phosphorus in alkaline-earth silicate glasses. J. Amer. Ceram. Soc. 69, C222-C223.

411

Chapter 14

Water — An Elusive Component As a component of silicate glasses and melts, water owes its importance to the dramatic influence it exerts even at very low concentrations on a variety of physical properties. This influence is particularly strong for silica-rich compositions. Near the glass transition, this is illustrated by the 10-fold lowering of the viscosity of pure SiO2 upon addition of 0.1 wt % water [Hetherington et al., 1964]. Although less, the effects of water on the properties of depolymerized melts remain significant. For instance, addition of 0.18 wt % water causes a 5-fold decrease of the viscosity of sodium trisilicate [Shelby and McVay, 1976]. It follows that water can exert a measurable influence even at the 10- or 100-ppm concentrations of a melt in equilibrium with the atmosphere. Water contents are much higher in magma where dissolved water originates from hydrous sediments brought deep into the mantle by subduction processes [see Poli and Schmidt, 2002]. Water also effects phase equilibria [e.g., Kushiro, 1972,1974], reaction kinetics, density, and viscosity. The rate of phase separation increases in water-bearing sodium-silicate liquids [McGinnis and Shelby, 1995]. Melt crystallization is favored because of enhanced fluidity and element diffusivity [Metrich et al., 2001]. Hydrous glasses are more prone to alteration. For these reasons, dissolved H2O affects fundamental geological processes ranging from melting of the Earth's mantle to magma ascent, eruption, and crystallization. In fact, there is probably not a single oxide that influences more the properties of silicate melts. All these effects depend markedly on both water content and silicate composition. Their study, however, is made experimentally difficult by a number of factors, (i) The range of water contents relevant to natural magma is wide. Owing to the low molar mass of water compared to that of other oxides, a not so high concentration of 5 wt % translates into about 15 mol % H2O on an oxide basis. With the obvious exception of silica, few oxides can indeed be as abundant as water, (ii) The dissolution mechanisms depend on both water content and silicate composition. As will be described below, water is not a real one-component oxide because it dissolves mainly in two forms, hydroxyl ions (OH") and molecular water, whose respective influence on melt properties must be distinguished, (iii) Considerable problems are encountered when measuring physical properties at the high pressures needed to dissolve significant amounts of water. For a long time, only water solubility and liquid-solid phase relations in hydrous systems were investigated because of the feasibility of phase equilibria experiments with the quenching method. (iv) The difficulty of quenching depolymerized melts is as serious in hydrous as in dry systems. Hence, most of the results obtained deal with melts that can be quenched easily, i.e., with aluminosilicate compositions near the meta-aluminous join. Of course, this

412

Chapter 14

Figure 14.1 - Melting temperatures in the systems (a) SiO,-H2O and (b) MgSiO3-H,O as a function of pressure with and without H,O. In the hydrous systems, pressure is water pressure [Kushiro et ai, 1969; Boettcher, 1984; Jackson, 1976]. The liquidus curve for enstatite under anhydrous conditions in (b) is simplified as it does not show incongruent melting between ambient pressure and about 0.5 GPa [Boyd et al, 1964]. domain represents only a small part of the composition range of actual interest in Earth sciences.

14.1. Phase Relations As described in Chapter 1, water solubility studies date back to Spallanzani's unsuccessful attempts at measuring water contents in basalt in the late 18th century. Following the first modern results obtained by Goranson [1936] on molten NaAlSi3Og, there is now a significant body of water solubility data. Although Wasserburg [1957] showed that the effects of water on solid-liquid phase relations can be large, these effects have been, in contrast, less extensively investigated. 14.1a. Melting in Hydrous Silicate Systems At pressures above ambient, the presence of any amount of H2O causes large reductions in melting temperatures. This effect depends on silicate composition. It is largest for silica-rich and aluminosilicate systems (Fig. 14.1). The melting temperature of quartz is lowered by about 500°C by a 0.5 GPa water pressure [Kennedy et al., 1962; Jackson, 1976], whereas the change is less than 200°C for enstatite [Kushiro et al., 1968]. The melting phase relations of enstatite are also affected by H2O. Enstatite melts congruently

Water — An Elusive Component

413

Figure 14.2 - Liquidus phase relations at 2 GPa in the system Mg,SiO4CaMgSi 2 O 6 -SiO, with and without excess H,0 as indicated on diagram [Kushiro,"l969].

above about 0.5 GPa under dry conditions [Boyd etai., 1964] but incongruently to forsterite + melt in the presence of water [Kushiro et ai, 1968]. Dissolved water also affects the activity of SiO r The SiO2 activity decreases as water is added to the system Mg2SiO4CaMgSi2O6-SiO2 where melts are olivine-normative under dry high-pressure conditions but quartz-normative when saturated with water (Fig. 14.2). Similar observations have been made for aluminosilicates. In the so-called haplogranite system, NaAlSi3O8-KAlSi3Og-SiO2 [Tuttle and Bowen, 1958; Luth et ai, 1964], the liquidus volume of quartz expands relative to Na- and K-feldspar with increasing water saturation pressure (Fig. 14.3). Further, the trajectory of the minimum (shown with a shaded arrow in Fig. 14.3) is toward the NaAlSi3O8 corner of the system as the water pressure is increased. Qualitatively, one might infer from these relations that not only does the activity coefficient of SiO2 decrease more than those of components needed to form feldspar, but that there is also an effect of dissolved H2O on the activity of Na2O and

Figure 14.3 - Shift of phase boundaries in the haplogranite system, NaAlSi3O8KAlSi3O8-SiO,-H,O with increasing water pressure [Tuttle and Bowen, 1958; Luth etai, 1964].

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Figure 14.4 - Phase relations in silicate-H2O systems, (a) Above the liquidus temperature, with pressure Pt < P,. (b) Solvus of the haplogranite-H,O system. The points marked e.p. and c.p. denote the eutectic and critical points. The section is polybaric with actual pressures indicated for a few data points [Bureau and Keppler, 1999]. K2O in the melt. Thus, one may surmise that the alkali metals in some manner are involved in the solution mechanism of H2O.

14.1b. Water Solubility To understand water solubility in silicate melts, it is instructive first to examine phase relations in hydrous silicates at superliquidus temperatures (see, for example, Paillat et al. [1992] for a detailed discussion). For any silicate-H2O system, there exists a pressure and temperature range where a water-saturated melt is in equilibrium with a silicatesaturated aqueous fluid. As depicted in Fig. 14.4a, the mutual solubility of these phases tends to increase with increasing temperature although the temperature dependence of water solubility can be negative in a composition interval close to the eutectic point. As a function of temperature, the solvus defined by the composition of both phases, thus, ends at a critical point beyond which a single supercritical fluid obtains. This situation can hold at pressures and temperatures relevant to melting processes in the Earth's interior. A case in point is the haplogranite system whose critical pressure and temperature are 1.69 GPa and 830°C [Bureau and Keppler, 1999]. As described by Paillat et al. [1992], the temperature dependence of water solubility could become positive with increasing pressure (Fig. 14.4a). In any case, the solvus shrinks markedly in such a way that not only the temperature but also the composition of the critical point varies [Shen and Keppler, 1997; Bureau and Keppler, 1999; Sowerby and Keppler, 2000]. Along the SiO2-NaAlO2 join, for example, the temperature of the critical point decreases isobarically with increasing Al/(A1+Si) (Fig. 14.5). In more complex

Water — An Elusive Component

415

Figure 14.5 - Pressuretemperature trajectories of critical point (see Fig. 15.4a) for the systems indicated [Bureau and Keppler, 1999]

systems, the topology of the solvus depends on other composition variables such as additional alkalis, fluorine and phosphorus [Sowerby and Keppler, 2002]. Unfortunately, relevant experimental data are at present limited. SiO^-H2O. Early studies on water solubility in silicate systems were conducted at low partial pressure of H2O and total pressure close to ambient [e.g., Tomlinson, 1956, Kurkjian and Russell, 1958; Moulson and Roberts, 1961; Shackleford and Masaryk, 1976]. Under these conditions, the solubility is proportional to the square root of the fugacity of H 2 O , / H 2 Q (Fig. 14.6). That relationship points to a simple solution mechanism whereby

Figure 14.6 - Water solubility in molten SiO, at 1000T as a function of the square root of water pressure [Moulson and Roberts, 1961].

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Chapter 14

Figure 14.7 - Solubility of water in SiO, melt as a function of water pressure [Kennedys al, 1962].

Figure 148 - Solubility of water in SiO, melt as a function of square root of fugacity of H,0 [Kennedy etal, 1962],

oxygen bridges in the 3-dimensionally interconnected network of vitreous SiO2 are replaced by OH-groups [Moulson and Roberts, 1961]: Si-O-Si + H2O o Si-OH..OH-Si

(14.1)

Figure 14.9 - Solubility of water in various silicate melts as indicated on figure as a function of square root of fugacity of H2O [data compilation by McMillan, 1994].

Water — An Elusive Component

417

Increasing Hfl pressure results in higher f^O solubility, Xmo, in SiO2 melt (Fig. 14.7) although the rate of increase, 3XH2O/3R is itself pressure-dependent. When the high-pressure data in Fig. 14.7 are plotted against fRl0, however, there is no longer a linear relationship between/H2Q and water solubility (Fig. 14.8) even though the chemical simplicity of the SiO2-H2O system might have suggested that water dissolves in molten silica in the same way at low and high pressure. One of the main reasons why this is so is because the volume term of reaction (14.1) depends on pressure perhaps, in part, resulting from the suggestion that the partial molar volume of H2O in hydrous melts may not be independent of pressure, but most likely because the molar volume of H2O decreases rapidly with increasing pressure [e.g., Burnham et al., 1969; Haar et al., 1984; Brodholt and Wood, 1994]. This feature notwithstanding, there are circumstances where even high-pressure H2O solubility remains proportional to / H 2 0 (Fig. 14.9). This linearity, observed for a Columbia River Basalt melt [Hamilton et al., 1964] and a melt composition in the system CaO-Al2O3-SiO2 [McMillan etal., 1986], however, should reflect canceling composition effects on solubility [McMillan, 1994]. Metal Oxide-SiO2-H2O. Even at low pressure, the metal/silicon ratio affects water solubility for K2O-SiO2 melts (Fig. 14.10). Similar results have been reported for the systems Na2O-SiO2 and Li2O-SiO2 as well as for ternary alkali-alkaline earth-silica melts [Kurkjian and Russell, 1958; Uys and King, 1963]. At fixed metal/silicon ratio, water solubility is negatively correlated with the ionization potential (or ionic radius) of the alkali metal [Kurkjian and Russell, 1958]. A similar trend is suggested by high-pressure data (Fig. 14.11), which also indicate a rapid decrease in H2O solubility with increasing Na/Si-values.

Figure 14.10 - Solubility of water in melts along the join K,-SiO2 at ambient pressure. Experiments conducted with melts in equilibrium with water steam at temperatures indicated [Kurkjian and Russell, 1958].

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Figure 14.11 - Solubility of water in melts along the join Na,O-SiO, at 1.3 GPa pressure and 1300°C (open symbols). Also shown is the solubility in CaSi4O9 melt under the same conditions [Mysen and Cody, 2004]. Mol % calculation based on 1 oxygen (0=1)

The deep minimum in water solubility at an intermediate K/Si ratio (near unity) indicates that at least two solution mechanisms are at work [Kurkjian and Russell, 1958]. One may be described by equation (14.1). Its importance diminishes, however, as the silica activity of the melt decreases with increasing K/Si-ratio. The chemical simplicity of the alkali-SiO2-H2O system dictates that the second mechanism involves the alkali metal unless strong composition-dependent variations in hydrogen bonding take place. The fact that there remains a linear relationship between H2O-solubility and/ H2O in H2Obearing alkali silicate glasses and melts [Russell, 1957] is consistent with either assumption

Figure 14.12 - Solubility of water in Na,O»4SiO, (circles) and Na2O«8SiO, (squares) as a function of temperature for the water (total) pressures indicated [Mysen and Cody, 2004]. Mol % calculation based on 1 oxygen (0=1)

Water — An Elusive Component

419

Figure 14.13 - Solubility of water in melts along the joins Na,O»4SiO, + A1,O3 (closed symbols) and CaO»4SiO, + A1,O3 (open symbols) as a function of A12O3 content at 1.3 GPaand HOOT [Mysen'and Wheeler, 2000; Mysen, 2002].

because the formation of either 2 Si-OH or one Si-OH and one alkali-OH per mol SiO2 retain this proportionality relationship. Measurements on sodium silicates [Mysen and Cody, 2004] indicate that the temperature dependence of water solubility depends on both Na/Si and pressure (Fig. 14.12). In the 0.8-1.65 GPa range, the solubility in Na2O»8SiO2 increases with temperature at a rate which itself increases with increasing pressure. The critical point for this composition is at T < 1100°C and P < 2 GPa, but Mysen and Cody [2004] could not determine these parameters with precision. In contrast, solubility slightly decreases with increasing temperature for Na2O»4SiO2 melt, causing the solubility difference with Na2O«8SiO2 to increase correlatively. We do note, though, that increasing pressure causes the negative temperature-dependence found for Na 2 O»4SiO 2 melt to diminish so that it would presumably be positive at higher pressure.

Figure 14.14 - Solubility of water in MAlSi3O8 melts as a function of ionic radius of M cation (Li, Na, K) at pressures indicated [Behrens et ai, 2001].

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Chapter 14

Figure 14.15 - Solubility of water in NaAlSLO-KA1SLO-SiO, melt as a function of temperature at the water (total) pressures indicated [Holtz et al., 1995].

Aluminosilicate-H2O. Water solubility in aluminosilicate melts is in some manner associated with reactions involving Al3+ because the feldspar liquidus volume shrinks relative to that of quartz with increasing water pressure in the system NaAlSi3Og-KAlSi3O8SiO2-H2O (Fig. 14.3). This inference is consistent with the negative correlation, at least at high pressure, between water solubility and Al2O3-content (Fig. 14.13) whether in peralkaline [Mysen and Wheeler, 2000; Mysen, 2002] or in peraluminous melts [Dingwell etal, 1997]. For melts along meta-aluminous joins, in contrast, water solubility increases with increasing A12O3 as observed for the Na and K systems [McMillan and Holloway, 1987], It is notable, however, that the influence of A12O3 on water solubility is considerably greater along the join Na2Si409-Al203 than along the analogous CaSi4O9-Al2O3 join (Fig. 14.13). Hence, it is possible that H2O solubility does not differ greatly along the SiO2-Ca05AlO2 and SiO2-NaAlO2 joins or, possibly, that solubility is greater in Cathan in Na-aluminosilicates. That suggestion is consistent with the extrapolation made from the trend shown in Fig. 14.14 for MAlSi3Og melts (M = K, Na, Li), which indicates that solubility is negatively correlated with the ionic radius, and, therefore, that it is positively correlated with the ionization potential of the metal. Such complex relationships indicate that there exist multiple solution mechanisms, and that alkalis and alkaline earths have different effects on water solubility in peralkaline and meta-aluminous silicate melts. The temperature dependence of solubility conforms to the scheme of Fig. 14.4. A change from negative to positive (Fig. 14.15) has been observed at water pressure between 0.2 and 0.5 GPa for one composition in the haplogranite system [Holtz et al., 1995]. Consistent with earlier data of Goranson [1936], a similar change has been reported by Paillat et al. [1992] for NaAlSi3O8, another meta-aluminosilicate melt. In summary, water solubility as a function of temperature and pressure is a complex function of composition. Because empirical models of prediction of H2O solubility are anchored in data at high Pn20, mostly for aluminosilicate melts near meta-aluminous

Water — An Elusive Component

421

Figure 14.16- Proportion of water dissolved as OH and as molecular H,O in NaAlSi3O8 and MORB (Mid-Oceanic Ridge Basalt) glass as a function of total water content [Dixon and Stolper, 1995].

joins [e.g., Wasserburg, 1957; Spera, 1974; Burnham, 1975; Silver and Stolper, 1985, among others], these models are unlikely to be reliable for compositions differing significantly from those of their input data base. 14.1c. Water solution: OH Groups and Molecular H^O The complex composition dependence of water solubility appears related to the existence of at least two different water species. The existence of OH groups in hydrous SiO2 glass has been well documented by a variety of spectroscopic techniques [Moulson and Roberts, 1961; Stolen and Walrafen, 1976; Stolper, 1982; McMillan and Remmele, 1986; Mysen and Virgo, 1986a; Farnan et al., 1987]. As early as in 1956, infrared spectra of hydrous alkali silicate glasses indicated that dissolved water may exist both as OH-groups and as molecular water [Scholze, 1956], a conclusion subsequently supported by additional studies with different silicate compositions [Orlova, 1962; Bartholomew et al., 1980; Bartholomew and Schreurs, 1980; Takata et al., 1981]. In a comprehensive infrared spectroscopy study of hydrous glasses quenched from high temperature at high pressure, Stolper [1982] concluded that there exists a systematic relationship between the proportion of dissolved water as OH and as molecular H2O. A more recent version of that relationship is shown in Fig. 14.16. At least for glasses, Stolper [1982] suggested that the relative abundance of OH groups and molecular H2O is predominantly a function of the total water content of the material. The principal solution mechanism is described by the equilibrium: H O (molecular) + O (melt) <=> 2 OH (melt)

(14.2)

This speciation reaction would, thus, account for the contrast between the distinctly nonlinear relationships between melt properties and water content below about 2 wt% (see, for example, Fig. 14.17) and near linear relationships at higher water concentration.

422

Chapter 14

Figure 14.17 - Diffusion coefficient of total water, £>waler, in NaAlSi3Og melt as a function of total water content of melt [Behrens and Nowak, 1997].

The original model by Stolper [1982] has subsequently been refined to take into account possible effects of silicate composition, temperature, and pressure. Silver et al. [1990] examined the effect of bulk chemical composition on the OH/H2O ratio for highly felsic glasses. In Fig. 14.18 is shown the evolution of OH and molecular H2O as a function of total water content (corresponding to the anorthite-wollastonite-quartz eutectic in this system, see Osborn and Muan [I960]) in a natural rhyolite [Newman et al., 1986] CaOAl2O3-SiO2 glasses [Silve et al., 1990]. The proportion of water dissolved as molecular H2O increases with increasing silica content. Because the rhyolite glass was quenched from a lower temperature (850°C) than the other glasses (1400°C), Silver et al. [1990] suggested that this difference caused, at least in part, the differences in water speciation. It is, of course, also possible that different fictive temperatures controlled by both composition and quenching rate may have affected the results in Fig. 14.18. In fact, Dingwell and Webb [1990] used estimated viscosities of hydrous melts, in conjunction

Figure 14.18 - Proportion of water dissolved as OH and as molecular H,0 in CaO-Al,O3-SiO, (CAS) glass and rhyolite glass (see text for detailed discussion of glass compositions) [Newman et al, 1986; Silver et al., 1990].

423

Water — An Elusive Component Table 141 AH and AS of reaction (15.2) at different H70 contents and pressure [Sowerby and Keppler, 1999] Total H,0 (wt %) 11.21 8.01 7.8 3.93 3.08 2.05 1.00

Pressure, GPa 1.0 0.45 0.5 0.0001 0.0001 0.0001 0.0001

AH (kJ/mol) 26.2 25.2 27.2 31.8 30.3 27.2 30.5

AS (J/mol K) 10.4 3.9 6.3 13.4 11.4 8.3 9.3

with available OH versus H2O speciation data for glasses obtained at different quench rates, to estimate a Gibbs free energy change of -25±5 kJ/mol for reaction (14.2) in rhyolite melt. According to this analysis, equilibrium (14.2) shifts to the right with increasing temperature, thus making analysis of 0H/H 2 0 of glasses an uncertain measure of water speciation in melts far from the glass transition. Because of this problem, water speciation has been investigated on melts via hightemperature and high-pressure infrared (IR) absorption spectroscopy [Nowak and Behrens, 1995, Shen and Keppler, 1995; Sowerby and Keppler, 1999]. This method relies on the relative variations in intensity of IR absorption bands. Consistent with original conclusions from quench rate and relaxation considerations [Silver et al., 1990; Dingwell and Webb, 1990], these observations indicate that the 0 H / H 2 0 ratio increases with increasing temperature (Fig. 14.19). There is some discussion as to pressure and temperature variations in the molar absorption coefficients needed to quantify these IR results [e.g., Withers et al., 1999; Withers and Behrens, 1999; Mandeville et al, 2002]. Nevertheless,

Figure 14.19 - Examples of Fourier Transform Infrared (FTIR) spectra of hydrous rhyolite melt (total water content: 3.93 wt %) and glass as a function of temperatures indicated [Sowerby and Keppler, 1999].

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Chapter 14

Figure 14.20 - (a) Concentration of water as molecular H2O and OH in NaAlSi3O8-KAlSi3O8-SiO2 melt as a function of temperature, (b) Equilibrium constant for reaction (14.2) as a function of temperature for the same melt composition [Nowak and Behrens, 1995]. the increase of 0H/H 2 0 determined from in-situ measurements follows the general trend shown in Fig. 14.20. From the temperature dependence of the equilibrium constant ^14.2 ~ t^OH^'Vmo'

(14.3)

the enthalpy of this reaction above the glass transition is about -30 kJ/mol for the investigated feldspar + quartz compositions. For these highly polymerized compositions, neither the entropy nor the enthalpy of reaction (14.2) depend significantly on total water content or pressure (Table 14.1). It must emphasized, however, that the relevant experimental data are limited. In light of the large effects of bulk chemical composition on H2O solubility and the differing effects of H2O on melt properties with melt composition, use of these in-situ thermodynamic data for significantly different compositions and conditions is not warranted. 14.2. Physical Properties of Hydrous Silicate Systems How water speciation affects the physical properties of hydrous melts is an important question. The viscosity and density of hydrous melts have been measured by the falling sphere method either in internally heated vessels [Shaw, 1963; Persikov et al., 1990] or in piston cylinder apparatus [Kushiro et al., 1976; Fujii and Kushiro, 1977]. Such measurements are tedious, however, and they can be performed only over restricted temperature intervals above the liquidus. Because the geophysically relevant conditions are generally subliquidus, these problems are compounded by the difficulties of extrapolating the measurements to lower temperatures. This applies especially to viscosity, for which Arrhenius laws cannot be extrapolated outside the narrow range of hightemperature measurements.

Water — An Elusive Component

425

Without observations near the glass transition range, the effects of water on the viscosity are poorly constrained and knowledge of the rheology of melts is incomplete. The situation changed when it was realized that, because of the slowness of water exsolution near the glass transition, water can be kept dissolved metastably at room pressure in the supercooled liquid state at concentrations close to saturation. It is this feature that allows accurate measurements to be performed at room pressure on water-bearing liquids [Lejeune et al., 1994; Richet et al., 1996]. From a combination of such results with data obtained at simultaneously high temperature and pressure, composition-property relationships can be determined over large P,Tintervals. The high-pressure experiments are limited to hydration of the melt under appropriate conditions. In this way, a wealth of data has been gathered rapidly not only for viscosity but also for thermal expansion and heat capacity. 14.2a Volume Properties A complication to be mentioned from the outset is that, owing to the high pressure of their synthesis, hydrous glasses are permanently compacted with respect to samples synthesized at room pressure (see section 2.3.c). The hydration pressure generally increases with the water content of samples. Hence, glasses from a given composition series are not strictly comparable when their configurations have been frozen in at different pressures. The effect is illustrated in Fig. 14.21 for a series of phonolite glasses. Since density is the simplest macroscopic measure of structure, this effect should be taken into account in structural studies. But a potentially more problematic effect results from the fact that, on heating, a compacted sample will relax to its 1-bar volume as already shown in Fig. 2.22 for hydrous phonolite glasses. Thermal expansion is made up of two different contributions: a relaxational and an isoconfigurational part. For the hydrous glass of Fig. 2.22, the former is approximately half the latter so that unbiased thermal expansion coefficient can be determined only for samples that have previously been fully relaxed at room pressure [Bouhifd et al., 2001 ]. Such a volume relaxation begins more than 100 degrees below the standard glass transition temperature, i.e., its onset is at temperatures at which structural

Figure 14.21 - Influence of the pressure of synthesis on the room temperature and pressure molar volume of hydrous phonolite glasses [Richet et al., 2000]. The dry sample was prepared at room pressure (0.1 MPa), the hydrous glasses under the water pressure indicated.

426

Chapter 14

Figure 14.22 - Room temperature and pressure molar volume of hydrous glasses against water concentration. Data from Silver et al. [1990], Schulze et al. [1996] and Dingwell et al. [ 1996] for rhyolite and haplogranite glasses; from Richet et al. [1996] for andesite, and Richet et al. [2000] for basalt.

relaxation induced by temperature changes is practically nonexistent under similar heating rates. As a light oxide, water is expected to lower the density of silicate glasses. A rather extensive set of density data exists for hydrous silicate glasses at room temperature to check this assumption. As apparent in Fig. 14.22, molar volumes are linear functions of composition between the anhydrous endmember and the most water-rich samples [Richet et al., 2000]. Interestingly, the volume data for all series of hydrous glasses extrapolate to the same value of 12.0±0.5 cm3/mol for the partial molar volume of pure H2O, VH 0 [Richet and Polian, 1998; Richet et al, 2000]. This composition-independent value, which translates into a density of 1.5 g/cm3, is the same as the molar volume of Ice VII [Hemley et al., 1987], the densest known polymorph of ice. From SiO2-rich to SiO2-rich glasses, water, thus, dissolves in a compact form and lowers less the density than might have been expected. Another noteworthy feature is that VH o does not depend on water speciation because it remains constant regardless of the relative abundances of hydroxyl ions and molecular water. Richet and Polian [1998] and Richet et al. [2000], thus, concluded that the volume change of reaction (14.2) is zero in glasses, which is in accord with spectroscopic observations that water speciation is the same for samples of the same hydrous composition quenched at different pressures [McMillan et al., 1986]. That the partial molar volume of water is independent of composition had already been stated by Ochs and Lange [1999] who had gone one step further by asserting that this also holds true for melts at high pressure and high temperature where water would increase both thermal expansion and compressibility. The pressure and temperature dependence of VH owas derived by Ochs and Lange [1997] from the volumes measured up to 1000°C and2l GPa by Burnham and Davis [1971] for a melt close to NaAlSi3Og composition. Ochs and Lange [ 1999] found that this pressure- and temperature-dependent VH o also accounts for dilatometry experiments made on a few other series of hydrous compositions quenched in a piston cylinder. The model of Ochs and Lange [1999] is a very useful starting point, but its predictions are unlikely valid quantitatively for wide ranges of conditions. This is indicated by measurements of relaxed volumes made on various hydrous supercooled liquids [Bouhifd et al., 2001]. The results plotted in

Water — An Elusive Component

427

Figure 14.23 - (a) Thermal exansion coefficient of hydrous phonolite glass and supercooled liquid against water concentration, (b) Comparison between the measured molar volume of hydrous phonolite glasses and supercooled liquids with the model predictions of Ochs and Lange [1999], shown as dashed lines, for the wt% water indicated. Data from Bouhifd et al. [2001]. Fig. 14.23 for hydrous phonolite compositions show that the thermal expansion coefficient is indeed a linear function of composition for supercooled liquids (and glasses as well). Although thermal expansion does increase with water content for both phases, the partial molar expansivity of water differs somewhat from the predicted values of Ochs and Lange [1999] and varies from a silicate composition to another. We finally turn to compressibility, which is needed to determine high-pressure densities. In this instance, the difficulty is that the relevant property is the adiabatic compressibility, /3S, or its reciprocal, the adiabatic bulk modulus, Ks, have to be measured either by ultrasonic or Brillouin scattering methods under very short experimental timescales (see Chapter 2). It follows that measurements on fully relaxed liquids are possible only at very high temperatures where the viscosity is so low that it is impossible to keep any water dissolved in a melt at room pressure. Such measurements have not yet been performed on silicate melts at simultaneously high pressures and temperatures. The only available information, thus, deals with hydrous glasses at room pressure. As expected, the less dense relaxed glasses are more compressible than the compacted samples (Fig. 14.24). The difference is slight, however, and in both cases a linear variation of the bulk modulus is observed with water content, indicating that water speciation does

Figure 14.24 - Bulk modulus of hydrous andesite glasses against water concentration. The "compacted" data refer to glasses synthesized at 0.2 or 0.3 Gpa, the "relaxed" data to samples annealed at room pressure [Richet and Polian, 1998].

428

Chapter 14

not influence the compressibility of hydrous glasses. For andesite glasses, this trend extrapolates to a value, Ks = 18 (3) GPa, which is close to the bulk modulus of ice VII, Ks = 23.9 (9) GPa [Richet and Polian, 1998]. As the high compressibility of Ice VII primarily results from the existence of weak hydrogen bonds, this similarity suggests that hydrogen bonding plays an important role in water solubility. Since then, new measurements made by Whittington et al. [unpub. data] on other series of hydrous glasses show that the partial molar bulk modulus of water is, in fact, a strong function of silicate composition. The compressibility of glasses is purely vibrational in origin. As such, it depends less sensitively on structure than the configurational part of the compressibility of liquids, which can represent the major contribution to f5s [Askarpour et al., 1993]. Hence, the compressibility of water in hydrous liquids should also be a strong function of silicate composition, with the consequence that model values of Ochs and Lange [1999] should be used with some caution at high pressure. In any case, the compressibility data for hydrous glasses demonstrate that bonding between the silicate framework and water, either as hydroxyl ions or as molecular H2O, varies widely. 14.2b. Heat Capacity and Enthalpy The technical difficulty of high-pressure measurements is the greatest for thermal properties [see Clemens and Navrotsky, 1986]. Hence, information on enthalpy and entropy of mixing has essentially been derived from thermodynamic analysis of phase equilibrium data. Along with solubility measurements, the aforementioned equation of state determined for a sodium aluminosilicate by Burnham and Davis [1971] has proven useful to determine the mixing properties of melts [Burnham and Davis, 1974]. An important conclusion drawn by Burnham [1975] and Burnham et al. [1978] is that mixing is ideal in aluminosilicates as long as it is considered in terms of structural units made up of 8 oxygen atoms. As it is difficult to separate enthalpy and entropy terms in Gibbs free energy expressions, it would be better to constrain, instead, thermodynamic analyses with reliable experimental thermal data. It is in fact possible to measure accurately at room pressure the heat capacity of hydrous glasses, and even that of supercooled liquids over a narrow interval above the

Figure 14.25 - Heat capacity of the same series of hydrous phonolite glasses and supercooled liquids as in Fig. 14.23. Unpublished data by Bouhifd et al. for the wt% water indicated.

