Landbolt-Börnstein Numerical Data and Functional Relationshps in Science and Technology Volume 19 Magnetic Properties of Metals Subvolume a 3d, 4d and 5d Elements, Alloys and Compounds

LANDOLT-BORNSTEIN Numerical Data and Functional Relationships in Scienceand Technology

N&v Series Editors in Chief: K.-H. Hellwege - 0. Madelung

Group III : Crystaland Solid StatePhysics

Volume 19 Magnetic Propertiesof Metals Subvolumea 3d, 4d and 5d Elements, Alloys and Compounds K. Adachi * D. Bonnenberg * J.J.M. Franse R. Gersdorf . K. A. Hempel K. Kanematsu - S.Misawa * M. Shiga M. B. Stearns * H. l?J.Wijn

Editor: H. P J.Wijn

Springer-VerlagBerlin Heidelberg New York London Paris Tokyo

ISBN 3-540-15904-5 Springer-Vcrlag Berlin Heidelberg New York ISBN o-387-15904-5 Springer-Verlag New York Heidclbcrg Berlin

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This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically those of translation, reprinting, reuse of illustrations, broadcasting, reproduction by photocopying machine or similar means, and storage in data banks. Under $54 of the German Copyright Law, where copies are made for other than private use, a fee is payable to “Verwertungsgesellschaft Wart”, Munich. 0 by Springer-Verlag Berlin Heidelberg 1986 Printed in Germany The use of registered names, trademarks, etc. in this publication does not imply, even in the absence ofa specific statement, that such names arc exempt from the relevant protective laws and regulations and therefore free for general use. Typesetting. printing and bookbinding: Briihlschc Universititsdruckerei, 2163/3020-5432 10

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Editor H. P. J. Wijn Institut IIir Werkstoffe der Elektrotechnik der Rheinisch-Westfalischen Technischen Hochschule Aachen, Templergraben 55, D-5100 Aachen

Contributors K. Adachi Department of Physics, Nagoya University, Chikusa-ku, Nagoya 464, Japan D. Bonnenberg Institut ftir Werkstoffe der Elektrotechnik der Rheinisch-Westfalischen Technischen Hochschule Aachen, Templergraben 55, D-5100 Aachen J. J. M. Franse Natuurkundig Laboratorium Amsterdam, Nederland

der Universiteit van Amsterdam, Valckenierstraat 65, 1018 XE

R. Gersdorf Natuurkundig Laboratorium Amsterdam, Nederland

der Universiteit van Amsterdam, Valckenierstraat 65, 1018 XE

K. A. Hempel Institut fir Werkstoffe der Elektrotechnik der Rheinisch-Westfalischen Technischen Hochschule Aachen, Templergraben 55, D-5100 Aachen K. Kanematsu Department of Physics, Nihon University, Kanda-Surugadai, Chiyoda-ku, Tokyo 101, Japan S. Misawa Department of Physics, Nihon University, Kanda-Surugadai, Chiyoda-ku, Tokyo 101, Japan M. Shiga Department of Metal Science and Technology, Kyoto University, Sakyo-ku, Kyoto 606, Japan M. B. Stearns Department of Physics, Arizona State University, Tempe, Arizona, 85287, USA H. P. J. Wijn Institut fI.ir Werkstoffe der Elektrotechnik der Rheinisch-Westfalischen Technischen Hochschule Aachen, Templergraben 55, D-5100 Aachen

Vorwort Metalle, Legierungen und Verbindungen, die such andere Elemente des Periodensystems enthalten (eine Inhaltsiibersicht fur den ganzen Band III/19 befindet sich auf der Innenseite des vorderen Buchdeckels). Da jedoch selbst geringe Mengen solcher Elemente einen grol3en EinfluD auf die Eigenschaften der Substanzen haben kiinnen, erschien esverniinftig, im jetzigen Teilband such d-Ubergangselemente und Legierungen mit kleinen, aber genau delinierten Zusatzen anderer Elemente aufzunehmen. Die Definition von ,,gering“ ist natiirlich weitgehend willkiirlich und hangt von der jeweiligen Legierung ab. In der Forschung und in der Literatur auf dem Gebiet des Magnetismus findet ein allmahlicher Ubergang im Gebrauch von cgs/emu-Einheiten zu SI-Einheiten statt. Es wurde jedoch davon abgesehen, alle Daten in den Einheiten eines einzigen Systems darzustellen, wie vorteilhaft dies such immer von einem systematischen Standpunkt aus betrachtet gewesenware. Stattdessen ist dem System von Einheiten, das die Autoren der zitierten Arbeiten urspriinglich benutzten, meistens der Vorzug gegeben. Damit treten cgs/emu-Einheiten bei weitem am hauligsten auf. Dem Benutzer des Bandes wird selbstverstandlich auf mehreren Wegen geholfen die Daten in das Systemvon Einheiten zu iibertragen, das ihm am gelaufigsten ist, so z. B. durch eine Liste der Delinitionen, Einheiten und Umrechnungsfaktoren fur die am htiufigsten auftretenden magnetischen Gr6Den. Besonderer Dank gebiihrt den Autoren fur die angenehme Zusammenarbeit, der LandoltBornstein-Redaktion, hier insbesondere Dr. W. Finger und Frau G. Burfeindt, fur die grol3e Hilfe beim Bewlltigen der redaktionellen Arbeit, sowie dem Springer-Verlag fur die Sorgfalt bei der Veroffentlichung dieses Bandes. Wie alle anderen Bande des Landolt-Bbrnstein wurde such dieser Band ohne finanzielle Hilfe von anderer Seite veriiffentlicht. Der Herausgeber

Aachen, September 1986

Preface Since the appearance in 1962of Landolt-Bernstein (6th Edition), Volume II, part 9, dealing with the magnetic properties of a wide variety of substances, the number of alloys and compounds with interesting magnetic properties has enormously increased. The preparation of these substancesaimed, in the first place, at a better understanding of the magnetic behaviour of the already well-known substances, but it also accelerated the industrial development of new magnetic materials with optimized properties for various applications. Progress in electronics as well as the development of new measuring techniques has also led to an enormous extension of the knowledge of intrinsic magnetic properties. Since 1970several volumes of the Landolt-Bornstein New Serieshave been devoted to, or at least contain data about, the magnetic properties of some special groups of substances.The present Volume 19 of Group III (Crystal and Solid-State Physics) will deal with the magnetic properties of metals, alloys and metallic compounds which contain at least one transition element. It was not attempted, however, to be very critical about the metallic character of the substances discussed. Where appropriate, semiconductors and even insulators have been included. Regarding the properties to be listed, not only data on magnetic properties but also on those nonmagnetic properties have been included which, to some extent, depend on the magnetic state of the metallic system. The literature that appeared until about one year before the publication of each subvolume has been covered.

VIII

Preface

The amount of information available has become so substantial that a larger number of subvolumes is neededto cover the reliable data on magnetic properties of metals. The data arc not arranged according to specific magnetic properties, but rather follow the lines of the various groups of magnetic substances.It appeared during the organization of the work that in this way the largest coherence within the contents could bc obtained. This was also reflected in the experience that in this way competent authors could be found who, in their contributions to this volume, covered important groups of metals, instead of a single, narrowly defined magnetic property. The first subvolumcs will deal with the intrinsic magnetic properties of metals, i.e. data on those magnetic properties are represented in tables and figures which depend only on the chemical composition and on the crystal structure of the metal. Data on properties that, in addition. depend on the preparation of the samples used in the mcasurcments, as is for instance the case for thin films and for amorphous alloys, will be given in the last subvolumc. A clean-cut division is of course illusory for at least two reasons. In the first place the properties of metals and alloys can be depend on the chemical purity and on the physical quality of the crystal. And moreover, in alloys the ordering of the various atoms in the crystal lattice may in some casesinfluence the magnetic properties. This first subvolumc, 111/19a,deals with the magnetic propcrtics of metals and alloys of the 3d. 4d, and 5d transition elements. Subsequent subvolumes will treat metals, alloys and compounds that also contain other elements of the periodic table (see the survey of contents for the Volume 19 on the inside front cover). However, since small amounts of such elements can have a large influence on the properties of the solvent, it appeared reasonable to include in the present subvolumc d transition metals and alloys that contain very small. but well-defined additions of other elements. The definition of “small” is of course rather arbitrary and may depend on the alloy under discussion. In the field of magnetism, there is a gradual transition from the use of cgs/emu units to SI units. It was. however, not intended to represent all data in the units of one system, regardless of how nice this would have been from a systematic point of view. Instead, mostly preferencewas given to the system of units that was originally used by the authors whose work is quoted. Thus cgs/emu units occur most frequently. Of course the user of the tables and figures is helped in several ways to convert the data to the units which he is most familiar with, see, e.g., the list of definitions, units and conversion factors for the magnetic quantities occurring most frequently. Many thanks are due to the authors for the agreeable cooperation, the Landolt-Biirnstein editorial office in Darmstadt, especially Dr. W. Finger and Frau G. Burfeindt, for the great help with the editorial work, and to the Springer-Verlag for the carefulness with respect to the publication of this volume. Like all other volumes of Landolt-Bernstein, this volume is published without outside financial support. Aachen, September 1986

The Editor

List of symbols Symbol

Unit

Quantity

Introduced in subsect.

A A AU-) AU-)

erg crnm3 A-2 Gcm3g-’ Oe-“2 MHzG-’

1.1.2.10 1.1.2.11 1.1.2.4 1.1.2.8

85 91 34 59

Ai A;

Oe-’

exchange stiffness constant area of extremal Fermi surface cross section magnetization expansion coefficient of H”’ term ratio of NMR frequency and spontaneous magnetization linear saturation magnetostriction coefficient forced linear saturation magnetostriction coefficient lattice parameter magnetization expansion coefficient of T” term electrical conductivity expansion coefficient bulk modulus magnetic induction applied magnetic flux density residual flux density rf field maximum energy product lattice parameter susceptibility expansion coefficient susceptibility expansion coefficient magnetoelastic coupling constant Curie constant per unit mass

1.1.2.6 1.1.2.6

48 49

1.1.2.9 1.3.8

73 513

a a, Oij B B B awl 4

A K-”

&h,, b bII b, bi c,

GOe A Oem2 K-2 dyn cmm2 cm3 Kg-’ m3K kg- ’ cm3K mol- ’ m3K mol-’ calK-’ mJK-’ A

cm c,. c,. C

bar G. T T T

c C

cij D Dn D(EA d E E

ms-’ Mbar eVA2 A-’ Mbar

J, erg ev, RY

E.3

ergcmm3

EF ES

eV meV

e

e2clQ

mms-’

F F(rl. El

(eV)- l

Page

XIX 1.1.2.8

59

1.3.4 1.3.2 1.1.2.6 1.1.2.3

506 494 48 30

1.1.2.9 1.1.2.9

72 73

1.1.2.5

41

1.1.2.9

72

1.3.1 1.1.2.9

491 73

Curie constant per mole heat capacity at constant pressure/volume lattice parameter concentration velocity of light elastic constant spin wave stiffness constant spin wave stiffness expansion coefficient electronic density of states at the Fermi energy inverse distance of nearest-neighbor plane Young modulus energy free energy per unit volume of magnetocrystalline anisotropy Fermi energy spin wave energy electron charge electric quadrupole splitting Stoner (Landau) enhancement factor spectral weight function

List of symbols

Symbol

Unit

F(Q) ?

G G Ghkl

MG Mbar A-’

9 9’

91

mms-’ mms-’

2

Oe, Am-’

90

H aPPl H.4 HC

H eff H hyp H hyp,eff H core H ext & H orb

2 Am-’ Oe Oe Oe Oe Oe Oe Oe Oe

Quantity

Introduced in subsect.

magnetic form factor of the unit cell magnetic crystal structure amplitude magnetic form factor dHvA frequency shear modulus free energy reciprocal lattice vector for hkl reflection spectroscopic splitting factor magnetomechanical ratio ground state splitting excited state splitting free energy expansion coefficient magnetic field applied magnetic field anisotropy field coercive field effective magnetic field magnetic hyperfine field effective magnetic hyperfine field Is, 2s and 3s core electron contribution to Hhyp external field contribution to Hhyp 4s electron contribution to H,,, unquenched orbital moment contribution

1.1.2.7 1.1.2.7

52 52

1.1.2.11

91

1.3.4 1.1.2.7

506 52

1.1.2.8 1.1.2.8 1.3.4

61 61 506 XIX

1.1.2.9 1.1.2.8

72 58

1.1.2.8 1.1.2.8 1.1.2.8 1.1.2.8

58 58 58 58

1.1.2.6 1.1.2.6

48 49

1.1.2.3

30

1.3.6 1.3.6 1.3.6 1.3.6 1.1.2.5

508 508 508 508 41

1.1.2.10 1.1.2.12 1.1.2.6

85 113 48

1.1.2.12

113

1.1.2.13

118

to

H hi res hi’ I I IS J

Oe

J K K Kl K orb

meV Mbar

Oe-’ mms-’

KS K Ku KS KR K&i

k’ k, k k b L L 1

Al/l M

ergcmw3 erg cmm3 erg crnm2

XIII

Page

Hhyp

resonance magnetic field magnetostriction coefficient forced magnetostriction coefficient nuclear spin quantum number exchange interaction constant isomer shift total angular momentum quantum number of atom exchange integral bulk modulus Knight shift d spin contribution to Knight shift d orbital contribution to Knight shift s contact contribution to Knight shift magnetocrystalline anisotropy constant uniaxial anisotropy constant surface anisotropy constant Kerr rotation coefficient expansion coefficient of 1, wavevector Fermi wavevector light extinction coefficient modulus of Jacobian elliptic function Boltzmann constant Widemann-Franz ratio film thickness interatomic distance thermal expansivity ion mass

List of symbols

XIV

Symbol

Unit

Quantity

hi

G

magnetization

Am-‘, T G Am-‘, T

spontaneous (saturation) magnetization

PB

nt m*

h’ hT hTA II

g-l, kg-’

n n Ii 40

states eV atom spin

P P P P P

kbar

Pelf

PB

PB

PB PB PB

Pi Plot PhdPd

PB

Porb

PB

Pspin Ei :Q

PB PB

PB ;I:

kHz mms-’ pVK-’

ii

QO q 4 4( R R R RO

A-’ A n RcmG-’ m3C’

Fourier transform of unit cell magnetization dynamic component of magnetization component of the magnetization in direction of the magnetic field at position x electron mass effective electron mass number of atoms per unit mass demagnetizing factor Avogadro constant shell parameter number of electrons per atom refractive index complex index of refraction

Introduced in subsect.

Page

XIX

1.1.2.7 1.1.2.10 1.1.2.7

52 85 52

1.1.2.12 1.1.2.12

113 113

1.1.2.5

41

1.1.2.6

48

1.1.2.3

30

1.1.2.3

30

1.1.1.3

7

1.1.1.3

6

density of states at energy E probability distribution expansion parameter of magnetocrystalline anisotropy expansion parameter of R, pressure atomic magnetic moment in paramagnetic phase atomic magnetic moment in paramagnetic phase, derived from Curie-Weiss law average magnetic moment (average) magnetic moment per atom (average)conduction electron magnetic moment per atom magnetic moment of impurity atom average localized magnetic moment per atom (average)magnetic moment of atom M orbital magnetic moment per atom spin magnetic moment per atom spin density wavevector wavevector of momentum transfer electric quadrupole splitting quadrupole shift thermoelectric power gyroelectric parameter amplitude of gyroelectric parameter phase of gyroelectric parameter wavevector expansion parameter of 1, atomic radius; distance electrical resistance reflectivity of light roll reduction ordinary (normal) Hall coefficient

1.1.2.8 1.1.2.13 1.2.1.2.12 1.2.1.2.12 1.2.1.2.12

61 118 269 271 271

1.1.2.6

48

1.1.2.13

118 XIX

xv

List of symbols

Symbol

Unit

Quantity

Introduced in subsect.

Page

QcrnG-l m3 C-l A

extraordinary (spontaneous, anomalous) Hall coefficient shell radius expansion parameter of 1, atomic long-range order parameter spin quantum number of atom spin density wave amplitude of n-th spin density wave harmonic neutron scattering function expansion parameter of magnetocrystalline anisotropy shape magnetostriction volume magnetostriction expansion parameter of 1, temperature temperature related to maximum in x annealing temperature ferromagnetic Curie temperature commensurate-incommensurate transition temperature spin glass freezing temperature Kondo temperature martensitic transition temperature melting point temperature Neel temperature superconducting transition temperature; transition temperature between two types of magnetic order spin flip transition temperature spin reorientation temperature tetragonal phase transition temperature transition temperature nuclear longitudinal (spin-lattice) relaxation time nuclear transverse (spin-spin) relaxation time nuclear relaxation times T,, T2 at position x in the domain wall time annealing time expansion parameter of 1, volume volume per atom molar volume velocity concentration Cartesian coordinates atomic number spin wave specific heat coeffkient linear thermal expansion coefficient ultrasonic attenuation coefficient Kerr effect direction cosine of angle between magnetization and crystallographic axis lattice specific heat coefficient

1.1.2.13

118 XIX

1.1.2.6

48

1.1.1.3 1.1.1.3 1.1.2.9 1.1.2.5

6 6 73 41

1.3.7 1.3.7 1.1.2.6

512 512 48

1.3.2

494

PB PB

K, “C K K K K K K K K, “C K K K K K K s s s S s

cm3 A3 cm3 ems-l

mJmol-’ Ke5j2 K-’ rad mJmol-’ Km4

1.1.2.8

59

1.1.2.6

48

1.1.2.13

118

1.1.2.12 1.1.2.5

113 41

1.1.2.13

118

XVI Symbol

List of symbols

Unit

Quantity

Introduced in subsect.

A2

coefficient in spin wave dispersion relation direction cosine of the direction in which the change in length due to magnctostriction is measured expansion coefficient of 1, expansion coefficient of magnetic susceptibility expansion coefficient of magnetic susceptibility magnon lincwidth of spin fluctuations electronic specific heat coefftcicnt gyromagnetic ratio fraction of 3d electrons in E, state amplitude of periodic lattice distortion exchange splitting band gap incommensurability parameter of spin density wave transverse (equatorial) Kerr effect critical exponent of r enhancement factor relating magnetic hyperfine field to spontaneous magnetization enhancement factor E at position x in the domain wall thermal expansivity strain dielectric tensor real part of dielectric tensor element imaginary part of dielectric tensor element ellipticity of light reflected in polar Kerr effect paramagnetic Curie temperature Debye temperature angle angle between magnetization and wavevector q of spin wave nuclear specific heat coeflicicnt light absorption index compressibility inverse correlation range of spin fluctuations photon wavelength thermal expansion thermal conductivity electron-phonon interaction constant Landau-Lifshitz damping parameter linear saturation magnetostriction forced linear magnetostriction expansion coefficient of i, expansion coefficients of %, volume magnetostriction fluctuation term in x(q, 8) Poisson ratio permeability of free space Bohr magneton nuclear Bohr magneton ground state nuclear magnetic moment frequency

1.1.2.9 1.1.2.6

72 48

1.1.2.6 1.3.4 1.3.2 1.1.2.9 1.1.2.13

48 506 493 73 118

1.1.2.11 1.1.2.11 1.1.1.3

92 92 8

1.1.2.12 1.1.2.9 1.1.2.8

113 73 58

1.1.2.8

58

1.1.2.12

113

1.1.2.3

30

1.1.2.9

72

1.1.2.13

118

1.1.2.9

73

1.3.1 1.1.2.10 1.1.2.6 1.1.2.6 1.1.2.6 1.1.2.6

491 85 48 48 48 50

1.1.2.3

30

1.1.2.8

61

0e-2 K-2 meV mJmol-’ Ke2 kHzG-’ A eV eV

K K rad. deg mJmol-‘K bar-’ A-’ w Wcm-‘K-l s-1

Oe-’

s-1

Page

List of symbols Symbol

Unit

Quantity

s-1

NMR frequency expansion coefficient of G density resistivity element of resistivity tensor Hall resistivity magnetoresistance tensile stress magnetic moment per unit mass

gcmm3 pR cm pQ cm @cm @cm kbar Gcm3 g-’ Am2 kg-’ Vsmkg-l Gcm3 mol-’ Am2 mol - 1 Vsmmol-’ Gcm3g-l Gcm3g-’ Gcm3g-’ R-l cm-’ R-‘cm-’ 0-l cm-l R-‘cm-’

S S

rad, deg eV cm3g-’ m3 kg-’ cm3mol- 1 m3 mol-l cm3cmm3 m3 mm3 cm3g-’ cm3mol-’ cm3g-l cm3g-’ cm3g-’ cm3mol-’

cm3mol-’ cm3mol-’

XVII

Introduced in subsect.

Page

1.3.4

506

1.3.8 1.1.2.13

513 118 XIX

magnetic moment per mole remanence spontaneous (saturation) magnetic moment per unit mass magnetic moment per unit mass for magnetic field in hkl direction electrical conductivity element of electrical conductivity tensor real part of electrical conductivity tensor element imaginary part of electrical conductivity tensor element reduced temperature pulse length average time between collisions angle work function magnetic mass susceptibility

XIX

1.1.2.4

34

1.1.2.12 1.3.8

113 513

1.1.2.11

91

1.1.2.11

94 XIX

magnetic molar susceptibility

XIX

magnetic volume susceptibility

XIX

high-field magnetic susceptibility low-field magnetic susceptibility initial magnetic susceptibility spin susceptibility of noninteracting electrons diamagnetic susceptibility of core electrons diamagnetic susceptibility orbital magnetic susceptibility d-orbital magnetic susceptibility spin-orbit interaction contribution to magnetic susceptibility orbital magnetic susceptibility Pauli spin susceptibility s, p, d spin susceptibility spin susceptibility ac susceptibility wavevector-dependent magnetic susceptibility wavevector- and frequency-dependent magnetic susceptibility

1.1.2.4

34

1.3.2

493

1.1.2.4 1.3.2 1.3.2

40 493 493

1.1.2.4 1.3.2 1.3.2

40 493 493

1.1.2.9 1.1.2.3

73 30

XVIII

List of symbols

Symbol

Unit

Quantity

4’ 4’

rad. deg

angle spin antisymmetric part of quasiparticle interaction function Landau parameter angular frequency cyclotron frequency spin wave dispersion relation volume magnetostriction spontaneous (saturation) volume magnctostriction forced volume magnetostriction

s-1 s-1 s-1

&!I,@H

Oe-’

Introduced in subsect.

Page

1.3.1 1.3.1

491 491

1.1.2.11 1.1.2.9 1.1.2.6

91 12 48

1.1.2.6

52

Definitions, units and conversionfactors In the SI. units are given for both defining relations of the magnetization, B = u,,(H + M) and B = poH+ M, respectively. u0=4rt. IO-‘Vs A-’ m- ‘, A: molar mass,e: mass density. Quantity

cgsjemu

SI

B

G=(ergcm-3)1/2 1Gs Oe = (ergcme3)*‘* IOes

T=Vsm-* 10-4T Am-’ 103/4rrAm- ’

H M

B=H+4nM G 1GG

P 5

5,

Ro.R,

P=MI' Gcm3 1 Gcm3s o= M/Q Gcm3g-’ lGcm’g-‘G a,,,=cA Gcm3mol-’ 1 Gcm3mol-‘2

B=p,(H+M)

B=p,H+M

Am-’ IO3Am-’

T 4~. 10-4T

P=MV Am* 10m3Am*

P=MV Vsm 47r.lO-l’Vsm u= M/Q Vsm kg-’ 4n.10-7Vsmkg-’ o,=aA Vsmmol-’ 4rr~10-‘“Vsmmol-1

~==M/Q

Am* kg- ’ 1 Am* kg-’ o,,,=aA Am* mol - ’ 10-3Am2mol-1

P=)IH

P=xH

cm3 lcm3; xv = x/v cm3crne3 1cm3cmw3& xg= x,-/e cm3g-r lcm3g-‘s Xltl=XgA cm3mol- ’ 1 cm3mol-’

m3 4n. 10m6m3 X”=XIV m3mm3 4nm3me3 xp= xv/e m3 kg-’ 4n.10-3m3kg-1 Xm=XpA m3 mol-’ 4rt~10-6m3mol-1

4~. 10e6 m3 X”=%lV m3 mw3 47rm3mm3 xp= XVI@ m3 kg- ’ 4x~10-3m3kgg1 Xlll=%gA m3mol-’ 47r~10-6m3mol-1

Q,,= R,Bf4nR,M, RcmG-’ IRcmG-‘g

ell = ROB+ P~R,M, m3C-’ 100m3C1

e,,=RoB+fW, m3C-’ 100m3Cr

P=%PoH m3

List of abbreviations AF AFo AF, AF, ARPES bee CAF CPA cw cw dCEP dhcp dHvA DM DOS EDC F FC fee FI FID FMR GM hcp KK KS L LA LEED LIAF LSDW MAG ME MSM NBS NMR P PAC PP If RKKY RRR RSM RT SAS sCEP SDW SE SG SRARPES

antiferromagnetic commensurate spin density wave state transverse incommensurate spin density wave state longitudinal incommensurate spin density wave state angle-resolved photoemission spectroscopy body-centered cubic commensurate spin density wave state coherent potential approximation Curie-Weiss-type paramagnetism continuous wave d conduction electron polarization double hexagonal close-packed de Haas-van Alphen diffraction method density of states energy distribution curves ferromagnetic field-cooled face-centeredcubic ferrimagnetic free induction decay ferromagnetic resonance giant magnetic moment hexagonal close-packed Kramers-Kroenig analysis Kohn-Sham potential Lifshitz point longitudinal acoustic low-energy electron diffraction longitudinal incommensurate spin density wave state longitudinal spin density wave magnetization Miissbauer effect moving-sample magnetometer National Bureau of Standards, nuclear magnetic resonance paramagnetic perturbed angular correlation technique Pauli-type paramagnetism radio frequency Rudermann-Kittel-Kasuya-Yosida residual resistance ratio rotating-sample magnetometer room temperature small-angle scattering s conduction electron polarization spin density wave spin echo spin glass spin-resolved, angle-resolved photoemission spectra

xx SRMO SWR SXPS TAS TE TIAF

TQ

TRM TSDW UPS vBH XPS

ZFC

List of abbreviations short-range magnetic order spin-wave resonance soft X-ray photoelectron spectroscopy triple axis spectroscopy thermal expansion transverse incommensurate spin density wave state magnetic torque measurement method thermoremanent magetization transverse spin density wave ultraviolet photoemission spectroscopy von Barth-Hedin exchange correlation potential X-ray photoelectron spectroscopy zero-field cooled

Ref. p. 221

1.1.1.1 Ti

1

1 Magnetic properties of 3d, 4d, and 5d elements, alloys and compounds 1.1 3d elements 1.1.1 Ti, V, Cr, Mn Survey Metal

Property

Fig.

Table

Ti

I$-) xm(T) (C/T> (T2> x&T)

1, 2, 4, 5, 7, 8 3 6

1

v Cr

a-Mn

9

SDW m magn. phase diagram xg(T) TN(x,14 (Ala) (4 04 latent heat (x) W/l) CT> elastic properties

10, 12-16, 19 11, 23 17, 18, 30 20-22 23-27, 29 19 28

magn. structure x,( T> e4,,,)

35 3638 39

T,(P, xl Knight shift (T)

4&42 43

icAT)

36, 38, 44 36,45 36 46,47

x,(T) L(T)

3 4 5

31 32-34

PMn

p-Mn y-Mn 6-Mn Mn-H

2

7 8

1.1.1.1 Ti Titanium metal is a Pauli paramagnet; no localized magnetic moments have been observed.Since Ti becomes superconducting below 0.4 K, probably no magnetic ordering occurs. The crystallographic structure of a-Ti, the most stable phase at room temperature, is hexagonal; in single crystals the magnetic susceptibility is therefore a function of the angle between the direction of the magnetic field and the c axis. Next to a-Ti, there are two other phases of Ti known: P-Ti, with a body-centered cubic crystallographic structure, which is stable above 1155K [56 M 11,and o-Ti, with a hexagonal crystallographic structure, stable only under high pressure, but metastable at pressure zero [74 D 11. The susceptibilities of all phases of Ti are given in Figs. 1...5 and Table 1. For the low-temperature specific heat properties, seeTable 2 and Fig. 6. Dilute alloys of titanium with aluminum have been investigated by [71 C 11,seeFig. 7, and, for completeness, also Fig. 8.

Frame, Gersdorf

2

[Ref. p. 22

1.1.1.1 Ti Table 1. Room temperature values of the magnetic masssusceptibility ,+ of cold-rolled commercial grade cr-Ti. for three directions of the magnetic field [77A 11. Measuring direction

Xe[10-6cm3g-‘]

Rolling direction Perpendicular to sheet Perpendicular to rolling

3.04 3.32 3.12

3.8 -105

I

Cm3 a-Ti

+rl

2.6 0

200

100

single cryslo

-xov 300

J , LOO

K

IO

I-

Fig. 1. Tempcraturc depcndcnccof the magnctic mass susceptibility xp of various polycrystallinc a-Ti specimcns,and of a single crystal of cc-Ti[7OC I]. Sample

Impurity in wt%

02

N2

TS HP ID

0.086 0.037 0.040

Crystal

0.0063

0.01I 0.004 0.037 0.003 Cr = 0.0078 Zr=0.002 A1=0.0015

Cl,

Mg

Sn

Fc

0.01 0.00I 0.01 0.009 (Fe, Cr. Ni) all < 0.001

Frame, Gersdorf

0.003

1.1.1.1 Ti

Ref. p. 221

1.50 10-6 :m3 s

I

60 40-6 cm3 ia

3.02 w6 -cm3 9

1.112

2.94

.34

2.90

.30

.& 2.86 I 2.82

U8

I

I

48

I_ G

,951 w ,950

I

141

2.78

.949

2.14

.948 DI

2.70

,947

4.683 8, 4.682

946

40 I 32 E

3

16

8

I 0

,945

I

I

I

I

200

400

600 T-

800

I

h

1000 K 12

Fig. 3. Temperature dependence of the crystalline anisotropy of the magnetic molar susceptibility. Ax, = xl1 -x1 of Ti, Zr, and Hf [74 V 11.

4.681 I u 4.680

3

-

4.679 4.678 4.677 0

50

100

150

200

250 K 3;oo

TFig. 2. Temperature dependence of the magnetic mass susceptibility xs of a single crystal of pure a-Ti compared with the temperature dependences of the lattice parameters a and c [67 E 11. The susceptibility of Ti is seen to be practically temperature-independent up to about 70K. The low-temperature upturn is accountable to a trace of dissolved Mn [71 C 11, see also [72V 11.

5.5 ;lOm" Ti -cm3 9

,-

--.--

?L-!L-I

4.5 t

2.75 2.50 0

50

100

150

200

250 K 300

a TFig. 4. Temperature dependence of the magnetic susceptibility xp ofpolycrystalline samples of a- and (a) Impurity content of the samples: C and 0: . 10m2at%; Al: < 1. 10m3at%; S, N, Cu, Fe, V, ~3. 10e4at%; other elements: < 1. 10m5at% [74D 13.

mass w-Ti. 5 1 Mn: each

2.51 0

500

1000

1500

K

2000

b) shows xn vs. T for an exteL=perature range: the different lines represent data of different authors.

Franse, Gersdorf

4

1.1.1.1 Ti

[Ref. p.

22

5.5 1O-6 Tj -cm3 g-

I

1.5

2? Fig. 5. Tcmpcraturc dcpcndcncc of the magnetic mass susceptibility lE. for two samples. I and 2. of polycrystallinc r-Ti and P-Ti [65 K I. 69 K I], Typical impurity content: Sample I: 0.001 wt%C: 0.00-7n?%Nz; 0.002 \vt?b 02; 0.005 \vt% Al: 0.002 vvt% Fc. Sample 2: 0.001 \vt?6 C: O.O02\vt% O>;
4.0 3.5 3.0 0

400

800

r-

1200

Table 2. Low-temperature specific heat ofpolycrystalline high-purity x-Ti: C=;T + /IT3. See Fig. 6 for graphical representation. For the impurities in the samples, see caption to Fig. 1 [7OC 11. Specimen

ID-l ID-2 HP

Heat treatment

Y mJmol-’

850 T, 100 h ‘) 850 ‘C, 100 h ‘) As cast

3.36 3.36 3.32

B mJmol-’

K-*

Km4

0.026 0.026 0.028

‘) Quenched into iced NaCl solution *) Furnace cooled. L.5 - mJ molK* 4.0

3.0 0

.

5

10

15

20

25 K* 30

Fig. 6. Low-tcmpcraturc spccilic heat C ofhigh-purity Ti. The ID specimens had been anncalcd at 850°C and either qucnchcd (ID-l) or furnace-cooled (ID-Z). The HP spccimen was mcasurcd in the as-cast condition. For the impurities in the samples. SW the caption to Fig. I [70 C I]. See also Table 2.

Frame, Gersdorf

00 K 420 420 410

1630 K 2003

1.1.1.1 Ti

Ref. p. 221

3.1 @ 9 3.0

3.0 I 2.9 H” 3.0

I 2.9;

2.9

3.0

3.0

2.9

2.91 0

I 100

I 200 T-

I 300

K

I 400

Fig. 7. Temperature dependence of the magnetic mass susceptibility xp ofa family ofsingle-phase (ol)Ti-Al alloys [71 c 11.

2.12 xl-6 cm3 9

2.56 I

x”

248 2.40

0

100

200

300

SKI K 500

I-

Fig. 8. Temperature dependence of the magnetic mass susceptibility xp of a single crystal Ti,Al compared with the temperature dependences of the lattice parameters

~71c i j.

Franse, Gersdorf

6

1.1.1.2 v/1.1.1.3 Cr

[Ref. p. 22

1.1.1.2 v Vanadium metal is a Pauli paramagnet. Neutron diffraction measurementsrevealed no localized magnetic moments: if they exist they are smaller than 0.01pII [77A 23. Since vanadium becomesa superconductor at 5.265K. probably no magnetic ordering occurs. Vanadium has a body-centered cubic crystallographic structure; the magnetic susceptibility is isotropic, and a smooth function of temperature above the superconducting transition. seeFig. 9; it is possible that 1 shows a very shallow maximum between IOOK and 200K [65 K 11. A good room temperature value is: ,~,=7.3' lo-‘m3/kg. Somctimcs discontinuities have been observed in the susceptibility and other physical propertics of V at temperatures between 120.‘.240 K. Rostoker and Yamamoto [5.5R l] observed a crystallographic transition at - 30 ‘C: this has not been confirmed by later investigations. Kostina [71 K l] found a peak in the susceptibilit) at 240 K. and corresponding anomalies in the resistivity and the Hall effect. Kondorskii [73 K l] found two peaks. respectively at 120K and 190K. and corresponding anomalies in the magnetostriction and thermal expansion. The nature of these not very reproducible anomalies, which were sometimes interpreted as a hypothetical antifcrromngnetic Nlel point. is at the moment not understood. The magnetomcchanical ratio of vanadium is g’= 1.18(10) [71 H 11. 6.5 nb ?- 3 6.0 I g 5.5

1.5 0

LOO

1200

800

1600 K 20

T-

Fig. 9. Temperature dependenceof the magnetic mass susceptibility xc for polycrystallinc V. Curve I: [65 K I], sampleimpurities. in [wt%]: 0.032C; 0.070,; 0.031N,; 0.001H,; others ~0.095. 2: [61 B I]. 3: [62T I]. 4: [53 K I].

1.1.1.3 Cr The crystallographic structure of chromium metal is body-centered cubic, and its magnetic structure is very pcculinr. Chromium is antifcrromagnctic at tempcraturcs below the N&l point (T,) of about 312K. This antiferromagnetism is, however. not caused by local magnetic moments aligning themselves antiparallel; Overhauser [62 0 l] showed that the antiferromagnetic ordering in chromium may be describedby a spi,~demit~ 11~71.c in the itinerant 3d-electrons, having a wavelength incommensurate with the lattice constant. For the concurrent sinusoidal periodic lattice distortion (strain wave), see[74T 11.Whereas in some other substances spin density waves only exist as excitations, in Cr metal at low temperatures the ground state is a spin densit) wave with a finite amplitude, set Fig. 10. Analytically, the magnetic moment per atom in antiferromagnetic Cr, as a function of the position in space.R, is given by: S(R)=S,cos(Q.R)+S,cos(3Q.R)+...,

where the main amplitude of the magnetic moment, S,, has a value of about 0.6 pu at low temperatures, and a value ofabout 0.2 p” just below TN [6.5A 11.S, is always directed along one of the cube axes of the body-centered cubic crystal lattice: S, is always directed opposite to S,, and has an absolute value of a few percent of S,, the “spin density wave” S(R) is therefore somewhat more “rectangular-like” than a pure sine function, see[81 I l] and Fig. 19.

Frame, Gersdorf

Ref. p. 221

7

1.1.1.3 Cr

The amplitude of the spin density wave, IS, +S,J, must not be confused with the averagemagnetic moment, which is given in Figs. 11 and 23; this average (rms) moment equals:

The wavevector of the spin density wave, Q, has an absolute value of nearly (but not exactly) 27c/a,where a is the lattice parameter; Q depends in a continuous way on temperature, pressure, amount of impurities, see Figs. 12.. .16, and Table 3. Q is also directed along one of the cube axes of the crystal; at temperatures between 124K and 312 K, S, and Q are perpendicular to each other (transversal polarization, AFl-phase); on cooling below 124K, S, rotates to a position parallel to Q (longitudinal polarization, AFZphase). This transition temperature is called the spin-flip temperature T,,. Normally, a single crystal of Cr in the AFl-phase consists of 6 types of domains, and a crystal in the AF2phase has 3 types of domains; in each type of domain Q and S, are parallel to one of the 3 different cube axes of the crystal, this state is therefore called the 3Q-state.Two different types of domain walls exist in chromium in the 3Q-state; both types show at low temperatures hysteresis in their motion [78 G 11. On cooling such a crystal through TNin an applied flux density of at least about 4 T, directed along one of the cube axes, it is possible to prepare a state in which the number of types of domains is reduced by a factor 3; there are now only domains with Q parallel to the direction of the applied field, this state is therefore called the lQ-state. When the field is switched off this 1Q-statepersists,aslong as the crystal is not heated to a temperature near TN;for the influence of this effect on the magnetic susceptibility, see Figs. 21 and 22. If a chromium crystal is deformed, or if impurities are present, a third antiferromagnetic phase with commensurate ordering is present. This phase, AFO, is the most simple antiferromagnetism: nearest neighbors are aligned antiparallel, i.e. Q = ~TE/U, see Fig. 17. At sufficiently high applied fields Bapp,there are, depending on the angle between II,,,, and Q, two different AFZphases possible, with, respectively, a small or large angle between S, and Q, seeFig. 18. The structure of the spin density wave can only be investigated by the interpretation of neutron diffraction measurements.With inelastic neutron diffraction measurements,the properties of magnetic excitations have also been investigated [Sl F 1, 81 B 3, 79 Z 11. The magnetic susceptibility shows no extraordinary features, see Figs. 20...22 and Table 4. Since a small oxygen contamination of Cr has a large influence on its susceptibility, and since it is difficult to obtain oxygenfree chromium, older values of x must be distrusted. In the AFl-phase in the lQ-state, the susceptibility measured along the direction of Q is somewhat higher than the susceptibility, measuredperpendicular to Q; for the AF2-phase the opposite is true. The magnitude of the small discontinuity in the magnetic susceptibility at 7$ therefore strongly depends on the applied field in which the specimen has been cooled through TN; this discontinuity may even disappear or change its sign (Fig. 21). For transition temperatures of chromium with small amounts of other transition metals, seeFigs. 23...25. Both T,, and TNof chromium depend on strains in the crystal and on external pressure,seeFigs. 25...29. For hydrostatic pressure holds: Wi -=-5.2(5).10-3K/bar aP

[SlW2],

w, -=-5.8(2).10-3K/bar aP

[68Ul],

and for tensile stress: _ = -2.0(2). 10m3K/bar [Sl W2], ap T,, depends on the square of an applied flux density Bappl,see Fig. 30. For the case that B,,,,JQ holds: zaKf = -0.174(3)K/T2 mpp*

[81 B 11.

A similar behaviour is reported for field-cooled, but polycrystalline Cr, the constant being -0.181 K/T2 in this case [68 S 11. Up to 16T the NCel temperature TNis independent of an applied magnetic flux density with an accuracy between +lOmK and -2OmK [8lBl].

Franse, Gersdorf

8

[Ref. p. 22

1.1.1.3 Cr

Accurate measurements show no detectable hysteresis of the NCel point TN in well-annealed, pure Cr [8OW2]; 7;, has a hysteresis of about 1 K [82 B 11. Free energy expressions,dependent on the applied field and/or the strain, are given by [81 B 21(near T,,) and [SOW 1] (near TN). Surface magnetization of Cr has been mentioned by [82S 11. The magnetic anisotropy torque of Cr in the 3Q-state,and of Cr in the IQ-state, was measuredby [64 M I]. It appears that both at Th.and ‘T;,chromium has a first-order phase transition [65A 11.The latent heat of transition at T,, is 0.04(2)J/mol [82 B 11. For the latent heat at TN,seeTable 5. The relative change in the volume at 7;, is - 1.4(6). 10m6[69 S 11,at TNthe change in volume could not be measured due to a change in the thermal expansion, see Fig. 31; it can be calculated to be about -2. 10e5. In the lQ-state. chromium shows a tetragonal or, depending on the previous treatment, an orthorhombic deformation (or magnetostriction) of the order of magnitude 10e5 [69 S 11. Small effectsof the magnetic ordering on the elastic constants have been investigated, seeFigs. 32...34 and Table 6. The magnetomechanical ratio of chromium metal is q’= 1.21(7) [71 H 11.

Table 3. Data for the magnetic period of the spin density wave in Cr, based on the position of the (100) satellite lines in the neutron diffraction spectrum [64K 11. Q: spin density wavevector, 6-l = (I -Qo/Zx)1: length of antifcrromagnetic modulation, see Fig. 10, divided by lattice constant a. T

K

Q@~

6-1

Cr

197 78

0.9554 0.9519

22.4(8) 20.8 *)

Cr -0.45 at% V

197 78

0.9480 0.9431

19.2(8) 17.6(8)

*) [62S 11.

Corner atoms

Body-center atoms

Body-center atoms

Corner otoms

Fig. 10.Spin density wave in Cr [Sl F 11.The magnetic moments oftwo successiveatoms on the body-diagonal of the cubic lattice arc antiparallel. The magnitude of the atomic moments on each sublattice is given by a sinusoidal function of the position.

Franse, Gersdorf

Ref. p. 221

1.1.1.3 Cr

Cr-V

0.960 t # Y 0.95E s

. v

0.952

0.948 0

Fig. 11. V concentration dependence of the rms average magnetic moment per atom, ~7,for Cr-V alloys, deduced from the total coherent magnetic neutron scattering near the position of the (100) reflection. Solid circle: [62 W 11, open circle: [64K 11, cross: Hamaguchi et al., see [64K 11.

0.2

0.4 r/r,

0.6

0.8

1.0

-

Fig. 12. Temperature dependence of the relative length Qa/2n of the spin density wavevector for Cr as a function of the reduced temperature T/T,, at various pressures [68Ul].

“piiZfX~-l “piiZfX~-l /Iv 0.964 0.962

3.2 Lo

I

l+C

’

1 c

0.960

0.958 t # 2 0.956 Q

I 3.6 ~lo-~

I 6!= ~(1-6.0.0)

“.tb

I

K

250

T-

Fig. 13. Incommensurability parameter 6 = 1 -Qu/2rc for a Cr-0.68 at% Mn single crystal as a function of temperature. The hysteresis in 6 persists outside the coexistence region of the commensurate-incommensurate phases [81 G 11. I: incommensurate AFl phase, C: commensurate APO phase (S= 0); the AF2 phase does not occur in this alloy.

0.948 0.946 0

12

3

4

5

6 kbar 7

P-

Fig. 15. Pressure dependence of the relative length of the spin density wavevector Qaf2x of Cr at two reduced temperatures [68 U 11.

For Fig. 14, see next page.

Franse, Gersdorf

10

1.1.1.3 Cr

[Ref. p. 22

0.972’:

0.967:

0.955:

Cr-0.8ot%Co I 1Cr-0.780t%Fe ‘Cr-l.OZot%Fe

> I/ I ) !

0.97X

0.9525

0.95oc

I

50

100

150

-ig. 14. Temperature dcpcndcncc ofthc rclativc length of hc spin density wavevector of Qo!2rr for scvcral Cr-based alloys (full curves). The broken curve gives Q0/2rt as ,xpcctcd from the thermal lattice expansion only [80 V 1). lomplications arise because of “Q-vector locking” and rreversibility. see also Fig. 13 [80 V I, 80 R 1, 82 L I].

200

250

300

K

350

Cr

1.c .W bar.

i

:ig. 16. Tcmpcrature dcpcndcnce of the hydrostatic ncssurc depcndcncc ofthc spin density wavcvcctor Qn/271 fCr, as determined from neutron diffraction (solid circles 76 F I]. squares [68 U I]). and from de Haas-van Alphcn reasurcmcnts at. essentially, zero prcssurc (asterisk: 76 F 11). and under high pressure (cross [SOV I]).

0.2

0

Frame, Gersdorf

50

100

150 I-

200

250 K :300

1.1.1.3 Cr

Ref. p. 221

60

0 0

100

200

300

400

K

500

Fig. 17. Magnetic phase diagram in Cr for (a) annealed sample,(b) swaged sample, and (c)crushed powder sample [Sl W 11. P: paramagnetic, AFO: commensurate, Q = 2x/a, AFl : transverse incommensurate, AF2: longitudinal incommensurate.

20 0 -16

-14

-12

-10

-8 A hf -

-6

-4

-2

K 0

Fig. 18. Phase diagram of Cr in high applied fields B,,,i as derived from ultrasonic attenuation experiments. Q and q are the wavevectors of the spin density wave (parallel to the z axis of the crystal) and the ultrasonic wave, respectively; 0 is the angle between B,,,, and Q. Solid and dashed lines give the position of, respectively, the peaks and humps in the ultrasonic attenuation a(T), separating distinct phases. (a): 0= 1ll”, (b): 0= 15.8”, (c): 0=21.3” [Sl B 11. I

Cr-2

I

1 Cr-?7at%V I r

Cr-0.3at%V-I I II

0

I

I

0.01 0.02

I

0.03

I

0.04

II

0.05

II

0.06

I

0.07

I

0.08

Fig. 19. Ratio of the third harmonic amplitude to the primary spin density wave amplitude S&S,, and the displacement amplitude of the periodic lattice distortion A ofpure Cr, Cr-Mn, and Cr-V alloys as a function ofthe incommensurability parameter 6, Q = 2x/4 1 - 6,0,0). The values determined from the rigid and the deformable spin model are shown by open and solid circles, respectively [Sl I 11.

Franse, Gersdorf

12

1.1.1.3 Cr

Iable 4. Magnetic mass susceptibility xF of Cr 163W 11. Impurities: 0.0008 wt%N,, 0.02 wt%O,; netal impurities: very low concentration. Set also Fig. 20.

l-

%g

T

K

10-6cm3g-’

K

10-6cm3g-’

100 150 200 250 290 3’0 370 420 470 520 570 620 670 720 770 820 870 920 970 10’0

3.082 3.121 3.148 3.185 3.210 3.23 3.24 3.27 3.30 3.32 3.34 3.40 3.42 3.43 3.46 3.47 3.52 3.56 3.61 3.64

1070 1120 1170 1220 1270 1320 1370 1420 1470 1520 1570 1620 1670 1720 1770 1820 1870 1920 1970 2020

3.67 3.71 3.74 3.75 3.76 3.81 3.88 3.90 3.93 4.02 4.05 4.09 4.14 4.18 4.22 4.23 4.24 4.26 4.29 4.32

%g

[Ref. p. 22

L.6 .10-5

cm3 9 42

I 3.8 ?T

I

I

I

20 IFig. 20. Tempcraturc dcpcndence of the magnetic mass susceptibility xp for polycrystallinc Cr. I: [58 L I]: II: [52M 11; III: [64M2]; IV and V: [64W I]; for sample impurities, see Table 4. 500

0.3 .lOP

1OOC

1500 K

r

cm: -is-

1 0.2 E ? P g 0.1

Fig. 22. Variation of the anisotropy of the magnetic mass susceptibility officld-cooled Cr at 85 K as a function ofthc applied flus density acting on the spccimcn as it cools through TX [66P I].

n Coolingfield

3.2, w

cm: 9 3.1

I

3.2

-

I

G-7 3.1

LOO K 500

a Fig. 21. Tempcraturc depcndencc of the magnetic mass susceptibility xp ofsingle-crystal Cr. (a) Cr cooled in zero applied field; zoo, and lo,, refer to mensurcmcnts along cube cdgcs and face diagonals, respcctivcly.

2.8 7

100

125

150

K

175

b (b) Cr cooled through TNin an applied flux density of 5 T acting along [OOI]. Open triangles: measurements along [OlO]; solid triangles: measurements along [OOl]; solid circles: mcasurcments along cube edge for Cr cooled in zero applied field, included for comparison [66P I], see also [64 M I].

Frame, Gersdorf

1.1.1.3 Cr

Ref. p. 221

13

Table 5. Latent heat of transition at the Nbel temperature TNfor a single crystal (SC), and a polycrystalline sample (PC) of Cr, as well as for various PC samples of diluted Cr alloys [75 B 11. Hysteresis is indicated by latent heat for increasing and decreasing temperature.

TNWI

Cr-sc Cr-pc Cr-0.6 Cr-0.3 Cr-0.4 Cr-2.2 Cr-2.7 Cra.3 Cr-1.9

at% at% at% at% at% at% at%

MO W Co Co Co Al Al

Latent heat [J mol-‘1

75Bl

73Al

Increasing T

Decreasing T

311.4 312

311.5 ‘) 312

l.lO(lO) 1.06(10)

0.97(10) 0.97(10)

303 303

304 304

0.80(8)

0.80(8)

298

298

0.98(10) 0.44(10)

0.85(9) -

300 325 300

300 324 300

0 0 0.36(6)

0 :.35(6)

310

310

0

0

‘) [7OS 1-J.

01 0

0 0

Landolt-Bornstein New Series 111/19a

2

L x-

6

at%

8

2

$ x-

6

at%

8

Fig. 23. Transition temperatures and rms average moments per atom, j, for Cr-X alloys. Transition temperatures are designated TN separating paramagnetic and transverse incommensurate phases for X=V, MO, Ta, W, or paramagnetic and commensurate (Q = 27c/a) phases for X=Mn, Ru, Rh, Re; T,, separating transverse and longitudinal incommensurate phases, and Tci separating commensurate and transverse incommensurate phases [66 K 11.

Franse, Gersdorf

14

.1.1.3 Cr

[Ref. p. 22

16 K kbor 12 I 0. =: e= m

8 4 310 K

Cr-Co a

I 285 LT 260

vFig. 24. Concentration depcndcncc of the N&cl tcmpcraturc Ts for Cr-V alloys. dcduccd from rcsistivity minima: open circle [64 K I]. solid circles [62 T 11.

Fig. 25. Nkl temperature TF:and its pressure dependence as functions of the Co concentration in Cr. derived from resistivity mcasurcmcnts [SOK 11.

I

compression I 320 K\ 1

300

h

!g@Jj

290

295

300

r, -

305

310

K 3

12

3

4

5

6

lkbor 8

P-

Fig. 26. Variation of the N&l tcmpcraturc TN with hydrostatic prcssurc p for 99.99% Cr [81 W 21, solid lint [65hl

0

Fig. 27. Pressure dependence of the Neel temperature T, and the spin flip temperature T,, of Cr [68 U I].

I].

Frame, Gersdorf

Ref. p. 221

1.1.1.3 Cr

325,

I

0

2

10.0 kbar 1.5 I 5.0 b 2.5 0 310

315

320

325

330

K 3:

4 kbor 6

TN-

Fig. 28. Variation of the NCel temperature TN of Cr (defined as the minimum in the temperature derivative of the resistivity) with the tensile stress 0 [Sl W 21.

0

-v a v -12

16.9” 22.5" 28.1" 33.8" I -10

lsf

-8

-6 AT,, -

-4

-2

K

Fig. 30. Depression ofthe spin-flip temperature, AT,,, of Cr by an applied flux density B,,,, making various angles 0 with Q along the z axis, determined from the positions of the peaks in the attenuation a(T) ofultrasonic waves with wavevectors q/IQ. The line corresponding to 0=0 is a least-squares fit to the data points [81 B 11.

Land&Bdmstein New Series 111/19a

Fig. 29. NCel temperature TNas a function ofpressure for the alloy Cr-3.38 at% Co [SOK 11.

-30 80

120

160

200 T-

240

-I

1 280 K 320

Fig. 31. Temperature dependence of the differential thermal expansivity E= Al/l of single-Q, single-crystal Cr. Solid curves, crosses, and circled crosses represent data. The dotted curve is a linear interpolation of E, between zero at TN and s,‘just above T,,. The dashed curve is the zero reference resulting from setting E,EO in the AFl phase. In the AFl phase s,=O, sp=(cl/al)-1, E, =(b,/a,)-1. In the AF2 phase &,=(~~/a~)--1, Ed =(cJaJ - 1 [69 S 11. LSDW: longitudinal spin density wave, TSDW: transversal spin density wave. The subscripts 1 and 2 refer to the AFl and AF2 phase, respectively.

Franse, Gersdorf

[Ref. p. 22

1.1.1.3 Cr

16

Table 6. Values of the elastic coeflicicnts of Cr as a function of temperature T [81 L I]. c,=(c,,+c,, K=f(r,,+2c,,). + 2c,,) ‘2. c = CJJ. c’=(c,*-c,*)/2. T K

CL

c

c+fc’

K

1.004 1.002 1.001 1.000 0.999 0.99s 0.996 0.995 0.994

1.476 1.473 1.471 1.469 1.467 1.464 1.462 1.460

1.687 1.721 1.750 1.777 1SO2 1.826 1.848 1.867 1.882 1.949 1.952 1.952 1.951 1.949 1.946

2.0 Mbar

Cr

Mbar 3.163 3.194 3.221 3.246 3.269 3.290 3.310 3.326 3.339 3.383 3.353 3.3Sl 3.378 3.373 3.365

320 330 340 350 360 370 3so 390 400 500 510 520 530 540 550

2c3

23

300

350 I-

400

450 K 500

1.4 131 '250

II I 300

I

I

I

I 350

I I 400 T-

I I 450

I I I I 500 K 553

Fig. 32. Bulk modulus K of Cr as a function of tempcraturc. Solid line: [8l L I], dashed line: [63 B I]. open circles: [7lP I], full circles: [79K 11. K=f(c,,+Zc,,).

1.415I 308

310

312

311

I 316

I 318 K 320

I-

Fig. 33. Shear moduli cJ., and c’ of Cr as functions of the tempcraturc. Solid line: [Sl L 11. open circles: [71 P 11, full circles: [79K 11. c’=j(c,,-c,J.

Fig. 34. Variation ofthc shear modulus c’=$(cI, -cr2) of Cr in the region of the N&cl point, Full circles: incrcasins x open circles: decreasing T [81 L I].

Frame, Gersdorf

Ref. p. 221

1.1.1.4 Mn

17

1.1.1.4 Mn a-Mn The phase of manganesemetal which is stable at room temperature, a-Mn, has probably the most complex crystallographic and magnetic structure of all elements.a-Mn has a cubic crystallographic symmetry, the cubic unit cell contains no less than 58 Mn atoms, distributed over 4 nonequivalent sites; the configuration of the surrounding of each site by the other Mn atoms is unique for each of the 4 different sites. Below the NCel temperature TN=95 K, a-Mn is antiferromagnetic; since the magnitudes of the magnetic moments of the Mn atoms on different sites are highly different, an antiferromagnetic ordering can only be achieved if the atoms of each site order antiferromagnetically among themselves; the magnetization vectors of the 4 different sublattices are not collinear. This structure, which has been analyzed by Yamada in 1970 [7OY l-31, is depicted in Fig. 35.

a-Mn j=l

3

4

1.59pg

~fJfJj) J-

Site II 1,

i=l

-0.50

0.58 in

7

s it eI

-

Table 7. Low-temperature values of the magnetic moments pMnon the various atom sites in a-Mn [7OY 21.

0.27

Site

Atoms/cubic cell

phi Cam,

I II III IV

2 8 24 24

1.9 1.7 0.6 0.25

Site III

&

j=l

@

@

7 @

Site l!L

IO

@Q.wB 0.13

”

0.11

Fig. 35. Magnetic structure of a-Mn below 95K as determinedby Yamada.Vectors representthe magnetic momentfor eachofthe 29 atomsin the primitive unit cell. The edgesof the right prisms give, in units [uLs],the componentsof the magneticmoment in, respectively,the x, y, z directions. Integersj number the atomsfor eachof the crystallographic sites 1...IV [70 Y l-31. From antiferromagnetic resonance measurements,Yamagata [72 Y l] concluded that the site II atoms are divided into two subtypes (each4 atoms/cubic cell) with a magnetic moment of 1.84ur, and 1.75un, respectively; also for sites III and IV the situation is probably more complicated than depicted above. The magnetic susceptibility of c+Mn is only slightly temperature-dependent; it shows a broad maximum above the Ntel point, but no anomaly near TN, see Figs. 36...38. A good room temperature value is xs = 11.7.10-* m3/kg. A weak ferromagnetism, often observed below 45 K, is probably due to contamination of the sample with Mn,O, [7OY 31. In antiferromagnetic a-Mn the differential magnetic susceptibility increasesby about 50% above its low-field value, if the applied field exceeds11T, seeFig. 39; this effect can possibly be interpreted as a change in the angle between the antiferromagnetic vectors of atoms on two different sites. Landolt-Bornctein New Series 111/19a

Franse, Gersdorf

[Ref. p. 22

1.1.1.4 Mn

18

In paramagnetic cc-Mn, the contributions of the ditlerent sites to the susceptibility has been analyzed by an interpretation of NMR measurements [8 1 M 1,8 1 M 23; the susceptibility of a site I atom is about twice that of a site II atom: the susceptibility of site III and site IV atoms is relatively small. Since there are four times as many site II as site I atoms. the major part of the total susceptibility is due to site II atoms. The effect of alloying cr-Mn with small amounts of V, Cr, Fe, Co or Ni on the susceptibility is small, see Fig. 38. The NSel point is shifted to lower temperatures by V and Cr, and to higher temperatures by Fe, Co, Ni and Ru. see Figs. 38, 41, 42. and Table 8. The N&l point of z-Mn is shifted to lower temperatures by application of pressure [74 M 23:

aT,

--=-l.7(2)~10-3K/bar,

af

set Fig. 40. In the temperature range 45 K 5 T< TNthe principal axis of the magnetic symmetry is along a [loo] direction [70)‘3]. The magnetic anisotropy torque of antiferromagnetic a-Mn has a complicated structure. Knight shifts for the various lattice sites in cc-Mn arc given in Fig. 43. II cm?5 .10

!

Mn

11.0, 40-6 cm3

.A' ?: j-7

wi 10

rm

I

15.01 lv

CL-Mn

-9

b/'

~-

-ii-.

I I

8 0

10.00

500

753

1000 I-

25

K

50

I-

10.0

IA

253

I

12.5

I

B

--j-l+Ih t

1

x" 1250 1500 1750 K 2000 9.5 r..?

Fig. 36. h4agnctic mass susceptibility zs vs. temperature for the various phases of Mn metal. Th’: Nkl tempcrature: T,,: melting point [69 K 23.

9.0I 0

50

100

150

200

'\

250

300 K 350

Ili.0 .10-' e-7 LItI-

a-Mn-1 at%3d

I

lYl.5

Fig. 37. Temperature dependence of the magnetic mass susceptibility xp of a-Mn. Impurity content: O.O04wt% Mg. 0.025 wt% S, 0.0055 wt% Ca; purity degree “4NS”. Curve I: nonoxidized Mn, curve 2: lightly oxidized Mn [69 K 21.

1.5 && 9 I 1.0 b 0.5

6.5 8.0 0

0 50

100

150 I-

200

250 K 300

5

11

1L

17

1

20

BOPPl-

Fig. 3s. Tempcraturc dcpcndcnce of the mngnctic mass susccptibility~~, ofrr-Mn (upper curves) and p-Mn (lower curies) contammg I at% of other 3d transition elements. The N&l temperatures TX. indicated by arrows. arc dctcrmincd as the minima in the rcsistivity vs. temperature cu~cs [74 M 11. XC also [73 N I].

Fig. 39. Magnetic moment per gram. G, vs. applied magnetic flux density at 77 K for a polycrystalline sample of a-Mn, in fields up to 20T [7l Z I]. Since the low-field values of cr are at variance with other data. these mcasuremcnts probably have qualitative significance only.

Frame, Gersdorf

Ref. p. 221

1.1.1.4 Mn

Table 8. NCel temperature TN and shift of NCel temperatures AT, = TN- T,(a-Mn) of a-Mn alloys containing lat% transition metals [74 M 11. Alloy

TN

840) l%(l) 118(l) 104( 1)

-12(l) 0 +15(1 +22(1 +

0 K

1

-5

D II p-10 I LIT

AT,

K a-Mn-Cr a-Mn cl-Mn-Fe a-Mn-Co a-Mn-Ni

19

-15

\

0 cc-Mn I . a-Mn-8at%Fe -20

9(1

0

2

4

6

8

kbar 10

P-

Fig. 40. Pressure dependence of the NCel temperature TN of a-Mn and of x-Mn,,,,Fe,,,,. The NCel temperatures are derived from the relative minima in the resistivity vs. temperature curves [74 M 21. 160 K I

140 120 100 t z 80 60 40

-10 8

20 -20 0 4 at"/.

0 2 -x-

0

-30 L

2 at% 4

V

Fig. 41. Neel temperature TN as derived from relative minima in the resistivity vs. temperature curves for various a-Mn alloys. Subscript A denotes annealed at 620 “C, while B denotes heated to 900 “C and annealed at 620 “C [73 W 11. Solid symbols: [73 W 11, open symbols: [71 w 11.

Landolt-Bdmstein New Series 111/19a

Cr

Mn

Fe

Co

N

Fig. 42. Rate of change of the Nirel temperature TN of a-Mn due to alloying of other 3d transition elements [74 M 11. Solid circles: [74 M l], open circles: [73 W 11, triangles: [71 W 2-J.

Frame, Gersdorf

1.1.1.4 Mn

20

’ 7;

[Ref. p. 22

, m-Mn

0

. . .

,

. . .

.

.

.

.

B a

.

.

. . A

-1

.

.

t .

.

. .a.*

.

I Fig. 43. Temperature dependence of the Kni_eht shift for the four dilkrcnt crystallographic sites I...IV m r-Mm It is not conclusive from the expcrimcnts whcthcr the

lh

G

53

150

10G

200

250 K 300

measuring points A and B apply to sites III and IV rcspcctivcly, or vice versa [Sl MI, 81M 21.

T-

p-Mn p-Mn is an allotropic modification of manganesewhich is only stable between 1000K and 1368K. It can, however. be retained at room temperature and lower temperatures as a metastable phase by quenching the hot metal in ice-cooled water. p-Mn has a complex cubic crystalline structure, with 20 atoms per cubic unit cell, divided over 2 different sites. The magnetic structure is. however, very simple: p-Mn is a Pauli paramagnet with a nearly temperatureindependent magnetic susceptibility, see Figs. 36 and 38. Introducing small amounts of Cr, Fe, Co or Ni into p-Mn has only a small influence on the susceptibility at room temperature. At lower temperatures, impurity atoms of Cr, Fe or Co cause an additional term in the susceptibility, proportional to l/T (if T> 80 K). This is explained by assuming that a Cr, Fe or Co atom in a surrounding of p-Mn has a local magnetic moment ofabout 1 pe. Ni atoms in p-Mn behave differently, [74 M I] and Figs. 38 and 44. -7

100

300 K

, fbMn'-lot%i3d

0

1

50

1

I

, /"

8

12

16 .1F3K-' 20

Fig. 44. Change of the magnetic mass susceptibility, Azr:= xa(alloy)-X&P-Mn), for alloys of p-Mn containing 1at% of other 3d elements, vs. inverse temperature. Dashedlint: Curie law correspondingto perf= I .73pn per solute atom [74 M I].

l/T -

Franse, Gersdorf

Ref. p. 221

1.1.1.4 Mn

21

y-Mn y-Mn is another allotropic modification of manganese,this phase is only stable between 1368K and 1406K. y-Mn can be stabilized at low temperatures by alloying manganesewith small amounts of C, Fe, Ni, Cu or Pd, and quenching the alloy from high temperatures. At high temperatures, y-Mn has a face-centeredcubic crystalline structure. The Mn-rich alloys in the y-phase at low temperature, however, are antiferromagnetic and have a substantial tetragonal deformation of the crystal lattice in the direction of the sublattice magnetization, which is along [OOl]; the ratio of axes, c/a, is 0.945 [71 E 11. At low temperatures, the magnetic moment of the Mn atoms in y-Mn is 2.1...2.3 un, and the Neel point is about 500K [71 E 11. The magnetic susceptibility as a function of temperature is given in Figs. 36 and 45.

IL .lOP cm3 9 I IO s

8

Fig. 45. Temperature dependenceof the magnetic mass susceptibility xeof y-Fe-Mn alloys, stabilized with 5 at% of Cu [71 E 11.

6

0

100

200

300 T-

400

500 K 600

6-Mn The fourth allotropic phase ofmanganese, S-Mn, is stable between 1406K and the melting point is at 1517K; it has a body-centered cubic crystallographic structure. Its magnetic susceptibility at high temperatures has been measured, seeFig. 36; no other magnetic data are available. Mn-hydrides The hydrides and deuterides of manganese have a hexagonal close-packed crystallographic structure; it appearsthat MnH 0.94is slightly ferromagnetic, with a Curie point near room temperature, [78 B l] and Figs. 46 and 47. 2.0 Gcm3 9 1.5

2.0 Gcm3 9 1.5

I 1.0 b

t b 1.0

0.5

0 0

50

100

150

200

250 K 300

T-

Fig. 46. Temperature dependenceof the mass magnetization u of MnH 0.94in an applied magneticflux density of 5T (open circles), the same for a-Mn (solid circles) [78 B l] Landolt-BOrnstein New Series 111/19a

0.25

0.50

x-

0.75

1.00

Fig. 47. Dependenceof the massmagnetization of Mn hydrides (open circles) and Mn deuterides(solid circles) on, respectively,the hydrogen and deuterium content x. Applied magneticflux density 5 T, temperature82K. For a-Mn prepared by decomposition of MnH,.,,, seehalf black point [78 B 11.

Franse, Gersdorf

22

References for 1.1.1 1

1.1.1.5 References for 1.1.1 52M 1 53K I 55R 1 56M I 5SLl 61 B 1 6201 62s I 62Tl 62T2 62 W 1 63B I 64K I 64 hl 1 64M2 64Wl 65A 1 65Kl 65M I 66K 1 66Pl 67El 68s 1 68U 1 69Kl 69K2 69s 1 7OCl 7OSl 7OY 1 7OY2 7OY3 71Cl 71 E 1 71Hl 71Kl

McGuire. T.R.. Kriessman, C.J.: Phys. Rev. 85 (1952) 452. Kriessman. C.J.: Rev. Mod. Phys. 25 (1953) 122. Rostoker. W., Yamamoto, A.: Trans. Am. Sot. Met. 47 (1955) 1002. McQuillan. A.D., McQuillan. M.K.:Titanium, London: Butterworth Scient. Publ. 1956. Lingelbach. R.: Z. Phys. Chem. N.F. 14 (1958) 1. Burger, J.P., Taylor, M.A.: Phys. Rev. Lett. 6 (1961) 185. Overhauser, A.W.: Phys. Rev. 128 (1962) 1437. Shirane, G., Takei, W.J.: J. Phys. Sot. Jpn. 17, B III (1962) 35. Taniguchi. S., Tebble, RX, Williams, D.E.G.: Proc. R. Sot. London A 265 (1962) 502. Taylor. M.A.: J. Less-Common Met. 4 (1962) 476. Wilkinson, M.K., Wollan, E.O., Koehlcr, W.C., Cable, J.W.: Phys. Rev. 127 (1962) 2080. Bolef. D.I.. Klerk, J. de: Phys. Rev. 129 (1963) 1063. Komura. S., Kunitomi. N.: J. Phys. Sot. Jpn. 20 (1964) 103. Montalvo. R.A.. Marcus, J.A.: Phys. Lett. 8 (1964) 151. Munday, B.C.. Pepper, A.R., Street, R.: Brit. J. Appl. Phys. 15 (1964) 611. Weiss. W.D., Kohlhaas, R.: Z. Naturforsch. A 19 (1964) 1631. Arrot, A., Werner, S.A., Kendrick, H.: Phys. Rev. Lett. 14 (1965) 1022. Kohlhaas, R., Weiss, W.D.: Z. Naturforsch. A 20 (1965) 1227. Mitsui. T., Tomizuta, CT.: Phys. Rev. 137 (1965) 564. Koehler. WC., Moon. R.M., Trego, A.L., Mackintosh, A.R.: Phys. Rev. 151 (1966) 405. Pepper, A.R.. Street, R.: Proc. Phys. Sot. 87 (1966) 971. Ebneter, A.E.: Thesis. Air Force Inst. of Techn., Wright-Patterson Air Force Base,Ohio USA 1967. Street. R., Munday, B.C., Window, B., Williams, I.R.: J. Appl. Phys. 39 (1968) 1050. Umcbayashi. H., Shirane, G., Frazcr, B.C., Daniels, W.B.: J. Phys. Sot. Jpn. 24 (1968) 368. Kohlhaas, R., Weiss. W.D.: Z. Angew. Phys. 28 (1969) 16. Kohlhaas. R., Weiss. W.D.: Z. Naturforsch. A24 (1969) 287. Steinitz. M.O., Schwartz, L.H., Marcus, J.A., Fawcett, E., Reed, W.A.: Phys. Rev. Lett. 23 (1969)979. Callings. E.W., Ho, J.C.: Phys. Rev. B2 (1970) 235. Steller. B.: Physica Scripta 2 (1970) 53. Yamada, T.: J. Phys. Sot. Jpn. 28 (1970) 596. Yamada. T., Kunitomi. N., Nakai. Y.: J. Phys. Sot. Jpn. 28 (1970) 615. Yamada, T., Tazawa. S.: J. Phys. Sot. Jpn. 28 (1970) 609. Callings. E.W., Gehlen, P.C.: J. Phys. F 1 (1971) 908. Endoh. Y., Ishikawa. Y.: J. Phys. Sot. Jpn. 30 (1971) 1614. Huguenin. R., Pclls. G.P., Baldock, D.N.: J. Phys. F 1, (1971) 281. Kostina, T.I., Shafigullina. G.A., Kozlova, T.N., Kuznetsov, V.I.: Phys. Met. Metallogr. (USSR) 32 (1) (1971) 203. 71Pl Palmer, S.B.. Lee. E.W.: Philos. Mag. 24 (1971) 311. Whittaker. K.C., Dziwornooh, P.A.: J. Low Temp. Phys. 5 (1971) 447. 71Wl 71 W2 Whittaker, K.C., Dziwornooh, P.A., Riggs, R.J.: J. Low Temp. Phys. 5 (1971) 461. Zavadskii, E.A., Morozov, E.M.: Sov. Phys. Solid State 13 (1971) 1263. 7121 72V 1 Volkenshtein. N.V., Galoshina, E.V., Romanov, E.P., Shchegolikhina, NJ.: Sov. Phys. JETP 34 (1972) 802. 72Y 1 Yamagata. H., Asayama, K.: J. Phys. Sot. Jpn. 33 (1972) 400. 73Al Arajs. S.. Rao, K.V., Astriim, H.U., De Young, T.F.: Physica Scripta 8 (1973) 109. 73K 1 Kondorskii. E.I., Karstens, G.E., Kostina, T.I., Shafigullina, G.A., Ekonomova, L.N.: Proc. Int. Conf. Magnetism ICM-73 (Moscow) I(1) (1973) 310. Nagasawa. H., Uchinami, M.: Phys. Lett. 42A (1973) 463. 73Nl 73 w 1 Williams jr.. W., Stanford, J.L.: Phys. Rev. B7 (1973) 3244. Degyareva, V.F., Kamirov, Yu.S., Rabin’kim, A.G.: Sov. Phys. Solid State 15 (1974) 2293. 74Dl 74M 1 Mekata. M.. Nakahashi, Y., Yamaoka, T.: J. Phys. Sot. Jpn. 37 (1974) 1509. 74M2 Mdri, N.: J. Phys. Sot. Jpn. 37 (1974) 1285. 74Tl Tsunota. Y., Mori, M., Kunimoto, N., Teraoka, Y., Kanamori, J.: Solid State Commun. 15 (1974)287. 74v 1 Volkenshtein. M.V., Galoshina, E.V., Panikovskaya, T.N.: Sov. Phys. JETP 40 (1975) 730. 75Bl Benediktsson. G., Astr6m, H.U., Rao, K.V.: J. Phys. F 5 (1975) 1966. 76Fl Fawcett, E.. Gricssen. R., Stanley, D.J.: J. Low Temp. Phys. 25 (1976) 771. Frame, Gersdorf

Referencesfor 1.1.1 IlAl llA2 18Bl 78Gl 79Kl 1921 80Kl 80Rl 8OVl 8OWl 8OW2 81Bl 81B2 81B3 81Fl 81Gl 8111 81Ll 81Ml 81M2 81Wl 81W2 82Bl 82Ll 82Sl

Landolt-Bornstein New Series IWl9a

23

Adamesku, R.A., Mityushov, E.A.: Phys. Met. Metallogr. (USSR) 43 (4) (1977) 70. Alikhanov, R.A., Zuy, V.N., Karstens, G.E., Smirnov, L.S.: Phys. Met. Metallogr. (USSR) 44 (3) (1977) 178. Belash, LT., Ponomarev, B.K., Tissen, V.G., Afonikova, N.S., Shekhtman, V.Sh., Ponyatovskii, E.G.: Sov. Phys. Solid State 20 (1978) 244. Golovkin, V.S., Bykov, V.N., Levdik, V.A.: Sov. Phys. Solid State 20 (1978) 651. Katahara, K.W., Nimalendran, M., Manghnani, M.H., Fisher, E.S.: J. Phys. F9 (1979) 2167. Ziebeck, K.R.A., Booth, J.G.: J. Phys. F9 (1979) 2423. Koning, L. de, Alberts, H.L., Burger, S.J.: Phys. Status Solidi A62 (1980) 371. Ruesink, D.W., Fawcett, E., Griessen, R., Perz, J.M., Templeton, I.M., Venema, W.J.: Int. Conf. on Phys. of Transition Metals 1980 (Leeds), p. 335. Venema, W.J., Griessen, R., Ruesink, W.: J. Phys. FlO (1980) 2841. Walker, M.B.: Phys. Rev. B22 (1980) 1338. Williams, I.S., Street, R.: J. Phys. FlO (1980) 2551. Barak, Z., Fawcett, E., Feder, D., Lorinck, G., Walker, M.B.: J. Phys. Fll (1981) 915. Barak, Z., Walker, M.B.: J. Phys. F 11 (1981) 947. Booth, J.G., Ziebeck, K.R.A.: J. Appl. Phys. 52 (1981) 2107. Fincher jr., CR., Shirane, G., Werner, S.A.: Phys. Rev. B24 (1981) 1312. Geerken, B.M., Griessen, R., Dijk, C. van, Fawcett, E.: Proc. Intern. Conf. Physics of Transition Metals, Leeds 1980, 1981,p. 343. Iida, S., Tsunoda, Y., Nakai, Y., Kunimoto, N.: J. Phys. Sot. Jpn. 50 (1981) 2587. Lahteenkorva, E.E., Lenkkeri, J.T.: J. Phys. F 11 (1981) 767. Murayama, S., Nagasawa, H.: J. Phys. Sot. Jpn. 50 (1981) 1189. Murayama, S., Nagasawa, H.: J. Phys. Sot. Jpn. 50 (1981) 1523. Williams, I.S., Street, R.: Philos. Mag. B43 (1981) 893. Williams, I.S., Street, R.: Philos. Mag. B43 (1981) 955. Benediktsson, G., Astrom, H.U.: Phys. Ser. (Sweden) 25 (1982) 671. Littlewood, P.B., Rice, T.M.: Phys. Rev. Lett. 48 (1982) 44. Siegmann, H.C.: J. Appl. Phys. 53 (1982) 2018.

Franse, Gersdorf

24

1.1.2.1 Fe, Co, Ni: introduction

[Ref. p. 134

1.1.2 Fe, Co, Ni 1.1.2.1 Introduction In the last two decadesprogresshas been made in the solution of the understanding of the origin and behavior of magnetism in the metallic 3d elements. These advances have been achieved by the replacement of the earlier thermodynamic approaches to magnetism with a microscopic understanding in which the magnetic behavior is related to the underlying electronic interactions within and between the atoms. This has been achieved becausea number of new and improved experimental techniques becameavailable along with the development of highspeedcomputers used for both complex data acquisition and analysis and for band structure calculations. Often in the past the interpretation of magnetic data was made in terms of a purely localized or itinerant model. We now know that these two extreme models are oversimplifications of the real situation and that the d valence electrons have both features.As a result, the type of behavior that is obtained is strongly dependent on the experiment performed. Experiments that probe the regions close to the nucleus such as nuclear magnetic resonance.neutron scattering. etc., are sensitive to the more local, atomic-like character of the electrons while other techniques such as specific heat, transport properties, dc Haas-van Alphen effectthat probe mainly the tails of the wave functions are sensitive to the nonlocal or itinerant character. Some of the significant techniques developed and achievements made in the recent years are: I. Neutron scattering techniques allowed the measurementsof the form factors, magnetization distributions and magnon dispersion relations. 2. The development of Miissbaucr and pulsed nuclear magnetic resonancespectroscopiesmade possible the determination of the shape of the s and d conduction-electron polarizations, which showed that the mechanism responsible for the origin of ferromagnetism in 3d metallic ferromagnets is the alignment of the “quasi-local” d moments by the polarized itinerant d electrons rather than by the s valence electrons as was the favored mechanism in the early 1960s. 3. Improvements in de Haas-van Alphen measurementslead to the determination of the Fermi surfacesof these complex metals. 4. The development of angle-resolved photoemission spectroscopy allowed the direct measurement of the excited-state exchange splittings and band structures. 5. The availability of high-speed computers made the complex calculations of the ferromagnetic band structures routine so that the effects of different approximations and potentials could easily be investigated. The transition elementsare ofgreat technological importance precisely becauseof the complex and versatile character of their outer electrons. This compilation will concentrate on presenting the current experimental data. It will discuss theory only in so far as it enhances the description of the data or when it is so symbiotic to the data, as in the case of band structure. that it is necessaryfor a sensible presentation of the data. There are numerous theoretical calculations aimed at describing particular experimental results; no attempt will be made to review theseor the present state of the agreement between the theoretical details and experiment. Data on alloys of Fe, Co and Ni are included in this compilation when they predominately provide information about the host.

1.1.2.2 Phase diagrams, lattice constants and elastic moduli At atmospheric pressure Fe undergoes the following transitions [670 I, 74D 11:

bee a

a fee

1665K

bee-liquid.

Earlier measurements[62 J l] found that the room-temperature phase transformation to a hexagonal close packed (hcp) structure occurred at 130kbar and the triple point at 775 K and 110kbar. More recent [71 G l] measurementshave found it to occur at 107(8)kbar with the triple point at about 750 K and 90 kbar. The theory of the phase diagram for Fe has been discussed by Grimvall [76G 11. At high temperature Co is fee and at low temperature it is hcp. The transformation is sluggish so that both forms coexist from room temperature to 450°C. The stable structure of Ni is fee.It has been claimed to have beenprepared in the hcp form by several workers [74D 11. It has also been prepared in the bee structure [74D 11.

Stearns

Ref. p. 1341

1.1.2.2 Fe, Co, Ni: phase diagrams, lattice constants

25

Table 1. Lattice constants, interatomic distances, atomic volumes and thermal expansion coefficients of Fe, Co, and Ni [74D 11. T

Phase

P

“C

i

ri

x

13

~1,bee ct, bee Y, fee Y, fee 6, bee a, bee E, hcp

2.86638(190) 2.9044 3.6467 3.6869 2.9315 2.805 2.468l)

3.956

2.482(8) 2.515(S) 2.579(12) 2.607(12) 2.5388(g) 2.429(S) 2.468(6) 2.408(6) 2.507(6) 2.497(6) 2.506(12) 2.492(12) 2.495(6) 2.484(6)

11.78 12.25 12.12 12.53 12.60 10.43

bar

Fe

20 910 910 1390 1390 23 23

1 1 1 1 1 130.103 130.103

co

20

1

a, hcp

2.5070(3)

4.0698(9)

Ni

20 20 20

1 1 1

P, fee fee hcp

3.5445(4) 3.5241(7) 2.495(12)

4.048(43)

20

1

bee

2.775(14)

-

2.403(8)

E lo-‘jK-’ 11.7; Fig. 3a

11.03 11.08

Figs. 3a, 4a

11.13 10.94(1)

12.5; Fig. 3a

10.91(16) 10.68(16)

‘) For pressure dependence,see Fig. 2.

.

6 calculated

P-

P-

Fig. la. Pressure-temperaturephasediagram for pure Fe [71G1].1:[62K1],2:[60C1],3:[63C1],4:[62J1],5: [65B1],6: [65B2], 7,8: [69M2],9: [71Gl].

Landolt-BBmstein New Series 111/19a

Fig. lb. Pressure-temperaturephase diagram for Co [63 K 11.hcp: a-Co and fee: P-Co. Other notation used to designate hcp and fee phases is E-CO and y-Co, respectively.

Stearns

[Ref. p. 134

1.1.2.2 Fe, Co, Ni: lattice constants

26

3.62, ii I

I

I

I

I

I

INifcc

I/

/I I

3.56 cc 3.56

I 3.59

1 3.52 D

3.57 I cl

2.91 a

2.91 a

2.92

2.92

2.86r D

a

I 60'3

300

I 900

I I 1200 "C 1530

Fig. 3a. Temperature dependcncc of the lattice constants of Fc, Co, and Ni above room temperature [67 K 23. 0

50

100

150

200 P-

250

300

kbor LOO

Fig. 2. Pressure dependence of the room-temperature values of the lattice constants and axial ratios of hcxagonal Fe: open circles [64C I]; solid circles [66 M I].

18

12 .1rj-5

16

AK.1

6 I

c,

3

3 0 -2OG b

0

200

400

600 I-

800 1000 12oo"cl~oo

Fig. 3b. Temperature derivative of the lattice constant, dn’dT. for Fe and B-Co [67 K 21.

Fig. 3c. Thermal expansion coefficient of Ni vs. tempcraturc (solid line) and the calculated (dashed lint) paramagnetic values [77 K 33. Curve 1: [65 W 13, 2: [68 C 11, 3: [64T I]. 4: [38 R I]. 5: [63 K 21.

0 C

200

400

600 T-

800

1000

1200 K 1400

Ref. p. 1341

1.1.2.2 Fe, Co, Ni: lattice constants

d

15.5II 605

610

615

620

625

630

635

27

640

645 K 650

Fig. 3d. Thermal coefficient near the Curie temperature of Ni. Data I: [77 K 3],2: [71 M I].

8 .lO-3 6 I : z

4 2

I

1.625 1.630

4.06 5 1.620 1.615

b a

0

100

200

300

400

500

600 K :

7-

Fig. 4a. Thermal expansion curves ofhcp Co. The dashed curves (3: [810 11) are obtained by fitting the bulk thermal expansion curve (I: [65 W 11)to the experimental points (2: [67 M 11). Land&-Bbmstein New Series IIV19a

1.610 0

100

200

300

400

500 K 600

T-

Fig. 4b. Plot of available c/a data for hcp Co with the predicted temperature dependence from a single-ion model of the anisotropy [84P I]. Curve 1: [48 E 11, 2: [36M1],3:[67M1],4:[36N1],5:[5401],6:[27Sl], 7: [5OT I], 8: [31 W 11, open circles: private communication of P. Goddard.

Stearns

[Ref. p. 134

1.1.2.2 Fe, Co, Ni: elastic constants

2s

Table 2. Room-temperature

values of the elasticity moduli of polycrystalline

Ref.

K

E

Fe, Co, and Ni.

G

P

Ref.

0.823 0.799 0.834

0.291 0.310 0.304

67Al 67Al 67Al

Mbar

Mbar Fe

1.681

61Rl

co

1.914

64Gl

Ni

1.836

60A 1

2.08 2.089 2.197

Table 3. Elastic stiffness constants of Fe and Ni as derived from ultrasound measurements on single crystals. c’=(c,, -c,,)/2. T “C

Cl1

C’

c44

Ref.

0.483 0.139 0.504

1.170 0.993 1.235

72Dl 72Dl 60A 1

Mbar Fe

25

880 Ni

RT

2.322 1.505 2.508

1.20I Mbor

a-Fe

0.95I 0.50,

I

/

1

I I

I

2.: I

2.0

z 1.9

I

Mbor/\l I

1.8

I

I

I

1 (

0.G

1.7 1.6

0.10

1.5 153

a

300

150

600

750 "C 900

Fis. 5a. Temperature depcndencc of the longitudinal elastic constant c, L of r-Fc as dcrivcd from ultrasonic measursmcnts. The expcrimcntal data points of [72 D l] are all within the drawn cuwcs. Also included arc the data points of (open circles) [66 L 11, (solid circles) [6S L 11.

\

0.35

I-

1 1% 0.30 I

L-i

Fig. Sb. Tempcraturc depcndencc of measured shear elastic constants c’=(c,,-c12)/2 and c44 of a-Fc as derived from ultrasonic mcasurcmcnts. The cxpcrimcntal data points of [72 D I] arc all within the drawn curves. Solid circles [6S L I].

o.loI 0

b

150

300

450

T-

600

750 "C

Ref. p. 1341

1.1.2.2 Fe, Co, Ni: elastic constants 1.3:IMbar 2. 1.3(I-

,-

l-

1.15

l.l[ lj 2 i-

0.5c

O.L7 I t 0.44

O.Ll 0.3F 3.4 Mbor 3.3

3.2 I u' 3.1

3.0

2.E 100

200

300

$00 T-

500

600

700 K 800

Fig. 6. Temperature variation of the elastic moduli of Ni ultrasonically measured at 10 kOe applied magnetic field. The vertical dashed line marks the Curie temperature

WAU

(a>c44, 0~1c’=h-~~~~/2~

cc>cL=hI+clz

+ 2c4,)/2. The dashed curve represents the extrapolation to low temperatures of the high-temperature data. Land&Bbmstein New Series 111/19a

29

1.1.2.3 Fe, Co, Ni:

30

[Ref. p. 134

paramagnetic properties

1.1.2.3 Paramagnetic properties The paramagnetic behavior is studied through the susceptibility above the Curie temperature. A localized magnetic moment follows the Curie-Weiss law given by dT)=

NP:U 3k,o

C, - T-O

Here p is the maximum value of the free-atom’s localized magnetic moment in direction of the applied magnetic field. J denotes the angular momentum quantum number of the atom, 9 the spectroscopicsplitting factor, and pa the Bohr magneton. N is the number of atoms per unit massand 0 the paramagnetic Curie temperature. The magnetic moment associatedwith itinerant electrons has an enhanced susceptibility and the general expression is given bj x(4.4 = %0(%4/C1 - I%,(%4 + 4%41 (2) where x0(4.(!I)is the wavevector- and frequency-dcpcndent susceptibility for a noninteracting systemofelectrons, I is an exchange -interaction constant, and I.(q.Q) is a fluctuation term which has been extensively discussedby Moriya et al. [73 M 3, 79 M 21. In general the itinerant part of the magnetic moment is more polarizable in an applied field than the local part so that the moment obtained by applying eq. (I) in the paramagnetic region results in the paramagnetic moment being larger than the moment obtained from magnetization measurementsin the ferromagnetic region. The susceptibility has been determined by magnetization measurements and neutron scattering, the magnetization measurementscorresponding to Q =O. From a plot of l/x vs. T obtained from magnetization measurementsthe paramagnctic Curie temperature @is obtained from the intercept with the temperature axis, the Curie constant C, and thus pcrris obtained from the slope.

Table 1. Paramagnctic properties of Fc, Co, and Ni. AT is the temperature interval for which the parameters of the Curie-Weiss law are determined. pa, denotes the magnetic moment per atom in the ferromagnetic phase extrapolated to T=OK. The ratio p/p,, gives an indication of the degree of localization or itineracy of the electrons forming the moment. A completely localized moment would have a value of one and a completely itinerant moment a large value > 10;e.g.Fe,,, ,Cr0.49has a ratioof 17.6(Tc=9K)and Ni0,43Pt0,57aratio of 17.2 ( Tc= 23 K) [78 W 11.Thus the moments of Fe, Co, and Ni are seento have a high degreeof localized character. Fig. a-Fe p-co Ni ‘) Liquid-Ni

la, b.d 3a 3b. c 3c

0 K + 1093(3) 1403...1428 654.1

c, 10m3cm3 K/g

AT

Peff

K

PB

22.0 20.8 5.546 8.55 16.7

1100...1180 1430...1710 740...970 1528...1728 1728...1928

3.13 3.15 1.613

PIP,,

Ref.

1.01 1.28 1.375

60A2 38Sl 63A2 73B2 73B2

‘) Ni does not obey a Curie-Weiss law; at temperatures above 970 K an additional temperature-dependent contribution 1, is found, seeFig. 4.

31

1.1.2.3 Fe, Co, Ni: paramagnetic properties

Ref. p. 1341 5 .lOC 9 iiT 4

I 3 G 2

1

0 750 a

850

950

1050

1150 “C 1250

T-

1100 b

Fig. la. Temperature dependence of the inverse paramagnetic mass susceptibility of Fe [60 A2]. I: [ 11W 11, 2: [17Tl], 3: [34P 11, 4: [38S I], 5: [56Nl], 6: [60A2].

A heating Q cooling I 1300 1500 “C 1700 T-

Fig. lb. Temperature dependence of the inverse paramagnetic mass susceptibility of Fe [56 N 11: 1: Liquid is supercooled, but &phase is not supercooled. 2: Both liquid and &phase are supercooled. 3: Liquid is supercooled to y-region.

4.10-l cm3 9 2

5.0 .in4

;;mc:=rri

! --.

1400 1500 1600 1700 1800 1900 2000K 2100 C

I

o Hopp~ = 181Oe 272

\

I2

Fig. lc. Temperature dependence of the inverse paramagnetic mass susceptibility of solid and liquid Fe [72 B 41.

1o-3 6, ir’t7 1 d

2

4

6

RIO

z

K 40

T-7, -

Fig. Id. Temperature dependence of the magnetic mass susceptibility of Fe above the ferromagnetic Curie temperature, Tc= 1044.1K. The straight line represents the relationship xp = K( T - 7”)” with n = - 1.33 [64A 21. Symbols indicate different applied magnetic fields. Landalt-Bbmstein New Series lll/l9a

Stearns

[Ref. p. 134

1.1.2.3 Fe, Co, Ni: paramagnetic properties

32

lo-',

cm3 9 6 4

2.5 .l FL UT!

2.0 2

I x”

10-2 8 6

4

“I 1103

1300 I-

1200

a

0 cooling I 1500 “C 1600 Vi00

2.10-3 1

4

2

b

Fig. 2a. Temperature dependence of the inverse paramagnetic mass susceptibility of fee Co [56N 11.

r-r,

6

Ni r, 0

cm3

d

12 10 I 8 -i! 6

0 5 0

a

.^

.^^^

10

K

20

Fig. 2b. Temperature dependence of the magnetic mass susceptibility of fee Co above the ferromagnetic Curie temperature, T,= 1388.2K, in an applied magnetic field H npp,= 181Oe. Straight lines represent tits to the data of the form xg = K( T- T,)” for various n [65 C 21.

16

.c

8

-

1100 1200 1300 1LOO 1500K 1600 I-

Fig. 3a. Tempcraturc dcpcndcncc of the inverse paramagnetic mass susceptibility of Ni. Samples 1 and 2: [63 A2],3: [I I W I], 4: [38 S 2], 5: [44 F I].

Stearns

\

2

33

1.1.2.3 Fe, Co, Ni: paramagnetic properties

Ref. p. 1341

\

,

I

n HoppI=45.3 Oe . 12.5 . 90.6 181.2 D 18 ,104 s cm3 17 I $16

8,10-'1 b

2

6

4

6

IO

K

1500

20

1600

1700

c

T-Tc -

Fig. 3b. Temperature dependence of the magnetic mass susceptibility of Ni above the ferromagnetic Curie temperature, Tc = 626.2 K, as measured for various applied magnetic fields I&.,,,. Straight lines represent fits to the data of the form xp =K( T- Tc” for various n [65A 11.

a

1100

1200

1300

1400

1500 K 1600

Fig. 4. The temperature-dependent susceptibility ofNi can be described with a Curie-Weiss law with an additional temperature-dependent susceptibility xa [63 A2].

Landolt-BOrnstein New Series lll/l9a

1900 K 2000

Fig. 3c. Temperature dependence ofthe inverse paramagnetic mass susceptibility of Ni near its melting point [73 B2].

1.0 40-6 cm3 Ti-

t IYIOO

1800 T-

Stearns

34

1.1.2.4 Fe, Co, Ni: spontaneous magnetization

[Ref. p. 134

1.1.2.4 Spontaneous magnetization, magnetic moments and high-field susceptibility bee Fe, hcp Co, fee Co and fee Ni The room-temperature magnetic phasesof Fe, Co, and Ni are ferromagnetic. The spontaneous magnetization data. oJT), quoted in the literature are obtained by extrapolating the magnetization a(7; H) to zero internal field. The general expression for the temperature and magnetic field dependenceof the magnetization per unit mass is given b) a(T.H)=~~(T)+A(T)H’IZ+X,,,(T)H,

(1)

where H is the internal field equal to the applied magnetic field minus the demagnetizing field. The second term on the r.h.s.ofthe equation is due to the effectof the magnetic field on the spin waves and xHF(T) is a susceptibility term that must be included at high fields. This term is attributed to various small contributions such as orbital and spin susceptibility of the 3d and 4s electrons [82P 11. fee Fe There has been extensive controversy about the magnetic properties of the feephaseof Fe (y-Fe) with several diverse results reported in the literature. From thermodynamic considerations on Fe it was suggested[63 W 1, 63 K 21 that y-Fe has two possible magnetic moment states depending on the lattice constant; a low-moment state at smaller lattice constants and a high-moment state at larger lattice constants. Band calculations indeed show that the magnetic moment of feeFe should undergo a rather rapid transition from a lower-moment state to a higher-moment state for a small variation in lattice constant, seeFig. 8. The rapid transition is manifestation of the flat (localized) E, bands being very near and intertwined with the Fermi level [78 M l] as seen in a band structure calculation of the paramagnetic state (seesubsect. 1.1.2.11on band structure). Conditions are thus favorable for small changesin the lattice constant to shift the E, bands through the Fermi level and thus causea rapid variation in the magnetic moment. Since feeFe is stable only at high temperatures two separatelines of study have developed. One concerns the nature of the magnetic properties of y-Fe which has been stabilized by various means at room and lower temperatures and the other is the state of y-Fe in the high-tempcraturc region. Neutron scattering measurements at 1320K have found y-Fe (a= 3.658A) to be paramagnetic with a magnetic moment of 0.9(1)~, [83 B 21. However. this moment may bc lessthan the actual magnetic moment since the characteristic interaction time of the neutrons was comparable to or slightly less than the spin-flipping time of the magnetic moment (see subsect.1.1.2.8). The low-temperature work has involved considerable controversy. This has usually arisen due to the difficulty of preparing samplesthat arc free from bee Fe which, if present, appears as a high-spin ferromagnetic state with a high transition temperature. In recent years many of the discrepancieshave been resolved by using measurement techniques such as Miissbaucr spectroscopy and neutron diffraction which are capable of correlating the structural properties with the ferromagnetic and antiferromagnetic phases as opposed to techniques which measure more macroscopic properties, such as LEED, X-ray diffraction and magnetization measurements. Since y-Fe is unstable at low temperatures it has been studied as coherent precipitates (~200...10OOA) in a Cu matrix and as pseudomorphic epitaxial thin films on a Cu substrate, seeTable 6. hcp Fe Miissbauer effect measurements down to 0.030K in the pressure range from atmospheric pressure to 21.5GPa detected no measurable hyperline field for the E-phase.This shows that the hcp phasehas no magnetic ordering down to 0.030K in this pressurerange [82 C 1,72 W 11.Massbauer effect measurementsin an applied magnetic field found that at 50 kOe, upon scaling from the 3d free-ion moment, the induced magnetic moment is ~0.08 pn. the susceptibility is 93. 10-4cm3/mol and the effective hyperfine field at the “Fe nucleus is H,,jp =030 Hap,+[82T 33. Seealso Fig. 5 in subsect. 1.1.2.8.

Stearns

1.1.2.4 Fe, Co, Ni: spontaneous magnetization

Ref. p. 1341

35

Table 1. The spontaneous magnetization crsand the high-field susceptibility ~nr, at various temperatures obtained by computer fit of the curves of Figs. la..e with the equation in subsect. 1.1.2.4.1. Applied field direction is indicated. For Fe and Ni no anisotropy in cs or xHF was found. See also Table 3 Fe and Ni [83P l-J, Co [83 P 21.

Fe [loo]

co [OOOl]

CO[ioiol

Ni [111]

T K

0s Gcm3g-’

XHF

4.21 24.79 51.06 75.34 100.51 131.55 165.81 197.45 226.34 254.53 286.41 4.21 24.79 55.31 75.28 100.46 131.31 165.30 197.01 225.69 254.67 286.61 4.21 24.79 55.36 75.28 100.51 131.31 165.50 196.81 225.74 254.67 286.66 4.21 25.00 50.08 75.15 100.51 131.08 165.49 196.71 225.74 254.82 286.66

222.671 222.596 222.367 222.071 221.825 221.443 220.937 220.346 219.736 219.049 218.210 163.82 163.79 163.68 163.54 163.50 163.44 163.39 163.29 162.99 162.93 162.62 163.00 162.98 162.70 162.65 162.64 162.58 162.46 162.40 162.26 162.08 161.86 58.872 58.810 58.698 58.550 58.349 58.063 57.671 57.223 56.724 56.121 55.370

3.60 3.66 3.70 3.81 3.84 3.79 3.76 3.70 3.81 3.90 3.95

10e6 cm3 g-r

a

1.59 1.64 1.58 1.52 1.48 1.37 1.21 1.11 1.13 1.18 1.12 For Figs. lb and c, see next page.

Land&Bdmstein New Series III/l9a

Fig. 1. Magnetization as a function of the magnetic field, at different temperatures below room temperature, of single crystals of Fe, Co, and Ni [83P 11. (a) Fe. The magnetic field is applied along, respectively, the [ 1001,[ 11l] and [ 1lo] directions [83 P 11.The measured change in flux was produced by moving the sample from one pick-up coil to a precisely matched pickup coil in series opposition in a highly uniform magnetic field. The calibration to absolute values was obtained from the measurements of Danan et al. [68 D l] on Ni as the standard of reference [83P 11. The data was accurately fit by eq. (1). It was observed that all the isotherms of magnetization curves had a continuous and welldefined, although small, curvature. Thus the usual procedure ofusing an averaged straight line to determine a,(T) is not valid for data of this quality.

Stearns

[Ref. p. 134

1.1.2.4 Fe, Co, Ni: spontaneous magnetization

36

60.0 Gcm3 9 59.5

5B.U

I+F

I

I 57.5

A225.75

b

I 1

163.35

I b 163X 56.5 16325 560

0

50

100

150

200 kOe 250

H-

C

Fig. lc. Ni. The magnetic field is applied along. respcctivcly, the [ill], [IOO] and [I IO] directions [83P 11.

16!25

Fig. lb. Co. The magnetic field is applied along, rcspcctivcly, the c axis and the [loo] direction in the basal plant [83P I]. b

HTable 2. Spontaneous magnetization a, and magnetic moment per atom, p,,, extrapolated to 0 K for Fe, Co, and Ni. In case of single crystals the direction of magnetization is indicated. 0s

Fe

Cl001 Co, hcp [0001-J [0001-J

poio]i

co, fee Ni

IIll

PSI

Gcm3g-’

PB

221.71 (8) 222.67 1 162.55 163.76 162.95 166.1 58.57(3) 58.872

2.216(l) 2.226 1.715 1.728 1.719 1.751 0.6155(3) 0.619

Stearns

Ref

68Dl 83 P 1 51M2 83P 1 83P 1 55Cl 68Dl 83Pl

1.1.2.4 Fe, Co, Ni: spontaneous

Ref. p. 1341

31

magnetization

Table 3. Survey of the spontaneous magnetization of Fe, Co, and Ni [82P 11. Direction of magnetization is indicated. See also Table 1. T

Fe [loo] co [OOOl] Ni [111]

0s

e

n/i,

7.93 7.87 9.0 8.9 8.97

1766 1717 1475 1447 528

8.91

493

K

Gcm3g-’

gcmm3

4.2 286.41 4.21 286.61 4.21 286.66

222.671 218.210 163.862 162.624 58.872 55.370

4nM,

G

G 22189 21580 18532 18 188 6636 6200

0.8

Fig. 2a. Reduced spontaneous magnetization a,( T)/o,(O) of [loo] bee Fe vs. reduced temperature T/T,. 1: [71C1],2:[82P2],3:[81H3].Thedataof[7lCl]was obtained by measuring the force on prolate ellipsoids in a field gradient while that of [81 H 31 was extracted from measurements of the ac susceptibility of iron whiskers. The data of [Sl H3] has been normalized to that of [71 C l] at room temperature and corrected for the lattice expansion to give B, in [Gcm3/g]. The reduced magnetization curve has been empirically fitted to a function [S 1 H 31: cT,(T) = CT,(O) (1 - z)B/(l - /3r + A?‘2 - W’Z) ,

_I 0.6 ” d \ kY 0.4

I

(2)

where /?=0.368, A=O.1098 and C=O.129.

0

I

0.2

a

I

I

0.4

I

0.6

0.8

IO

0.4 0.6 r/r, -

0.8

1.0

T/T, -

1.0

0.8

I - 0.6 0 \6” G 0.4

0.2

0 b

c!

r/r, -

Fig. 2b. Reduced spontaneous magnetization of Co vs. reduced temperature. I: fee [71 C 11, 2: [OOOl] hcp [SZP 11. Land&-Bbmstein New Series III/I%

0.2

Fig. 2c. Reduced spontaneous magnetization of [l 1l] Ni vs. reduced temperature. 1: [71 C 11, 2: [82P 11, 3: [69 K 11.

Stearns

[Ref. p. 134

1.1.2.4 Fe, Co, Ni: spontaneous magnetization

38 15.0 jc& 9 12.5

10.0

I 1.5 b

2.5

1035

1OLO

1015

1050

1055

1060

1065 K 10

I-

Fig. 3. Magnetization of Fe for various applied magnetic fields in the neighborhood of the ferromagnetic Curie temperature [64 A23.

15.: Gem' 9 12.5

1oc

500 Oe

I b 1.5

LOO

I 300 z 2 200

5s

2.E 100 c 1389

a

0 1385

1390

1395

1

1400 K l&O5

I-

1388

K 13

b ‘:

Fig. 4a. Magnetization offcc Co sphere in various applied maenetic fields in the neighborhood of the ferromagnetic Cuhc temperature [65 C I].

Fig. 4b. T, offcc Co as a function ofapplied magnetic field. Tc is the Curie tempcraturc derived from the magnetization curve in an applied field, see Fig. 4a. as the temperature at which CTstarts to decrease [65 C I].

Stearns

Ref. p. 1341

1.1.2.4 Fe, Co, Ni: spontaneous magnetization

39

8

I b

6

100

620

625

630

635

K

0 640

b

T-

a

Fig. 5a. Magnetization of Ni in various applied magnetic fields in the neighborhood of the ferromagnetic Curie temperature [65A 11.

622

623

62L

625 T; -

626

627 K 628

Fig. 5b. T&as a function of applied magnetic field for two Ni spheres A and B with, respectively, 1Oppm Fe and 0.01 wt% Fe. Td is the Curie temperature derived from the magnetization curve in an applied field as the temperature at which 0 starts to decrease [65A 11.

Table 4. Curie temperature and pressure dependence of the Curie temperature of Fe, Co, and Ni. Metal

T, K

Fe, bee

1044(2) 1044 1045(3) 44 ‘)

Fe, fee co, fee

Ni, fee

1388(2) 1398 1390.0 624.0(3) 627 631(2) 627(l)

Ref.

O.OO(3); Fig. 6

0.5 ‘); Fig. 9 O.OO(5)

0.36(2); Fig. 7

64A2 72Ll 71Cl 79Ll 65Cl 72Ll 71Cl 61Ml 72Ll 71 c 1 65Al

800 I h 700 600

‘1 TN. “) W’ildp),=o.

300 0

IO

20

30

40

50

60 kbor70

PFig. 6. Curie temperature (solid line and circles) and cl-y phase boundary (broken line) of pure Fe as a function of pressure. (In the insert are shown three different series of measurement for the shift of Curie temperature. The temperature scale has been enlarged 10 times). Magnetic determination ofthe a-y phase upon heating and cooling [72L 11. Land&Bdmstein New Series 111/19a

Stearns

1.1.2.4 Fe, Co, Ni: spontaneous magnetization

40

[Ref. p. 134

3.2

2x I y" Q 25

0

50

75 P-

125 kbar150

100

1.6

Fig. 7. Shift of the Curie tempcraturc for Ni as a function of pressure measured with opposed Bridgman anvils [74B I]. The results obtained by [72L I] in a belt apparatus are shown for comparison (dashed curve). 70, K

I

I

I

atbcc) -

Fig. 8. Calculated and measured magnetic moments per Fe atom for fee (curves 2...4) and bee (curve I) Fe as a function of the lattice constant. The lattice constants of room temperature bee Fe and fee Cu are indicated by arrows on the abscissas. The experimental moments are shown by asterisk for bee Fe and by circles for fee Fe, obtained from neutron scattering 5 [83 B 21, 6 [62A I] and Mossbauer effect 7 [63 G l] measurements obtained by scaling Hhyp to the a-Fe moment. Calculated curves I and 2 [83 B 1],3 [Sl K I], 4 [77A I].

60

10 0

A

I

10

20 P-

30 kbar 40

Fig. 9. Pressure dependence of the Necl tempcraturc of y-Fe in Cu [79L I]. dTs:,ldp=0.5K kbar-‘. Different symbols indicate different runs. Table 5. High-field susceptibility xHF and relative anisotropy of the magnetization at 4.2 K for Fe, Co, and Ni. Applied field strength up to 50 kOe. Also estimations of Pauli susceptibility xs and orbital contribution to the susceptibility, xL, are given [72 R 11. Direction of applied fields is indicated. For xHF, see also Table 1. Fe XHF

[lo+

co

cm3 mol- ‘1

xs [10-6cm3mol-‘] xL [10-6cm3mol-1] (0 111- 01ooh b 110 -~,ooY~, (~1*1--~11oY~s (a,,,-~,cM,,c

266(2) 305(9) [loo] 231(15) 69...98 110...142 - 7.8. lo-’ - 3.5.10-s - 4.3.10-s -

265(2)

21...40 ~2240 w450.10-5

Ni

Ref.

113(l) [111] 116(l) [llO] 118(l) [loo] llO(7) [ill] 129(10) 40...55 77...82 18.10-5 13.10-5 5.10-5 -

72R2 72R2 72R1 69Fl 69s 1 72R2 72R2 72R2 72R2 72R2 72R2

1.1.2.5 Fe, Co, Ni: magnetocrystalline

Ref. p. 1341

41

anisotropy

Table 6. Magnetic properties of fee Fe. P: paramagnetic, F: ferromagnetic, AF: antiferromagnetic, RT: room temperature. Sample y-Fe, bulk at 1320K precipitates in Cu-matrix: a=3.59...3.61 A particle size: x25OA x7ooA

Magnetic state

pFe

P

0.9(1)6)

TN K

PB

AF, P at RT AF

55(3) 67(2) 67 g4) 46

0.75 6OA epitaxial films on Cu: electrolytic [110] y-Fe, 3OA ‘) [ill] y-Fe, 6.*.80A

F at RT F at RT

four layers separated by Cu (ill), (110) or (100) layers, lg...25 A ‘) 2, 3, “) “) 6,

H hw

kOe

x24(6) x 23(6)

:::8(13) 3,

Measuring method

Ref.

polarized neutron scattering

83B2

Mijssbauer sp. Mijssbauer sp. neutron diff. neutron diff. Miissbauer sp. ‘)

63G1 63Gl 7OJl 62Al 79 L 1

FMR “) magnetization “)

71Wl 7662, 77Kl

Mijssbauer sp.