Water — An Elusive Component

429

Figure 14.26 - Enthalpy of mixing of hydrous glasses at room pressure and temperature. Data for albite (Ab) and hamplogranite glasses by Clemens and Navrotsky [1986] and for trachyte glasses by Richet et al. [2004].

glass transition (Fig. 14.25). Two general features are observed in such Differential Scanning Calorimetry measurements made on small samples. First, the heat capacity change at the glass transition increases with increasing content. Second, this increase is essentially due to the fact that the heat capacity of the glass at the transition becomes increasingly smaller than the Dulong-and-Petit limit of 3 R g/atom K (see section 2.3a) with increasing water concentration. Consistent with the temperature-induced increases of configurational entropy, formation of hydroxyl ions is favored by high temperatures [Behrens and Nowak, 2003]. For water-bearing melts, the configurational heat capacity, thus, is related to the shift to the right of the speciation reaction (14.2) at high temperatures. Such heat capacity data are also needed to determine enthalpies of mixing (AHJ. Solution calorimetry experiments in lead borate at 700°C have been made for this purpose by Clemens and Navrotsky [1986] on albite and haplogranite compositions (Fig. 14.26). Because pure water could not be investigated, it is difficult to determine the actual AHm from these results. For this reason, Sahagian and Proussevitch [1996] and Zhang [1999] chose to reanalyze the equation of state data of Burnham and Davis [1971] to determine the temperature and pressure dependence of AHm, the influence of water speciation being taken into account by Zhang [1999]. As described by Richet et al. [2005], more accurate values can be obtained from solution calorimetry experiments made for silicic compositions which dissolve readily in hydrofluoric acid solutions. In this case the major advantages of the method are the high precision of the measurements and the fact that the enthalpy of solution of pure water can also be measured so that the reference enthalpy of a mechanical mixture of water and silicate is accurately known. The results obtained in this way at 50°C for hydrous trachyte glasses suggest an enthalpy of mixing of about 10 kJ/mol at the highest water contents investigated (Fig. 14.27). Such a determination would be inconsistent, however, because the data do not refer to the same structural state (glass for silicates and liquid for water). Even for glasses, the data are inconsistent in view of the systematic decrease of fictive temperature with increasing water content shown by the T data of Fig. 14.25. Truly isothermal values for a given high temperature, T, can be obtained readily, however, provided that C data are available for the glass and supercooled liquid phases, on the one hand, and that the enthalpy of water and steam is known as a function of temperature

430

Chapter 14

Figure 14.27 - Ideal enthalpy of mixing of water and a trachyte melt at 0.3 GPa and 1300 K [Richet et al., 2004]. From the anhydrous endmember to pure water, the fit to the data (solid line) practically coincides with by the linear variation (dashed line) of Ht for a mechanical mixture of the two endmembers. Similar results have been obtained for albite and phonolite melts [Richet et al, 2005]

[Haar et al., 1984], on the other. When these enthalpy adjustments are made, it appears that AHm is basically zero at temperatures higher than 1000 K, and also at a few hundred MPa if enthalpies are adjusted for the effect of pressure (Fig. 14.27). In other words, as far as enthalpy is concerned, Burnham's contention that mixing is ideal has been vindicated for SiO2-rich aluminosilicate compositions. 14.2c. Viscosity Near the Glass Transition Because obsidians generally are hydrous, they were obvious starting materials to determine the profound effects of water on viscosity [Leonteva, 1940; Sabatier, 1956]. Then, measurements under water pressure were pioneered by Saucier [1952] and Shaw [1963]. The latter observations, made with the falling sphere method, and the compaction experiments of Friedman et al. [1963] showed that the presence of 4 wt % water in a molten obsidian reduces the viscosity by 6 orders of magnitude near the glass transition. Other information on these effects were provided by determination of the influence of water on the glass transition temperature of simple silicates [Acocella et al., 1983], which suggested depressions of viscosity by orders of magnitude through addition of a few wt % water. Likewise, Jewell and Shelby [1988] and Jewell et al. [1993] found that the activation energy for viscous flow of alkali silicates and aluminosilicates is a significant function of water content at the level of a few hundred ppm (Fig. 14.28). In contrast, the effects observed for larger water concentrations at high pressure were much smaller. For andesite melts, Kushiro et al. [1976], for instance, reported only a 20-fold decrease of viscosity with 4 wt % water at 2 GPa, which was nonetheless about 5 times larger than that observed for the viscosity of the dry melt between room pressure and 2 GPa. Measurements above the glass transition have allowed the differing effects of water at low and high temperatures to be determined. To illustrate the usefulness of the method, the observations made at room pressure for a series of hydrous andesite supercooled liquids over nearly 4 orders of magnitude are shown in Fig. 14.29. The influence of water is, in fact, so strong that considerable extrapolations would be required to compare

Water — An Elusive Component

431

Figure 14.28 - Activation energy of high-temperature viscous flow of Na,O3Si0, melt as a function of water content [Jewell and Shelby, 1988].

isothermal viscosities from 0 to 4 wt % water. Of particular interest is the increasing departure from Arrhenian variation of viscosity with increasing water content that are apparent in Fig. 14.29 even though the measurements cover narrow temperature ranges. The temperature of the measurements was varied in a random way in the investigated interval. By itself, the strong sensitivity to volatile content demonstrates that no water was lost during the experiments as any such loss would have been signaled by a departure from the trend set by measurements made at lower temperatures. Likewise, any significant variation of water content throughout the investigated samples would have caused heterogeneous deformation. Accordingly, infrared analyses made to determine water speciation did not reveal variations of water contents at a small scale. The complementary nature of high- and room-pressure measurements is apparent in Fig. 14.30. Owing to the slight intrinic pressure-dependence of viscosity, the low-

Figure 14.29 - Viscosity of hydrous andesite supercooled liquids against reciprocal temperature for the water contents indicated (wt %) [Richet etal, 1996].

Chapter 14

432

Figure 14.30 - Viscosity of hydrous andesite liquids for the water contents indicated. Measurements made at room pressure at high viscosity and for the water-free sample at low viscosity [Richet et al., 1996], and at high-pressure for the other measurements [Kushiro et al, 1976].

temperature, room-pressure data join smoothly with the high-pressure experiments. Consistent with the trends generally observed for silicates, another important feature apparent in Fig. 14.30 is the convergence of the viscosity data at high temperatures. When fitting empirical TVF equations to these measurements, In rj = A +

B/(T-Tl),

(14.4)

one finds that the pre-exponential parameter, A, can be considered constant, at least for a given series of liquids [Richet et al., 1996]. An important consequence is that hightemperature viscosity measurements can be made for the single anhydrous endmember at ambient pressure to determine this parameter for any hydrous silicate series. The complete

Figure 14.31 - Viscosity of andesite liquids against water content at the temperatures indicated [Richet et al., 1996].

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433

Figure 14.32 - Standard glass transition temperature of hydrous melts. Andesite: Richet et al. [1996], haplogranite (HPG, Dingwell et al, 1996], basalt and rhyolite: Richet et al. [1997], tephrite: Whittington et al. [2000].

viscosity-water content relationships obtained in this way are represented in Fig. 14.31 for a few temperatures. This plot shows more clearly how the tremendous depressing effects of water on viscosity observed near the glass transition tend to level off at higher contents and higher temperatures. In addition, the data of Fig. 14.31 illustrates that the socalled crystallization curtain does not prevent viscosity from being determined between the liquidus temperature and the glass transition. When determined from such a minimum amount of data, these relationships agree with measurements made both at high [Kushiro et al., 1976] and at low [Liebske et al., 2003] temperatures on hydrous andesites. Indeed, new measurements have confirmed that the effects of high pressures on viscosity are also small even near the glass transition range [Schulze et al., 1999; Liebske et al, 2003]. With the same method, the viscosity of a number of other hydrous melts has been measured. Silicic compositions have received particular attention, with studies devoted to haplogranite [Dingwell etal, 1996], leucogranite [Hess and Dingwell, 1996], rhyolite [Richet et al., 1997; Dingwell et al., 1998; Stevenson et al., 1998] and albite melts [Whittington et al., 2005]. Less polymerized compositions have also been investigated with tephrite [Whittingron et al, 2000], basalt [Richet etal, 1997; Giordano etal, 2003], phonolite [Giordano et al, 2000; Whittington et al, 2001; Romano et al, 2003], and trachyte [Whittington etal, 2001; Romano et al, 2003]. A convenient way to summarize some of these results is to compare the decrease of the standard glass transition temperature with increasing water content (Fig. 14.32). Clearly, the depressing effect of water is much greater for polymerized {e.g., HPG, rhyolite) than for depolymerized {e.g., basalt, tephrite) melts, offsetting the markedly opposite trend that prevails for anhydrous compositions. A surprising consequence of these trends is that hydrous rhyolite becomes less viscous than hydrous basalt at water contents higher than about 2 wt %. An empirical model of prediction of these variations has been proposed in terms of separate effects of the silicate matrix, hydroxyl, and molecular water [Deubener et al, 2003].

434

Chapter 14

Figure 14.33 - Temperature of the 1012 Pa s isokom as a function of water content for the melt compositions indicated [Romano et a/., 2001].

Besides, the effects of the M-cation has been investigated by Romano et al. [2001 ] in alkali and alkaline earth meta-aluminosilicate melts (Fig. 14.33). From at least about 0.5 wt % H2O to higher water content, the dependence on water content of the 1012 Pa s isokom for Li-, Na-, and K-meta-aluminosilicate melts is similar (Fig. 14.33). This dependence differs from that observed for peralkaline and alkaline earth aluminosilicate melts. These observations cannot be readily explained in terms of different degree of depolymerization of the melt [Romano et al, 2001; Jewell et al, 1993]. Rather, they could be due to different solution mechanisms of water, for example, to differences in Al<=>Si ordering, depending on whether an alkali or an alkaline earth is needed for chargebalance of Al3+ in tetrahedral coordination. Finally, viscosity-temperature relationships have also been determined through high-pressure measurements on viscous liquids like haplogranite [Schulze et al, 1996] and albite [Suzuki et al, 2002]. Similar variations are observed in all cases, indicating that the differing trends of Fig. 14.32 are related to differing anionic frameworks and not to changes in the relative abundances of M-cations. As for anhydrous melts (see section 2.3d), the deviations of viscosity from Arrhenian laws result from the temperature dependence of Sconf which is itself determined by the configurational heat capacity (C c°n*). The increasing fragility of melts with water content apparent in Fig. 14.30 thus is consistent with the correlative increases of Ccpon^ illustrated in Fig. 14.25, which are partly due, as described above, to dissociation of molecular water into hydroxyl ions. The first applications of this formalism to the viscosity of hydrous granitic and disilicate melts have been made by Baker [1996] and Davis [1998], respectively. Here, we will not discuss further quantitative applications of Adam-Gibbs theory. We will just note that, as made for dry melts [Richet, 1984], configurational entropies could be determined from viscosity and be used in thermodynamic modeling of phase equilibria involving hydrous melts.

Water — An Elusive Component

435

Figure 14.34 - Diffusion coefficient, D, of Si and Na in granitic melt as a function of water content at temperatures indicated [Watson, 1994].

14.2d. Diffusion Coefficients and Electrical Conductivity Dissolved H2O also affects the diffusion coefficient, D, of melt components [Watson, 1979,1981; Harrison and Watson, 1983,1984;Baker, 1991; Mungall and Dingwell, 1994]. The increase is larger for a network-former such as Si4+ than for a network-modifying cation like Na+ (Fig. 14.34). The difference between DSi and DNa decreases with increasing water content, especially at low solubility. However, the former remains orders of magnitude smaller than the latter. The diffusivity of water itself depends on water content [Lapham et al., 1984; Chekhmir et al., 1988; Zhang et al, 1991a,b; Doremus, 1995; Behrens and Nowak, 1997]. The dependence is first exponential, below about 2 wt %, and then approximately linear (Fig. 14.17). These variations qualitatively agree with the observations of Chekhmir et al. [1988] and Zhang et al. [1991a,b] that the diffusion profiles of water in silicate melts cannot be modeled with a single diffusion coefficient. Molecular H2O and OH-groups have to be distinguished, instead, so that the bulk diffusion of water is expressed as: dX

water -

d

D\

n

^XH2O

n n n +l/2DoH

^r-^{ ^°^r

^r}

d

*OH }

(14-5>

where X designates mol fraction, x, distance, and /, time. Nowak and Behrens [1997] observed that the diffusivity of H2O is approximately the same in pure NaAlSi3O8, (SiO2)29(KAlSi3O8)71 and (SiO2)28(NaAlSi3O8)38(KAlSi3O8)34 melts. They proposed that, at least in these highly polymerized aluminosilicate melts, the diffusivity of water is nearly independent of composition. Because of the good agreement of their data with results for rhyolitic melts by Karsten et al. [1982], Shaw [1974], and Lapham et al. [1984], they further assumed that this statement could be generalized to all felsic melts, with the provision that predictions of Dwater to within 200% of experimental data were indicating "good" agreement. At least for total water contents less than 1 wt %, however, £>waler could be 2 orders of magnitude higher in more mafic composition such as basalt [Zhang and Stolper, 1991; Nowak and Behrens, 1997]. For tracer diffusion, there is also a negative correlation between £>water and degree of melt polymerization. For

436

Chapter 14 Table 14.2. Concentration of species in SiO,-H,O glasses [Farnan et ai, 1987] HOO cone. wt % 2.5 8.7

Q3/(Q3+Q4)

OH Cone. wt %

Molec. H,O wt %

0.086 0.235

1.26 3.21

1.24 5.49

example, £>water is about 3 orders of magnitude smaller for SiO2 supercooled melt (nominal NBO/Si = 0) than for Na 2 Si 3 0 7 (nominal NBO/Si = 0.67) near 1300°C with -0.02 wt % H 2 O [Scholze and Mulfinger, 1959; Moulson and Roberts, 1961]. Cation diffusion is closely related to electrical conductivity. Intriguing observations have been made in this respect by Takata et al. [1981, 1984] who reported that both sodium diffusivity and electrical conductivity in sodium trisilicate melts depend markedly on water content, with minimum values near 3-4 wt % water which are analogous to those observed in the mixed alkali effect. Similarities and differences between the effects of water and alkali oxides on the volume and transport properties of melts have been discussed by Richet et al. [2000]. A depressing effect water on electrical conductivity has also been described for a variety of simple compositions [Satherley and Smedley, 1985]. 14.3. Water and Silicate Melt and Glass Structure The pronounced effects of dissolved H2O on chemical and physical properties of silicate glasses and melts suggest that H2O is a very efficient depolymerizing agent. Most structure models inferred from the property behavior involves formation of OH-groups, whether in the simplest SiO2-H2O melts systems or in chemically complex natural magmatic liquids. Formation of OH-groups has been considered the main depolymerization mechanism. 14.3a. SiO2-H2O In the Raman spectra of hydrous silica glass materials, the pronounced band near 970 cm"1 (Fig. 14.35) has been assigned to Si-OH stretch vibrations [Stolen and Walrafen, 1976; McMillan and Remmele, 1986]. Its growth with increasing water content in the melts is consistent with increasing abundance of Si-OH bonds as the water content increases. As suggested by its slight asymmetry [Mysen and Virgo, 1986a], this band could consists of two symmetric Gaussian bands assigned to Si-OH vibrations with different bond characteristics. In other words, there may exist two geometrically distinct Si-OH groups. In the Raman spectra (Fig. 14.35), molecular H2O is evidenced by a band near 1600 cm 1 , which is commonly assigned to H-O-H bending motions and, thus, attests to the existence of molecular H2O [Paterson, 1982; Reimers and Watts, 1984]. Other features in the Raman spectra of hydrous SiO2 glasses (Fig. 14.35) are found between 300 and 650 cm 1 . They indicate changes in the 3-dimensionally interconnected rings of the structure of vitreous

Water — An Elusive Component

Figure 14.35 - Unpolarized Raman spectra of hydrous SiO, glass with water contents as indicated on individual spectra [Mysen and Virgo, 1986a].

437

Figure 14.36 -29Si-'H CP MAS NMR spectra of hydrous SiO, glass for the indicated water contents [Farnan et al, 1987].

SiO2 such that the proportion of rings with the smaller number of SiO4 tetrahedra diminishes with increasing water concentration [Mysen and Virgo, 1986a]. Additional information on the structure of hydrous SiO2 melt has been gained from 29 Si MAS NMR and cross-polarization (CP) MAS NMR [Farnan et al, 1987]. The former spectra offers insight into changes in proportion of silicate species in the melt, whereas the latter provide information on spatial association between protons, H+, and silicon, Si4+. Silicon-29 CP MAS NMR spectra of hydrous SiO2 glass with 2.5 and 8.7 wt % H2O show that protons exist near Q2-, Q3-, and Q4-species (Fig. 14.36). Note, however, that these CPMAS spectra cannot be used as a direct measure of proportion of the species. That could be done from extrapolation of the data back to zero contact time [Cody et al, 2005], or from single-pulse 29Si MAS NMR. Such measurements, summarized in Table 14.2 [Farnan et al, 1987], illustrate how hydrous SiO2 glass depolymerizes as H2O is dissolved. In this Table, the proportion of OH and molecular H2O was calculated from the abundance of Q3 species in the glasses. Farnan etal. [ 1987] did not attempt to quantify the small proportion of Q2-species identified in the 29Si CP MAS NMR spectra. If this

438

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Figure 14.37 - Raman (a) and 'H MAS NMR (b) spectra of hydrous SiO2 glass as a function of total water content as shown on figures. See text for more details [Mysen and Virgo, 1986a; Kohn etal, 1989]. were done, the degree of depolymerization of the hydrous glasses would be higher than indicated in Table 14.2 and, therefore, the proportion of OH groups relative to molecular H2O would also be higher. Further details on the nature of the dissolved OH groups and molecular H2O in silicate glasses and melts have been obtained from vibrational spectroscopy, neutron diffraction, and »H MAS NMR [Stolper, 1982; Paterson, 1982; Spierings, 1982; Silver and Stolper, 1989; Mysen and Virgo, 1986a, b; McMillan and Remmele, 1986; Zotov et al, 1996; Eckert etal., 1988; Kohn et al, 1989; Zavel'sky etal, 1998; Zeng etal, 1999; Schmidt et al, 2001]. These data offer information on cation-OH interaction and the extent to which hydrogen bonding may play a role. Hydrogen-1 MAS NMR and Raman spectra of quenched SiO2+H2O melts with different total water contents are shown in Fig. 14.37. Increasing water content results in increasing Raman intensity between 3000 and 3500 cm"1 (Fig. 14.37a). This is the frequency region of fundamental OH vibrations, where both frequencies and intensities are affected by hydrogen bonding [e.g., McMillan and Remmele, 1986]. The frequency shifts to increasingly lower values the stronger the hydrogen bonding [e.g., McMillan et al, 1993]. The two sharp bands near 3600 cm 1 in the Raman spectra of SiO2-H2O glasses

Water — An Elusive Component

439

can be assigned to stretching in OH-groups associated with silicon [McMillan, 1994]. The frequency depends in part on the strength of the cation-OH bond and can be as low as 3400 cm"1 for alkali-OH or alkaline earth-OH bonds [Mysen and Virgo, 1986a]. The 'H MAS NMR spectra of hydrous SiO2 glass are also sensitive to the local environment near the proton [Bartholomew and Schreurs, 1980; Eckert et al, 1988; Kohn et al, 1989]. This effect is seen in the 'H MAS NMR spectra of SiO2-H2O glasses with different water contents (Fig. 14.37b). In the spectrum of SiO2+2.5 wt % H 2 O, Kohn et al. [1989] observed a peak near 3.1 ppm due to dissolved water in the form of Si-OH, and a broader resonance centered near 4.2 ppm which they assigned to molecular H2O. For samples with higher total water content, Kohn et al. [ 1989] retained the same interpretation. They suggested additional details as to the exact nature of the hydrogen bonding and also pointed out, from the spinning side band relationships, that molecular H2O exists as individual molecules and not as a liquid-like structure. 14.3b. Metal Oxide-Silica Systems Addition of alkali or alkaline earth oxides to SiO2 melt and glass offers the possibility of further interactions. The possibility also exists for ordering of H+ and metal cations among nonbridging oxygen in melt structures. Such complexities are indicated by many properties of hydrous metal silicate melts (Figs. 14.1, 14.10-14.12, 14.19). Despite the fact that most natural magmatic liquids are peralkaline, structural information on water dissolved in such melt compositions is nowhere near as common as data on meta-aluminous compositions [Mysen and Virgo, 1986a; Kummerlen et al., 1992; Schaller and Sebald, 1995; Zotov et al., 1996, 1998; Zotov and Keppler, 1998; Xue and Kanzaki, 2004; Cody et al., 2005]. A large fraction of these studies focused on H2O in Na2Si4O9 (NS4) melt and glass. Recently, additional structural data for other hydrous alkali and alkaline earth silicate glasses have become available [Cody et al., 2005; Xue and Kanzaki, 2004].

Figure 14.38 - Correlation function of anhydrous and D2O-bearing Na,O»4SiO, glass (NS4) for the indicated deuterium oxide contents [Zotov et al, 1996].

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Chapter 14

Figure 14.39 - Silicon-29 MAS NMR spectra of Na,O»4SiO, glass (NS4) with the indicated water contents [Kiimmerlen et al., 1992].

Correlation functions from neutron diffraction of deuterated and anhydrous NS4 glass clearly show the first oxygen deuterium distance (D-Ol) at almost exactly 1 A (Fig. 14.38). From the absence of peaks near 1.9 and 2.4 A, Zotov et al. [1996] suggested that the D2O molecules are isolated in the structure. Furthermore, the spectra show that the first Si-0 (Si-Ol) and oxygen-oxygen (O-Ol) distances are essentially unaffected by the dissolved

Figure 14.40 - Concentration of Q4-, Q3-, and Q2-species in Na,O»4SiO, glass (NS4) as a function of water contents. Insert shows bulk polymerization of the same glass as a function of total water content [Zotov and Keppler, 1998].

Water — An Elusive Component

441

Figure 14.41 - FTIR spectra of Na,O4Si0, glass (NS4) for the water contents indicated [Zotov and Keppler, 1998].

D2O. That observation led Zotov et al. [1996] to conclude that the first SiO4 tetrahedra are not affected by dissolved water (D2O). They did note, however, that there are changes in the 2nd-nearest oxygen distances suggesting, therefore, that solution of water in Na 2 Si 4 0 9 melt may affect medium-range order, and not short-range order in the glasses. Finally, the linear decrease of correlation length with increasing water content is consistent with dissolved D2O causing depolymerization of the Na2Si4O9 network. Depolymerization of alkali silicate melts upon solution of H2O is also consistent with the 29Si MAS NMR and CP MASNMR data from the system Na 2 Si 4 0 9 -H 2 0. The cross-polarization experiments show that protons can be found near Q2-, Q3-, and Q4-species in the melt [Kiimmerlen et al., 1992] and that the H+ probably exhibits a preference for the Q2-species, which has the highest number of nonbridging oxygens [Cody etal., 2005]. The overall effect is depolymerization, as illustrated by the increase of the Q3-abundance relative to that of Q4 with increasing water content in the 29Si MAS NMR spectra of Na 2 Si 4 0 9 +H 2 0 quenched melts (Fig. 14.39). In a more detailed study, Zotov and Keppler [1998] noted that there is a significant concentration of Q2-species in addition to Q3 and Q4. From combined 29Si MAS NMR, Raman, and infrared spectroscopic examination of these materials, they also observed that, whereas the concentration of Q2 increases monotonously with increasing water content, the abundance of Q3 actually passes through a weak maximum at intermediate contents (Fig. 14.40). From their infrared spectra (Fig. 14.41), Zotov and Keppler [1998] also noted that evolution of the 0H/H 2 0 in the NS4 glass with water content (Fig. 14.42) shows the same general topology as other aluminosilicate glasses with the H2O/OH ratio increasing with total water content (Fig. 14.16). However, the abundance of OH-groups relative to molecular H2O was considerably higher than in aluminosilicate glasses even though the opposite result would have been expected from the lower fictive temperature of their NS4 glasses. There is, thus, a clear composition dependence on the proportion of OH and molecular H,O. In fact, Cody et al. [2005], when recalculating OH/H2O from Qn-abundance in NS4 melt with 7.5 wt % H2O quenched

442

Chapter 14

Figure 14.42 - Concentration of water as molecular H,O and OH in Na,O4Si0 2 glass (NS4) as a function of water contents (dashed and solid lines) compared with the evolution of molecular H.,0 and OH from Figure 15.16 [Zotov and Keppler, 1998].

from 1300°C at 1.3 GPa, suggested that as much as 80 % of the dissolved water must have existed in the form of OH-groups under these conditions prior to quenching. Mysen and Cody [2003] extended the examination of hydrous quenched alkali silicate melts to a series of compositions in the system Na2O-SiO2 with a fixed amount of H2O (-7.5 wt %). The evolution of the Q4- and Q3-abundance as a function of the NBO/Si of the melt is compared in Fig. 14.43 with the Q4- and Q3-abundance evolution in the anhydrous Li2O-SiO2, Na2O-SiO2, and K2O-SiO2 glasses as a function of alkali content [Maekawa et al., 1991]. Although there are differences in detail, the general topology of all the Q4- and Q3-abundance trajectories resemble one another. This led Mysen and Cody [2003] to conclude that, at least in simple metal oxide silicate glasses, H+, when dissolving

Figure 14.43 - (a) Abundance of Q"-species in glasses as a function of Na/Si of composition with 14 mol % R,0 (calculated with O=l) in solution and (b) as a function of degree of polymerization (NBO/Si) (solid symbols) compared with the same evolution in binary alkali silicate glasses [Maekawa et al., 1991; Mysen and Cody, 2003].

Water — An Elusive Component

443

in the form of OH-groups, may be treated in structural terms similar to other networkmodifying cation such as alkali metals. Furthermore, they noted from the Raman spectra of the glasses with different Na/Si-ratio, that the principal solution mechanism of water to form OH-groups involved individual Qn-species in a manner qualitatively similar to that proposed by Zotov and Keppler [1998] for hydrous Na 2 Si 4 0 9 glass. Thus, for highly polymerized melts, the principal mechanisms can be expressed with the equations, Q4 + H2O <=> Q3(H),

(14.6)

and Q4 + H2O <=> Q2(H).

(14.7)

For less polymerized melts, where the abundance of Q4-species is negligible, water interacts with bridging oxygen to transform Q3- into Q2-species as follows: Q3 + H2O <=> Q2(OH).

(14.8)

Equations (14.6 -14.8) are all depolymerization reactions. Whether or not Na+ reacts with H2O to form Na-OH bonding could not be ascertained in that study. However, one interpretation of water solution in M2O-SiO2 melts (Figs. 14.10 and 14.11) is of the form: M2O + H2O <^> 2M(0H).

(14.9)

The mechanism described by equation (14.9) involves scavenging of network-modifying alkali metals to form these OH-complexes. Such a mechanism would serve to polymerize the silicate network. The importance of this solution mechanism in alkali silicate melts is not clear. Xue and Kanzaki [2004] reported, however, that a mechanism analogous to equation (14.9) is consistent with 'H and 29Si NMR spectra of hydrous alkaline earth silicate glasses. 14.3c. Aluminosilicate Melts and Glasses Most studies of water solution mechanisms in silicate melts have focused on feldsparrich glasses often nominally near meta-aluminosilicate joins. In these, as in other glasses and melts, water is dissolved in the form of OH groups and as molecular H 2 O. It has been suggested that the OH/H2O ratio may depend on the feldspar composition and the Al/(A1+Si) ratio [Silver et aL, 1990; Romano et ah, 1995]. It is not clear whether these observations from glasses can be extrapolated to aluminosilicate melts as the fictive temperatures in those studies were variable and the OH/H2O-ratio depends on temperature [e.g., Nowak and Behrens, 1995; Shen and Keppler, 1997]. As for other silicate systems, the principal structural tools used to determine the principles that govern interaction between the aluminosilicate network and dissolved

444

Chapter 14

Figure 14.44 - (a) Unpolarized Raman spectra of NaAlSi,O6 and SiO, glass with 5 wt % H,0 dissolved. Shaded band is discussed in text, (b) Raman shift of shaded band (a) as a function of water content for Al/(Al+Si)-ratios indicated on individual curves, (c) Raman shift of shaded band (a) as a function of Al/(A1+Si) for the wt % H,O indicated [Mysen and Virgo, 1986b]. water have been vibrational and NMR spectroscopy. In many ways, Raman spectra of quenched melts along the join SiO2-NaAlO2-H2O exhibit gradual changes in a manner similar to that observed in the spectra of anhydrous glasses and melts (see Chapter 9). In the hydrous system, the main peak near 970 cm 1 in Al-free SiO2-H2O may have counterpart at a slightly lower frequency in the spectra of the Al-bearing glasses (Fig. 14.44) [see also McMillan and Holloway, 1987; McMillan et al, 1993]. In other words, this peak might be assigned to (Si,Al)-OH stretching. There are, however, several features of this Raman band that makes this assignment problematic, (i) Its frequency is insensitive to substitution of 'H with deuterium (2H) even though, in the SiO2-H2O spectra, the 970 cm 1 Si-OH peak shifts by approximately the fraction expected if its frequency resulted from the mass ratio relationship:

VHlvD=4mHlmD

'

(14.10)

Water — An Elusive Component

445 where vis frequency and m is mass [Mysen and Virgo, 1986a]. (ii) The frequency of this band is a positive function of water content (Fig. 14.44b). It is not clear why increasing water content would cause the frequency of a vibration assigned to (Si,Al)-OH to shift to higher wavenumber. (iii) There is, however, a relationship between this band and the Al/(A1+Si) of the system as its frequency, for fixed total water content, shifts to lower values as Al/(A1+Si) of the melt increases (Fig. 14.44c). Mysen and Virgo [1986b] suggested that the band should not be assigned to an (Si,Al)-OH vibration, therefore, but to vibrations involving nonbridging oxygen, Si, and Al. Neither interpretation is, however, without problems.

Figure 14.45 - (a) 29Si MAS NMR spectra of (SiO,)90(NaAlSi3Og)10 glass with 3.8 wt % H,0 (solid line) and anhydrous glass (dashed line), (b) Position of peak maximum in spectra such as in (a) for hydrous (solid line) and anhydrous (dashed line) glasses as a function of composition, (c) Full width at half height, FWHM, from spectra such as in (a) for hydrous (solid line) and anhydrous (dashed line) glasses as a function of composition [Schmidt et al, 2000].

A range of nuclear magnetic resonance techniques has been applied to characterize solution mechanisms of water in melts along the meta-aluminous join, SiO 2 -NaAlO 2 , with single pulse and cross-polarization MAS NMR, as well as triple quantum MAS NMR [Schmidt et al., 2000; Padro et al, 2003]. An example of a single-pulse 29Si MAS NMR spectrum of a glass composition, (SiO 2 ) 90 (NaAlSi 3 O g ) 10 , with 3.7 wt % total water content is shown in Fig. 14.45a. The OH/(OH + H2O) of this sample (and other samples on the SiO 2 NaA10 2 join), as determined by Schmidt et al. [2000] with static 'H NMR at 140 K, is 0.375. The spectrum of this glass shows a maximum at -110 ppm (solid line in Fig. 14.45a), whereas the anhydrous equivalent has its peak maximum near -100 ppm (dashed line in Fig. 14.45a). The frequency difference between the peak maxima of the hydrous and anhydrous samples decreases, however, as the samples become more aluminous (Fig. 14.45b) and their full width

446

Chapter 14

Figure 14.46 - 27A1 3Q MAS NMR spectra of anhydrous (a) and hydrous (b) (3.8 wt% H,O) NaAlSiO4 glass [Padro et al., 2003]. (c). Quadrupolar coupling constant for hydrous (3.8 wt % H,0 - solid line) and anhydrous (dashed line) glasses along the join SiO,-NaAlO2 as a function of silicate composition, (d) Isomer shift of 27A1 for hydrous (3.8 wt % H2O - solid line) and anhydrous (dashed line) glasses along the join SiO,-NaAlO2 as a function of silicate composition [Schmidt et al, 2000]. at half height becomes more similar (Fig. 14.45c). In short, the 29Si MAS NMR spectra of the hydrous and anhydrous glasses show some differences at high SiO2 content. These differences decrease, however, and essentially vanish as the samples become more aluminous [Schmidt et al, 2000]. One interpretation of the 29Si MAS NMR spectra of hydrous SiO2-NaAlO2 glasses is, therefore, that as the samples become increasingly aluminous, there is diminishing evidence that the aluminosilicate network interacts with dissolved water. For Al-poor samples such as (SiO2)90(NaAlSi3O8)10, Schmidt et al [2000] found that the difference in peak position with contact time in the cross-polarization experiments is consistent with some Q3(OH)species in analogy with similar data for SiO2-H2O quenched melts [Farnan et al, 1987]. However, this difference, as in the case for other NMR parameters (Fig. 14.45), lead them to conclude that this depolymerization mechanism is less important in more aluminous samples.

Water — An Elusive Component

447

Figure 14.47 - (a) 23Na MAS NMR spectra of hydrous (3.8 wt % H,0 - solid line) and anhydrous (dashed line) of glasses along the join SiO2-NaAlO,. (b) Mean isomer shift of 23Na from spectra of hydrous (3.8 wt % H,0 - solid line) and anhydrous (dashed line) of glasses along the join SiO NaAlO, [Schmidt et al., 2000]. Single pulse 27A1 MAS NMR spectra [Kohn et al., 1992; Schmidt et al., 2000; Oglesby et al., 2002; Padro et al., 2003] are not very useful because these spectra show at best only subtle variations, i.e., a small line narrowing with increasing water content. Only minor changes are observed in the 27A1 3Q MAS NMR spectra as well (Fig. 14.46a,b). None of the spectra exhibit any evidence for Al3+ in any coordination state with oxygen other than 4. Schmidt et al. [2000] observed a slight decrease in quadrupolar coupling constants upon hydration (Fig. 14.46c). They concluded that the electric field gradient around the Al-nucleus is lower in hydrous glasses, an observation that they found inconsistent with depolymerization of A1O4 polyhedra upon solution of water in the aluminosilicate melts [Mueller et al., 1986]. From the similar evolution of the 21 Al chemical shift with bulk Al/(A1+Si) in spectra of both hydrous and anhydrous glasses, Schmidt et al. [2000] concluded that, except perhaps for silica-rich compositions, Al is not involved in formation of OH-groups on this join.