77K2, 83Hl

AF, P at RT 20...40

Large fraction of a-Fe appears also in the spectrum. Presenceof a-Fe can not be excluded. Independent of thickness. Estimated, see [70 J 11. K,=-2.0.104ergcm-3. May be less than the actual moment.

1.1.2.5 Magnetocrystalline

anisotropy constants

The anisotropy constants K,, K,, . . . are defined for cubic lattices such as Fe and Ni by expressing the free energy of the crystal anisotropy per unit volume by E,=Ko+K,S+K2P+K3S2+K4SP+...

(1)

with s = u;u; + c7.g;+ c&;

and P = ct2c12u2 1 2 3r

where cli, clj, elkare the direction cosines of the angle between the magnetization vector and the crystallographic axes. For hexagonal lattices, such as Co, it is more convenient to use the definition

where 4 is the angle between the magnetization and the c axis, and 0 is the angle in the basal plane. The measurementsare usually made on single-crystal spheresin a field large enough to remove the domain walls (called technical saturation). It is usually assumed that all the work done in changing the direction of magnetization is used to overcome the crystal anisotropy. The most common techniques used to measure this work are: 1. Measurements of the torque required to change the direction of the saturation field (TQ). 2. Measurements of the magnetization in different crystallographic directions with a moving (MSM) or a rotating (RSM) sample magnetometer. Land&Bbmstein New Series 111/19a

Stearns

1.1.2.5 Fe, Co, Ni: magnetocrystalline

Ref. p. 1341

41

anisotropy

Table 6. Magnetic properties of fee Fe. P: paramagnetic, F: ferromagnetic, AF: antiferromagnetic, RT: room temperature. Sample y-Fe, bulk at 1320K precipitates in Cu-matrix: a=3.59...3.61 A particle size: x25OA x7ooA

Magnetic state

pFe

P

0.9(1)6)

TN K

PB

AF, P at RT AF

55(3) 67(2) 67 g4) 46

0.75 6OA epitaxial films on Cu: electrolytic [110] y-Fe, 3OA ‘) [ill] y-Fe, 6.*.80A

F at RT F at RT

four layers separated by Cu (ill), (110) or (100) layers, lg...25 A ‘) 2, 3, “) “) 6,

H hw

kOe

x24(6) x 23(6)

:::8(13) 3,

Measuring method

Ref.

polarized neutron scattering

83B2

Mijssbauer sp. Mijssbauer sp. neutron diff. neutron diff. Miissbauer sp. ‘)

63G1 63Gl 7OJl 62Al 79 L 1

FMR “) magnetization “)

71Wl 7662, 77Kl

Mijssbauer sp.

77K2, 83Hl

AF, P at RT 20...40

Large fraction of a-Fe appears also in the spectrum. Presenceof a-Fe can not be excluded. Independent of thickness. Estimated, see [70 J 11. K,=-2.0.104ergcm-3. May be less than the actual moment.

1.1.2.5 Magnetocrystalline

anisotropy constants

The anisotropy constants K,, K,, . . . are defined for cubic lattices such as Fe and Ni by expressing the free energy of the crystal anisotropy per unit volume by E,=Ko+K,S+K2P+K3S2+K4SP+...

(1)

with s = u;u; + c7.g;+ c&;

and P = ct2c12u2 1 2 3r

where cli, clj, elkare the direction cosines of the angle between the magnetization vector and the crystallographic axes. For hexagonal lattices, such as Co, it is more convenient to use the definition

where 4 is the angle between the magnetization and the c axis, and 0 is the angle in the basal plane. The measurementsare usually made on single-crystal spheresin a field large enough to remove the domain walls (called technical saturation). It is usually assumed that all the work done in changing the direction of magnetization is used to overcome the crystal anisotropy. The most common techniques used to measure this work are: 1. Measurements of the torque required to change the direction of the saturation field (TQ). 2. Measurements of the magnetization in different crystallographic directions with a moving (MSM) or a rotating (RSM) sample magnetometer. Land&Bbmstein New Series 111/19a

Stearns

1.1.2.5 Fe, Co, Ni: magnetocrystalline anisotropy

42

[Ref. p. 134

3. Ferromagnetic resonance experiments (FMR). The anisotropy constants depend weakly on the applied field at high fields (> 5.. .lO kOe) and vary greatly in some temperature ranges. Due to this it is necessaryto specify how the data was treated in order to obtain the anisotropy constants. Comparisons with anisotropy constants obtained from various band structure calculations are discussedin [78 G I. 71 F 1] as well as in a number of papers listed in [SOW 11. Table 1. Magnetocrystalline anisotropy constants of Fe, as derived from magnetization (M,, M,,) and torque (TQ) measurements.M,: analysis, above technical saturation, of the magnetization perpendicular to the applied field vs. direction of Harp, in the plane indicated. M ,i: analysis, below saturation, of the magnetization parallel to the applied field. direction as indicated, vs. H,,,,. Method

T

K,

K2

K

K3

Ref.

0.22 -0.64

82T4 82T4 82T4

lo5 ergcme3 4.2

M,; [111]

4.70 5.35 5.64

1.90

MI; [1101 20

TQ

5.20

-0.158

77

M, (110)

2.41

TQ TQ ‘1 TQ 2,

4.48 5.31 5.56 5.15 5.15 5.02

TQ TQ TQ Xnc7

4.81 4.75 4.50 4.71

M, (110)

MI, iIll M,, Cl111

273

1.94

0.202 0.25 -0.62 0.711

1.79 -0.154

0.012

-0.012 ZO.195

w -0.13

68Gl 82T4 82T4 82T4 68K 1 66Kl 73 El 68Gl 66Kl 81H3

‘) K, vs. H at constant T, extrapolated to zero field. 2, T vs. H at constant K,, extrapolated to zero field. 3, ac susceptibility measurementson whiskers. 6 405 -erg

cm3 0.E a5

Fe cm3 0 + ox

I g’

erg

s" ?O <

t <

CI Y -r ot 6 v +o+ +++ 0 -LL t 0 900 1000 K 1’ 800 1000K 1200 LOO 600 200 0 ITb a Fig. la. Temperaturedepcndenccof magnctocrystalline K, (3), K2(4)and K, (5)extrapolated to infinite magnetic amsotropy constants of Fe as obtained from torque field. Note the expandedscalefor K, and K,. [72 B I]: K, mcnsurcmcnts[66 K I,68 G I], fcrromagnctic rcsonancc (6). [81 H 31: K, (7). [72B I] and ac susceptibility [Sl H 33. [66K I]: K, Fig. lb. Expanded plot of K, near Tc for Fe. For extrapolated to zero magnetic field of (I) K, vs. H at symbols,seeFig. la. constant Tand (2) TVS.H at constant K, data. [68 G I]: 0.2

-2

Stearns

43

1.1.2.5 Fe, Co, Ni: magnetocrystalline anisotropy

Ref. p. 1341

10.0

.in6

Ice I

3

Ii 5.0 2.5

aI I I I I I I I I IW

-2.51" I __^ .lS.U I

I

I

I

I

2:

I

I

I

I Rriddmon 1

I

I I I lO.OM/

I

&octhski

I

I

I

I

I

I

I

1

1

1

1

1

1

I

1

y

float zone

/-

1 1.5 ,’ c \ \ \

5.0

2.5 Ob

5.0

I

I

I

I

x

2.5 OC 50

h

B, 150

250

350

Fig. 2. Temperature dependence of magnetocrystalline anisotropy constants of single crystals of hcp Co grown in different ways [84P 11. (a) K,, (b) Kz, (c)basal plane anisotropy constant K,.

Landolf-Bdmstein New Series 111/19a

Stearns

1.1.2.5 Fe, Co, Ni: magnetocrystalline anisotropy

44

[Ref. p. 134

10.0

Fig. 3. Temperature dependcncc of the first and second order uniaxial magnctocrystallinc anisotropj constants. K, and K,, for hcp Co: I: single crystal [61 B43, 2: [54B I], 3: [77 B I], 4: [67 K 41.5: [64 K I], 6: [Sl 0 I]. 7: [70 S I], 8: [54 S l-j, 9:[67Tl]. 10:[84P I].

.in6 I

I

h

I

I

20 .I05 e's

cm3

Fig. 4. Magnetic field dependcncc of the first (a) and second (b) order uninsial magnctocrystallinc anisotropy constants of hcp Co at various tempcraturcs. Note the espanded scale of the vertical axis for the cun’cs above 480 K [Sl 0 I].

i

$- 10 5 0 0

8.0 ,105

I co

T= 4.2K

s

100

200

300 I-

400

500

K 600

1.6 .106 -erg

cm3

290K-

1.3 1.1 1.2 1.0 I 9 1.0 0.8 0.82 0.78 0.68 0.6L

557K

0.60 0.56

OS0

616K-

0.46 0

a

3

6

9 HOPPl-

12

15 kOe

3

6

9 HOPPl-

12

15 kOe 18

1.1.2.5 Fe, Co, Ni: magnetocrystalline anisotropy

Ref. p. 1341

0” 500

525

575 K 600

550

Fig. 5. Temperature dependence of the angle 6 between the direction ofspontaneous magnetization and the c axis of a single crystal of hcp Co [61 BS]. Points: data. Curve: calculated from sine = (-K1/2K2)“‘.

Table 2. Magnetocrystalline anisotropy constants for fee Co [54 S 11. T “C 500 550 600 650 700 750 800 850 900 950

Kl

K2 t

lo5 ergcme3 - 2.30 - 1.60 - 1.09 -0.80 -0.60 -0.41 -0.23 -0.15 -0.09 - 0.09

-4.31 -3.80 -3.21 -2.50 - 1.91 - 1.35 - 1.03 -0.76 -0.57 -0.36

\

21

IO 0

.

I

200

400

600

~BOO

1000 K 1200

Fig. 6. Temperature dependence of the magnetocrystalline anisotropy constants Kr and Ks in fee Co [64 D 11.Solid circles: [62 R 11,open circles: [54 S 11.The measurements in [62R l] were with ferromagnetic

Land&-Bdmstein New Series lWl9a

Stearns

1.1.2.5 Fe, Co, Ni: magnetocrystalline

46

[Ref. p. 134

anisotropy

Table 3. Magnetocrystalline anisotropy constants for Ni as derived from magnetization (M,, MIi) and torque (TQ) measurements.Seecaption to Table 1 for details on magnetization measurements. T K

K2

K3

6

Ref.

-12.92(l) - 12.82(6) - 12.97(2) - 12.58 - 12.42 - 12.64

4.79(7)

0.80(S) 0.80(1) 1.32(8) 1.61 0.81

0.32(7)

8214 82T4 78Gl 82T4 82T4 76A2’)

-

0.96(8)

Met hod

Kl 105ergcm-3

4.2

M, (110) M, (100)

TQ M,, Cl101 M,, Cl001 TQ *I M, (110) M, (100) TQ TQ *I

77

4.71(5) 3.26 6.20 2.48

8.45(l) 8.43(6) 8.42 8.36

-LO(l) 2.95

- 1.43(6) - 1.4(2) - 1.64

0.83

-0.66(8)

82T4 82T4 68Fl 76A2

‘) The higher order anisotropy constants were shown to be strongly dependent on the truncation in the procedure. It is concluded that it is never possible to describe the anisotropy of Ni with only K I and K,. *I &,,I in (110) plane.

analysis

Table 4. Magnetocrystalline anisotropy constants of Ni [68 F 11.Two different methods for analyzing the torque curves were used, leading to different values. T K

K,

K2

K3

103ergcm-’ 296

-

195

- 248

77

- 842 - 843 -1168 -1173 -1214 - 1233

20 4.2

57

-

23 26 90 80 83 90 410 390 410 530

0 - 10 - 11 -164 -160 -310 -350 -340 -230

Table 5. Pressure dependence of the first order magnetocrystalline anisotropy constant at room temperature in the pressure range up to 3 kbar [64 V 11. FC &%[kbar-‘1 1

-0.40.10-2

co -0.35.10-2 (tentative)

Ni -0.7(l).

10-2

Ref. p. 1341

1.1.2.5 Fe, Co, Ni: magnetocrystalline anisotropy

-6

a

-00

25

50

75

K 100

Ni .,J gi

b

0 0

100

200

300

500 K 60[

400

T-

Fig. 7. Temperature dependence of magnetocrystallir anisotropy constants ofNi.(a)K,. I: [68 F 1],2: [74T 1 3: [77 B 2],4: [77 0 11.Solid line: calculation [77 0 l].( K,, K,, and K,. Accuracy ofdata is considerably reduce near 7”: dashed lines in the insert [68 A l].(c)K,. I and, [76A 1],3: [69 F 2],4: [77 B 21. Solid line is to guide t1 eye through confidence limits [76A 11.

-1 .I05 erg 3 0 C

80

160

K

2

% kOe 0.75

T-

I s a 2 0.50 a 2 ; 0.25

02

-100

-50

0

50

“C

II

Fig. 8. Relative change of the first order magnetocr: stalline anisotropy constant K, of Ni with magnetic fiel H as a function of temperature [63 V 11. HappI = 10k0

Landolt-BOrnstein New Series 111/19a

Stearns

48

[Ref. p. 134

1.1.2.6 Fe, Co, Ni: magnetostriction

1.1.2.6 Magnetostriction

coefficients

Magnetostriction has the same origin as the anisotropy, namely, the orientation effectsof the nonspherical electron cloud of the atoms due to spin-orbit coupling. The linear magnetostriction,l=Al/l, is the change in length /caused by an applied field. It is defined relative to the completely demagnetizedstate.There is difficulty in summarizing the data for cubic crystals, such as Fe and Ni, since the various workers have used different coefficients to describe I. depending on how they have grouped the various terms. Generally the measurements are made using a strain gauge technique [47G 11. The magnetostriction coefficients hi are related, for cubic systems,to the magnetoelastic coupling constants h, to h, by the relations: ho= -bol(c,,+2c,,)> h,=-bJ(c1,+2c~dr

h,= -b,l(c,,-cl,), h,=-b&1,-c,,),

h,=b,lc,,t As=--k&,,,

(1)

wherec,,,c,,, and cd4are the elastic stiffnessconstants. The magnetoelastic constants are directly related to the strain dependenceof the interaction energies.The isotropic terms dominated by b. originate from the exchange energy while the anisotropic terms originate from the anistropy energy. Fe Listed below are someof the definitions and the equivalence for someof various coefficients which have been used to describe the linear saturation magnetostriction 1, of Fe: Definitions: i.,=h,(p-l/3)+2h,~+It,s+h,(r+2.~/3-1/3)+2h,t

f-4

[67B I],

i.,=A,+A,p+A,q+A,s+A,rfA,t

E.,=~~%“~‘~~;K~~‘, P i j

[39B1,51Bl],

p=a,y,~

(3)

[70Dl],

(4)

where s = a:a$ + a$a: + a:af p=a:/3:+a$?22+a$?: (5)

q=ala2PIP2+a2a3B2P3+a3aIB3Pl r=af/lf+a;/li+a‘$: r=ala2a:BlB2+a2a3atP2B3+a,alatp,pl.

zi arc the direction cosinesof the magnetization (applied field) and pi the cosinesof the direction in which the change in length is measured. For quantities K and /? in eq. (4) see [70D 11. Relations between various coefficients are given by A,=2h,, A,=2h,, A,= -(h,+h,)/3, A,=hs+2hJ3, A,=h,, A,=h,, ly-4=h 4r P4=h,. %‘l-* = h, + 6h,/7 , F2=hz+h5/7, P0=3(ho+h,/5), P4=3h3,

(6) (7)

If h r and A, are much larger than the other coefficients the notations Iloo = 2/3 h, and 1, r, = 2/3 h, are used. The volume magnetostriction, Q = AVIV, is much smaller than the linear magnetostriction. The anisotropic contribution caused by domain rotation is given for Fe by o=3h,s.

(8) The forced linear magnetostriction coefficients Ai describe the increase of I. with applied field strength above the saturation field, l.‘=aAJi3H. They are defined in analogy to eq. (3) and are attributed to the various small contributions such as the orbital and spin susceptibilities of the 3d and 4s electrons in high fields.

Landolt-Rornrtcin Phv Scricr 111’19a

49

1.1.2.6 Fe, Co, Ni: magnetostriction

Ref. p. 1341

Table la. Linear saturation magnetostriction coefficients hi and forced magnetostriction constants !rl for a single crystal of Fe at various temperatures [61 G 11.

T

h,

K

h,

h3

h,

h,

& ‘)

35 35.0 35.5 36.2

h’,

.l()-lOOe-l

.10-6 4 77 190 293

h;

-45 -44.8 -39.9 -34.0

4 3 4 2

-

-

2.0 1.6 1.7 1.8

0.6 1.0 0.4

-0.1 0.0 -0.2

I) ho=1.5(1)~10-‘00e-’ and h;, h; of the order of +l. 10-lOOe-’ found by [65 S 21 over the whole temperature range.

was

Table lb. Coefficients of forced linear magnetostriction of Fe at 293 K. A;

4

A;

Ak

-7.3 -0.53

-5.1 0.20

A;

Ref.

12.0 1.8

68W2 56Cl

. 10-‘“Oe-’ 5.0 0.42

0

200

I 400

600 T-

-2.9 -1.1

800

1000 K 1200

Fig. 1. Variation of the first linear magnetostriction coefficient hl of Fe as a fimction of temperature. I: [59T1],2:[61G1],3:[68W2],4:[71D2],5:[83Dl]. 0

200

400

600

800 K 1000

T-

Fig. 2. Temperaturevariation of the linear magnetostriction coefficientsAi of single crystal Fe [68 W 21. Land&Bbmstein New Series lW19a

Stearns

1.1.2.6 Fe, Co, Ni: magnetostriction

50

[Ref. p. 134

CO The widely used notation for the linear saturation magnetostriction for Co is [54 B l] i., = %,,(s’2- s’aJIJ) + I.& 1- a:) (1 - j?:) -s’“] + &[( 1- a:)bf - s’a,jlJ

+ 4l.,s’a,fl,

,

(9)

where s’=rx,~,+a2/?2. The direction cosines relate to the orthogonal axes (l(x), 2(y), 3(z)E c axis), not to the hexagonal axes.Note that with this definition h=O when the direction of magnetization and length change are both along the c axis so that for Co the change in length is measured from this initial state.

-80

-120

-160 -200

-100

0

100 I-

200

300 "C 4

Fig. 3. Variation with temperature of the linear magnctostriction cocnicicnts of single crystal Co. Also shown is the volume magnctostriction, I.,,= ).A+ ,IB+ I.,, and ).,,--I., [69H I]. Room-tempcraturc values: ,In = -50.10-6, %,= -107.10-6, %,=126. lO-(j, 1, =-105,10-6, %,~=-31~10-6, which agree with the earlier values of Bozorth [54 B I].

Ni [71

Again different definitions for I., exist in the literature for Ni. One is given by eq. (3). Another is given by L 1-j: i.,=h,+k,(p-1/3)+21~,q+h,(s-1/3)+h,(r+2~/3-1/3)+2h,t.

(10)

The relation between the coefficients is the sameas that given by eq. (6) with the exception that A,=h,-(Ir,+h,+h,)/3.

At present there seemsto be no satisfactory theory to representthe magnetostriction behavior of thesemetals [71 L 1, 71 B 1-J.

Stearns

Ref. p. 1341

1.1.2.6 Fe, Co, Ni: magnetostriction

51

Table 2. Room-temperature linear saturation magnetostriction coefficients for single crystal Ni.

h,

hz

h,

h,

h,

Ref.

6.3(10) 3.4(6) 0.2...1.4

0.2(5) 0.2(9) 1.4

70Fl 71 B 1 71Ll

.10-6 -98 (3) -98.5(14) -94

-41.5(10) -43.1(5) -43

0.3(5) 0.1(9) -0.5

Table 3. Room-temperature forced magnetostriction constants of Ni.

h;

h:,

Ref.

-0.84 -0.43 0.0(l)

-0.33 -0.18 0.0(l)

64Ll 71Ll 6582

h6 lo-“Oe-’ 0.26 0.40 0.2(l) ‘)

8 w” I

‘) At 1.5K: hb=0.4(1). 10-‘OOe-l.

4

c”

12 w6

x-6 I -95 I

I

I

I

I

8

Js

-60

4

-55 ,

-5c I

0 8 m6

I

P

m 2: 4

-45 .m6 -41: 50

100

150 T-

200

250 K 300

0

100

200 T-

Fig. 4. Variation of the magnetostriction constantshi for two Ni single crystals as a function of temperature [71 L 11.

Land&-BOrnstein New Series 111/19a

Stearns

K

300

1.1.2.7 Fe, Co, Ni: Form factors, magnetic moment distribution

52

[Ref. p. 134

4 .10-‘1 Oe-’ i

-10 -5

-12 0.25

a

0.50

I/i, -

0.75

1.

0.25

b

0.50 T/T, -

0.75

Fig. 5. Variation of (a) the forced longitudinal and transversemngnctostriction, (C?LBH) ,, and (X,CUf),, rcspectlvely,and (b) the forced volume magnctostriction, SW’SH.asa function ofrcduccd tempcraturc(TC=613K) for polycrystalline Ni. The forced volume magnctostriclion. obtnincd by adding (X,GH) ,, and 2(8./W), extrapolated to OK, was 1.4. 10-‘OOe-‘. This value is in agrccmcntwith that obtnincd for the forced isotropic volume magnctostriction value of [65S2]. so that the anisotropic term 3h’,/5 is very small in comparison with theso-calledexchangeterm 311;.(a)I: [69 T 11.2:[36 D I] and (b) I: [69T I]. 2: [65 F I]. 3: [65 S 21.

1.00

Table 4. Forced volume magnetostriction at room temperature for Fe, Co, and Ni. &O/ClH

Ref.

4.3 ‘) 6 Fig. 5

6532 54Bl 69Tl

. 10-lOOe-’

Fe co Ni

‘) Increasing almost linearly with temperature to a value of 8.9 .lO-“Oe-’ at 600K.

1.1.2.7 Form factors, densities and magnetic moments The elastic magnetic form factors f have been directly obtained in polarized neutron scattering experiments as the ratio of measured Bragg scattering amplitudes to the amplitude for forward scattering, the latter being proportional to the magnetic moment per unit cell. Measurements are usually taken at room temperature. The distribution of the spin density throughout the unit cell is calculated from the Fourier inversion of the magnetic crystal structure amplitudes F,,,,

where m(x) is. at position x. the component of the magnetization in direction of the applied field. G,,, denotes the reciprocal lattice vector for the hkl reflection and V is the volume of the unit cell. F,,,, obtained from the Bragg scattering amplitude for the hkl reflection, coincides, for wavevectors Q=G,,,, with the nonnormalized elastic magnetic form factor of the unit cell, F(Q) = 5 d3xm(x) eiQ’*. F(Q) equals the Fourier transform M(Q) of the magnetization of the unit cell, see Fig. lb. Stearns

1.1.2.7 Fe, Co, Ni: Form factors, magnetic moment distribution

52

[Ref. p. 134

4 .10-‘1 Oe-’ i

-10 -5

-12 0.25

a

0.50

I/i, -

0.75

1.

0.25

b

0.50 T/T, -

0.75

Fig. 5. Variation of (a) the forced longitudinal and transversemngnctostriction, (C?LBH) ,, and (X,CUf),, rcspectlvely,and (b) the forced volume magnctostriction, SW’SH.asa function ofrcduccd tempcraturc(TC=613K) for polycrystalline Ni. The forced volume magnctostriclion. obtnincd by adding (X,GH) ,, and 2(8./W), extrapolated to OK, was 1.4. 10-‘OOe-‘. This value is in agrccmcntwith that obtnincd for the forced isotropic volume magnctostriction value of [65S2]. so that the anisotropic term 3h’,/5 is very small in comparison with theso-calledexchangeterm 311;.(a)I: [69 T 11.2:[36 D I] and (b) I: [69T I]. 2: [65 F I]. 3: [65 S 21.

1.00

Table 4. Forced volume magnetostriction at room temperature for Fe, Co, and Ni. &O/ClH

Ref.

4.3 ‘) 6 Fig. 5

6532 54Bl 69Tl

. 10-lOOe-’

Fe co Ni

‘) Increasing almost linearly with temperature to a value of 8.9 .lO-“Oe-’ at 600K.

1.1.2.7 Form factors, densities and magnetic moments The elastic magnetic form factors f have been directly obtained in polarized neutron scattering experiments as the ratio of measured Bragg scattering amplitudes to the amplitude for forward scattering, the latter being proportional to the magnetic moment per unit cell. Measurements are usually taken at room temperature. The distribution of the spin density throughout the unit cell is calculated from the Fourier inversion of the magnetic crystal structure amplitudes F,,,,

where m(x) is. at position x. the component of the magnetization in direction of the applied field. G,,, denotes the reciprocal lattice vector for the hkl reflection and V is the volume of the unit cell. F,,,, obtained from the Bragg scattering amplitude for the hkl reflection, coincides, for wavevectors Q=G,,,, with the nonnormalized elastic magnetic form factor of the unit cell, F(Q) = 5 d3xm(x) eiQ’*. F(Q) equals the Fourier transform M(Q) of the magnetization of the unit cell, see Fig. lb. Stearns

Ref. p. 1341

53

1.1.2.7 Fe, Co, Ni: Form factors, magnetic moment distribution

The magnetic moment densities measuredby neutron scattering are the net spin polarizations in the direction of the applied field, averaged over the resolution function related to the finite number of Bragg reflexions being taken into account in evaluating the Fourier sum. In [62 S 21 this resolution function had a width of 0.2A. In contrast the magnetic moments obtained from hyperfine experiments measure the 4s or 3d conduction electron polarization contributions. A detailed analysis of the form factor values includes both quenched and unquenched orbital momentum, core polarization of the inner electrons, the 4d conduction electrons and the symmetry population of the 3d quenched electrons. This analysis assumesa magnetization distribution based on free-atom wave functions [62 S 31. Another Fourier analysis technique assumesthat the moment density is composed of a constant average magnetization and a periodic localized contribution. An atomic moment of 2.37(4)pa was found for Fe [71 M 21.

Table 1. Contributions in pn per atom to the atomic moments of Fe, Co, and Ni as obtained from two different analyses of room-temperature coherent polarized neutron scattering data: (i) form factor analysis assuming a magnetization distribution based on free-atom wave functions and (ii) Fourier analysis assuming a periodic localized and a constant average magnetization. The total magnetic moment is simply related to the forward magnetic scattering amplitude. This amplitude was determined for Fe to be 0.589(6). lo-l2 cm per atom from the refractive bending of a thermal neutron beam [71 S 61, corresponding to a magnetic moment per atom of 2.180prr.For the paramagnetic state,seeTable 2 for Fe; for Ni the magnetic form factor in the paramagnetic state at 1060K and in an applied field of 13kOe was determined from the first five Bragg reflections. It was found to be similar to the room-temperature values, indicating that there is no gross change in the localized part of the spin density at this temperature [67 C 11. Metal

Form factor analysis 3d spin

Fe co Ni

2.25 1.86(7) 0.656

3d orbit

Fourier analysis Constant average

0.14 0.13(l) 0.055

Relative population 3,

-0.21 1.2) - 0.28(7) -0.0105

T 2!3

E,

47% “) 81(l)%

53% 19(l)%

Ref.

3d

6232 64M 1 66M2

2.37(4) 1.96(4) 0.68(2)

Constant average

-0.19 -0.25 -0.10

Ref.

71M2 71M2 71M2

‘) The use of this crystal field model has been criticized and it is suggested that the regions of negative polarization are caused by a spin dependence of the radial part of the d electron wave function [71 D 11. ‘) Band calculations have found a variety of 4s polarization values. Sometypical values are -0.011 us/atom [68 W 11,a small positive polarization [71 D l] and -0.024... - 0.040pe/atom [77 C l] which are much smaller than the value of -0.21 pa obtained from the neutron data analysis. “) For spherical symmetry this would be 60% T,, and 40% E, ‘) A Fourier inversion of the data is in agreementwith the model consisting of a nearly spherical distribution of spin density composed of a positive spin-polarized, 3d’ 4s2 free-atom like, contribution plus a constant negative contribution.

Table 2. Average magnetic moment per atom, P, for Fe in the paramagnetic state as obtained from polarized neutron scattering [83 B 23. Fe bee fee Landolt-BBmstein New Series 111/19a

T

P

K

PB

1273 (1.25 T,) 1320

1.3(l)

The characteristic neutron interaction time of theseexperiments, w lo- I3 s, is expected to be slightly longer or comparable to the localmoment spin-flipping time (sometimes referred to as the transverse spin fluctuation time [78 M2, 7911, 79 M2]). Thus the values measured are likely to be lower than the actual local moment.

0.9(l)

Stearns

1.1.2.7

54

Fe, Co, Ni: Form factors, magnetic moment distribution

[Ref. p. 134

-0.1 0

0.2

0.4

0.6

0.8

1.0 A-’ 1.2

sinB/L Fig. la. Circles show the measured elastic magnetic form factor values of Fe (the size indicates the experimental accuracy). Wavcvcctor of momentum transfer: Q =4rcsmt?‘L. All 26 crystal reflections out to the 622 reflection corresponding to a maximum sin0/l. of I.157 A- ’ have been studied. Essentially no tempcraturc depcndenceofthcdistributionofthcdircctionalconfiguration of the magnetic scattering amplitude was found for Fe [62 S 31.The solid and dashed curves are the calculated spherical free-atom form factors for the two electron configurations 3ds and 3dh4s2, rcspcctivcly, [6l W 23.

1.5 1.0 0.5 0 1.0 b

1.5

2.0

2.5

3.0

3.5

4.0

0 (reciprocal lattice units I-

Fig. lb. Fourier transform of the magnetic moment density as measured by inelastic neutron scattering from phonons along different crystallographic directions in Fe4 at% Si. The smooth curves arc interpolations of the expcrimcntal elastic form factors. For data points without error bars the uncertainties are equal to or smaller than the size of the points. Note that the inelastic points lie slightI) lower than the elastic form factors in the [ IOO] and [I IO] directions and slightly above in the [I II] direction [8l S I].

Stearns

Ref. p. 1341

1.1.2.7 Fe, Co, Ni: Form factors, magnetic moment distribution

Fig. 2. Magnetic moment density distribution obtained from the Fourier inversion of the data of Fig. la over (a) the (100) face and (b) the (110) diagonal plane of the Fe unit cell. The asymmetric contour lines show that the 3d electrons are asymmetrically distributed around the Fe nucleus. The values of the spin densities are in units of

h/A31> C62S21.

Fig. 3. Magnetization distribution in the interstitial region of the Fe unit cell, obtained by averaging over a cube size of0.5 8. The numbers correspond to the magnetization in [kG]. Negative magnetization was found to occur in a series of interlocking rings throughout the Fe lattice [66 s 31.

Landolt-Biirnstein New Series IWl9a

Stearns

55

56

1.1.2.7 Fe, Co, Ni: Form factors, magnetic moment distribution

[Ref. p. 134

0.81 co hcp 0.7 p 0.6

o hcp Co fee

l

COD.92 ho0

0.5

I 0.1

t 0.3 0.2 0 0’ 04

0.i

---

fJ73K

-

300 K 0.5

0.6 ti-’ 0.7

sin 0 /A -

0 -0.1 0.2

0.6

0.6

0.8

H’

Fig. 5. Form factor offcc Co at 600 “C (dots)compared tf the form factor at room temperature (crosses) [63 M 1: Curves rcprcsent smooth interpolations. Wavevector c momentum transfer: Q = 47tsin O/I..

1.0

Fig. 4. Measured magnetic form factor of hexagonal Co (open circles) [64 M I] and fee Co--8 at%Fe (solid circles) [59N I]. Wavevector of momentum transfer: Q = 471sin O/L. The solid line emphasizes the almost sphcrical symmetry of the hexagonal form factor. The form factor for Co showed no dependence on temperature between 78 and 300K.

(0.0)

co.gfl

0.9

Ni

E f

0.8 1

0.7

/

B &

1

. measured o calculated

1

l *

0.5

I

-A

I

Fig. 6. Projection of magnetic moment density on has; plane of hcp Co. Lower right diagram shows projecte position of atoms in orthorhombic unit cell. Dashed line’ indicate portion of cell shown in density map [64 M I]

0.5 R ;

0.L ZN 0:

0.3

%

0.2

9: 6% e” FiR

0.1

90 5

0 -0.1 I 0

0.2

0.L

I

I

0.6

0.8

I

1.0 Yi’ Iu

Fig. 7. Comparison of the measured (solid circles) ant calculated (open circles) free atom magnetic form factors o Ni. Wavevector ofmomentum transfer: Q =4n sin8/7,.Thc measured magnetic form factor was determined from the first 27 Bragg reflections. The model used in the calculatec form factor consisted of a uniform negative spin contri bution of -0.019 pa/A3,aspincontribution obtained fron unrestricted Hartrcc-Fock calculations for Ni + + [60 W 1 61 W 43, an orbital part and a core contribution [66 M 21 The inelastic magnetic form factor in the [ 1001directior was found to be the same as that ofthe elastic form facto] [8l S I].

sin 0 /1 -

Stearns

Ref. p. 1341

57

1.1.2.7 Fe, Co, Ni: Form factors, magnetic moment distribution

a 7-

Ni nucleus

Ni nucleus

Ill01

w

-

0 -0.0085#

-0.0085

-0.0085

I

-;s

-0.0085

b a T-

Ni nucleus

Fig. 8. Contour maps of the magnetic moment density in Ni obtained by Fourier inversion of the data for (a) the (100) plane and (b) the (110) plane. The numbers labelling the contours give the magnetization in [ur,/A3], [66 M 21.

0

100

200

300

400

500

600 K 700

Fig. 9. Temperature dependence of the T,, and E, subband magnetizations per atom in Ni as derived from the temperature dependence ofthe 333 and 511 reflections in a polarized neutron scattering experiment [81 C2].

Land&-Bdmstein New Series IIl/19a

Stearns

1.1.2.8 Fe, Co, Ni: hyperfine fields, isomer shifts, relaxation

58

time

[Ref. p. 134

1.1.2.8 Hyperfine fields, isomer shifts and relaxation time The hypcrfinc magnetic fields have been mainly determined using three techniques: nuclear magnetic resonance (NMR), Massbauer effect spectroscopy (ME) for Fe and variations of the perturbed angular correlation technique. A number of books and review articles are written on the subject [64 W 1,65 F I,71 F 1, 74V 11.Only results from NMR and Miissbauer effect measurementswill be discussed here. Magnetic hyperfine field Hhrp NMR experiments measure the hyperlinc fields by observing the Zeeman splitting of the ground state of nuclei having nuclear magnetic moments, i.e. of nuclei with angular moment quantum number I+O. The resonance linewidths of ferromagnetic materials are naturally relatively large, of the order of 0.5 kOe. These widths are attributed to anisotropy fields and defects.Spin-echo and modulated continuous wave (cw) NMR techniques are used to study these materials. The Miissbauer effect measuresthe magnetic hyperline fields and electric quadrupole fields from the Zeeman splittings of the ground and excited states of the nuclear transitions. These splittings are obtained by varying the relative velocity of the source and absorber [62P l] and are given in the practical unit [mms-‘1. Miissbauer effect measurementscan not be made on Co. 61Ni, having a 67.4keV y-ray, is a possible but poor ME nucleus, “Fe an excellent one. The hyperfine field Hhypis made up from several contributions which can be represented by f&p = Hcorc+ Has+ Hart,+ Ha, .

(1)

H coreis due to the Fermi contact interaction of the spin-polarized Is, 2s, and 3s core electrons. H,, is the contact term arising from the spin polarization of the 4s conduction electrons which is due to exchange and hybridization interactions with the d spin moment. Herbis the field contribution from the dipolar interactions from any unquenched orbital momentum on the central atom. H,,, is due to external influences such as applied fields. demagnetizing tields and Lorentz fields. This contribution is zero in cubic Fe, Co or Ni when there are no applied or demagnetizing fields, such as in domain walls for NMR experiments or in thin films magnetized in the plane of the films for Miissbauer effect measurements. Enhancement factor E An applied rf field causesthe electron moments to oscillate, the much smaller nuclear moments will then follow the motion of the electron moments. The rf fields at the nuclei in the domains thus undergo an enhancement by a factor of E, .c.= fh,,,IM, ,

(2)

which is about 200 for Fe and 150for Co and Ni [6OP 11.The rf fields at nuclei in domain walls undergo further enhancement depending on the position of the nuclei in the wall. The finite angles between electron spins in the domain walls causethe magnetic moments of wall nuclei to be turned through larger angles than the moments of domain nuclei. Furthermore the walls have been shown to be pinned around their periphery and to oscillate in a drumhead-like fashion [67 S 11.Due to the angle between electron spins being greatest at the center of the wall, the enhancement E is greatest at the wall center, E,,,and in Fe decreasesas: E(X)= E,,sechx

(3)

to the domain value at the edgesof the wall, where x is in units of the wall width. The enhancement at the wall center is a factor of 30...100 over that in the domains [67 S 11.The wall enhancement factors are dependent on the purity and heat treatment ofthe material since theseaffect the domain wall areas[71 S 33.The drumhead wall motion model [67 S 1] has been extended to include a finite excitation bandwidth and a finite spectral distribution of resonance frequencies [79 B 21. Because of the larger enhancement in the walls spin-echo measurementson Fe, Co, and Ni usually measure domain wall nuclei. Isomer shift The valence state of the atoms can be obtained from the isomer shifts, i.e. the shifts in the position of the center of the Miissbauer pattern which are dependent on the charge density at the nucleus [67I 1, 74V 1). Stearns

Ref. p. 1341

1.1.2.8 Fe, Co, Ni: hyperfine fields, isomer shifts, relaxation

time

59

Relaxation times 7” and T, The nuclear longitudinal (spin-lattice), T,, and transverse (spin-spin), T,, relaxation times are measuredwith the spin-echo technique. There are a number of relaxation mechanismspresent in the transition metals. They are the contact interaction with s electrons [5OK 11,dipolar and orbital interaction with non-s electrons [63 0 11, core polarization [64 Y 11;spin-spin interaction via virtual magnons [SSS 1,58 N 1,59 S l] and spin interaction with domain walls [61 W l] and bulk magnons [69 S 23. Care must be taken in measuring relaxation times so that the rffield applied is small enough so that it doesnot move the wall to a different part of the sample,and thus to different nuclei, during the course of the measurement. Becauseof the variation of enhancement factor with position in the domain walls the nuclear spins undergo a complex rotation distribution. It is also been shown that the domain walls vibrate like drumheads [71 S 31. Thus the shapes of the relaxation curves differ widely from exponential behavior and are strongly dependent on the product of the rf field B, and the pulse length r which determine the turning angle, 8=ysB,z, of the nuclear spins, y being the gyromagnetic ratio of the nuclei. It has been shown that for Fe the relaxation rates vary with positions in the walls as: -=- 1 W4

1 T,LOZ

sech’x

(4)

and are thus largest at the center of the walls [69 S 21. To, and To2are the longitudinal and transverse relaxation times at the center of the wall and x is measured in units of the wall thickness. It is clear from Fig. 13a that meaningful longitudinal relaxation times can not be obtained by assuming an exponential decay but that the details of the excitation and motion of the spins must be considered. Also the relaxation rates have been found to be somewhat dependent on the purity and heat treatment of the sample.Due to these complications in the domain walls the literature unfortunately contains a wide variety of ill-defined relaxation times for Fe, Co, and Ni with few details of the operating conditions or analysis procedures used in obtaining the relaxation times. Many of theseresults are thus of questionable value as can be seenfrom the wide range of measured relaxation times listed in Table 5. The behavior of the spins in the domains is much simpler and the results for such spins should be more reliable. The transverse relaxation time is obtained by measuring the echo height of a pair of pulses separated by a variable time. In caseswhere the relaxation times are comparable to the nuclear lifetime the Mossbauer effect can also give information about the relaxation times. Fe, Ni For Fe and Ni the spin-echo technique has a resolution which is about a factor of 10 greater than that of the Mijssbauer effect technique. The temperature dependence of the hyperfine field is found to be slightly different from that of the magnetization [61 B 21. A proportionality factor A(T) has been defined by v(T) =4Wf,(T)

>

(5)

where v(T) is the measured hyperfine field resonance frequency and M,(T) is the spontaneous magnetization. co Many complex effectsare seenin Co spin-echo experiments which do not occur for Fe and Ni. These are due to a number ofproperties of Co such asthe large nuclear moment and the 100% isotopic abundance of sgCowhich allows nuclear spin-spin (Suhl-Nakamura) interactions to be important in contrast with dilute isotopic materials, the large anisotropy fields in the hcp phase and the two possible phases of Co at low temperatures. The anisotropy field in hcp Co causesthe hyperfine fields of the domain wall nuclei to vary with position in the wall. This results in the NMR spectrum of hcp Co being very broad. Other unusual effectsseenin Co are single pulse echoes [72 S l] and enhancement of a modulation field on the spin-echo envelope [77 S 11. Due to all these complexities the hyperfine field values quoted in the literature for Co are often not well defined.

Landolt-Bbmstein New Series III/I%

Stearns

60

[Ref. p. 134

1.1.2.8 Fe, Co, Ni: hyperfine fields, isomer shifts, relaxation time Table la. NMR frequencies and magnetic hyperfinc fields of Fe, Co, and Ni. Metal

T

Nucleus position

K

Fe, bee

Co, hcp

wall center wall edge

co, fee Ni

4.2

46.64

RT

45.43

4.2 RT 4.2 RT 4.2 RT 4.2 RT

Hhsn

KHz

Ref.

kOe

-339(l) ‘) - 339.0(3) -330 - 330.4(3) - 225.7‘) -218 -217.7 2 -212 -215 3, -211 - 75(l) - 69(l)

228 220.5 219.9 x214.5 217.23, 213.1 28.46 26.04

61 B2 71 Vl 61Bl 71Vl 72Kl 72Kl 72K1 72Kl 6OPl 6OPl 63Sl 63Sl

‘) An upper limit for the anisotropy for a single crystal is 1OOOe[SO0 11. +8W)kOe [72K 11. ‘1 H hjp.IIc-Hhyp.lc= ‘) Extrapolated from high-temperature values. Table 1b. Temperature dependence of the NMR frequency for 57Fe in iron [61 B I].

T

T K

LHz

K

KHz

77 193 297 351 397 438 490 543

46.52 46.09 45.43 44.99 44.55 44.09 43.42 42.58

607 683 693 701 719 730 756 785

41.45 39.73 39.39 39.32 38.68 38.39 37.72 36.79

Table 2. Measured, by a technique which combines Miissbauer and internal conversion electron spectroscopy [74 S 2, 84 B 11, and calculated individual ns shell contributions to the hyperfine magnetic field of Fe metal in [kOe]. Fe band structure calculations are quoted for both the exchange correlation potential of von Barth-Hedin (vBH) and a Kohn-Sham (KS) local-exchange potential. Shell

Contribution to Hhrp[kOe] Measured

Calculated 1s 2s 3s 4s total

[68 w l] - 14 -739

-409

[75 D 1) -623 + 243 + 33 +210 -347

vBH [77C l] - 21 -388

KS [77C 13 - 67 -451

[74S2] - 1640(390) +517(240)

-213

-343

‘1

‘) The measured total field is - 339 kOe which includes about 25 kOe of orbital field. So the sum of the contributions from the ns electrons is about -365 kOe. Clearly there is a large unresolved discrepancy between the calculated and measured 2s values.

Ref. p. 1341

1.1.2.8 Fe, Co, Ni: hyperfine fields, isomer shifts, relaxation time

61

Table 3. Room-temperature parameters used for correction of hyperfine frequency and spontaneous magnetization to constant volume. Note that (i%/ap),/ v is opposite in sign for Fe from that for Co and Ni. Calculations [79 J l] confirm that this behavior of the hyperfine magnetic fields with pressure is reasonable. 1 av - v ( aP > T . 10Y4kbar- 1

Metal

Fe co Ni

i av v aP T -(->

Ref.

1

Ref.

MS

. 10m4kbar-l

- 5.92 - 5.28 - 5.4

49Bl 49Bl 60 Al

aM (

aP 9

Ref. T

. 10m4kbar-’

-1.66(l) 6.13 (fee) 9.2(l)

61B2 6051 79Rl

-2.83(25) -2.18 (hcp) -2.9

Table 4. Mijssbauer effect parameters for 57Fe (I= l/2) in practical units. 90: ground state splitting PO: ground-state nuclear magnetic moment excited state splitting in nuclear Bohr magnetons u,, 91: H hyp: hyperfme field dQ: quadrupole shift K: Knight shift Property

Unit

90

mms-’ mms-’ mms-’

CiQ PO

H hyp

he

T=4.3 K

T=298K

4.0117(10) 2.2931(10) 0.0088(25) 0.09024(7)

+ +

+

-339.0(3)

3.9098(g) 2.2342(g) 0.0023(15)

-330.4(3)

Ref. 71Vl 71Vl 71Vl 65Ll 71Vl

0.0078(10)

K’)

‘) Measured in an applied field up to 20 kOe.

Table 5. Paramagnetic phase d electron contribution to hyperfine field, H,,,,,(d), ferromagnetic phase hypertine field Hhyp,R divided by the respective magnetic moments per atom,p and pa,,orbital contribution to the Knight shift, Korb, and orbital susceptibility xv”, corrected to constant volume and OK, for Co and Ni [SOS 11. Hhyp,,(d)/P kOehB Co solid liquid Ni

-121(7) - 128(7) - 140(8) -113(5)‘)

h&Pat

Korb B

- 127 -128

%

XV” .10-3cm3mol-1

1.5(2) 2.1(2) 1.84(20)

0.14(4) 0.18(5) 0.18(5)

‘) Not corrected to constant volume, the correction is about +3 kOe [78 S 11.

Landolt-Bornstein New Series 111/19a

Stearns

61Kl 64Kl 60K2

[Ref. p. 134

1.1.2.8 Fe, Co, Ni: hyperfine fields, isomer shifts, relaxation time 24c MHz 2oc 16C I * 12c

200

600

100

800

K

0

1000

T-

200

400

600

800

1000

1200 K 1L'

T-

b

30 w: 24 18 I a 12 6

0

100

200

C

300 I-

LOO

500

600 K 7

Fig. lax:. NMR frequency Y vs. temperature in the ferromagnetic state of(a) “Fe in bee Fe metal, I: [SOS I], 2:[61Bl];(b)5gCoinfccCometal,1:[80S1],2:[60Kl], 3:[63LI];(c)61NiinNimetal,l:[80S1],2:[70Rl];cw mcasurcmcnts in natural Ni, 3: [63 S 11.

230 MHz

100

200

300

LOO

500

600

700

d Fig. Id. Temperature dependence ofthe “Co wall center and wall edge NMR frcquencics in hcp Co. The dashed curve rcprcscnts the data in the feephase [72 K I], set also [63 F 11. Stearns

K

63

1.1.2.8 Fe, Co, Ni: hyperfine fields, isomer shifts, relaxation time

Ref. p. 1341 t 1.0 ;; J, 0.9 s Gy 0.8 0 II : 0.7 -2 0.6

0.96

I ;; 0.92 11 " -3 =; 0.88

0.80 0

0.2

0.4

0.6 r/r,

0.8

-

Fig. 2. (a) The solid curve is the measured reduced spontaneous magnetization as a function of reduced temperature for Fe (see Fig. 2a in subsect. 1.1.2.4). The circles are the measured reduced hyperfine field tiequencies vs. reduced temperature as measured by Budnick et al. [61 B I]. Both of these measurements are made at constant pressure. (b). Reduced proportionality constant A/A( T = 0) as defined in eq. (5) vs. reduced temperature; the solid line is for the hyperfine field and magnetization data corrected to constant volume [61 B2]; circles are for the uncorrected constant-pressure data shown in (a). The decrease in A/A(T=O) is about 5% lower, than MJA4,(T=O) at T/!&x0.8. It is not surprising that the magnetization and hyperfine field temperature dependences are not identical since they are sensitive to and depending on the detailed electronic band structure and their variation with temperature is expected to differ in a number of ways [71 S 2,72 B 23.

Land&-Bdmsfein New Series 111/19a

0

0.2

0.6

0.4

I 0.8

1.0

r/r, -

Fig. 3. Reduced hyperfine field frequency v and magnetization as a function of reduced temperature as derived from NMR measurements for Ni. (a) at constant pressure, I: [80 S 1],2: [63 S 1],3: [26 W 1],4: [69 K l], and (b) corrected to constant volume. The difference between the reduced magnetization and hyperfine field decreases from a maximum of about 6% to about 3% after correcting to constant volume [80 S 11.

Stearns

[Ref. p. 134

1.1.2.8 Fe, Co, Ni: hypcrfine fields, isomer shifts, relaxation time

64

0

20

40

60

a

80

100

120kbar140

P-

O

10

20

45.5

30

40 kOe

50

Howl -

Kc

Fig. 5. Relative hypertine field Hhgp/Ha.pp,at the “Fe nucleus in E-Fe as a function of the applied field. Data were taken at pressure of 15.0 and 21.5 GPa [82T 33.

45.1 -1400 45.0 -1200 44.9 0

b

10

20

30

40

50

60 kbor70

-1000

P-

Fig. 4. Room-temperature variation of the magnetic hypcrfinc ficld of Fe with pressure as dcrivcd from (a) relative M&batter effect mcasurcmcnts. diffcrcnt symbols referring to different pressure runs [68 M I], see also [6S S I]. and (b) NMR frequency measurements [63 L 21. Triangles indicate pressure calibration by linear interpolation of the data represented by circles.

-800 -600 z s-400 I -200 0 kOe

200

-200 kOe 0 0

0.5

1.0

1.5

2.0

2.5 pB 3.0

Fig. 6. Hypcrtine field at nuclei of atoms dissolved in Fe, Co, and Ni lattices, plotted against the host magnetic moments. The signs of the fields are not always given in the original literature see [65S 11, where also various other dissolved atoms are considered.

Stearns

Landolr-Rornmin NW Scricr 111/19a

Ref. p. 1341

Fig. 7. Si atoms act as near perfect magnetic holes in the Fe lattice so that it was possible to obtain the change in the hyperfine fields of Fe atoms caused by the alloying of Si. Fe,Si contains atoms with three widely seperated hyperfine fields: Fe(D) with 8 nearest neighbor (nn) Fe(A) atoms; Fe(A) with 4 nn Fe(D) and 4 nn Si Si atoms; and the Si atoms themselves. This allows a determination of hyperfine field contributions due to at least the first six neighbor shells of an Fe atom. The NMR frequency variations as a fnnction of Si content for Fe-Si ordered alloys for the first six neighbor shells are indicated by ANnn, N= 1..~6. The shifts indicated by the vertical arrows labeled ANnn are the hyperfine field contributions due to an Fe atom in the Nth shell. The notation is: &, where m is the number ofFe@) atoms in the Inn shell and n the number of Fe atoms in the 4nn shell to a Fe(A) atom, all the other shells out to the 8nn contain Fe atoms; D,, where m is the number ofFe atoms in the 2nn shell, all the other shells out to the 5nn contain Fe atoms; Si:, where m is the number of Fe(D) atoms in the 3nn shell and n is the number of Fe atoms in the 6nn shell, all the other atoms out to the 9nn shell are Fe atoms. Since the hyperfine field of Fe is negative (points in the opposite direction) with respect to the magnetization, an increase in the frequency due to a neighboring Fe atom corresponds to a negative polarization of the s conduction electrons [71 S 11. The results of these measurements have led to the conclusion that conduction electron polarization of the s electrons can not be responsible for the exchange interaction between the Fe atoms. Polarization by a sufficiently small number of itinerant d electrons, leading to d conduction electron polarization can lead to a positive exchange interaction. Similar reasonings hold for Co and Ni [71 S 2, 66S1,74S1,76Sl].

50lMHz

Fe-Si

o3 =

7.5 0

0.5

1.0

02 -

4 Do Pr

46

42

I e 38

34

30

26 17

I

I

I

19

21

23

SI -

-2.5

1.5

2.0

2.5

3.0

Fig. 8. Frequency shift (Av)~caused by adding an Fe atom into the Nth shell over the number present in Fe,Si vs. shell radius r. A positive shift corresponds to a more negative Hhyp. This can be attributed to a negative s conduction electron polarization contribution caused by the added Fe atom. This polarization is directly proportional to the measured shift. Where error bars are not shown the error is less than the size of the symbols [71S 11.

Landok-Bbmstein New Series 111/19a

65

1.1.2.8 Fe, Co, Ni: hyperfine fields, isomer shifts, relaxation time

Stearns

I

25 at%

1.1.2.8 Fe, Co, Ni: hyperfine fields, isomer shifts, relaxation time

66 0

[Ref. p. 134

0.045

mm 5

mm 0,;30

-0.03

0.015 0

-0.12 0

-0.015

25

50

1

75

100 kbar 1

P-

?ig. 9a. Change of the isomer shin with pressure for bee %.rclativc tozcro-pressurcisomcr shift.diffcrcnt symbols ndicating dilfcrent pressure runs [68 M I], xc also 168S I]. In [67 121 many data arc given ofthc isomer shift If 5’F~ in transition metals under prcssurc.

t I -0.0301 $ -0.075 -0.090 -0.105 -0.120 -0135

-01sn 0

b

IO

20

30

40 P-

50

60

kbor 80

Fig. 9b. Prcssurc dcpcndencc ofthc isomer shill ofy-Fe in copper at room temperature and 79 K. Velocity scale is rclativc to iron at room temperature [79 L I]. Symbols rclatc to diffcrcnt prcssurc runs.

210 kHz

193

I 170 Q n

153

13s 0

\ 100

200

300 I-

400

500 K 600

Fig. IO. Temperature dependence of the electric quadrupole splitting dQ and anisotropy in the hyperfine field of the wall edge nuclei. In the hcp phase of 59Co dQ=172(5) kHz at 290K and 207(5)kHz at 4.2K. The temperature variation of this splitting is similar to that of the ratio c/a. The anisotropy in the hyperfinc field at 4.2 K was measured to be +8.0(l)kOe. It arises from dipolar and orbital fields with the orbital field being about twice as large as the dipolar field [72 K I].

Stearns

Ref. p. 1341

1.1.2.8 Fe, Co, Ni: hyperfine fields, isomer shifts, relaxation time

67

1250 , kHz 59co 1000 hcp ' 1 t $ ?