448

Chapter 14

The 23Na MAS NMR data of these glasses do, however, indicate some effect of dissolved water (Fig. 14.47). The chemical shift is distinctly less negative than in the spectra of anhydrous SiO2-NaAlO2 glasses and evolves quite differently with Al/(A1+Si) than in anhydrous glasses (Fig. 14.47b). Hence, Schmidt et al. [2000] asserted that, in glasses and melts along the join SiO2-NaAlO2, the main effect of dissolved water is interaction between Na+ and water, a mechanism similar to that described by Kohn et al. [1992]. It is possible that this interaction also gives rise to the 17O MAS NMR signal in spectra of K- and Na-Aluminosilicate glasses, which Oglesby et al. [2002] suggested to reflect strong cation-OH interactions in the sample. No depolymerization of the aluminosilicate melt structure was proposed as this process would have been reflected in both 29Si and 27A1 MAS NMR spectra [Kohn et al, 1992; Schmidt et al, 2000]. The structural model for hydrous SiO2-NaAlO2 glasses summarized above is problematic. Even though it is consistent with the NMR data, it does not allow for assignment of the Raman band near 900 cm1 in the hydrous glasses. If dissolved H2O were not interacting with the aluminosilicate melt network, vibrational spectra would not be affected either, contradicting experimental observations. An alternative interpretation of the NMR data is that the 29Si chemical shift from Q4 units is shifted to lower (less negative) values. The reason is that, in a melt with coexisting Q3- and Q4-species, Al would tend to favor the Q4 units thus shifting its chemical shift toward that of Q3 in less aluminous systems [Allwardt et al, 2003; Mysen et al, 2003]. As the system becomes more aluminous, the 29Si MAS NMR might not resolve these features. Furthermore, lack of resolution in 27A1 MAS NMR spectra is also possible because situations exist where the chemical shifts of Q3- and Q4-species are nearly identical [Stebbins, 1995]. In addition, Oglesby et al. [2002] suggested from 17O MAS NMR spectra of hydrous Ca05AlSi3O8 glasses that there is, indeed, evidence of interaction between OH-groups and Al-O-Al bonds. 14.4. Temperature Effects Relaxation of hydrous silicate glasses reveals that examination of a quenched silicate glass does not always provide quantitative information on the structure of its melt [Dingwell and Webb, 1990; Silver etal, 1990]. In fact, the kinetics of the water speciation reaction [equation (14.2)] have been used to deduce cooling histories of volcanic rocks, for example [Zhang et al, 1995, 1997]. It is well established that, at temperatures above the glass transition range (Fig. 14.20), equilibrium (14.2) shifts to the right with an enthalpy change of the order of 30 kJ/mol, at least for felsic melts near the meta-aluminosilicate join [Behrens and Nowak, 2003; see also section (14.2a)]. Very limited data suggest that this equilibrium is not sensitive to pressure [Sowerby and Keppler, 1999]. That conclusion implies that the volume change of reaction (14.3) is near 0 [Richet and Polian, 1998]. If, however, molecular H2O exists as isolated molecules as suggested, for example, by Kohn et al. [1989] and Zotov et al [1996] for SiO2-H2O and Na2Si409-H20 melts, negligible volume change may be

Water — An Elusive Component

449

Figure 14.48 - Unpolarized Raman spectrum of water-saturated K,Si4O9 melt at 0.9 GPa and 940°C taken in-situ (solid line) compared with spectrum of anhydrous K 7 Si 4 0 9 melt at ambient pressure and 660°C [Mysen, 1998].

reasonable given the small ionic radius of H+. Whether or not the information on the water speciation reaction can be applied to other silicate melts with different degree of polymerization and Al/(A1+Si) remains an open question. To our knowledge, the effect of temperature above the glass-transition range on the structure of hydrous silicate melts has been addressed in only one preliminary study of the system K 2 Si 4 0 9 -H 2 0 to about 0.9 GPa and 640°C. This temperature likely is above the glass-transition temperature [Mysen, 1998]. An example of Raman spectra recorded in-situ in that study is shown in Fig. 14.48 together with the spectrum of anhydrous, supercooled K2Si4O9 liquid at 660°C and ambient pressure. It is evident from this comparison that, even though the major features of the two spectra resemble one another, there are also distinct differences. Mysen [1998] suggested that, in addition to the main spectral feature near 1100 cm 1 assigned to Si-O stretching in Q3 units, there is a distinct intensity increase near 950 cm 1 that can be assigned to similar vibrations in Q2 units. Whether or not H+ is bonded to nonbridging oxygen in these structural units is not altogether obvious. It is notable, however, that the Raman frequencies (1100 and 950 cm 1 ) are the same as those in the anhydrous liquid. Given the premise that in SiO2-H2O glass with about 1200 ppm, there appears to be only Si-OH bonding (reflected in an Si-OH stretch band near 970 cm"1 [Stolen and Walrafen, 1976]), it seems plausible that H+ bonded to nonbridging oxygen in Q3 and Q2 units would result in a decrease of the frequency of Raman bands assigned to Si-O' stretching in these units. Therefore, one may speculate that the similar frequencies of the 1100 and 950 cm"1 bands in anhydrous and hydrous K 2 Si 4 0 g suggest that there may be insignificant fractions of H+ on this site in the melt. There is also a distinct band near 800 cm"1 in the high-temperature spectrum of watersaturated K2Si4O9 melt (Fig. 14.48). This band occurs at the same frequency as that in the Raman spectrum of silicate-saturated aqueous fluid in the SiO2-H2O system [Zotov and Keppler, 2000] where the band was assigned to Si-O" stretching in isolated SiO4 tetrahedra

450

Chapter 14

(Q°). Mysen [1998] assigned the 800 cm1 in the spectrum of water-saturated K2Si4Og melt to a similar vibration. On the basis of these kinds of data, it was suggested, that at least for melts in the K2Si4O9 - H2O system, H+ exhibits a strong preference for nonbridging oxygen in the most depolymerized Qn-species available, whereas K+ was bonded to nonbridging oxygen in more polymerized Qn-species. This proposed ordering of H+ and K+ among energetically nonequivalent nonbridging oxygen is conceptually similar to that discussed for other metal cations in metal silicate melts in section 7.4a. Whether or not the features in Fig. 14.48 are quenchable and are, therefore, retained in hydrous glass is not completely clear. Mysen [1998] did note that the 1100 cm1 band shifts to near 1000 cm1 in the hydrous K2Si409 glass and the band near 800 cm"1 was no longer visible. Those observations are consistent with the suggested H+/K+ ordering (and, perhaps, conceptually similar structural features in other systems) not being entirely quenchable. 14.5. Application to Some Properties of Hydrous Melts Bowen [1928] referred to water in magmatic systems as a "Maxwell's Demon" because, as he put it, it can do whatever one wants it to. Interestingly, for most of his career Bowen did not think that water was important and argued, even during the granite controversy that water did not play an important role in granite formation [Bowen, 1948]. His first publication on melting phase relations in the presence of H2O did not appear until 1950 [Bowen and Tuttle, 1950]. Bowen's opinions notwithstanding, solution of water in silicate melts has profound effects on their properties, The solidus temperature depression of silicate melts, now known for almost any system relevant to rock-forming processes, results in part from the dilution of the silicate solution, but depends also on the nature of the interaction between dissolved water and the silicate structure. The observation that water causes a larger depression of the solidus temperature of highly polymerized melt systems compared with depolymerized systems (Fig. 14.1) probably is the result of water causing more extensive depolymerization of highly polymerized melt structure than those that are depolymerized even in the absence of H2O. Depolymerization of a melt via solution of water also results in a decrease of the activity of SiO2 because the 3-dimensionally interconnected network is broken up to form more less polymerized entities. As a result, liquidus volumes of highly polymerized silicate minerals shrink relative to less polymerized minerals. A classic example of this effect is the observation that at high pressure, enstatite (MgSiO3) melts congruently at least to 3 GPa pressure [Boyd et ah, 1964], whereas in the presence of excess H2O, enstatite melts incongruently to form olivine+melt [Kushiro et al, 1968]. This change in melting relations caused by the decreased silica activity results in the effect on the olivine/ pyroxene liquidus boundary in Fig. 14.2.

Water — An Elusive Component

451

The shift in the "granite minimum" (Fig. 14.3) away from the SiO2 apex toward more feldspar-rich compositions with increasing PH2O is probably related to interaction between dissolved water and the alkali aluminate components in the melt. For melt compositions as aluminous as those corresponding to this minimum, structural data summarized above [Mysen and Virgo, 1986b; Schmidt et al., 2000] indicate that dissolved water does not interact with Si-0 bonds, but instead interacts either with the alkalis or Al3+ or both. As a result, the activity of feldspar components in the system decreases relative to that of SiO2 thus leading to the expansion of the liquidus volume of quartz shown in Fig. 14.3. The complex relationships between solubility of water in silicate melts and melt composition reflect multiple solution mechanisms. Decreasing solubility with increasing metal/silicon ratio probably reflect competition between solution to form Si-OH groups from bridging oxygen [equations (14.6-14.8)] on the one hand and, possibly, formation of alkali-OH groups on the other [equation (14.9)]. Such competing solution mechanisms may also help explain the rapidly decreasing enthalpy of solution of hydrous alkali silicate glasses with increasing alkali content [Kurkjian and Russell, 1958] and the observation that the effect of water on silicate melt viscosity and high-temperature activation energy of viscous flow decrease rapidly as the water content of the melt increases (Fig. 14.28). Competing solution mechanisms involving alkali metals, alkaline earths, and alumina likely explain why the solubility of water in meta-aluminosilicate melts depends on the identity of the metal cation (Fig. 14. 13). In this case, solubility could reflect a combination of relative stabilities of alkali and alkaline earth-OH complexing and the relative stability of tetrahedrally coordinated Al3+ as a function of the nature of the charge-balancing cation. According to Kohn et al. [1992], Kohn [2000], Schmidt et al [2000], and Padro et al. [2003], the stability of alkali-OH complexes would be the dominating factor suggesting that increasing ionization potential of the metal favors such complexes [see also Xue and Kanzaki, 2004]. This model has a problem, however, because in Al-free silicate melts, the water solubility decreases with increasing ionization potential of the metal cation [Kurkjian and Russell, 1958; Mysen, 2002], whereas in meta-aluminosilicate melts, the water solubility may increase with increasing ionization potential of the alkali metal [Behrens et al., 2001]. On the other hand, if bridging Al-0 bonds, where 14|Al3+ is chargebalanced with metal cations, dominate the solution mechanism, at least for aluminous melts such as molten feldspars [Mysen and Virgo, 1986b; Oglesby et al., 2002], the Al-O bond strength likely decreases with increasing ionization potential of the charge-balancing cation.This makes such bonds more susceptible to interaction with water to form OHgroups. The latter model would also be consistent with increasing solubility of water in meta-aluminosilicate melts with increasing ionization potential of the metal cation. 14.6. Summary Remarks 1. Water in silicate system depresses silicate melting temperatures far more than expected from simple models based on dilution of the silicate solution with H2O. The extent of

452

2.

3.

4.

5.

6.

Chapter 14

this depression also depends on silicate composition because the solution mechanisms of water in silicate melts depend on composition. Liquidus phase relations of Al-free silicate systems are affected by water because the activity of SiO2 decreases as dissolved water causes depolymerization of the melt. In Al-bearing systems, the liquidus volumes of silica polymorphs tend to expand relative to those of Al-bearing minerals because water interacts primarily with the aluminate components in the melt. Transport properties of silicate melts are sensitive to dissolved water because the silicate network is depolymerized by dissolved water. However, this effect diminishes with increasing water content in part because molecular H2O becomes increasingly important and, in part, because hydrolysis of network-modifying components in melts becomes increasingly important. Energetics of solution becomes less important with increasing water contents of silicate glass and melt because the concentration of (Al,Si)-O-(Al,Si) bridging bonds needed to be broken during dissolution decreases. The partial molar volume of H2O is independent of composition in glasses, with a value of 12 cmVmol under ambient conditions. In liquids, it varies with pressure and temperature and likely varies with the silicate composition. The volume of the speciation reaction is zero, in agreement with the lack of pressure effects on water speciation. Configurational heat capacity is positively correlated with water content, which means that deviations of viscosity from Ahrrenian variations also increase.

References Acocella J., Tomozawa M., and Watson E. B. (1983) The nature of dissolved water in sodium silicate glasses and its effect on various properties. J. Non-Cryst. Solids 65, 355-372. Allwardt J. R., Lee S. K., and Stebbins J. F. (2003) Bonding preference of non-bridging O atoms: Evidence from 17O MAS and 3QMAS NMR on calcium aluminate and low-silica Caaluminosilicate glasses. Amer. Mineral. 88, 949-954. Askarpour V., Manghnani M. H., and Richet P. (1993) Elastic properties of diopside, anorthite, and grossular glasses and liquids: A Brillouin scattering study up to 1400 K. J. Geophys. Res. 98, 17683-17689. Baker D. R. (1991) Interdiffusion of hydrous dacitic and rhyolitic melts and the efficacy of rhyolite contamination of dacitic enclaves. Contrib. Mineral Petrol. 106, 462-473. Baker D. R. (1996) Granitic melt viscosities: Empirical and configurational entropy models for their calculation. Amer. Mineral. 81, 126-134. Bartholomew R. F. and Schreurs J. W. H. (1980) Wide-line NMR study of protons in hydrosilicate glasses of different water content. J. Non-Cryst. Solids 38 & 39, 679-684. Bartholomew R. F, Butler B. L., Hoover H. L., and Wu C.-K. (1980) Infrared spectra of watercontaining glasses. J. Amer. Ceram. Soc. 63, 481-485. Behrens H., Meyer M., Holtz F, and Nowak M. (2001) The effect of alkali ionic radius, temperature, and pressure on the solubility of water in MAlSi3O8 melts (M=Li, Na, K, Rb). Chem. Geol. 174, 275-289.

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Zhang Y., Stolper E. M., and Wasserburg G. J. (1991b) Diffusion of a multi-species component and its role in oxygen and water transport in silicates. Earth Planet. Sci. Lett. 103, 228-240. Zhang Y., Stolper E. M., and Ihinger P. D. (1995) Kinetics of the reaction R,0+0=20H in rhyolitic and albitic glasses: Preliminary results. Amer. Mineral. 80, 593-612. Zhang X., Jenkins J., and Xu Z. (1997) Kinetics of the reaction H,0+0=20H in rhyolitic glasses upon cooling: Geospeedometry and comparison with glass transition. Geochim. Cosmochim. Acta 61, 2167-2174. Zotov N. and Keppler H. (1998) The influence of water on the structure of hydrous sodium tetrasilicate glasses. Amer. Mineral. 83, 823-834. Zotov N. and Keppler H. (2000) In-situ Raman spectra of dissolved silica species in aqueous fluid to 900°C and 14 kbar. Amer. Mineral. 85, 600-603. Zotov N., Keppler H., Hannon A. C, and Soper A. K. (1996) The effect of water on the structure of silicate glasses - A neutron diffraction study. J. Non-Cryst. Solids 202, 153-163. Zotov N., Delaplane R. G., and Keppler H. (1998) Structural changes in sodium tetrasilicate glass around the liquid-glass transition: A neutron diffraction study. Phys. Chem. Minerals 26, 107-110.

461

Chapter 15

Volatiles I. The System C-O-H-S The system C-O-H-S comprises a large variety of volatiles including numerous hydrocarbons. However, most of these species are unstable at the temperatures relevant to formation of silicate melts and glasses. We will restrict ourselves, therefore, to reduced and oxidized sulfur species (S2~, SO2, and SO3) and simple reduced and oxidized species in the system C-O-H (H2, CH4, CO, and CO2). 15.1. Sulfur Sulfur in silicate glasses and melts can exist in different oxidation states. The oxidation state of sulfur, in turn, affects its solubility and solution mechanisms and, ultimately, its effects on melt properties [e.g., Richardson and Fincham, 1956; Nagashima and Katsura, 1973; Buchanan and Nolan, 1979; Mysen and Popp, 1980; Wendlandt, 1982; Sosinsky and Sommerville, 1986; O'Neill and Mavrogenes, 2002; Paris et al., 2001]. Interaction between oxidized sulfur and melts as a function of metal/silicon ratio of the melt has been examined through equilibrating Na2O-SiO2 melts with SO2+1/2O2+N2 gas mixtures [Holmquist, 1966]. Under the assumption that the equation, SO2+ l/2O2+ O2- <=> SO42",

(15.1)

describes the solution mechanism of oxidized sulfur in melts, Holmquist [1966] concluded that the sulfur solubility, expressed as SO3, then is: log(mol % SO3) = log[PSO2+ (P o /- 5 ] + log Y.

(15.2)

The variable, Y, contains the effect of oxygen activity and the conversion from wt % sulfate to mol % SO3. The PSCh and PQ are partial pressures of SO2 and O2, respectively. The SO3 solubility depends on Na/Si ratio of the melt (Fig. 15.1). The slope of the curves suggests that sulfur does, indeed, dissolve as SO42~-groups and not as more polymerized S-O-containing compounds [Holmquist, 1966]. Oxygen fugacity affects sulfur solubility in silicate melts because of possible reduction of sulfate to sulfide [e.g., Nagashima and Katsura, 1973; Carroll and Rutherford, 1988; Wallace and Carmichael, 1994; O'Neill and Mavrogenes, 2002]. The minimum sulfur content as a function of oxygen fugacity for sulfur-saturated melts on binary metal oxide-

462

Chapter 15

Figure 15.1 - Relationship between SO3 content in Na2O-SiO2 melt (compositions indicated on individual curves) and gas pressure [Holmquist, 1966].

silica joins (Fig. 15.2) is similar to that seen for melts in the CaO-Al2O3-SiO2 system [Fincham and Richardson, 1954]. This minimum exists, at least in principle, because two sulfur solution mechanisms govern the S solution behavior. One involves sulfur oxidation and the other sulfur reduction. For sulfur oxidation, one can write, 0.5S2+ 1.5O2+ O2(melt) o SO42-(melt),

(15.3)

Figure 15.2 - Sulfur solubility relations in Na2O-SiO2 melts against of oxygen fugacity. (a) Solubility as a function o f ^ at 1200°C and ambient pressure, (b) Equilibrium constants for reactions (16.3) and (16.4) as a function of/o, [Nagashima and Katsura, 1973].

Volatiles I. The System C-O-H-S

463

Figure 15.3 - Proportion of oxidized sulfur (SO42~) in sulfur-saturated natural melts (closed symbols) and melts on the joins K2O-SiO2 and Na2O-SiO2 (open symbols) (modified after data summary by Carroll and Webster [1994]).

with the equilibrium constant:

Kl63=aS02-/Jh~2-(f02)1-5.

(15.3b)

For sulfur reduction, we can write the expression, 0.5S 2 + O 2 (melt) <=> S2-(melt) + 0.5O 2 ,

(15.4)

with the equilibrium constant: Kl63=<*so2-'TpS^*(fo2)1'5.

(15.4b)

Equilibrium (15.3) dominates at high/ O v whereas equilibrium (15.4) becomes increasingly important as the oxygen fugacity decreases [Nagashima and Katsura, 1973]. The inferences on sulfur solution mechanisms from solubility relations have been documented from S Ka x-ray wavelength shift, which depends on sulfur oxidation state [e.g., Carroll and Rutherford, 1988; Wallace and Carmichael, 1992, 1994; Jugo et al., 2005]. A rapid change in sulfur oxidation occurs within about 2 orders of magnitude of the oxygen fugacity defined by the QFM oxygen buffer (Fig. 15.3) (QFM: quartz-fayalitemagnetite oxygen buffer, see Huebner [1971] for description). More detailed XANES experiments with sulfur-saturated silicate glasses and sulfur-bearing minerals by Paris et al. [2001] substantiate this conclusion. Sulfur solubility also varies with the fugacity of sulfur [Richardson and Fincham, 1956; Abraham et al, 1960; Sosinsky and Sommerville, 1986; Seo and Kim, 1999]. It

464

Chapter 15

Figure 15.4 - Sulfur solubility in melts at 1400°C and ambient pressure in the system CaO-MgOA12O3 (a) as a function of/O2 at log/ s = -1.91, and (b) as a function of/S2 at log/ O2 = -10.28 [O'Neill and Mavrogenes, 2002]. increases with increasing fSn and decreasing/^ (Fig. 15.4). On the premise that sulfur may replace oxygen in some portion of a silicate melt, M 2 O + 0.5S 2 <=> M 2 S + 0.5O2,

(15.5)

the concept of sulfur capacity, C s , was developed [Fincham and Richardson, 1954]:

Cs = WttfoJf^.

(15.6)

In equation (15.6), Wtt is the weight fraction of a given oxide, i, and/ S i and/ O i are the fugacities of sulfur and oxygen, respectively. The effect of oxide concentration on the

Figure 15.5 - Sulfur capacity, Cs, as a function of mol fraction of metal oxides, CaO and FeO, in CaO-SiO2 and FeO-SiO2 melts [Abraham et al., I960].

Volatiles I. The System C-O-H-S

465

sulfur capacity can be dramatic (Fig. 15.5), probably reflecting different affinities of S2~ for specific cations in the melt such as Fe2+ rather than Ca2+. Sulfur capacity subsequently has been the subject of considerable experimental effort [e.g., Haughton etal., 197'4; Buchanan and Nolan, 1979; O'Neill and Mavrogenes, 2002; Moretti and Ottonnello, 2003]. O'Neill and Mavrogenes [2002] proposed, for example, that sulfur capacity can be related to silicate composition via the expression: \nCs=Ao + *ZXMAM M

(15.7)

This equation is derived from the equilibrium condition for reaction (15.5): \nXs =-\nys + -LXM{i4,2O -fJ.^2S)/RT + 0.5\n(fS21fo2). M

(i5.8)

Here, Xs and ys are mol fraction and activity coefficient of sulfur in the melt, XM is mol fraction of metal, HM o and VM s are chemical potential of oxide and sulfide, respectively, and/^ and/ 0o are fugacity of sulfur and oxygen. Equation (15.7) has been calibrated with 150 experimental data points for natural melt compositions. Those calibrations were, then, used to back-calculate the sulfur capacity of these 150 melts (Fig. 15.6). One must caution, though, that only chemically complex natural compositions were employed. This carries the possibility of offsetting effects. Thus, application of a calibrated equation (15.7) to compositions outside the composition range for which the calibration was carried out should be conducted with caution. Although little information exists on the structural response of the silicate melt to dissolved sulfur, some general comments can be made. First, solution of oxidized sulfur to form SO42" groups involves transfer of oxygen from the silicate to the sulfur species

Figure 15.6 - Sulfur capacity, Cs, in 150 natural melt compositions (observed) compared with values calculated as described in text [O'Neill and Mavrogenes, 2002].

466

Chapter 15

[see, for example, equation (15.3)]. One can illustrate sulfate reactions with the simplified expression using a monovalent metal cation, M + , for illustrative purposes as follows: 2Q n + 2M + + SO 3 <=> 2Q n+1 + M 2 SO 4

(15.9)

Here, M 2 SO 4 represents a sulfate species and Q n and Q n+1 are silicate species. Equation (15.9) implies, therefore, that solution of oxidized sulfur in silicate melts to form sulfate species results in polymerization of the silicate network. Second, we can write analogous reactions with sulfide species in silicate melts. Again, oxygen will be transferred from the silicate to the sulfide species. If, by analogy with equation (15.9), we assume formation of a sulfide complex with a monovalent metal, M + , a formalized sulfide reaction is: 4Q n + S 2 + 4M + o 4Q n+1 + O 2 + 2M 2 S.

(15.10)

As a result, sulfide solution mechanisms imply polymerization of the silicate network just as sulfate solution. Therefore, the higher the sulfur content, whether oxidized or reduced, the more polymerized the silicate network. 15.2. Volatiles in the System C-O-H The main volatiles of interest in the C-O-H system are H 2 O, H 2 , CO, and hydrocarbons. Fluid compositions in this system most relevant to igneous processes in the Earth are those limited by the graphite saturation surface and the join CO 2 -H 2 O-H 2 (Fig. 15.7a).

Figure 15.7 - Gas speciation in the system C-O-H. (a) Composition relations and stability field of graphite at HOOT and 1 GPa. (b) Gas speciation along the dashed line in (a) at 1400°C and 1 GPa [Holloway and Blank, 1994].

Volatiles I. The System C-O-H-S

467

An example of the fluid speciation along the dashed line in Fig. 15.7a is shown in Fig. 15.7b. Hydrocarbons that are more polymerized than methane (CH4) constitute less than 1 % of even the maximum fraction of CH4 that can be generated within the restrictions illustrated in Fig. 15.7a [Holloway and Blank, 1994]. Polymerized hydrocarbons will not be considered further in this chapter. Water, which is a principal component in the C-O-H system was discussed in chapter 15, and will not be discussed further here. 15.2a. Hydrogen The solubility and solution mechanisms of hydrogen have been studied in only a few melt and glass compositions. These are SiO2 [Shackleford et al., 1972; Faile and Roy, 1971; Bell et al., 1962], NaAlSi3O8 [Luth and Boettcher, 1986; Luth et al, 1987], and CaMgSi2O6 [Luth et al., 1987] melts and glasses. The solubility of hydrogen in SiO2 glass is a linear function of pressure near and below ambient at temperatures well below the glass transition (1208°C - see Chapter 5). The enthalpy of solution (-13 kJ/mol) is comparable to those of the noble gases in silicate

Figure 15.8 - Pressure-temperature trajectories of the liquidus curves of silicates in equilibrium with H2O-H2 fluid at the oxygen fugacity of the iron-wustite oxygen buffer [Huebner, 1971]. (a) Relationships for Ab (NaAlSi3O8) with the molar H2/(H2+H2O) in the gas marked with small horizontal lines, (b) Relationships for Di (CaMgSi2O6) with the molar H2/(H2+H2O) in the gas marked with small horizontal lines. In both diagrams, the trajectories marked H20-"X" represent calculation from ideal solution of a component, X, in the same amount as H2 in the hydrogenbearing experiments [Luth and Boettcher, 1986].

468

Chapter 15

Figure 15.9 - Raman spectra of NaAlSi3O8 glass formed by quenching hydrogen-saturated and volatile-free (H2-free) melts, (a) Spectrum in the frequency range of 1st order Si-0 scattering, (b) Spectrum in the frequency range of 1st order H-0 scattering [Luth et al., 1987]. melts (Table 17.1). At higher temperature (800°C and 1050°C) in the same pressure range, the solubility is proportional to the square root of pressure. That relationship, coupled with infrared absorption spectra of the high-temperature silica glass [Bell et al., 1962; Faile and Roy, 1971], are consistent with formation of OH-groups upon solution of hydrogen in fused silica. In the pressure and temperature regime of the Earth's upper mantle (P > 0.5 GPa, T > 800°C) at the oxygen fugacity of the iron-wustite oxygen buffer, H 2 can reach concentrations in excess of 80 mol % in the system H-0 [Luth et al., 1987]. Although the hydrogen solubility in silicate melts under these conditions has not been measured directly, freezing-point depression of silicates caused by H2-rich H 2 O+H 2 fluids suggest that H 2 cannot be treated as a simple ideal diluent of H 2 O (illustrated as component "X" in Fig. 15.8). The effects of hydrogen on freezing-point depression of silicates are either the result of greater deviations from unity of the activity coefficient of H 2 O in H 2 O+H 2 mixtures than in H2O+X ("X" denotes a component in ideal mixing with H 2 O), or hydrogen interacts chemically with the silicate melt structure. Luth and Boettcher [1986], relying on results of gas mixing calculations by Kerrick and Jacobs [1981], and Boettcher [1984], and Shaw [1963] suggested that the activity coefficients are near unity in H 2 O+H 2 gas mixtures under these pressure and temperature conditions. Thus, the liquidus temperature depressions of silicates in equilibrium with H 2 O+H 2 volatiles at pressures above 0.5 GPa indicate chemical reaction between hydrogen and the silicate melt structure [Luth and Boettcher, 1986]. The structural inference from the liquidus temperature depression in silicate-H2OH 2 systems (Fig. 15.8) is substantiated by Raman spectra of NaAlSi 3 O 8 -H 2 glass quenched

Volatiles I. The System C-O-H-S

469

at high pressure (Fig. 15.9). Here, there is evidence for depolymerization of the aluminosilicate network in the hydrogen-containing glass (arrow in Fig. 15.9a). Furthermore, the Raman spectrum near 3600 cm-1 has a strong band (marked OH/H 2 O in Fig. 15.9b), assigned to O-H stretch vibrations, as a well as a narrow band near 4200 cm 1 that was assigned to molecular H 2 [Luth et al., 1987]. As discussed in Chapter 14, a rapid decrease in Raman intensity below 3600 cm-' is consistent with limited hydrogen bonding. When significant portions of the OH groups exist in the form of molecular H 2 O, hydrogen bonding in the glass is pervasive [Mysen and Virgo, 1986]. That is not the case here. The data (Fig. 15.9) are in accord, therefore, with at least a portion of the hydrogen dissolved in NaAlSi 3 O 8 melt forming OH-groups via chemical reaction with the silicate network. Although the details of this interaction cannot be extracted from the Raman spectra, solution of hydrogen in silicate melts at high pressure and temperature results in depolymerization of the silicate. 15.2b. Reduced, Carbon-Bearing C-O-H Volatiles Significant fractions of methane (CH4) and carbon monoxide (CO) can exist in the C-O-H system at high temperature [e.g., French, 1966; Kerrick and Jacobs, 1981; Saxena and Fei, 1988]. The equilibrium relations in the C-O-H system are, however, such that experimental examination of interaction between CH 4 and silicate melt and CO and silicate melt necessarily will involve additional fluid components such as H 2 in CH 4 -H 2 and CO 2 in CO-CO 2 . Methane (CH4). Methane solubility in silicate melts has not been determined directly. However, silicate liquidus temperatures in the presence of CH4-rich fluids are lower than

Figure 15.10 - Liquidus pressure-temperature trajectories of Di (CaMgSi2O6) saturated with CH4+H2 in equilibrium with graphite and of volatile-free Di [Eggler and Baker, 1982].

470

Chapter 15

Figure 15.11 - Liquidus phase relations at 2.8 GPa in a portion of the system CaO-MgO-Al2O3-SiO2, either volatilefree or in equilibrium with CH4+H2 fluid and graphite [Eggler and Baker, 1982].

those of anhydrous silicates (Fig. 15.10). Thus, methane must be significantly soluble in silicate melts at high pressure and temperature [Eggler and Baker, 1982; Taylor and Green, 1987]. The expansion of the olivine liquidus volume in the system CaO-MgO-Al 2 O 3 -SiO 2 CH 4 -H 2 (Fig. 15.11) compared with the volatile-free CaO-MgO-Al 2 O 3 -SiO 2 system [Kushiro and Yoder, 1974] resembles the effect of H2O (see Chapter 14). These general conclusions are in accord with experiments by Green et al. [1987] who found in the system Mg 2 SiO 4 -NaAlSiO 4 -SiO 2 at 2.8 GPa that the enstatite/forsterite liquidus boundary shifts toward SiO 2 upon addition of CH 4 . Thus, solution of CH 4 in silicate melts lowers the activity of silica. Such a mechanism would cause depolymerization of the silicate melt [Eggler and Baker, 1982]. A number of possible reactions can be written to accommodate the apparent depolymerization of silicate melts upon dissolution of CH 4 [Eggler and Baker, 1982; Taylor and Green, 1987]. These reactions could involve breakage of Si-O-Si bridges in the melt through formation of Si-CH 3 or Si-OH bonds, or both. Taylor and Green [1987], from infrared spectroscopic studies of methane-saturated aluminosilicate glasses formed by temperature-quenching at 3 GPa, concluded that there is no evidence for Si-CH3 groups in the glass, but that Si-OH bonds, reduced carbon, and possibly silicon monoxide exist in these materials. These structural features are consistent with depolymerization of methane-bearing silicate melts Carbon Monoxide. Carbon monoxide solubility experiments require consideration of the shift of the equilibria, C02+Co2CO,

(15.11)

Volatiles I. The System C-O-H-S

All

Figure 15.12 - Gas speciation in the C-O system in equilibrium with graphite as a function of temperature and pressure [Egglei et al., 1979].

and 2CO + O 2 <=> 2CO 2

(15.12)

with pressure, temperature and oxygen fugacity. The highest CO concentrations are reached at the graphite saturation surface. The mol fraction of CO in the fluid, CO/(CO+CO 2 ), decreases rapidly, however, with increasing pressure at constant temperature and with decreasing temperature at constant pressure (Fig. 15.12). Fluids with CO/(CO+CO 2 ) between 0.7 and 0.95 and with nearly pure CO 2 have been equilibrated with natural basalt melt at 1200°C as a function of pressure between about 50 and 150 MPa [Pawley et al., 1992]. The carbon solubility (expressed as CO2) is a linear function of CO 2 fugacity in the fluid phase (Fig. 15.13). At these comparatively

Figure 15.13 - Total carbon solubility (expressed as CO2) as a function of CO2 fugacity, fCOr for a tholeiite melt in equilibrium CO, CO2, and graphite (closed symbols) and in equilibrium with a CO2-rich fluid (open symbols). Equation represents least squares fit through all the data points and through the origin [from Pawley et al., 1992].