I

I

6

I

750

2 500 w + ; 250 0 230 MHz 220

Fig. 11. High-held Knight shift of 5gCo in ferromagnetic single-crystal hcp Co at 4.2 K. Circles and squares refer to different spherical samples. Curve 1: observed NMR frequency v vs. applied magnetic field, v= ve -yeffHappJ2n. Curve2: difference between the resonance frequency expected for yerf=y5’ and the observed NMR frequency vs. applied field. ysg/2n = l.O054(20)kHz/Oe. Note that for H .,,,<4nM/3 the sphere is no longer technically saturated and v, even within domains, will not follow the broken part of curve I, but will remain essentially constant. The experimental high-field Knight shift of hcp Co at 4.2 K is: K=(y,,,-y59)/y59=0.0194(25),

I 200 :, 190 180

leading to a spin susceptibility for the d electrons of xd =65(25). 10-6cm3/mol and an orbital contribution of xVV= 0.202(25). lo- 3cm3/mol [76 F 11.By comparing the large value of xd with a calculated value [721 l] it was concluded that hcp Co has spin-up d electrons at the Fermi level.

600

800

1000

1200 T-

160 150 0

1400

IO

IS00

20

30 LO HWI -

1800

Fig. 12. Knight shift K vs. temperature in paramagnetic Ni and Co. Open symbols: solid state; closed symbols: liquid state. Ni: 1: [SOS 1],2: [78 S 11, Co: 3: [SOS 1],4: [74E 11.

Land&B6mstein New Series 111/19a

Stearns

K 2000

50

60 kOe 70

65

1.1.2.8 Fe, Co, Ni: hyperfme fields, isomer shifts, relaxation

time

Table 6a. Observed and calculated longitudinal relaxation times, T,, for Fe, Co, and Ni under various conditions. The calculated times are for the s-contact and d-orbital contributions [66 W 21. Clearly the calculated times (rates) for nuclei in the walls are much too large (small) supporting that the dominant relaxation takes place by interaction with the magnons [69 S 23. The agreement is better for the domains where the applied field introduces an energy gap so that the nuclei can not interact with the bulk magnons. Thus the orbital relaxation processbecomes dominant here.H,,,, =0 indicates the presenceof domain walls, whereas H,,,,, + 0 suggeststhe absenceof walls. Metal

Nucleus position

Fe

(calculated) wall center wall. Happ,= 0

co 2)

domain. Hnpp,$0 (calculated) wall center wall edge wall, Hnpp,=0

domain, H,,,, =0 Ni 3,

(calculated) wall center wall. H,,,, = 0

domain, H,,,, + 0

T K 4.2 RT 4.2 4.2 4.2 4.2 RT RT 17 RT RT 4.2 4.2 RT RT 4.2 4.2 4.2 4.2 4.2 RT RT 4.2

T ms 2900...5200 II(l) 0.16(3) IO...500 36 590 400(200) 0.9...6.5 0.25 6500(2000)“) 40...70 0.027(3) 0.35(4) 0.2...17 19 0.1...0.5 0.12 60 M 0.03 100~~~180 6(l) 15...25 27 x 25 0.35 0.16 50(3) ‘1

Ref. 66W2 69 S 2 69 S 2 61 W I 61R2 66W2 71s4 61 Wl 64C2 71 s4 66W2 73B3 73B3 61Wl 66W2 61 Wl 7282 6651 7OSl 66W2 71Al 61 Wl 66W2 70Bl 61 Wl 65Cl 71C2

‘) For pulse times lessthan 150ms. A decay time of 400 ms is found for pulse times greater than 200ms [7l C2, 73S23. This has been attributed to surface oxidation [7l C 21 or quadrupole broadening in the spin-3/2 Ni system [73 S 21. 2, Due to the large NMR frequency spread of nuclei in the domain walls of hcp Co, the Co results are often even more ambiguous than those of Fe and Ni. 3, Pure Ni has a very small coercive field, so here special care must be taken to keep the applied rfficld small so that the equilibrium position ofthe walls doesnot change during the rf pulse sequence.This may account for some of the difficulties in obtaining reproducible results on Ni. 4, fee at 77K.

Stearns

[Ref. p. 134

1.1.2.8 Fe, Co, Ni: hyperfine fields, isomer shifts, relaxation

Ref. p. 1341

69

time

Table 6b. Measured transverse relaxation times T, for Fe, Co, and Ni under various conditions. Harp,=0 indicates the presence of domain walls. Metal Fe

Nucleus position

wall, Harp,= 0 wall, Harp1= 0

Ni

wall center wall, Harp,= 0

ms

4.2 RT 4.2 4.2 RT 4.2 4.2 RT RT 4.2 4.2 RT

1w 0.14(3) lo*.*500 90 0.9...6.6 0.088 0.006 0.025 0.006 1.0(2) 8 0.35

6932 6932 61Wl 61R2 61Wl 61Wl 72S2 61Wl 72S2 71Al 61Wl 61Wl

T

wall center

co

T,

Ref.

K

Table 7. Measured relaxation times Toi, To, and enhancement factors e0at the center of domain walls for various Fe samples [69 S 21. Sample purity, form

T, 1Cmsl

Natural s‘Fe 99.999%, 1. ..lO urn Natural 57Fe 99%, 3...5pm 90.7%, “Fe Natural 5‘Fe, 1 at% Co

L Cmsl

co

T=4.2K

T=295K

T=4.2K

T=4.2K

T=295K

11(l) *) 10(l)

0.16(3)

11(l) *)

6100(300)

25OOO(2000)

0.14(3)

w 2000

5 500

% 2Z(2)

60(5) 170(20)

*) The temperature dependence for the 99.999% natural Fe sample were found to be (ToIT)-’ =22(2) s-l K-l and (T,,T)-’ =28(3) s-l K- ‘. This is evidence that the main mode ofrelaxation is via emission or absorption of single bulk magnons [69 S 21 rather than by wall excitations which would be temperatureindependent [61 W 2, 64 J 11. Table 8. Enhancement factors E of Ni as measured by continuous wave (cw) and pulsed NMR experiments. Using the drumhead model it has been estimated that, for resonable distributions of domain wall areas in Fe and Ni, the maximum enhancement factor is about five times the average enhancement factor [70 W 11. rf system cw cw cw cw pulsed pulsed pulsed Land&Biirnstein New Series 111/19a

Sample purity, form

K

99.999%, 10pm 99,99%, < 60 urn 99.95%, 5 mm 99.998% rod 99.995%, 40 pm pure powder single crystal, rod

RT RT RT RT RT 1.3...77 RT

T

Stearns

&

Ref.

av. 7000 av. 1600 av. 33500(4000) av. 32000 max. 4500 max. 4000(500) av. 43000

63S2 65Cl 70R2 70R2 69K2 71Al 72Hl

1.1.2.8 Fe, Co, Ni: hyperfine fields, isomer shifts, relaxation time 1.5 '3 !" 1.0 I

I 5.16 (12ms) I 0 I

~

1.4

5.10~10ms) ,

1.0 4 1 a

:

Y 2.3.2.3 (Ems)

I

f

6?0-' 1 8 6

[Ref. p. 134

Fig. 13a. Typical longitudinal relaxation data taken at 4.2 K of the free-induction-decay (FID) amplitude of the second of two pulses as a Lmction of the time between pulses in a spin echo nuclear magnetic resonance experiment. The data, shown as the points, was taken on 99% pure natural Fe in the form of 3...S~lrn spheres. The numbers given near each curve are the maximum turning angles in [rad] of the spins for, respectively, the first and the second pulses and, in parentheses, the longitudinal relaxation time for nuclei at the wall centers, TO,. The value of TO, was obtained by fitting the data with the drumhead model of the domain walls as shown by the solid curves. The maximum turning angles are determined by the pulse length and the strength of the applied rf field [69S2].

b

t 2x-' 1

I

8

-

0.25

0.50

0.75

I

I

I

1.00 ms 1.25 ! 7-I

7K

IO 8 6

2 I I

a

0

10

20

30

40

t-

50

60 ms 70

0 b

I

,

5

10

1

,

I

15

20

I

ms 25

I-

Fig. 13b. Typical transverse relaxation data of the echo height in a nuclear magnetic resonance experiment as a function of the time between two pulses for a 99.999% pure Fe sample at 78 K and 4.2K. The curves are calculated according to eq. (4). The numbers labeling each curve give, in [rad], the maximum turning angles of the spins for the two pulses and, in parentheses, the value of TO2corresponding to the calculated curve [69 S 23.

Stearns

71

1.1.2.8 Fe, Co, Ni: hyperfine fields, isomer shifts, relaxation time

Ref. p. 1341

.s-1 2

t 1

‘i3 4

2 ,‘

2 If 6 4 2

IO

IO-'

2

4681

46BlD

2

2

4 K 10’

7-

c

Fig. 13~. Variation of the transverse relaxation rate for Fe nuclei at the center of the wall as a function of temperature. The solid line corresponds to (TT,,) -’ =28(3)s-‘K-’ [69S2]. 60 s-1K-1 55 50

~

lo3 10-3

c a

10-l

450 600 7-

750

900 K 1050

Fig. 14a. (Tr 7) - ’ and (T, T) - ’ vs. temperature for Fe. The curves are guides to the eye intended to emphasize the difference between bulk samples and powder samples. The inset gives for bulk samples a plot of TZ-’ vs. E = 1- T/T, on a log-log scale, T,= 1034.2K. The peak in the (T,T)-’ bulk data near 600 K is not understood [SOS 11. Landolt-Biirnstein New Series 111/19a

I b

1600 K 2000

7-

Fig. 14b. (TIT)-’ and T,T)-’ vs. temperature for Co: (Tl T) - ’ is represented for liquid (solid circles) and solid (open circles) phases; triangles represent (T2T’-l in the solid state [80 S 11. For Fig. 14c, see next page.

Stearns

1.1.2.9 Fe, Co, Ni: Spin wave properties

12

0 c

100

200

300

400

500

600

[Ref. p. 134

700 900 llOOK1300

I-

Fig. 14c.(T,T)-’ and(T,T)-’ vs.temperaturefor Ni.The curves are guides to the eye intended to indicate the difference in (T,T)- ’ between natural and enriched samplesand between bulk and powder samples.The peaks in the (T,T)-’ bulk data are not understood [8OS I].

1.1.2.9 Spin wave properties Introduction Magnons are the elementary collective excitations of the spin system in magnetic materials. In the linear approximation for T
E, = C(Mri) + waKfJ (fi4q) + a.kJ,,, + 4wk&f, sin2RJI ‘j2 ,

(1)

where If,,, is the sum of any anisotropy field and the internal field, Hnppl-47tNM,, and N is the demagnetizing factor in the direction of magnetization. e4 is the angle between q and the direction of magnetization. The last term in eq. (1) is due to dipole-dipole interactions between spins and it is generally neglected for spin wave treatments. For cubic lattices and only nearest-neighbor exchange interaction, J,and for (q. I)2 < 1 (where lis the nearest-neighbor distance), the dispersion relation along symmetry directions is Wq) = Dq2,

(2)

where D = 2JSn2 is called the spin wave stiffnessconstant, S is the spin per atom and a is the lattice constant. On keeping higher order terms in q. I and longer range exchange terms, D becomes [71 M l] D=fLsC12J(r), I

(3)

where I is now the distance to the various lattice sites. In practice the dispersion relation is often taken as hco(q)= Dq2(1- Pq’) . Stearns

(4)

1.1.2.9 Fe, Co, Ni: Spin wave properties

12

0 c

100

200

300

400

500

600

[Ref. p. 134

700 900 llOOK1300

I-

Fig. 14c.(T,T)-’ and(T,T)-’ vs.temperaturefor Ni.The curves are guides to the eye intended to indicate the difference in (T,T)- ’ between natural and enriched samplesand between bulk and powder samples.The peaks in the (T,T)-’ bulk data are not understood [8OS I].

1.1.2.9 Spin wave properties Introduction Magnons are the elementary collective excitations of the spin system in magnetic materials. In the linear approximation for T
E, = C(Mri) + waKfJ (fi4q) + a.kJ,,, + 4wk&f, sin2RJI ‘j2 ,

(1)

where If,,, is the sum of any anisotropy field and the internal field, Hnppl-47tNM,, and N is the demagnetizing factor in the direction of magnetization. e4 is the angle between q and the direction of magnetization. The last term in eq. (1) is due to dipole-dipole interactions between spins and it is generally neglected for spin wave treatments. For cubic lattices and only nearest-neighbor exchange interaction, J,and for (q. I)2 < 1 (where lis the nearest-neighbor distance), the dispersion relation along symmetry directions is Wq) = Dq2,

(2)

where D = 2JSn2 is called the spin wave stiffnessconstant, S is the spin per atom and a is the lattice constant. On keeping higher order terms in q. I and longer range exchange terms, D becomes [71 M l] D=fLsC12J(r), I

(3)

where I is now the distance to the various lattice sites. In practice the dispersion relation is often taken as hco(q)= Dq2(1- Pq’) . Stearns

(4)

1.1.2.9 Fe, Co, Ni: Spin wave properties

Ref. p. 1341

13

Due to spin wave excitations at finite temperatures the temperature dependenceof the magnetization is given by [66K 1, 56D 1,71 M l] M,(T) =M,(O) [l -u~,J~‘~ -u,,~T~‘~ - . ..] ,

(5)

u3,2=2.612gpa[ks/4xlFJ”‘2/M,(0) =2.612 gpBVo[k,/4.rcD]3’“/j7a,,

(6)

where

where V, is the volume per atom, k, the Boltzmann constant, and fia,tthe average magnetic moment per atom. Including the two-magnon interactions (dynamical interactions) D becomestemperature-dependent as given by (7) where D is given by eq. (3) and p = S C 14.J(I) 30. This temperature dependenceis the samefor the itinerant [I I/ model as for the Heisenberg or localized model of ferromagnetism. The quantity in brackets in eq. (7) is called the renormalization factor. The dynamical interaction also introduces a T4 term in eq. (5) for the magnetization. The interaction of the spin waves with the electrons which have been excited out of their zero-temperature ground state gives rise to a T2 term [641 l] so that D(T)=D,-D,T2-D2T5’2.

(8)

At high enough CJvalues or excitation energies it becomespossible to excite single particle spin flip excitations (often referred to as Stoner excitations) so the dispersion curve mergesinto the singe1particle excitation band. Paramagnetic region In the paramagnetic region for small momentum transfers in the critical region, the neutron scattering function S(Q, E) for an isotropic magnet can be written as [84 S 1, 84 W 21

%QtEl = 2kBTdq)F(q,El 1_ ex;r$k

B

T) 3

(9)

where q is the reduced wavevector associatedwith the momentum transfer Q and E is the energy transfer. x(q) is the wavevector-dependent susceptibility. At small q, x(q) can be taken of the form

(10) where x is the inverse correlation range of the spin fluctuations and x(O)denotes the static susceptibility. The spectral weight function F(q, E) at small E 4 k,T, where spin diffusion theory is valid, is a Lorentzian centered at zero energy,

F(q,E) =

w Nt-%d12+ E2)’

whereW = &Wdq 5/2 A is a constant and f(x/q) is the Resibois-Piette function [70 R 31.A modified form of F(q, E) for higher tempe;atures and larger q values was proposed to fit the data [84 W 21 F(q, E) N {T/(r2 + E2)}@‘, where r=Aq6

and E(E)=

with 6 and a suitably chosen. Landolt-Bbmstein New Series fWl9a

1 1+a[(IEI -r)/r]

for for

IElrr IEl zr

(12)

1.1.2.9 Fe, Co, Ni: Spin wave properties

74

[Ref. p. 134

Measuring methods Magnetization (MAG) Very accurate magnetization measurementsat low temperature can according to eq. (8) give information on spin wave properties. Since the net magnetization is a macroscopic quantity it is difficult to obtain detailed information about spin waves from these measurements. Neutron scattering (SAS, DM and TAS) The spin wave dispersion relation can be measuredmore directly by inelastic scattering of thermal neutrons. This is the most reliable way to investigate spin waves and single particle excitations. Essentially three different experimental methods [68 S 31 of neutron scattering have been used: 1. Small angle scattering (SAS) [65 L 2, 68 S 21 utilizes the fact that the form of the dispersion relation is quadratic at small q values. This, plus the conservation of energy and momentum for single-magnon scattering, restricts the scattering to small angles. The cut-off angle of the scattering is given by sin-‘(ti2/2mD), so by observing this angle D can be determined without any energy analysis of the incident or scattered beams.For thermal neutrons the cut-off angles are x l/2” for q values of ~0.05 8,-l. Using the quadratic approximation of eq.(2) this method determines D for small values of q ~0.05 A- ‘. In actual practice the magnetic field and dipolar terms in eq. (1) complicate the analysis as discussed by Stringfellow [68 S 21. 2. The diffraction method (DM) [67 A 23 is similar to the SAS method but is carried out around reciprocal lattice points. It can be generalized to include a quartic term as in eq. (4) and is useful in the q range of 0.05...0.25/?-‘. 3. The most direct method is triple axis spectroscopy (TAS) which consists of monochromizing the incident neutron beam and energy analyzing the scatteredneutron beam.This method thus requires a large single crystal, a high-flux reactor and a precise knowledge of the resolution function of the spectrometer. Measurements with this method can be made by keeping the neutron momentum change fixed, constant-Q scans [61 B3], or keeping the neutron energy change fixed, constant-E scans [68 S 33. The q range is 20.03 ?I-‘. Both the DM and TAS methods are often carried out with polarized neutrons. Spin wave resonance (SWR) Spin waves can also be measured with microwave resonance where the spin wave stiffness constant D is defined [5SK l] by: o/y=H,,,,-4xM,+Dq2/gp, and q=nn/L, (9) where n is an integer, I, is the film thickness, o is the microwave angular resonance frequency and y is the gyromagnetic ratio. Such measurementscorrespond to small q values of <0.03&l. Table la. Spin wave stiffness constants derived from the temperature dependence of the spontaneous magnetization (MAG) and from the magnetic hyperfine field (HYP). For the constants, seeeqs.(2) and (5)...(8). Metal Fe

a32

123j2

.10-6~-3’2

. lO-gK-5/2

3.42(30)

2.2(10)

3.4(2) 3.01(15)

l(l)

a3,2/a5,2

K

1550

Do

Dl

meVA2

. 10e3meVA2Km2

280 31l(10)

0.60(8)

Ni

6.64(60)

18.5(30)

7.5(2) 7.38(11)

15(2)

360

MAG

82P1, 83Pl 72A1 63 A 1 73Rl 56Dl 82P1, 83Pl 82P1, 83Pl 75Al 63Al 77Rl 56Dl

580 422

MAG

308(10) zz 0’)

Ref.

MAG MAG HYP Theory MAG

4540 hcp Co z 1.5 ‘)

Meas. method

362 393(6) 2600 ‘) For T> IOOK only. Stearns

+ 1.05

MAG MAG HYP theory

Table lb. Spin wave stiffness constants of Fe, Co, and Ni obtained from neutron scattering and spin wave resonance experiments (SWR). For constants, seeeqs.(4) and (8). Metal Fe

D, meV A2

Dl meVA2 Kw2

350(20)

4.9(3). 10-4 ‘)

314(10)

D

T

meV A2

K

281(10)

1.0

280

0.26

1.6(5). 1O-3 2,

2O.e.300 295 295...1036 RT and Tc 4K...0.4 T, RT

Fig.

Method

Sample

Ref.

9b 1 2, 8 3 9a

SWR TAS “) TAS, qO.2/% SAS TAS, constant E,

film single crystal single crystal single crystal polycrystal Armco Fe

66Pl 68S3,69Cl 6883 74Ml 6882 73Ml

TAS, constant E TAS, constant E DM SWR DM SWR DM SAS

Fe4at% Si Fe-12 at% Si Fe-12 at% Si single crystal single crystal single crystal film Co-6at% Fe film single crystal single crystal

7

TAS, constant E

single crystal

6a 1oc

TAS, constant E TAS, constant E TAS, constant E

single crystal single crystal single crystal

73Ml 75Ll 75Ll 84Ll 6883 68S3 64P1 67Pl 63Pl 67Pl 6882 6882 73M2, 81Ll 73M2, 81Ll 73M2,81Ll 69M3, 74Ml 69Ml 69Ml

o.3A-‘~q~o.7A-1

260 230(7) w 140 307(15) 510 490

hcp Co fee co

360(40)

Ni

420(40)

0.47 0.82(20) 0.32(10) 1.8 3.3

384(20)

3.1(10)

391(20) 410 125 593 505 280 433 400

1.0

RT RT ’ T, 10 295 295 4.e.295 RT

TAS, constant E 4 5 5 9c 9d

0.68 0.98

RT RT T, 4.2 RT ’ T, RT z T, 295

‘) D2=-0.35~10-5meVA2K-5/2. “) D,= -5.7(22). 10-5meVA2K-5’2. 3, Constant-E scans for Es> iOmeV, and constant-Q scans for Es< 10meV.

[Ref. p. 134

1.1.2.9 Fe, Co, Ni: Spin wave properties

76

6

5 I G4 3

2

1

0

0.05

0.10

015 U-

0.20

0.25 8;! 0.30

Fig. 2. Spin wave dispersion in Fe along [I IO] as a function of temperature. The measurements were made with incoming neutron energies of 10meV, 13 meV, and 20mcV [68S3].

U-

Fig. 1. Constant-E scan TAS-measured spin wave dispcrsion relation for various directions in a single crystal ofFe at 295 K. The dashed line corresponds to the Hciscnbcrg model with D=281 meVA* and /I=l.OA* [68S3], see also [73 M I].

I

LA Phonon Y I

Fig. 3. Spin wave spectra for Fe-12at% Si at various tempcraturcs around the Curie point [74 M I, 75 L I]. Tc =970 K.

Stearns

1.1.2.9 Fe, Co, Ni: Spin wave properties

Ref. p. 1341

77

meV CO hcp [OOOII T=295K 25 -

IO

5

0

0.05

0.10

0.15

0.20 A-’ 0.25

9v fi =ZOOmeV a 300meV0 350 meV

/

0.2

0.8 A-’

Fig. 5. Spin wave dispersion relation for hcp Co at 295 K along the hexagonal c axis. [68 S 31.

1.0

9-

Fig. 4. Spin wave spectrum ofpure Fe at 10 K assuming an isotropic spin wave dispersion relation. Incident neutron energies Ei of 200, 300, and 350meV have been used to measure the magnetic excitations from 40... 160meV. The solid curve shows the results of fitting the dispersion relation to the experimental data in which D and b were found to be approximately 307meVA’ and 0.32A2, respectively, [84 L 11.The dashed curve is calculated from using D = 325 meV A2 and fi = 0.9 A2 [69 C 11.

I 141: meV

“Ni

12cI

IOC

200 meV EC 160

I cu” 60

t‘z d-

40

20

0

0 viT!dds .

b 9Fig. 6b. Room-temperature spin wave dispersion curve for the [ 11I] direction of 60Ni. ZB shows the position of the zone boundary [85M I]. The solid curve is from calculations [85 C 1, 83 C 11. Land&-Bbmstein New Series lWl9a

0.1

0.2

I3.3

0.4

0.5

0.6 I-’

a 9Fig. 6a. Spin wave spectra for 6oNi at room temperature for the three high-symmetry directions [69 M 3, 74 M 11, see also [69 M 11.

Stearns

78

1.1.2.9 Fe, Co, Ni: Spin wave properties

[Ref. p. 134

300 m@! 250

0

0.5

C

1.0 Q-

60)

I

I

I

0

OS

0.2

0.3

I

/

rl

I/

Y

/

/I

I

I

1.5 A-' 2.0

Fig. 6c. Room-temperature spin wave dispersion curve for the [IOO] direction in a 60Ni crystal indicating the crossing of the acoustic and optical spin wave branches [S5M I], SW also [79M I]. The solid line is from calculation [SSC 11. While this calculation gives a fair qualitative representation ofthc data. notable departures are observed for the larger q values. ZB: position ofzonc boundary.

0.4

0.5

0.6 A-: 0.7

9-

Fig. 7. Spin wave dispersion in Ni at various temperatures as derived from constant-E scan TAS [73 M 2. 81 L I].

500 meVA2

40’ me\'1

400

al a

400

I

I

!

I

I

I

P P

. 200

200

400

600 l-

800

l

l

1000 K 1:

Fig. 8. Temperature depcndencc ofthc spin wave stiffness constant D for Fe [6S S 33.The broken line corresponds to thin film mensuremcnts by spin wave resonance [66P 11.

00

0.2 I

I

0.2 0.4

0.4

0.6 (t I/l, 15'2-

I

I

0.6

0.8

0.8

1.0 I

1.0

a l/l, Fig. 9a. Tempcraturc dependence of the spin wave stiffness constant D for Fe and Ni vs. (T/Tc)“’ measured by SAS [68 S2]. Note the linear region between 0.4 < T/T,< 0.9 in agreement with eq. (8).

Stearns

79

1.1.2.9 Fe, Co, Ni: Spin wave properties

Ref. p. 1341

2m' Fe

/

4

2

10-311

IWJ2-

b Fig. 9b. Temperature dependence of the spin wave stitfness constant D for Fe plotted against (T/Q2 for D< T/T, < 0.42. The solid line is eq. (8)with values given in Table lb. The dashed curve is the result from spin wave resonance experiments [66P 11.

2

2

L

K IO3

4

T-

C

Fig. 9c. Temperature dependence of the deviation of the spin wave stiffness constant D of Fe from the lowtemperature value D,, as derived from spin wave resonance experiments on films at 9.3 GHz [66P 11. 2.10' ,

PI 5.9 .I@! erg cm

I

I

I

I

I

I

,

I 2

I

6

8

IO2

2

I K 4.10'

I III

I/l

4

5.8

I

2

67 \

ll

0

d

1

2

3

T312-

4

e

Fig. 9d. Temperature dependence of the spin wave stitiess constant D of Co as derived from spin wave resonance experiments on films at 9.2 GHz [64P 11. lo-” ergcm’~62.41 meVA2. Land&-Bdrnstein New Series 111/19a

IV I IO

5 40JK"L 6

T-

Fig. 9e. Temperature dependence of the deviation of the spin wave stiffness constant D of Ni from the lowtemperature value D, as derived from spin wave resonance experiments on films at 9.2 GHz [63 P 11.

Stearns

1.1.2.9 Fe, Co, Ni: Spin wave properties

80

I

I I

102 8

23

I I

6 I

I,"r

m'

I I

'

- - slope:

‘

10 I 2.w

‘

I

I

6

8

I 1P

2

L

I I lo-

6

8

2.10-1

10-s

4

2

6

b

(I,-r)r,a Fig. IOa. Spin wave stiffness constant D for Fe plotted against (T,-- 7)/T, on a log-log scale. The linear tit shows that the spin wave energies are being renormalizcd to zero at T, follovcing a power law that is very close to that followed by the magnetization [69 C 11.

ll 10-2 tI,-rl/r,

6

6

a

lo-'

Fig. 10~. Spin wave stiffness constan t D for Ni plotted --..:--‘ (lc/T ?-\,-I^” - I,, I,.. rrnl.3 1 ,, IC “11 a rug-rug DLCILG The data indicate that D is scaling as the magnetization. A fit to the straight line would indicate that D-+0 as T+ .Tc [69 M I].

aga,,lsL

10 2.10-3 i

2

Fig. lob. Spin wave stiffnessconstant D for polycrystalline kc Co plotted against (T,- T)/T, on a log-log scale. The values for D were derived from only those data estimated to lie within the hydrodynamic region [77 G I].

2

C

[Ref. p. 134

5 8W

2

1

6 B

lo-!

2

‘

681

30

40

(1,-T )/I, -

0

10

20

50

60

70

80

90

Fig. 1I. Constant-Escan TAS measurements ofthe roomtcmpcraturc spin wave intensity vs. spin wave energy for the three high-symmetry directions in Fedat% Si [73 M I].

meV

110

81

1.1.2.9 Fe, Co, Ni: Spin wave properties

Ref. p. 1341

0

IO

20

30

40

50

60

70

80

90

100 meV 120

Fig. 12. Room-temperature TAS measurements of the spin wave intensity vs. spin wave energy for the three highsymmetry directions in Ni [69 M 31.

2

2-

0

IO

20

30

40

50

60

70

80 meV 90

Fig. 13. TAS measurements of the integrated intensity of the spin wave scattering as a function of spin wave energy and temperature for the [ 11l] direction in Ni [S 1 L 11,see also [73 M 21.

Land&-Biirnstein New Series 111/19a

Stearns

[Ref. p. 134

1.1.2.9 Fe, Co, Ni Spin wave properties

82

Table 2. Magnetic properties of c1and y-Fe in the paramagnetic phase. d: inverse of nearest plane distance. cc-Fe at 1113K [85 B l] d [A-‘] r [mcV] at q=O.O4A-’ r [meV] at q=O.15&’ r [mcV] at q=0.45A-’ % [A-‘] 6

3.06 (bee) 0.038 0.73 14 0.158 22

y-Fe at 1198K [85 B l]

y-Fe at 1300 K [85 M 33

2.98 (fee) 0.77 ‘) 3...4 >8 ‘) 0.25...1 1...1.5

0.3(0.07) 2) 1.7(1.0)2) 7.1 0.4 z 1.3

‘) Assuming x=0.4&‘. 2, Extrapolated from mcasuremcnts at higher q values assuming 6= 1.3. In parentheses: extrapolated values assuming 6 = 2. Fig. 14. Peak position in Fe near Tc for constant-E scans. Open circles: [75 L I] and solid circles: [84 W 21. The curves show calculations for pure (x=0) and modified (a(=O.l) Lorentzian forms of S(Q, E), eqs. (9...12) with A= 142.3meVA5/2 [84W2].

me! 70

I

51Fe-120t%Si I I I I 303

-10 a

10

20 E-

30

40 meV 50

Fig. 15a. Constant-Q scans of the paramagnetic spin flip scattering in pure Fe at q=0.47k1 in the [IIO] direction at T= 1.02 Tc [84W I]. The arrow points to the “pcrsistcnt spin wave ridge” seen in constant-E scan data [75 L 11, see also [85 M 23. E,: final neutron energy, Q: momentum transfer, q: reduced wavevector.

" 250 c E .g 2oc :. '5 153 103

I b

0

-5

0

5

c

10

15

20 meV

Fig. l5b. Constant-Q scans of the paramagnetic spin flip scattering for 54Fe -12at% Si at T= 1.05 Tc with better resolution than that of the data in [84 W 21. It is stated that structure is beginning to develop out near 20meV and that the crossover from spin diffusive behavior to propagating spin wave behavior occurs at (1~0.43 A-’ in Fe [85 M 23. Stearns

83

1.1.2.9 Fe, Co, Ni: Spin wave properties

Ref. p. 1341

1

150 counts 5min 120

110 100 90 -I,

0

4

8

12 16 20 E-

24 28

32 meV 40

1 90 ;I g

Fig. 16. Constant-Q scans of the paramagnetic spin flip scattering at T= 1.06 Tc in the [ll l] direction of 60Ni for higher q values, showing that the scattering peaks occur at Unite energies rather than at E=O. This behavior of the scattering at the higher q values is interpreted as due to heavily damped propagating spin waves rather than spin diffusion. The solid curves are a least-squares fit to a damped harmonic oscillator form of the spectral weight function. The crossover from spin diffusive to propagating spin wave behavior occurs at q % 0.25 A- 1 [SS M 21. The dashed curve in the q =0.31 A-’ plot is that expected for the resolution used in [83 S 1,84 S 21. Note that the data t?om Fig. 7 would give the peak at x45meV for qzO.4A-‘, as indicated in Fig. 17. E,: Final neutron energy, Q: momentum transfer, q: reduced wavevector.

60

I

1 0

0.1

0.2

0.3

a

0.4

0.5

30

40

I 0.6 8-l

9-

600 counts 5min 500 400 I g 300 al -E - 200

0 -10

b

0

IO

20

50 meV 60

E-

Fig. 17. Demonstrations for ‘joNi at T= L$+ 100 K of (a: the peak in constant-E scans, q in [ 11l] direction, and (b: the diffusive nature in constant-Q scans for q = 0.40 A-' The solid lines are calculated with a linewidth r = 25 meV, see eq. (1I), and the appropriate resolution convolution [84 S 21. The arrow indicates where the peak should occur for a propagation spin wave [73 M2 74M 11. There is considerable controversy about the existence ofpropagating spin waves and the nature of thf magnetic excitations seen above Tc in Fe and Ni, E,: fina neutron energy, Q: momentum transfer, q: reducec wavevector. Landolt-Biirnstein New Series 111/19a

Stearns

1.1.2.9 Fe, Co, Ni: Spin wave properties

84

r

.

[Ref. p. 134

Fe- 5at% Si .

7=1273K

I

L .

\ I 60Ni 11111 ‘~“‘or~

f .

I 0 [OOll . Ill01 ,J ill11

.

.

/

\ \

.

\ \ \ \

.

.

0 1

\ \

f

\ \ \, \

3

Fig. IS. Polarized neutron energy-integrated paramagnctic scattering from Fe5 at% Si at 1273K along the highsymmetry directions [82B2]. f(Q): atomic magnetic form factor. M2(Q) = 12k,7j(q). Q: momentum transfer. q: reduced wavevector.

2 25 y s 20

2244 ‘\

\ \ \ \

15

\

15.54

\

-\

\

‘\, \

10

--&lI,+lOOK

pi,, = 2.5ap:

0

1.03

1.06

1.09

1.12

1

Fig. 19. Energy-integrated neutron scattering function for “Ni vs. Q in [ 11I] direction. M2( Q)= 3k,Tl(q). The q > 0 data was obtained from polarized and unpolarized neutron paramagnetic scattering measurements at several temperatures above Tc. The q=O points were obtained from the static susceptibility. The horizontal line gives M2(Q) when there is no correlation between atomic moments, M2( Q) = p& [84 S 21.

Stearns

Ref. p. 1341

1.1.2.10 Fe, Co, Ni: g factors, ferromagnetic resonance

85

1.1.2.10 g factors and ferromagnetic resonance properties Ferromagnetic resonance (FMR) is described by the equation of motion [55 G 11 dM

~=yMxH,,,+~Mx8’M-~Mx~

dt

M,”

(1)

YW

where A is the exchange stiffness and 1 is a microscopic relaxation parameter. H,, includes applied fields, demagnetizing fields and anisotropy fields. y = -gua/fi denotes the gyromagnetic ratio. Eq. (1) must be solved along with Maxwell’s equations and the exchange boundary conditions am/i% = (K,/A)m, where K, is the surface anisotropy, m represents the dynamic components of the total magnetization, i.e. the deviation from the undisturbed magnetization, and the derivative is taken along the outward normal to the sample surface.There is a significant contribution to the linewidth from the “exchange-conductivity” mechanism, the 2nd term on the r.h.s. of eq. (l), as well as from the ,I term [74B 1, 55 A 1, 59 R 1, 65 H 11. For a uniaxial system the second term on the r.h.s. of eq. (1) must be replaced by %A, -MxV:M+M,”

2YAIIMxV;M. M,2

The analysis of the earlier experimental results did not include the second and third terms on the r.h.s. of eq. (l), so the parameters obtained are not reliable and will not be quoted.

Table 1. Spectroscopic splitting factor g and ferromagnetic resonance damping parameter 1 for Fe, Co, and Ni. Metal Fe Co hcp

Ni

Sample whisker whisker crystal ‘) whisker crystal crystal

T K

;Hz

RT.. .950 4...300 RT 4...700 350 300 RT...650 4...300

9.6; 23; 31 70 71.52 60 37 135 23; 32 22

9

a .1o*s-’

Fig.

Ref.

2.09

1.3 0.7

1 2

1

4?

2.3 2.3

53)

72Bl 74Bl 64Fl 74Bl 74Bl 74Bl 69Bl 74Bl

2.18(l) 2.18 2.18 2.18 2.21 2.2

‘) Magnetcrystalline anisotropy constants: K, = 5.22. lo6 erg cmM3 and K, = 0.91. lo6 erg cme3. ‘) Rapid increase < 100K and slow increase from 100...700 K. 3, Rapid increase < 100K which saturates at z 35 K.

Land&-BOrnstein New Series III/I%

Stearns

1.1.2.10 Fe, Co, Ni: g factors, ferromagnetic resonance

86

[Ref. p. 134

Table 2. Room-temperature values of the linewidth AH of the ferromagnetic resonance lines of Fe and Co whiskers and bulk-grown Ni crystals. Metal Fe hcp Co

Magnetization direction %[lOO] [OOOl] (disk)

PO11 fee co Ni

[1111 [lOOI,Cl111 (cylinder) (cylindrical crystal)

AH Oe

&Z

9.2 36.2 71.5 71.5 37.0 (350K) 60 135 9.2 36.2 9.2 36.2 23.3 31.8 9 22

Ref.

32 158 900 950...1200 155 205 340 110 220 460 550 410 x650 130 300

Table 3. Summary of the measured g’ values from the magnetomechanical factor for Fe, Co, and Ni. Metal

g’

Fe

1.938(6) 1.936(8) 1.927(4) 1.929(6) 1.919(6) 1.932(8) 1.917(2)‘) 1.919(2)2) 1.928(4)3, 1.866(2) 1.859(4) 1.854(8) 1.850(4) 1.838(3) 1.837(4) 1.831(4) 1.830(6) 1.837(2) 1.835(2)4)

co

Ni

‘) 2, 3, “)

g=d/W-

2.077(10)

2.193(9)

2.198(6)

Cylinder. Ellipsoid. Mean value. Weighted average value.

1)

Ref. 44Bl 51Ml 51 s 1 52Bl 55Sl 57M 1 6OSl 6OSl 61Ml 44Bl 52Bl 52Sl 56Sl 6682 52Sl 5582 5582 6OSl 62S1

64F2 64F2 64F2 64Fl 74Bl 74Bl 74Bl 64F2 64F2 64F2 64F2 69B1 69Bl 74Bl 74Bl

Ref. p. 1341

1.1.2.10 Fe, Co, Ni: g factors, ferromagnetic resonance 3.5,

I

I

I

I

I

I

kOe Fe

87

I II Y= 9.6 GHz

I

l0

3.0

I

2.5

i mJ 0 0 83

o 11001 whisker

I 2.0

E rt 1.5

0

I

0.7

kOe

Fe

x 0

v= 9.6GHz

l 0

I

0.6

0 0% I

0.5

I 0.4 9 d 0.3 0.2

0.1 C

Fig. 1. (a) Resonance field and (b) peak-to-peak linewidth for FMR as a function of temperature for single crystal [ll l] and [loo] whiskers ofFe at 9.6 GHz. The full lines were computed using eq. (1) for parameter values: A(T) = 1.9. 10e6 M,( 7)/)/M,(300) erg/cm, g= 2.09, I= 1.3 . lOas-i and surface anisotropy K, = 0.03 erg/cm’. A frequency-independent relaxation parameter L fits reasonably well for 300 K < T< 950 K but at higher temperatures the observed resonance fields and linewidths are much smaller than those computed using the lowtemperature parameters. In order to obtain fits to the data in this region it is necessary to make both g and 1 vary with temperature [72 B 11. Crosses: [66 H 11. Fig. 2. Temperature variation of FMR peak-to-peak linewidth in Fe [loo] whiskers at 70 GHz. The full line was obtained using eq. (1) with the parameters A = 1.9 . 10m6erg/cm, 1=0.7. 108s-’ and Z&=0.1 erg/cm’, and nonlocal conductivity theory [65 H l] with C, = 1.5 . 10z4cm- 1s- l. It was concluded that I varied less than a factor of 2 over this temperature range [74 B 11. Land&BBmstein New Series IIM9a

I

3.0

s z ';; 2.5

” 2 , 2 d

Stearns

2.0

I.? IS 50

100

150

T-

200

250 K :

88

[Ref. p. 134

1.1.2.10 Fe, Co, Ni: g factors, ferromagnetic resonance

0

100

200

300

400

500

600

700

800 K !300

Fig. 3. Composite data on the observed temperature variations of the ferromagnetic relaxation parameter I, in Fe, Co, and Ni. The data for Fe is from [66H 1, 72 B 1, 74Bl]; for Co from [74Bl] and for Ni from [65Rl, 71 A2,74 B I]. 0.8 kOe

0.6 I z 0.4

0.2

0

100

200

300

400

Fig. 4. Temperature variation of the peak-to-peak linewidth for FMR in [OOOI] whiskers of hcp Co at about 60GHz. The full lint was derived using eq. (1) with the parameters 9=2.18, I.= 1. lo-as-‘, K,=O, A= A, = 2.78. lOmaerg/cm has been taken from neutron scattering data, 4rrM,= 17.9kg, and conductivity theory with parameters Q= 10.6pRcm and C = 1024cm-1 s-l [74B I]. For T> 250K normal coiductivity theory [55A 1, 59 R I] was used. while for Ts250 K nonlocal conductivity theory [65 H I] was used. Fig. 5. Angular dependence of the external resonance magnetic field (V=71.52 GHz) for two thin disks of single crystal hcp Co in which (1) the plane is parallel to the [OoOl] axis (points on curve I) and (2) the plane is perpendicular to the [OOOI] axis (points on curve 2). In case 1. ~3denotes the angle between the easy axis of the crystal and the direction of H; in case 2, w denotes the angle between an arbitrary direction in the sample plane and direction of H. The finI curves are the calculated angular dependences [64F I]. Open and solid circles refer to different samples.

500

600

K

700

26 kOe 2.

I *

f 16

Stearns

12

8 0

n

2

rod

Ref. p. 1341

1.1.2.10 Fe, Co, Ni: g factors, ferromagnetic resonance

Fig. 6. Measured and calculated (fnll lines) angular dependence of the FMR field at various temperatures of a disc-shaped single crystal of hcp Co at 36.97GHz. The angle v is the angle between the magnetizing field and the [OOOI] axis, both in the disc plane. Tin c”C] : I) 20,2), 250, 3) 275, 4) 300, 5) 325, 6) 350, 7) 375, 8) 400. At all temperatures the value obtained for the g factor was 2.02 which is significantly different from other measured values of 2.18 [73 0 11.

7.0 kOe

Ni

kOe 9.5

9s I L a? 8.F:

8.0

Fig. 7. Temperature variation of the observed FMR field for a cylindrical single crystal of Ni in (a) the [loo] and [l 1I] directions at 23.3 GHz and (b) the [IOO] direction at 3 1.8GHz. The full line was obtained using eq. (1) with g = 2.21. The different symbols stand for results of different heating cycles. The lower-temperature data is good to EZ10% [69B 11. Landolt-Bbmstein New Series IWl9a

89

90

1.1.2.10 Fe, Co, Ni: g factors, ferromagnetic resonance

II

0.2 b 0

50

100

150

200 7-

250

300

1.50 kOe 1.25

0.25

I

50

I

100

I

I

150 T--

200

I

I

350 "C 400

Fig. 8. Variation ofthe observed FMR peak-to-peak linewidth with temperature of a cylindrical single crystal of Ni for (a) the [IOO] and [l I I] directions at 23.3 GHz and (b) the [ 1001direction at 3 I .8 GHz. The full curve was calculatedwith%=2.3~10ss-‘andg=2.21 [69Bl].The different symbols stand for results of different heating cycles.

0

[Ref. p. 134

I

250 K 300

Fig. 9. Temperature variation of FMR peak-to-peak lincwidth in single crystal cylinders of Ni at 22 GHz. The symbols represent diffcrcnt samples with resistivity ratios varying between 60...170 [74 B I].

Ref. p. 1343

1.1.2.11 Fe, Co, Ni: Fermi surfaces, band structures, spin polarizations

91

1.1.2.11 Fermi surfaces, band structures, exchange energies and electron spin polarizations Introduction In the last decade the band structures of Fe, Co, and Ni have undergone extensive study by a variety of experimental techniques as well as numerous band calculations (seee.g. A.P. Cracknell in Landolt-Bornstein, New Series,Group III, vol. 13c.).One of the problems that arises in comparing the experimental data and the calculations is that the band structure calculations are of the ground state of the systemwhereasthe experiments, of necessity,always perturb the system.This difficulty is well known in studies of atomic energy levels where an emitted electron emergeswith less energy than its ground state binding energy becausethe remaining electrons becomemore tightly bound due to decreasedscreening of the nucleus. The usual rationalization of this difficulty in solid state studies is to argue that the Fermi level remains unchanged and the energy levels near it also undergo negligible shifts upon perturbing the systemand thus the measurementsgive a reasonable,accurate picture of the ground state and can be compared to band structure calculations. This type of rationalization obviously depends on the time and energy scalesof the measurements.At extremely small times such that the readjustment of the electron cloud has not yet occurred the usual concept of the Fermi level is not applicable. Measurements that occur over long times (> 10-i’ s)and involve small energy excitations such asde Haas-van Alphen measurements perturb the systemleast and thus most closelv measurethe ground state.Although even in thesemeasurementsa dependence of the spin-orbit splittings on the applied magnetic field directio;has often been seen. Measuring methods a) de Haas-van Alphen (dHvA) measurements The dHvA oscillations are periodic in the inverse of the magnetic induction B-i with the frequency f given by (1) where A is an extremal area of cross section of the Fermi surface in a plane normal to B. Thus the Fermi surface can be obtained by measuring the dHvA frequencies as a function of the applied magnetic field direction. b) Magnetoresistance The magnetoresistance is the relative change of the electric resistivity in a high magnetic field defined by: Aeleo = (e(B) - eo>leo

(2)

where Q,,is the resistivity in zero field. It gives information about the presenceof open orbits and the connectivity of the Fermi surfacewhen the effect of collisions on the motion of the carriers is negligible compared to the effect of the magnetic field [64 F 21.This requires pure single crystal samplesand low temperatures in high fields such that w,z < 1,where o,( = eB/m*c) is the cyclotron frequency, z is the averagecollision time and m* is the effective massof the electrons or holes. The variations of the magnetoresistancewith magnetic field can be related to the orbits of the carriers on the Fermi surface. The power dependence of the magnetoresistance on the field, Aeleo = bB:

(3)

gives further information about the Fermi surfaces.If the magnetoresistance is large and n = 2 (unsaturated), the metal is compensated (has an equal number of electrons and holes) and open orbits are indicated by sharp minima in the magnetoresistance. If the magnetoresistance is low and saturation occurs (n < 1) for most field directions, the metal is uncompensated and open orbits are indicated by sharp maxima in the magnetoresistance. For data on magnetoresistance, seesubsect. 1.1.2.13. c) Photoemission Photoemission experiments do not measure the initial ground state energies but the difference in energy between the initial ground state and the final ionized state. A classic discussion of the interpretation of measured energy levels was given by Parratt [59 P 11.Due to the emission of an electron there is decreasedshielding of the nucleus in the final excited state. This causesthe valence electron statesto be more tightly bound so that, except for the electrons at the Fermi level which are pinned, the electrons are emitted with less energy than they would Land&Bbmstein New Series 111/19a

Stearns

1.1.2.11 Fe, Co, Ni: Fermi surfaces, band structures, spin polarizations

92

[Ref. p. 134

have if they came from the unperturbed ground state energy. The measured energy levels thus are shifted up relative to the initial ground state energies.This effect may be small for some valence states and increaseswith distance from the Fermi level. set Fig. 1.

Fig. 1.Schematicshifts in the measuredenergylevelsdue to perturbing the energy levels by the photocmission process.Heavy lines depict the unperturbed ground state

ground state. t: majority spin, 1: minority spin

Wovevector -

Table 1. Measured dHvA frequencies A Fermi wavevectors k,, number of itinerant d electrons per atom assuming free electron behavior, n(d,), polarization and the paramagnetic Fermi wavevector kt!’ for the spherelike Fermi surfaces of Fe [73 B 11. Spin up: majority spin, spin down: minority spin. Property

Crystal plane

Spin

I CMGI ‘)

up down up down up down

kf l3+71 II Polarization [%] k;” [271/o]

(100)

(111)

(110)

436 71 0.51 0.24 0.28 0.030 80 0.42

370 52 0.495 0.18 0.25 0.012 90 0.40

349 58 0.43 0.19 0.17 0.014 85 0.35

r) Accuracy + 1%. Table 2. Measured room-temperature values A, and calculated values A, [77C l] of the exchange splitting for Fe.

AC Symmetry

eV

point

Crystal surface

Ref.

eV 1.5(2) 2.08(10) 2

1.3 1.8

P, I-;, 1-’ 25

(111) (110)

80El 82Tl 83Fl

4

(100)

Table 3. Measured exchange splitting A, for Fe at high temperatures (T,= 1043K). T

4

K

eV

973 983 886

1.2 1.8 1.7

Symmetry point

MJM,(T=O)

A,/Am(RT)

Ref.

P4

0.60 0.56 0.73

0.80 0.90 0.85

80El 81H2 83H2, 83Rl

T;,(T2,)

l-25

Ref. p. 1341

1.1.2.11 Fe, Co, Ni: Fermi surfaces, band structures, spin polarizations

93

Table 4. Slope (df/dp)/f of the change in the dHvA frequency with pressure of single crystal Ni. 7: majority spin, -1:minority spin. The subscripts of the field direction symbols refer to the f vs. p plots in Fig. 19. Part of Fermi surface:

Spin-up neck t

Field direction:

c1111,

Clq3

f$[lO-‘kbar]

8.0(12)

6.6(25)

Spin-down ellipsoid 4 [llllb

6.6(25) 6(l)

Ref.

c1m

WOI,

lS(8)

-0.8(8) 1.2(3)

77Vl 75A2

Table 5. Measured room-temperature exchange splitting A,,,and band gaps 6, for Ni as obtained from angle-resolved photoemission spectroscopy. Spin-resolved photoemission experiments on (110) surface of Ni gave the same splittings [83 R 11, The region of k-spaceX,(S,) is comprised of considerable hybridization between d and sp states, thus leading to a smaller exchange splitting. t: majority spin. Symmetry point

Crystal surface

u34)

(110)

‘)

X&34)

(110)

US4)

(110)

r-m,) near L3(Ax) near L&J near L [ii21 near L [l lo] l/2 (W-X)

(110) (111) (111) (111) (100) (100)

A, eV

Ref.

4n eV

0.17 0.17 0.18(2) 0.33 0.31(3) 0.30 0.33(2) 0.26(5) 0.28(5)

o.l5’0,:;5(L,t)

o.lO-‘;::s(X,t)

80H2 81H1,81H2 83Rl 81H2 79Hl 82Ml 80Gl 80E2 80E2

‘) The measuredband splittings are consistently smaller than those given by tirstprinciple one-electron band calculations using the local-density approximation which yield values in the range of 0.4.. .0.6eV [77 W 11.The measuredd band widths are also narrower than those obtained from these calculated band structures. How much thesediscrepancies are due to inadequacies in the local-density approximation or how much is due to the excited-state effectsinherent in photoemission experiments is not known and very difficult to determine.

Table 6. Measured excited-statesexchange energiesper spin,Jg,and calculated ground state exchange energies.Jp for the sameregions of k-spaceas the quoted measuredvalues for Fe, Co, and Ni. KS: Kohn-Sham potential, vBH: von Barth-Hedin potential. J in [eV].

JE ‘) Jdd c

Fe (r,‘J

Ref.

1.00(5) 0.85 (vBH) 1.1 (KS)

77Cl 77Cl

co m

Ref.

Ni 04

Ref.

75Bl

0.63(5) 0.92 (vBH) 1.27 (KS)

77Wl 77Wl

0.8(2) 0.88 (KS)

‘) Obtained from the measured exchange splitting A, divided by the total spin, Jid = AJp,, in un. Landok-Bbmstein New Series llVl9a

Stearns

94

1.1.2.11 Fe, Co, Ni: Fermi surfaces, band structures, spin polarizations

[Ref. p. 134

Table 7. Spin polarizations, in [%I, of Fe, Co, and Ni as derived from various experiments. Ato: photon energy, @: work function. Method

Fe

co

Ni

Photoemission

34(l)

17(2)

‘) *I Tunneling between polycrystalline film and superconductor

26.6 30 0.44(2) 0.45 3)

17.5 20 0.34(4) -

3(2) 5(3) g(3) 5.6 6 0.11 0.103)

?%i-@ eV 2 5 16 > 10
Ref. 73Al 76El 79Bl 73Tl 7782

‘) Calculated for the case that all the valence band electrons are excited, i.e. Pspinlti3d

+w

&in

in

PB.

2, Calculated for the case that mainly d-bandelectrons arc excited, i.e.p,,,,/n,,,p,,,,in un. 3, Calculated.

4

t

Fig. 2. First Brillouin zone of the bee lattice.

Stearns

Land&Bornstein New Scrie5 111/19a

Ref. p. 1341

1.1.2.11 Fe, Co, Ni: Fermi surfaces,band structures, spin polarizations

95

440 MG 400 360

200

I *-

160 70 60

_-Field direction

a

0 0"

15" 30" Field direction

b [IO01

. .

IOOI) I

0" [OOII c

15"

30"

45"

60"

75"

Ill11 Field direction

90 5" [I101

30"

I

15" [OIOI

Fig. 3. Graph (a) shows the variation of the intermediate and high dHvA frequency in Fe for B in the (ii0) plane. Dots: [73 B I], solid line: [71 G 2, 74 G 11. Graph (b) shows more detailed variation of the dHvA frequencies for field directions in the (001) plane [80 L 1,84 L 21. Graph (c) is the variation of the E dHvA frequency branches in Fe for B in the (001) and (IiO) planes. Solid circles: field-sweep data. open circles: beat measurements. Sample rotation data for B equal to (open triangles upwards) 33.56 kG, (open triangles downward) 36.11 kG, (solid triangles upward) 46.28 kG and (solid triangles downward) 61.26 kG. [71 G 21. For Fermi surface and extremal orbits, see Fig. 4.7 : majority spin, 1: minority spin.

Landolt-BOrnstein New Series lll/l9a

Stearns

1.1.2.11 Fc, Co, Ni: Fermi surfaces, band structures, spin polarizations

Fig. 4. The Fermi surface ofFc obtained from dHvA measurcmcnts [71 G 2, 73 B l] for (a) and (II) majority spin and (c)minority spin. The electron and hole pockets along the k, axis have been left out for clarity. The main features ofthc Fermi surface arc a central spherical-like surface for both the majority spin and minority spin clcctrons and a number of pocket and rod-like hole surfaces. There are still some questions of whether the rod-like hole surfaces have a gap in their structure near N. Greek symbols correspond to extrcmal orbits.