472

Chapter 15

Figure 15.14 - Total carbon solubility, expressed as CO2, as a function of pressure at 1700°C in NaAlSi3O8 and CaMgSi2O6 melts in equilibrium with CO-CO2-graphite (solid symbols and solid lines) and with nearly pure CO2 (dashed lines) [Eggler et al., 1979].

low pressures, the CO simply acts, therefore, as a diluent of the fluid phase with no measurable CO solubility in the melt. Results of similar experiments between 0.1 and 2 GPa at temperatures below 1550°C did yield CO contents up to several percent [Thibault and Holloway, 1994]. The total carbon content in melts in equilibrium with graphite and CO+CO 2 fluid in their experiments was lower than in equilibrium with CO2 alone. The only other high-pressure experimental CO solubility data are from the systems CaO-MgO-SiO2-C-O and NaAlSi3O8-C-O in the 2-3 GPa pressure range at 1700°C [Eggler et ai, 1979]. The carbon solubility, expressed as CO 2 , in CaMgSi 2 O 6 and NaAlSi 3 O 8 melts is greater in equilibrium with mixed CO+CO 2 fluids than in equilibrium with nearly pure CO 2 fluid (Fig. 15.14). It is not clear why the solubility is greater for CO than for CO 2 in these high-pressure experiments, whereas the converse is true in those of Thibault and Holloway [1994] . We note, however, that there are significant compositional differences between the silicate melts in those two studies. That could account for the

Figure 15.15 - Pressure-temperature trajectories of the liquidus curves of silicates in equilibrium with CO2 (solid lines and solid symbols), volatile-free and water-saturated (dashed lines), (a) Relationships for albite (NaAlSi3O8) [Eggler and Kadik, 1979]. (b) Relationships for diopside (CaMgSi2O6) [Eggler and Rosenhauer, 1978].

Volatiles I. The System C-O-H-S

473

Figure 15.16 - Pressure-temperature trajectories of melting relationships in the system CaO-MgO-SiO2-CO2. Di: diopside (CaMgSi2O6), En: enstatite (MgSiO3), Fo: forsterite (Mg2Si04), Dol: dolomite [CaMg(CO3)2] [Eggler, 1975].

differences in the two series, but no experimental data exist with which to characterize relationships between CO solubility and silicate melt composition. Studies of carbon speciation in the glasses formed by quenching the melts by Eggler et al. [1979] and Thibault and Holloway [1994] point to formation as CO32- bearing entities as the only form of dissolved carbon. Exactly how this takes place is not clear, because transformation of CO to CO32- requires oxidation of carbon [Pawley et al., 1992]. Presumably, carbon oxidation may involve reduction of some of the Si4+ to Si2+, for example. How this possible reduction of Si4+ to Si2+ affects silicate melt structure depends on whether Si2+ is a network-former or a network-modifier. This question remains unanswered. 15.2c. Carbon Dioxide Carbon dioxide is an essential components in many melting processes in the Earth's interior. For example, melting temperatures of mantle rocks and the composition of the partial melts are sensitive to CO2 content (Fig. 15.15). Solubility, property, and structural data are needed to characterize such processes. Properties. Our knowledge of the solubility and solubility mechanisms of CO2 in silicate melts is better than those of CO and CH4. For example, the temperature depression of silicate liquidii caused by CO2 in the melt ranges from negligible to several hundred degrees [Eggler, 1975,1976; Mysen and Boettcher, 1975; Eggler and Kadik, 1979; Eggler and Rosenhauer, 1978; Boettcher et al, 1987; Boettcher, 1984; Wyllie, 1984]. The extent of this temperature depression depends on silicate composition (Fig. 15.15). The liquidus temperature depression also varies with pressure. In the CaO-MgO-SiO2-CO2 system at pressures between points S and I in Fig. 15.16, there is a depression in excess of 200°C. Silicate systems involving depolymerized melts are more sensitive to CO2 than highly polymerized melts [Huang and Wyllie, 1974; Eggler and Rosenhauer, 1978; Eggler and Kadik, 1979; Boettcher, 1984].

474

Chapter 15

Figure 15.17 - Liquidus phase relations in the system Mg2SiO4-CaMgSi2O5-SiO2C0 2 at 1.5 and 3.0 GPa (solid lines) [Eggler, 1974] compared with the liquidus relations volatile free and with excess H,0 (dashed lines) [Kushiro, 1969].

The invariant point, olivine+diopside+enstatite+melt, in the system Mg 2 Si04CaMgSi 2 O 6 -SiO 2 is sensitive to CO 2 content and total pressure (Fig. 15.17). Its shift away from the SiO 2 apex is consistent with increasing activity coefficient of SiO 2 in the melt [Eggler, 1974], which, in turn, is in agreement with increasing polymerization [e.g., Eggler and Rosenhauer, 1978]. These phase relations contrast with those in the system Mg2SiO4-CaMgSi2O6-H2O where the olivine+diopside+enstatite+melt invariant point shifts toward the SiO 2 apex with increasing H 2 O content, reflecting decreasing activity coefficient of SiO 2 in the melt [Kushiro, 1969]. The phase relations in Figs. 15.14-15.17 suggest that the CO 2 solubility in silicate melts depends on pressure and temperature. The CO 2 solubility increases with pressure and decreases with temperature (Fig. 15.18). Negative temperature dependence of CO 2

Figure 15.18- Pressure and temperature relations of CO2 solubility in Na2O-SiO2 melts, (a) Relationship to pressure at 1100°C of Na2Si03 melt [Eitel and Weyl, 1932]. (b) Relationship with temperature at ambient pressure of 0.43Na2O0.57Si02 melt [Pearce, 1964].

Volatiles I. The System C-O-H-S

475

Figure 15.19- CO2 solubility as a function of melt composition along the join Na2OSiO2 at 1050°C and ambient pressure [Pearce, 1964].

solubility, which is quite profound for the 0.43Na2O»0.75SiO2 melt composition in Fig. 15.18b, has been a subject of some debate at higher pressures and higher temperatures. Whether the temperature dependence of CO 2 solubility is negative or positive depends on pressure, temperature, and bulk composition much as does the H 2 O solubility in silicate melts (see Chapter 15). Compared to that of H 2 O (Chapter 15), the solubility of CO 2 is more dependent on silicate composition (Fig. 15.19). In the Na 2 O-SiO 2 system under near ambient conditions, the (Na/Si)/2 ratio is equivalent to NBO/Si of the melt. Thus, one might surmise that CO 2 solubility is positively correlated with melt depolymerization (NBO/Si) whether in this simple system or in more complex systems. In fact, Brooker et al. [2001a], from solubility data of melts in the system Na 2 O-CaO-MgO-Al 2 O 3 -SiO 2 -CO 2 at 1.5 GPa and

Figure 15.20 - CO2 solubility as a function of nominal melt NBO/T at 1.5 GPa and 1275°-1600°C in the system Na2O-CaOMgO-Al2O3-SiO2 [Brooker et al., 2001a].

476

Chapter 15

Figure 15.21 - (a) CO2 solubility along the join (Cao.5Mg05)0-Si02 at 1600°C and 2 GPa as a function of NBO/Si of the melt, (b) CO2 solubility along the join Ca2SiO4-Mg2SiO4 at 1500°C and 3 GPa [Holloway etal, 1976]. temperatures in the 1250°-1600°C range, proposed that NBO/T is the principal composition (and, therefore, structure) variable governing the CO 2 solubility (Fig. 15.20). A more detailed examination of how composition affects CO 2 solubility reveals, however, that in addition to NBO/T, the ionization potential of the metal cation must be considered [Holloway et al, 1976]. In the CaO-MgO-SiO 2 -CO 2 melts, for example, the solubility is, indeed, positively correlated with NBO/Si (Fig. 15.21a). However, it is also positively correlated with the Ca/Mg-ratio (Fig. 15.21b), which suggests that when CO 2 forms CO 3 2 - carbonate complexes in the melt, their stability is affected by the ionization potential of neighboring metal cations. A positive correlation between ionization potential of the metal cation and extent of deformation of the carbonate group, well known in crystalline carbonate structures [White, 1974], has also been observed in CO2-saturated silicate melts [Sharma et al., 1988]. It is possible, therefore, that the extent of steric hindrance of the CO32- triangular geometry controls the relationship between CO 2 solubility and the type of metal cation(s). This proposal implies, for example, that at fixed pressure, temperature, and NBO/Si of a melt, the CO 2 solubility depends on cation properties in the order K+>Na+>Ca2+>Mg2+. Solution Mechanisms. The solution mechanisms of CO 2 lend themselves to structural determination with methods such as 13C MAS NMR, Raman, and infrared absorption spectroscopy, as well as numerical simulations. There is a distinct difference in 13C chemical shift from NMR spectroscopy depending on whether the species is CO 2 or CO32- (Fig. 15.22). The intensity relationships of the 13C resonance in CO 2 and CO32- can be used as a measure of CO 2 /CO 3 2 - abundance ratio

Volatiles I. The System C-O-H-S

All

Figure 15.22 - (a) Carbon-13 MAS NMR spectra of CO2-saturated NaAlSiO4 and Na2CaAlSi07 melts [from Kohn etal, 1991]. (b) Fourier-transform infrared absorption spectra of CaMgSi2O6CO2 and NaAlSiO4-CO2 glasses [Fine and Stolper, 1985, 1986] [Brooker etal., 1999]. In infrared absorption spectroscopy, the absorption doublet assigned to CO 3 2 - groups is well separated from that of CO 2 (Fig. 15.22b). These intensity ratios can be calibrated and used for the same purpose [e.g., Stolper et al., 1987; Nowak et al, 2003]. A cursory glance at Fig. 15.22b suggests that CO 2 and CO32- abundance in melts depend on the silicate composition. For example, carbon dioxide in CaMgSi 2 O 6 melt is dissolved as CO32- only, whereas in NaAlSi 2 O 6 melt there are both CO32- and molecular CO 2 . Thus, it appears that the proportion of CO32- relative to molecular CO 2 in silicate melts is positively correlated with depolymerization of the melt [Mysen and Virgo, 1980; Brooker et al., 2001b]. Even for nominally fully polymerized aluminosilicate melts, the CO 3 2 7CO 2 ratio is positively correlated with the Al/(A1+Si) [Mysen, 1976]. In fact, Stolper et al. [1987] used CO 2 and CO32- relationships in NaAlSi 3 O 8 -CO 2 melts to calculate relevant thermodynamic parameters of carbon dioxide dissolved as molecular CO 2 and as CO32-. This could be done because total carbon dioxide content, as well as proportions of molecular CO 2 and CO32- in the NaAlSi 3 O 8 melt, are both temperature- and pressuredependent. 15.3. Structure and Melt Properties There is comparatively little data on the effect of dissolved C-O-H-S volatiles on the structure of silicate and aluminosilicate melts. Instead, the solution mechanisms have been often inferred from properties of these materials. In the case of CH 4 , CO, S, and H 2 , there is some information on their speciation in silicate melts. However, the data are

478

Chapter 15

rare and solution mechanisms have been inferred principally on the basis of property behavior. In some cases, such as CO2-bearing melts, it is well know from structural studies that a principal solution mechanism of formation of CO32- complexes. Formation of such species requires that the silicate melt solvent becomes more polymerized. It follows that any melt property that depends on silicate polymerization will depend on CO 2 content. This is evident in liquidus phase relations of CO2-bearing silicate systems, which show that the activity coefficient of SiO 2 decreases with increasing CO 2 content. It is also likely, although not well known, that transport properties of CO2-bearing melts will respond to silicate polymerization resulting from formation of CO32- groups. One could propose, for example, that melt viscosity will increase, and Si and O diffusion will decrease with increasing CO 2 content. Limited viscosity data of CO2-bearing melts do not, however, bear this out [Brearley and Montana, 1989; White and Montana, 1990; Bourgue and Richet, 2001 ]. In all cases, the viscosity either decreases or is insensitive to carbon dioxide content. Evidently, the viscous behavior reflects not only CO 2 -induced melt polymerization. 15.4. Summary Remarks 1. Sulfur dissolves in silicate melt both in oxidized and reduced form. Thus, its solubility depends on both oxygen and sulfur fugacity. The sulfur solubility is positively correlated with melt depolymerization, NBO/T, and with the ionization potential of metal cations in the melt. Interaction of sulfur with silicate involves exchange with oxygen and resultant polymerization of the melt. 2. The principal volatiles in the C-O-H system, aside from H 2 O, are CO 2 , CO, CH 4 , and H 2 . Hydrogen dissolves in molecular form and by forming OH-groups through interaction with the silicate. Dissolved as OH-groups, H 2 causes silicate depolymerization. Methane solubility is complex, but is probably dominated by formation of OH-groups, reduced carbon, and depolymerization of the silicate network. 3. Carbon monoxide dissolves primarily as CO32-, which requires reduction of one or more components of the silicate network. This can also result in melt depolymerization. Carbon dioxide solution involves formation of both molecular CO 2 and CO32- groups whose proportions depend on temperature, pressure, and melt composition. Formation of carbonate results in polymerization of the silicate melts. References Abraham K. P., Davis M. W., and Richardson F. D. (1960) Sulphide capacities of silicate melts. J. Iron Steel Inst. 196, 309-312. Bell T., Hetherington G., and Jack K. H. (1962) Water in vitreous silica. Part 2: Some aspects of hydrogen-water-silica equilibria. Phys. Chem. Glasses 3, 141-146. Boettcher A. L. (1984) The system SiO2-H2O-CO2: Melting solubility mechanisms of carbon and liquid structure to high pressures. Amer. Mineral. 69, 823-834.

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Boettcher A. L., Luth R. W., and White B. S. (1987) Carbon in silicate liquids: The systems NaAlSi3O8-CO2, CaAl2Si2O8-CO2, and KAlSi3O8-CO2. Contrib. Mineral. Petrol. 97, 297-304. Bourgue E. and Richet P. (2001) The effects of dissolved CO, on the density and viscosity of silicate melts: A preliminary study. Earth Planet. Sci. Lett. 193, 57-68. Brearley M. and Montana A. (1989) The effect of CO2 on the viscosity of silicate liquids at high pressure. Geochim. Cosmochim. Ada 53, 2609-2615. Brooker R. A., Kohn S. C, Holloway J. R., McMillan P. R, and Carroll M. R. (1999) Solubility, speciation and dissolution mechanisms for CO2 in melts on the NaAlO2-SiO2 join. Geochim. Cosmochim. Ada 63, 3549-3566. Brooker R. A., Kohn S. C, Holloway J. R., and McMillan P. F. (2001a) Structural controls on the solubility of CO2 in silicate melts. Part I: Bulk solubility data. Chem. Geol. 174, 225-239. Brooker R. A., Kohn S. C, Holloway J. R., and McMillan P. F. (2001b) Structural controls on the solubility of CO2 in silicate melts. Part II: IR characteristics of carbonate groups in silicate glasses. Chem. Geol. 174, 241-254. Buchanan D. L. and Nolan J. (1979) Solubility of sulfur and sulfide immiscibility in synthetic tholeiite melts and their relevance to Bushveld complex rocks. Can. Mineral. 17, 483-494. Carroll M. R. and Rutherford M. J. (1988) Sulfur speciation in hydrous experimental glasses of varying oxidation states: Results from measured wavelength shifts of sulfur X-rays. Amer. Mineral. 73, 845-849. Carroll M. R. and Webster J. D. (1994) Solubilities of sulfur, noble gases, nitrogen, chlorine, and fluorine in magmas. In Volatiles in Magmas (eds. M. R. Carroll and J. L. Holloway), pp. 231280, Mineralogical Society of America. Washington DC. Eggler D. H. (1974) Effect of CO2 on the melting of peridotite. Carnegie Instn. Washington, Year Book 73, 215-224. Eggler D. H. (1975) Peridotite-carbonatite relations in the system CaO-MgO-SiO2-CO2. Carnegie Instn. Washington, Year Book 74, 468-474. Eggler D. H. (1976) Does CO2 cause partial melting in the low-velocity layer of the mantle? Geology 2, 69-72. Eggler D. H. and Baker D. R. (1982) Reduced volatiles in the system C-H-O: Implications to mantle melting, fluid formation and diamond genesis. Adv. Earth Planet. Sci. 12, 237-250. Eggler D. H. and Kadik A. A. (1979) The system NaAlSi3O8-H2O-CO2: I. Compositional and thermodynamic relations of liquids and vapors coexisting with albite. Amer. Mineral. 64, 1036-1049. Eggler D. H. and Rosenhauer M. (1978) Carbon dioxide in silicate melts. II. Solubilities of CO2 and H2O in CaMgSi2O6 (diopside) liquids and vapors at pressures to 40 kb. Amer. J. Sci. 278, 64-94. Eggler D. H., Mysen B. O., Hoering T. C, and Holloway J. R. (1979) The solubility of carbon monoxide in silicate melts at high pressures and its effect on silicate phase relations. Earth Planet. Sci. Lett. 43, 321-330. Eitel W. and Weyl W. (1932) Residuals in the melting of commercial glass. J. Amer. Ceram. Soc. 15, 159-166. Faile S. P. and Roy D. M. (1971) Dissolution of hydrogen in fused silica. J. Amer. Ceram. Soc. 54, 533-534. Fincham C. J. B. and Richardson F. D. (1954) The behavior of sulphur in silicate and aluminate melts. Proc. Roy. Soc. London A223, 40-62.

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Fine G. and Stolper E. (1985) The speciation of carbon dioxide in sodium aluminosilicate glasses. Contrib. Mineral. Petrol. 91, 105-112. Fine G. and Stolper E. (1986) Dissolved carbon dioxide in basaltic glasses: Concentration and speciation. Earth Planet. Sci. Lett. 76, 263-278. French B. M. (1966) Some geological implications of equilibrium between graphite and a C-H-O gas phase at high temperatures and pressures. Rev. Geophys. 4, 223-253. Green D. H., Falloon T. J., and Taylor W. R. (1987) Mantle-derived magmas - roles of variable source peridotite and variable C-H-0 fluid composition. In Magmatic Processes: Physicochemical Principles (ed. B. O. Mysen), pp. 139-154, Geochemical Society. University Park. Haughton D. R., Roeder P. L., and Skinner B. J. (1974) Solubility of sulfur in mafic magmas. Econ. Geol. 69,451-467. Holloway J. R. and Blank J. G. (1994) Application of experimental results to C-O-H species in natural melts. In Volatiles in Magmas.(eds. M. R. Carroll and J. R. Holloway), pp. 187-230, Mineralogical Society of America. Washington DC. Holloway J. R., Mysen B. O., and Eggler D. H. (1976) The solubility of CO2 in liquids on the join CaO-MgO-SiO2-CO2. Carnegie Inst. Washington Year Book 75, 626-631. Holmquist S. (1966) Oxygen ion activity and the solubility of sulfur trioxide in sodium silicate melts. J. Amer. Ceram. Soc. 49, 467-473. Huang W.-L. and Wyllie P. J. (1974) Eutectic between wollastonite II and calcite contrasted with thermal barrier in MgO-SiO2-CO2 at 30 kilobars, with application to kimberlite-carbonatite petrogenesis. Earth Planet. Sci. Lett. 24, 305-310. Huebner J. S. (1971) Buffering techniques for hydrostatic systems at elevated pressures. In: Research Techniques for High Pressure and High Temperature (ed. G. C. Ulmer). Ch. 15. Springer. Berlin. Jugo P. J., Luth R. W., and Richards J. P. (2005) Experimental data on the speciation of sulfur as a function of oxygen fugacity in basaltic melts. Geochim. Cosmochim. Ada 69, 497-504. Kerrick D. M. and Jacobs G. K. (1981) A modified Redlich-Kwong equation for H2O, CO2 and H2O-CO2 mixtures at elevated pressures and temperatures. Amer. J. Sci. 281, 735-767. Kohn S. C, Brooker R. A., and Dupree R. (1991) 13C MAS NMR: A method for studying CO2 speciation in glasses. Geochim. Cosmochim. Acta 55, 3879-3884. Kushiro I. (1969) The system forsterite-diopside-silica with and without water at high pressures. Amer. J. Sci. 267-A, 269-294. Kushiro I. and YoderH. (1974) Formation of eclogite from garnet lherzolite: Liquidus relations in a portion of the system MgSiO3-CaSiO3-Al2O3 at high pressure. Carnegie Instn. Washington Year Book 73, 266-269. Luth R. W. and Boettcher A. L. (1986) Hydrogen and the melting of silicates. Amer. Mineral. 71, 264-276. Luth R. W., Mysen B. O., and Virgo D. (1987) Raman spectroscopic study of the behavior of H2 in the system Na2O-Al2O3-SiO2-H2. Amer. Mineral. 72, 481-486. Moretti R. and Ottonello G. (2003) A polymeric approach to the sulfide capacity of slags and melts. Metall. Trans. B 34, 399-410. Mysen B. O. (1976) The role of volatiles in silicate melts: Solubility of carbon dioxide and water in feldspar, pyroxene, feldspathoid melts to 30 kb and 1625 degrees C. Amer. J. Sci. 276,969-996. Mysen B. O. and Boettcher A. L. (1975) Melting of ahydrous mantle. II. Geochemistry of crystals and liquids formed by anatexis of mantle peridotite at high pressures and high temperatures

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as a function of controlled activities of water, hydrogen and carbon dioxide. J. Petrol. 16, 549-590. Mysen B. O. and Popp R. K. (1980) Solubility of sulfur in CaMgSi2O6 and NaAlSi3O8 melts at high pressure and temperature with controlled fg2 and f$2. Amer. J. Sci. 280, 78-92. Mysen B. O. and Virgo D. (1980) Solubility mechanisms of carbon dioxide in silicate melts: A Raman spectroscopic study. Amer. Mineral. 65, 885-899. Mysen B. O. and Virgo D. (1986) Volatiles in silicate melts at high pressure and temperature. 1. Interaction between OH groups and Si4+, Al3+, Ca2+, Na+ and H+. Chem. Geol. 57, 303-331. Nagashima S. and Katsura T. (1973) The solubility of sulfur in Na2O-SiO2 melts under various oxygen partial pressures at 1100°C, 1250°C, and BOOT. Bull. Chem. Soc. Japan 46, 3099-3103. Nowak M., Porbatzki D., Spickenbom K., and Diecrich O. (2003) Carbon dioxide speciation in silicate melts: A restart. Earth Planet. Sci. Lett. 207, 131-139. O'Neill H. S. C. and Mavrogenes J. A. (2002) The sulfide capacity and sulfur content at sulfide saturation of silicate melts at HOOT and 1 bar. J. Petrol. 43, 1049-1087. Paris E., Giuli G., Carroll M. R., and Davoli I. (2001) The valence and speciation of sulfur in glasses by x-ray absorption spectroscopy. Can. Mineral. 39, 331-339. Pawley A. R., Holloway J. R., and McMillan P. F. (1992) The effect of oxygen fugacity on the solubility of carbon-oxygen fluids in basaltic melt. Earth Planet. Sci. Lett. 110, 213-225. Pearce M. L. (1964) Solubility of carbon dioxide and variation of oxygen ion activity in sodasilicate melts. J. Amer. Ceram. Soc. 47, 342-347. Richardson F. D. and Fincham C. J. B. (1956) Sulfur and silicate in aluminate slags. J. Iron Steel Inst. 178,4-15. Saxena S. K. and Fei Y. (1988) Fluid mixtures in the C-H-0 system at high pressure and temperature. Geochim. Cosmochim. Acta 52, 505-512. Seo J.-D. and Kim S.-H. (1999) The sulphide capacity of CaO-SiO2-Al2O3-MgO (-FeO) smelting reduction slags. Steel Research 70, 203-208. Shackleford J. F., Studt P. L., and Fulrath R. M. (1972) Solubility of gases in glass. II. He, Ne, and H2 in fused silica. J. Appl.Phys. 43, 1619-1626. Sharma S. K., Yoder H. S., Jr., and Matson D. W. (1988) Raman study of some melilites in crystalline and glassy states. Geochim. Cosmochim. Acta 52, 1961-1967. Shaw H. R. (1963) Hydrogen-water vapor mixtures: Control of hydrothermal atmospheres by hydrogen osmosis. Science 139, 1220-1222. Sosinsky D. J. and Sommerville, I. D. (1986) The composition and temperature dependence of the sulfide capacity of metallurgical slags. Metall Trans. B 17, 331-337. Stolper E., Fine G., Johnson T., and Newman S. (1987) Solubility of carbon dioxide in albitic melt. Amer. Mineral. 72, 1071-1085. Taylor W. R. and Green D. H. (1987) The petrogenetic role of methane: Effect on liquidus phase relations and the solubility mechanisms of reduced C-H volatiles. In Magmatic Processes: Physicochemical Principles (ed. B. O. Mysen), pp. 121-138, Geochemical Society. University Park. Thibault Y. and Holloway J. R. (1994) Solubility of CO2 in a Ca-rich leucitite: Effect of pressure, temperature, and oxygen fugacity. Contrib. Mineral. Petrol. 116, 216-214. Wallace P. and Carmichael I. S. E. (1992) Sulfur in basaltic magma. Geochim. Cosmochim. Acta, 56, 1863-1874. Wallace P. J. and Carmichael I. S. E. (1994) Speciation in submarine basaltic glasses as determined by measurement of S Ka x-ray wavelength shifts. Amer. Mineral. 79, 161-167.

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Wendlandt R. F. (1982) Sulfide saturation of basalt and andesite melts at high pressures and temperatures. Amer. Mineral. 67, 877-885. White W. B. (1974) The Carbonate Minerals. In Infrared Spectra of Minerals (ed. V. C. Farmer), Ch. 12, Mineralogical Society of London. London. White B. S. and Montana A. (1990) The effect of H2O and CO2 on the viscosity of sanidine liquid at high pressures. J. Geophys. Res. 95, 15683-15694. Wyllie P. J. (1984) Constraints imposed by experimental petrology on possible and impossible magma sources and products. Phil. Trans. R. Soc. Lond. A 310, 439-456.

483

Chapter 16

Volatiles II. Noble Gases and Halogens Noble gas distribution and isotope systematics offer constraints on the evolution of volatiles in the Earth. Halogens, in particular F and Cl, can be important in magmatic processes in the Earth's crust. Fluorine, which can be dissolved in silicate melts in quantities in excess of 1 wt % at ambient pressure, affects melt properties in many ways similar to that of H2O. This feature has important consequences for magmatic processes in the upper portions of the Earth's crust. Chlorine impacts less on melts and melt properties. Its importance in igneous processes stems from its tendency to form stable complexes with economically important metals. 16.1. Noble Gases Two primary interests drive characterization of the solubility of noble gases, (i) Their chemical interaction with silicate melts and glasses offers a window through which we may examine how neutral species can dissolve in silicate melts, and, thereby, how silicate structure can accommodate such atoms or molecules [Doremus, 1966; Studt et al., 1970; Shackleford etal., 1972; Shelby, 1976]. (ii) In the Earth, the solubility of noble gases and the partitioning of these gases between silicate melts and crystals can be used to address degassing events over the Earth's history [Jambon, 1994]. 16.1a. Solubility The solubility of noble gases in glasses and melts is negatively correlated with their atomic radii (Fig. 16.1). This relationship holds in simple chemical systems such as SiO2 [e.g., Doremus, 1966; Shelby, 1976], binary metal oxide silicates [Shibata et al., 1998], in ternary and quaternary aluminosilicates [Roselieb et al., 1992; Schmidt and Keppler, 2002], and in chemically more complex natural igneous melts [e.g., Hiyagon and Ozima, 1986; Lux, 1987; Jambon, 1987; Carroll and Stolper, 1991,1993;Broadhurste/a/., 1990, 1992; Chamorro et al, 2002]. At pressures near or below ambient, the solubility of individual noble gases in silicate melts obey Henry's Law (Fig. 16.1a). This law states that for gas, r, its solubility, Xt, is proportional to its partial pressure in the gas phase, Pi, via a proportionality constant, Kf. Xi = KiPi.

(16.1)

484

Chapter 16

Figure 16.1 - Solubility behavior of noble gases in silicate melts, (a) Solubility in basalt melt [from Jambon etal., 1986]. (b) Henry's Law constant, K, from noble gas solubility measurements in natural and synthetic silicate melts (equation 16.1) [Kirsten, 1968; Hayatsu and Waboso, 1985; Hiyagon and Ozima, 1986; Lux, 1987]. The value of K[ (Henry's Law constant) for a given silicate composition is negatively correlated with the atomic radius of the noble gas (Fig. 16.1b). Noble gas diffusivity also decreases and activation energy of diffusive flow increases with increasing atomic radius [Roselieb et al, 1992]. Furthermore, the K(-value increases with increasing silica content of a melt. For example, the upper values in the/Q-range of Lux [1987] in Fig. 16.1b is for a natural andesite melt, whereas the lower value is that for less silica-rich basalt. In other words, the solubility of any noble gas in a silicate melt increases with increasing SiO 2

Figure 16.2 - (a) Xenon and neon solubility in melts on the Na2O-SiO2 join, (b) Argon solubility in silicate melt compositions indicated as a function of their NBO/Si [Shibata et al, 1998].

485

Volatiles II. Noble Gases and Halogens Table 16.1. Enthalpy of solution, AHS (kJ/mol), of noble gases in silicate melts 0.7Na 2 OSi0 2

0.6Na2O«SiO2 0.23Na 2 OSi0 2

He Ne

34.4±3.6

40.1±7.8

30.3±7.4

Ar Kr Xe

22.6±6.9 12.1 ±0.2 -26.6±38.1

40.5±23.5 67.1±17.9 149±22

45.3+11.1 80.2+24.3 126+22

SiO2

Reference

-40.5 -75.6

Shelby [1976] Shibata etal. [1998] Shelby [1976] Shibata et al. [1998] Shibata et al. [1998] Shibata etal. [1998]

content (Fig. 16.2a). When the solubility is expressed relative to the noble gas concentration in a gas phase, at least in simple chemical systems near ambient pressure, it depends only on the nominal NBO/Si of the silicate melt (Fig. 16.2b). Lux [1987] suggested that the Henry's Law constant in equation (16.1) can be related to the radius of the noble gas, r/, and two constants, a and b, as in: K[ = a exp(-br/).

(16.2)

In this equation, b is a constant independent of silicate composition, whereas constant a is positively correlated with overall polymerization of the melt whether chemically simple [Shibata et al., 1998] or complex [Jambon, 1987; Lux, 1987]. The solubility of noble gases in pure SiO 2 glass and melt [Doremus, 1966; Shackleford et al., 1972; Shelby, 1976] also appears consistent with this relationship. The temperature-dependence of noble gas solubility is slight and can be either positive or negative [Shackleford etal., 1972; Lux, 1987; Shibata etal., 1998]. In natural silicate melts, the enthalpy of solution, AHS, derived from this temperature-dependence is positive and ranges from near 5 to about 20 kJ/mol [Lux, 1987]. For Ar and larger noble gases, the AHS decreases with increasing atomic radius in binary metal oxide silicate melts [Shibata

Figure 16.3 - Solubility of He and Ne gas in SiO2 melt as a function of gas fugacity. Dashed lines indicate the expected trends if solution behavior follows Henry's Law [Shelby, 1976].

486

Chapter 16

et al., 1998]. Furthermore, AHS becomes increasingly sensitive to melt polymerization (equivalent to metal/silicon ratio) as the atomic radius of the noble gas increases (Table 16.1). Noble gas solubility in silicate melts and glass increases with increasing pressure [e.g., Shackleford et al, 1972; Shelby, 1976; Jambon et al, 1986; White et al., 1989; Carroll and Stolper, 1991; Chamorro-Perez et al., 1996; Ozima, 1998; Schmidt and Keppler, 2002]. In contrast to the low-pressure trends, the solubility deviates negatively from Henry's Law at high pressure [Shelby, 1976; Carroll and Stolper, 1991]. These deviations increase with increasing pressure and with noble gas atomic radius (Fig. 16.3). 16.2b. Solution Mechanisms The solubility mechanisms of noble gases in silicate melts and glasses have been modeled on the assumption that the gas occupies holes in the structure. That dissolved noble gases may be treated in such structural terms, at least in silica glass, is consistent with Kr x-ray absorption data of SiO 2 glass (Fig. 16.4). Wulf et al. [1999] found the data accord with model where a single Kr atom dissolved in the silica structure without next-nearest Kr. In other words, there are no Kr clusters. Similar structural roles of other noble gases are implicit in early models of solution mechanisms in fused silica. For example, Doremus [1966] concluded that the solubility ratio of the noble gas in silica melt and in coexisting gas yields a free volume of 3 %. This number is smaller, however, than that suggested by Shelby [1976] who concluded, by using a Langmuir adsorption model, that accessible free volume for Ne and He is on the order of l-2»10 21 atoms/cm3. Recast as done by Doremus [1966], this value corresponds to a free volume of about 10-20 %. Carroll and Stolper [1991] used the partial molar volumes obtained from solubility measurements to estimate the porosity of SiO 2 glass. The partial molar volume of the noble gases was estimated by fitting solubility data to pressures slightly above 0.1 GPa to a function of noble gas actvity, ang, of the form:

Figure 16.4 - Fourier-transform of x-ray absorption data for Kr in vitreous SiO2 [Wulfetal, 1999].