Stearns

[Ref. p. 134

Ref. p. 1341

1.1.2.11 Fe, Co, Ni: Fermi surfaces, band structures, spin polarizations

2 E-V 0 t -2 G L -4 -6 -8

-4 -6 -8

F

Fig. 5. The calculated band structure of Fe. The Greek symbols at the Fermi level correspond to the frequencies found in dHvA measurements as shown in Fig. 3, see e.g. [66 W 3, 71 D 1, 71 M 1, 75 S 1, 77 C 1, 78 M 11. Near the center of the Brillouin zone r) the lowest band is due to sp-like electrons and the upper five bands are the d-bands: at r the lower three have Tag symmetry while the upper two have E, symmetry. Upon moving away from the Ipoint in k-space the symmetry character of the electrons becomes mixed thus the reference to E, and T,, in these regions is used merely to label the states and is not to be taken literally. As can be already seen the E, bands are quite flat over large regions of k-space indicating that these states have high effective mass and quasi-local character. These are the d states that are responsible for a large part of the Fe moment (= 2 ut,). One of the T,, bands (indicated by the heavier line) is seen to have a high degree of curvature corresponding to a low effective mass comparable to that of free electrons, di. From both the dHvA measurements and the band calculations it is found that there are about 0.25 spin-up and 0.02 spin-down di electrons in these bands. These d-like electrons are highly mobile and it has been suggested that they are responsbile for the ferromagnetic alignment of the quasi-local moment [63 S I,73 S 11. For the minority spins s-d hybridization occurs in the H direction near the region where the T,, bands cross the Fermi level. This causes the electron lens and hole pockets that allow open orbits in the H direction [71 G 21. In all other directions the itinerant d bands have little or no sp character at E,. Another feature is that both the E, states responsible for the major part of the moment of Fe are far from and do not cross the Fermi level. Thus they are not affected by alloying Fe with other elements and this accounts for the simple magnetic behavior of Fe alloys, such as simple dilution, etc.

Landolt-Bornstein New Series 111/19a

98

1.1.2.11 Fe, Co, Ni: Fermi surfaces, band structures, spin polarizations

1

6

10

18 eV 26

IJ

t

eV

-

I‘

A

H

A

Fig. 6. Dispersion curves, E(k), measured by ultraviolet photoemission spectroscopy (UPS) for Fe along the A and F directions and, near H, along the A direction arc shown by circles. Only Ax/F3 symmetry bands are seen for normal emission with s polarization. The crosses denote weak features [80 E I]. The final-state energy scale gives the final-band energies used to determine thecomponent k normal to the crystal surface. Solid and dashed lines denote the majority and minority bands, respectively, calculated using a vBH potential [77 C I]. Solid and open triangles denote the Fermi surface crossings of, respcctively, the majority and minority bands determined from dHvA data. Ei: initial-state electron energy, Et: final-state electron energy.

Stearns

[Ref. p. 134

Ref. p. 1341

1.1.2.11 Fe, Co, Ni: Fermi surfaces, band structures, spin polarizations

Fig. 7. Calculated density of states for the minority and majority spin states ofFe [75 S 11.The two higher energy, narrow peaks, sitting on the broad background are mainly due to the quasi-localized E, bands. It has been suggested that the condition necessary for electrons in a given subband to be “localized” is that the bandwidth of that subband be less than or comparable to the exchange energy I, responsible for spin splitting A of the bands; where A =2SI, and S is the spin quantum number [73 S 11.For Fe, A is calculated to be between 1.3...1.6 eV [77 Cl],so I, is -0.7eV. In this view it is the width of those individual subbands which give rise to the moment that is the important consideration in determining the spatial character of the moment, not the over-all d bandwidth.

Land&Bbmstein New Series III/l9a

Stearns

99

1.1.2.11 Fe, Co, Ni: Fermi surfaces, band structures, spin polarizations

-6

-4

-2

0

[Ref. p. 134

eV

E-E, -

Fig. 8. (a) Spin polarization ofangle- and energy-resolved photoemission from (100) Fe as a hmction of the binding energy of the electron. (b) Energy distribution curve measured simultaneously with the spin polarization [83 F I]. In: photon energy.

-8

-6

-4

-2

0

L a 1, eV 2

E-E, Fig. 9. Separated spin-up and spin-down intensity curves corresponding to Fig. 8. The peaks A, B, and C correspond to symmetriesA,J,A,T,and As?, respectively.Top: Band structure of Fe sampled along the T-A-H direction [77 W I] indicating the exchange-sp!it bands of AS symmetry which are the allowed initial states for normal emission from normal incident light [83 F I].

Stearns

Landolr-Bornwin Ncu Srricc 111/19a

Ref. p. 1341

1.1.2.11 Fe, Co, Ni: Fermi surfaces,band structures, spin polarizations

101

H

K

H

3 201

Fig. 10.First Brillouin zone, symmetry points and axes for the hcp structure.

L

\

+

rioiol

(1210)

1.8 -

(0001)

1.6 1.4 1.2 cd

I

90”

60”

I

30”

01 Field dired

n

Fig. 11. Angular variation of dHvA frequencies for hcp Co. Dots: [73A2], crosses: [72Rl]. Note that as yet none of the large-radius Fermi surface features have been seen. t: majority spin. Landolt-BOrnstein New IWl9a

Series

Stearns

[00011

H

102

1.1.2.11 Fe, Co, Ni: Fermi surfaces, band structures, spin polarizations

Fig. 12. Fermi surfaces of hcp Co proposed from calculations of [70 W I] as modified to agree with the experimental data. (a) majority spin band, (b) minority spin band, (c) minority spin band around I, (d) minority spin band around L. In (a), (b), and (c) the solid lines are From the calculations. The dashed lines in (a) arc modifications to agree with measured dHvA data [72 R I]. In (d) modifications have been made around the U points as suggested from magnetoresistance measurements [73 C I]. Extremal orbits arc indicated.

Stearns

[Ref. p. 134

Ref. p. 1341

1.1.2.11 Fe, Co, Ni: Fermi surfaces,band structures, spin polarizations

a

r

M

Fig. 13a. Fermi surface cross sections in the T-A-L-M plane of the Brillouin zone of hcp Co according to several band structure calculations, showing a considerable disagreement. Curve 1: [68 C2], 2: [70 W 2],3: [75 B 11, 4:

[77S3].

b

Minority spin

Majority spin

Fig. 13b. Fermi surface cross sections from a selfconsistent spin-polarized band structure calculation of hcp Co. The numbers refer to the number of occupied bands in each region [84 J 11.

Landolt-BOrnstein New Series 111/19a

104

1.1.2.11 Fe, Co, Ni: Fermi surfaces, band structures, spin polarizations

[Ref. p. 134

0.8 RY 0.6

I 0.4 b. 0.2

0 M

l-

I

I

I

I

I

I

K

l-

A

1

H

A

Fig. 14. Energy bands of hcp Co in some high-symmetry directions [84J I]. Full lines are the majority bands, broken lines the minority bands. As can bc seen many of the general features that were present for Fe also exist for Co. Namely, the moment is mainly due to some flat, localized d band states being filled for the majority band and empty for the minority band. There are also seen to be parabolic free-electron-like d bands which provide the polarized itinerant d electrons that align the localized d spins. Thus clearly the spin-up d-bands arc not full, a condition that is sometimes referred to as “weak itinerant electron ferromagnetism”.

-r

A

r

L

eV

-$ (0001)

~(000~)

(00001

Fig. 15. Selected spin-up (open circles) and spin-down (solid circles) bands obtained by angle-resolved photoemission experiments on hcp (0001) Co [80 H I] for 9 eV < fro < 30 eV. Corresponding theoretical spin-up (solid 1ine)and spin-down (dashed line) bands calculated including Coulomb correlation effects with the Coulomb integral, U = I .5 eV [82 T 21. The calculations were made by transforming fee Co bands ofMoruzzi et al. [78 M I] into hcp bands by an interpolation scheme with the same parameters in both crystalline structures. The optimum U values obtained for Fe and Ni by this approach are 1 eV and 2eV, respectively. t: majority spin, 1: minority spin.

Ref. p. 1341

1.1.2.11 Fe, Co, Ni: Fermi surfaces,band structures, spin polarizations

6. CO hw majority spin dotes

:

60 t

minority spin

40 -

20 0 0

,,, ,,I, I

0.2

0.4

0.6

Ry 0.8

E-

Fig. 16.Calculated density-of-states for ferromagnetic hcp Co [84 J 11.

Fig. 17. First Brillouin zone for the fee structure.

Land&-BOrnstein New Series IIVl9a

Stearns

105

[Ref. p. 134

1.1.2.11 Fe, Co, Ni: Fermi surfaces, band structures, spin polarizations

106

10.34 MG 10.32

15.60 MG 15.55

15.50

4

b

15.45 6.5 b!G

I 15.LO \- 2.71 MG

0

6.0 -

T

2.70

0

o!

ST

0

2.69

0

r;,1

1

0

2.68-T

1

I

1

t:.

2.67

2.5I /,y K(Olll

I 30"

I 15"

I I 45" 60" Llllll xl0011 Field direction I

0"

15"

I

30"

I 75"

0

KlllOl

Fig. 18. Orientation dependence of the dHvA frequencies in Ni [67 T 2, 68 S 43. The lower frequency branch has been identified as due to the neck-like intersections ofthe spin-up Fermi surface with the Brillouin zone face in the L [I I I] direction. This sheet of the Fermi surface is similar to the Fermi surface of Cu; however, the area of contact aith the Brillouin face is about ten times smaller than that ofCu. The IO...25 MG frequencies are associated with the hybridized spd hole pockets near X. Strong spin-orbit induced effects which are dependent on the magnetic field direction are seen in topology along the T-X axis [67Hl,68Rl,70Zl].

11.00I 0

2

6

k

8

10 kbor

P-

Fig. 19. Change of dHvA frequency with pressure of a single crystal of Ni (eJ6ek/e4k z 3000) at I .5 K. Table 4 lists the values of the slopes, (df/dp)/f, for the applied field in various directions [77 V I]. CL,b: dHvA frequency branches, see Table 4 for magnetic field directions.

Stearns

Ref. p. 1343

1.1.2.11 Fe, Co, Ni: Fermi surfaces, band structures, spin polarizations

107

a (100)

Fig. 20. Cross sections of the Ni Fermi surface in (a) the (110) plane and @) the (100) plane. The solid lines are from calculations [77 W 11. The circles, triangles, and squares are the experimental dHvA results of R.W. Stark and coworkers [77 W I]; the dotted lines are due to the measurements of Tsui and Stark [67 T 2, 68 S 41. The letters designate the various surfaces. 1: minority hole pocket around Xs; 2: minority hole pocket around X,; 3: minority arm hole surfaces surrounding the outer Brillouin zone edges; 4: majority Cu-like electron surface around r; 5: minority electron surface around r. There is considerable spd electron hybridization in some regions of the Ni Fermi surfaces as noted. The electron surfaces 4 and 5 have mainly itinerant d character in the K direction and are highly hybridized with the sp electrons in the X and L directions. i: itinerant, 1: localized. Landok-Bbmstein New Series 111/19a

Stearns

1.1.2.11 Fe, Co, Ni: Fermi surfaces, band structures, spin polarizations

108

[Ref. p. 134

B15 I

10 4

25 '

20 I

3

kG

30 I

35 I

Ni (loo) v=277 GHz 1=1.5 K

5

15 HWI -

10

20

25

kOe

30

Fig. 21. Azbel-Kaner cyclotron resonance in Ni showing the third through seventh subharmonic peaks of a relatively light effective mass, m*/m, =0.86, identified as the minority spin d band hole pocket having its major axis along [OOI] [73G I]. dR/dB: surface impcdance signal 8

6

1.5”

15”

22.5" 30" Field direction -

31.5"

45' IO111

Fig. 22. Anisotropy of the cyclotron effective mass observed in Ni. Many experimental traces for the belly masses showed beat structure with the number p of resonance peaks between beats ranging from 5 to 7. Such traces analyzed as arising from two groups of electrons having the effective masses denoted by the triangles. The circles denote heavy effective masses from traces that did not display beats [73 G I]. r: majority spin, 1: minority spin, WI:,: average effective mass, me: freeelectron mass.

Stearns

Ref. p. 1341

1.1.2.11 Fe, Co, Ni: Fermi surfaces,band structures, spin polarizations

109

-8

r

A

x

2

I w

I 0

Fig. 23. Calculated energy bands in Ni along several symmetry directions [77 W 11.Majority spin (t) states are denoted by solid lines and minority spins (1) by dashed lines. The two minority hole pockets surrounding X are not found in Fig. 10. However, Gersdorf [78 G l] has suggested that measurements of magnetocrystalline anisotropy provide evidence of the existence of minority X, hole pockets with an effective mass ofabout 197~. Such a high effective mass would be very difficult to see with dHvA measurements. An additional complication may arise in that it has been found that spin-orbit splitting is dependent on the direction of magnetization near X [7OZ l] and thus applying a high magnetic field may perturb the system so that under these conditions the dHvA measurements are no longer of the ground state of Ni. Photoemission experiments found that X,1 is 0.04 eV [81 H 21 and 0.06eV below E, [83 R 11.

A

l60eV

K

Ni / /

20 1 Lqy LL IO-

O-

-2.5 -

Fig. 24. Portions of the energy levels of Ni along the F-X direction as determined from photoemission spectra. The data points show the measured dispersion of the A1 band and a few critical points [80 E 21. The dashed curve is the free-electron final-state band. The solid curves below E, are from calculations of Wang and Callaway with the vBH potential [77 W 1, 74W l] and above E, from Smulowicz and Pease [78 S 21. Land&-Bornstein New Series IIl/l9a

-5.0 -

-1.5 1. -10.0L 0 l~I

0.89 4 -

A-’

1 X

S

X

110

1.1.2.11 Fe, Co, Ni: Fermi surfaces, band structures, spin polarizations

eV

25

20

15

XS 1

3 ., II

10

Al

-6-

1

-Tl-

A

Fig. 25. Measured E vs. k energy band dispersions for Ni [78 E 1, 79 H I] as dcrivcd from photoemission spectra. The unoccupied bands just above the Fermi lcvcl and their Fermi level crossings are drawn after Zornbcrg’s calculation [70 Z I] which was fit to the dHvA data. The lowest band has been extrapolated by a free-electron parabola matched to the experimental points. The tinalstate energy scale gives the final-band energies used to determine the component of k normal to the crystal surface. Only a portion ofthe lower A, band is seen owing to smaller matrix elcmcnts. The A2 and Ai bands arc not shown since normal emission from them is forbidden by the selection rules for dipole transitions [77H I]. Ei: initial-state electron cncrgy, E,: final-state electron energy.

n

x

s

K

Fig. 26. Expcrimcntally derived energy bands around the X-point of the Brillouin zone of Ni. Points represent line positions from least-squares fits to the photoemission data. Triangles rcprcscnt dHvA data. The bands along A(X) seenin normal emission from Ni (100)whiIe those along S(X) arc seen in normal emission from Ni (1 IO). Dashed bands are dipole forbidden under those conditions [8l H 21. T: majority spin, 1: minority spin. Ei: initial-state electron energy.

Stearns

[Ref. p. 134

Ref. p. 1341

1.1.2.11 Fe, Co, Ni: Fermi surfaces, band structures, spin polarizations

states eVatom spin

majorlry spin

total

20 -

-2-

IO-

z E LIZ

401 states tTiG$

total

20IO-

t

o-

-8

-6

-4

-2

0 E-

2

4

6 ev 8

Fig. 27. Density of states (DOS) for the von Barth-Hedin model [72 B 31 as a fknction ofenergy for Ni. The s, p, and d components are shown separately as well as the totals for each spin. The smooth curves on the total DOS plots represent the total number of electrons in, respectively, the majority and minority spin bands [79A 11. The majority d band is seen to have a small density ofstates at E,. The minority bands are seen to have a high density of states at E,. This is due to quasi-localized “E,-type” spindown bands existing at the Fermi level. In contrast with Fe where the minority “Es” bands lie well above E,, these bands intersect E, in Ni giving rise to the complex magnetic behavior of Ni alloys. The valence electrons of solute atoms (even sp elements) hybridization with the valence electrons ofNi causing slight changes in the band structure near E, which in turn causes small changes in the moment of Ni atoms in the region surrounding the solute atom. These small moment perturbations on the host Ni atoms lead to a large net total moment change per solute atom, as is observed for Ni alloys. This behavior is to be contrasted with that of Fe which shows simple dilution upon the addition of sp solutes due to the Fermi level occurring in a region oflow density of states, see Fig. 7. Landolt-Bdrncfein New Series 111/19a

-62 z

Stearns

111

112

1.1.2.11 Fe, Co, Ni: Fermi surfaces, band structures, spin polarizations

[Ref. p. 134

Ni

j

-0.75

-0.53

-0.25

0 ev

0.25 00 -0.75 -0.50 -0.25

0 eV 0.25

Ei-fF 1.0 1 0.9

5; II 0.6 ” q ; 0.4 0.2

1, = 651 K c

0

, 0.2

I 0.4

I 0.6 l/l,

I 0.8

I 1.0

I 1.2

I 1.4

-

Fig. 28. Angle-resolved photoemission spectra at (a) T= 293 K and (b) at T= 693 K, showing (c) the temperature dependence of the exchange splitting. The expcrimental conditions ensured that only one band was observed within z I eV of E, [78 E I]. The short-dashed lines in (a) and (b) indicate the background. In (c)the lint marked (3) corresponds to the behavior of a local moment while that marked (2) to the behavior of a purely itinerant moment. The experimental behavior (curve I) is seen to bc in between indicating that the moment of Ni has both local and itinerant character. Other analyses and interpretations of similar data have also been proposed [78 M I. 83 H 2.85s I J. 7: majority spin, 1: minority spin. &: initial-state clcctron energy.

Stearns

Landolr-Rornwin I. ,. . ..I. a

Ref. p. 1341

1.1.2.12 Fe, Co, Ni: optical constants, magneto-optical

effects

113

1.1.2.12 Optical constants, magneto-optic Kerr or Faraday effect The optical constants can be obtained from a variety of experimental measurements.Other desired constants are then derived by using a Kramers-Kroenig (KK) analysis. The most commonly used constants are the complex index of refraction fi= n+ik, the dielectric or permittivity constant E”=s’+is” and the optical conductivity 6=o’+ia”. These are all related by 4rcio”. gj = dij + IJ. 0 For anisotropic materials these quantities become tensors. For low-intensity radiation the dielectric tensor can be expanded into parts that are even or odd powers of M [71 L l] fp=E”,

El= [$

&‘=n2-k2

!!

and E’!= 2nk,

ZJ

+i [iI

-??= {:I

.

(2)

odd in M

even in M

For M in the z-direction s:, = E&= E:, = sGZ = 0. The Kerr or Faraday magneto-optic effectsarise from the skyand $, terms. They are due to the spin-photon interaction in which the light quanta are elastically scattering from a magnetic crystal without any change in the direction of propagation but with a spatial rotation of 7c/2of the polarization direction. Thus the direction of polarization of light is changed when the light is reflected by the surface of a magnetized sample.The values of s& and E&are obtained from a measurementof the angle of rotation of the polarization, ccThis angle is proportional to the magnetization of the sample. The various configurations of the orientation of the magnetization of the sample, the surface of the sample, and the plane of incidence of the light lead to three classesof Kerr effects. 1. Polar Kerr or Faraday effect Magnetization perpendicular to the surface of the sample, normal incident linearly polarized light: the polarization is rotated through an angle CI~given by uK= K,M

(3)

where K, is the polar Kerr constant and M the magnetization. 2. Longitudinal (or meridional) Kerr effect Magnetization parallel to the surface of the sample and parallel to the plane of incidence of the linearly polarized light: the reflected light is elliptically polarized, its major axis being rotated with respect to the oscillation plane of the incident light by an angle CI. 3. Transverse (or equatorial) Kerr effect Magnetization parallel to the surface of the sample and normal to the plane of incidence of the linearly polarized light: linearly polarized light with E parallel to the plane of incidence (p-polarized) undergoes a change of intensity, AI, when reflected from a sample which is subjected to alternating magnetization, induced by an applied magnetic field oscillating in time. The equatorial Kerr effect is given by the relative change of intensity. S=AIJI. The values of skyand E& can be derived from 6.

Landolt-Biirnstein New Series 111/19a

Stearns

(4)

1.1.2.12 Fe, Co, Ni: optical constants, magneto-optical effects

114

In :V 0.64 0.77 0.89 1.02 1.14 1.26 1.39

1.51 1.64 1.76 1.8s 2.01 2.13 2.26 2.38 2.50 2.63 2.75 2.88 3.00 3.12 3.25 3.37 3.50 3.62 3.74 3.87 3.99 4.12 4.24 4.36 4.49 4.61 4.74 4.86 4.9s 5.11 5.23 5.36 5.4s 5.60 5.73 5.85 5.9s 6.10 6.22 6.35 6.47 6.60

Fe

Ni

co

n

k

n

k

nk

3.17 3.11 3.09 3.03 2.97 2.92 2.96 2.94 2.87 2.86 2.92 2.88 2.94 2.95 2.86 2.74 2.67 2.59 2.48 2.35 2.24 2.12 2.02 1.93 1.85 1.78 1.74 1.69 1.67 1.65 1.64 1.62 1.59 1.56 1.53 1.51 1.50 1.48 1.48 1.47 1.47 1.47 1.47 1.49 1.47 1.45 1.42 1.35 1.29

6.12 5.39 4.83 4.39 4.06 3.79 3.56 3.39 3.28 3.19 3.10 3.05 2.99 2.93 2.91 2.88 2.82 2.77 2.71 2.65 2.58 2.50 2.43 2.35 2.27 2.19 2.12 2.06 2.00 1.94 1.88 1.84 1.79 1.75 1.70 1.66 1.61 1.57 1.53 1.49 1.47 1.44 1.43 1.41 1.40 1.40 1.39 1.37 1.35

3.87 3.61 3.42 3.17 2.94 2.78 2.65 2.53 2.40 2.31 2.25 2.19 2.13 2.05 1.97

7.79 7.26 6.77 6.31 5.88 5.50 5.16 4.88 4.64 4.45 4.27 4.11 3.96 3.82 3.68

1.88 1.81 1.74 1.67 1.61 1.57 1.53 1.50

3.55 3.41 3.28 3.17 3.05 2.93 2.82 2.71

3.47 3.14 2.96 2.79 2.65 2.48 2.40 2.26 2.13 2.06 1.99 1.99 1.96 1.92 1.85 1.82 1.78 1.73 1.71 1.70 1.72 1.72 1.70 1.74 1.78 1.84 1.93 2.01 2.02 2.03 2.03 2.01 1.96 1.89 1.82 1.73 1.65 1.57 1.49 1.43 1.38 1.34 1.32 1.29 1.28 1.28 1.29 1.29 1.26

1.49 2.61 1.48 2.52 1.46 2.44 1.45 2.37 1.44 2.31 1.44 2.25 1.44 2.19 1.44 2.14

1.44 1.44 1.44 1.45 1.45 1.46 1.47 1.47

2.09 2.04 2.01 1.97 1.93 1.91 1.89 1.87

1.45 1.43 1.41 1.38 1.36 1.32 1.29 1.26 1.21 1.16

1.86 1.85 1.84 1.82 1.78 1.75 1.71 1.67 1.63 1.59

9.09 7.96 7.08 6.43 5.93 5.55 5.23 4.97 4.73 4.50 4.26 4.02 3.80 3.61 3.42 3.25 3.09 2.95 2.82 2.69 2.57 2.48 2.40 2.32 2.26 2.22 2.19 2.18 2.18 2.20 2.23 2.26 2.29 2.30 2.32 2.31 2.29 2.25 2.20 2.15 2.09 2.02 1.96 1.89 1.82 1.75 1.69 1.64 1.60

[Ref. p. 134

Table 1. Room-temperature optical constants for polycrystalline Fe, Co, and Ni determined from inverting reflection and transmission measurements of p-polarized light, of 0.64...6.6eV photon energy, incident at an angle of 60”. The estimated error for k is f 1.5% and for n +4% [74 J 11.The imaginary part E” for Ni was seen to be independent of temperature from 78 to 423 K [75 J 11.

a

1

2

3

1

2

3

k

hV-

5

eV 6

5

eV 6

Fig. la. Optical conductivities of polycrystalline Fe and Co calculated from the optical constants in Table 1 [74J 11.The width of the curves representsthe experimental accuracy.

Stearns

Ref. p. 1341

0.6

4

115

1.1.2.12 Fe, Co, Ni: optical constants, magneto-optical effects

“% D. ?

1.0

a.5

‘5

i.0

I k.5Q 4)

-6S

I.0

-7.:

1.5

-9s 0 b

5

3 ia

15 /Iv-

Fig. lb. Measured normal (11”) incidence reflectivity ofFe for photon energies ranging from 2eV...2leV at 0.1 eV intervals and E’ and E” calculated from KK analysis [76 M 11.

Fig. lc. E’ and s” vs. photon energy for Ni derived from: (solid line) electron energy loss spectra [79 F 11; (dotted curve) reflectivity and transmission data [74 J l] ; (dashed curve) optical absorption data [69 S 41.

Land&Bbmstein New Series 111/19a

Stearns

116

1.1.2.12 Fe, Co, Ni: optical constants, magneto-optical effects 3s .10-'

[Ref. p. 134

6.0 IO“ rod 4.5

rad 1.5

-6.0

-1.5 -9.0

6.0

-10.5 -12.0 2

1

3

4

eV

/IV-----

Fig. 2. Polar Kerr effect curves ah derived from the arithmetic mean of the s and p-wave data for Fc, Co, and Ni, The samples wcrc 99.99% pure plates subjcctcd to mechanical polishing. annealing and electrolytic polishing before measurcmcnts. The dashed curves wcrc calculated from values of E& and E:,. dctcrmincd from equatorial Kerr effect mcnsurcmcnts, see Figs. 3a. b, c [68 K I].

1.25

For Fig. 3. see next page. 2 xl-'

m: 0

I 8 -2

0.25 0

U

40 i

-0.25 0

roil c

I -2 B -4

-5 0

0.5

1.5

1.0 L-

2.0 pm

0.5

1.0

1.5

2.0

2.5

3.0 ev 3.5

/Iv-

Fig. 4. Wavelength dependence of the longitudinal Kerr angle of rotation for Ni, measured with (a) s-polarized light (E normal to plane of incidence) at an incident angle of 60” and (b) p-polarized light (E in plane of incidence) at an incident angle of 75”. The sample was a 10008, film evaporated onto a glass substrate at 200 “C in a vacuum of 2.6. IO-* bar and annealed for about 2 h. (c) Photon energy dependence of E& and czr for Ni as derived from the data of (a) and (b) [69 Y 1J.

117

1.1.2.12 Fe, Co, Ni: optical constants, magneto-optical effects

Ref. p. 1341

Fig. 3. Equatorial Kerr effect of (a) Fe, (b) Co, and (c) Ni for different angles cp of incident light. For sample description, see caption to Fig. 2 [68 K 11.

a 31

It%

I

,

I

I

ieV)*I coIBBI I

I

I

I

I I

-2 b

10.0 40-3 1.5

5.0

$0.25

2.5

0

-2.5

-035lc 0

-5.0 -7.5 Ic 0

Landolt-BBmstein New Series III/19a

9 I I\,

\I

91 II

‘3-o.50 “.b;”

I -

!,

1

2

3 hv-

b

5

eV 6

1

2

I 3

hv-

4

5

eV 6

Fig. 5. (/Iv)~&~ and (h~)~e!&vs. photon energy for (a) Fe, (b) Co, and (c) Ni as derived from measurements of the &nsvkrse K&r effect given in Fig. 3 [68 K I]. The dashed curves calculated from S for rp= 75” (Figs. 3) and the polar Kerr effect CI~(Fig. 2).

Stearns

118

[Ref. p. 134

1.1.2.13 Fe, Co, Ni: specific heat

.,& s-2 I

1 ;A lo* 3. 0 -$ -1 -2

0

2

6

L

8

10 ev 12

Fig. 6. Room-tempcraturcvalues of oa:,. and ocr~,of Ni as a function of photon energy measured with the transvcrsc Kerr e&t. The samples were ~~5000A evaporated films of 99.9% purity Ni. These curves are directly comparableto those of Fig. 5c over their similar photon energy ranges[77 E I].

1.1.2.13 Specific heat, resistivity, magnetoresistance, Hall coefficients, Seebeck coefficients and thermal conductivity The standard expression for the Hall resistivity (in cgs-units) is E. r 1 =p,,=R,B+4nR,M,

where E, is the transverse electric field appearing for a given longitudinal current .I,. R, is called the normal or ordinary Hall coefficient and R, the spontaneous, extraordinary or anomalous Hall coefficient. Strong applied field and temperature effects are seen due to transition from the low field (w,re 1) to the high field (w,r$ 1). The general expression for the Seebeckcoefficient or thermoelectric power, the potential difference generated by a temperature difference across a sample, is given by

where k, is the Boltzmann constant, e the electron charge, E the energy of an electron, Qthe electrical resistivity and p(E) is the electrical resistivity for the metal with Fermi level at energy E. The Wiedemann-Franz ratio is defined as I/CT, where 3, is the thermal conductivity and Q the electrical resistivity. For a simple, ideal metal it is a constant, La= (71ka/e)~/3 =2.44. 10m8V2/K2, called the Lorentz number. Table 1. Low-temperature specific heat coefficients and Debye temperatures for Fe, Co, and Ni [65 D 11.Fe and Ni: least-squaresfit to C,=yT+PT3 + aT3j2. Co: least-squaresfit to C,=yT+/IT3+~/T2, where x/T2 is a nuclear contribution. /3= 12n4N,k,/50& N,: Avogadro’s number.

Fe co ‘) Ni

Y mJ K-‘mol-’

B mJ K-4mol-’

a

00

mJ K-5’2 mol-’

K

4.755(15) 4.38(l) 7.039(16)

0.0184(7) 0.0199(7) 0.0179(7)

0.021(12)

472.7(60) 460.3(77) 477.4(62)

0.011(13)

‘) x=4,99(6)mJKmol-‘.

Stearns

Landolr-Ro,rn
118

[Ref. p. 134

1.1.2.13 Fe, Co, Ni: specific heat

.,& s-2 I

1 ;A lo* 3. 0 -$ -1 -2

0

2

6

L

8

10 ev 12

Fig. 6. Room-tempcraturcvalues of oa:,. and ocr~,of Ni as a function of photon energy measured with the transvcrsc Kerr e&t. The samples were ~~5000A evaporated films of 99.9% purity Ni. These curves are directly comparableto those of Fig. 5c over their similar photon energy ranges[77 E I].

1.1.2.13 Specific heat, resistivity, magnetoresistance, Hall coefficients, Seebeck coefficients and thermal conductivity The standard expression for the Hall resistivity (in cgs-units) is E. r 1 =p,,=R,B+4nR,M,

where E, is the transverse electric field appearing for a given longitudinal current .I,. R, is called the normal or ordinary Hall coefficient and R, the spontaneous, extraordinary or anomalous Hall coefficient. Strong applied field and temperature effects are seen due to transition from the low field (w,re 1) to the high field (w,r$ 1). The general expression for the Seebeckcoefficient or thermoelectric power, the potential difference generated by a temperature difference across a sample, is given by

where k, is the Boltzmann constant, e the electron charge, E the energy of an electron, Qthe electrical resistivity and p(E) is the electrical resistivity for the metal with Fermi level at energy E. The Wiedemann-Franz ratio is defined as I/CT, where 3, is the thermal conductivity and Q the electrical resistivity. For a simple, ideal metal it is a constant, La= (71ka/e)~/3 =2.44. 10m8V2/K2, called the Lorentz number. Table 1. Low-temperature specific heat coefficients and Debye temperatures for Fe, Co, and Ni [65 D 11.Fe and Ni: least-squaresfit to C,=yT+PT3 + aT3j2. Co: least-squaresfit to C,=yT+/IT3+~/T2, where x/T2 is a nuclear contribution. /3= 12n4N,k,/50& N,: Avogadro’s number.

Fe co ‘) Ni

Y mJ K-‘mol-’

B mJ K-4mol-’

a

00

mJ K-5’2 mol-’

K

4.755(15) 4.38(l) 7.039(16)

0.0184(7) 0.0199(7) 0.0179(7)

0.021(12)

472.7(60) 460.3(77) 477.4(62)

0.011(13)

‘) x=4,99(6)mJKmol-‘.

Stearns

Landolr-Ro,rn
Ref. p. 1341

1.1.2.13 Fe, Co, Ni: specific heat 75

801 -2--

T

J

76.0 I

Kmol 75

Kmol 70 I 65

$0 55 55

I L?

50 45 1000

1025

1050

1075 K 1100

45

Fig. 2. Temperature dependence of the specific heat of Fe around Tc. Tc and the critical exponents U=E’ were evaluated to be 1041.32K and -0.120 (lo), respectively [74L 1-J

40 35 30

40 J

25

Kmol 38

20 z 15. 300

600

900

"Eprn

2

1200

1500

1800 K 2100

Fig. 1. Temperature dependence of the specific heat of Fe, Co, and Ni above room temperature. T, is the melting temperature [68 B 11.

I 36 L? 34

32

40 -J-

Kmol 38

TFig. 3. Temperature dependence of the specific heat of Ni around Tc. Tc and the critical exponents C(=CL’were evaluated to be 631.58 K and -0.10(3), respectively [71 C 31. The data was reevaluated giving 631.52K and -O.O89(2),respectively [74L 11.1: [65P 1],2: [65 B 3],3: [38 S 31, solid line: [71 C 31.

I * 36

34

40 J Kmol 3E I z 3E

34 630

631

632 T-

Landolt-B6’msfein New Series lW19a

633

K

634

Fig. 4. Temperature dependence of the specific heat of Ni near Tc showing the effects of (a) crystalline inperfections on the apparent rounding of the maximum and (b) various magnetic fields applied parallel to the plane of single crystals [71 C 31. A: annealed single crystal; B, D: annealed polycrystals; C: deformed, unannealed single crystal. I: zero applied field, 2: 25 Oe, 3: 60 Oe, 4: 120Oe, 5: 240 Oe.

Stearns

120

1.1.2.13 Fe, Co, Ni: specific heat, resistivity

[Ref. p. 134

7.11 mJ Kzmol

mJ K2mol

7.07

I

I k 7.03 I: z. Qa

7.2

)- 7.1 \ z 5.1

,h 4.80

4.16

C”

J" 1.9 6.8 0

4.12 0 2.5

5.0

7.5

10.0

12.5

15.0

OX

0.8

1.2

Fig. 5. Variation of C,IT vs. T* of Fe and Ni at low temperature. Evaluating 7 and /I from C,=yT+/IT3gave )I=4,780(l)mJK-*mole’ and 0,=463.7(ll)K for Fc and y=7.059(l)mJK-2mo!-1 and 0,=459.4(18)K for Ni [65D I]

Fig. 6. Variation of(C,-j?T3)/Tvs. T”2 of Fe and Ni at low temperature. Evaluating 7 and c(, the spin wave cocffcient, from C, = yT+ /?T3+ crT3*, where the lattice contribution was determined from the elastic constants, gave y=4.746(3)mJK-*mol-‘, a=0.028(2) mJK-5:2 mol-‘forFeandy=7.014(5)mJK-2mo!-~,~=0.038(3) mJ Km5/* mol-’ for Ni (65D I].

125 &h

251

0

250

1.6 K"' 2.0

K2 20.0

500

750

1000

1250 "C 15

Fig. 7.Temperature dependence ofresistivity e ofpolycrystallinc Fe, Co, and Ni. All measurements are related to the sample dimensions at room temperature [67 K 33, see also [64A I]. Chemical composition of the samples in mm : Fe: 5OC, 5OSi, 16Mn, IOP, 6OS, 500,, and ION,. Co:
Stearns

Ref. p. 1341

121

1.1.2.13 Fe, Co, Ni: resistivity 0.300,

I

I

I

I

45

50

I

I

I

I

K 0.250 0.225 I k 0.200 -n \ ar I

0.12

n.mI

I

0.125

I

I

I

I

I

I

I

I

1000 1010 1020 1030 1040 1050 1060 1070K 1080 a TFig. 8. Temperature derivative of the resistivity of single crystals of 99.99% pure Fe plotted as a function of (a) temperature near Tc (the data has been normalized to those in [67K 11) and (b) specific heat after the linear lattice background has been subtracted. a = 100 J K- ’ mol- ‘. The linearity of the curves suggests the same temperature dependence for de/dT and C, -lOOt,wheret=T/Tc-landC,in[JK-‘mol-’].The critical exponents were found to be a=~‘= -0.120(10) [74 s 31.

0.075I 40 b

55 60 Go-af-

65

J/Kmol

27.C pQcm 26.5

I 26.0 Qn 25.5 z 652 z hII

25.0

5 6.50 cw 24.5

6.48 6.46 0

0.3

0.6

T-

0.9

1.2

1.5 K 1.8

Fig. 9. Relative electrical resistivity e/&T=293 K) as a function of temperature for a [loo] Fe whisker in a longitudinal applied magnetic field of 570 Oe [70 T 11.

Land&BOrnstein New Series 111/19a

24.0 6

6

XLX I

700 710 K 7; TFig. 10.Variation ofthe electrical resistivity with tempers ture of 5 N purity polycrystalline Co, RRR= 140(10), i the immediate vicinity of the cl-p transformation. Th experimental points obtained on heating are indicated 1: dots and those on cooling by crosses [73 L 11.

Stearns

122

[Ref. p. 134

1.1.2.13 Fe, Co, Ni: resistivity, magnetoresistance 87.6 mg Qcm

87.5 I 87.4 O87.3 87.2 87.1 0

12

3

4

5

6

K7

Fig. 1I. Low-tcmpcraturc electrical rcsistivity of a polycrystalline pure Co sample(e295/e4,2 = 66.6)annealedat 1040°C for 3 h [65 R2].

0.99 0.98 0.97 0.96 372 "C 376

Fig. 12. Electrical resistivity e(7) and dg/dT of Ni vs temperaturein the region near 7” [70 Z 21.

Table 2. Characteristics of the Fe specimen of Figs. 13...15 [67 D 11. Specimen

Symbol in Figs.

Whisker axis, current direction

Direction ‘) of H,,,,

Direction of Hall probes

Transverse shape and/or dimensions mm

Fe2 Fe3

cross triangle upward circle square triangle downward

Canal Cl111

[ii01 [ii01

[llZ] [ll?]

hexagonal side 0.32 hexagonal side 0.21

Cl001 uw Cl001

c0101 COlOl COlOl

WI WI WI

0.40 x 0.40 0.35 x 0.53 0.34 x 0.26

Fe5 Fe7 Fe12

‘) For the transverse configuration (Figs. 14and 15);in the longitudinal configuration (Fig. 13)H,,,, is along the whisker axis.

Stearns

Ref. p. 1341

1.1.2.13 Fe, Co, Ni: magnetoresistance

123

0.9 t 0.8 G s 0.7

5

0.6 0.5I 0 a

0.8

I

I0.3

I 0.6

I 0.9

I 1.2 kOe 1.5

&0.7

HOPPi -

Fig. 13. Variation of the relative longitudinal magnetoresistance, eH/eO of several Fe whiskers at 4.2K in applied fields in (a) low-field region and (b) high-field region. For specimen characteristics, seeTable 2 [67 D 11, see also [73 M 41.

0.6

1

0.5 0

IO

20

b

I

-‘k5 Fe Fe2 2.175

HOPPI 1 J

I

1.50

-

Fig. 14. Variation ofthe relative transverse magnetoresistance ofseveral Fe whiskers at 4.2 K with applied field. See Table 2 for specimen details [67 D 11.~TcM,:demagnetizing field strength.

4.550 10 4.525I Fml.

y.xq.

.”

I Hopp, = 20kOe \

I

2125y [I121 2.looL 4.625 .10-s 52

HOPPl

40 kOe 50

HOPPl -

2.200

-5 G 1.25

1

30

k

[ii01

hi21

I

I

I

I

I

I

I

II

cl.“Y

.10-s Q

4.75

4.25 4.00 Fig. 15. Anisotropy of the transverse magnetoresistance for several Fe whiskers at 4.2 K and 20 kOe applied field. See Table 2 for specimen details [67 D 11.

Landolt-BBmstein New Series III/I%

Stearns

roio1

rodii

3.75I -90”

- 60”

-30” 0” 30” 60” Magneticfield direction -

rod11 I 90”

[Ref. p. 134

1.1.2.13 Fe, Co, Ni: magnetoresistance

124

40

30

i

$20 d”

10

0 -1000

0

-500

500

Oe lOi0

HOPPl-

Fig. 16. Low-field longitudinal magnctorcsistancc for [ 11I] axial Fe whisker. Giant peak near Hap,,,=0 is due to multidomain structure [73 C I]. T=4.2K. RRR=4600.

5250,

250

Fe Ii001

t&p! 1 J

Fe [iii1

4750 I G 24500 153 a ’ 90”

I

15” Magnetic

I

!

45” 0” field direction

4250

D

I

90” 4000 90”

20[l-

60”

30” Magnetic

0”

30”

60”

90”

field direction

18:lt i? 161 3 $

l-

1-k 45” Magnetic

45”

0”

field

90”

Fig. 17. Transvcrsc magnetoresistance rotation curve for high-quality Fe whiskers with crystal axes and current parallel to the [ IOO], [ lOI], and [ 11I] directions. (a) H,,,, = 141 kOe,RRR= IllO;(b)H,,,,= 141 kOe,RRR=860; (4 Hnpp,= 148kOe, RRR=4600; T=4.2K. The sharp minima indicate that there are narrow bands of open orbits in several crystallographic directions [73 C I], see also [64 R I] and [64 F 23. Directions ofthc magnetic field as well as low-index planes the field lies in are indicated.

direction

Stearns

hndnlr-Bornrlcin NCN Scrirs 111’19a

Ref. p. 1343

1.1.2.13 Fe, Co, Ni: magnetoresistance

Fe [Ill1 3 I 4750 D -Go0 2 4250

20

40

60

80 HWI -

100

120 kOe 140

Fig. 18. Field dependence curves of the transverse magnetoresistance of Fe showing Shubnikov-de Haas oscillations corresponding to frequencies of 1.5MG. Relevant orientations are specified in the figure on the right [73 C 11, T=4.2K.

2

IO2 20 a

4

6 8 IO/

5-

2

kG 4.10L

IO2 20 b

6

6 610’ 5-

2

kG4-10L

20

c

Fig. 19. Log-log plots of the relation AQ/Q~= aB” for the transverse magnetoresistance of Fe, with values of n indicated by the slopes determined from the solid lines. (a, b): [l 1l] axial Fe specimen in transverse orientation. Maximum at 3 (the circled 3) is indicated in Fig. 18. (c): [l lo] axial Fe specimen in transverse orientation [73C I]. T=4.2K.

Landolt-Bmxfein New Series 111/19a

Stearns

4

6

8 10’

B-

2

kG 4.10’

[Ref. p. 134

1.1.2.13 Fe, Co, Ni: magnetoresistance

126

!b4 i ,; ; i 1

2,2011i I

I

I

I

0

20

10

60

a

I

I

I

I

80

100

120

90”

kOe

Hcq! -

60”

C

30” 0” 30” Magnetic field direction

J 10” off c oxis in ( 1170 11lO ) plone Hoppl = 150 kOe

13.1j-

,

6.0 -

0

I 10

I 60

I 80

I 100

I 120

I kOe

90”

1E

HOPPl-

b

90”

0”

Magnetic field direction

Fig. 20. Transverse magnctorcsistance rotation diagrams and ficld sweeps for Co specimens. (a) Current in the basal plant parallcl to a [ilOO] direction. (b) Current in the (1120) plant 40” off the c axis, RRR=383. (c)Current parallcl to the c axis, RRR=204 [73 C 11. T=4.2 K. arc indicated by arrows. Shubnikov-de Haas oscillations

2.0,

co

I

I

LO” off c axis in (ll?O)

Hopp, II IO001

0”

plone

1

I

I

1

1

I

I

20

LO

60

80

100

120

I

1LO kOe

HOPPl -

Fig. 21. Shubnikov-dc Haas oscillations in Co observed for the field to the c axis and the current 40” off the c axis in the (1120) plane [73C I]. T=4.2K. Stearns

28 i”

,“pr;;;;r:II”“‘j,o

/ I 20

60”

90”

127

1.1.2.13 Fe, Co, Ni: magnetoresistance

Ref. p. 1341

5 0

8

12 n-

16

20

2L

Fig. 22. Plot of oscillation number n against l/B for experimental data of Fig. 21 [73 C 11.

Ni I.4 - J II l1101 1.21.0 0.8 0.6 ox-

rl

BFig. 24. Field dependence of the magnetoresistance of Ni The angles 4 and f3refer to the sample orientations and field directions as described in Fig. 23: 1 cj = 15” 8~ -78”;

2 4~15~‘; lj)= -16”;

8= -6”[62F

Magnetic field direction 6’

Fig. 23. Anisotropy of the magnetoresistance of Ni in a field of 18 kG, which is rotated (angle 0) about a direction making an angle 4 with the [ 1101axis of the sample in the tilt plane, the latter containing the [l lo] axis, i.e. the direction of current, and making an angle of x25” to the (001) plane. The vertical arrows indicate the field directions for which the field dependence of the magnetoresistance is shown in Fig. 24 [62 F 11. T=4.2 K. Land&-Bbmstein New Series 111/19a

Stearns

11. T=4.2K.

3 q$=O’; e=O”;

4 4~0

[Ref. p. 134

1.1.2.13 Fe, Co, Ni: Hall coefficient

12s

Ch

G -2.5

0.5

I sr” -5.0

I

-75

d

0

-0.5

-10.0 -12.5 0

150 200 250 K 300 TFig. 25. Temperature dcpcndcncc of the (a) ordinary, R,, and (b) extraordinary. R,. Hall coefftcicnts for Fc, Co, and 7%. The samples wcrc 99.99% pure polycrystallinc materials with residual resistance ratios RRR=Q~~~/c)~,~~ of I I.5 (Fe). 66.3 (Co), and 57.2 (Ni) [60 V I]. 50

100

a

VI

-20r 0

I 25

I

I

I

50

75

100 I-

I

I 125

-2.0 0

I

I 150

Fig. 26. Dcrivativc of the Hall rcsistivity, d&d& as a function of tempcraturc for a high-purity [I I I] Fc whisker (RRR=4000). showing that dp,,ldB is clearly not a constant below 80K [74K I]. see also [75C I, 79 hl I].

50

100

150

200

250 K 300

b

I 200 K 225

175

Jo.:

Skm Fe I1111 G 3

T I 2

4r"

1

Fig. 27. Variation of the extraordinary Hall cocflicicnt with tcmpcraturc ofthc same sample as in Fig. 26. R, was calculated from the intcrccpt of the Hall rcsistivity obtained by extrapolating to B=O. Two approsimatc fits have been used for extrapolation: e,, = R,B + 4rrR,M, (lincar analysis) and Q,,= R,B+4nRJ4,+ CB’ (quadratic analysis) [74 K I]. RRR = 4000. Stearns

0 . lineor analysis -1

0 quadratic analysis I I I I 150 200 K 250 I-

Ref. p. 1341

1.1.2.13 Fe, Co, Ni: Hall coefficient

129

200 200 .mg Bcm 100

I G

O

-100

-200 0

50

100

150

I

-1

200 kG 250

I 100

50

Fig. 28. Hall resistivity as a function of B for [loo] Fe whiskers of various purities at 4.2K. Bll[OOl], Vull[OlO] and Jll[lOO] [75C 11. T=4.2K.

I 150

I 200 kG 250

Fig. 29. Derivative of the Hall resistivity, d&dB, as a function of B for the RRR= 7320 Fe whisker shown in Fig.28 at 4.2K [75 C 11.

C

-25

I 5 G

-50

-75

x,

I + Fe[llll RRR=4000 H=20...150kOe 21 Fe [I111 RRR=$OOO H =l5...45kOe -100 3 l Fe(polycrystal) sample I’ H = 15. . . 70 kOe 4 A Fe(polycrystal) sample1 H = 15 . ..70kOe TFe [Ill] 1 Fe[lOOl H=15...30 kOe

-1251 0

I 10

I 20

30

40

40'2 G/

B’QtlFig. 30. Kohler plot of the relative Hall resistivity QH/e0 vs. B/Q, for various Fe samples where e0 is the zero-field resistivity. The quantity B/Q, is proportional to w,z. Data 1 and 2 on the [ill] axial whisker with KKK=4000 was taken with Sll[llz] and Vull[ilO] [75 C 11. Data 3 and 4 are from [73 M 41 for the polycrystals and the solid lines from [67D 11. T=4.2K.

-cI-

-4 -3

G I -2 Fig. 3 1. Applied field dependence of Hall resistivity muat a variety of temperatures for a polycrystalline Ni sample with RRR=650. The major impurity was 15 at. ppm Fe. Data points are omitted for clarity [Sl H 41.

Land&Bbmstein New Series lWl9a

.loi Qclr

Stearns

IO

20

30 HOPPI

40 -

50 kOe 60

[Ref. p. 134

1.1.2.13 Fe, Co, Ni: thermoelectric power

130

1.2 I 1.0 5 Q 0.8 0.6

I

I

$ 0

0 relative to PI

I

-2

D

4 -6 -A i300

850

900

950

1000 1050 1100 1150K1200 I-

Fig. 33. Thcrmoclcctric power or Seebeck coefficient Q and relative resistivity e/e0 of Fe at high temperatures [69S3]. 1:[69S3],2:[67K3],3: [62K2].4: [35B 11.5: [69 S 3-j, 6: [67 B 23.

20 !A! K 10

0

600 800 "C II300 IFig. 32. Seebcck coetlicicnt Q of Armco Fe (RRR = 11.O) and hisher-purity Fe (RRR = 26.2) measured with rcspcct to Pt (top curves). and absolute (bottom curves) [66 F 11. 200

-10

ulo

I m -20

-30

-40 -50 0

250

500

750 7-

1000

1250 K 1500

Fig. 34. Temperature dcpcndcncc of the absolute thcrmopower of Fc [6OL I], 5N pure Co (RRR=l40(10)) [72L2,73Ll]and5NpureNi(RRR=220(10))[76Ll]. The dashed extension for Co is the data of [69 V 11.

131

1.1.2.13 Fe, Co, Ni: thermoelectric power

Ref. p. 1341 1.1

2.

1.0

K

t 0.9 0 20.8

-7.5

0.7 -15.0 I cr

0.6

-22.5

-30.0 1 IO 1050 1100 1150 1200 1250 1300 1350 1400 1450 K 1500 7-

Fig. 35. Thermoelectric power and relative resistivity of Co at high temperatures [69 S 31.1: [69 S 3],2: [67 K 31, 3: [62 K2], 4: [35 B I], 5: [69 S 31.

-7.5 0 I -5.0

0

12

3

5

4

6

Kl

Fig. 36. Low temperature absolute thermoelectric power of the same Co sample described in Fig. 11 [65 R2].

G

Y -15

2 0.6

I -20 cI

I 550

600

650

I

I

I

700

750

800

I I-30 850 K 900

Fig. 37. Thermoelectric power and relative resistivity of Ni at high temperatures [69 S 31.1: [69 S 3],2: [67 K 3],3: [69K2],4:[35B1],5:[69S3].

Landolt-BOrnstein New Series 111/19a

Stearns

132

1.1.2.13 Fe, Co, Ni: thermoelectric power, thermal conductivity

[Ref. p. 134

p!’

11 615

640 6L5 K 650 635 TFiS. 3% Sccbcck volta~c of 99.999% pure polycrystallinc Ni with rcspcct to a Pt rcfcrencc vs. tcmpcraturc in the vicinity of r, [71 T I].

620

625

630

605

625

615

635

645

K

655

I-

Fig. 39. The continuous curve is the spccitic heat for Ni dcrivcd from the Sccbcck voltage mcasuremcnts shown in Fig. 38. The points arc the magnetic contribution to the specific heat from [71 C 33 shown in Fig. 3. Thcrc are no adjustiblc parameters in either set of data [71 T I].

0.8 u cm K 0.7

I 0.6 3.1 & 0.5

I c,r

/ii K2

60 40

-I 2.1 = ‘5

20

2.5

0.4

0.3

0.2 200

400

600

T-

800

01 0

1000“C I,

Fis. 40. Thermal conductivity of Armco Fc as a function of temperature for several runs. Solid lint. average value [60 L I]: long dashes [36 h4 21: dash-dot [39P I]; short dashes [5S L I].

200

400

600 I-

800

2.3 1000 “C 1 ‘0

Fig. 41. Electrical resistivity Q and Wiedemann-Franz ratio of Armco Fe: L, [60 L I]; L2 [39P 11.

Stearns

Ref. p. 1343 2.4) W cmK 2.1

1.1.2.13 Fe, Co, Ni: thermal conductivity I

I

I

isIcoI I I

I

I

133

I

I I I 1.00 0.75 k0 7 2 0.50 0.25

0

600

900 7-

1200

1500 K 1801

Fig. 43. Variation with temperature of the reduced Wiedemann-Franz ratio of Co: 1 is the same sample as in Fig. 42; 2 [57 W 11; 3 [68Z 13; 4 [64P 21; circles [68W3]. L,=2.44~10-8VZK-2.

0.6

0

300

300

600

900 7-

1200

1500 K 1800

Fig. 42. Thermal conductivity 1 of Co as a function of temperature. 1, same Co samnle sample as described in Fin. Fig. 34 circles [68Zl]; [73Ll]; 2 [57Wl]; 3 [6iZl]; 4 [64P2]; cikles [68W3]. 2.i W cmK

2.0 1.8

I 1.6

%-z1.4

1.2 0.8

0.6 0

200

400

600

800

IFig. 44. Thermal conductivity i of Ni as a function of temperature: I, the same Ni sample as described in Fig. 34 [76L 11; 2 [59W 11; 3 [65P2], specimen 5; 4 [65N 11, specimens 0) and a,; 5 [64K2]; circles [69 521. Landolt-BOrnstein New Series 111/19a

0.6 0

1000 K 1200

200

400

600 T-

800

1000 K 1200

Fig. 45. Variation with temperature of the reduced Wiedemann-Franz ratio of Ni. Legend is the same as in Fig. 44 except that the results of [64 K 21 are illustrated with solid squares and 6 [76 W 11. L,=2.44. 10-8V2K-2.