Volatiles II. Noble Gases and Halogens

ang(P,T) = ang{Po,To)

fng T

^' \

exp- f V^(P,T)/RT + f W°{P0)IRT

487

. (16.3)

In this expression, the subscript ng denotes a noble gas, subscript o, reference state; T and P, pressure and temperature, /, fugacity, V, molar volume, and AH the molar enthalpy difference between the noble gas and that of the noble gas dissolved in the melt and a reference state. The partial molar volumes in silica glass are 16.4±1.4, 10.3±2.3, and 5.510.8 cm3/mol for Ar, Ne, and He, respectively [Carroll and Stolper,1991]. The porosity calculations by Carroll and Stolper [1991] yielded results similar to those of Shelby [1976] with a negative correlation between the number of available holes for gas solution and the size of the noble gas. The deviations from Henry's Law at pressures above - 0 . 1 GPa (Fig. 16.3) are probably due to changes in free volume with pressure. In other words, the compressibility of the melt structure, even that of pure SiO2, affects available volume within which to dissolve the gas. This conclusion accords with the structural data of supercooled SiO2, which undergoes several percent compression between ambient pressure and about 3 GPa (see Chapter 5 and Seifert et al. [ 1983]). The increasing deviation from Henry's Law with the size of the noble gas atom (Fig. 16.3) lends further support to this suggestion. A discontinuous decrease in the pressure dependence above 5 GPa may suggest a collapse of the 3-dimensional structure [Chamorro-Perez et al., 1996; Schmidt and Keppler, 2002]. It should be noted, though, that without dissolved noble gas there is no evidence for a structural collapse of the SiO2 structure until pressure reaches 15 GPa and more (see Chapter 5 and also Hemley et al. [1994] for review of high-pressure structure of vitreous SiO2). Thus, there may be a minimum porosity below which noble gases cannot be accommodated in the melt structure. This argument is not without questions, however, because the solubility plateau near 5 GPa, at least in tholeiitic melt compositions, occurs at higher pressures for Xe than for Ar [Schmidt and Keppler, 2002]. One is left with the conclusion, therefore, that there is interaction of some form between the dissolved noble gas and the silicate melt solvent. The nature of this interaction is not clear. 16.2. Halogens Property and structure information of halogen-bearing glasses and melts are limited to chlorine and fluorine. For chlorine-bearing systems, data are restricted mostly to solubility. Quantitative data on solubility are less common for fluorine, but an extensive database of other properties and of structure of glasses and melts exists.

488

Chapter 16

Figure 16.5 - Effect of HC1 on liquidus depression of water-saturated NaAlSi3O8 at 275 MPa [Wyllie and Turtle, 1964].

16.2a. Chlorine A major reason for the interest in Cl in melts is its role in enrichment processes of economically important metals in nature. Modeling of such processes requires an understanding of solubility and solution mechanisms of chlorine in silicate melts at high pressure and high temperature. Solubility. Addition of chlorine to the albite-H 2 O system causes a temperaturedepression of the hydrous albite (NaAlSi3O8) solidus on the order of 100-200°C at several hundred MPa total pressure (Fig. 16.5). Wyllie and Tuttle [1964] pointed out, however, that in a chemically more complex system, such as granite, the solidus temperature actually increases with increasing HC1 content. The solubility of chlorine in water-rich silicate melts is unusual (Fig. 16.6) compared with other volatiles because it decreases with increasing pressure [e.g., Webster and Holloway, 1988; Shinohara et al, 1989; Metrich and Rutherford, 1992; Signorelli and Carroll, 2000,2002]. In water-deficient systems, the relationship with pressure is positive

Figure 16.6 - Chlorine solubility as a function of pressure in pantellerite and rhyolite melts [Metrich and Rutherford, 1992].

Volatiles II. Noble Gases and Halogens

489

Figure 16.7 - Chlorine solubility (a) as a function of (Na+K)/Al of natural and synthetic phonolite melts [Signorelli and Carroll, 2002] and (b) as a function of NBO/T for natural and synthetic rhyolite and trachyte melts [Metrich and Rutherford, 1992; Signorelli and Carroll, 2002]. [Webster and De Vivo, 2002]. The driving force behind this negative pressure-dependence of chlorine solubility in melts coexisting with an aqueous fluid is a large partial molar volume difference of chloride complexes between the fluid and the melt [Metrich and Rutherford, 1992; Webster and De Vivo, 2002]. Wyllie and Tuttle [1964] suggested that Cl solubility depends on silicate composition, thereby explaining the effects of HCl on the pressure/temperature trajectories of aluminosilicate solidii. Composition-dependent Cl solubility has also been used to explain the pronounced influence of silicate composition of Cl partitioning between silicate melts and coexisting aqueous fluid [Shinohara et al., 1989; Webster et ai, 1999; Signorelli and Carroll, 2002]. In water-saturated melts systems, the chlorine solubility is positively correlated with the (Na+K)/Al ratio of the melt as well as its NBO/T-value (Fig. 16.7). It should be noted, though, that increasing (Na+K)/Al ratio likely results in increasing NBO/T of the melt. Thus, it is not clear whether the correlations of chloride solubility with both (Na+K)/Al and NBO/T are, in fact, interrelated. Transport Properties. The viscosity of Na-Ca and Na-Ba silicate melts increases slightly with increasing Cl content [Hirayama and Camp, 1969]. Hirayama and Camp [1969] noted, however, that there were problems with Cl loss from the melts during their viscosity experiments. This problem could result in increased viscosity because the Cl loss was associated with a decrease in Na and an increase in Si concentration. However, their viscosity results are consistent with those of Baker and Vaillancourt [1995] whose measurements for NaAlSi 3 O 8 melt at high pressure also indicate an increase with increasing Cl concentration. In a more Na-rich Al-free composition (Na 2 O»2SiO 2 ) at ambient pressure, Dingwell and Hess [1998] found that the effect of Cl on melt viscosity is negligible, but that there may be a small decrease at high Cl contents and at temperatures

490

Chapter 16

Figure 16.8 - Viscosity of Na2O»2SiO2 melt as a function of chlorine content at temperatures indicated [Dingwell and Hess, 1998].

below the glass transition (Fig. 16.8). At temperatures above the glass transition, there is no discernible effect of Cl on the melt viscosity. Solution Mechanisms. The chlorine solubility data and the influence of chlorine on liquidus phase relations of silicates [Wyllie and Tuttle, 1964; van Groos and Wyllie, 1969] suggest comparatively simple solution mechanism of Cl in melts forming perhaps chloride complexes with alkalis and alkaline earths. For example, increased Cl concentration results in the appearance of quartz on the liquidus of NaAlSi 3 O 8 -H 2 O-HCl [Wyllie and Tuttle, 1964]. That observation is consistent with a decrease in the activity of aluminosilicate components, a feature that could be explained by extracting Na + from its

Figure 16.9 - Chlorine-35 MAS NMR spectra of Cl-bearing glasses [Stebbins and Du, 2002].

Volatiles II. Noble Gases and Halogens

491

charge-balancing role of Al3+ in tetrahedral coordination to form Na-Cl complexes in the melt. Chlorine-35 MAS NMR data of Cl-bearing Na-silicate and Na-aluminosilicate glasses suggest metal chloride speciation in silicate melts [Stebbins and Du, 2002]. The 35C1 NMR spectra (Fig. 16.9) exhibit only one peak that, in analogy with the 35NMR spectra of crystalline chloride compounds, was assigned to alkali chloride or alkaline earth chloride [Stebbins and Du, 2002]. There is no effect on the 35C1 chemical shift upon adding Al to the glass. This observation led Stebbins and Du [2002] to conclude that Al-Cl bonding is not an important structural feature of Cl-bearing silicate melts. There is, however, an effect of the cation type (alkali and alkaline earth) on the 35C1 chemical shift [Stebbins and Du, 2002], which indicates that the stability of metal chloride species in silicate melts depends on the metal cation(s). The observation that ionization potential of the metal cation does, in fact, affect the solubility of Cl in melts is in agreement with this solubility model [Webster and De Vivo, 2002]. 16.2b. Fluorine Experimental studies of properties of F-bearing silicate melts has focused on thermodynamic and transport properties, with lesser emphasis on solubility. This relative scarcity in quantitative solubility data is, in part, due to the experimental challenges associated with fluorine solubility measurements. Structural data for F-bearing silicate glasses and melts are more extensive than for Cl-bearing materials. Liquidus Phase Relations. Liquidus phase relations in F-bearing silicate and aluminosilicate systems suggest complicated relationships between solubility and silicate composition and considerably greater F than Cl solubility [van Groos and Wyllie, 1967, 1969; see also review of relevant data by Carroll and Webster, 1994]. The difference can reach more than an order of magnitude at ambient pressure. Liquidus phase relations of F- and Cl-bearing systems differ. Wyllie and Turtle [ 1964] noted, for example, that the liquidus volume of quartz in the NaAlSi3O8-H2O-HF system

Figure 16.10 - Liquidus phase relations in the system NaAlSi3O8-KAlSi3O8SiO2-H2O with fluorine added as indicated on figure [Manning, 1981].

492

Chapter 16

Figure 16.11 - Effect of HF on liquidus depression of water-saturated NaAlSi3O8 at 275 MPa [Wyllie andTuttle, 1964].

is considerably larger than in the equivalent NaAlSi 3 O 8 -H 2 O-HCl. In the hydrous "haplogranite" system (NaAlSi3Og-KAlSi3O8-SiO2-H2O), addition of fluorine leads to an expansion of the quartz relative to the feldspar liquidus volume (Fig. 16.10). Furthermore, addition of HF to NaAlSi 3 O 8 -H 2 O at a few hundred MPa total pressure depresses the solidus temperature by several hundred degrees more than addition of equal concentrations of HC1 (Figs. 16.5, 16.11). We also note that the H 2 O solubility decreases at constant temperature and pressure as the fluorine content increases [Holtz et al., 1993],

Figure 16.12 - Boundaries between one and two liquids in (a) alkaline earth-SiO2-fluoride systems [Ershova and Olskanskii, 1957] and (b) alkaline earth (Me) fluoride-Al2O3-SiO, systems [from Ershova, 1957].

Volatiles II. Noble Gases and Halogens

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Table 16.2 Concentration of fluorine (expressed as alkaline earth fluoride, MeF2) in silicate glasses (modified after data compilation by Carroll and Webster [1994]). Maximum MeF2 Mol%

Temperature, °C

System

10 34 37 40 42 43 46

50 mol % SiO2 >1450 >1450 >1565 >1420 >1410 >1410 >1410

MgF2-Mg0-Si02 SrF2-Sr0-Si02 BaF2-Ba0-Si02 MgF2-Al2O3-SiO2 CaF2-Al2O3-SiO2 SrF2-Al203-Si02 BaF2-Al203-Si02

16 17 19 21

75 mol % SiO2 >1420 >1410 >1410 >1410

MgF2-Al203-Si02 CaF2-Al203-Si02 SrF2-Al2O3-SiO2 BaF2-Al2O3-SiO2

whereas dissolved Cl tends to enhance the solubility of H2O [van Groos and Wyllie, 1969]. At ambient pressure, the fluorine content of alkaline earth silicate melts in equilibrium with fluorine-rich immiscible melts in the 1450-1565°C range decreases with increasing ionization potential of the alkaline earth cation (Fig. 16.12). The solubility also increases with decreasing SiO2 content of alkaline earth silicate melts [Ershova, 1957; Ershova and Olshanskii, 1957] (see also Table 16.2). Furthermore, increasing A12O3 content leads to increasing solubility (Fig. 16.10b). The behavior of F contrasts with that of Cl, which

Figure 16.13 - Viscosity of NaAlSi3O8 and NaAlSiO4 melts as a function of temperature with and without fluorine added (as indicated on individual curves) [Dingwell etal, 1985].

494

Chapter 16

Figure 16.14 - Viscosity at 1200°C and ambient pressure of NaAlSi 3 O 8 melt as a function of fluorine, H 2 O, or Na 2 O added [Dingwell and Webb, 1992].

does not seem dependent on Al content although it does vary with the ionization potential of metal cation [Webster and De Vivo, 2002]. Transport and Related Properties. Fluorine causes a larger viscosity decrease than chlorine at the same concentration in Na-Ca and Na-Ba silicate melts [Hirayama and Camp, 1969]. The effect on high-temperature viscosity and activation energy of viscous flow is profound (Fig. 16.13). The magnitude of this effect can resemble that of equivalent concentrations of H 2 O and Na 2 O (Fig. 16.14). The viscosity is also a function of the overall degree of polymerization of the melt [Dingwell, 1989]. For meta-aluminosilicate melts such as NaAlSi 3 O 8 and NaAlSiO 4 , which are nearly fully polymerized [Taylor and Brown, 1979; Neuville and Mysen, 1996], the influence of F on melt viscosity diminishes as the melt becomes increasingly aluminous (Fig. 16.15). The viscosity of CaMgSi2O6 melt (with nominal NBO/T=2) is much less sensitive

Figure 16.15 - Viscosity at 1400°C and ambient pressure of NaAlSi3O8, NaAlSiO4, and CaMgSi2O5 melts as a function of fluorine content [Dingwell, 1989].

Volatiles II. Noble Gases and Halogens

495

Figure 16.16 - Fluorine-19 MAS NMR spectra of F-bearing glasses of composition indicated on individual spectra [Stebbins andZeng, 2000].

to F content than that of meta-aluminosilicate melts such as NaAlSi3O8 and NaAlSiO4 (with nominal NBO/T=0) (Fig. 16.15). The relative change in glass transition temperature is also much greater for highly polymerized NaAlSi3O8 than for depolymerized CaMgSi2O6 [Dingwell and Webb, 1992]. Solution Mechanism. Reasonably comprehensive structural studies of F-bearing silicate glasses and melts have been carried out with vibrational and NMR spectroscopic tools. Structural models have also been developed via numerical simulations. In a chemically simple systems such as SiO2-F, the Raman spectra of glasses have been interpreted in terms of depolymerization of the SiO2 structure via replacement of one or more bridging oxygen with F [Rabinovich, 1983; Yamamoto et ai, 1983]. In principle, this mechanism is the same as that of replacing bridging oxygen with OHgroups in SiO2-H2O melts and glasses (see Chapter 15). Raman spectroscopic investigations of F-bearing metal oxide-silica glasses have suggested formation of metal fluoride species [Takusagawa, 1980; Luth, 1988]. Interestingly, Luth [1988] proposed that in the system CaO-SiO2-F2, formation of Ca-F species may, in fact, result in polymerization of the silicate network because Ca is scavenged from its network-modifying position in F-free melts to form Ca-F bonds in F-bearing melts. This interpretation, in principle, accords with the solution model from the 19F MAS NMR spectra of F-bearing metal oxide silicate glass where Stebbins and Zeng [2000] found evidence only for metal fluoride species (Fig. 16.16). Na-F bonding dominates over K-F and Ca-F bonding over Na-F, respectively, in F-bearing mixed K-Na and Ca-Na silicate glasses [Stebbins and Zeng, 2000]. In other words, in Al-free metal oxide glasses, fluorine exhibits preference for metals with the largest ionization potential. In this regard, the structural role of metal fluoride species resembles that of metal chloride species in silicate melts. Properties of F-bearing aluminosilicate melts are consistent with not only the formation of metal-fluoride bonds, but also with interaction between the silicate network

496

Chapter 16

Figure 16.17 - (a) Fluorine-19 MAS NMR spectra of Na,O4Si0, glasses with 0, 5, and 10 mol % A12O3 added, (b) Abundance (relative area from 19F MAS NMR spectra) of fluorine species of Na,O»4SiO, glasses+Al2O3 expressed as Al/(A1+Si) of the glasses. See text for discussion of notations, NF, CF, NAF, and TF [Mysen et al, 2004]. and fluorine. The exact solution mechanism depends on the silicate composition as inferred from Raman spectra of fluorine-bearing melts along SiO 2 -NaAlO 2 [Mysen and Virgo, 1985]. Dissolved fluorine is a more efficient depolymerizer the lower the Al/(A1+Si) of the materials along this join. This suggests variable proportions of Na-F and Al-F bonding in these melts. Subsequent NMR spectroscopic work on F-bearing aluminosilicate glasses have shed considerable additional information on the details of how F interacts with the aluminosilicate network. The importance of Al-F bonding has, for example, been more clearly demonstrated from NMR spectroscopy [Schaller et al, 1992; Zeng and Stebbins, 2000]. However, the Al-F-bearing species cannot simply be A1F3 but must involve both oxygen and metal cations other than Si 4+ and Al 3+ [Zeng and Stebbins, 2000; Liu and Tossell, 2003; Mysen and etal, 2004]. Under certain circumstances, some of the aluminum may undergo transformation from 4- to 5- and 6-fold coordination at least for highly aluminous melts such as CaAl 2 Si 2 0 8 [Stebbins et al, 2000]. The fluorine speciation in peralkaline aluminosilicate melts and involves metalfluoride bonds, and Al-fluorine species that also include metals and oxygen [Liu and Tossell, 2003; Mysen etal, 2004]. A few 19 FMAS NMR spectra of Na 2 04Si0 2 +Al 2 0 3 +F glasses illustrate this complexity (Fig. 16.17). The four peaks in these spectra (marked with arrows in Fig. 16.17a) were assigned to different F-bearing species [Mysen et al, 2004]. The peak near -220 ppm is the main peak in Al-free glass (marked NF), and remains with up to 7.5 mol % A12C>3. Its frequency is nearly coincident with that of crystalline NaF (-225 ppm) [e.g., Kreinbrink et al, 1990; Miller, 1996]. The peaks at 145, -170, and -190 ppm (marked TF, NAF, and CF, respectively, in Fig. 16.17) occur

Volatiles II. Noble Gases and Halogens

497

only in Al-bearing glasses and are likely, therefore, to reflect some form of Al-F bonding [Kohn etal, 1991; Schaller etai, 1992; Stebbins etai, 2000; Liu and Nekvasil, 2001; Liu and Tossell, 2003]. Mysen et al. [2004] concluded that the -145 ppm peak probably reflects a topaz-like structure (TF), the peak near -170 ppm (NAF) being assigned to mixed AlO-F-Al tetrahedra with F/O between 0.33 (1 F and 3 O per Al) and 1 (2 F and 2 O per Al), and the one near -190 ppm to a cryolite-like structural entity (CF in Fig. 16.17). The 19F MAS NMR data, combined with 29Si MAS NMR and high-temperature Raman spectroscopic data, have been used to illustrate the interaction between F and the aluminosilicate network by using monovalent metal cations, M+. In peralkaline silicate melts, one can write several solution reactions to illustrate how these F-bearing entities can be formed as follows: 2Q3 + 2M+ + MF <=> 2Q4 + M3OF.

(16.4)

Formation of such F-species causes silicate polymerization. There are several solution mechanisms of fluorine in aluminosilicate glasses and melts. For the topaz-like species (TF), one can write: 6MAlSi 4 O 10 +3F 2 ^2Al 2 (Al 3 )F 2 -i-6M + +4Q 3 +Q 2 + 19Q4.

(16.5)

In this type of reaction, some of the tetrahedrally coordinated Al3+ in the aluminosilicate melt structure is released to form species that may resemble A12(A1O3)F2. The result of this mechanism is depolymerization of the silicate melt structure. Formation of cryolite-like species (CF) in aluminosilicate melts was originally inferred from liquidus phase relations in hydrous quartzo-feldspathic systems [Manning et al., 1980; Manning, 1981]. That inference is consistent with spectroscopic data, and we can write: 3MAlSi4O10+ 3F2 <=> M3A1F6 + 2A13+ + 6Q3+ 6Q4.

(16.6)

Equivalent expressions could be written for mixed (O,F)-containing species such as M(M3A1F5O). It is unclear from available structural data how the solution of NAF structural entities takes place. It is likely that formation of these entities also causes depolymerization of the aluminosilicate network. The process has not been determined. 16.3. Structure and Melt Properties Structural data suggest that only metal-chloride speciation occurs. In binary metal oxide silicate melts, polymerization is implied because network-modifying metals are scavenged to form the metal chloride complexes. In aluminosilicate melts, formation of metal chloride

498

Chapter 16

species can create complications with AP+-charge-balance. Thus, melt properties that depend on the structural behavior of Al3+ will be affected. It is possible, for example, that the small but real expansion of quartz liquidus volumes could reflect structural interactions of this nature. For fluorine, structural data not only suggest metal-fluoride species but also complicated interactions involving the remainder of the aluminosilicate network. How such species affect the melt structure and melt properties depends on the melt composition. The influence of fluorine on melt properties often differs from that of chlorine, in particular for highly polymerized melts such as those along or near meta-aluminosilicate joins. Properties that depend on melt polymerization (e.g., transport properties) indicate that dissolved F causing silicate depolymerization, as observed in the comparatively similar effect of Na2O, H2O, and F on the high-temperature viscosity of NaAlSi3O8 melts. In addition, the large freezing-point depressions in F-bearing silicate systems is in qualitative accord with depolymerizing the melts. However, solution of F in such melts also results in changes in Al/(A1+Si) of the silicate network because F interacts with Al3+ in the aluminosilicate in a manner that scavenges at least some AP+ from the network. These changes are reflected, for example, in rapidly expanding liquidus volumes of quartz relative to feldspar as F contents increase. Solution of fluorine in Al-free or Al-deficient peralkaline silicate melts have much less of an effect on properties of depolymerized than on properties of highly polymerized silicate melts. Most likely this difference is because the solution mechanism of fluorine in melts of this type predominantly involves interaction between F and the metal cation(s). That mechanism is conceptually similar to that of Cl solution where the effect on melt properties is also small. 16.4. Summary Remarks 1. Solubility of noble gases and halogens in silicate melts is a pronounced function of the type of volatile, temperature, pressure, and silicate melt composition. 2. Noble gases dissolve in monatomic form and probably occupy cavities in the melt structure. The size of the gas atom as well as those of the cavities that accommodate them govern the solubility. 3. Halogens dissolve by interaction with metal cations (alkali metals and alkaline earths), aluminum, and silicon in melts. However, the solution mechanisms of the two main halogens, chlorine and fluorine, differ as chlorine interacts only with the metal cations such as alkalis and alkaline earths, whereas fluorine can form bonding with all cations in melts. This difference accounts for the large differences in their solubility and also for their different influence on properties of silicate melts.

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References Baker D. R. and Vaillancourt J. (1995) The low viscosities of F+H2O-bearing granitic melts and implications for melt extraction and transport. Earth Planet. Sci. Lett. 132, 199-211. BroadhurstC. L., Drake M. J., Hagee B. E., and Bernatowicz T. J. (1990) Solubility and partitioning of Ar in anorthite, diopside, forsterite, spinel, and synthetic basalt liquids. Geochim. Cosmochim. Ada 54, 299-309. Broadhurst C. L., Drake M. J., Hagee B. E., and Bernatowicz T. J. (1992) Solubility and partitioning of Ne, Ar, Kr, and Xe in minerals and synthetic basalt melts. Geochim. Cosmochim. Ada 56, 709-723. Carroll M. R. and Stolper E. M. (1991) Argon solubility and diffusion in silica glass: Implication for the solution behavior of molecular gases. Geochim. Cosmochim. Ada 55, 211-226. Carroll M. R. and Stolper E. M. (1993) Noble gas solubilities in silicate melts and glasses: New experimental results for argon and the relationship between solubility and ionic porosity. Geochim. Cosmochim. Ada 57, 5039-5052. Carroll M. R. and Webster J. D. (1994) Solubilities of sulfur, noble gases, nitrogen, chlorine, and fluorine in magmas. In Volatiles in Magmas (eds. M. R. Carroll and J. L. Holloway), pp. 231280, Mineralogical Society of America. Washington DC. Chamorro-Perez E., Gillet P., and Jambon A. (1996) Argon solubility in silicate melts at very high pressures. Experimental set-up and preliminary results for silica and anorthite melts. Earth Planet. Sci. Lett. 145, 97-107. Chamarro E. M., Brooker R. A., Wartho J.-A., Wood B. J., Kelley S. P., and Blundy J. D. (2002) Ar and K partitioning between clinopyroxene and silicate melt to 8 GPa. Geochim. Cosmochim. Ada 66, 507-519. Dingwell D. B. (1989) Effect of fluorine on the viscosity of diopside liquid. Amer. Mineral. 74, 333-338. Dingwell D. B. and Webb S. L. (1992) The fluxing effect of fluorine at magmatic temperatures (600-800°C): A scanning calorimetric study. Amer. Mineral. 77, 30-33. Dingwell D. B. and Hess K.-U. (1998) Melt viscosities in the system Na-Fe-Si-Si-O-Cl-F: Contrasting effects of F and Cl in alkaline melts. Amer. Mineral. 83, 1016-1021. Dingwell D. B., Scarfe C. M., and Cronin D. J. (1985) The effect of fluorine on viscosities in the system Na2O-Al2O3-SiO2: Implications for phonolites, trachytes and rhyolites. Amer. Mineral. 70, 80-87. Doremus R. H. (1966) Physical solubility of gases in fused silica. J. Amer. Ceram. Soc. 49, 461-462. Ershova Z. P. (1957) Equilibrium of immiscible liquids in the systems of the MeF2-Al203-Si02 type. Geochem. International 4, 350-358. Ershova Z. P. and Olshanskii Y. I. (1957) Equilibrium of immiscible liquids of the MeF2-MeOSiO2 type. Geochem. International 3, 257-267'. HayatsuA. andWabosoC. E. (1985) The solubility of rare gases in silicate melts and implications for K-Ar dating. Chem. Geol. 52, 97-102. Hemley R. J., Prewitt C. T., and Kingma K. J. (1994) High-pressure behavior of silica. In Silica: Physical Behavior, Geochemistry and Materials Properties (eds. P. J. Heaney, C. T. Prewitt, and G. V. Gibbs), pp. 41-82, Mineralogical Society of America. Washington DC. Hirayama C. and Camp F. E. (1969) The effect of fluorine and chlorine substitution and fining of soda-lime and potassium-barium silicate glass. Glass Techn. 10, 123-127.

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HiyagonH. andOzimaM. (1986) Partition of noble gases between olivine and basaltmelt. Geochim. Cosmochim. Acta 50, 2045-2057. Holtz R, Dingwell D. B., and Behrens H. (1993) Effects of F, B2O3, and P2O5 on the solubility of water in haplogranitic melts compared to natural silicate melts. Contrib. Mineral. Petrol. 113, 492-501. Jambon A. (1987) He solubility in silicate melts: Atentative model of calculation. Chem. Geol.,62, 131-136. Jambon A. (1994) Earth degassing and large-scale geochemical cycling of volatile elements. In Volatiles in Magmas (eds. M. R. Carroll and J. R. Holloway), pp. 479-517, Mineralogical Society of America. Washington DC. Jambon A., Hartwig W., and Braun O. (1986) Solubility of He, Ne, Ar, Kr and Xe in a basalt melt in the range 1250°-1600°C. Geochemical implications. Geochim. Cosmochim. Acta 50, 401-409. Kirsten T. (1968) Incorporation of rare gases in solidifying enstatite melts. J. Geophys. Res. 73, 2807-2810. Kohn S. C, Dupree R., Mortuza M. G., and Henderson C. M. B. (1991) NMR evidence for fiveand six-coordinated aluminum fluoride complexes in F-bearing aluminosilicate glasses. Amer. Mineral. 76, 309-312. Kreinbrink A. T., Sazavsky C. D., Pyrz J. D., Nelson D. G. A., and Honkonen R. S. (1990) Fastmagic-angle-spinning 19F NMR in inorganic fluorides and fluoridated apatitic surfaces. J. Magn. Reson. 88, 267-276. Liu Y. and Nekvasil H. (2001) Ab initio study of possible fluorine-bearing four- and five-fold coordinated Al species in aluminosilicate glasses. Amer. Mineral. 86, 491-497. Liu Y. and Tossell J. A. (2003) Possible Al-F bonding environment in F-bearing Na-aluminosilicate glasses from calculation of 19F NMR shifts. J. Phys. Chem. B 107, 11280-11289. Luth R. W. (1988) Raman spectroscopic study of the solubility mechanisms of F in glasses in the system CaO-CaF2-SiO2. Amer. Mineral. 73, 297-305. Lux G. (1987) The behavior of noble gases in silicate liquids: Solution, diffusion, bubbles and surface effects, with application to natural samples. Geochim. Cosmochim. Acta 51, 1549-1560. Manning D. A. C. (1981) The effect of fluorine on liquidus phase relationships in the system QzAb-Or with excess water at 1 kb. Contrib. Mineral. Petrol. 76, 206-215. Manning D. A. C, Hamilton C. M. B., Henderson C. M. B., and Dempsey M. J. (1980) The probable occurrence of interstitial Al in hydrous F-bearing and F-free aluminosilicate melts. Contrib. Mineral. Petrol. 75, 257-262. Metrich N. and Rutherford M. J. (1992) Experimental study of chlorine behavior in hydrous silicic melts. Geochim. Cosmochim. Acta 56, 607-616. Miller J. M. (1996) Fluorine-19 magic-angle spinning NMR. Progr. Nucl. Magnetic Res. 28,255-281. Mysen B. O. and Virgo D. (1985) Structure and properties of fluorine-bearing aluminosilicate melts: The system Na2O-Al2O3-SiO2-F at 1 atm. Contrib. Mineral. Petrol. 91, 205-220. Mysen B. O., Cody G. D., and Smith A. (2004) Solubility mechanisms of fluorine in peralkaline and meta-aluminous silicate glasses and melts to magmatic temperatures. Geochim. Cosmochim. Acta 68, 2745-2769. Neuville D. R. and Mysen B. O. (1996) Role of aluminum in the silicate network: ln-situ, hightemperature study of glasses and melts on the join SiO2-NaAlO2. Geochim. Cosmochim. Acta 60, 1727-1738. Ozima M. (1998) Noble gases under pressure in the mantle. Nature 393, 303-304.

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Rabinovich E. M. (1983) On the structural role of fluorine in silicate glasses. Phys. Chem. Glasses 24, 54-56. Roselieb K., Rammensee W., Buttner H., and Rosenhauer M. (1992) Solubility and diffusion of noble gases in vitreous albite. Chem. Geol. 96, 241-266. SchallerT., Dingwell D. B., Keppler H., Knoller W., Merwin L., and Sebald A. (1992) Fluorine in silicate glasses: A multinuclear magnetic resonance study. Geochim. Cosmochim. Ada 56, 701-707. Schmidt B. C. and Keppler H. (2002) Experimental evidence for high noble gas solubilities in silicate melts under mantle pressures. Earth Planet. Science Lett. 195, 277-290. Seifert F. A., Mysen B. O., and Virgo D. (1983) Raman study of densified vitreous silica. Phys. Chem. Glasses 24, 141-145. Shackleford J. E, Studt P. L., and Fulrath R. M. (1972) Solubility of gases in glass. II. He, Ne, and H2 in fused silica. J. Appl. Phys. 43, 1619-1626. Shelby J. E. (1976) Pressure dependence of helium and neon solubility in vitreous silica. J. Appl. Phys. 47, 135-139. ShibataT., Takahashi E., andMatsuda J.-I. (1998) Solubility of neon, argon, krypton, and xenon in binary and ternary silicate systems: A new view on noble gas solubility. Geochim. Cosmochim. Acta62, 1241-1254. ShinoharaH., Iiyama J. T., and Matsuo S. (1989) Partition of chlorine compounds between silicate melt and hydrothermal solutions: I. Partition of NaCl-KCl. Geochim. Cosmochim. Ada 53, 2617-2630. Signorelli S. and Carroll M. R. (2000) Solubility and fluid-melt partitioning of Cl in hydrous phonolitic melts. Geochim. Cosmochim. Ada 64, 2851-2862. Signorelli S. and Carroll M. R. (2002) Experimental study of Cl solubility in hydrous alkaline melt: Constraints on the theoretical maximum amount of Cl in trachytic and phonolitic melts. Contrib. Mineral. Petrol. 143, 209-218. Stebbins J. F. and Du L.-S. (2002) Chloride sites in silicate and aluminosilicate glasses: A preliminary study by 35C1 solid-state NMR. Amer. Mineral. 87, 359-363. Stebbins J. F. and Zeng Q. (2000) Cation ordering at fluoride sites in silicate glasses: A highresolution 19F NMR study. J. Non-Cryst. Solids 262, 1-5. Stebbins J. F., Kroeker S., Lee S. K., and Kiczenski T. J. (2000) Quantification of five- and sixcoordinated aluminum ions in aluminosilicate and fluoride-containing glasses by high-field. high-resolution 27A1 NMR. J. Non-Cry st. Solids 275, 1-6. Studt P. L., Shackleford J. F., and Fulrath R. M. (1970) Solubility of gases in glass - A monoatomic model. J. Appl. Phys. 41, 2777-2780. Takusagawa N. (1980) Infared absorption spectra and structure of fluorine-containing alkali silicate glasses. J. Non-Cryst. Solids 42, 35-40. Taylor M. and Brown G. E. (1979) Structure of mineral glasses. II. The SiO2-NaAlSiO4 join. Geochim. Cosmochim. Ada 43, 1467-1475. Van Groos K. and Wyllie P. J. (1967) Melting relationships in the system NaAlSi3O8-NaF-H2O to 4 kb pressure. J. Geol. 76, 50-70. Van Groos A. F. K. and Wyllie P. J. (1969) Melting relationships in the system NaAlSi3O8-NaClH2O at one kilobar pressure, with petrological applications. J. Geol. 77, 581-605. Webster J. D. and Holloway J. R. (1988) Experimental constraints on the partitioning of Cl between topaz rhyolite melt and H2O and H2O+CO2 fluids: New implications for granitic differentiation and ore deposition. Geochim. Cosmochim. Ada 52, 2091-2105.