Stearns

134

References for 1.1.2

1.1.2.14 References for 1.1.2 Books and review articles Bozorth. R.M.: Ferromagnetism D. Van Nostrand Co, Inc. Princeton, N.J. 1951. Herring. C.: Magnetism. Vol. IV (Rado. G.T., Suh!, H., eds.),New York: Academic Press 1966. Marsha!!. W., Lovesey, S.W.: Theory of Thermal Neutron Scattering Oxford: Clarendon Press 1971. Fabian, D.J., Watson. L.M. (eds.): Band Structure Spectroscopy of Metals and Alloys, New York: Academic Press 1973. Fawcctt, E.: Adv. Phys. 13 (1964) 139. Portis. A.M.. Lindquist, R.H.: Magnetism, Vol. HA (Rado, G.T., Suh!, H., eds.),New York: Academic Press1965, p. 357. Keffcr. F., in: Handbuch der Physik, Berlin. Heidelberg. New York: Springer 18 (1966) 1. Kessler,J.: Rev. Mod. Phys. 41 (1969) 3. Eastman, D.A.. in: Electron Spectroscopy (Shirley, D.A., ed.), Amsterdam: North-Holland Pub!. Co. 1972, p. 487; in: Techniques of Metals Research VI (Passaglia, E., ed.), New York: Interscience 1972, p. 413. Smith. N.V.: Crit. Rev. Solid State Sci. 2 (1972) 45. lngnlis. R.. van der Woude. F., Sawatzky, G.A.: Mdssbauer Isomer Shifts (Shenoy, G.K., Wagner, F.E., eds.), Amsterdam: North-Holland Publ. Co. 1974. Hiiffncr. S.: Photocmission in Solids II, Topics in Applied Physics Vol. 27, (Ley, L., Cardona, M., eds.),Berlin, Heidclbcrg. New York: Springer 1979. Him&. F.J.: Appl. Optics. Dec. 1 1980. Wohlfarth, E.P., in: Ferromagnetic Materials (Wohlfarth, E.P., ed.), Amsterdam: North-Holland Pub!. Co. 1 (19SO)2. Campbell. LA., Fert, A.. in: Ferromagnetic Materials (Wohlfarth, E.P., ed.), Amsterdam: North-Holland Publ. co. 3 (19S2)747. Special references 11W 1 17Tl 26W1 21s 1 31w 1 34P 1 35B 1 36M I 36M2 36Nl 3SR I 3SSl 3ss2 3SS3 39B 1 39P 1 44Bl 44Fl 47Gl 48E 1 49B 1 50K I 50Tl 5lMl 51 M2 51Sl 52Bl 52Sl 54Bl

Weiss, P., Focx. G.: Arch. Sci. Natl. 31 (1911) 89. Terry, E.M.: Phys. Rev. 9 (1917) 394. Weiss. P., Forrcr, R.: Ann. Phys. 5 (1926) 153. Sekito, S.: Sci. Rep. Tohoku Univ. 16 (1927) 545. Wyckoff, R.W.G.: The Structure of Crystals. Chcm. Cat. New York 1931, p. 204. Potter. H.H.: Proc. R. Sot. London Ser. A 146 (1934) 362. Borelius. G.: Handbuch der Metallphysik, Leipzig: Akad. Verlagsgesellschaft 1 (II) (1935) 400 Marick, L.: Phys. Rev. 49 (1936) 831. Maurer. E.: Arch. Eisenhiittenw. 10 (1936) 1945. Neuburgcr, MC.: Z. Kristallogr. 93 (1936) 7. Rosenbohm, E.: Physica 5 (1938) 385. Stoner, E.C.: Proc. R. Sot. London Ser. A 165 (1938) 372. Sucksmith. W., Pearce, R.R.: Proc. R. Sot. London Ser. A 167 (1938) 189. Sykes, C., Wilkinson. H.: Proc. Phys. Sot. (London) 50 (1938) 834. Becker. R., Doring. W.: Ferromagnetismus, Berlin: Springer 1939. Powell. R.W.: Proc. Phys. Sot. 51 (1939) 402. Barnctt. S.J.: Proc. Am. Acad. Arts Sci. 75 (1944) 109. Fallot. M.: J. Phys. Radium 5 (1944) 153. Goldman. J.E.: Phys. Rev. 72 (1947) 529. Ellis. W.C., Greiker. E.S.: Metals Handbook ASM, Cleveland, Ohio 1948, 113. Bridgman. P.W.: Physics of High Pressures,London: Be!! 1949, p. 167. Korringa, J.: Physica 16 (1950) 601. Taylor. A.: J. Inst. Met. 77 (1950) 585. Meyer. A.J.P.: Ann. Phys. 6 (1951) 171. Meyer. H.P., Sucksmith, W.: Proc. R. Sot. London Ser. A 207 (1951) 427. Scott, G.G.: Phys. Rev. 82 (1951) 542. Barnett, S.J., Kenny, G.S.: Phys. Rev. 87 (1952) 542. Scott. G.G.: Phys. Rev. 87 (1952) 697. Bozorth, R.M.: Phys. Rev. 96 (1954) 311.

References for 1.1.2 5401 54Sl 55Al 55Cl 55Gl 55Sl 5532 56Cl 56Dl 56Nl 56Sl 57Ml 57Wl 58Kl 58Ll 58Nl 58Sl 59Nl 59 P 1 59Sl 59Tl 59Wl 60Al 60A2 6OCl 6051 60Kl 60K2 6OLl 6OPl 6OSl 6OVl 6OWl 61Bl 61B2 61B3 61B4 61B5 61 G 1 61Kl 61Ml 61 R 1 61R2 61Wl 61W2 61W3 61W4 62Al 62Fl 62Jl 62Kl 62K2 62Pl 62Rl 62Sl 62S2 Landolt-B6’mstein New Series III/19a

135

Owen, E.A., Jones, D. Madoc: Proc. Phys. Sot. (London) Sect. B 67 (1954) 456. Sucksmith, W., Thompson, J.E.: Proc. R. Sot. London Ser. A 225 (1954) 362. Ament, W.S., Rado, G.T.: Phys. Rev. 97 (1955) 1558. Crangle, J.: Philos. Mag. 46 (1955) 499. Gilbert, T.L.: Phys. Rev. 100 (1955) 1243. Scott, G.G.: Phys. Rev. 99 (1955) 1241. Scott, G.G.: Phys. Rev. 99 (1955) 1824. Calhoun, B.A., Carr, W.J., Jr.: Conf. on Mag. Magn. Mater., A.I.E.E., New York 1956, p. 107. Dyson, F.J.: Phys. Rev. 102 (1956) 1217. Nakagawa, Y.: J. Phys. Sot. Jpn. 11 (1956) 855. Scott, G.G.: Phys. Rev. 104 (1956) 1498. Meyer, A.J.P., Brown, S.: J. Phys. Radium 8 (1957) 161. White, G.K., Woods, S.B.: Can. J. Phys. 35 (1957) 656. Kittel, C.: Phys. Rev. 110 (1958) 1295. Lucks, C.F., Deem, H.W.: ASTM Special Publ. #227 (1958) 7. Nakamura, T.: Progr. Theoret. Phys. (Kyoto) 20 (1958) 542. Suhl, H.: Phys. Rev. 109 (1958) 606. Nathans, R., Paoletti, A.: Phys. Rev. Lett. 2 (1959) 254. Parratt, L.G.: Rev. Mod. Phys. 31 (1959) 616. Suhl, H.: J. Phys. Radium 20 (1959) 333. Tatsumoto, E., Okamoto, T.: J. Phys. Sot. Jpn. 14 (1959) 1588. White, G.K., Woods, S.B.: Philos. Trans. R. Sot. London 251 (1959) 273. Alers, G.A., Neighbours, J.R., Sato, H.: J. Phys. Chem. Solids 13 (1960) 40. Arajs, S., Miller, D.S.: J. Appl. Phys. 31 (1960) 986. Claussen, W.F.: Rev. Sci. Instrum. 31 (1960) 878. Jones, R.V., Kaminov, I.P.: Bull. Am. Phys. Sot. 5 (1960) 175. Koi, Y., Tsujimura, A., Yakimoto, Y.: J. Phys. Sot. Jpn. 15 (1960) 1342. Kondorskii, E.I., Sedov, V.I.: Zh. Eksp. Teor. Fiz. 38 (1960) 773; Sov. Phys. JETP 11 (1960) 561. Laubitz, M.J.: Can. J. Phys. 38 (1960) 887. Portis, A.M., Gossard, A.C.: J. Appl. Phys. 31 (1960)205 S. Scott, G.G.: Phys. Rev. 119 (1960) 887. Volkenshtein, N.V., Fedorov, G.V.: Zh. Eksp. Teor. Fiz. 38 (1960) 64; Sov. Phys. JETP ll(l960) 48. Watson, R.E., Freeman, A.J.: Phys. Rev. 120 (1960) 1125. Budnick, J.I., Bruner, L.J., Blume, R.J., Boyd, E.L.: J. Appl. Phys. 32 (1961) 120s. Benedek, G.B., Armstrong, J.: J. Appl. Phys. 32 (1961) 106S. Brockhouse, B.N.: Inelastic Scattering of Neutrons in Solids and Liquids, Vienna: Internat. Atomic Energy Agency 1961, p. 113. Barnier, Y., Pauthenet, R., Rimet, G.: C.R. Acad. Sci. Ser. B 252 (1961) 283. Barnier, Y., Pauthenet, R., Rimet, G.: CR. Acad. Sci. Ser. B 253 (1961) 400. Gersdorf, R.: Thesis, University of Amsterdam, The Netherlands 1961. Kouvel, J.S., Wilson, R.H.: J. Appl. Phys. 32 (1961) 435. Meyer, A.J.P., Asch, G.: J. Appl. Phys. 32 (1961) 330. Rayne, J., Chandrasekhar, B.S.: Phys. Rev. 122 (1961) 1714. Roberts, C.: C.R. Acad. Sci. Ser. B 252 (1961) 1442. Weger, M., Hahn, E.L., Portis, A.M.: J. Appl. Phys. 32 (1961) 124s. Watson, R.E., Freeman, A.J.: Phys. Rev. 123 (1961) 2027. Winter, J.M.: Phys. Rev. 124 (1961) 452. Watson, R.E., Freeman, A.J.: Acta Crystallogr. 14 (1961) 27. Abrahams, S.C., Guttman, L., Kasper, J.S.: Phys. Rev. 127 (1962) 2052. Fawcett, E., Reed, W.A.: Phys. Rev. Lett. 9 (1962) 336. Johnson, P.C., Stein, B.A., Davis, R.S.: J. Appl. Phys. 33 (1962) 557. Koi, Y., Tsujimara, A., Hihara, T., Kushida, T.: J. Phys. Sot. Jpn. 17 (1962) 96. Kolomoets, N.V., Vedernikov, M.V.: Sov. Phys. Solid State 3 (1962) 1996. Preston, R.S., Hanna, S.S.,Heberle, H.: Phys. Rev. 128 (1962) 2207. Rodbell, D.S.: J. Phys. Sot. Jpn. 17 (1962) 313. Scott, G.G.: Rev. Mod. Phys. 34 (1962) 102. Shull, C.G., Yamada, Y.: J. Phys. Sot. Jpn. 17, Supp. B-III, (1962) 1.

Stearns

136

6283 63A I 63A2 63C’l 63G1 63K I 63 K 2 63 K 3 63L 1 63L2 63M 1 6301 63 P 1 63S1 63Vl 63Wl 64Al 64A2 64C 1 64C2 64D 1 64F 1 64F2 61G 1 641 1 635 1 64K 1

64K2 64Ll 64M 1 64P 1

64P2 64Rl 64Sl 64Tl 64V 1 64 W 1 64Yl 65Al 65B I 65B2 65 B 3 65Cl 65C2 65D1 65F 1 65L 1 65L2 65Nl 65P 1 65P2

Refcrcnccs for 1.1.2 Shull. C.G.. in: Electronic Structure and Alloy Chemistry of the Transition Elements (Beck, P.A., ed.), New York: Intcrscience 1962. p. 69. Argyle. B.E.. Charap. S.H.. Pugh, E.W.: Phys. Rev. 132 (1963) 2051. Arajs. S.. Colvin. R.V.: J. Phys. Chcm. Solids 24 (1963) 1233. Clougherty. E.V., Kaufman, L.: High Pressure Measurements (Giardini, A.A., Lloyd, E.C., eds.). Washington: Buttcrworths 1963, p. 152. Gonser. U., Mecchan, C.J., Muir. A.H., Wiedersich, H.: J. Appl. Phys. 34 (1963) 2373. Kennedy. G.C., Newton. R.C.: Solids Under Pressure,New York: McGraw Hill Inc. 1963, ch. 7. Kirby. R.K.. in: American Institute of Physics Handbook, 2nd Ed., New York: McGraw-Hill Inc. 1963. pp. 464. Kaufman. L.. Cloughcrty, E.V., Weiss, R.J.: Acta Metall. 11 (1963) 323. LaForce. R.C.. Toth. L.E., Ravitz. S.F.: J. Phys. Chem. Solids 24 (1963) 729. Litstcr. J.D., Bencdek. G.B.: J. Appl. Phys. 34 (1963) 688. Menzinger, F., Paoletti. A.: Phys. Rev. Lett. 10 (1963) 290. Obata. Y.: J. Phys. Sot. Jpn. 18 (1963) 1020. Phillips, T.G., Rosenberg. H.M.: Phys. Rev. Lett. 11 (1963) 198. Strecvcr. R.L., Bcnnctt, L.H.: Phys. Rev. 131 (1963) 2000. Veerman. J., Franse. J.J.M., Rathenau, G.W.: J. Phys. Chcm. Solids 24 (1963) 947. Weiss, R.J.: Proc. Phys. Sot. 82 (1963) 281. Arajs. S., Calvin. R.V.: Phys. Status Solidi 6 (1964) 797. Arajs. S., Colvin. R.V.: J. Appl. Phys. 35 (1964) 2424. Clendenen. R.L., Drickamcr, H.G.: J. Phys. Chem. Solids 25 (1964)865; Phys. Rev. A 135 (1964) 1643. Cowan. D.L.. Anderson, L.W.: Phys. Rev. I35 (1964) A 1046. Doyle, W.D.. Flanders, P.J.: Proc. Int. Conf. Ma&n., Nottingham, Inst. Phys. and Phys. Sot., London 1964. p. 751. Frait. Z.: Brit. J. Appl. Phys. 15 (1964) 993. Frait. Z.. Heinrich, B.: J. Appl. Phys. 35 (1964) 904. Gschneider. K.A., Jr.: Solid State Phys. 16 (1964) 276. Izuyama. T.: Phys. Lett. 9 (1964) 293. Janak. J.F.: Phys. Rev. 134 (1964) A 411. Kouvel. J.S., Hartclius, C.C.: J. Appl. Phys. 35 (1964) 940. Kirichenko, P.I.. Mikryukov, V.E.: Teploliz. Vys. Temp. 2 (1964) 939. Lourens. J.H.J., Albcrts. L.: Solid State Commun. 2 (1964) 141. Moon. R.M.: Phys. Rev. 136 (1964) A 195. Phillips. T.G.. Rosenberg.H.M.: Proc. Int. Conf. Ma&n., Nottingham, Inst. Phys. and Phys. Sot. 1964, p. 306. Powell. R.W.: Cobalt 24 (1964) 1. Reed.W.A., Fawcctt. E.: Phys. Rev. 136 (1964)A 422; Proc. Int. Conf. Magn., Nottingham, Inst. Phys. and Phys. Sot. 1964, p. 120.J. Appl. Phys. 35 (1964) 754. Sparks. M.: Ferromagnetic Relaxation Theory, New York: McGraw Hill Inc. 1964. Totskii, E.E.: Teploliz, Vys. Temp. 2 (1964) 205. Vecrman. J., Rathcnau. G.W.: Proc. Int. Conf. Magn., Nottingham, Inst. Phys. and Phys. Sot. 1965. Wertheim. G.W.: Miissbaucr Effect: Principles and Application, New York: Academic Press 1964. Yafet, Y., Jaccarino. V.: Phys. Rev. 133 (1964) A 1630. Arajs. A.: J. Appl. Phys. 36 (1965) 1136. Bundy. F.P.: J. Appl. Phys. 36 (1965) 616. Blackburn. L.D., Kaufman, L., Cohen. M.: Acta Mctall. 13 (1965) 533. Braun. M.. Kohlhans. R.: Phys. Status Solidi 12 (1965) 429. Cowan. D.L.. Anderson. L.W.: Phys. Rev. A 139 (1965) 424. Calvin. R.V., Arajs. S.: J. Phys. Chcm. Solids 26 (1965) 435. Dixon. M.. Hoare. F.E., Holden, T.M., Moody, D.E.: Proc. R. Sot. London Ser. A 285 (1965) 561. Freeman. A.J.. Watson. R.E.: Magnetism IIA (Rado, G.T., Suhl, H., eds.),New York: Academic Press 1965. p. 167. Lochner. R.P., Geschwind. S.: Phys. Rev. 139 (1965) A 991. Londe. R.D.: J. Appl. Phys. 36 (1965) 884. Neimnrk. B.E.. Bykova, T.1.: Inzh. Fiz. Zh. 8 (1965) 361. Panel. R.E., Stansbury, E.E.: J. Phys. Chcm. Solids 26 (1965) 757. Powell. R.W.. Tye. R.P., Hickman, M.J.: Int. J. Heat Mass Transfer 8 (1965) 679.

References for 1.1.2 65Rl 65R2 65Sl 6582 65Wl 66Fl 66Jl 66Hl 66Kl 66Ll 66Ml 66M2 66Pl 66Sl 6682 6633 66Wl 66W2 67Al 67A2 67Bl 67B2 67Cl 67Dl 67Hl 6711 6712 67Kl 67K2 67K3 67K4 67Ml 6701 67Pl 67Sl 67Tl 67T2 68Al 68Bl 68Cl 68C2 68Dl 68Fl 68Gl 68Kl 68L1 68Ml 68Rl 68Sl 6882 6883 6834 68Wl 68W2 68W3 6821

137

Rodbell, D.S.: Physics 1 (1965) 279. Radhakrishna, P., Nielsen, M.: Phys. Status Solidi 11 (1965) 111. Shirley, D.A., Westerbarger, G.A.: Phys. Rev. 138 (1965) A 170. Stoelinga, J.H.M., Gersdorf, R., DeVries, G.: Physica 31 (1965) 349. White, G.K.: Proc. Phys. Sot. 86 (1965) 159. Fulkerson, W., Moore, J.P., McElroy, D.L.: J. Appl. Phys. 37 (1966) 2639. Jaccarino, V., Kaplan, N., Walstedt, R.E., Wernick, J.H.: Phys. Lett. 23 (1966) 514. Heinrich, B., Frait, Z.: Phys. Status Solidi 16 (1966) K 11. Klein, H.-P., Kneller, E.: Phys. Rev. 144 (1966) 372. Lord, A.E., Beshers,D.N.: J. Appl. Phys. 36 (1966) 1620. Mao, H.-K., Bassett, W.A., Takahashi, T.: J. Appl. Phys. 37 (1966) 272. Mook, H.A.: Phys. Rev. 148 (1966) 495. Phillips, T.G.: Proc. R. Sot. London Ser. A 292 (1966) 224. Stearns, M.B.: Phys. Rev. 147 (1966) 439. Scott, G.G.: Phys. Rev. 148 (1966) 525. Shull, C.G., Mook, H.A.: Phys. Rev. Lett. 16 (1966) 184. Walstedt, R.E., Jaccarino, V., Kaplan, N.: J. Phys. Sot. Jpn. 21 (1966) 1843. Wakoh, S., Yarnashita, J.: J. Phys. Sot. Jpn. 21 (1966) 1712. d’Ans-Lax: Taschenbuch fur Chemiker und Physiker (Lax, E., ed.),Berlin, Heidelberg: Springer 1967. Alperin, H.A., Steinvoll, O., Nathans, R., Shirane, G.: Phys. Rev. 154 (1967) 508. Benninger, G.N., Pavlovic, A.S.: J. Appl. Phys. 38 (1967) 1325. Blat& F.J., Flood, D.J., Rowe, V., Shroeder, P.A., Cox, J.E.: Phys. Rev. Lett. 18 (1967) 395. Caglioti, G., Cooper, M.J., Minkiewicz, V.J.: J. Appl. Phys. 38 (1967) 1245. Dheer, P.N.: Phys. Rev. 156 (1967) 637. Hodges, L., Stone, D.R., Gold, A.V.: Phys. Rev. Lett. 19 (1967) 655. Ingalls, R.: Phys. Rev. 155 (1967) 157. Ingalls, R., Drickamer, H.G., DePasquah, G.: Phys. Rev. 155 (1967) 165. Kraftmakher, V.A., Romashina, T.Y.: Fiz. Tverd. Tela 9 (1967) 1851; Sov. Phys. Solid State 9 (1967) 1459. Kohlhaas, R., Dunner, P., Schmitz-Pranghe, N.: Z. Angew. Phys. 23 (1967) 245. Kierspe, W., Kohlhaas, R., Gonska, H.: Z. Angew. Phys. 24 (1967) 28. Kadena, Y.: J. Sci. Hiroshima Univ. Ser. AI1 31 (1967) 21. Muller, S., Dunner, P., Pranghe, N.S.: Z. Angew. Phys. 22 (1967) 403. Orr, R.L., Chipman, J.: Trans Met. Sot. AIME 239 (1967) 630. Pickart, S.J.,Alperin, H.A., Minkiewicz, V.J., Nathans, R., Shirane, G., Steinsvoll, 0.: Phys. Rev. 156 (1967) 623. Stearns, M.B.: Phys. Rev. 162 (1967) 496. Tajima, K., Chikazumi, S.: Jpn. J. Appl. Phys. 6 (1967) 897. Tsui, D.C.: Phys. Rev. 164 (1967) 669. Aubert, G.: J. Appl. Phys. 39 (1968) 504. Braun, M., Kohlhaas, R., Vollmer, 0.: Z. Angew. Phys. 25 (1968) 365. Clark, A.F.: Cryogenics 8 (1968) 231. Connolly, J.W.D.: Int. J. Quantum Chem. 11s (1968) 257. Danan, H., Herr, A., Meyer, A.J.P.: J. Appl. Phys. 39 (1968) 669. Franse, J.J.M., deVries, G.: Physica 39 (1968) 477. Gengnagel, H., Hofmann, U.: Phys. Status Solidi 29 (1968) 91. Krinchik, G.S., Artem’es, V.A.: Sov. Phys. JETP 26 (1968) 1080. Lease, J., Lord, A.E.: J. Appl. Phys. 39 (1968) 3986. Moyzis, J.A., Jr., Drickamer, H.G.: Phys. Rev. 171 (1968) 389. Ruvalds, J., Falicov, L.M.: Phys. Rev. 172 (1968) 508. Southwell, W.H., Decker, D.L., Vanfleet, H.B.: Phys. Rev. 171 (1968) 354. Stringfellow, M.W.: J. Phys. C (Proc. Phys. Sot.) l(2) (1968) 950. Shirane, G., Minkiewicz, V.J., Nathans, R.: J. Appl. Phys. 39 (1968) 383. Stark, R.W., Tsui, D.C.: J. Appl. Phys. 39 (1968) 1056. Wakoh, S., Yamashita, J.: J. Phys. Sot. Jpn. 25 (1968) 1272. Williams, G.M., Pavlovic, A.S.: J. Appl. Phys. 39 (1968) 571. Wilkes, K.E.: Thesis, Purdue Univ. Lafayette, In. 1968. Zinovev, V.F., Krentsis, R.P., Petrova, L.N., Gel’d, P.V.: Fiz. Met. Metalloved. 26 (1968) 60.

Landolt-Bbmstein New Series 111/19a

13s 69BI 69C 1 69Fl 69F2 69H 1 695 1 6952 69K I 69K2 69 h1 1 69 M 2 69 M 3 69s I 69S2 69S3 69S4 69-l-l 69V 1 69Y1 70BI 70D1 70Fi 7051 70R 1 70R2 70R3 7OSl 7os2 70Tl 70 w 1 70 w 2 7021 7022 71Al 71A2 71Bl 71Cl 71C2 71c3 71Dl 71 D2 71Fl 71 F2 71Gl 71G2 71Ll 71 L2 71Ml 71 hI2 71M3 71Sl 71s2 71s3 71s4 71S6 71T1 71Vl

Referencesfor 1.1.2 Bhagat, S.M., Chicklis, E.P.: Phys. Rev. 178 (1969) 828. Collins. M.F., Minkiewicz. V.J., Nathans, R., Passel, L., Shirane, R.: Phys. Rev. 179 (1969) 417. Foncr. S., Freeman. A.J., Blum, N.A., Frankel, R.B., McNiff, E.J., Praddaude, H.C.: Phys. Rev. 181 (1969) 863. Fransc. J.J.M.: PhD Thesis, University of Amsterdam, The Netherlands 1969. Hubert, A., Unger, W., Kranz, J.: Z. Physik 224 (1969) 148. Jain. SC.. Narayan, V., Gocl, T.C.: Br. J. Appl. Phys. 2 (1969) 101. Jackson. P.J., Saunders. N.H.: J. Sci. Instrum. 2 (1969) 939. Kaul. R.. Thompson, E.D.: J. Appl. Phys. 40 (1969) 1383. Koster. E., Turrcll. B.G.: Can. J. Phys. 47 (1969) 1231. Minkiewicz. V.J.. Collins. M.F., Nathans, R., Shirane, G.: Phys. Rev. 182 (1969) 624. Millet. L.E.. Decker, D.L.: Phys. Lett. 29A (1969) 7. Mook. H.A., Nicklow, R.M., Thompson, E.D., Wilkinson, M.K.: J. Appl. Phys. 40 (1969) 1450. Stoclinga. J.H.M., Gersdorf, R., deVrics, G.: Physica 41 (1969) 457. Stearns. M.B.: Phys. Rev. 187 (1969) 648. Schrodcr. K.. Giannuzzi. A.: Phys. Status Solidi 34 (1969) K 133. Shiga. M., Pells. G.P.: J. Phys. C 2 (1969) 1847. Tangc. H., Tokunaga, T.: J. Phys. Sot. Jpn. 27 (1969) 554. Vcdernikov. M.V.: Adv. Phys. 18 (1969) 337. Yoshino, T., Tanaka. S.: Opt. Commun. 1 (1969) 149. Bancroft. M.H.: Phys. Rev. B2 (1970) 182. Du Tremotet De Lachcisserie, E.: Ann. Phys. (Paris) 5 (1970) 267. Franse. J.J.M., Stolp, M.: Phys. Lett. 32A (1970) 316. Johanson. G.J., McGirr, M.B., Wheeler, D.A.: Phys. Rev. Bl (1970) 3208. Rotter. M., Sedlak. B.: Czech. J. Phys. B20 (1970) 1285. Reeves.G.K., Street. R.. Wilson, G.V.H.: J. Phys. C 3 (1970) S230. Resibois. R.. Piette. C.: Phys. Rev. Lett. 24 (1970) 514. Sievert, J.D., Zehler. V.: Z. Angew. Phys. 30 (1970) 251. Shaw, E.D.: Phys. Rev. B 2 (1970) 2746. Trussel. C.W., Christopher, J.E., Coleman, R.V.: J. Appl. Phys. 41 (1970) 1424. Wilson. G.V.H., Perczuk. B., Reeves,G.K.: J. Phys. C 3 (1970) S241. Wakoh, S.. Yamashita, J.: J. Phys. Sot. Jpn. 28 (1970) 1151. Zornberg. E.I.: Phys. Rev. B 1 (1970) 244. Zumsteg. F.C., Parks, R.D.: Phys. Rev. Lett. 24 (1970) 520. Asik. J.R., Stearns, M.B.: Bull. Am. Phys. Sot. 16 (1971) 403. Anders. W., Bastian. D., Biller, E.: Z. Angew. Phys. 32 (1971) 12. Bower, D.I.: Proc. R. Sot. London Ser. A 326 (1971) 87. Cranglc. J.. Goodman, G.M.: Proc. R. Sot. London Ser. A 321 (1971) 477. Chornik. B.: Phys. Rev. B 4 (1971) 681. Connelly, D.L., Loomis. J.S., Mapother, D.E.: Phys. Rev. B3 (1971) 924. Duff, K.J., Das, T.P.: Phys. Rev. B3 (1971) 192, 2294. Du Plessis. P. De V., Viljocn, P.E., Albcrts, L.: J. Phys. F 1 (1971) 328. Feldman. D., Kirchmayr, H.R., Schmolz, A., Velicescu, M.: IEEE Trans. Magn. Mag. 7 (1971) 61. Franse. J.J.M.: J. Phys. Paris C l-32 (1971) 187. Gilts. P.M., Longenbach. M.H., Marder, A.R.: J. Appl. Phys. 42 (1971) 4290. Gold. A.V., Hodges. L., Panousis, P.T., Stone, D.R.: Int. J. Magn. 2 (1971) 357. Lee. E.W., Asgar, M.A.: Proc. R. Sot. London Ser. A 326 (1971) 73. LeGall. H.. Jamet. J.P.: Phys. Status Solidi (b) 46 (1971) 467. Major. J., Mezci. F., Nagy, E., Svab, E., Ticky, G.: Phys. Lett. 35A (1971) 377. Moon, R.M.: Int. J. Magn. l(1971) 219. Maglic. R., Mueller, F.M.: Int. J. Magn. 1 (1971) 289. Stearns. M.B.: Phys. Rev. B4 (1971) 4069. Stearns. M.B.: Phys. Rev. B4 (1971) 4081. Stearns. M.B., Ullrich, J.F.: Phys. Rev. B4 (1971) 3825. Streever, R.L., Caplan. P.J.: AIP Conf. Proc. 5 (1971) 1185. Schneider, C.S., Shull, C.G.: Phys. Rev. B3 (1971) 830. Tang, S.H.. Craig, P.P., Kitchens, T.A.: Phys. Rev. Lett. 27 (1971) 593. Violet. C.E.. Pipkorn, D.N.: J. Appl. Phys. 42 (1971) 4339.

References for 1.1.2 71Wl 72Al 72Bl 72B2 72B3 72B4 72Dl 72Hl 7211 72Kl 72Ll 72L2 72Rl 72R2 72Sl 7282 72Wl 73Al 73A2 73Bl 73B2 73B3 73Cl 73El 73Gl 73Ll 73Ml 73M2 73M3 73M4 7301 73R 1 7382 7383 73Tl 74Bl 74Dl 74El 74Gl 7451 74Kl 74Ll 74Ml 74Sl 7432 7483 74Tl 74Vl 74Wl 75Al 75A2 75Bl 75Cl 7.5Dl 75Jl 75Ll Landoll-BBmstein New Series III/l9a

139

Wright, J.G.: Philos. Mag. 24 (1971) 217. Aldred, A.T., Froehle, P.H.: Int. J. Magn. 2 (1972) 195. Bhagat, S.M., Rothstein, M.S.: Solid State Commun. 11 (1972) 1535. Butler, M.A., Wertheim, G.K., Buchnan, D.N.E.: Phys. Rev. B5 (1972) 990. von Barth, U., Hedin, L.: J. Phys. C 10 (1972) 1629. Briane, M.: C.R. Acad. Sci. Ser. B275 (1972) 673. Dever, D.J.: J. Appl. Phys. 43 (1972) 3293. Hafen, G., Bromer, H., Schwink, Ch.: Int. J. Magn. 3 (1972) 59. Ishida, S.: J. Phys. Sot. Jpn. 33 (1972) 369. Kawakami, M., Hihara, T., Koi, Y., Wakiyama, T.: J. Phys. Sot. Jpn. 33 (1972) 1591. Leger, J.M., Loriers-Susse, C., Vodar, B.: Phys. Rev. B 6 (1972) 4250. Laubitz, M.J., Matsumura, T.: Can. J. Phys. 50 (1972) 196. Rosenman, I., Batallan, F.: Phys. Rev. B5 (1972) 1340. Rebouillat, J.P.: Thesis Grenoble 1972. Stearns, M.B.: AIP Conf. Proc. No. 10 (1972) 1644. Stearns, M.B.: unpublished. Williamson, D.L., Bukshpan, S., Ingalls, R.: Phys. Rev. B6 (1972) 4194. Alder, H., Campagna, M., Siegmann, H.C.: Phys. Rev. B8 (1973) 2075. Anderson, J.R., Hudak, J.J., Stone, D.R.: AIP Conf. Proc. No. 10 (1973) 46. Baraff, D.R.: Phys. Rev. B8 (1973) 3439. Briane, M.: C.R. Acad. Sci. Paris 276 (1973) 3789. Butler, M.A.: Int. J. Magn. 4 (1973) 131. Coleman, R.V., Morris, R.C., Sellmyer, D.J.: Phys. Rev. B8 (1973) 317. Escudier, P.: Thesis, Grenoble, quoted in [80 W]. Goy, P., Grimes, C.C.: Phys. Rev. B7 (1973) 299. Laubitz, M.J., Matsumura, T.: Can. J. Phys. 51 (1973) 1247. Mook, H.A., Nicklow, R.M.: Phys. Rev. B7 (1973) 336. Mook, H.A., Lynn, J.W., Nicklow, R.M.: Phys. Rev. Lett. 30 (1973) 556. Moriya, T., Kawabata, A.: J. Phys. Sot. Jpn. 34 (1973) 639; 35 (1973) 669. Majumda, A.K., Berger, L.: Phys. Rev. B 7 (1973) 4203. Onoprienko, L.G., Shiryaeva, O.I., Shur, Y.S.: Sov. Phys. Solid State 15 (1973) 757. Riedi, P.C.: Phys. Rev. BS (1973) 5243. Streever, R.L., Caplan, P.J.: Phys. Rev. B7 (1971) 4052. Stearns, M.B.: Phys. Rev. B 8 (1973) 4383. Tedrow, P.M., Meservey, R.: Phys. Rev. B7 (1973) 318. Bhagat, SM., Lubitz, P.: Phys. Rev. B 10 (1974) 179. Donohue, J.: The Structure of the Elements, New York: J. Wiley&Sons Ltd. 1974. El-Hanany, U., Warren, W.W.: Bull. Am. Phys. Sot. 19 (1974) 202. Gold, A.V.: J. Low Temp. Phys. 16 (1974) 3. Johnson, P.B., Christy, R.W.: Phys. Rev. B9 (1974) 5056. Klaffiy, R.W., Coleman, R.V.: Phys. Rev. B 10 (1974) 2915. Lederman, F.L., Salamon, M.B.: Phys. Rev. B9 (1974) 2981. Mook, H.A., Lynn, J.W., Nicklow, R.M.: AIP Conf. Proc. 18, American Institute of Physics 1974, p. 781. Stearns, M.B.: Phys. Rev. B9 (1974) 2311. Song, C., Trooster, J., Benczer-Koller, N.: Phys. Rev. B 9 (1974) 3854. Shacklette, L.W.: Phys. Rev. B 9 (1974) 3789. Tokunaga, T.: J. Sci. Hiroshima Univ. 38A (1974) 215. Van der Woude, F., Sawatzky, G.A.: Phys. Lett. 12C (1974) 335. Wang, C.S., Callaway, J.: Phys. Rev. B 9 (1974) 4897. Aldred, A.T.: Phys. Rev. B 11 (1975) 2597. Anderson, J.R., Heiman, P., Schirber, J.E., Stone, D.R.: AIP Conf. Proc. No. 29, Mag. Magn. Mater. (1975) 529. Batallan, F., Rosenman, I., Sommers, C.B.: Phys. Rev. B 11 (1975) 545. Coleman, R.V.: AIP Conf. Proc. No. 29 (1975) 520. Duff, K.J., Das, T.P.: Phys. Rev. B 12 (1975) 3870. Johnson, P.B., Christy, R.W.: Phys. Rev. Bll (1975) 1315. Lynn, J.W.: Phys. Rev. B 11 (1975) 2624.

Stearns

140 75Sl 76Al 76A2 76E1 76F 1 76Gl 76G2 76Ll 76Ml 76s I 76S2 76 W 1 77Al 77Bl 77B2 77Cl 77E 1 77Gl 77H 1 77K 1 77 K 2 77K 3 7701 77R 1 77s1 77s2 77s3 77V! 77 w 1 78E 1 78Gl 78 hl 1 78Sl 78s’ 7833 7s w 1 79Al 79B1 79B2 79F 1 79H 1 7911 795 1 79L 1 79 h,l 1 79 hf 2 79R I 80El SOE:! 80G 1 SOH! 80H2 SOL 1

Referencesfor 1.1.2 Singh. M.. Wang. C.S., Callaway, J.: Phys. Rev. B 11 (1975) 287. Amighian. J., Corner. W.D.: J. Phys. F 6 (1976) L 309. Auhcrt. G.. Ayant. Y., Bclorizky, E., Casalegno, R.: Phys. Rev. B 14 (1976) 5314. Eib. W.. Alvarado, S.F.: Phys. Rev. Lett. 37 (1976) 444. Fekete. D., Grayevskey, A.. Shaltiel. D., Goebel, U., Dormann, E., Kaplan, N.: Phys. Rev. Lett. 36 (1976) 1566. Grimval!. G.: Physica Scripta 13 (1976) 59. Gradmann. U., Kummerlc. W., Tillmanns, P.: Thin Solid Films 34 (1976) 249. Laubitz. M.J., Matsumura. T., Kelly, P.J.: Can. J. Phys. 54 (1976) 92. Morovec. T.J., Rift. J.C., Dexter, R.N.: Phys. Rev. B13 (1976) 3297. Stearns, M.B.: Phys. Rev. B 13 (1976) 1183. Stearns. M.B., Feldkamp, L.A.: Phys. Rev. B 13 (1976) 1198. Watson. T.W., Flynn. D.R., Robinson. H.E.: NBS Washington, D.C. 1976, unpublished data. Andersen. O.K.. Madsen, J., Paulsen, U.K., Jepsen, O., Kollar, J.: Physica 86-88 B (1977) 249. Burd. J.. Huq. M.. Lee. E.W.: J. Mag. Magn. Mater. 5 (1977) 135. Birss. R.R., Keeler, G.J., Shepherd, C.H.: Physica 8&88B (1977) 257. Callaway. J.. Wang. C.S.: Phys. Rev. B 16 (1977) 2095. Erskine. J.L.: Physica 89 B (1977) 83. Glinka. C.J.. Minkiewicz. V.J., Passcll, L.: Phys. Rev. B 16 (1977) 4084. Hermanson. J.: Solid State Commun. 22 (1977) 9. Kummerlc. W., Gradmann, U.: Solid State Commun. 24 (1977) 33. Keunc. W., Halbauer. R., Gonser. U., Lauer, J., Williamson, D.L.: J. Appl. Phys. 48 (1977) 2976; J. Mag. Magn. Mater. 6 (1977) 192. Kollie. T.G.: Phys. Rev. B 16 (1977) 4872. Ono. F.: J. Phys. Sot. Jpn. 43 (1977) 1194. Riedi. P.C.: Phys. Rev. B 15 (1977) 5197. Searle. C.W., Kunkel, H.P., Kupca. S., Maartcnsc, I.: Phys. Rev. B 15 (1977) 3305. Stearns. M.B.: J. Mag. Magn. Mater. 5 (1977) 167. Singa!. C.M.. Das. T.P.: Phys. Rev. B16 (1977) 5068. Vinokurova. L.I.. Gaputchcnko, A.G., ltskcvich, E.S.: JETP Lett. 26 (1977) 317. Wang. C.S.. Callaway, J.: Phys. Rev. B 15 (1977) 298. Eastman. D.E., Him@. F.J.. Knapp, J.A.: Phys. Rev. Lett. 40 (1978) 1514. Gersdorf. R.: Phys. Rev. Lett. 40 (1978) 344. Moruzzi. V.L., Janak. J.F., Williams, A.R.: Calculated Electronic Properties of Metals, New York: Pergamon Press 1978. Segransan. P.J.: Chabrc. Y., Clark. W.G.: J. Phys. F8 (1978) 1513. Smulowicz. F.. Pcasc, D.M.: Phys. Rev. B 17 (1978) 3341. Stearns. M.B.: Phys. Today 31 (1978) 34. Wohlfarth. E.P.: J. Mag. Magn. Mater. 7 (1978) 113. Anderson. J.R.. Papaconstantopoulos, D.A., Boyer, L.L.. Schirbcr, J.E.: Phys. Rev. B20 (1979) 3172. Brinfcr. A.. Campagna. M.. Fcdcr, R., Gudat, W., Kisker, E., Kuhlmann, E.: Phys. Rev. Lett. 42 (1979) 1705. Blacha. A., Bromer. H.: Verhandl. DPG(VI) 14 (1979) 176. Feldkamp. L.A., Stearns. M.B.. Shinozaki. S.S.: Phys. Rev. B 20 (1979) 1310. Himpsel. F.J., Knapp. J.A.. Eastman, D.E.: Phys. Rev. B 19 (1979) 2919. Ishikawa. Y.: J. Mag. Magn. Mater. 14 (1979) 123. Janak. J.F.: Phys. Rev. B 20 (1979) 2206. Liu. C.M., Ingalls, R.: J. App!. Phys. 50(3) (1979) 1751. McAlister. S.P., Hurd, C.M.: J. Appl. Phys. 50 (1979) 7526. Moriya. T.: J. Mag. Magn. Mater. 14 (1979) 1. Riedi. P.C.: Phys. Rev. B20 (1979) 2203. Eastman. D.E., Himpse!. F.J., Knapp, J.A.: Phys. Rev. Lett. 44 (1980) 95. Ebcrhardt. W., Plummer. E.W.: Phys. Rev. B21 (1980) 3245. Gerhardt. U., Maetz. C.J., Schutz, J., Dietz. E.: J. Mag. Magn. Mater. 15-18 (1980) 1141. Himpsel. F.J., Eastman, D.E.: Phys. Rev. B21 (1980) 3207. Heimann. P., Neddermeyer, H.: J. Mag. Magn. Mater. 15-18 (1980) 1143. Lonzarich. G.G.: Electrons at the Fermi Surface (Springford, ed.), Cambridge: University Press 1980, ch. 6. Stearns

References for 1.1.2 8001 8OSl 81Cl 81C2 81Hl 81H2 81H3 81 H4 81Kl 81Ll 810 1 81Sl 82Bl 82B2 82Cl 82Ml 82Pl 82P2 82Tl 82T2 82T3 82T4 83Bl 83B2 83Cl 83Dl 83Fl 83Hl 83H2 83Ll 83Pl 83P2 83Rl 83Sl 84Bl 84B2 84Jl 84Ll 84L2 84Pl 84Sl 8482 84Wl 84W2 85Bl 85Cl 85Ml 85M2 85M3 85Sl

Land&-BBmstein New Series lWl9a

141

Oppelt, A., Kaplan, N., Fekete, D.: J. Mag. Magn. Mater. 15-18 (1980) 660. Shaham, M., Barak, J., El-Hanany, U., Warren, W.W., Jr.: Phys. Rev. B22 (1980) 5400. Clauberg, R., Gudat, W., Kisker, E., Kuhlmann, E., Rothberg, G.M.: Phys. Rev. Lett. 47 (1981) 1314. Cable, J.W.: Phys. Rev. B 23 (1981) 6168. Himpsel, F.J., Heimann, P., Eastman, D.E.: J. Appl. Phys. 52 (1981) 1658. Heimann, P., Himpsel, F.J., Eastman, D.E.: Solid State Commun. 39 (1981) 219. Hanham, S.D., Arrott, AS., Heinrich, B.: J. Appl. Phys. 52 (1981) 1941. Hurd, C.M., Shiozaki, I., McAlister, S.P.: J. Appl. Phys. 52 (1981) 2214. Kiibler, J.: Phys. Lett. 81 A (1981) 81. Lynn, J.W., Mook, H.A.: Phys. Rev. B23 (1981) 198. Ono, F.: J. Phys. Sot. Jpn. 50 (1981) 2564. Steinsvoll, O., Moon, R.M., Koehler, W.C., Windsor, C.G.: Phys. Rev. B24 (1981) 4031. Brown, P.J., Deportes, J., Givord, D., Ziebeck, K.R.A.: J. Appl. Phys. 53(3) (1982) 1973. Brown, P.J., Capellmann, H., Deportes, J., Givord, D., Ziebeck, K.R.A.: J. Mag. Magn. Mater. 30 (1982) 243. Cort, G., Taylor, R.D., Willis, J.O.: J. Appl. Phys. 53 (1982) 2064. Maetz, C.J., Gerhardt, U., Dietz, E., Ziegler, A., Jelitto, R.J.: Phys. Rev. Lett. 48 (1982) 1686. Pauthenet, R.: J. Appl. Phys. 53 (1982) 2029 and 8187: C.R. Acad. Sci. Ser. B295 (1982) 331, 1067. Pauthenet, R., Picoche, J.C., Rub, P.: C.R. Acad. Sci. Ser. B295 (1982) 121, 331, 1069. Turner, A.M., Erskine, J.L.: Phys. Rev. B25 (1982) 1983. Treglia, G., Ducastelle, F., Spanjaard, D.: J. Physique 43 (1982) 341. Taylor, R.D., Cort, G., Willis, J.O.: J. Appl. Phys. 53 (1982) 8199. Tung, C.J., Said, I., Everett, G.E.: J. Appl. Phys. 53 (1982) 2044. Bagayoko, D., Callaway, J.: Phys. Rev. B28 (1983) 5419. Brown, P.J., Capellmann, H., Deportes, J., Givord, D., Ziebeck, K.R.A.: J. Mag. Magn. Mater. 31-34 (1983) 295. Callaway, J., Chatterjee, A.K., Singhal, S.P., Ziegler, A.: Phys. Rev. B28 (1983) 3818. Du Tremolet de Lacheisserie, E., Mendia Monterroso, R.: J. Mag. Magn Mater. 31-34 (1983) 837. Feder, R., Gudat, W., Kisker, E., Rodriguez, A., Schroder, K.: Solid State Commun. 46 (1983) 619. Halbauer, R., Gonser, U.: J. Mag. Magn. Mater. 35 (1983) 55. Hopster, H., Raue, R., Guntherodt, G., Kisker, E., Clauberg, R., Campagna, M.: Phys. Rev. Lett. 51 (1983) 829. Lynn, J.W.: Phys. Rev. B 11 (1983) 6550. Pauthenet, R.: Conf. on High Field Magn. (Date, M., ed.),Amsterdam: North-Holland Publ. Co. 1983, p. 77. Pauthenet, R.: C. R. Acad. Sci. Paris V 297(II) (1983) 13. Raue, R., Hopster, H., Clauberg, R.: Phys. Rev. Lett. 50 (1983) 1623. Steinsvoll, O., Majkrzak, C.F., Shirane, G., Wicksted, J.: Phys. Rev. Lett. 51 (1983) 300. Benczer-Koller, N.: private communication. Brown, P.J., Ziebeck, K.R.A., Deportes, J., Givord, D.: J. Appl. Phys. 55(6) (1984) 1881. Jarlborg, T., Peter, M.: J. Mater. 42 (1984) 89. Loong, C.-K., Carpenter, J.M., Lynn, J.W., Robinson, R.A., Mook, H.A.: J. Appl. Phys. 55(6) (1984) 1895. Lonzarich, G.G.: J. Mag. Magn. Mater. 45 (1984) 43. Paige, D.M., Szpunar, B., Tanner, B.K.: J. Mag. Magn. Mater 44 (1984) 239. Shirane, G., Steinsvoll, O., Uemura, Y.J., Wicksted, J.: J. Appl. Phys. 55(6) (1984) 1887. Steinsvoll, O., Majkarzah, CF., Shirane, G., Wicksted, J.P.: Phys. Rev. B 30 (1984) 2377. Wicksted, J.P., Shirane, G., Steinsvoll, 0.: Phys. Rev. B 29 (1984) 488; J. Appl. Phys. 55 (1984) 1893. Wicksted, J.P., Biini, P., Shirane, G.: Phys. Rev. B30 (1984) 3655. Boni, P., Shirane, G., Wicksted, J.P., Stassis,C.: Phys. Rev. B31 (1985) 4597. Cooke, J.F., Blackman, J.A., Morgan, T.: Phys. Rev. Lett. 54 (1985) 718. Mook, H.A., McPaul, D.: Phys. Rev. Lett. 54 (1985) 227. Mook, H.A., Lynn, J.W.: J. Appl. Phys. 57 (1985) 3006. Murani, A.P.: unpublished. Stearns, M.B.: J. Appl. Phys. 57 (1985) 3030.

Stearns

1.2.1 Fe Co Ni: introduction

142

[Ref. p. 274

1.2 Alloys between3d elements 1.2.1 Alloys between Fe, Co or Ni Introduction In this section the magnetic properties of binary and ternary alloys between the elements Fe, Co or Ni are given. aswell as the influence ofsmall amounts ofothcr elements(designatedby X in the Survey) on the properties of the alloys. Nonmagnetic properties arc given in as far as they depend on the magnetic state of the alloy. Secondary mn_rneticproperties like permeability, coercive force, hysteresis losses,etc., which depend to a large degreeon the preparation technique. crystal size. and on the various treatments of a polycrystalline sample.can be found in subvolume 19d dealing with the properties of technically applied magnetic materials. Fe Co system In Fi_g.I the equilibrium phase diagram of the Fc-Co system is rcproduccd [82 K 11. The equintomic alloy FcCo shows a CsCI type ordering. The phaseboundary between the Co-rich feephases (~-CO)and hcp phases(E-CO)is shown in Fig. 2. The uncertainty for very low Fe concentrations reflects the variation in the experimental results. The crystal structures of the hcp phasesarc shown in Fig. 3. The lattice constants and related properties arc given in Figs. 4 and 5. Fe -Ni system In Fig. 6 the equilibrium phase diagram of the Fe-Ni system is reproduced [82K 11. For the mnznctic propcrtics at room tempcraturc the preparation technique of the alloy is of prime importance. For Fe-rich alloys the transformation of the cubic crystal structure from beeto fee,the y-y transition, has a pronounced temperature hysteresis. see Fig. 7 [SSH 1). This diffusionless mnrtcnsitic transition is supprcsscdeven at liquid-He tempcraturcs in an alloy consisting of small particles [62K 11. Also minor substitutions with a third kind of atom. e.g. Si, or by the addition of interstitial atoms. e.g. C or N, the fee phase can bc more or less stabilized in the cooling process. Thin films with 20...40 at% Ni have after deposition the beestructure, but they can bc transformed to the fee lattice as a result of heating [67 S2], which gives a possibility to study the magnetic propcrtics of bee and fee Fe, -,Ni, alloys in the same composition range. Alloys having a composition around about 25 at% Ni have not beenestablished as a stable Fe,Ni compound. nor has a supcrlattice been found. Morcovcr alloys with about 20,..35at% Ni are in a metastable state. Their magnetic propcrtics, which have been and arc still the subject of cxtendcd investigations, dcpcnd to a high degree on the distribution of Ni and Fe atoms in the alloy [79 G 11.Their very low thermal expansion coeflicient: lirst indication [l897G I]. and the almost temperature-independent elastic coefficients, first indication [20G 11,of these alloys at room temperature arc the basis for the technically important Invar and Elinvar alloys, rcspectivcly. These propcrtics arc lossed when the mctastablc “invar” state is destroyed, for instance by electron irradiation at temperatures up to about 250 ‘C. The alloy distintegrates into two phases,a Ni-rich FeNi and a Ferich Fc,Ni phase [79 C 11.The magnetic propcrtics of the y-phase can be examined in the residual austenite by means of neutron diffraction experiments. Coexistence of ferromagnetism and antiferromagnetism at low temperature is then established in invar Fc-Ni alloys [SOY 11. The alloy FeNi, and alloys in a wide composition range around this point can bc obtained with the atoms ordered in a Cu,Au-type superlatticc crystal structure when appropriate annealing and cooling cycles are applied. SW Figs. 8a. b and 9. The supcrstructurc is stabilized by atoms like Si and Mn [69G I] and by Ge [70G I]. it is destroyed by additions of Cr or MO [69G 1] and by Cu [70G 11. The FeNi, alloys form the basis for the technically very important Permalloys, which have abnormally high magnetic susceptibilities at room tempcraturc. first indication [lo P 11,according to [51 B I]. The alloy FeNi can be in an ordcrcd state with the AuCu structure. Co-Ni system In Fig. 17 the equilibrium phase diagram of the Co-Ni system is reproduced [58 H 11. Lattice constants and related propcrtics arc given in Fig. 18. Bonnenberg, Hempel, Wijn

Survey For band structures and Fermi levels, see A.P. Cracknell in Landolt-Bornstein, NS, vol. 111/13c,1984. Subsection 1.2.1.1 1.2.1.2.1 1.2.1.2.2

1.2.1.2.3 1.2.1.2.4

1.2.1.2.5

1.2.1.2.6 1.2.1.2.7 1.2.1.2.8 1.2.1.2.9 1.2.1.2.10 1.2.1.2.11 1.2.1.2.12 1.2.1.2.13 1.2.1.3

Properties Phase diagrams, lattice parameters Paramagnetic properties Hypertine magnetic field, isomer shift Spin waves Atomic magnetic moment, magnetic moment density, g and g’ factor Spontaneous magnetization, Curie temperature High-field susceptibility Magnetocrystalline anisotropy Magnetostriction Magnetomechanical properties, elastic moduli, sound velocity Thermomagnetic properties Galvanomagnetic properties Magneto-optical properties Ferromagnetic resonance properties References

Fe, -,Ni, Fig.

Table

1...5

6...16

1

19...21

22...26

Fe, -.Jo, Fig.

Table

29...37

2, 3

63...71, 75, 76, 88

4 9...12, 16

94...102

18

137

21

144...150 173...176 196

73, 82

101, 102, 97, 98, 121

144 22 192, 194, 196, 197

207, 212 224,225 247

Fe-Co-X Fig.

29, 30

32, 38...40, 42...48, 50...53 54...59 70, 72...88

3

138...143

21

262.. .264

Table

Co-Ni-X Fig.

2

35, 36

7, 8 11, 12, 15...17

73, 82, 90, 91

17, 18

35, 36, I 41,49, 51*..53

5, 6, 7 11...14, 73, 16 77...82 19,20

208...211, 213...221 226.. .242, 243.‘.245 247...261

Co,-,Ni, Fig.

27,28

94, 102, 103...134

144, 152...164, 166...171 177, 186 190...206

Fe-Ni-X Fig.

59...62 70, 75, 88, 89...93

101, 102, 135, 136 97, 98,111, 120...122, 131...134 142, 143

101, 102

144,165,172 144, 151, 165...171

144, 171, 172

23, 25...27

182 192, 194, 196, 197

187...189

28

210, 217

222, 223

231, 232, 244

243, 246, 237,241

29

24

1.2.1.1 Fc--Co-Ni: phase diagrams, lattice parameters

144

[Ref. p. 274

1.2.1.1 Phase diagrams, lattice parameters Fe 17d

co10 /,

"C

20

30 1

40

I,

/

60 I

70

80

I,

,

,

I,

I,

/

s 9

Fe- Co /

1633

co 50 I

90wt%100 I, I

I

I

!’ i

lL95’C

1X:

Fig. 1, Equilibrium phase diagram of the Fc-Co system. The curves lab&d T, rcprcscnt the ferromagnetic Curie points for the various alloys [82 K I]. T,,: melting point tcmpcraturc.