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Webster J. D. and De Vivo B. (2002) Experimental and modeled solubilities of chlorine in aluminosilicate melts, consequences for magma evolution, and implications for exsolution of hydrous chloride melt at Mt. Somma-Vesuvius. Amer. Mineral. 87, 1046-1061. Webster J. D., Kinzler R. J., and Mathez E. A. (1999) Chloride and water solubility in basalt and andesite melts and implications for magma degassing. Geochim. Cosmochim. Ada 63, 729-738. White B. S., Brearley M., and Montana A. L. (1989) Solubility of argon in silicate liquids at high pressures. Amer. Mineral. 74, 513-529. Wulf R., Calas G., Ramos A., Buttner H., Roselieb K., and Rosenhauer M. (1999) Structural environment of krypton dissolved in vitreous silica. Amer. Mineral. 84, 1461-1463. Wyllie P. J. and Tuttle O. F. (1964) Experimental investigation of silicate systems containing two volatile components. III. The effects of SO3, P2O5, HC1, and Li2O in addition to H2O on the melting temperatures of albite and granite. Amer. J. Sci. 262, 930-939. Yamamoto K., Nakanishi T., Kasahara H., and Abe K. (1983) Raman scattering of SiF4 molecules in amorphous fluorinated silicon. J. Non-Cryst. Solids 59&60, 213-216. Zeng Q. and Stebbins J. F. (2000) Fluoride sites in aluminosilicate glasses: High-resolution 19F NMR results. Amer. Mineral. 85, 863-867.

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Natural Melts Natural melts are formed by partial melting of rocks. Their composition is governed by the composition of the source rock, pressure, and temperature of melting, and by partial crystallization of minerals before final emplacement in the Earth's interior or on its surface. The melts that ultimately cooled to form magmatic or igneous rock. They comprise about 10 major element oxides (Table 17.1). The objective of this chapter is to describe structure and properties of such melts. We will do this by applying the data often obtained from chemically simple systems such as those of binary metal silicate and ternary metal aluminosilicate melts to the much more complicated natural glasses and melts. 17.1. Structure of Magmatic Liquids We will use major groups of igneous rocks to infer how their compositions govern the structure of their melts. To this end, chemical data from [http://earthchem.org] for rhyolite, phonolite, andesite, and tholeiite are employed (Table 17.1). Only analyses for which complete major element compositions are tabulated have been used. 17.1 a. Degree of Polymerization, Network Formers, and Network Modifiers The degree of polymerization (NBO/T) of natural melts at or near ambient pressure at temperatures above their liquidus can be calculated quantitatively from chemical composition with the procedure summarized in chapter 4 (Table 4.2). The distribution of Table 17.1 Average compositions of major magmatic liquids [http://earthchem.org] No of analyses SiO 2 TiO 2 A12O3 FeO(T) MnO MgO CaO Na2O K2O P2O5

Tholeiite 532

Phonolite 560

50.29±2.37 2.06±0.82 14.79±1.82 10.94±1.59 0.1810.03 7.1512.5 10.09+1.38 2.4110.55 0.53+0.38 0.2610.12

56.5613.72 0.8710.63 19.3115.40 4.02+1.73 0.24+1.05 2.4711.86 1.18+2.28 8.21+1.57 5.2311.01 0.2110.20

Andesite 1967

Rhyolite 764

57.5114.08 0.9311.55 16.9311.45 7.0811.85 0.1410.05 3.9011.82 7.1711.85 3.4210.77 1.5110.86 0.23+0.13

72.1813.52 0.3910.29 13.2311.50 2.9011.79 0.1010.19 0.4810.51 1.5311.24 4.03+1.09 3.7911.42 0.09+0.09

Chapter 17

504 I

I

I

I

I

I

I

rhyolite(0.03) 30

\ phonolite(0.18) 20

-

\ \ 10

0

0.0

andesite(0.38)

\ \ A\

0.2

0.4

0.6

tholeiite(0.83)

A

0.8

1.0

1.2

Figure 17.1 - Distribution of nonbridging oxygens per tetrahedrally coordinated cations, NBO/T, of melts of major rocks groups as indicated. Numbers in parentheses are the NBO/T-values corresponding to the maximum of the individual distribution curves. The number of analysis within each group is the average values in Table 17.1 [analyses from http://Earthchem.org].

1.4

NBO/T NBO/T within each group is nearly log-normal (Fig. 17.1). Although there is some overlap in NBO/T-values, each group has a distinct maximum in its distribution function. These maxima decrease systematically as the melts become more felsic. The average NBO/Tvalue of each of the groups follows the same trend (0.83±0.21, 0.41±0.16, 0.20±0.18, and 0.09±0.08, for tholeiite, andesite, phonolite, and rhyolite melts, respectively). The tetrahedrally coordinated cations in natural melts are for the most part Si4+ and 3+ Al . Tetrahedrally coordinated Al3+ requires charge-balance ust as in simple systems (see section 4.2a). An understanding of how charge-balance in natural melts is accomplished is important because the structural environment near alkalis and alkaline earths serving to charge-balance trivalent tetrahedrally coordinated cations differs from that around the same cations when serving as network-modifiers [e.g., Ispas et al., 2002; Cormier et al., 2003; Xue and Stebbins, 1993; Lee and Stebbins, 2003]. We can calculate the fractions of charge-balancing cations from structural and thermodynamic data of aluminosilicate melts. Structural data are consistent with all or nearly all Al3+ residing in Q4-species in silicate melts and glasses (see Chapter 9) at least in the NBO/T-range relevant to natural magmatic liquids. Thus, heat of solution data of glasses near meta-aluminosilicate joins [Navrotsky et al., 1985] can be used to establish the relative stability of alkali and alkaline earth charge-balanced Al3+ (and, perhaps, Fe3+). Those thermodynamic data indicate near equal stability of (KA1)4+ and (NaAl)4+ chargebalance followed by (Ca0 5A1)4+ and, finally, (Mg^Al) 4 *. This hierarchy is in accord with that suggested by Hess and Wood [1982] from their study of Al-partitioning between immiscible silicate melts. The several thousand analyses of natural melts considered here indicate that K+, Na+, and Ca2+ serve to charge-balance tetrahedrally coordinated cations (Fig. 17.2). Ferrous iron and Mg2+ never serve in this structural role. For andesitic and less felsic melts, the main charge-balancing cation is Ca2+. The proportion of Ca2+ relative to (Na+K)+, however, decreases with more felsic melts so that in rhyolite and phonolite alkali charge-balanced

505

Natural Melts phonolite

tholeiite 100

100

I

• I

•

Na+K

.a

to T3
CO

T3

I

J2

60

-

40

—o

•

d> to

e

O 0 0.0

0.8

•

SB

m

CO

20

O 0

f o

-mCS


C

oCa

utio

fiA8

4

1

m

1B

Is

0.4

^Hb^ •-•

1

-

Na+K -

*-;

60

jg

40

D) CO

1

1

•1

0

•CO

0.2

80

dis

40 -ma's

a °

I

100

s-ba

% 60

2

I

O»

1.5

rhyolite

I

80

I 1.0

0.5

NBO/T

andesite o

«•

Ca

NBO/T 100

-

0

20

O

oo

a

0

CO

o jg co .a

_

80

3

•*

• • 1 0.6

NBO/T

Na+K 1 0.8

-I 1.0

.c O

20 0

| ^ F .

1 Ia5

s o

^

o

1 H 1 Ull E u 1 I D O

0.2

8 _

Ca

n

Koi

J

•

Sffii* o^o

L^

0.0

# O

0

o#

fT^

rn 1

0.4

1

-

0.6

NBO/T

Figure 17.2 - Percentage of Na+K and Ca serving to charge-balance Al3+ in tetrahedral coordination in magmatic liquids as indicated on individual panels. The number of analysis within each group is the number in the average values in Table 17.1 [analyses from http://Earthchem.org]. Al3+ dominates over Ca+-charge-balanced Al3+ (Fig. 17.2). Among the four rock groups evaluated here, phonolite melts have the highest proportion of alkali charge-balanced Al3+ and tholeiite melts the lowest. In andesitic and tholeiitic melts, all available Na+K is consumed for this purpose, whereas there exist some compositions among rhyolite and phonolite where there is excess Na+K over that required to charge-balance Al3+ in tetrahedral coordination. A consequence of the results in Fig. 17.2 is that in the most felsic liquids (phonolite and rhyolite) about 20% or less of total alkalis are network-modifiers, and between 20 and 80 % of total Ca2+ serve the same purpose (Fig. 17.3). In less felsic melts such as

Chapter 17

506 tholeiite

phonolite

100 BF

100


0.8

NBOAT

1.2

andesite 100 9

E

o

80 o

o

E o

60

~

CD

0

O

ent

CO

y

20

n

0

TO

^£

m 0.2

o

°

Mi 0.4

c

O% rfD

Pet* 0.6

> o 0

00 n |O 3 ° • Mg o Ca • Na

0.8

1.0

NBOAT

Figure 17.3 - Percentage of Na+K and Ca serving as network-modifiers in magmatic liquids as indicated on individual panels. Note that the percent of Mg is offset by 1 % from 100 % for clarity. The number of analysis within each group is the number in the average values in Table 17.1 [analyses from http://Earthchem.org]. andesite and tholeiite, alkali metals are never network-modifiers because Na+K serve exclusively to charge-balance Al3+ in tetrahedral coordination. A fraction of Ca2+ is also a network-modifier in such melts, whereas Mg2+ and Fe2+ are always network modifiers (Fig. 17.3).

Natural Melts

507

17.1b. Q'-Species The distribution of alkali metals and alkaline earths between charge-balancing and network-modifying structural positions (Figs. 17.2, 17.3) leads to the conclusion that Qn -speciation in natural melts for the most part is best modeled as alkaline earth aluminosilicate melts. Alkali aluminosilicate structure components contribute only to some rhyolitic and phonolitic melts. The structural data of alkali-alumina-silica and alkaline earth-alumina-silica melts, without exception, are consistent with an equilibrium of Qn-species of the type (see Chapter 9): 2Qn oQ" +1 +Q nl .

(17.1)

In alkali aluminosilicate melts in the NBO/T-values less than unity, more than 98% of the structure can be described with n = 3. About 95 % of the rock analyses used in our discussion of molten rock have NBO/T<1, which suggests that Q4, Q\ and Q2 are the principal species in most natural magmatic liquids. As alkaline earths rather than alkalis are the principal network-modifying cations, we need to consider how these cations may affect the equilibria among the Qn-species. Structural data for CaO-SiO2 and MgO-SiO2 melts do not reach compositions even as polymerized as NBO/Si = 1 because of liquid immiscibility [Osborn and Muan, 1960; see also Fig. 6.1]. For melts with NBO/Si > 1, Raman data suggest that the abundance of Q3-species is significantly suppressed compared with alkali silicate melts [Frantz and Mysen, 1995]. This observation is consistent with structural data from binary alkali oxide melts, which indicate that equation (17.1) shifts to the right with increasing ionization potential of the alkali metal (see Chapter 7). Addition of Al3+ to any metal oxide melt system drives reaction (17.1) further to the right because this Al3+ exhibits a strong preference for Q4-species over the less polymerized Q3- and Q2-species [Mysen et al., 1981; Merzbacher et al., 1990; Mysen, 1999; Lee and Stebbins, 2000; Cormier et al., 2003; Neuville et al., 2004]. This preference can also lead to formation of even less polymerized species such as Q1 [Mysen, 1999]. Quantitative structural information for alkaline earth aluminosilicate glasses and melts needed to compute Qn-concentrations in natural melts is not available, however. Nevertheless, it is clear from existing data that the 3 dominant species are Q\ Q\ and Q2 with subordinate fractions of Q'-species. Most likely Q4- and Q3-species dominate in rhyolite and phonolite melts, whereas Q2 species are more significant in andesite and less felsic magmatic liquids. In all melts, Al3+ resides primarily in Q4 structural units. 17.2. Properties of Magmatic Liquids Physicochemical properties of natural melts are needed to describe the formation and evolution of magmatic rocks. A large experimental data base of melt properties and mineral/melt equilibria has been developed from direct experimental determination. Some of these have been used

508

Chapter 17

to create empirical models to describe and predict property behavior. However, use of empirical models without theoretical basis to model properties of melts outside the range of compositions used to formulate the model must be exercised with great caution. From the information discussed in the previous chapters, quantitative and more qualitative comments can be made on how structure and properties natural melts can be correlated. Some principles will be presented here. Purely empirical models based on regression of properties as a function of oxide composition will not be discussed unless the results of such regression can be evaluated in melt structural terms. In the application of property data from chemically simple systems to more complicated natural silicate melts (magmatic liquids), mixing of multiple networkmodifying cations in principle require consideration of the so-called "mixed alkali effect" [Day, 1976]. This effect results in variations in physical properties that cannot be explained in terms of simple mixing models and occurs whenever either alkalis or alkaline earths compete for specific sites in silicate melts [Yap and Elliott, 1995; Habasaki et al, 1995; Park and Cormack, 1999]. Existing simulation and experimental data, however, are insufficiently detailed to be applied quantitatively to natural silicate melts. Therefore, this effect will not be considered in the discussion in this chapter. 77.2a. Molar Volume and Melt Density Molar volume (density) information is critical for our understanding of magmatic processes in the Earth. Measurements for the most part have been carried out so as to extract partial molar volumes, thermal expansion, and compressibility of oxide components in the melts [e.g., Bottinga and Weill, 1970; Bottinga ef a/., 1982,1983; Lange and Carmichael, 1987; Kress and Carmichael, 1991]. A number of detailed studies focus on behavior of specific oxides or small groups of oxides [e.g., Dingwell and Brearley, 1988; Kress and Carmichael, 1991; Tangeman and Lange, 1996]. For melts containing all the major components in natural magmatic liquids, Lange and Carmichael [1987] concluded that the molar volume, V, of a melt (with the exception of Ti-bearing melts) is,

i=\

()

where X. is mol fraction and y-t is partial molar volume of oxide, i. In this treatment, y(is considered independent of melt composition. Thermal expansion and compressibility were considered constant and are, therefore, independent of composition, temperature, and pressure. Whereas the Lange and Carmichael [1987] data were obtained with chemically complex melts resembling natural compositions, Bottinga et al. [1982, 1983] used data from simple binary and ternary melt systems to develop a data base and algorithms that could be used to calculate molar volume and thermal expansion of natural silicate melts.

509

Natural Melts i

1

A

•

%L

eiite(242)^

c

CO

2 201/

10-

vX

/

A / -

22

XA

/

1 I1 24

i

- rhyolite(2 28.8)"

30-

|OI

Figure 17.4 -Distribution of molar volumes of melts of major rocks groups as indicated. Numbers in parentheses are the volumes corresponding to the maximum of the individual distribution curves. Molar volume calculated with the model of Bottinga et al. [1982, 1983]. The number of analysis within each group is the same as in the average values in Table 17.1 [analyses from http://Earthchem.org].

1

ite (26.4)

40

to

/ / ">

\1

0) V

j

? / Y \ // ™/A

o

-c

7/\ y

26

••=

\

°- \

28

Molar volume, cm 3 /mol

30

This treatment has the advantage in that effects of individual oxides could be more clearly identified than in the multicomponent treatment by Lange and Carmichael [1987]. At constant temperature, the molar volume in this treatment is,

1=1

(17.3)

where V* is a constant,;' are components A12O3, Na 2 O, K2O, MgO, CaO, and FeO, xA is the mol fraction of A12O3, and A", are constants associated with components,;. This treatment does, therefore, take into account effects of bulk composition and, in particular, the role of A12O3.There is also an exponential term needed to account for thermal expansion, but this will not be discussed here. We will use the Bottinga et al. [1982, 1983] formulations to calculate molar volume of natural magmatic liquids. From this calculation, the molar volume distribution of tholeiite, andesite, phonolite, and rhyolite melts are distinctly different with the volume maxima increasing the more felsic the melts (Fig. 17.4). The average molar volumes for each group of melt follows the same trend (24.2±0.8, 25.9±0.8, 27.9±1.1, and 27.9±0.5 cmVmol for tholeiite, andesite, phonolite, and rhyolite melts, respectively). Expressed in terms of molar volume as a function of NBO/T of the melts, it decreases systematically with decreasing degree of melt polymerization (Fig. 17.5), a trend resembling that observed in binary metal oxide melt systems (see Bottinga and Richet [1995] for summary of relevant data). Thus, natural magmatic liquids resemble simple silicate melts in that the partial molar volume of nonbridging oxygen is less than that of bridging oxygen.

Chapter 17

510 1

ou

i

O ^ k phonoli!e{560)

; !

o

• • o o


28 '

basalt phonolite andesite rhyolite

o

I

phonolile(560)

o

^fl^fc^o^H

o

24 •

•

22

0.0

0.5

1.0

1.5

2.0

NBO/T

Figure 17.5 - Molar volume of natural melts indicated as a function of their NBO/T. Molar volume calculated with the model of Bottinga et al. [1982, 1983]. Numbers in parentheses denote the number of data points within each rock group [analyses from http://Earthchem.org].

The volume relationship of natural magmatic liquids does show a spread of about 1 cm 3 /mol for any NBO/T-value (Fig. 17.5) suggesting that even though the main control is the proportion of nonbridging oxygens, other factors such as alumina content also play a role. The Al/(A1+Si) ratio, however, alone does not explain the spread because the relationship between volume and NBO/T remains between 0.5 and 1.0 cmVmol even for melts with fixed Al/(A1+Si) (Fig. 17.6a). In fact, as shown by the absence of correlation between molar volume and Al/(A1+Si), if there is an influence of Al3+ it is more subtle than simple proportions of Al3+ relative to Si4+. One refinement would be to consider the fact that all Al3+ likely resides in Q4 species in natural melts. Absent detailed knowledge of proportion of Q4-species in natural melts, this effect cannot be tested. Another refinement is the type of charge-compensation of Al3+, which is also a factor that requires more structural data from alkaline earth aluminosilicate melts before realistic testing can be carried out. Finally, the proportion of nonbridging oxygen in each of the Qn-species of the melt differs. As the partial molar volume of each of the Qn-species, therefore, must also be

Natural Melts

o o CD

| (0

o

-

25.5

_

i

i

i

i

AI/(AI+Si)=0.25±0.01 _

25.0 •

24.5

_

24.0

-

23.5

m

mjtm

-

o o

25.0

24.5

to

#^

"5

24.0

.

23.0 _ a i

0.4

25.5

.£

1

•<5rf « ^SP

o

vol

•i

26.0

511

0.6

i

i

0.8

1.0

••

•

••

•

.i

1.2

0.24

0.26

0.28

0.30

NBO/T

Figure 17.6 - Molar volume of tholeiite melts as indicated as (a) a function of their NBO/T with Al/(Al+Si)=0.25±0.01, and (b) as a function of Al/(A1+Si) with NBO/T=0.80±0.05. Molar volume calculated with the model of Bottinga et al. [1982, 1983]. [Analyses from http://Earthchem.org]

different, any variation in Qn-species abundance driven by different network-modifying cation will cause the molar volume to change. In summary, molar volumes of natural melts are semi-quantitatively correlated with melt polymerization. There are, however, additional factors indicated from simple system studies. These cannot be quantified for chemically complicated natural melts, however, until more structural data of alkaline earth aluminosilicate melts become available. 17.2b. Viscosity Viscosity impacts virtually all aspects of magmatic processes. Rheological data are needed to assess how the structure of natural silicate melts governs their viscosity. One could accomplish this by measuring the viscosity of all possible types of magmatic liquids. This is, of course, an unrealistic method. Viscosity models have been developed on the basis of more limited data. An early and, in principle, successful approach to this problem was the model by Bottinga and Weill [1972]. They assumed that the viscosity of a silicate melt could be expressed as an additive function of the mol fractions of their oxide components, x, within narrow ranges of their concentration (10 mol %), (17.4) except in the case of Al3+ where aluminate components were used and an equivalent fraction of charge-balancing cations was subtracted from the appropriate oxide. The D. is

Chapter 17

512

a regression coefficient obtained by fitting viscosity melt data from a variety of simple systems. A fundamental question about this model is whether melt viscosity is additive. In other words, can the Z> coefficients be independent of melt composition? In light of more recent work on melt viscosity (see, for example, Richet and Bottinga [1984], Toplis [1998]), constant Devalues are not likely to be accurate. A fairly comprehensive viscosity model (in terms of the size of the experimental data base) is that of Giordano and Dingwell [2003,2004]. Their input data are experimental viscosity measurements of natural melt compositions, which carry the potential of canceling composition effects, as is also true for other such models. We will, nevertheless use calculated viscosities of natural melts using this model, log r] = c,+[c2c3/(c3+,SM)],

(17.5)

where cy, c2, and c3 are numerical parameters derived by least-squares fitting and carry only temperature as a variable. The SM is the molar oxide sum, Na,O+K,O+CaO+MgO+MnO+FeO ,12. The fact that SM does not contain contributions 2

°

2

total

from either of the major components, SiO2 and A12O3, is cause of concern because the concentration of these two oxides are important factors in melt viscosity. Most likely, their influence is hidden in the complex nature of the c 1 3 parameters. Viscosity in the 1200°-1600°C temperature range was calculated with this model to obtain a high-temperature activation enthalpy of viscous flow, AH . In this temperature range, the calculated melt viscosities are Arrhenian, which yields the activation enthalpies of high-temperature viscous flow for tholeiite, andesite, phonolite, and rhyolite melts shown in Figs. 17.7 and 17.8. The maxima in the energy distribution of individual groups cover about 50 kJ/mol with, broadly speaking, an increase in both the maximum values

10

- /

0

130

rhyolite(166)

- I *" I

>

'[

20

phonoliite(1 51)

CD Q_

30

>

o

ioleiite(1

40

-/ \ I1 j ancles ite(-145)

50

\

140

150

160

170

Activation enthalpy, kJ/mol

180

Figure 17.7 - Distribution of hightemperature (1200°-1600°C) activation enthalpy of viscous flow of major melts of major rocks groups as indicated. Numbers in parentheses are the activation energies corresponding to the maximum of the individual distribution curves. Activation enthalpies were calculated with the model of Giordano and Dingwell [2003, 2004]. The number of analysis within each group is the number in the average values in Table 17.1 [analyses from http://Earthchem.org].

513

Natural Melts |

1

180 •

o

E

1

|

• • 0 0

1o

i !

basalt phonolite andesite rhyolite

_

—

170 '

: <

—3 "*;

—

160

alpv

x7

—

ion

0

«^^&' " 150 ,

"Jo .> 0 <

: 140

• 130

—

0.0

• «

0

1

0.5

*1

^ ^

•

1

•

1.0

•

• 1 1.5

2.0

NBOAT Figure 17.8 - High-temperature (1200°-1600°C) activation enthalpy of viscous flow of natural melts indicated as a function of their NBO/T. Activation enthalpies were calculated with the model of Giordano and Dingwell [2003, 2004]. Numbers in parentheses denote the number of data points within each rock group [analyses from http://Earthchem.org]. and in the average activation enthalpies as the melts become more felsic (average AH = 135±3, 142±5, 146±5, and 167±7 kJ/mol, for tholeiite, andesite, phonolite, and rhyolite melts, respectively). The calculated activation enthalpy of viscous flow of these natural melts decreases as an exponential function of NBO/T with a rapid decrease in the NBO/T-range between about 0 and about 0.3 and a much slower decrease as the NBO/T increases further (Fig. 17.8). This trend is similar to that of high-temperature activation enthalpy of viscous flow of melts along binary metal oxide-silica joins where AH is nearly independent of metal/silicon ratio above about 0.3 to values near 0.5 [Bockris et ai, 1955, 1956]. The range in natural melts is, however, only about 15 % of the range from metal oxide systems in the same

Chapter 17

514 o

n 155 150 -

<0 CD

i

m

* 1

O (£

145 -

i

i

• phonolite O andesite

_

170

• phonolite O andesite

NBOAT=0.20±0.05

AI/(AI+Si)=0.25±0.01

o

O

140 -

a

O i

0.24

0.28

0.32

1 1 130

0.4

0.6

1.0

NBO/T

Figure 17.9 - High-temperature (1200°-1600°C) activation enthalpy of viscous flow of phonolite and andesite melt (a) as a function of their Al/(A1+Si) at NBO/T=0.20±0.05, and (b) as a function of NBO/T at Al/(Al+Si)=0.25±0.01. Activation energies were calculated with the model of Giordano andDingwell [2003, 2004] [analyses from http://Earthchem.org]. NBO/Si-range. This difference is likely because of the A12O3 content of natural melts. Alumina causes distinct reductions in AH [Riebling, 1964, 1966; Toplis et ai, 1997]. There is considerable scatter in the AH -trend in particular for intermediate compositions such as andesite and phonolite melts (Fig. 17.8). This scatter may be in part because natural melts contain significant proportions of Al3+. That would be consistent with observations from simple aluminosilicate systems where there is a negative correlation between Al/(A1+Si) and high-temperature activation enthalpy [Riebling, 1999; Toplis et al.,1997]. Such an effect can also be discerned in the calculated viscosity trends of natural melts (Fig. 17.9a). Interestingly, the activation energy of andesite melts is more sensitive to Al/(A1+Si) than phonolite melt. That may be because a larger fraction of tetrahedrally coordination Al3+ in phonolite melt is charge-balanced by alkalis than in andesite melt (Fig. 17.2). We also note that for melt with nearly constant Al/(A1+Si) the scatter in the AH versus NBO/T is considerably reduced (Fig. 17.9b). The remaining scatter in Fig. 17.9b is probably because even in binary metal oxide systems, the high-temperature activation enthalpy of viscous flow is also somewhat dependent on the type of networkmodifying cations [Bockris et al., 1955, 1956]. In the natural melts, there are several different network-modifying cations (for the most part Ca, Mg, and Fe2+). 17.2c. Volatiles in Magmatic Liquids In natural melts, the most important volatiles are H2O, CO2, and sulfur species (Fig. 17.10). Among these, H2O has received by far the most attention and will be discussed here. For other volatiles, our understanding remains too limited for detailed discussion. Reviews

515

Natural Melts

I 1200 1000

3

o

800

W

600

2? c g 2

C + O +A

400 200

C + O +A C + O +A C + O +A

o

§

O

M-degassed mantle C-crust O-ocean A-atmosphere

M

H2O

Carbon as CO 2

Sulfur as S

J.M

F+Cl

Figure 17.10 - Concentration of major volatile components in the silicate earth [Jambon, 1994].

of their solubility and solubility mechanisms can be found in Holloway and Blank [1994] and Carroll and Webster [1994]. Even in the case of water, however, our understanding of its behavior in natural melts often is not quantitative. This, most likely is because the complexity of its solution mechanisms in silicate melts has yet to be fully appreciated. For example, for H2O nearly all experimental data on structure and properties have been conducted with melts at or near meta-aluminosilicate where the melts are fully or nearly fully polymerized (see Chapter 9). Information from such systems can be used with some confidence for highly polymerized natural aluminosilicate melts such as rhyolite (Fig. 17.1). However, application to less felsic melts such as andesite and basalt is not straightforward because so little data exist on which basis one could develop an understanding of water solution mechanisms in these melts. Those limitations notwithstanding, several water solution models have been proposed [e.g. , Spera, 1974; Burnham, 1975; Silver and Stolper, 1985, 1989; Dixon and Stolper, 1995]. All but the model developed by Stolper and coworkers are largely empirical. Those models were developed based on limited water solubility data and, in one case [Burnham, 1975], with the aid of some thermodynamic data of simple water-bearing aluminosilicate melts. Those models will not be discussed further here. The model by Stolper and coworkers [Silver and Stolper, 1985, 1989; Dixon and Stolper, 1995] is probably the only one with the potential to be used to characterize water solubility in silicate melts regardless of silicate composition. It has a melt structural foundation in that it takes advantage of the fact that water dissolves partly as molecular H O and partly as OH-groups, and is based on the equilibrium, H,O(melt) <=> O(melt)+2OH(melt),

(17.6)

Chapter 17

516 P H2 o, MPa 200

400

600

Figure 17.11 - Water solubility in silicate melts calculated by Dixon et al. [1995] (line) compared with experimental determination of solubility (data points). 200

400

600

800

f H 2 o, MPa

where O(melt) denotes oxygen in the melt with no distinction between bridging and nonbridging oxygen. By fitting spectroscopic data of the proportion of molecular H2O and OH-groups in silicate glasses, and combining those results with an evaluation of the equilibrium between water as molecular H2O in melts and H2O in coexisting fluid, Dixon and Stolper [1995] reproduced the water solubility in a range of chemically simple as well as more complicated natural basalt melts (Fig. 17.11). It should be noted that there are several assumptions in this model. These require further attention. It was assumed that the partial molar volume of water in silicate melts, V'HLO > is independent of water content and melt composition (12±1 cmVmol). This is not a universally accepted conclusion because reported V'HVO - v a m e s range from near 0 to > 20 cmVmol [Burnham and Davis, 1971; Hodges, 1974; Silver and Stolper, 1989; Silver et al, 1990; Ochs and Lange, 1997, 1999; Richet and Polian, 1998; Mysen and Wheeler, 2000; Mysen, 2002]. Most recent data converge on values near 12 cm3/mol for water in silicate glass. This is not necessarily a constant value in silicate melts, however, because the thermal expansion (and compressibility) of glasses and melts differ significantly. It is known that V'HVO depends on Al/(A1+Si) of the melt probably because the solution mechanisms of water does [Mysen, 2002]. There may also be effects of ionization potential of the metal cation at least in binary metal oxide silicate and ternary metal oxide aluminosilicate melts [Mysen and Wheeler, 2000]. We do not have much, if any, information on effects of pressure and concentration of water in the melts. It was also assumed that the enthalpy of solution of water is equal to that reported for water in NaAlSi3O8 melt [Silver and Stolper, 1985]. Whether or not this is a valid assumption requires experimental verification. It seems reasonable to assume, though, that because water solubility mechanisms depend on silicate melt composition and perhaps also on pressure (see Chapter 15), there may be variations in enthalpy of solution that need to be taken into account when modeling solubility of water in natural silicate melts.

517

Natural Melts

Finally, the solubility model of Stolper and coworkers requires experimentally determined concentrations of OH-groups and molecular H2O at high temperature and pressure. In the Silver et al. [1990] and earlier applications of the model, they relied on spectroscopic data from hydrous silicate glasses. The OH/H2O ratio depends, however, on temperature above the glass transition (Chapter 14, see also Dingwell and Webb [1990]; Nowak and Behrens [1995, 2001]; Shen and Keppler [1995]; Sowerby and Keppler [1999]). We do not know how these temperature relations may affect the water solubility in natural magmatic liquids. Thus, even though the Stolper solution model has the potential to characterize the solubility of water in natural magmatic liquids, much additional experimental data are needed before it can be used with confidence for all melt compositions. 17.2d. Mineral/Melt Equilibria A central goal in studies of relationships between structure and properties of silicate melts is the ability to describe liquidus phase relations and element partitioning between mineral and melts for natural compositions. Some of the most important principles were discussed in Chapters 3, 6-9. Attainment of this goal requires structural understanding of activity-composition relations in silicate melts and minerals. Our understanding of silicate melts is not yet at a stage where this can be fully realized although some principles have been identified (see Chapter 7). Alternative models that rely on liquidus phase relations, thermodynamic data, and formulation of a regular solution model of chemically complicated silicate melts are available, however, as codified, for example, in the MELTS model [Ghiorso and Sack, 1995]. We emphasize that this model is not based on melt structural information. Thus, it is not possible to discuss liquidus phase relations calculated by this model in melt structural terms. Element partitioning between minerals and melts is another area subject to considerable effort because this knowledge is central to characterization of the evolution r

100

i

i

i

i

i

i

i

i

i

10 CD c LU

0.1

• Rhyolite • Andes ite Hawaiite Nephelinite • Olivine basalt

0.01 I

La

I

Ce

I

Pr

I

I

I

I

I

I

I

I

I

I

I

I

Pm Eu Tb Ho Tm Lu Nd Sm Gd Dy Er Yb

Figure 17.12 - Rare earth (REE) partition coefficients between garnet and melt (wt ratio, garnet/melt) from phenocryst/matrix pairs of natural rocks as indicated [Irving and Frey, 1978].