65Ol’l. co

i 14X 139’d

I

I

I

I

i’-Fe 12c: lllS’C7

110: 1 1CX

;

95: 89

/

7G2 633 535 400 3OL 10

20

30

40

50

60

70

80

90 at%100

IFe 600

1 2 4 5 at% 6 0 3 a co FeFig. 2a. Tcmpcraturc hysteresis of the phase boundary between the Co-rich fee phases (y-Co) and hcp phases (E-CO) [82 K I]. Fig. 2b. Phase diagram in the dilute Fc,Co, -I alloy system as dcrivcd from dilatation curves [84 I I].

I

FexCol-x

“’

o . therm.expansion

0 0 co

0.01

Bonnenberg, Hempel, Wijn

0.02

0.03 x-

0.04

0.05

0.06

Ref. p. 2741

145

1.2.1.1 Fe-Co-Ni: phase diagrams, lattice parameters

Fig. 3. ABAB-hcp and ABAC-double hcp (dhcp) crystal structures of the Co-rich Fe-Co alloys [73 W 11.

111,

I

2.86

1”

bee

@‘I

Fe,Col_l, (RT)

“..I

hcp A0 ,

11.2-

-/ l

dhcp ABA1

’

I AI

11.1

fee

I -I

I

I

I

0.06

0.08

~ I 2.85 D

2.8L

2.83 0 Fe

0.2

0.6

OA

0.8

’

x-

Fig. 4. Room-temperature values of the lattice parameter a of bee Fe, $o, alloys [72 S 11, data from [41 E 11.

2.500I 0 CO

0.02

0.04 x-

0

Fig. 5. Lattice constants, c/a and volume per atom, V,, of Fe&To, --I alloys at room temperature for less than 10 at% Fe [73W 1,7403].

Land&BBrnstein New Series 111/19a

Bonnenberg, Hempel, Wijn

1.2.1.I Fc -Cog--Ni:phase diagrams, lattice parameters Ni

Nifa'

I

10

20

30

[Ref. p. 274

LO

so

fin

70

En

9nw1%inn

in00

2001 0 Fe

10

20

I I I 30

III co

50

I 60

\

70

80

90 0t% in0

NiFig. 6. Equilibrium phnsc diagram of the Fe -Ni system. The ct~rvcs labeled Tc rcprcscnt the fcrromagnctic Curie points for the various alloys [82 K I]. T,: melting point tempcralurc.

Ni

For Fig. 7, xc next page.

Ni-

520

.

I 510

FeNi

693 f

70 72 71 76 ot% 78 Ni a Fig. 83. Occurrcncc ofsupcrstructurc in the FcNi, region. as dcduccd from Miisshnucr cffcct spectroscopy [82 K I]. SW also the original work [77 D I. 77 D 2. 79 D I].

.

Ni

b 0 Fe Fig. 8b. Cu,Au type structure of the ordered FeNi, [77 D I].

Bonnenberg, Hempel, Wijn

Ref. p. 2741

1.2.1.1 Fe-Co-Ni: phase diagrams, lattice parameters Fe ,oooO I

Ni5

IO

15

20 I

25 II

30 wt% 35 II II

'I

'I

800

\

-100 -200 0 Fe

90%

5

IO

15

20

25

30 at% 35

Ni-

Fig. 7. Temperature hysteresis of the cl-y transition of Ferich Fe-Ni alloys. The field between the curves I and 3 are the points with more than 90% E- or y-phase when the alloy is heated or cooled through the corresponding temperature range, respectively, as is indicated by the arrows [58 H 11. 750 “C 600

450 _I 300

150

0

300

600 900 Annealing time -

1200 h

1500

Fig. 9. Annealing conditions for the high degree of FeNi, long-range ordering as derived from the order-sensitive magnetocrystalline anisotropy. Curve 1: [53 B 11, 2: [83 H2]. Land&Bbmstein New Series 111/19a

Bonnenberg, Hempel, Wijn

147

1.2.1.1 FeCo-Ni:

14s

phase diagrams, lattice paramctcrs

[Ref. p. 274

2.86L

3.6 1

kX

3
2.863

3.5 2.862 I 0 3c‘-

I 0 2.861

3’ 2&CI

3.:

\ 2.85!I

3.: 0.2 a

Fe

0.6

0.4

0

1.0

0.8

X-

1)

NI

Fiz. IOn. Lattice parameter n at various tcmpcraturcs as dcpcrtdcnt on the composition of fee Fe,-,Ni, alloys [71S I]. dat:t from [37 0 I ,..3].

te

0.01 0.02 0.03 x-

Fig. IOh. Lattice paramctcr at room temperature for bee Fe, -,Ni, alloys. Upper broken line: Vegard’s law for a hypothetical bee Ni with an interatomic distance equal to that offcc Ni; lower broken lint: the interatomic distance in Ni is corrcctcd to allow for the contraction due to the change in coordination [55 S 21. 1 kX& 1.002A.

3.600 H 3.595

I 3.590 0 3.585

3.575 0.21

0.28

0.32

0.04 0.05

0.36 0.40 x-

0.44

0.18

I

Fig. I I. Room-tcmpcraturc values of the lattice paramctcrs o of the fee invar-type Fe, -,Ni, alloys before and after irradiation with 2 McV electrons with an intensity of IO’” clcctrons,‘cm2. Solid circles: [4l 0 I]. other symbols: [79 c I].

Bonnenberg, Hempel, Wijn

Ref. p. 2741

1.2.1.1 Fe-Co-Ni: phase diagrams, lattice parameters

3.620

3.615

3.610

3.605

3.600 I 0 3.595

3.590

x=0.3. 3.585

/

3.580 0.24

3.570l-l -200

4I. .J.: t

-100

0

l

1

02 - ---3

100

J-l.-Ld

200 T-

extrapolation of a paromognetic lattice constant to 15°C

300

400

500 "C 600

Fig. 12. Lattice parameter a offcc Fe, -,Ni, invar alloys as dependent on temperature. Arrows indicate the Curie 3: temperatures. Curves 1: [69A3], 2: [3701...3], extrapolation from the paramagnetic state.

Landolt-BOrnstein New Series III/I%

Bonnenberg, Hempel, Wijn

149

1.2.1.1 FeCo--Ni:

150

[Ref. p. 274

phase diagrams, lattice parameters

3.61 A 3.5: I 5 35 3.5s " 1.000, -4 ? CJ 1.000~

3.5: I-

Fig. 13.Tcmperaturc dcpcndcncc ofthc lattice pnrnmctcr !I of fee Fc,,5Ni,,, invnr alloy [79C I]. Curve I: annealed sample. 2: sample irradintcd at 250-C with 1. lOI elcclronskm2

0.997

0.991 0

10

20

30

kbor

Fig. 14. Relative lattice spacing ala(p=O) vs. pressure at various tcmpcraturcs for a fee Fc,,,Ni,,, invar allo) [790 33. Arrows indicate fcrromagnctic to paramqnctic transition; xc [67 G 23.

I2.6E O.U. I

2.6:)-

2.64 i

I L

Table 1. The atomic volume in [A31 of Fe, -,Ni, alloys in bee and fee modifications as measured on thin films [74 L 11.

2.6;,-

Fe,-,Ni, 2.6[l-

bee fee

1 0.75 xFig. IS. Concentration dcpcndcncc of the avcragc atomic radius for Fe, -,Ni, alloys. r, at T= 0 K. calculated on the basis of Libcrman-Pcttifor’s virial theorem. The solid curve holds for the fcrromngnctic state. the dashed curve for the paramngnctic state. The arrow indicates lhc transition bctwccn both states [8l K I]. Measuring points according to [67P 21. I a.u.~O.529 A. 0.25

0.23

0.28

0.335

0.37

11.795

11.783 11.490

1I.771 11.528

11.758 11.586

\

. RT o I=OK 2.5tI-0 Fe

x

0.50

Bonnenberg, Hempel, Wijn

11.451

Ref. p. 2741

1.2.1.1 Fe-Co-Ni: phase diagrams, lattice parameters

9.0

151

I

Fe,-,Ni, I

5 /

I

T=-273"C(P+) I

I

I

I

I

0.2

0.4

0.6

0.8

8.6

?C 0 Fe

/

\/v/

I

/

x-

Fig. 16. X-ray densities of Fe,-.Ni,

1.0 Ni

alloys [Sl B 11.

Ni-

I

20

16OC 1495°C “C

I

40

60

3.540 3.540,

80 wt% 100

Tm

I

I

!O

40

I

I

I

60

80

100

kX

1152°C

Co- Ni 12oc

.L? z s

1115°C . .

3.535

-4c

hI 800

I

‘\

3.530

\

-\.

fee

I \.

42O’C

400

‘\

,’

\

E

hcp ‘1, 0

\ 20

\ 360°C

c z

40

60

3.525 r

80 at% 100

Ni -

Fig. 17. Equilibrium phase diagram of the Co-Ni system. T,: melting point temperature [SS H 11.

3.520 P 3.515oL Ni

co-

co

Fig. 18. Lattice parameters of Co-Ni alloys annealed at 900 “C and slowly cooled to room temperature in 14 days [5OTl]. lkX&l.O02A.

Landolt-Bornstein New Series 111/19a

Bonnenberg, Hempel, Wijn

1.2.1.2.1 Fe-Co-Ni: paramagnetic properties

152

1.2.1.2 Magnetic properties 1.2.1.2.1 Paramagnetic properties

4.5 40' 9 3 4.0

/ ‘elex Cox

,

y-w I

'x = 0.073

3.5

3s

I T,-

2.:

2s

1:

1.

0.

I-

a

Fig. 19a. Tempcraturc dcpcndcncc of the invcrsc paramagnetic mass susceptibility 1; ’ of Fc, -.$o, for the fee alloys, whcrc x 5 0.76, and for the hexagonal alloys, where x20.76. The arrows indicate the hystcrcsis in the a-y transformation [43 F I].

Bonnenberg,

Hempel,

Wijn

[Ref. p. 274

Ref. p. 2741

1.2.1.2.1 Fe-Co-Ni: paramagnetic properties

153

1.0

0 6

1000

1200

1400

"C

1601

b Fig. 19b. Temperature dependence of the inverse paramagnetic mass susceptibility xi’ for different Fe-Co alloys, measured during cooling and heating the specimens [56N 11.

Fig. 20. Curie constant per mole C,, for the Fe,-$0, alloys [43 F 1,44F 11.

4

“f

0 Fe

0.25

0.50 x-

0.75

1.00 co

Fig. 21. Phase diagram of Fe,-$0, alloys, with indication of the extrapolated paramagnetic Curie temperature 0 of the high-temperature phase [43 F 11.Triangles: phase transformation temperature, squares: Tc, circles: 0. Landolt-BOrnstein New Series 111/19a

I

Fe,-,Ni,

a TFig. 22. (a) Temperature dependence of the inverse paramagnetic mass susceptibility xi’ of the alloys y-Fe,-,Ni, for x=0.388.,.1 [6OC 11. See also Fig. 103 [61 K 1,44F 11.

Bonnenberg, Hempel, Wijn

154

1.2.1.2.1 Fe-Co-Ni

paramagnctic propertics

[Ref. p. 274

4 *lo4 9 cm3 2

600

I

800

b

1000

00

1200 K 11

1100

1300 K 1500

I-

Fig. 2%. Tempcraturc dcpcndcncc of the invcrsc paramqnctic mass susceptibility xi ’ for invar-type y-Fe, -,Ni, alloys. x=O.27.~.0.388. Mcasurcmcnts carried out for incrcasinc fcmncraturcs. The sham incrcasc in x; ’ vs. Tcorrcsponds to the structural transition a-ty [63 C I]. SW also for polycrystallinc material [Sl 0 I]. L

Fig. 22~. Tempcraturc depcndcncc of the inverse mass susceptibility 1;’ for y-phase alloys Fe,-,Ni, with x=O.O47...0.193 [62C I],

.

90 Gcm3 9 lxI

61

I b

5: ICI 1.6

533

550

600

653

700

750

800

850

900

950

Fig. 23. Tempcraturc dcpcndcncc of the inverse mass susceptibility x; ’ and the magnetic moments per unit mnss u ofsingle crystals of Fc, -INi, invar alloys. T, is the fcrromagnctic Curie tempcraturc [79 C2]. Bonnenberg,

Hempel,

Wijn

1000

1050 K 1

155

1.2.1.2.1 Fe-Co-Ni: paramagnetic properties

Ref. p. 2741

cm3

”

cm3 5 .I@ 9

2

zl7

1 I

6

6

3

5

2

4

I 1

3

I

41

-k?

v

"V,

4

t 2

-i.n "0

cg

2

5

I

I

x=0.59

I 4 3

I-A

;omt: 700

a

900

/P-l

:::yz 1 1100

1300

1 500

1500 "C 1700

700

900

1100

T-

T-

Fig. 24a. Susceptibility curves of Fe, -,Ni, alloys in the neighborhood of their melting points, for x = 0.40...0.89. Vertical arrow indicates melting point (average value between liquidus and solidus temperature) [57 N 11.

1.5 n4 -cm3 mol t E 0.5 27 0 -0.5 I 0

b

Fe

0.25

0.50

x-

0.75

1.00 Ni

Fig. 24b. Discontinuity of susceptibility Ax,,, of Fe, -,Ni, alloys [73 B 11. AX,,,= xm,,- xrn,:, xrn,t = x measured in liquid phase, xm,s=x measured m solid phase.

Landolt-Bornstein New Series 111/l%

2

Bonnenberg, Hempel, Wijn

1300

0 1500°C 1700

156

[Ref. p. 274

1.2.1.2.1 Fe-Co-Ni: paramagnctic properties

1033 K 503' G I Q -530 -10% -15X -2033 0

a

0.2i

0.53

0.75

x-

Fe

1

400

600

800

b

Ni

Fig. 2%~ Paramagnctic Curie tempcraturc 0 and the effective paramagnctic moment per atom pen for the y-phase alloys Fe, -,Ni, [62 C I].

1000 I-

1200

1400 "C 1600

Fig. 25b. Tempcraturc dcpcndencc of the inverse paramagnetic mass susceptibility for diffcrcnt Fe -Ni alloys. measured during cooling and heating the specimens [56 N 1-J.

.V”

-1 250 K

5 cm3K

m-! i 4

40.6

-cm3 9

000

75 750

I 60 -c-r I 0

L5

500

250

0 0 Fe

0.2

0.6

0.L x---r

[

0 1.0

Ni

Fig. 26. Curie constant per mole. C,. and paramagnctic Curie tempcraturc. 0. for the solid (s) and the liquid (I) state. respectively. of Fc, -,Ni, alloys. as derived from the straight lines in Fig. 24a [57 N 11.

a

0 900

1050

1200

1350

1500

1650 "C 1800

I-

Fig. 27a. Temperature dependence of the paramagnetic mass susceptibility zr for the alloys Co,Ni, --I [77S I].

Bonnenberg, Hempel, Wijn

1.2.1.2.2 Fe-Co-Ni: hyperfine field, isomer shift

Ref. p. 2741

2

0 700

I.01

900

1100

1300

0

1500 “C Ii

b TFig. 27b. Temperature dependence of the inverse paramagnetic mass susceptibility for different Co-Ni alloys; measured during cooling and heating the specimens [56N 11.

0.2

Ni

0.4 x-

0.6

0.8 CO

Fig. 28. Effective paramagnetic moment pen as derived from the paramagnetic susceptibility as well as the paramagnetic Curie temperature 0 for Co,Ni, --x alloys [77 S 11. Open circles: derived from measurements in the molten state, solid circles: derived from measurements in the solid state.

1.2.1.2.2 Hyperfine magnetic fields, isomer shifts

230 kOe

380 kOe

zI 225 w z? xz 220

I

3201 0 Fe

I 0.2

0.4 x-

I 0.6

0.8

1.0 co

Fig. 29. Variation of the effective magnetic hypertine field

H syp,eff at 57Fe nuclei vs. Co concentration of Fe, $0, alloys. Values obtained by extrapolating roomtemperature data to 0 K according to the increase of the spontaneous magnetization [63 J I], see also [70 M 11.

Landolt-Bdmsfein New Series 111/19a

21s 0

CO

0.05 0.10 015 0.20 0.25

x-

Fig. 30. Effective magnetic hyperfine field H,,,, effat 5gCo nuclei in fee Fe,Co, --x single crystals plotted as a function of the composition [77B 11. T=77.3K. The solid line represents calculated values.

Bonnenberg, Hempel, Wijn

1.2.1.2.2 Fe-Co-Ni: hyperfine field, isomer shift

Ref. p. 2741

2

0 700

I.01

900

1100

1300

0

1500 “C Ii

b TFig. 27b. Temperature dependence of the inverse paramagnetic mass susceptibility for different Co-Ni alloys; measured during cooling and heating the specimens [56N 11.

0.2

Ni

0.4 x-

0.6

0.8 CO

Fig. 28. Effective paramagnetic moment pen as derived from the paramagnetic susceptibility as well as the paramagnetic Curie temperature 0 for Co,Ni, --x alloys [77 S 11. Open circles: derived from measurements in the molten state, solid circles: derived from measurements in the solid state.

1.2.1.2.2 Hyperfine magnetic fields, isomer shifts

230 kOe

380 kOe

zI 225 w z? xz 220

I

3201 0 Fe

I 0.2

0.4 x-

I 0.6

0.8

1.0 co

Fig. 29. Variation of the effective magnetic hypertine field

H syp,eff at 57Fe nuclei vs. Co concentration of Fe, $0, alloys. Values obtained by extrapolating roomtemperature data to 0 K according to the increase of the spontaneous magnetization [63 J I], see also [70 M 11.

Landolt-Bdmsfein New Series 111/19a

21s 0

CO

0.05 0.10 015 0.20 0.25

x-

Fig. 30. Effective magnetic hyperfine field H,,,, effat 5gCo nuclei in fee Fe,Co, --x single crystals plotted as a function of the composition [77B 11. T=77.3K. The solid line represents calculated values.

Bonnenberg, Hempel, Wijn

[Ref. p. 274

1.2.1.2.2 Fe-Co-Ni: hyperfinc field, isomer shift

158

Hhyp-

3 280.1 283.9 287.1 290.9kOe 297.9329.6 334.3 I , I I I 1 h.99

339.0 3L3.7

Co0.01 2K

51Fe

spin -echo

spin -echo

superregeneration

superI regenerotion

II

kOe 35: I

I

I

I

/b-i I

I

I

I

I

I

I

5 282 285.5 289 292.5 MHz 299.545.35 46.00

16.65

I

17.30

I

MHz L8

a Fig.31a.Hypcrfineticld,H,,.,.spcctrafors9Coand “Fein alloy mcasurcd with spin-echo and an ~~~~~~~~~~~~ super-regenerative NMR tcchniqucs at 4.2 K [68 R 23.

Fe- Co

I

I

Li.5

15.0

b

I

I L6.5

17.5

48.0

k8.5

280

MHz ’

1’ -

C

Fig. 31b. S’Fc spin-echo NMR spectra in Fc-Co alloys at 1.35K [70B 11.

285

I

I

290

295

0.2 , MHz300

Y-

Fig. 31c...e. s9Co spin-echo zero-field NMR spectra for Fe-Co alloys. The main peak corresponds to single Co sites, the satellite lines S,, S,, and S, are assigned to first. second and third neighbor pairs, respectively, while S; and S’i correspond to nearest-neighbor Co triplets [83P 21, see also [71 S4]. (c) Alloys anncalcd at 700°C and quenched in ice water, (d) Fe,,,&o,,,, spectrum on enlarged scales,(e) Fe,,,,Co,,Oz, solid circles: annealed at 700°C and open circles: annealed at 900°C.

Bonnenberg, Hempel, Wijn

Ref. p. 2741

280 Fig. 31d.

1.2.1.2.2 Fe-Co-Ni: hype&e

285

290

295

field, isomer shift

285

I

MHz 300

Y---

Fig. 31e.

8.0 Fe

8.5

9.0 co

9.5

10.0 Ni

Fig. 32. Effective magnetic hyperfine field Hhyp,eff at 57Fe nuclei in Fe-Co and Fe-Ni alloys at room temperature relative to the field in metallic iron, plotted as a function of the number II ofb and 3d electrons per atom. The data in the range Fe,,,Ni,,, to Fe,,,Ni,,,(n= 8.4...9) where the Curie points are low have been corrected to take account of incomplete saturation at room temperature [61 J 11. Points for Co and Ni agree well with the results given by [60 W I].

Landolt-Bdmrtein New Series 111/19a

Bonnenberg, Hempel, Wijn

290

295

MHz 300

1.2.1.2.2 Fe-Co-Ni: hyperfine field, isomer shift

160

[Ref. p. 274

I

263

283

270

290

300 MHz:310

I’ -

0.16,

Y-

b

Fig. 33a. 59Co spin-echo NMR spectra ofFeO,s+,Coo,s-, allovs at 77 K for ordered samples annealed for 30 days at 55O’“C. S, corresponds to Co atoms with another Co atom replacing Fe in the 1st ncarcst neighbor shell. S, corresponds to Co atoms with a 2nd nearest neighbor Co atom replaced by Fe [76 M 41. I

I

Fig. 33b. s9Co spin-echo NMR spectra of Fe,,,Co,,, at 77 K for alloys annealed for various periods at a temperaturc of 550°C [76M4]. (1) As quenched. (2) annealing time 5 min., (3) annealing time 35 min., (4) annealing time 30 days

I

I

kOe H,,,(57Fe) -

Fig. 33~. Distribution function P(H,,J of the “Fc hypcrfinc field in disordcrcd Fe,,sCo,,S alloy at various temperatures. as derived from Miissbauer spectra [79 N I].

Bonnenberg, Hempel, Wijn

390

Ref. p. 2741

280,

1.2.1.2.2 Fe-Co-Ni: hyperfine field, isomer shift

I

I

I

I

I

3751 kOe

I

. .

I s

I

161

I

I

I

300

”

225 s 5 x 150

1801 0

100

200

300

400 T-

500

600

700 K 800

x-

Fig. 34. Temperature dependence of the effective hyperfine field Hhyp,eff for “‘Sn on Co sites in Fe,,,Co,,, containing 1 at% of Sn. The dashed curve represents the relative spontaneous magnetization [72 H 41, see also [78 C 11.

Fig. 35. Effective average ‘?Fe magnetic hyperfine field Hhyp, eff, substituted Fe,,&Ii,-X?oX),,,, and Fe,,~,$-XM~~f,5 ata&% [79 B 11.

Table 2. Variation

Feo.65 (Nil-xCox )0.35

A

of the effective hyperfine

derived from specific heat measurements. polated to OK. Alloy Fe

co

H hmeff 95.2

I

100

I

I

200 300 HhYPP7Fe) -

I

400 kOe 5

Fig. 36. Distribution function P(H,,,,J of the 57Fe hyperfine field as calculated from the Miissbauer spectra of Feo.65Wl-xCoxh3~ alloys at 80 K [79 B 11.

Landolt-Biirmtein New Series 111/19a

82.8 41.3 8.5 -

Extra-

Ni

at%

0

field,

H hyp,effat 5gCo nuclei in Fe-Co and Co-Ni alloys as

Ref.

kOe 4.8 17.2 58.7 91.5 100 60 65 50 33.4 20 10 6

Bonnenberg, Hempel, Wijn

40 35 50 66.6 80 90 94

314(9) 293(10) 256(3) 223 (4) 219(4) 161(3) 162 143 120 106 94 88

59Al 59Al 59Al 59Al 59Al 59Al 68Hl 68Hl 68Hl 68Hl 68Hl 68Hl

[Ref. p. 274

1.2.1.2.2 Fe-Co-Ni: hyperfine field, isomer shift

162

Table 3. Isomer shifts for “Fe in Fe-Co and Fe-Ni alloys. Alloy

Composition

IS (“Fe) mms-’

Ref.

Fe,-,Co,

x10.9 -

0.05 1)

Fe, -,Ni,

0.18<x
ferromagnetic part: +0.29(5) 2, antiferromagnetic part: +0.18(5) ferromagnetic part: -0.123) +o.24) (Fig. 53)

6351, 70M 1 74c.5

Fe 0.67%.33 ‘) 2, 3, 4,

64Nl 81Hl

Positive with respect to pure Fe. Relative to 57Fe in Cr. Shifts from phase to phase. As compared to stainless steel.

6.0

/

A disordered.ground

Fei-XCO, ,

a-+y phase boundary x = 0.34 0,..12at% H

74c5, 68A1 6351

A

.10~2 mm s

Fe,.xN~y

v disordeied.quenched v l ordered 0 - 4.5

I ,

Fe

x-

co

Fig. 37. “Fe isomer shift (rclativc to pure Fe; solid symbols) and quadrupolc splitting (open symbols) as functions of composition for ordcrcd and disordcrcd Fe, _XCo, at room tcmpcraturc [70 M 11.

k 2c 9

I

I

I

-6

-4

-2

I

I

RT T=77.3K I

I

0 2 1 mm/s 8 VFig. 38. “Fe Miissbauer spectra ofpowders of the invartype fee alloys Fe, -,Ni, at room temperature and at liquid N, temperature [64 N 11. Set also [75 G 1, 79 G 2, 74 C 23. For an explanation ofthc paramagnetic peak. see [69K 11. For Miissbaucr spectra of bulk samples. see [73Rl, 71 P 1,72T3].

Bonnenberg, Hempel, Wijn

Ref. p. 2741

1.2.1.2.2 Fe-Co-Ni: hyperfine field, isomer shift

163

400 kOe 0.8

0

x-

0.2

0.4

Fig. 39. Room-temperature values of the 57Fe hypertine Hhyp. eff in Fe, -,Ni, alloys obtained from arc-casted and spectroscopically standardized materials [63 J 11.See also [73 M 11; for an explanation on the basis of two electronic configurations of the Fe atoms, see [63 W 11. For discussions on the asymmetry of the Miissbauer spectra ofy-Fe, -XNi, alloys, see [74 W 1,75 B 1,77 H 21.

field

0.8

0.6

T/T, -

Ni

Fig. 40. Relative effective 57Fe hyperfine field h = f&p, e&hyp. eu(OK) for three Fe-Ni alloys, as dependent on the relative temperature T/T, [73 M 21, see also [79 H 21.

1.0

0.8

1.4

I

I

.-?

0.6

$l 1.0

< t?

p

0

‘./

c;

a 0.8 E. 2 0.6

2 0.4

0

Fel-x NI, 1.2

I

/ WP

0.4 T=77.3K I

0.;

0.8 T/T, -

Fig. 41. Dependence of the ballistically measured relative magnetic moment a/g,,, and of the effective 57Fe hyperfine field h = Hhyp,,rJHhyp, err(4.2 K) as derived from Mijssbauer experiments on the relative temperature T/Tc for the invar alloy Fe,,,7,Nio,31sMn,,,,,Si~,~~~. Tc =413 K, B,,= 126 Gcm3 g-l (calculated), H,,,,,,r(4.2 K) = 280 kOe. The solid line represents c/a0 as calculated form local molecular field theory [75 M 11. See also [74 W 1, 75 M 43. For invar alloys stabilized by several at% of Co or Cu, see [71 K 11.

Land&BBmstein New Series 111/19a

T

0.2 0.29

0.31

0.33

0.

xFig. 42. Concentration dependence of the reduced s7Fe hyperfine field Hhyp and the reduced magnetic moment p at 77.3 K for the invar powder alloys Fe, -.Ni,. The quantities have been related to the values found for the sample composition x = 0.34 (Hhyp= 330kOe). The isomer shifts are very small [64N 11. See also [74S4, 69A3,68N I].

Bonnenberg, Hempel, Wijn

164

1.2.1.2.2 Fe-Co-Ni: hyperfine field, isomer shift

60 I

I

I

Ni, t koe Felmx I LO T 2% z .\ !. Q z‘y .l. 2 20 4

[Ref. p. 274

I

I

. . T

I = L.2K

0’ 0.175 a9175

0.225 x-

0.275

0.325

Fig. 43. Concentration depcndcncc of the cllicctivc hypcrline field as dcrivcd from “Fc M&Jx~ucr spectra at 4.2K for fine particles of the invar alloys Fc, -,Ni, [68AI].

LOO kOe

I

FeNi,

350 70

I increasing 1 decreasing7. A metostobledlsordered sample

l

I 250 2 E 200 = ? r“, =z 150

U.J

x = 0.372 200

0

200 300 kOe H,j;PFel--Fig. 4-1. Tcmpcraturc-dcpcndcnt distribution function P( H,,,) of mqnctic hypcrfinc liclds at “Fc nuclei in fee Fe, -,Ni, alloys as detcrmincd from Mfissbaucr spectra. Tht temperature is indicated in terms of the rcduccd tcmpcrnturc [71 T3]. For a thcorctical trcatmcnt of the local environment effect on the distribution function of H ,!,.sec[83Kl.S3K2]. 100

400

600

800

K 1000

Fig.45. Effcctivc hypcrfinc field H,j,,,,I vs. temperature 7 at “Fc nuclei in FeNi,. In the insert the transition region for the ordering is given on a larger scale [77 D 2). set also [79 D I].

Bonnenberg, Hempel, Wijn

165

1.2.1.2.2 Fe-Co-Ni: hyperfine field, isomer shift

Ref. p. 2741

Cl.11 FeNi 03c

RT

OSIE O.OE 0.07 1 0.06 E ; 0.05 0.04

0.03

0.02

0.01

0 2jo

290

3do

3io

320

330

340

kOe

h Fig. 46. Probability distribution P(Hhyp) of the roomtemperature hyperfine fields as derived from analysis of the 57Fe Miissbauer spectra. The continuous curve is derived from a model-independent method applied to as-rolled FeNi,. The number in the brackets represent the number of Fe atoms in the first and second nearest neighbor shells [79N 11. The vertical lines are derived from a model-dependent method of analysis adopted by [77D2].

Landolt-Bdmstein New Series III/l%3

Bonnenberg, Hempel, Wijn

360

1.2.1.2.2 Fe-Co-Ni:

166

50

0

hypcrlinc

100

150

[Ref. p. 274

field, isomer shift

250 kOe 300

200

HW a Fig 47x Probnbility distribution P(H,,,.,) al various tcmpcraturcs for the hypcrfinc fields as derived from hfiissbnucr spectra of 57F~ in disordcrcd alloys of FcNi, [79 N I].

I

0.125

p. 0100 s ;; 0.075 0.050 0.025

!

250 200 300 kOe 350 HhYP Fig. 47b. Probability distribution P(H,,,) as in (a) but now for disordered FeNi [79N I].

b

50

100

150

Fig. 48. Influence of uninsial stress g within the elastic limit on the distribution function of the 57Fe maenetic hypcrfine field H,,, for tvvo invar alloys (a) Fc 36wt% Ni and (b) Fc ~30wt% Ni at room tcmpcrature [74Ti].

Fe-Ni RT

Fig. -curve

I

I

0

100

200 Hh,; ?'Fe) -

300 kOe LOO

Ni wt%

&/mm* 5,

H,‘) kOc

h2)

4, A supcrposcd curve rclatcd to a paramagnetic contribution. ‘) I kg/mm* g-98.0665 bar.

Bonnenberg, Hempel, Wijn

Ref. p. 2741

1.2.1.2.2 Fe-Co-Ni: hyperfine field, isomer shift

0.12

I

I

I

I

I

167

I

7=4K

T=4K

I

0.09

-Z 0.06 .2 3 4 0.03 0

I

I

I I Feo.635 Nio.do0.105

T-4K

I

I T=4K

Fe0.605 Nio.doo.lo5

0.09 -= 0.06 s c 0.03 0 0

100

200 Hhyp-

300 kOe 400 0

100

200 Hhe -

300 kOe 400

Fig. 49. Probability P(Hhyp) ofthe 57Fe hyperfine field as calculated from the Mijssbauer spectra of four different Fe-Ni-Co alloys measured at 4K in (a and b) the absence of an applied magnetic field, and in (c and d) the presence of an applied magnetic field [77 M 11. 420,

Fe0.67N’0.33 T=77K

---

0

/\

C free carburized

100

200 Hhyp(57Fe)-

300

kOe

4

Fig. 50. Analytical curves of the distribution function P(iY,,,) for the internal hyperfine field of the invar Fe 0.67%.33 at 77 K for C free and the carburized sample [Sl H 11.

Landolt-BCmstein New Series 111/19a

I

Fig. 51. Magnetic hyperfine field Hhyp of Fe atoms vs. the distance r from an interstitial C atom in a bee Fe-6 wt%, Ni-1.8wt% C alloy. 1st (0) and 1st (t) denote the first neighboring Fe atom for the octahedral and the tetrahedral interstitial C atom, respectively [74 S 31.

Bonnenberg, Hempel, Wijn

1.2.1.2.3 Fe-Co-Ni : spin waves

[Ref. p. 274

0.14 mm 052

2I

010 0.08

---

H free fl-hybride

0.06 004 45 % 30, 15 0 0

6

3

9

12 at%

15

H-

Fig. 52. Internal magnetic field distributions P(H,,,) as derived from MGssbnuer spectra mcasurcd at 77K on rolled heat-treated and polished specimen with a thickness of 30pm. Solid lines show those of alloys bcforc hydrogenation. broken lines show those of hydrides

Fig. 53. Effective hypcrfine field for “Fe isomer shift relative to pure Fe and the fraction of the weak ferromagnctic component of an Fc,,,,No,,,, invar alloy at 77 K for various grades of hydrogenization expressed as the H content [Sl H I].

[79S4].

Spin waves

1.2.1.2.3

Table 4. The second-moment exchange integrals J, in between atom pairs in Fe-Co alloys [K], 1 K t 0.0862 meV.

Znd-moment exchange integral [K] bee ‘)

J’? Fc Fe J’?‘Fc Co

J’? coco

~500

x800 %400

?

fee2)
>o >o

‘) As derived from Curie and ordering temperatures [SOL 11. 2, [78Bl].

Bonnenberg, Hempel, Wijn

1.2.1.2.3 Fe-Co-Ni : spin waves

[Ref. p. 274

0.14 mm 052

2I

010 0.08

---

H free fl-hybride

0.06 004 45 % 30, 15 0 0

6

3

9

12 at%

15

H-

Fig. 52. Internal magnetic field distributions P(H,,,) as derived from MGssbnuer spectra mcasurcd at 77K on rolled heat-treated and polished specimen with a thickness of 30pm. Solid lines show those of alloys bcforc hydrogenation. broken lines show those of hydrides

Fig. 53. Effective hypcrfine field for “Fe isomer shift relative to pure Fe and the fraction of the weak ferromagnctic component of an Fc,,,,No,,,, invar alloy at 77 K for various grades of hydrogenization expressed as the H content [Sl H I].

[79S4].

Spin waves

1.2.1.2.3

Table 4. The second-moment exchange integrals J, in between atom pairs in Fe-Co alloys [K], 1 K t 0.0862 meV.

Znd-moment exchange integral [K] bee ‘)

J’? Fc Fe J’?‘Fc Co

J’? coco

~500

x800 %400

?

fee2)
>o >o

‘) As derived from Curie and ordering temperatures [SOL 11. 2, [78Bl].

Bonnenberg, Hempel, Wijn

169

1.2.1.2.3 Fe-Co-Ni: spin waves

Ref. p. 2741

Table 5a. Spin wave stiffness constant D of Fe,Ni, -x alloys. [75H2]: x

Ni

0.05

0.4

0.5

0.6

0.68

D2,,, CmeVA’l

460(15) 525(15) 0.47 0.88

365(10) 400(10) 0.43 0.91

235(10) 250(10) 0.34 0.94

200(5) 200(5) 0.38 1

140(5) 160(5) 0.46 0.88

70(5)

Da.,KCmeVA21

293 K/T, D,,, KID~.~K [83Pl]:

x

TNCKI

D [meV A21

0.77

0.658

0.653

0.646

0.630

0.614

0.598

0.550

21(l) 77.0

21.0(15) 86.8

19.5(20) 87.8

17(l) 102.0

14.0(15) 123.7

W2) 131.7

5(l) 170.4

Table 5b. Spin wave stiffnessconstant D, at 0 K, quadratic temperature coefficient D, of the spin wave constant and the coefficient j? of the quadratic term in the spin wave dispersion relation as derived from low-temperature magnetization curves measured on single crystals of Fe,Ni, --x alloys [83 N 21. X

0.496 0.406 0.302 0.198 0.102 Ni

e

as

gcme3

Gcm3g-’

8.256(5) 8.362(5) 8.510(5) 8.640(5) 8.772(5) 8.917(5)

162.11 145.70 125.88 101.87 80.345 58.549

Pat

XHF

DO

~~

10m6cm3g-’

meVA2

1.663 1.501 1.304 1.060 0.8403 0.6154

4.71 3.67 2.88 2.22 2.16 2.06

245(20) 300(20) 370(20) 390(20) 450(20) 530(20)

600 meVW2 500

400

t

300

Q 200 100

0 0 Ni

0.1

0.2

0.3

0.4

0.5

0.6

0.7

x-

Fig. 54.Variation ofthe spin wave stiffnessconstant D for single crystals of Fe,Ni,-, as determined from smallangle neutron scattering [75 H 21, squares[64 H I], see also [76M 11,and spin wave resonance:open triangles [67 R I], solid triangles [73 M I] and circles [75 H 21.See also[72B1,76K1,70W1,68M1,65W1].Forvalues deducedfrom high-field susceptibility measurements,see [71Hl]; for theory, see [79Yl, 79Y2, 76E1, 76H2, 75R1,73Rl]. Landolt-Bbmstein New Series IW19a

Bonnenberg, Hempel, Wijn

D2

10-7~-5/2

L

0.3(l) 0.25(10) 0.8(2) 0.6(2) 0.8(2) 1.1(l)

5.0(10) 5.0(10) 3.5(10) 4.0(10) 3.5(10) 2.5(5)

1.2.1.2.3 Fe-Co-Ni: spin waves

170

2LO me\!A’

[Ref. p. 274

meVA2Fe,., Ni,

I f

550

2iO

/.. 500

I/:

60

250

30

0.L

0

(r/r,P

-

0.6

7.5 A2

I

1.0

5.0

a

l- --_

9 2.5

0.5 0 0.1

0.8

0.6

0.7 x-

0.8

0.9

1.0 Ni

Fig. 55~.Quadratic temperature cocflicicnt D, ofthc spin wave stiffness constant of fee Fc, -,Ni, alloys. derived from mn,onctization mcasurcmcnts (I) and neutron scattcrin_c (2...4). I: [83N2], 2: [75H 21. 3: [7912], 4: [73 M 31.

0.9

1.0 Ni

---_ Y

1.- -.

i .l. ‘I 0 7 A2

0.8

0.9

t0.5

+5

~6 -7 l 8

FelexNlx

I

G

0.7 x-

01

~2 v3 x4

Fig. 55b. Low-temperature spin wave stiffness constant Do for fee Fc,-,Ni, alloys, derived from magnetization mcasurcmcnts (I) and neutron scattering (2...8). 1: [83 N 2). 2: [75 H 2],3: [79 12-j, 4: [64 H 1-J 5: [73 M 31. 6: [68 M I], 7: [70 W I], 8: [76 M 21.

Fepx Ni,

t

C

0.5

b

Fig. 55a. Temperature variation of the exchange stiffness constant D as derived from neutron spin wave scattering esperimcnts for two single crystals, Fc,,,Ni,,, and Fe,,,Ni,,,, [79 121. For the spin wave stiffness constant and its temperature variation as detcrmincd from magnetization mcasurcmcntson a single crystal ofFe,,,,SNi,,,,, invnr alloy. see [80 N I].

1.5 .lO" K-s!?

/

200

a

T

0 -6 04

0.5

d

0.6

0.7 x-

1.0 Ni

Fig. 55d. CocfTicient j3 of the quadratic term in the spin wave dispersion relation for Fe, -,Ni, alloys. I: magnetization mcasurcmcnts [83 N 23. The value for x =0.45 is from [83N 33.2: neutron scattering [68 M I, 71 A23.

Bonnenberg, Hempel, Wijn

Ref. p. 2741

1.2.1.2.3 Fe-Co-Ni: spin waves

171

1.5 meV

1.0 i

Fig. 56. Magnon linewidth r as determined by neutron spin wave scattering on a single crystal of Fe,,,,Ni,,,, measured at different temperatures and plotted as a function of the square of the magnon wavevector 4. For comparison the same property is given for other ferromagnetic substances [79 121.

0.5

0

0.03

0.06

0.09

0.12

0.15 A-2 0.18

lC TH;

I

I

5

x =0.32 I

I

I

IO

15

I

I

I

20

THz

25

Fig. 57. Intrinsic magnon linewidth r vs. energy of the magnon as determined by inelastic neutron scattering from disordered single crystals of Fe,-,Ni, in various crystal directions hkl. 1 THz P 4.136 meV. Open and solid symbols refer to different spectrometers [80 H 11.

Table 6. Exchange integrals J between atom pairs in Fe, -.Ni, alloys as derived from inelastic small-angle scattering of neutrons by spin waves.

I 0.8

Exchange integral [meV] bee ‘)

JFe-Fe JFe-Ni JNi-Ni

fee ‘)

fee “)

+ 18.2(5)

- 9.0(26)

-41(13)

+39(5)

- 8(l) +38(4)

+ 52(3)

+ 52(5)

-

‘) Second moments [64 H 11. ‘) [75M2].

n

1.0

< 0.6 2 0.4 0.2 0 0.2 0.3 0.4

0.5

0.6 0.7 0.8 x-

0.9 1.0 Ni

Fig. 58. Effective magnetic exchange parameter J for fee Fe, -,Ni, alloys relative to JNi,the quantity for pure Ni. I: specific heat measurements [73 T 2],2: Curie temperature measurements [73 T 2],3: neutron scattering experiments [64H 1],4: spin wave resonance [67 R 11. Landolf-Bbmstein New Series III/l%

Bonnenberg, Hempel, Wijn

1.2.1.2.3 Fe-Co-Ni: spin waves

172

[Ref. p. 274

Table 7. Spin wave stiffness constant D of Co-Ni alloys and Fe,,,,Ni,,,,.

Fe o.19Nio.sl Ni Coo.lNio.9 Coo.2Nio., Coo,3Nio.7 Coo.4Nk6 Co, -xNi,

D

T

meV A2

K

WW

FT

139(12) 160(50) 68(20) 83(17) 94(20) 90(24) 116(10) Figs. 59, 60 Fig. 59

RT RT RT RT RT :T’ RT low temp.

Fig. 60

Measuring method

Ref.

photoacoustically photoacoustically spin wave resonance spin wave resonance spin wave resonance spin wave resonance spin wave resonance photoacoustically spin wave resonance inelastic neutron spectroscopy ma&n. measurements

83D 1 83D 1 77Cl 77c1 77Cl 77Cl 77Cl 83Dl 72H3

700 meV8* 600

200

/ /,/

./

/

,’

9.8

9.9

/

/*

100


0 9.2

9.3

9.L

9.5

9.6

9.7

/I-

10.0 Ni

Fig. 59. Spin wave stiffness constant D as derived from inelastic neutron scattering vs. the avcragc number n of 4s and 3d clcctrons per atom for fee Co-Ni (open circles) and Fe-Ni (open triangles) alloys [77 M 31, as well as for pure Ni, solid circle: [75H2] and solid triangle: [73 M 33. Lower solid line: spin wave resonance data for Co-Ni alloys [72 H 33. Dashed line: rigid band model calculations by [71 W I].

Bonnenberg, Hempel, Wijn

77M3 76M1

Ref. p. 2741

500,

m&H2

1.2.1.2.3 Fe-Co-Ni: spin waves

II

173

1

Col-xNi, I

-r-m

400.-

T

I 300 a” 200 01 0

/’

100 4

S’

/

/’

?f

“OW co

0.6 3.8 1.0 xNi Fig. 60. Variation of spin wave stiffness constant D, as derived from low-temperature magnetization measurements vs. composition for fee Co,-,Ni, alloys. Open circles: [76 M 11, solid circles: [72 H 31, triangles: [67P 11, dashed line: calculated [71 W 11.

0.2 0.4 0.6 0.8 1.0 Ni xco Fig. 61. Exchange stiffness constant A vs. composition for Co,Ni, --):alloys [72 H 31. The relation between A and the spin wave stiffness constant D is given by D = 2Afiy(M,, where y is the gyromagnetic ratio and M, is the spontaneous magnetic moment per unit ofvolume. Single crystal measurement: x=0.85, A=0.8.10-6ergcm-’ [75W 11.

Table 8. The second-moment exchange integrals J between atom pairs in Co-Ni alloys. 2nd-moment exchange integral

CmeVl

JL?oL

Jg- Ni J$$,‘-Ni

fee ‘)

fee “)

21(2)

l(3) b(4) 52(2)

37(4) 51(5)

hcp ‘)

-

10.0(5) 45(25) 738(500)

r) Magnetization measurements [76 M I]. “) Spin waves [72 H 21.

0

0.2

OX

0.6

1..O Ni Fig. 62. Variation ofthe exchange parameters J(‘) and J(O) for fee Co, -,Ni, alloys as derived from the spin wave stihhess constant D and the Curie point Tc, respectively. a: lattice parameter, S: average spin quantum number/atom, z: number of nearest neighbor atoms [76 M 11. c

LO

Landolt-Bbmstein New Series 111/19a

Bonnenberg, Hempel, Wijn

x-

0.8

1.2.1.2.4

174

1.2.1.2.4 Atomic

Fe-Co-Ni: magnetic moment, g-factor

magnetic

moment,

magnetic

moment

density,

[Ref. p. 274

g and g’ factor

2.5

Pa 2.4

I 23 h 2.2 2.1 0

a

0.1

0.2

0.3

0.4

0.5

0.6

x-

Fe

0.7

co

Yig. 63a. Mean magnetic moment per atom j,, as dcrivcd iom magnetization mcasurcmcnts for bee Fc, -XCo, alloys [69 B I]. b

x-

Fe

CO

Fig. 63b. Average spin polarization &,in,a, of disordered Fe,-$0, alloys at OK [84V I]. Solid circles: experimental results [69 B I] taking into recount the 9 factors from [61 M I], open circles: calculated using tight binding scheme with single-site, t%ll-orbital interactions [84V 11.

3.2

Pa

1.8E PO 1.82 1.75 I Ih 1.7c 1.7: 0.2

0.4

0.6 1.7[

Fig. 64. Atomic ma?nctic moments p,+ and pcO in bee Fe, _,Co, alloys. Trlanglcs: neutron diffuse scattering data [63C2. 64G I]. open circles: calculation results based on the tight-binding model of 3d electrons with allowance for local-environment effects [79 H 21, solid circles: mean atomic magnetic moment for the alloy [69 B I].

2

a

4

ot% 10

6

8

0.6

0.8 at% 1.0

r

1.728

MS l.72&

Fe-Co 1 hcp I

I 1.720

I0.1%

1.716

Fig. 65. (a) Mean magnetic moment j,, in hcp, dhcp and fee Fe-Co alloys as derived from the saturation magnetization of polycrystalline samples at 4.2 K. (II) Enlarged graph for the hcp region [73 W 21. Bonnenberg,

1.71

‘I 0

b

CO

Hempel, Wijn

0.2

0.4

Fe-

Fe

Ref. p. 2741

1.2.1.2.4 Fe-Co-Ni: magnetic moment, g-factor

175 11 220

0

5.16 3.76 2.11 0.93 0.37

0.5 0 0 Fe

0.2

0.6

0.4

0.8

x-

Fig. 66. Mean magnetic moment per atom as derived from magnetization measurements of fee Fe, -$o, alloys precipitated from Cu, as a function ofconcentration. The solid lines in the figure indicate the magnetic moment of bulk Fe-Co alloys [69 N 11.

00; jg-Lzq

536

1.0 co

3.76 2.11 093 0.37

032

0

-0.05

-0.09 400

000

Fig. 67. Map ofthe magnetic moment density,in [&A3], for a Co,.,,Fe,.,, alloy in the (100) plane [70 D 11.

111 ---

2 6 Ps -27 4 I F

2

-2 0

Fig. 68. Map ofthe magnetic moment density, in [+,/!I~], for a Coo.92Feo.osalloy in the (110) plane [70 D 11.

Landolt-BOrnstein New Series 111/19a

0.1

0.2

0.3

0.4

0.5

0.6

Fig. 69. Magnetic moment density distribution m along the three major crystal axes in Co,,,,Fe,,,, [70 D 11.

Bonnenberg, Hempel, Wijn

176

1.2.1.2.4 Fe-Co-Ni: magnetic moment, g-factor

1

I

I

I

‘\I

I\

I

I ‘\ I \Ir

1

1.88

'Ll 1.87 1.86 1.85

1.84 1

l-

o Fe-Co,Co-Ni . Fe- Ni I I

1.83

Y

I rn L”

I lR?I 26.00 26.25 26.50 26.75 27.00 27.25 27.50 27.75 28.00 Ni Fe z-

Fig. 70. Magnctomcchanical factor g’ for Fc, Co, Ni, and their binary alloys as dcpcndent on the mean atomic number z. The dashed lines arc computed from the properties of the constituent elcmcnts [69 S 1).

220,

I

I

I

Fe,.Jo, 2.16

2.12

.’

/’

/’ ,/ /

/’

0 .,’

. /

‘

a II 0,

I

.

.

. .

I

2.00 0

0

Fe

I 0.2

0.4

0.6

0.8

x-

1.0 CO

Fig. 71. Spectroscopic splitting factor g for Fc, -,Co, alloys. Solid circles arc the g values mcasurcd by ferromagnctic rcsonancc [61 M I]. Solid symbols indicate 9 values dcrivcd from the magneto-mechanical factor g’ through the relation l/g+ l/g’= I. Squares: [44 B I], triangles: [52B I]. Dashed lint: calculated from the properties of the constituent elements. For a calculation of the electronic spin and orbital magnetization, see [69 R I].

Bonnenberg, Hempel, Wijn

[Ref. p. 274

Ref. p. 2741

Table 9. Magnetic moment distribution in Fe, Jo, alloys [70D 1, 72M3, 62S2]. g: gyromagnetic ratio derived from magnetic form factors as obtained from polarized neutron scattering &,: mean atomic moment &: average conduction electron polarization per atom y: fraction of 3d electrons in an E, state 9

X

0.9175 0.8865 0.883 0.858 0.91 0.91 ‘) 1.00

2.17 2.14 2.16 2.16

Y 0.472(1) 0.474(2) 0.476(1) 0.478(l) 0.471(11) 0.463(13) 7

Pat

PE

PB

PB

2.057(40) 2.15(6) 2.15(4) 2.06(3) 1.99(2) 1.75(2) 1.86(7)

-0.39(3) -0.43(7) -0.46(3) -0.33(2) -0.31(3) -0.28(7) -0.28(7)

Table 10. Magnetomechanical ratio g’ for Fe-Co alloys [69 S 11.

Ref.

Composition

9’

Fe Fe-20 wt % Co Fe-50 wt% Co Fe-75 wt% Co Fe-90 wt% Co co

1.919(2) 1.918(2) 1.916(2) 1.902(2) 1.862(2) 1.838(2)

70Dl 70Dl 70Dl 70Dl 72M3 72M3 6282

‘) At 600°C. “) Inapplicable.

Table 11. Room-temperature values of the relative orbital magnetic moment, por,,/&,,for binary alloys between Fe, Co or Ni, as obtained from Einstein-de Haas gyromagnetic ratio measurementsaccording to the relation g’= 2- 2por,,/&. .Z: mean atomic number [69 R 11.The values g’ are from [62 S 1, 66 S 1, 69 S 11. Fe

co

Ni

wt% 100 90 75 75 50 65 25 10 50 0 0 0 0 0 35 0 25 0 0 10 0

Landolt-BOrnstein New Series lll/l9a

177

1.2.1.2.4 Fe-Co-Ni: magnetic moment, g-factor

0 0 25 0 50 0 75 90 0 100 90 85 80 75 0 70 0 50 25 0 0

0 10 0 25 0 35 0 0 50 0 10 15 20 25 65 30 75 50 75 90 100

26.00 26.18 26.24 26.48 26.49 26.68 26.74 26.90 26.98 27.00 27.10 27.15 27.20 27.25 27.28 27.30 27.48 27.51 27.75 27.79 28.00

4.22(12) 4.44(22) 4.28(9) 4.49(22) 4.38(9) 4.60(9) 5.15(10) 7.41(15) 4.80(24) 8.81(9) 8.05(16) 7.88(8) 7.64(15) 7.70(15) 5.04(20) 7.93(8) 5.54(22) 8.34(16) 8.17(8) 6.38(32) 8.92(9)

Bonnenberg, Hempel, Wijn

1.919(2) 1.915(4) 1.918(2) 1.914(4) 1.916(2) 1.912(2) 1.902(2) 1.862(2) 1.908(4) 1.838(2) 1.851(3) 1.851(2) 1.858(3) 1.857(2) 1.904(4) 1.853(2) 1.895(4) 1.846(3) 1.849(2) 1.880(6) 1.835(2)

[Ref. p. 274

1.2.1.2.4 Fe-Co-Ni: magnetic moment, g-factor

178

Table 12. Room-temperature values of electron spin magnetic moment pspin and orbital magnetic moment porbper atom of binary alloys between Fe, Co or Ni. Also the relation 9-l +g’-‘ between the spectroscopic splitting factor 9 (obtained from interpolation ofdata from [61 M 11) and the magnctomechanical factor 9’ (obtained from interpolation of the data from [62S 1, 66 S 1, 69 S 11) is indicated [69 R 11. Fe

Ni

co

Porb Pfl

PSpi” Pa

g-‘+g’-’

0.0918(33) 0.0962(76) 0.1036(37) 0.0910(62) 0.1047(37) 0.0638(28) 0.1085(34) 0.1353(35) 0.0729(48) 0.1472(34) 0.1291(41) 0.1228(31) 0.1156(38) 0.1127(28) 0.0676(43) 0.1121(28) 0.0618(37) 0.0986(31) 0.0725( 18) 0.0539(27) 0.0508 (12)

2.083(23) 2.070(46) 2.319(26) 1.934(43) 2.288(25) 1.322(28) 2.096(21) 1.691(17) 1.447(32) 1.523(15) 1.475(18) 1.436(18) 1.397(26) 1.350(15) 1.273(28) 1.301(15) 1.053(24) 1.083(13) 0.8 15(V) 0.790( 19) 0.518(6)

1.009 0.9994 0.9986 0.9985 0.9920 0.9987 0.9930 0.9980 0.9987 1.002

wt%

90

0 0

75 75 50 65 25 10 50 0 0 0 0 0 35 0 25 0 0 10 0

25 0 50 0 75 90 0 100 90 85 80 75 0 70 0 50 25 0 0

100

0 10 0 25 0 35 0 0 50 0 10 15 20 25 65 30 75 50 75 90 100

1.001 1.005 0.998

2.0 Ilri 1.5

I I<

I1.1

O!i-

a

-0

Fe

0.2

0.4

0.6

x-

0.8

1.0 Ni

Fig. 72a. Variation of the mean magnetic moment per atom j,, with composition for Fe, -xNi, alloys as dctcrmined from the mcasurcmcnts of the saturation magnctization [7OC2]. Bee: solid circles [63C4]; fee: open circles [63 C43. crosses [52 K I], triangles [70 C 23.