518

Chapter 17 I

i

I

i

.

i

a

2.0 1.5

_

15-

|j>10 • •

3/silicat e melt

20

1.0 0.5 > >

CO i1 C

'

5 -1068°C

i i i i i i 0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 NBO/T

0.0 -0.5

0.0

Figure 17.13 - Partition coefficients for (a) between clinopyroxene (cpx) and melt as a function of NBO/T of the melt at 1068T [Toplis and Corgne, 2002], and (b) between liquid Fe and silicate melts as a function of NBO/T of the silicate melt [Jaeger and Drake, 2000]. of igneous rocks [e.g., Green, 1994]. Partition coefficients (element concentration in mineral/element concentration in melts) can vary widely, however, as a function of melt composition [e.g., Watson, 1977; Hart and Davis, 1978; Jurewicz and Watson, 1988; Colson et al., 1988; Libourel, 1999; Jaeger and Drake, 2000; Walter, 2001; Toplis and Corgne, 2002]. An example with rare earth partitioning between garnet and natural magmatic liquids illustrates the effect (Fig. 17.12). The observation that the activity of high field strength cations in silicate melts often are simple functions of SiO2 content lends further support to this concept [e.g., Watson and Harrison, 1983; Ellison and Hess, 1986]. Furthermore, in simple systems, the Si/O ratio of melts has long been known to be a useful measure of the effect of melt composition of mineral/melt element partitioning [e.g., Watson, 1977; Hart and Davis, 1978]. It follows that the activity-composition relations in silicate melts depend on melt composition and, therefore, on melt structure. It has been proposed that melt polymerization, NBO/T, can be used to quantify effects of melt composition of partition coefficients [Mysen and Virgo, 1980; Walker and Thibault, 1995; Jana and Walker, 1997; Jaeger and Drake, 2000]. However, there is no unifying relationship between partition coefficients and the NBO/T of the melt (Fig. 17.13). These relationships are sometimes linear [Mysen and Virgo, 1980; Jaeger and Drake, 2000], but more often than not are nonlinear functions of NBO/T [Kohn and Schofield, 1994; Toplis and Corgne, 2002]. It is likely that the different relations between partition coefficients and NBO/T of the melt exist because most geochemically important trace elements are network modifiers. Network-modifying cations exhibit preference for nonbridging oxygen in individual Q n -species in silicate melts (section 7.4a). The abundance of Q n -species is never a linear function of melt composition (e.g., Fig. 7.8). One would expect that the activity/ solution relations of such elements in silicate melts and, therefore, their mineral/melt

519

Natural Melts 0.36

0.24 0.0

1.0

NBO/T

2.0

3.0

1.0

1.5

2.0

2.5

NBO/T

Figure 17.14- Exchange equilibrium coefficients [(see equation (17.8)] for (a) Fe2+ and Mg between coexisting olivine and silicate melt at 1350-1380°C, ambient pressure and-log/ O2 = 7.5 [Kushiro and Mysen, 2002] and (b) for Ca and Mn between olivine and melt at 138O°C, ambient pressure, and -log/ O2 = 0.68 [Mysen and Dubinsky, 2004] both as a function of NBO/T of the melt. partitioning, reflects Qn-species abundance whether in simple systems or in chemically more complicate natural melts. There is, for example, a striking similarity of the topology of Fe2+-Mg and Ca-Mn olivine/melt exchange equilibrium coefficients and NBO/T of the melts in the 8-component system K 2 O-Na 2 O-CaO-MgO-MnO-FeO-Al 2 O 3 -SiO 2 (Fig. 17.14) and the Q3-abundance evolution with NBO/T of the melt. This system comprises nearly all the major element components of natural melts. It has been suggested that relationships such as those in Fig. 17.14 reflect changes in activity coefficients ratios of the pairs of cations, Fe2+/Mg and Ca/Mn, in the melt as Q" abundance changes [Kushiro and Mysen, 2002; Mysen and Dubinsky, 2004]. This is because for the principal exchange equilibrium of two components, i and j , z(melt)+/(melt) <=> j'(mineral)+/'(melt)

(17.7)

with the exchange equilibrium constant: i

=

[ai(mineral)»aj(melt)]/[<2i(melt)«aj(mineral)],

(17.8)

where ^(mineral/melt) is the activity of i in the mineral/melt, the exchange equilibrium constant, KD \_j m i n e r a l / m e I t , is proportional to the activity coefficient ratio, = Constant»[yi(melt)/yj(melt)],

(17.9)

provided that the solution behavior of the elements in the mineral is Henrian or Raoultian. From relationships such as those in Fig. 17.14, the activity coefficients of cations in silicate melts can be correlated with their ionization potentials, Zlr2. For a pair of network-

520

Chapter 17

modifying cations with different Z/r2, / and j , with Z/r2(j)>Z/r2(i), exchange equilibrium constants between crystal and melt will exhibit a minimum or a maximum at intermediate NBO/T of the melt. This behavior of KQ-_ / i s because the ionization potential (and possibly crystal field stabilization effects when relevant) of cations i andj governs ordering of / andy among nonbridging oxygen in coexisting Qn-species in the melt (see chapter 4). Thus, melt composition effects governing Qn-speciation and electronic properties of bonding within and between Qn-species also control mineral/melt element partitioning. 17.3. Summary Remarks 1. Structural data from chemically simple melt systems can be applied to chemically more complicated natural systems to extract systematic relationships with melt composition, degree of polymerization (NBO/T), and distribution of alkali metals and alkaline earths between network-modifying positions and charge-balancing positions for tetrahedrally coordinated Al3+. 2. It follows from those relationships that alkaline earths are the dominant networkmodifying cations in natural melts. Thus, the Qn-speciation likely is governed by structural relationships such as those in alkaline earth silicate and aluminosilicate melt systems. 3. Properties that can be related to polymerization and Qn-speciation do, therefore, exhibit systematic relationships to these variables in natural melts. These include volume and transport properties. 4. Other melt properties that are functions of Qn-speciation include activity/composition relations and, therefore, element partitioning between coexisting minerals and melts. Ultimately, such relations also govern liquidus phase relations. 5. Ideally, characterization of many melt properties should be possible in terms of partial molar quantities of the Qn-species, aluminate components, and so on. This approach has been successful for properties such as heat capacity and molar volume in binary silicate melts [Mysen, 1995]. It could be extended, in principle, to complex natural melts once we have quantitative speciation data and partial molar quantities associated with structural species. References Bockris J., O'M., Mackenzie J. O., and Kitchener J. A. (1955) Viscous flow in silica and binary liquid silicates. Trans. Faraday Soc. 51, 1734-1748. Bockris J. O. M., Tomlinson J. W., and White J. L. (1956) The structure of liquid silicates. Trans. Faraday Soc. 52, 299-311. Bottinga Y. and Weill D. F. (1970) Densities of liquid silicate systems calculated from partial molar volumes of oxide components. Amer. J. Sci. 269, 169-182. Bottinga Y. and Weill D. F. (1972) The viscosity of magmatic silicate liquids: A model for calculation. Amer. J. Sci. Ill, 438-475.

Natural Melts

521

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Holloway J. R. and Blank J. G. (1994) Application of experimental results to C-O-H species in natural melts. In Volatiles in Magmas, (eds. M. R. Carroll and J. R. Holloway), pp. 187-230. Mineralogical Society of America. Washington DC. Irving A. J. and Frey F. A. (1978) Distribution of trace elements between garnet megacrysts and host volcanic liquids of kimberlitic to rhyolitic composition. Geochim. Cosmochim. Ada 42, 771-787. Ispas S., Benoit M., Jund P., and Jullien R. (2002) Structural properties of glassy and liquid sodium tetrasilicate: comparison between ab initio and classical molecular dynamics simulations. J. Non-Cryst. Solids 307, 946-955. Jaeger W. L. and Drake M. J. (2000) Metal-silicate partitioning of Co, Ga, and W: Dependence on silicate melt composition. Geochim. Cosmochim. Ada 64, 3887-3895. Jambon A. (1994) Earth degassing and large-scale geochemical cycling of volatile elements. In Volatiles in Magmas (eds. M. R. Carroll and J. R. Holloway), pp. 479-517. Mineralogical Society of America. Washington DC. Jana D. and Walker D. (1997) The influence of silicate melt composition on distribution of siderophile elements among metal and silicate liquids. Earth Planet. Sci. Lett. 150,463-472. Jurewicz A. J. G. and Watson E. B. (1988) Cations in olivine. Part I: Calcium partitioning and calcium-magnesium distribution between olivines and coexisting melts, with petrological applications. Contrib. Mineral. Petrol. 99, 176-185. Kohn S. C. and Schofield P. F. (1994) The importance of melt composition in controlling traceelement behaviour: An exprimental study of Mn and Zn partitioning between forsterite and silicate melt. Chem. Geol. 117, 73-87. Kress V. C. and Carmichael I. S. E. (1991) The compressibility of silicate liquids containing Fe2O3 and the effect of composition, temperature, oxygen fugacity and pressure on their redox states. Contrib. Mineral. Petrol. 108, 82-92. Kushiro I. and Mysen B. O. (2002) A possible effect of melt structure on the Mg-Fe2+ partitioning between olivine and melt. Geochim. Cosmochim. Ada 66, 2267-2273. Lange R. A. and Carmichael I. S. E. (1987) Densities of Na2O-K2O-CaO-MgO-Fe2O3-Al2O3-TiO2SiO2 liquids: New measurements and derived partial molar properties. Geochim. Cosmochim. Ada 51, 2931-2946. Lee S. K. and Stebbins J. F. (2000) The structure of aluminosilicate glasses: High-resolution I7O and 27A1 MAS and 3Q MAS NMR study. J. Phys. Chem B. 104, 40091-4100. Lee S. K. and Stebbins J. F. (2003) The distribution of sodium ions in aluminosilicate glasses: A high-field Na-23 MAS and 3Q MAS NMR study. Geochim. Cosmochim. Ada 67, 1699-1710. Libourel G. (1999) Systematics of calcium partitioning between olivine and silicate melt: Implications for melt structure and calcium content of magmatic olivines. Contrib. Mineral. Petrol. 136, 63-80. Merzbacher C, Sherriff B. L., Hartman S. J., and White W. B. (1990) A high-resolution 29Si and 27 A1 NMR study of alkaline earth aluminosilicate glasses. J. Non-Cryst. Solids 124, 194-206. Mysen B. O. (1995) Experimental, in-situ, high-temperature studies of properties and structure of silicate melts relevant to magmatic temperatures. Eur. J. Mineral. 7, 745-766. Mysen B. O. (1999) Structure and properties of magmatic liquids: From haplobasalt to haploandesite. Geochim. Cosmochim. Ada 63, 95-112. Mysen B. O. (2002) Solubility of alkaline earth and alkali aluminosilicate components in aqueous fluids in the Earth's upper mantle. Geochim. Cosmochim. Ada 66, 2421-2438. Mysen B. O. and Dubinsky E. (2004) Mineral/melt element partitioning and melt structure. Geochim. Cosmochim. Ada 68, 1617-1634.

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n

2n+2

Jo

Richet P. and Polian A. (1998) Water as a dense icelike component in silicate glasses. Science 281, 396-398. Riebling E. F. (1964) Structure of magnesium aluminosilicate liquids at 1700C. Can. J. Chem. 42, 2811-2821. Riebling E. F. (1966) Structure of molten sodium aluminosilicate liquids containing at least 50 mol% SiO, at 1500°C. J. Chem. Phys. 44, 2857-2865. Shen A. and Keppler H. (1995) Temperature-dependence of water speciation in silicate melts: Insitu FTIR spectroscopy to 10 kbars and 1000°C. EOS 76, 647. Silver L. and Stolper E. (1985) A thermodynamic model for hydrous silicate melts. J. Geol. 93, 161-178. Silver L. and Stolper E. (1989) Water in albitic glasses. J. Petrol. 30, 667-710. Silver L., Ihinger P. D., and Stolper E. (1990) The influence of bulk composition on the speciation of water in silicate glasses. Contrib. Mineral. Petrol. 104, 142-162. Sowerby J. R. and Keppler H. (1999) Water speciation in rhyolitic melt determined by in-situ infrared spectroscopy. Amer. Mineral. 84, 1843-1849. Spera F. J. (1974) A thermodynamic basis for predicting water solubilities in silicate melts and implications for the low velocity zone. Contrib. Mineral. Petrol. 45, 175-186. Tangeman J. A. and Lange R. A. (1996) Thermal expansivity of iron-bearing sodium silicate melts. EOS, Trans. Amer. Geophys. Union 77, 834. Toplis M. J. (1998) Energy barriers associated with viscous flow and the prediction of glass transition temperatures of molten silicates. Amer. Mineral. 83, 480-490.

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Toplis M. J. and Corgne A. (2002) An experimental study of element partitioning between magnetite, clinopyroxene and iron-bearing silicate liquids with particular emphasis on vanadium. Contrib. Mineral. Petrol. 144, 22-37. Toplis M. J., Dingwell D. B., and Lenci T. (1997) Peraluminous viscosity maxima in Na2O-Al2O3SiO2 liquids: The role of triclusters in tectosilicate melts. Geochim. Cosmochim. Ada 61, 2605-2612. Walter M. J. (2001) Core formation in a reduced magma ocean: New constraints from W, P, Ni, and Co. Transport of Materials in the Dynamic Earth, 152-153, Misasa, Japan. Walter M. J. and Thibault Y. (1995) Partitioning of tungsten and molybdenum between metallic liquid and silicate melt. Science 270, 1186-1189. Watson E. B. (1977) Partitioning of manganese between forsterite and silicate liquid. Geochim. Cosmochim. Ada 41, 1363-1374. Watson E. B. and Harrison T. M. (1983) Zircon saturation revisited; temperature and composition effects in a variety of crustal magma types. Earth Planet. Sci. Lett. 64, 295-304. Xue X. and Stebbins J. F. (1993) 23Na NMR chemical shifts and local Na coordination environments in silicate crystals, melts and glasses. Phys. Chem. Minerals 20, 297-307. Yap A. T.-W. and Elliott S. R. (1995) A study of mixed alkali effect in disilicate glasses using 7Li nuclear magnetic resonance. J. Non-Cryst.Solids 192&193, 207-211.

525

Subject Index acmite, 103, 326, 327, 361 glass, 361 activation enthalpy diffusion, 247, 248, 277, 278 viscosity, 116, 117, 145, 221, 390, 512, 513,514 activity coefficient, 202, 203, 204, 207, 244, 245, 268, 308, 330, 339, 389, 403, 414, 430, 438, 490, 499, 503, 544 sulfur, 490 coefficients ratio, 544 silica, 203, 204, 243, 268, 308, 389, 403, 414, 418, 430, 438, 475, 477, 499, 503 titanium, 389 activity-composition relations, 137, 139, 203, 204, 218, 248, 268, 414, 542, 543 aegirine, 326 Al-avoidance, 298 albite, 106, 110, 115, 259, 274, 292, 303, 417, 454,455,458,459,497,513 liquidus curve, 303 Alexandria, 30 algorithm, 533 alkali chloride, 516 aluminate, 137, 145, 258, 276, 286, 287, 291, 292, 476, 477, 536, 545 aluminosillicate crystalline, 292, 296, 299 tricluster, 289, 306 amorphization, 160, 161 amphibole, 40 amulet, 26 anatase, 394 andesite glass, 452, 453 hydrous, 458 melt, 455, 539 supercooled liquid, 455 angle

distribution intertetrahedral, 248, 294 Si-O-Na, 230 intertetrahedral, 99, 128, 129, 176, 177, 178, 179, 180, 181, 185, 232, 293, 296, 300, 303, 304 intratetrahedral, 248 O-Si-O, 116,229,235,236 Si-O-Si, 157, 159, 175, 176, 177, 178, 179, 181, 182, 184, 185, 199, 229, 230, 304 average, 175, 176, 182, 185, 304 distribution, 175, 176, 177, 229, 230 T-O-T, 99, 129, 294, 296 annealing, 27, 29, 30, 41, 43, 44, 45, 113, 118, 374, 384 anorthite, 98, 100, 106, 110, 118, 134, 259, 260, 262, 292, 298, 326 disordered, 100, 101 antimony, 26 apatite, 412, 413, 417 apparatus internally heated, 449 piston cylinder, 449 aqueous fluid, 514 silicate-saturated, 439, 474 Arab conquest 30 Archimedean, 208, 209, 210 argon solubility, 509 Armenia, 35 Arrhenian, 62, 171, 185, 214, 215, 217, 275, 276, 537 departure from, 456 Asia, 29 asthenosphere, 39 atomic number, 127 Auvergne, 37, 39 Avogadro's number, 105

B Babylonia, 30 barometer, 32

526 basalt, 36, 37, 39, 41, 52, 329, 341, 342, 349, 415, 437, 451,458, 460, 496, 509, 540, 541 hydrous, 458 prism, 36, 37 tholeiitic, 328 basicity, 206, 208, 218, 331, 332, 351 optical, 207, 208, 268, 338 Belgium, 29 beryl, 31 bitumen, 36 blast furnace, 42 Bohemia, 30, 34 bond Al-Cl, 516 Al-F, 521,522 Al-O, 70, 100, 133, 134, 142, 143, 148, 257, 261, 285, 289, 292, 307, 476 angle, 72, 110, 111, 126, 129, 130, 181, 224, 228, 230, 233, 234, 237, 247, 299, 363 compression, 309 distortion, 366 distribution, 175, 176, 177, 230, 294 O-Si-O, 116,229,235,236 T-O-T, 99, 129, 294, 296 B-O-Si, 115 bridging Si-O-Si, 141,403 Ca-F, 520 covalent, 94, 99, 126, 128 defect, 234 disorder, 47 distance Al-BO, 292 Al-NBO, 292 Al-O, 133, 285, 289 O-D, 465 double, 419, 420 energy, 99, 100, 127, 141 hydrogen, 113, 443, 453, 463, 464, 494 ionic, 42, 47, 49, 86, 94, 95, 96, 97, 98, 99, 107, 114, 126, 127, 128, 130, 134, 138, 140, 142, 144, 146, 148, 149, 159, 172, 204, 208, 210, 213, 214, 216, 239, 240, 246, 248, 258, 260, 262, 278, 303, 317,

Subject Index 325, 329, 332, 339, 340, 342, 351, 360, 375, 382, 442, 444, 445, 474 length Al-O, 99, 130 Fe-O, 361, 362, 374 M-BO, 236 M-NBO, 236 Si-O, 129, 177, 181, 183, 234, 360 van derWaals, 126 T-O, 99, 133, 135, 360 metallic, 52, 126,317,330 M-O, 99, 100, 101, 159, 207, 261 Na-F, 520 Si-O, 70, 100, 116, 133, 145, 148, 159, 181, 198, 199, 241, 257, 272, 476 Si-OH, 461,495 strength, 83, 96, 99, 101, 107, 113, 126, 127, 128, 130, 140, 141, 142, 145, 147, 148, 149, 158, 159, 198, 224, 233, 240, 261,274,296,307,325,476 Al-O, 275 Pauling, 99 Si-O, 225, 275 T-O, 99, 100, 129, 133, 135, 140, 247, 360, 365 valence, 368 bonding energetics, 126 hydrogen, 443, 453, 463, 464, 494 boroxol ring, 48, 162 boson peak, 108 bridge Al-O-Al, 112,298 oxygen, 129, 423, 441 P-O-Al, 426, 431 Si-O-Al, 286 Si-O-P, 420, 422, 423 Si-O-Si, 179, 495 Ti-O-Si, 384 Ti-O-Ti, 402 Brillouin scattering, 61, 69, 71, 75, 80, 162, 166, 168, 169, 211, 212, 273, 452 Bronze age, 25

527

Subject Index

Ca-BO, 132, 289, 290 calcium Tschermak, 106 calorimetry differential scanning, 454 drop, 162 solution, 103, 145, 201, 266, 454 HF, 145 Ca-NBO, 132, 289, 290 carbon oxidation, 498 solubility, 496, 497 speciation, 498 carbon dioxide solubility, 498 solubility mechanism, 498 carbon-metal alloy, 42 carbon monoxide solubility, 495, 497, 498 Carnegie, 41 carnegieite, 106, 116, 117, 260 cartography, 37 cation charge-balancing, 131, 133, 134, 135, 292, 303, 309, 476, 529, 536 coordinated tetrahedral, 99, 130, 131, 136, 137, 246, 248, 398, 529 modifying cations, 71, 87, 106, 111, 121, 138, 139, 140, 149, 170, 197, 213, 247, 248, 318, 327, 328, 339, 341, 532, 533, 539, 545 network-modifying, 71, 87, 88, 106, 111, 121, 138, 139, 140, 148, 149, 170, 197, 210, 213, 247, 248, 318, 327, 328, 337, 339, 341, 369, 374, 378, 382, 460, 468, 532, 533, 536, 539, 545 tetrahedrally coordinated, 49, 98, 99, 130, 131, 133, 135, 136, 137, 246, 248, 398, 529 trivalent, 529 celsian, 262 central force model, 178, 179, 296 chain-like, 230, 232 chalcogenide, 52, 88 character acid-base, 204

ionic, 126, 127, 159 charcoal, 34 charge distribution, 97 electrical, 86, 95, 96, 98, 127, 130, 140, 198, 239, 246, 278, 303, 375, 382 residual, 97 charge-balance, 131, 134, 149, 171, 256, 285, 288, 293, 306, 307, 309, 341, 415, 418, 419, 420, 476, 529, 530, 535, 539 alkaline earth, 293 aluminum, 256, 290, 292, 294, 296, 309, 387, 388 capacity, 309 cation ionization potential, 263, 306 charge-balancing alkali, 532 alkaline earths, 532 charge-carrier, 247 chemical shift, 131, 133, 138, 139, 176, 233, 234, 236, 242, 286, 288, 289, 291, 421,

423,472,473,516 27

A1, 289 isotropic 27 Al, 287, 289, 292 China, 29, 35 chloride alkaline earth, 516 complexe, 514, 515, 522 chlorine solubility, 513,514,516 Clausius-Clapeyron, 165 clay, 28 clinoenstatite, 225 cluster, 99, 129, 130, 135, 136, 149, 403, 406 aluminate, 286 krypton, 511 silicate, 179 Ti-O, 398 coal, 34, 36 cobalt, 26 coesite, 157 columnar, 37 compaction, 80, 81, 167, 455 permanent, 81, 167, 168, 169

528 complex alkali-OH, 476 chloride, 514, 515, 522 component high-velocity, 371 volatile natural melt, 540 composition eutectic, 86, 87, 211, 262, 327, 330, 333 compound mixed, 326 ternary, 260, 261, 325, 326, 385, 386, 387 compressibility, 74, 78, 80, 81, 88, 102, 129, 146, 147, 162, 168, 169, 179, 185, 211, 212, 240, 241, 272, 273, 279, 304, 308, 337, 346, 397, 451, 452, 453, 512, 533, 541 adiabatic, 74, 75, 80, 168, 212, 271, 452 configurational, 81, 273 equilibrium, 168 partial molar, 168 polyhedron, 241 vibrational, 168 compression, 34, 80, 81, 161, 166, 167, 168, 181, 247, 273, 303, 309, 346, 512 mechanisms, 181,273 conductivity electrical, 42, 46, 62, 70, 76, 107, 119, 143, 207, 208, 214, 215, 246, 247, 248, 340, 461 ionic, 204 configuration atomic, 33 electronic, 317 spin, 317 configurational entropy theory, 58, 190, 246 configurational entropy temperature, 392 configurational heat capacity temperature, 263, 403 configurational property, 139 constant Boltzmann, 105 dielectric, 43 equilibrium, 430, 449, 487 Planck, 105 continent, 25, 52

Subject Index convection, 52 cooling rate, 39, 45, 60, 61, 70, 73, 74, 76, 77, 79, 86, 88, 114, 162, 210, 258, 259, 261 coordination 5-fold, 120, 285, 368, 370, 398, 399 aluminum 5-fold, 293 number, 287, 289, 292 change enthalpy, 368 Fe2+ 4-fold, 369, 370 Fe3+ 6-fold, 367, 368 number, 95, 97, 107, 108, 127, 128, 224, 248, 261, 286, 287, 289, 291, 292, 306, 395, 399, 400, 406 aluminum 6-fold, 289, 305 oxygen, 99, 127, 128, 138, 149, 241, 263, 278, 286, 288, 317, 368, 369, 370, 378, 395, 399 silicon, 242 octahedral Fe3+, 367 Ti4+, 385 polyhedron oxygen, 95, 96, 120, 183, 360, 373 sphere, 133, 135, 257 state, 136, 348, 367, 368, 374, 378, 394, 395, 404, 405, 472 Fe3+, 348, 367, 368, 378 titanium, 394, 404 tetrahedral Fe2+, 370 Fe3+, 131, 149,360,378 titanium, 385 titanium, 394, 395, 399, 400, 401, 402, 404 4-fold, 394, 399, 404 6-fold, 394, 395 octahedron, 399 transformation, 137, 183, 241, 305, 306, 376, 378, 420 aluminum, 303 Fe3+, 376 partial, 183, 304, 306, 309 aluminum, 304, 309

529

Subject Index pressure, 240 Si, 247 titanium, 391 temperature, 402 coordination state oxygen, 472 cordierite, 87, 110, 259, 260, 325 correlation time, 70 corrosion, 52, 323, 382 corundum, 159, 269, 285 melting, 285 covalent, 94, 99, 126, 127, 128, 159 crater, 36, 37 Creation, 36 cristobalite, 94, 109, 116, 117, 146, 159, 160, 162, 163, 165, 166, 173, 174, 178, 179, 180, 184, 203, 243, 262, 323, 384, 385, 388, 390, 414 structure, 180 unit-cell, 385 critical point, 161, 197, 199, 200, 384, 439, 440, 444 solvus, 384 crucible, 320, 328 crust, 40, 156, 508 oceanic, 52 crystal glassy, 112, 113 crystal chemistry, 126, 369 crystal glass, 34 crystallite, 342 crystallization, 39, 43, 52, 60, 77, 78, 87, 88, 103, 157, 158, 160, 169, 196, 199, 209, 258, 262, 328, 329, 333, 340, 342, 382, 436, 458, 528 incipient, 217 cullet, 30 curve liquidus, 492, 497 cycle geological, 39

Debye model, 109 Debye-Huckel, 207 deformation viscous, 68

D

densification silica, 167 density electron, 134 equilibrium, 165 glass titanosilicate, 396 hydrous melt, 449 silica, 164, 165, 167 density-composition relationship, 209, 211 density of states, 100, 102, 105, 106, 108, 109, 110,263 dephosphorization, 42, 268 depolymerization melt pressure, 247, 378 depression freezing-point, 86, 87, 201, 261, 267, 268, 323, 384, 387, 523 liquidus temperature, 498 deshielding, 132, 133, 234 29 Si, 234 desulfurization, 42, 268 devitrification, 35, 39, 49, 256 differentiation magmatic, 52, 156, 316 diffusion, 42, 71, 87, 112, 144, 145, 218, 246, 248, 277, 278, 323, 339, 340, 341, 342,

351,460,461,503 activation enthalpy, 247, 248, 277, 278 alkali, 214, 278 chemical, 339 coefficient, 144, 145, 323, 460 phosphorus, 413 tracer, 217, 218, 460 diffusion coefficient, 144, 145, 323, 460 diffusivity, 46, 70, 87, 89, 143, 171, 172, 173, 218, 246, 277, 278, 339, 341, 342, 436, 460,461,509 water, 460 dilatometry, 65, 66, 74, 75, 80, 164, 209, 451 dimer, 226,423 diopside, 101, 118, 119, 231, 497, 498, 499 disilicate, 74, 75, 234, 239, 240, 244, 246, 329, 331, 333, 383, 391, 392, 459 dislocation, 112

Subject Index

530 disorder atomic, 60 dispersion, 49, 50 disproportionation, 197, 232 dissolution, 103, 318, 333, 397, 436, 477, 495 distance cation-oxygen, 95 interatomic, 47, 72, 80, 126 Li-Li, 236 radial, 135, 299 T-O, 98, 99, 360, 361 distribution hyperfine field, 371 radial, 48, 132, 133, 134, 135, 227, 228, 295, 299, 360 Dolomieu, 39 donor electron, 198, 207 Dulong-and-Petit, 79, 102, 163, 263, 454 durability, 256

E Egypt, 25, 26, 29 Einstein function, 105, 108 electricity, 32 electrolysis, 213 electromotive force, 204 electron, 126, 127, 134, 198, 205, 207, 208, 317, 322, 323, 339, 340, 341, 342 electronegativity, 127, 149 electrostatics, 32 element aliovalent, 27, 329, 331 empiricism, 32 enamel, 28, 34 endurance thermal, 256 enthalpy activation, 141, 170, 171, 181, 182, 214, 225, 246, 247, 248, 278, 307, 416, 455, 476,509,519,539 isothermal, 217 of transport, 141 viscosity, 225, 247, 307, 416, 476, 519 energy barrier, 73, 82, 147, 148, 214, 216

bond, 99, 100, 127, 141 calculation, 178 distribution, 537 electrostatic, 127 free minimization, 224, 226 gap ionic, 127 Gibbs free solution, 200 K-edge, 398 penalty, 178 potential, 72, 73, 80, 82, 83, 116, 129, 147, 161, 177 surface, 129 potential, 116, 129 thermal, 72, 73, 161, 198,264 England, 34, 41,49 enstatite, 87, 94, 110, 259, 260, 388, 389, 414, 437, 475, 495, 498, 499 aluminous, 87, 259 enthalpy configurational, 79, 266 barrier, 264 fusion, 103, 163, 244 mixing, 454 of reaction, 240, 430, 449 premelting, 118 solution, 103, 145, 266, 267, 388, 389, 406,454,476,492,510,541 rutile, 388, 389 vitrification, 103 enthalpy-composition relationship, 267 entropy chemical, 112, 276 configurational, 77, 78, 79, 82, 83, 84, 85, 86, 88, 89, 110, 111, 112, 115, 117, 147, 164, 199, 215, 216, 219, 247, 263, 266, 276, 392, 454, 459 temperature, 392 fusion, 103, 113, 164, 174, 332 mixing temperature, 308 molar partial, 107 premelting, 118

Subject Index residual, 84, 105, 110, 111, 113, 115, 164 topological, 112 envelope absorption, 371 equation Arrhenius, 141,215 Eyring, 144 Gibbs-Duhem, 204, 225, 396 Nernst-Einstein, 143 Stokes-Einstein, 143, 144 TVF, 45, 83, 85, 214, 457 equilibrium constant, 205, 206, 238, 239, 243, 309, 320, 329, 332, 338, 383, 428, 449, 488, 544 exchange constant, 545 internal, 62, 72, 77 metal-slag, 268 mineral/melt, 542 solid-liquid, 103, 327 thermodynamic, 45, 61, 88, 194, 202, 345 erosion, 39 Ethiopia, 35 Eurasia, 35 Europe, 27, 30, 38 eutectic, 86, 87, 196, 197, 198, 199, 211, 212, 217, 261, 262, 267, 274, 323, 326, 327, 330, 333, 384, 385, 387, 439, 447 expansion thermal, 29, 43, 44, 50, 60, 72, 75, 76, 80, 81, 88, 102, 118, 162, 164, 165, 166, 167, 168, 179, 185, 208, 209, 210, 256, 269, 270, 382, 384, 394, 395, 402, 450, 451,452,533,534,541 configurational, 78, 80 glass phonolite, 452 silica, 185,384 expansivity partial molar, 452

falling sphere method, 449, 455 fayalite, 320, 323, 328, 348, 368, 370 feldspar, 40, 259, 300, 418, 438, 445, 449, 468,476,517,523

531

ferrobasalt, 414, 415 fiber glass, 42, 51,66 fictive temperature, 45, 62, 76, 81, 84, 88, 101, 103, 109, 165, 199, 210, 211, 239, 266, 332, 333, 395, 447, 454, 466, 468 field gradient electric, 472 field strength, 49, 198,543 Fingal cave, 38 fingerprinting, 230, 231 flint glass, 34, 48, 49 flow viscous, 45, 68, 71, 74, 141, 142, 143, 144, 147, 148, 157, 158, 170, 173, 214, 216, 217, 246, 247, 392, 415, 455, 456, 537, 538, 539 fluoride species, 520 fluorine solubility, 516 solution mechanism, 523 flux, 30, 34,40, 340, 341,342 force constant, 139, 296, 423 forsterite, 87, 96, 103, 110, 198, 225, 259, 388, 389, 414, 438, 495, 498 Fourier-transform, 502, 511 fragility, 158, 276, 459 framework anionic, 70, 96, 98, 99, 100, 111, 257, 262, 344, 459 France, 29, 37, 38, 39 frequency exchange, 237 temperature, 184 fresnoite, 398, 399 fugacity gas, 510 oxygen, 316, 317, 318, 320, 321, 328, 329, 330, 331, 332, 334, 336, 337, 338, 343, 346, 348, 351, 376, 378, 383, 384, 486, 487, 488, 492, 496 sulfur, 488, 490 fulgurite, 51 function correlation, 361, 465

Subject Index

532 Einstein, 105, 108 furnace vault, 34

gap miscibility, 52, 195, 196, 197, 198, 207, 218, 257, 258, 259, 263, 272, 323, 326, 327, 328, 384, 385, 386, 387, 388, 412, 413 gas dissolved, 39 gas constant, 74, 79, 111, 141, 200, 203 gehlenite, 103, 119, 259, 260, 326 geology, 35, 36, 41 geophysics, 41 Germany, 34, 38, 42, 49 Gibbs free energy, 160 Gibbs free energy mixing, 199, 200, 205, 207, 245 glass blowing, 29 ceramics, 382 lunar, 382 maker, 25, 26, 27, 28, 29, 35, 160, 215, 316 oxidized, 363 phonolotic, 450 soda-lime, 30 stained, 30, 62 tempered, 34 titanosilicate, 382 transparency, 31 transparent, 29, 316 glass formation, 47, 82, 86, 87, 88, 89, 215, 256, 259, 261, 262, 324, 326, 327, 334, 385, 386 glass transition dilatometric, 60, 275, 277 range, 61, 62, 63, 69, 76, 77, 89, 102, 163, 169, 170, 184, 185, 209, 236, 238, 257, 276, 299, 303, 342, 406, 450, 458, 473 standard, 77, 458 temperature, 60, 66, 74, 75, 76, 77, 84, 104, 147, 157, 168, 183, 237, 239, 246,

248, 266, 274, 275, 384, 450, 455, 458, 520 gold, 31 gradient geothermal, 40, 41 granite minimum, 417, 476 primordial, 39 graphite saturation surface, 496 Greece, 29 group Si-OH, 461,476 Gruneisen, 241 Guettard, 36, 37, 38

H haplogranite, 335, 414, 415, 417, 438, 439, 445,451,454,458,459,517 hardness, 256 hearth, 27 heat capacity, configurational, 73, 78, 79, 84, 88, 114, 116, 117, 118, 120, 121, 172, 185, 202, 215, 245, 246, 263, 273, 276, 309, 347, 391,406,454,459 temperature, 309 high-temperature, 162 isobaric, 79, 102 isochoric, 79, 101, 105 low-temperature, 104, 138, 263, 278, 298 partial molar, 163, 201, 264, 265, 390, 391 vibrational, 79 heat conduction, 41 helium solubility, 510 hematite, 40, 103, 317, 320, 325, 327, 332, 342, 345 Henry's Law, 544 hercynite, 113, 114 hexacelsian, 262 hindrance steric, 197, 198, 199, 204, 235, 239, 243, 257, 278, 328, 334 hydrogen, 113, 374, 443, 453, 463, 464, 494 hydrolysis, 159, 477

533

Subject Index hydroxyl abundance, 451 hygroscopic, 261 hyperfine field distribution, 371 hyperfine parameter, 135, 321, 363, 370, 371, 372, 375

Japan, 29 jewelry, 26, 28, 35 join pseudobinary, 261

K ice I, 113 ice VII, 451,453 ideality, 263, 268, 389 deviation from, 389 igneous, 25, 36, 39, 40, 41, 51, 52, 201, 204, 284, 292, 316, 327, 382, 491, 508, 528, 543 immiscibility, 52, 202, 218, 256, 257, 258, 351,385 liquid, 42, 49, 52, 139, 196, 199, 201, 202, 204, 207, 212, 215, 216, 301, 324, 326, 327, 328, 334, 382, 384, 385, 388, 399, 412,532 metastable, 200 inertness chemical, 28, 31, 172 ingot, 29, 30 interaction chemical, 225, 508 structural, 414, 425, 523 internal friction, 194, 214 invariant point, 499 inversion degree, 113, 114 Ireland, 38 isokom, 274, 275, 459 isomer shift Fe2+, 372 Fe3+, 363, 365, 375 isostasy, 39 isostructural, 62, 71, 105, 384 isotope radioactive, 172 Italy, 29, 31,38, 39 jadeite, 106, 303

K-edge, 398, 401,422 titanium temperature, 402 kiln, 27, 28 kinetics crystallization, 262 of reaction, 436

L lapis lazuli, 26 lattice, 49, 82, 100, 106, 109, 113, 385 hexagonal, 113 parameter, 385 lava, 36, 37, 39 source, 39 layer sedimentary, 25 L-edge, 398, 399, 420, 421 lense concave, 31 leucite, 40, 262, 327, 328 libration coupled, 110 ligand, 95,98, 127, 138 lime, 25, 159 limestone, 39 Lipari Islands, 35 liquid magmatic, 137, 284, 413, 417, 461, 464, 530, 531, 532, 533, 534, 536, 542, 543 peralkaline, 464 natural NBO/T-range, 529 relaxed, 452 strong, 157 supercooled, 65, 73, 76, 77, 78, 80, 82, 88, 89, 161, 184, 201, 237, 266, 267, 301, 373, 374, 450, 451, 452, 453, 454, 456

534

Subject Index

Ti-bearing viscosity, 392 liquidus boundary, 319, 389, 404, 414, 475, 495 branch, 202, 203, 212, 389 curve, 492, 497 albite, 303 enstatite, 437 disilicate, 245 field, 418 mineral, 224 phase, 87, 139, 156, 157, 180, 184, 185, 197, 224, 225, 226, 243, 244, 260, 307, 308, 324, 382, 384, 385, 388, 412, 417, 503,515,522,542,545 phase boundary, 388 phase equilibrium, 225 phase relations, 139, 224, 226, 244, 260, 308, 382, 384, 412, 417, 503, 515, 522, 542, 545 surface tridymite, 308 temperature, 60, 78, 87, 88, 194, 217, 245, 260, 261, 262, 265, 268, 274, 275, 292, 305, 323, 324, 325, 327, 342, 385, 386, 391,439,458,494,498 depression, 498 trajectory, 243, 494 volume feldspar, 445, 517 quartz, 438, 476, 516 olivine, 495 Lorentzian, 237, 371 luster, 35

M magma, 25, 52, 137, 156, 284, 316, 412, 413, 417, 461, 464, 475, 508, 528, 530, 531, 532, 533, 534, 536, 542, 543 ascent, 436 crystallization, 436 eruption, 436 generation, 382 ocean, 52 magnesiowiistite, 324, 351 magnetite, 320, 328, 329, 342

mantle, 52, 436, 498 marble, 39 Mars, 52 Maxwell model, 64, 67, 68, 69, 71, 73 Maxwell relationship, 75, 84, 85, 86 Mediterranean, 30 melt depolymerized quenching of, 436 properties of, 436 Fe-bearing, 337, 345, 346, 348, 372, 373 hydrous density, 449 viscosity of, 447 immiscible, 261, 518 Al-partitioning, 529 sulfur-saturated, 486 water-saturated, 439, 514 melting congruent, 94, 437, 475 curve coesite, 156 quartz, 156 incongruent, 94, 386 temperature, 41, 43, 49, 103, 104, 115, 117, 119, 120, 158, 160, 161, 165, 261, 385, 437, 476, 498 thermodynamics, 179, 180 melting curve, 156, 160, 161, 165, 169 mercury, 32, 48 Mesopotamia, 25, 27, 28 meta-aluminosilicate glass alkali, 298 melt, 142, 293, 307, 308, 415, 416, 445, 459,476,519,520 meta-aluminosilicate glass, 132, 133, 293, 294, 298, 309 meta-aluminous join meta-aluminous, 256, 257, 261, 262, 263, 265, 266, 267, 268, 271, 272, 273, 274, 275, 276, 277, 279, 335, 388, 436, 445, 470 metallurgist, 25, 27, 42, 215 metallurgy, 34, 42 metaphosphate, 427

535

Subject Index metasilicate, 198, 200, 202, 234, 236, 246, 272, 333, 334, 366, 404 methane solubility, 494, 503 mica, 40 microscope, 32, 40 petrographic, 196 Middle Ages, 31 Middle East, 26, 29 Millefiori glass, 28 mineralogy, 41 miscibility, 52, 195, 196, 197, 198, 207, 218, 257, 258, 259, 263, 272, 323, 326, 327, 328, 384, 385, 386, 387, 388, 412, 413 gap, 52, 195, 196, 197, 198, 207, 218, 257, 258, 259, 263, 272, 323, 326, 327, 328, 384, 385, 386, 387, 388, 412, 413 titanium, 388 mixed alkali effect, 214, 246, 461, 533 mixing enthalpy, 87, 199, 200, 201, 207, 267, 268, 454, 455 hydrous glass, 454 entropy, 85, 199, 200, 201, 207, 245, 247, 308, 309, 453 temperature, 308 Gibbs free energy, 199, 200, 205, 207, 245 property, 225, 244, 453 mixture gas, 367, 486 mobility alkali, 71 alkali ion, 214 atomic, 60, 70, 72, 73, 78, 94, 112, 114, 116, 120,277 mode bending, 231,232 Si-BO, 231 internal, 101, 106 stretching, 231 Si-NBO, 232 vibrational Ti-O, 400 modulus bulk, 167, 168, 272, 346, 397, 452, 453 shear, 68, 69, 167 molar volume

alkali titanosilicate glass, 396 rutile, 394 TiO2, 394, 395 molecular dynamics, 97, 117, 198, 286, 289, 291, 292, 296, 300, 361, 369, 370 molecular orbitral calculation, 132 molecule, 106, 126 moment magnetic, 317 monomer, 226 absorption envelope, 371 Mossbauer absorption envelope, 371 motion cooperative, 148 diffusive, 145 mullite, 259, 260, 324

N Na-BO, 132, 133, 290 Na-NBO, 132,236,290 naturalist, 35, 36, 37 NBO/A1, 289,290, 291 NBO/P, 136 NBO/Si, 137, 226, 230, 232, 233, 240, 243, 246, 247, 374, 376, 428, 461, 467, 500, 501,509,510,532,539 NBO/T, 49, 98, 136, 137, 197, 202, 204, 210, 256, 257, 264, 268, 284, 285, 293, 300, 301, 302, 306, 308, 319, 335, 337, 364, 367, 376, 378, 401, 402, 403, 405, 406, 414, 415, 500, 503, 514, 519, 520, 528, 529, 532, 534, 535, 536, 538, 539, 543, 544, 545 neighbor second-nearest, 47, 106 neon solubility, 509 nepheline, 106, 117, 134, 135, 259, 260, 341 Netherlands, 33 network aluminosilicate, 137, 417, 426, 427, 428, 468,471,494,521,522,523 former, 98, 256, 319, 336, 382, 393, 414 modifier, 114, 164, 216, 256, 319, 414, 427,531,543 random, 48, 49, 164, 173, 174, 342

Subject Index

536 silicate, 48, 140, 148, 149, 207, 246, 319, 329, 376, 377, 397, 399, 400, 403, 416, 422, 423, 425, 431, 468, 477, 491, 494, 503, 520, 523 distortion, 248 Newtonian, 33 Niniveh, 27 noble gas distribution, 508 solubility mechanism, 509 noble gases solubility, 508, 510 nucleating agent, 329, 382 nucleation, 43, 86, 87, 88, 146, 160, 200, 224, 286, 301, 328, 329 nucleus, 132, 233, 234 iron, 371 magnetite, 329 Na, 132, 133, 138 P, 426 Si, 139,233,423

O obsidian, 28, 35, 455 ocean floor, 52 octahedron, 95, 96, 138, 346 distorted, 370 olivine, 40, 95, 97, 114, 139, 324, 325, 328, 340, 341, 351, 414, 475, 495, 499, 544 liquidus volume, 495 olivine-normative, 438 optical basicity, 207, 208, 268, 338 optics, 31, 34 order long-range, 46, 47, 95, 101, 112, 116, 120, 318 medium-range, 47, 49, 109, 110, 202, 211, 391,402,406,466 short-range, 47, 72, 80, 105, 106, 107, 120, 162, 263, 278, 298, 406, 466 order-disorder, 113, 114, 115, 121 origin aqueous, 36, 39 orthopyroxene, 139 oscillator, 105, 106, 108

oxidation, 159, 316, 318, 329, 331, 338, 339, 340, 341, 342, 349, 486, 487, 488, 498 sulfur, 487, 488 oxidation state, 316, 486 sulfur, 486 oxygen activity, 331,337, 486 anion, 95, 376 bridging, 97, 129, 132, 140, 148, 166, 172, 198, 205, 206, 218, 228, 231, 233, 240, 246, 248, 256, 257, 292, 296, 306, 419, 420, 421, 428, 468, 476, 520, 534 buffer, 320, 336, 488, 492 coordination number, 99, 127, 128, 138, 149, 241, 263, 278, 286, 288, 317, 368, 369, 370, 378, 395, 399 coordination number Fe2+, 369, 378 diffusivity, 173, 218 free, 205, 206 fugacity, 316, 317, 318, 320, 321, 328, 329, 330, 331, 332, 334, 336, 337, 338, 343, 346, 348, 351, 376, 378, 383, 384, 486, 487, 488, 492, 496 nonbridging energetically non-equivalent, 475 nonbridging distribution, 529 non-equivalent, 139, 140, 149, 236 polyedron, 96, 138, 149, 403 terminal, 131,420

packing atomic, 105, 208, 269 pair distribution, 174 Pantelleria, 35 parameter hyperfine, 135, 321, 363, 370, 371, 372, 375 partial molar volume K2O, 396 TiO2, 394, 395, 396, 404 partition coefficient, 413, 542, 543

Subject Index partitioning, 308, 333, 378, 404, 413, 416, 508,514,542,543,544,545 element, 542 mineral-melt, 137 titanium, 404 Pelehair, 51 peraluminosity, 306, 413 peraluminous, 143, 256, 262, 263, 269, 271, 272, 279, 284, 288, 289, 306, 335, 413, 425, 427, 445 periclase, 159, 225 peridotite, 88 petrology, 40, 316 igneous, 201 phase amorphous, 77, 94, 95, 97, 101, 156, 161, 185, 197 phase diagram ternary, 260 phase equilibria solid-liquid, 382 phase separation, 49, 112, 196, 199, 257, 258, 267, 285, 286, 328, 436 phase transition kinetic, 72 phenocryst, 38, 39 philosophical egg, 31 Phoenicia, 29 phonolite, 82, 450, 455, 458, 514, 528, 529, 530, 532, 534, 537, 538, 539 glass, 450 hydrous, 81,450,452,453 phosphate, 136, 208, 415, 416, 420, 421, 423, 424, 425, 426, 427, 428, 429, 430, 431, 432 pig iron, 42 plagioclase, 278 plaster, 25 plasticity, 31, 112, 113 plate tectonics, 52 point defect, 112 polyamorphism, 161, 162 metastable, 161 polyhedron, 95, 96, 126, 127, 138, 149, 197, 198, 287, 321, 362, 370, 371, 372, 401, 402, 403, 406, 472 geometry

537 Fe3+-O, 365 metal oxide, 240, 241 Ti-O, 406 polymer organic, 46 silicate, 226, 376, 401, 423, 431, 503, 522 polymer model, 207, 225 polymerization melt, 137, 216, 226, 319, 337, 376, 378, 402, 405, 413, 460, 503, 511, 523, 534, 536, 543 phosphate, 420, 421 silicate, 376, 401, 423, 431, 503, 522 polymorph, 94, 109, 113, 117, 157, 158, 160, 161,451 A12O3, 285 silica, 156, 157, 161, 164, 169, 173, 174, 177, 179, 225, 307, 404, 477 porcelain, 35 pore, 33 porosity glass silica, 511 Portugal, 38 potential chemical, 200, 202, 203, 225, 341, 490 interatomic, 72, 79, 80, 117 ionization, 127, 128, 134, 139, 142, 146, 149, 159, 196, 198, 199, 202, 204, 212, 216, 218, 235, 238, 239, 243, 246, 257, 263, 267, 278, 292, 294, 303, 306, 307, 309, 334, 339, 366, 378, 385, 395, 397, 404, 405, 442, 445, 476, 503, 516, 518, 519,520,532,541,544,545 site, 99, 127, 128, 145 pre-edge intensity titanium, 400 premelting, 117, 118 enthalpy, 118 entropy, 118 onset, 118, 119 range, 118, 119 pressure fictive, 81 structure, 240 property configurational, 78, 108, 265, 308, 406

Subject Index

538 elastic, 169,211 optical, 31 physicochemical, 224, 431, 432 transport, 62, 143, 208, 246, 248, 279, 412, 431,461,503,516,523,545 protoenstatite, 414 pseudocrystalline structure, 146, 173, 232 pseudowollastonite, 118, 119, 259, 260, 319, 326, 342, 385, 388, 390, 404 Puy de Dome, 37 pyroxene, 38, 40, 97, 106, 324, 325, 327, 328,

329,342,351,475

Qn-species, 138, 232, 233, 234, 236, 237, 238, 239, 240, 241, 243, 244, 245, 248, 292, 301, 306, 308, 309 abundance temperature, 238, 302 distribution aluminum, 308 proportion, 234, 235, 246, 302, 423, 430, 462, 466,468, 532 quadrupolar coupling, 472 quadrupole splitting, 363, 364, 366, 370, 372, 375 quartz, 31, 34, 40, 44, 48, 94, 95, 105, 117, 156, 157, 159, 160, 161, 162, 163, 165, 166, 176, 180,181, 303, 320, 327, 418, 445,449,515,517,523 melting temperature, 160, 437 quartz-fayalite-magnetite, 320, 488 quartz-normative, 438 quenching method, 41, 436 quenching rate, 286, 332, 333, 372, 373, 447

R radial distribution x-ray, 47, 133, 135,299 radius atomic, 508 ionic, 86, 95, 96, 97, 98, 107, 114, 127, 130, 138, 140, 144, 148, 149, 172, 210, 239, 240, 248, 258, 260, 278, 303, 317, 325, 351, 382, 442, 444, 445, 474 proton, 474

nonpolar, 127 random network model, 49, 164, 173, 174, 342 reaction acid-base, 204 depolymerization, 468 disproportion, 197 order-disorder, 113, 114, 115, 121 speciation water, 473, 474 reaction water speciation:, 473, 474 rearrangement cooperative, 82, 83, 161, 216 redox condition, 27, 316, 320, 336 equilibrium titanium, 383 reaction, 27, 71, 207, 268, 316, 317, 321, 329,339,351 scale, 320 titanium, 382 reduction pressure, 182 reaction, 316, 339 sulfur, 487, 488 refraction, 33, 49, 50, 225, 269 index of, 34, 76, 146, 194, 325, 382, 395 region glass-forming, 199, 261, 262 relaxation, 44, 45, 46, 60, 62, 63, 64, 65, 66, 67, 68, 70, 71, 72, 73, 74, 75, 77, 80, 81, 82, 83, 85, 87, 113, 114, 119, 165, 168, 181, 182, 211, 212, 215, 233, 236, 271, 299,341,384,448,451 bulk, 69 configurational, 64, 69, 80 density, 165 enthalpy, 76 kinetics, 64, 65, 66, 80, 113 mechanism, 60, 70 network, 70, 71 secondary, 60 silicate glass hydrous, 473

Subject Index

539

structural, 46, 60, 68, 69, 70, 71, 72, 76, 83, 214, 215, 236, 238, 384, 299 theory, 83, 147,215,216,392 time, 65 spin, 237 spin lattice, 298, 299 vibrational, 63, 64, 69 volume, 65, 67, 70, 81,450 resistivity electrical, 213, 214 rheology melt, 450 Rhine, 29 rhyolite, 335, 447, 448, 451, 458, 513, 514, 528, 529, 530, 532, 534, 537, 538, 540 hydrous, 458 ridge mid-ocean, 52 rigidity, 43 shear, 68 ring distribution, 178, 296 geometry, 179, 182 puckered, 177, 182 statistics, 299 structure, 179, 180, 182, 296 3-dimensional, 177, 180, 182, 295, 304, 461 systematics, 178, 180 rock magmatic evolution, 532 Roman empire, 29 rutile, 105, 382, 384, 388, 389, 401, 404 volume molar, 394

S Salicornia, 30 sand siliceous, 29, 30, 34 sanidine, 292 sapphirine, 87, 259 Sardinia, 35 saturation iron, 330 water, 438

scattering scoria, 36 Scotland, 38, 39 Scriptures, 36 sediment, 36,436 sedimentation, 39 self-diffusion, 119, 246, 248 separation phase, 49, 112, 196, 199, 257, 258, 267, 285, 286, 328, 436 sheet-like, 232 shell electronic, 317 shielding, 133,423,426 shock thermal, 29, 50 Si-BO, 228, 229, 231, 232, 233, 292 Sicily, 35 side band spinning, 424, 425, 426, 464 Sidon, 29 silica activity coefficient of, 203, 204, 268, 308, 389, 403, 414, 430, 438, 499, 503 amorphous, 157 crystalline, 47, 98, 104, 109, 115, 128, 145, 157, 199,225,241,243 density, 164 glass porosity, 511 molten, 157, 160, 163, 165, 168, 174, 175, 178, 180, 182, 185, 198,212,440 saturation, 156 vitreous, 146, 173, 174, 175, 176, 177, 178, 181, 182, 183, 230, 296, 304, 398, 441,511,512 TEM, 176 silicate crystal ferromagnesian, 369 silicic acid, 204 silicon 6-fold, 242 silicophosphate, 422 simulation molecular dynamics, 97, 117, 198, 289, 292, 361

540 numerical, 128, 129, 132, 139, 161, 174, 176, 179, 184, 224, 228, 232, 248, 286, 288, 289, 290, 291, 294, 423, 426, 520 structure, 232 Si-NBO, 228, 229, 231, 232, 233, 240, 292 site tetrahedral, 98, 101, 113, 131, 170, 334, 385 slag, 42 sodium, 141, 145, 148, 170, 227, 228, 229, 234, 305 solid solution crystalline, 94, 111 solidus, 194, 256, 417, 418, 475, 513, 517 temperature, 256, 418, 475, 513, 517 solubility apatite, 413 argon, 509 carbon, 496, 497 carbon dioxide, 498 carbon monoxide, 495, 497, 498 chlorine, 513, 514, 516 fluorine, 516 helium, 510 hydrogen, 492 mechanism, 397, 403, 418, 419, 425, 443, 445, 459, 470, 476, 477, 486, 491, 502, 503, 511, 513, 522, 523, 540, 541 carbon dioxide, 498 hydrogen, 492 noble gas, 509 water, 468, 540 methane, 494, 503 neon, 509 noble gas, 508, 510 phosphorus, 413, 431 rutile, 388 water, 436, 437, 439, 440, 442, 443, 444, 445, 446, 453, 476, 540, 541, 542 xenon, 509 solution enthalpy, 145, 267, 388, 389, 406, 454, 476,492,510,541 water, 541 free energy Gibbs, 200 heat of, 307, 529

Subject Index mechanism, 397, 401, 403, 418, 419, 424, 425, 427, 439, 440, 443, 445, 446, 459, 468, 470, 476, 477, 486, 491, 502, 503, 511, 513, 515, 521, 522, 523, 540, 541 fluorine, 523 TiO2, 397 titanium, 403 nonideal, 265 solution mechanism oxidized sulfur, 486 sulfur, 487, 488 solvent, 103, 145, 207, 503, 512 solvus, 196, 197, 198, 199, 201, 203, 257, 384, 439 critical point, 384 temperature, 257 topology, 440 Spain, 30, 38 speciation carbon, 498 gas, 491,496 metal chloride, 522 metal fluoride, 523 phosphate, 420, 431 reaction, 204, 338, 446, 454, 477 silicate, 430 water, 447, 448, 449, 451, 452, 454, 456, 473, 474, 477 species Ca-F, 520 metal fluoride, 520 oxidized C-O-H, 486 sulfur, 486 proportion, 462 reduced C-O-H, 486 structural, 227, 232, 289, 404, 545 sulfate, 491 Spectroscopy 57 Fe Mossbauer, 365, 368 absorption optical, 370 x-ray, 374 Brillouin scattering, 61, 69, 71, 75, 162, 166, 168,169,212,273,452

Subject Index diffraction neutron, 227, 228, 236, 237, 248, 361, 364, 399,402, 406, 419, 420, 463, 465 x-ray, 176 hyper-Raman, 110 infrared, 183, 446, 448, 456, 466, 495, 502 absorption, 502 luminescence, 365, 366 Mossbauer, 135, 321, 322, 345, 362, 366, 367,371,372,373,375 neutron, 173 NMR, 70, 112, 115, 119, 132, 136, 138, 139, 174, 175, 176, 177, 213, 228, 230, 233, 234, 236, 237, 242, 269, 285, 286, 287, 288, 290, 291, 292, 293, 294, 297, 298, 300, 301, 304, 305,400,402, 420, 421, 422, 423,424,425, 427,462,463, 464,465, 466,468, 469, 470, 471, 472, 473, 502, 515, 516, 520, 521, 522 17 O, 140, 235, 243, 287, 288, 290 23 Na, 131, 132, 138 27 Al, 286, 288, 293, 305 temperature, 286 29 Si, 133, 134, 139, 232, 233, 234, 237, 239,241,242,294,298 31 P, 136 cross-polarization, 462, 466, 470, 471 hydrous silica, 462,464, 471 multinuclear, 286 temperature, 237, 239 optical, 207, 370 Raman, 48, 100, 101, 109, 115, 116, 117, 118, 119, 120, 138, 178, 179, 182, 183, 184, 185, 231, 232, 233, 234, 237, 239, 241, 242, 247, 285, 292, 296, 297, 298, 365, 366, 373, 374, 397,400, 401, 402, 403, 419,420, 422,423, 428,461,462, 463, 468, 469, 474, 493, 494, 520, 521 in-situ, 238, 474 pressure, 182 silica glass, 461, 463 temperature, 184, 373 resonance quadruple, 399 vibrational, 100, 101, 230, 232, 233, 373, 404, 463, 473

541 XAFS, 370,402 XANES, 322, 342, 374, 398, 399,401, 404, 422, 488 titanium, 398 x-ray, 47, 114, 118, 173, 174, 175, 176, 183, 230, 285, 298, 363, 374, 404 x-ray absorption, 322, 369, 398, 420, 421 krypton, 511 XRDF, 133 spectroscopy infrared silicate hydrous, 446 spectrosopopy photon correlation, 66 spectrum electromagnetic, 316 L-edge Ti, 398 spinel, 103, 113, 114, 329, 341, 369 staurolite, 368, 369 steel, 40,41,268 stishovite, 95, 105, 109, 157, 161, 162, 183, 384 strain, 44, 67, 68, 171 strain rate, 68 strength compressive, 256 tensile, 42, 256, 382 stress, 34, 41, 42,44, 63, 68, 69, 162, 168 breaking, 42 internal, 28, 33, 34, 44, 51 nonhydrostatic, 82 shear, 67, 68 structural unit, 96, 120, 138, 139, 140, 141, 146, 149, 177, 202, 224, 226, 230, 232, 233, 234, 237, 240, 241, 245, 246, 248, 295, 296, 300, 301, 303, 308, 309, 376, 403, 423, 453,474, 532 structure aluminate, 291 anionic, 100, 230, 246 open, 182 pressure, 240 property-based, 243 relaxation, 46, 60, 68, 69, 70, 71, 72, 76, 83, 214, 215, 238, 384

542 temperature, 102, 172, 184, 202, 230, 263, 292, 299 subduction, 436 subliquidus, 338, 385, 449 subsolidus temperature, 303 substitution, 34, 99, 111, 130, 131, 135, 136, 143, 164, 256, 262, 263, 304, 307, 335, 336, 350, 393, 398, 406, 469 random, 133 fugacity, 488, 490 sulfur capacity, 489, 490 supercooling, 258 superheating, 160, 185 superliquidus temperature, 85, 319, 372, 439 superposition principle, 63 surface saturate graphite, 491, 496 surface tension, 194 symmetry long-range, 72 Syria, 25 system binary, 168, 194, 199, 200, 201, 205, 206, 210,212,334 complex, 327, 387 multicomponent, 168, 199, 206, 207, 225, 226, 328 ternary, 260, 325

tablet, 27, 28 Tammann-Vogel-Fulcher, 45, 83, 85, 214, 457 technique diffraction, 373 telescope, 32 Temkin model, 207, 338 temperature annealing, 30, 44, 45 critical, 196, 197, 199, 258, 384, 387 fictive, 45, 76, 81, 101, 109, 165, 199, 210, 239, 266, 333, 395, 447, 468 glass transition, 60, 66, 74, 75, 76, 77, 84, 104, 147, 157, 168, 183, 237, 239, 246,

Subject Index 248, 266, 274, 275, 384, 450, 455, 458, 520 liquidus diopside, 231 titanosilicate, 385 reciprocal, 45, 83, 158, 172, 213, 216, 239, 273,277,331,350,413 solidus, 256, 418, 475, 513, 517 solvus, 257 subsolidus, 303 superliquidus, 85, 319, 372, 439 temperature scale Geophysical Laboratory, 160 International, 160 tephrite, 81,458 tetrahedron Al-O-F-Al, 522 FeO4, 135 silicate, 96, 129, 182, 185, 233, 248 SiO4, 130, 156, 159, 180, 181, 185, 230, 295 tetrasilicate, 97, 148, 196, 240, 303 texture, 41 thermal analysis differential, 44, 66 thermal expansion configurational, 78, 80 thermal history, 45, 61, 65, 66, 67, 73, 76, 88, 109, 114, 162, 164 thermocouple, 43 thermometer, 32, 50 thermometry gas, 43 tholeiite, 496, 528, 529, 530, 531, 534, 537, 538 time annealing, 384 titanite, 385 magnesium, 385 titanosilicate glass, 382 density, 396 liquidus temperature, 385 melt, 385, 391, 392, 394, 395, 402, 403, 404 rheology, 390

543

Subject Index volume, 389 volume-composition, 396 titanyl, 399 TMS, 226 trace element, 35, 137, 412, 416, 543 trachyte, 454, 455,458, 514 trade route, 30, 35 trajectory liquidus, 494 transformation discontinuous, 62 transition liquid-liquid, 161 optical, 316 transmutation, 31, 33 transport behavior, 247 property, 225 tricluster, 256, 271, 277, 287, 288, 309 aluminum, 288, 309 tridymite, 94, 105, 156, 174, 176, 180, 243, 262, 308, 323, 327, 390, 414 liquidus surface, 308 trimer, 226 Tunisia, 35 Turkey, 35

U unmixing, 200, 218, 257, 258, 328, 385, 389 kinetics, 257 liquid, 52, 196, 197, 212, 325, 327, 328, 382 metastable, 218, 328 upper mantle, 137

valence, 316, 323, 346 state, 194, 318, 329, 351 velocity compressional, 169 shear, 169 sound, 69, 74, 75, 166, 211, 212, 272, 273 compressional, 75, 271 hypersonic, 75 longitudinal, 74, 271

Venus, 52 vessel, 29, 31,34 Vesuvius, 39 vibration internal, 100 lattice, 100 stretch, 232, 296, 400, 420, 421, 423, 461 494 stretching Si-O, 474 Si-OH, 461 stretch-Si-OH, 461 Ti-O, 397, 400, 401 viscoelastic, 67, 68 viscometry, 61, 425 viscosity Arrhenian, 157,459 equilibrium, 62, 171 high-temperature, 141, 142, 275, 348, 351, 393,457,519,523 hydrous liquid andesite, 457 hydrous melt, 455, 458 isothermal, 306 liquid Ti-bearing, 392 magmatic liquid, 536, 537 melt, 41, 137, 141, 144, 160, 246, 247, 248, 274, 308, 339, 414, 415, 416, 431, 476,503,514,515,519,537 CO2-bearing, 503 fluorine, 519 pressure, 247 non-Arrhenian, 215 pressure, 308, 456 relaxation time, 70 shear, 68 sodium trisilicate, 436 viscosity-composition relationship, 275, 276 vitrification, 33, 42, 81, 86, 87, 88, 194, 199, 258, 262, 325, 385, 387 composition range, 261 vitrified brick, 28 volatile C-O-H-S, 502

544 species carbon dioxide, 539 sulfur, 539 water, 539 volcanic, 35, 36, 37, 38, 39, 40, 52, 473 volcano, 36, 52 extinct, 36, 37, 40 volume additivity, 269 change, 64, 240, 247, 451, 473 contraction, 33 free, 185,511,512 liquid silica, 165 melting, 161 molar, 105, 118, 164, 165, 166, 209, 210, 212, 225, 240, 269, 271, 306, 307, 343, 344, 345, 346, 394, 395, 396, 406, 442, 450, 451,452, 511, 512, 533, 534, 535, 536, 545 A12O3 liquid, 306 distribution, 534 magmatic liquid, 534, 535 natural melt, 535 natural tholeiite melt, 536 partial, 165, 166, 209, 210, 240, 269, 271, 306, 343, 344, 345, 346, 394, 395, 396, 404, 406, 442, 451, 477, 511,512,514,533,534,535,541 partial oxide, 533 partial molar K2O, 396 water, 442, 451,477, 541

Subject Index phonolite glass, 450, 452 relaxation, 65, 67, 70, 81, 450 TiO2, 394 titanosilicate melt, 389, 403 volume-composition, 208, 209, 396 W water fugacity, 440 molecular, 446, 447, 449, 453, 461, 462, 463, 464, 466, 467, 468, 473, 477, 494, 540,541,542 saturation, 438 solubility, 436, 437, 439, 440, 442, 443, 444, 445, 446, 453, 476, 540, 541, 542 solution mechanism, 397,401, 403,418, 419, 424, 425, 427, 439, 440, 443, 445, 446, 459, 468, 470, 476, 477, 486, 491, 502, 503, 511, 513, 515, 521, 522, 523, 540, 541 species, 446, 447, 448, 449, 451, 452, 454, 456, 473, 474, 477 wave acoustic, 69, 74, 75, 109 Werner, 39 Western Europe, 30 wollastonite, 385 wiistite, 317, 318, 320, 344

xenon solubility, 509