0.4 b

0.8

0.6 X-

1.0 Ni

Fig. 72b. Average magnetic moment per atom p,, and high-field susceptibility xHF in a magnetic field H,,,, =16.5 kOc at a temperature of 4.2K for fee Fe,-,Ni, alloys. Open circles: [83N2], crosses: [63C4], solid circles: [77 Y 11, squares: [77 R I].

Bonnenberg, Hempel, Wijn

1.2.1.2.4 Fe-Co-Ni: magnetic moment, g-factor

Ref. p. 2741

2.2

I

I

I

179

I p

Feo,7(Re,Pt,.,)0.3

,

$1 ~JC~,.,p(Fe,Nil-,)o.92C00.08

1.8

0.8

01 8.0

I 8.1

(Feo.715 %.2do.gaMno.06 i i i

I 8.2

8.3

8.4

I 8.5 fl-

I 8.6

8.7

8.8

8.9

Fig. 73. Variation ofthe mean magnetic moment per atom j&t as a function of the number n of valence electrons per atom for various invar alloys. Open circles and triangles (T=4.2K): [68Cl], see also [69K 11. Solid symbols refer to data from various other authors, mostly extrapolated to 0 K, see [68 C 11.

,a' 1.5 14" 1.0 0.5 0 0 Ni

0.1

0.2

0.3

0.4 x-

0.5

0.6

0.7

I

Fig. 74. Magnetic moment attributed to Fe and Ni atoms in Fe,Ni,-, alloys as obtained from neutron scattering experiments [72 M 21. Solid circles: [55 S 11, triangles: [62 C 21, open circles: [72 M 21.

Land&-Bbmstein New Series lWl9a

Bonnenberg, Hempel, Wijn

9.0

[Ref. p. 274

1.2.1.2.4 Fe-Co-Ni: magnetic moment, g-factor

180

Table 13. Magnetic moments J),,~and pNi attributable to Fe and Ni atoms in Fe, -XNi, alloys, as derived from maenctic structure factors obtained from neutron scattering with either polarized (pol) or unpolarized (unpol) neutrons at room temperature. For theoretical calculations basedon various theories, see[71 H 2: 72 H 1,7.5R I, 79 I 1.81 K 11for coherent potential approximation; [74 M3, 78 H 1,79 H 1,79 H 2,SOH 1,83 K 1,83 K 21 for similar calculations takin_c into account a chemical local environment effect; [79 M 21 for Hartree-Fock approximation in the itinerant electron theory. The samples arc polycrystalline, unless otherwise stated. Fe,r_ Ni I

Sample

X

0.10 0.10 0.32 0.34 0.35 0.40 0.40 0.499 0.50 0.601 0.70 0.70 0.743 0.75 0.80 0.85

0.90

disordered disordered ‘) crystal. invar invar crystal. invar disordered ‘) disordered disordered crystal. disordered disordered annealed disordered disordered crystal. disordered crystal, ordered ‘) polycrystalline disordered ‘) disordered disordered

PPe

PNi

PF~PNI

Ff3

Pa

lb

2.41(8) 2.4I (4) 1.10 1.8o(15)3) 2.3(25)2, 2.44(8) 2.42(17) 2.60 2.54(16) 2.65 3.02(12) 2.66(9) 2.91 3.13(15) 3.10(l) 2.97(15) 2.99(l) 2.56(33) 2.58(14)

0.94(20) 0.93(10) 0.64 0.87(20)3, 0.83(6) 0.82(13) 0.67 0.78(4) 0.65 0.63& 0.09 0.63+-0.08 0.60 0.63(5) 0.68(5) 0.62(5) 0.64(5)

0.46

1.93(20) 2.06(21) 2.31(22) 2.35(20)

Measuring method

Ref.

Pal unpol Pal Pal unpol unpol Pal unpol unpol unpol unpol unpol unpol Pal Pal unpol unpol unpol unpol

63C2 62C2 82C1 7913 65C2 62C2 63C2 55Sl 73Cl 55Sl 62C2 62C2 55Sl 73Cl 73c1 55Sl 74Nl 74Nl 62C2

‘) In thesepolycrystallinc samplesstill an appreciable amount ofshort range order is present,which has been accounted for [62 C 2, 73 C 11.For a calculation of the local environment effect on the magnetic states of the atoms. see [79 H I. 79 M 21. 2, In the paramagnetic state the apparent iron atomic moment is pFe= 1.4(3)~,. see also [83 N 11. 3, AI 77 K. pee= 2.41(15)IL,,and pNi =0.82(5) 11~[79 131. 0 CoCr P CoMn

v CoNi A FeCo v FeNi D Ni Cr m Ni Cu q n

NiMn NiV

7 NiCu

01

8.5

I 9.0

I 9.5

10.0

8.0

8.5

9.0

/I-

Fig. 75. Mean magnetic moment per atom p,, plotted against the avcragc number PIof 3d and 4s electrons per atom for binary alloys with the same fee structure

Fig. 76. Mean magnetic moment per atom jj,, plotted against the average number II of 3d and 4s electrons per atom for binary alloys with the same bee structure

[63C4]. NiCu [SSA I]. FcCo, CoNi [29W I]. FcNi [63C4]. NiCr. NiV. NiMn [32S 11, CoCr, CoMn [57C2].

[63C4].

Bonnenberg, Hempel, Wijn

Table 14. Analyses of the magnetic moments of Fe, -xNi, alloys. pi,, is the mean localized atomic moment, pFeand pNi are the localized moments of the Fe and Ni atom, respectively. p,. is the conduction electron polarization per atom and pat the mean atomic moment derived from the magnitude of the volume magnetization. y is the fraction of 3d electrons in E, orbitals. X

0.34 0.50 0.505(10) 0.75

Sample single crystal, invar ‘) single crystal, disordered single crystal, 3” mosaic spread single crystal, disordered ordered

Y

Ref.

1.56

0.446 0.479 0.456(12)

7913 7913 73Cl

1.61(3)

0.49(3)

74M2

-

1.15“)

0.375(17)

73Cl

-0.07

1.22“)

0.462(13)“)

73Cl

T

PFe

PNi

K

PIOC

PC,

Pat

PB

PB

PB

PB

PB

300 77 300

1.80(H) 2.41(15) 2.54(16)

0.87(20) 0.82(5) 0.78(4)

1.48(2) 1.87(l) 1.66(8)

-0.18(3) -0.22(5) -0.10

300

-

-

1.78(2)

-0.17(3)

300

3.13(15)

0.63(5)

1.25

300

3.10(l)

0.680(5)

1.29

‘) In the disordered invar alloys, x = 0.40 and x = 0.37, a mean antiferromagnetic component is found at 4.2 K of p,, = 0.5(1) uB and 0.63(l) l.tB,respectively, where the bar refers to the average related to the various surroundings of the atoms in the disordered alloy [80 D 31. A Neel point TN= 15 K was derived from the temperature dependence of the peak intensity of the antiferromagnetic neutron scattering spectrum [73 D 11. ‘) See [53 W 11. 3, Applies to Fe atoms only.

1.2.1.2.4 Fe-Co-Ni: magnetic moment, g-factor

182

[Ref. p. 274

2.0 PE

1

1.5

1.5 I I+;1.0

0.5

0

0.6 Y-

0.3

0.9

0

1.2

Fig. 77. Depcndencc of the mean magnetic moment per atom A, derived from the extrapolated spontaneous mqnetixttion at OK and at atmospheric prcssurc on the hydrogen content of disordcrcd fee Fc, -,Ni,H, alloys. The dashed-dotted line is calculated for NiH; [78A I].

2.5

2.5

5.0 Al -

1.5 at%

Fig. 78. Mean magnetic moment per atom j,, vs. Al concentration for fee Fe -Ni--AI alloys [67 B 11.

I

Fe-Ni-Al

. Fe-Ni o 5at%Al A lOat%Al

1

1.5

n 1s"

1.0

0.5

0 8.00

8.25

8.50

8.75

9.00 /7-

9.25

9.50

9.75

Fig. 79. Mean magnetic moment per 3d-atom j&, vs. number n of valcncc electrons per atom for FcNikAI alloys [67 B I], solid triangles [39 S I]. The dashed line is calculated for random alloys containing 20at% Al.

Bonnenberg, Hempel, Wijn

10.00

Ref. p. 2741

0

1.2.1.2.4 Fe-Co-Ni: magnetic moment, g-factor

0.2

0.4

a

0.6

0.8

01

b

Fig. 80a. Mean magnetic moment per atom j,, for (I) Fe, -,Ni,, and (4 Feo.95-xW~o.05 (3) Feo.95 -xNi,Mno.05

0

1.0

x-

C77 M 21.

0.2

183

0.3

06

0.5

0.6

x-

Fig. 80b. Average magnetic moments of Mn atoms in FeNi alloys obtained at room temperatures by means of diffuse scattering of polarized neutrons. Circles: [83 I 11, triangle: [74C 11. Solid curve: theoretical prediction according to CPA theory [77 J 11, broken curve: experimental values by NMR [78 K 21.

I Fe

I CO

I Ni

9

10

I

%

B'

- Be Al Si . n + e -0 q o 0 8 e q e o q o

(Fe-Cr)-8' (Fe-V)- B' (Fe-Co)-B' Co-B' (Co-Ni)-B' (Fe-Nil-B' I

8X

8.5

8.6

8.7

8.8 /I-

8.9

9.0

9.1

5I.2 n-

Fig. 81. Mean magnetic moment per atom Pat vs. the number n of4s and 3d electrons for doped Fe, -,-,Ni,M, alloys [75 K 11. Curve

I

2

3

4

Y WI M

0

4.8

4.5

3.0

Co

Cu Ti

Landolt-Bornstein New Series III/l9a

5

6

7

8

9

5.0

8.0

Mn Mn Cr

5.0

8.8

Cr

11.0 Cr

Fig. 82. Initial variation of the mean magnetic moment per atom with the atomic concentration c of Be, Al or Si, dji,,/dc for various 3d alloys. The curves hold for values of c up to about lOat%. The alloys are designated by the number n of4s and 3d electrons per atom [71 B 11.Value for (Fe-NikAl from [67 B 11.

Bonnenberg, Hempel, Wijn

184

1.2.1.2.4

Fe-Co-Ni

[Ref. p. 274

magnetic moment, g-factor 00; I I -\

\

\

‘-A-/

/---I \ \

\ \ \ 1

050

000 a

nucleus

IlOOl-

L

Q,/$ ,/ ,@

0 ;; /

----/

,A

l/ _---

and %21Nio,79

Bonnenberg,

\ \

0

nucleus

2

C74S 51.C73 C

Hempel,

Fe0.1LNi0.86 disordered

/

Fig. 83. Magnetic moment density maps for Fe-Ni alloys as determined by polarized neutron technique. Contour lines arc labeled in [pn/A3]. Positive contours (solid lines) represent point dcnsitics while the zero contours (dashed lines) represent an average density within a sphere of radius 0.44,k (a) Parallel (100) planes for ordered FeNi, [73C 1J. @) (001) planes for disordered FC O.ld%.lh

,’

c \

0’ I I

nucleus

/

//I----

Wijn

Il.

Ref. p. 2741

1.2.1.2.4 Fe-Co-Ni:

magnetic

moment,

g-factor

185

2.16

I b232

2.08

2.04

0

20

40

60

80 wt% 100

NI2.00I Fe

0.2

0.4

x-

0.6

1.0 Ni

0.8

Fig. 84. Spectroscopic splitting factor g of Fe,-xNi, alloys. Open circles are the g values measured by ferromagnetic resonance [61 M 11. Solid symbols indicate g values derived from the magnetomechanical factor g’ through the relation l/g + l/g’ = 1. Squares: [44 B 11, triangles (upward): [52 B 11, triangles (downward): [56 S 11.Dashed line: calculated from the properties ofthe constituent elements.

Fig. 85. Spectroscopic splitting factor g of Fe-Ni alloys. Circles [76 B 21, disordered single crystals. The solid curve designates mean values obtained by [73P 1, 73 M 1, 610 11. For an FeNi, annealed ordered sample: dashed line. The lower point at 75 wt% Ni applies to an irradiated sample, considered to result in a higher degree of ordering [76 B 21.

ZJqIqq Fig. 86. Temperature dependence of the spectroscopic splitting factor g ofsingle crystals of FeNi alloys [76 B 21.

0

100

200

300 T-

400 “C 500

2.4

1.6 030

Landolt-Bbmstein New Series IIl/19a

0.15

0.20

0.25

0.30 x-

0.35

0.40

0.45

0.50

Fig. 87. Variation of the spectroscopic splitting factor g with composition for thin crystalline films of Fe, -,Ni, as determined from spin wave 0.55 spectra [72 B I].

Bonnenberg, Hempel, Wijn

[Ref. p. 274

1.2.1.2.4 Fe-Co-Ni: magnetic moment, g-factor

186

[ 2.2C

x \

Ni ’

2.15

I

I

I

I

1.90

1.95

75 EIOat%Ni

‘CO

g-2 =2I

ca 2.10

2D5 v Fe-Co 200 1 I

1.85

2

9’Fig. 88. Room-tempcraturc values of the spectroscopic splitting factor n plotted vs. the magnetomechanical 9’ factor for Fe -Ni, Fe Co, Co-Ni [61 M I]. The 9 value of Co has been extrapolated from the g of the Fe-Co and Co-Ni alloys. The numbers beside the points give the concentration in [at%] of the clement added.

Table 15. Atomic magnetic moments for Co,,,,Ni,,,, [65C 11. Alloy

PI31

IPro-PNil

co

0X9(2)

1.26(4)

1.14(2)

1.12(4)

0.25Ni0.75

%.s-Nio.5

0

0.25

0.50

and Co,,,Ni,,,

PNi

PC0

1.84(5) -0.05(5) 1.70(3) 0.58(3)

0.75

or

or

0.58(2) 1.21(2)

0.W) 1.70(3)

1.00

xFig. 89. Atomic magnetic moments pen and pNi in Co, -,Ni, alloys. Open circles: [65 C I], triangles: [63 C2, 63C3]. The curves drawn arc based on the coherent potential approximation (CPA) [77 M 41, see also [72 H I].

Bonnenberg, Hempel, Wijn

1.2.1.2.4 Fe-Co-Ni:

Ref. p. 2741

Table 16. Mean magnetic moment contributions [71 A 1,70 A 11, Ni [66 M 11. co o.91Feo.,,

Coo.65Nio.35 1.342(6) 0.105(6) 1.421(9) -0.184(12)

1.820(10) 0.135(8) 1.993(21) -0.308(25)

Pat Porb

Pspin PC0

magnetic moment, g-factor

per atom, in [pB], for fee Co-Ni alloys at room temperature

Coo.50Nio.50

%.25%75

1.173(23) 0.097(5) 1.217(8) -0.141(25)

0.876(5) 0.072(4) 0.927(6) -0.123(9)

3r 600 K

0.712(5) 0.062(4) 0.737(6) - 0.087(9)

\ f 1:

-. -.

240

:/

0.3

0.6

0.9

1.2

i

P

111

1.5

Fig. 90. Mean magnetic moment per 3d atom pa,t derived Tom low-temperature magnetization measurements and T, for hydrogenated Co, -,Ni, alloys. The H concentration is given by the ration between the number of H atoms and metal atoms [SOA 11.

\

-\ \ \~~

\ -\, \ \

Id 0

\ 1 \.

-1 -

1

". ;; 0

I 0.1

0

"');

IOOK

n-

LandoIl-Bbmstein New Series 11~19~3

i

t

I

0

\

h’T

2'

360

I Mn 0.02

\

1

I

0.579(5) 0.053(3) 0.621(5) -0.095(7)

I ~>l
IT

480

Ni

Coo.lo%90

“+A--~.~ f-b

IZ

187

0.2

0.3 x-

0.4

0.5

0.6

Fig. 91. The mean magnetic moment &,” of the Mn atoms in OxNil -xlo.9sMno.02 alloys [79S2]. Dashed line: calculation based on the coherent potential approximation (CPA) [76 J I].

Bonnenberg, Hempel, Wijn

1.2.1.2.4 Fe-Co-Ni: magnetic moment, g-factor

188

[Ref. p. 274

Te \\ ‘\O \‘1 \’ \ \ a&co ,/ -_ ’ \\‘\\\ \\ -0.008 \ /’

Fig. 92. Sections of magnetic moment density for Coo. l%.9 in (a) the (100) plane and (b) the (110) plane. as obtained by Fourier inversion of the magnetic structure factors. Contour lines arc labclled in [un/A3]. In the region removed from atomic positions the density is averaged over a cubic volume of edge 0.56 A [71 A I].

000

99

.r-\

/ ,/ ,’

/ \ L.--

\ ‘\, y\ 1 i

Table 17. Magnetomechanical ratio g’ for Co-Ni alloys, Fe content: 0.1...0.2at% [66S 11.

\ ‘\

-o.oo8p,8-3

Of

\ >

-\

\

\

---Y

\

,/ \ \

\ I

\

O/Y’

,/

,1-y”

I

I

I

Alloy

9’

Co-75 at% Ni Co-50 at% Ni Co-30 at% Ni Co-25 at% Ni Co-20 at % Ni Co-15 at% Ni Co-lOat% Ni

1.849(2) 1.846(3) 1.853(2) 1.857(2) 1X58(3) 1.854(2) 1.851(3)

00;

1

/

COJ.~ Ni, 0 .

__-- 1 ---

(’

0 0 . 0 x.-,“-- 0 0 -:- c .

0.6

1.0 Ni

Bonnenberg,

Fig. 93. Spectroscopic splitting factor g ofCo, -,Ni, alloys vs. composition. Open circles arc the g values mcasurcd by ferromagnetic resonance [61 M I]. Solid symbols indicate g values dcrivcd from the magnetomcchanical factor g’ through the relation l/g+l/g’= 1. Squares: [44 B I], triangle: [52 B I]. Dashed line: calculated from the propcrtics ofconstitucnt clcmcnts. Hempel,

Wijn

Ref. p. 2741

1.2.1.2.5 Fe-Co-Ni:

spontaneous magnetization,

Curie temperature

189

1.2.1.2.5 Spontaneousmagnetization, Curie temperature

9.0 9 Tic Fe-Co,Fe-Ni, Fe-Si 8.6

I 8.2 9F

600 650

i

I

750

I

“C

E

Fig. 95. Spontaneous magnetic moment c’s of the alloy as a function of temperature in the %dh,.5 vicinity of the atomic order-disorder transition temperature [78 B 21.

Table 18)Magnetization data for bee Fe, -$!o, alloys at OK [69B 11. X

0.05 0.10 60 80 wt% 100 0.20 Fe Co.Ni.Si Co.Ni,Si 0.28 Fig. 94. Spontaneous magnetic moment cs (OK) and 0.40 o, (290 K) for Fe-Co [29 W 11, Fe-Ni [29P 1, 21 and 0.50 Fe-Si [36 F l] alloys, as well as the density Q of these 0.60 alloys [62 K 21. 0.70

0 20 xl

Land&BOrnstein New Series llVl9a

o,(O)[G cm3g-l]

Lt CPBI

Slow cool

Fast quench

Slow cool

Fast quench

226.90 232.39 240.33 242.00 240.20 236.04 222.92 211.00

226.90 232.39 240.50 242.00 237.37 229.16 219.94 209.96

2.275 2.336 2.429 2.457 2.456 2.425 2.303 2.192

2.275 2.336 2.431 2.457 2.425 2.355 2.272 2.181

Bonnenberg, Hempel, Wijn

1.2.1.2.5 Fe-Co-Ni: spontaneous magnetization, Curie temperature

190

[Ref. p. 274

163.0 I Gcm3 Fe-Co I Is925

178 GT' 9 175

I

162.0

b

161.5

I

161.0 16OSr 30

33

36

39

L2

I 15 kOe 19

HVP’ b Fig. 96a. b. High-ticld portions of the magnetization curves at 4.2K for Fe-Co alloys [73 W 23. (a) 0...8.06 at% Fe, (b) 0...0.89 at% Fe.

zc

25

30

a

35

45 kOe 50

40

o-p!Hy

I Gci,? So Co0.9de0.0t2

’

I

I

Fig. 96~. Room-tempcraturc magnetization curves along the o axis and c axis of a single crystal of Co,,,,Fe,,,,,. The numbers I...6 and the arrows indicate the sequence of the mcasurcmcnts. The curves 5 and 6 were measured after applying a field of 18kOe parallel to the c axis for 30 nun-and 3-h, rcspcctivcly [83T 21.

I

I

2oc Gem' Q

Hopp:= 5kOe

15c

I b IOC

0

V

I

I

I

I

3

6

9 Ho>,, -

12

C

I

I

15 kOe 18

Ni

0

0.16

0.08

0.21,

x-

Fig. 98. Magnetic moment u in a magnetic field of about 5 kOe vs. composition for Fe,,,,(Ni, -rCo,)0,35 and Feo.6S(Ni,-,Mn,h.35

F? 01“i.

20

60

80 -

CO

alloys C74E

II.

Fig. 97. Room-temperature volume magnetization. 4rrh4, in a magnetic field of 1.5kOc for Fe -CoPNi alloys [62 K 21, originally from [27 K 1, 28 E I, 29 E I, 29 M I]. Broken curves arc the Curie tcmpcraturcs Tc.

Fe

Bonnenberg, Hempel, Wijn

1.2.1.2.5 Fe-Co-Ni: spontaneous magnetization, Curie temperature .

Ref. p. 2741

bee

/

191

/-

fee

1’ 900 I b-Y 600

I

01 0 Fe

20

40

60 co -

’

I

90 at% :OO co

Fig. 99. Curie temperatures in the binary alloy system FeCo [5SH 11.

I -4.0

400

Q -4.5 ?

350

s -5.0

300

-5.5

250

-6.0

0.10 x-

-6.5 ( 0

0:15

Fig. 101. Curie temperature Tc vs. composition for (solid and (open circles) circles) Feo.6dW -xCo,h35 %65WLMnxh35

alloys C74E

11.

0.6

0.8

1.0

co

Fig. 100. Curie temperature of fee Fe,-$0, alloys precipitated from Cu as a function of Co concentration. The solid lines indicate the Curie temperature of bulk alloys [69 N 11.

450

0.05

0.4

x-

500

200 2ooON 0

Landolt-Bbmctein New Series lll/l9a

0.2

-3.0 K kbar -3.5

550 K

t k-!!

0

Fe

0.05

0.10 x-

0.15

0.20

Fig. 102. Pressure derivative of the Curie temperature, dTJdp, as a function of composition in Feo,dW -xCox1~.35and in Feo,60Jil -xMnxh.35 alloys [74E 11.

Bonnenberg, Hempel, Wijn

192

1.2.1.2.5 Fe-Co-Ni: spontaneous magnetization, Curie temperature 200

10000 9

Gcm3 9

cm!

175

8750

7500 6250

I 125

b

100

5000 I 7s

,

3750

I

2500

,

1253

1 II

100

200

300

LOO

500

600

0 700 K 800

I-

Fig. 103.Magnetic moment per gram u at ticld strength of 2 kOc and 8 kOc (lower and upper solid curves through circles. rcspcctivcly). and the reciprocal values of the magnetic mass susceptibility xp (dashed curves through trianglcs)as functions oftempcraturc for Fc, -INi, alloys. When the measuring tcmpcraturcs wcrc lowcrcd, the x=0.3 and x=0.328 alloys underwent a martcnsitic transformation. starting at 256 K and I48 K, rcspcctivcly [6l K I].

1st

I 101

b

0 a

100

200

300 I-

400

500

Fig. 104. (a) Magnetic moment per gram r~in a magnetic licld of 7.79 kOe and (b) the extrapolated ferromagnetic Curie tcmpcraturc T, (02=0) mcasurcd on vacuumanncalcd single crystals ofFc, -,Ni, invar alloys [73 H I]. see also [7902. 77Y I].

Bonnenberg, Hempel, Wijn

"C

600

[Ref. p. 274

Ref. p. 2741

1.2.1.2.5 Fe-Co-Ni: spontaneous magnetization, Curie temperature

193

1.; 40' g&l 92

01 I

“b 0.4

1 = k.2 K

165 160 I b 155 b lL5.65

c

162.05 !

130 0 a

50

100 H-

1

150kOe 2‘00 b

Fig. 105a. Magnetic moment per unit mass (r vs. internal magnetic field H for a single crystal of Fe,,,,,Ni,,,,, along the easy axis of magnetization. At the lower temperature a hysteresis is found when a field above a certain critical field H,, is applied. At 4.2K, H,, =60(10)kOe for Fe,,,,,Ni,,,,, [83P 11, see also [8ON I].

Landolt-Bdmkn New Series lll/l9a

0

I

I

I

I

3

6

9

12

I

15 kOe 18

HOPP’ -

Fig. 105b. Variation of the magnetic moment per gram with applied magnetic field, Happ,, at a temperature of 4.2 K for spherical single crystals of fee Fe, -XNi, alloys. The arrows indicate the magnitude of the demagnetizing field strength H, [83N2].

Bonnenberg, Hempel, Wijn

1.2.1.2.5 Fe-Co-Ni: spontaneous magnetization, Curie temperature

194

[Ref. p. 274

160r Gcm3 9

0.15

120 HcJs'=l5OkDe

\

~

I

I d 80

e G.iO 2 I

0.05

3.k

40

4

E

I

-L

5

0

10 I-

0 increasing . decreasing

0

15 K

Fig. 106. Maximum contribution of the mctamagnctism ofweak amplitude,cr,,,,. as dependent on tcmpcraturc for an b 6&‘i~.3sJ invnr alloy in a maynctic field up to I50 kOe. The spontaneous ferromagnetic moment at 0 K is about 176Gcm3g-’ [SOY I].

I

0 increasing . decreasing I 0

I 7

100

"C 600

I-

Fig. 107. Spontaneous magnetic moment G, for FeNi,. Open circles: measured with increasing tcmpcraturc; solid circles: measured with decreasing temperature. the cooling rate being too rapid for ordering. Curve 1: sample cooled at 0.23 “C/h, 2: sample cooled at I .37 ‘C/h, both rates slow enough to obtain a relatively high degree of ordering [53 W I].

1 T

0

-2K

0

200 I-

400

"C 600

Fig. 10s. Spontaneous magnetic moment gs for two Fc -Ni alloys. Open circles: mcnsurcd with increasing tempcraturc. solid circles: measured with dccrcnsing tcmpcraturc. cooling rate 0.23 ‘C/h [53 W I]. 0

Fe

0.2

OX

0.6 x-

0.8

1.0 Ni

Fig. 109.Extrapolated spontaneous magnetization at 0 K. vs. composition for fee Fe,-,Ni, alloys. Solid line: [Sl B 11. solid circles: [72 B I], open circles: [73 M I].

Bonnenberg, Hempel, Wijn

Ref. p. 2741

1.2.1.2.5 Fe-Co-Ni: spontaneous magnetization, Curie temperature

Table 19. Spontaneous magnetization per gram at OK, a,(O), and Curie temperature Tc for various fee Fe, -.Ni, alloys [53 W 11. X

0.45 0.50 0.55 0.60 0.65 0.68 0.70 0.72 0.74 0.75 0.76 0.78 0.80 0.81 0.85

o,(O)[Gcm3 g-l]

T, iX1

Rapidly cooled (disordered)

Slowly cooled (ordered)

Rapidly cooled (disordered)

Slowly cooled (ordered)

168.6 160.5 152.4 143.6 133.4 128.6 124.0 120.0 115.8 113.4 111.3 106.4 101.9 98.8 90.2

170.3 162.1 154.0 144.7 135.9 131.7 128.0 124.6 121.0 118.8 116.0 107.7 102.9 100.6 91.0

468(2) 520 558 592 613 616 614 608 600 598 589 585 577 571 543

494(5) 543 580 616 636 668 680 696 691 681 654 624 599 584 543

Fig. 110. Reduced spontaneous magnetic moment a&,(OK) as a function of reduced temperature T/T, for fee alloys Fe, -,Ni, [63 C4].

Landolt-BBrnstein New Series 111/19a

Bonnenberg, Hempel, Wijn

195

196

1.2.1.2.5 Fe-Co-Ni:

spontaneous

magnetization,

[Ref. p. 274

Curie temperature

Fig. 1I I. Solid circles show the rcduccd spontaneous magncti7ation o/u,, as a function ofrcduccd temperatures T/7’,‘, for the invar alloy u,=125Gcm3g-‘,

1.0

717,-

I 0

0.05

1.c: -

.

0.10 . L

The small amount of Mn lowers the temperature of the martcnsitic transition to the bee phase from l30K to below 4.2 K. (The curve is the result of local molecular ticld calculations.) Open circles rcprcsent the relative values of the avcragc effective hypcrfinc field. /I = l?hyp,erl/&,efr (4.2 K). I?,,,,,,, (4.2 K)= 280 kOc. The average refers to the various neighborhoods ofan Fe atom [75M I]. For the local environment effect. see also [83 K I], For a comparison of the temperature depcndcncc of the magnetization with the integrated intcnsity of the magnon spectra. see [79 123.

1000 Y

0.15 I 10

T,=413(2)K

/

G Fe,., Ni,

0.20 Ni /

Y c.93 3 <-“ \

r/7, n

nnz

750

-

Y

n,n

I 2 500

250

n

VI

0

30

90

60

120

K 150

I

I

I

I

-100

0

100

200

1

K 300

7-&-

I-

Fig. 112. Expcrimcntally dctcrmincd tcmpcraturc variations of the rcduccd mngncti7ation MS/M, (OK) for Fc,,,Ni,,, and Fc,,,,Ni,,,, single crystals. For comparison also the results for pure Ni arc given. The solid curves arc calculated by spin wave theory using the spin wave stiffness constants of Fig. 551 [8l 0 23. See also [SOI I. 76K I].

Fig. 113. Temperature depcndcncc of the held-induced magnetization M measured with a pulse field of 1000kOe for various invar alloys Fe, -,Ni, in the paramagnetic state. Ni data arc given for comparison. The temperature scale is shifted for each material in such a way that their Curie points T, fall togcthcr [77 H I]. For more evidence regarding a magnetic phase transition brought about by an external magnetic field. see [82 W I].

Bonnenberg, Hempel, Wijn

Ref. p. 2741

197

1.2.1.2.5 Fe-Co-Ni: spontaneous magnetization, Curie temperature

0 .I@ bar0 w5 atm-’

-0.5

0

RT ==--.-

I

-1.0

%

I 4

-ig -1.5

-3

-2.0

-4 a

0 Fe

0.2

0.4

0.6

7

-2.5 0.30

0.8

x-

I

I 8

12

I 16 kbar 20

P-

Fig. 114~. Pressure dependence of the relative magnetization M/M(p=O) ofa fee Fe0.65Ni,,,, alloy at 4.2 K and room temperature [81 H 21.

Land&-BBrnstein New Series 111/19a

0.42

Fig. 114b. Relative change of the spontaneous magnetic moment with pressure vs. Ni concentration at various temperatures for Fe, -,Ni, invar alloys [69 M I].

f 0.8

I 4

0.38 x-

;;t 0.9 II 4 r

0.7I cl

62 K ‘I

0.34

b

Fig. 114a. Relative change of the spontaneous magnetic moment under a change of the applied hydrostatic pressure for Fe,-.Ni, alloys at room temperature. 1 atme 1.013bar. Open circles: [37 E 11, squares: [58 G 11, triangles: [59K 11, solid circles: [61 K 11.

0 RT A I=77K

Bonnenberg, Hempel, Wijn

1.2.1.2.5 Fe-Co-Ni: spontaneous magnetization, Curie temperature

198

0

30 kg/mrr2

20

10

[Ref. p. 274

LC

Fig. 115.Increase ofthe magnetization. AM, in a magnetic field of 950Oc, resulting from an applied mechanical tension u within, or somewhat above, the elastic limit for Fe-Ni invar alloys. The results are closely related to incomplete a+y transitions as revealed by X-ray spectra [80T4]. I kg/mm’c98.0665 bar. (a) Invar with 30,3l or 35 wt% Ni: room-tempcraturc curves. reversible. Invar with (b) 34 wt% Ni and (c) 36 wt% Ni: curves for various temperatures. Invar with (d) 32 wt% Ni and (e) 36wt% Ni: increasing (open circles), decreasing (solid circles) tension. The highest tension is beyond the elastic limit.

r

0 0

10

20

30

kg/mm2

4

Fig. 116. Relative change of the room-tempcraturc spontaneous magnetization A~,/~, of invar-type FeNi alloys as caused by plastic deformation. The degree of deformation is semi-quantitatively expressed by the avcrage strain E over the specimen [71 E I]. For 36wt% Ni values for AG,/G, of -0.013 and -0.024 were found for E= 0.07 and 0.14, respectively [73 V I].

28

Bonnenberg, Hempel, Wijn

30

32

3L Ni -

36 ~1% 38

199

1.2.1.2.5 Fe-Co-Ni: spontaneous magnetization, Curie temperature

Ref. p. 2741

I Feo.ssNlo.34

60 Gcm3 9 5.5 40-” 40~” cm3 9 5.0

I

I

40

0 as irrodioted . I=675K. Ih n 723K. Ih . 993K. Ih

I

b 20 Happl= 2 kOe

4.0

65 l

I

I

0

(110) [OOII roll

A . fnnlirllnl

40

20

rnll

60

I L

b

0

I 4.5 2

3

550

450

650

T-

K

Fig. 118. Influence of neutron irradiation and annealing on the magnetization vs. temperature curve of an Fe 0.d%34 invar alloy. Magnetization measured at the field strength of 2 kOe, irradiation with 1MeV neutrons, 1.72. 1013 neutrons/scm’ for 6 days [83 M 21.

I

13.5 3.5 % 100

80

RFig. 117. Changes in spontaneous magnetic moment per gram, 0, and in high-field susceptibility xHF as a function of roll reduction R for a fee single crystal of Fe,,,,Ni,,,,. The reduction of thickness of the disk was performed in steps, each reduction step being about 10...15% reduction in thickness [68 C 11.

-0.5l

20

0

40

60

80

K 100

T-

Fig. 119. Temperature dependence of the displacement Hdispl and the half width H, of the hysteresis loop for a monocrystal Fe,,64Ni,,3, alloy. Similar results obtained for Fe concentrations between 50 and 90 at% indicate the presence of a unidirectional anisotropy, possibly caused by the presence ofboth a ferro - and an antiferromagnetic phase [83 R 11.

I

1.25

z 1.00

0

kG

I

I

Fe0.685 Ni0.315 - c

fee

A I

a

0

I

I

51 0

100

150

200

250

300 “C 350

T-

Fig. 120. (a) Temperature dependence of the magnetization per unit volume, M, for a fee Fe,,,,,Ni,,,,, alloy with various concentrations of C, measuring field strength 8 kOe. Samples quenched from above 750°C in water. Samples measured at increasing temperatures. @) M vs. T as in (a) but now measured at decreasing temperatures after a preceeding heating up to 370 “C [69A 11. Land&Bbmstein New Series 111/19a

b

-273 -200

Bonnenberg, Hempel, Wijn

-100

100

0

I-

200

300 “C 400

1.2.1.2.5 Fe-Co-Ni: spontaneous magnetization, Curie temperature

200

1

2.1

kG Fe,.,Ni, -C 2.0

1.81

0.9 I 0

fee

,

I

[Ref. p. 274

I 7 = 30°C Hops,7 8kOe-

V.V”J

I

I

0.2

0.4

0.6 0.8 wt % 1.0 cFig. 120~.Magnetization mcasurcd in a field of 8 kOc of fee Fe, -,Ni, alloys with various concentration ofC. The samples wcrc qucnchcd to room tcmpcraturc. The measuring points dcnotcd L wcrc found after annealing for 20 h at 450 “C. Measuring temperature 30 “C [69A I]. C

6 Feo.sgR Nim: C0s.o~~

1.5 kli I 1.0 i

3.5

l-

l-

Fig. 121. Tempcraturc dependence of the spontaneous magnetic moment per unit volume M, as well as the temperature dcpcndcncc of the forced linear magnctostriction in high magnetic liclds, CV./aH, for the alloys Fe-Ni. FeNiXu and Fc -Ni-Co [7l K I].

Bonnenberg, Hempel, Wijn

I-

Ref. p. 2741

201

1.2.1.2.5 Fe-Co-Ni: spontaneous magnetization, Curie temperature

0

1

2 3 cu -

4 at% 5 0

3

4 at% 5 0

2

1

3

4 at% 5

Mn-

120 Gcm3 1910

80

0

12

2

4 at%

MO-

Fig. 122. Spontaneous magnetic moment per unit mass, crs,at room temperature, vs. the concentration of various additives to ordered and disordered alloys of FeNi,

[53 W 11. Open circles: cooled at 0.23 “C/h, solid circles: cooled rapidly in furnace, triangles: air quenched from 700 “C, squares: water quenched from 700 “C. 1000

Table 20a. Change of the Curie temperature with hydrostatic pressure for Fe-Ni alloys [72 L 11. Composition

6

Al-

K

T,

ts(p=O)

K

K kbar-’

800

600

Fe Fe-30 wt% Ni Fe-36 wt% Ni Fe-53 wt% Ni Fe-64 wt % Ni Fe-75 wt% Ni Fe-93 wt% Ni

1044 334 491 788 873 858 708

0 -4.9 -3.5 -1.66 -0.40 0.60 0.52

Table 20b. Change of the Curie temperature of invartype Fe-Ni alloys under influence of a hydrostatic pressure p. The Curie temperature is derived from permeability measurements [72 D 11, see also [68W 11. Composition

T, K

Fe-28 at % Ni Fe-29 at% Ni Fe-30 at% Ni Fe-3 1 at % Ni Fe-32 at % Ni Fe-33 at% Ni Fe-34 at% Ni Fe-35 at% Ni Fe-36 at% Ni Fe42 at % Ni Landolt-Bbmstein New Series 111/19a

278 301 381 400 417 429 470 521 574 667

K kbar-’ -7.7(3) -7.0(2) -5.2(2) -4.8(2) -4.8(3) -5.0(3) -4.5(3) -3.9(2) -3.5(l) -2.6(l)

I

hy 400

200I-

0I_

0 Fe

I

I

I

I

I

0.2

0.4

0.6

0.8

1.0 NI

xFig. 123. Dependence of Curie temperature Tc on composition for fee Fe,-,Ni, binary alloys. Solid circles: [63 C4], open circles: [69A3]. See also [68 B 11.

Table 20~. Change of the Curie temperature with hydrostatic pressure for Co-Ni alloys [72 L 11. dT, -j-$=0)

Composition

K kbar-’

co Co-30 Co-45 Co-60 Co-75 Co-93

1398

wt% Ni wt% Ni

1219 1125

wt% Ni wt% Ni wt% Ni

1022 903 723 627

Ni

Bonnenberg, Hempel, Wijn

0 0.55 0.84 0.76 0.68 0.66 0.36

1.2.1.2.5 Fe-Co-Ni: spontaneous magnetization, Curie temperature

202

633

Fig. 124. Evidence for a low-tempcraturc short-range antifcrromagnetic ordering in the ferromagnetic matrix of invar type Fe, -,Ni, alloys has been derived from smallangle neutron scattering. In the magnetic phase diagram Tc dcnotcs the ferromagnetic Curie temperature of the long-range ferromagnetic ordering and 7” is the upper limit of the tempcraturc for the existence of the shortrange antiferromagnetically ordered clusters. From an analysis of low-tempcraturc Miissbauer spectra of powder samples the N&cl tcmpcraturcs TN of the alloys were found to range from 24 to 30 K for values ofx from 0.18 to 0.28 [74 C 53. The broken curve denotes the ferromagnetic Curie temperature T, of the fee phase when no martcnsitic phase transformation would have occurred (M, is proportional to the spontaneous magnetization of the ferromagnetic phase.) [79G I]. See also [73 D 1, 75 M 3, 77 M 23, for a model, see [79 K I].

K

40: I k 20:

c

1

53

[Ref. p. 274

8.4

8.8

'

000

kO

K

40

800

30 I = =. ", s'

600

20

400

1

600 200

10

t 500 P-!? 0 Fe

x-

400

Fig. 125. FCCmagnetic phase diagram of the Fe,-,Ni, alloys, showing the Curie tempcraturc and the N&cl tcmpcraturc (Ts for xSO.22). as well as the effcctivc hypertine fields Hhjp,rrI for “Fe at 4.2 K. )I indicates the number of 4s and 3d electrons per atom [79 G 21.

300 028

036

032

040

x-

Fig. 126. Time dcpcndcnce of the Curie points of various Fe, -INi, invar alloys, derived from mcasuremcnts of the magnetic permeability. The points ofcurve 2 were mcasured aRcr storage of the samples of curve I at room tempcraturc for four years [74 D I, 80 D 23.

Bonnenberg, Hempel, Wijn

203

1.2.1.2.5 Fe-Co-Ni: spontaneous magnetization, Curie temperature

Ref. p. 2741

2

1000

K kbar

K Fe-Ni r, ,

800

600 I hy 400 -80

-100 -120 0

IO

20

\ 30

40

50 kbar 60

02r-8

80 wt%

P-

100

NI-

Fig. 127. Pressure shift of the Curie temperature, AT,, for fee Fe-Ni alloys [72 L 11. See also [54P 1, 61 K 11, for theory, see [83 F 1, 81 W 11.

Fig. 128. Curie temperature T, and the pressure derivative ofthe Curie temperature dTJdp for Fe-Ni alloys [72 L 11.

650 K

K

600

600

I

550

b-Y500 400I 200

1 350

I 500

650

/-

800

950 K 1100

Fig. 129. Effect of annealing at various temperatures on the Curie temperature of an Fe,,,,Ni,,,, invar alloy irradiated with 1.72. 1013 neutrons/scm’ for 6 days. Neutron energy: 1 MeV. Annealing effect on a splat quenched sample [8OM l] is given for comparison [83 M 21.

500 I 625 450 400 350 300

3ooOW 0

5

IO

15

20 kbar 25

Fig. 130. Dependence of the Curie temperature Tc on the hydrogen pressure pH2for the alloys Fe,-.Ni,. Open circles refer to hydrogen atmosphere, solid circles to an atmosphere of an inert gas [76P 11.

Land&-Bbmstein New Series 111/19a

Bonnenberg, Hempel, Wijn

204

1.2.1.2.5 Fe-Co-Ni: spontaneous magnetization, Curie temperature OJLl

90

,

K FeiFxNix-C

-

ok I

[Ref. p. 274

I

dp\ Fe,.,Ni,-Zat%C \

60

? I? n

\ ‘P

30

0 0.20

0.25

0.30

0.35

b

xFig. 13lb. Influcncc of the C content on the Curie temperature of fee Fc, -,Ni, invar alloys. The measurin_r points apply to a concentration c of about 2at% C [68 B I], see also [69A 1, 67 G I].

a cFig. 131n. Influence of C on the Curie tcmpcraturc of Fe,. ..Ni, alloys. Solid circles: [68 B I]. crosses: [Sl L I].

1.5,

I

/

/

“1 Fei_,Ni,-Ti

/

/

/

1.2

I

0.9

f ‘

OE

0.3

0 ___

Fig. 132. Influence ofTi on (a) the low-tcmpcrature value ofthc spontaneous magnetization M, and (b)on the Curie tcmpcrature T, of fee Fe, -,Ni, alloys [73 K 21. Curve

1

2

3

4

5

6

at%Ti

0

0.72

2.0

2.6

3.0

4.75

Bonnenberg, Hempel, Wijn

205

1.2.1.2.5 Fe-Co-Ni: spontaneous magnetization, Curie temperature

Ref. p. 2741 800

800

K

K

700

700

600

600 I 500 h”

t ,500

400

400 3oc 2OC 0.25

0.30

0.35

0.40

0.45

I

I

U

x-

800,

I

I

8001

I

KI

I

I

I

I

I

I

I

600

600

I 500 62

I so0 &y

400

400

300 2001 0.25

I 0.30

I 0.35

I 0.40

I 0.45

0.50

2001 0.25

I 0.35

I 0.30

I

I

0.40

0.45

0

x-

X----c

Fig. 133.Influence ofvarious additives on the Curie points offcc Fe, -xNi, invar alloys. The specimens were annealed for 2 h at 900 “C and furnace-coled. The C-containing samples were quenched in water [73 K 11. See also [68 K 1 and 70K 11. 625, I I I I I I I “C Feh3-Fe eN&Cu

I

575 2

t

-

FeNi - Ni I I I

FeNi,-Mn

1 550 h” 525 500

475 Fig. 134. Influence of solute atoms on the Curie temperature of disordered FeNi, [53 W 11.

450 o

I

2

3

4 soiute

Land&-Bdmstein New Series 111/19n

Bonnenberg, Hempel, Wijn

5 -

6

7 at%

1.2.1.2.5 Fe-Co-Ni: spontaneous magnetization, Curie temperature

[Ref. p. 274

lkbor 1.0 -K kbor 0.8

0

20

40

60

80 v/t % 100

NI -

Fig. 135.Curie tcmpcraturc T, and prcssurc derivative of the Curie tcmpcraturc. dT,idp. as a function of Ni concentration in Co -Ni alloys [72 L I].

450 40-L

1 H-m..

450 .10-G

300 0

II

lllrll

I 7\

100

200

300

HL.,

400

1111111

500 "i

600

:ip 136 Maqnrfi7ntinn nfCo0,25Ni0,75 single crystals as ..__..__.. -I-r..-- .icld of 1.3kA/m (16.3 kOe) at various temperatures. Open circles: measured directly lftcr applying the magnetic field. solid circles: measured j000..~20000min after application of the magnetic field .n, L&M 21

Bonnenberg, Hempel, Wijn

Ref. p. 2741

1.2.1.2.6 Fe-Co-Ni:

high-field susceptibility

207

1.2.1.2.6 High-field susceptibility For theories, models and calculations, see[SOS 1,79 H 1, 79 I 1, 79 S 3, 79 Y 2,77 K 2,72 H 1, 71 S 3, 69 S 23.

/J4

+I 4 -cm3 cm3

1.2 mg

rJ.Bm

I A

2

atomA

0.8 0.6 l

0.2

0.4 0.6 0.8 1.0 xFig. 138.High-field susceptibility xHFof Fe, -.Ni, alloys, measuredin a magnetic field of 40 kOe at liquid helium temperature [79 R 1, 72R2, 74R 11. 0

H’ 0.4

0 0

0.2

0.4

Fe

0.6

0.8

1.0 co

x-

Fig. 137.High-field susceptibility xHFfor Fe, $0, alloys [66 S2,69 S41.n: number of4s and 3d electronsper atom, xs: spin wave contribution, xp: Pauli-paramagnetism contribution, xorb:orbital contribution, xdia:total diamagnetic contribution.

Table 21. The high-field susceptibility xHFas measuredat various temperatures for Fe-Co and Fe-Ni alloys. The spin wave contribution to the high-field susceptibility, ~u~,~,was calculated taking into account total exchange energies W [69S4]. 10-12~Batom-1A-‘m~0.444~10-6cm3mol-1. Alloy Fe

co

Ni

at% 100 94.4 83.6 73.8 69.7 65.0 49.7 25.5 7.5 91.1 80.4 71.1 0 0

0 5.6 16.4 26.2 30.3 35.0 50.3 74.5 92.5 0 0 0 (single) (POlY)

Land&-Bbmstein New Series 111/19a

0 0 0 0 0 0 0 0 0 8.9 19.6 28.9 100 100

T,

XHF

K

10-‘2~Batom-‘A-‘m 4.2 K 77K

1043 1104 1210 1272 1313 1340 1405 1260 1340 1023 993 863 631 631

520(35) 530(35) 500(35) 360(35) 360(35) 300(35) 310(35) 290(35) 430(35) 630(35) 630(35) 1400(90) 290(35) 300(25)

W

XHF,S

595(35) 555(35) 585(35) 455(35) 445(35) 400(35) 385(35) 350(35) 540(35) 870(35) 890(35) 1960(60) 330(35)

301K 1060(50) 1120(50) 1290(50) 920(50) 900(50) 670(50) 700(50) 540(50) 990(50) 1580(60) 1650(120) 725(35)

Bonnenberg, Hempel, Wijn

10-12u,atom-’ A-’ m 77K 301K eV 105(15) lOO(15) 90(15) 85(15) 80(15) 80(15) 70(15) 75(15)

590(80) 555(80) 500(80) 475(80) 460(80) 450(80) 410(80) 425(80)

0.21 0.22 0.23 0.24 0.25 0.25 0.26 0.29

llO(15) 115(15)

625(80) 645(80)

0.22 0.22

70(5)

440(30)

Ref. p. 2741

1.2.1.2.6 Fe-Co-Ni:

high-field susceptibility

207

1.2.1.2.6 High-field susceptibility For theories, models and calculations, see[SOS 1,79 H 1, 79 I 1, 79 S 3, 79 Y 2,77 K 2,72 H 1, 71 S 3, 69 S 23.

/J4

+I 4 -cm3 cm3

1.2 mg

rJ.Bm

I A

2

atomA

0.8 0.6 l

0.2

0.4 0.6 0.8 1.0 xFig. 138.High-field susceptibility xHFof Fe, -.Ni, alloys, measuredin a magnetic field of 40 kOe at liquid helium temperature [79 R 1, 72R2, 74R 11. 0

H’ 0.4

0 0

0.2

0.4

Fe

0.6

0.8

1.0 co

x-

Fig. 137.High-field susceptibility xHFfor Fe, $0, alloys [66 S2,69 S41.n: number of4s and 3d electronsper atom, xs: spin wave contribution, xp: Pauli-paramagnetism contribution, xorb:orbital contribution, xdia:total diamagnetic contribution.

Table 21. The high-field susceptibility xHFas measuredat various temperatures for Fe-Co and Fe-Ni alloys. The spin wave contribution to the high-field susceptibility, ~u~,~,was calculated taking into account total exchange energies W [69S4]. 10-12~Batom-1A-‘m~0.444~10-6cm3mol-1. Alloy Fe

co

Ni

at% 100 94.4 83.6 73.8 69.7 65.0 49.7 25.5 7.5 91.1 80.4 71.1 0 0

0 5.6 16.4 26.2 30.3 35.0 50.3 74.5 92.5 0 0 0 (single) (POlY)

Land&-Bbmstein New Series 111/19a

0 0 0 0 0 0 0 0 0 8.9 19.6 28.9 100 100

T,

XHF

K

10-‘2~Batom-‘A-‘m 4.2 K 77K

1043 1104 1210 1272 1313 1340 1405 1260 1340 1023 993 863 631 631

520(35) 530(35) 500(35) 360(35) 360(35) 300(35) 310(35) 290(35) 430(35) 630(35) 630(35) 1400(90) 290(35) 300(25)

W

XHF,S

595(35) 555(35) 585(35) 455(35) 445(35) 400(35) 385(35) 350(35) 540(35) 870(35) 890(35) 1960(60) 330(35)

301K 1060(50) 1120(50) 1290(50) 920(50) 900(50) 670(50) 700(50) 540(50) 990(50) 1580(60) 1650(120) 725(35)

Bonnenberg, Hempel, Wijn

10-12u,atom-’ A-’ m 77K 301K eV 105(15) lOO(15) 90(15) 85(15) 80(15) 80(15) 70(15) 75(15)

590(80) 555(80) 500(80) 475(80) 460(80) 450(80) 410(80) 425(80)

0.21 0.22 0.23 0.24 0.25 0.25 0.26 0.29

llO(15) 115(15)

625(80) 645(80)

0.22 0.22

70(5)

440(30)

[Ref. p. 274

1.2.1.2.6 Fe-Co-Ni: high-field susceptibility

20s

5.0 ,

Fe;-x Ni,

I

I

I

I

/

I

@ Fe,.x Ni,

H = LOkOe

cm3 9 fee

-I1

H = 4OkOe.IlOOi

i i Lb-4 i i I -

3.5 3.0 I % 2.5

u

I

x

7”

L.”

253 303

350 400 450

a

500 550 600

v-

650 K 700

I-

1.5

L,

-n

/

\

Fig. 139~ High-field susceptibility x,,r of Fe, -,Ni, invar alloys mcnsurcd in a mngnctic ticld of 4OkOc and in a temperature range from room tcmpcraturc up to above the Curie tempcraturc T, [79 Y 31. 250 300

350

400 150 500 550

600

650 K 703

Ib Fig. l39b. The high-field susceptibility at higher temperatures for some single crystals of fee Fe, -,Ni, invar alloys [83Y I].

9 w

2.5 0 253 C

cm3 mol 303 350

400 450 500 550

600 650 K 700

I-

7

Fig. 139~. Temperature dependcncc of the high-ticld susceptibility lur for a single crystal ofan Fe,,,,,Ni,,,,, invar alloy at two diffcrcnt internal mngnctic ficld strcn_rths [84Y I].

6 I 5 k x4

150 200 250 K 3 IFig. 140. Temperature dependence of the high-ticld susceptibility I,,~ mcasurcd bctwccn 30 and 80 kOc for various fee Fe, -,Ni, alloys [7l Y I]. Seealso [71 H I] and [77 Y I] for comparable results. 0

Bonnenberg,

Hempel,

50

Wijn

100

Ref. p. 2741

_8.0

1.2.1.2.6 Fe-Co-Ni: high-field susceptibility

8.2

fl8.4

8.6

8.8

(

209

2.0 luq yBm itom A 1.8

1.6

1.2 t 1.0 & w 0.8

I IO GE

0.6

0.4

3.2

0

40

0 i

Fig. 141. Susceptibility in high-fields (2...16 MA/ mr25...201 kOe) as a function of the composition Fe,-.Ni, at various temperatures. n: number of 4s and 3d electrons per atom, xorb: contribution of orbital paramagnetism, xdia: total diamagnetic contribution [69S4], see also [66S2].

80

120

160

200

240

280kOe320

H-

a 16 .10-c cm3 cm3 12 IO I E8 6

0 120 160 200 240 280kOe320 40 80 Hb Fig. 142. High-field susceptibility xHF ofthe fee invar type alloys Fe, -xNi, and (Fe, -xNi,),,,,Cr,,,, as dependent on field strength H. The Cr content stabilizies the fee structure. (a) T=300 K, (b) T=4.2 K [740 11.

Landolt-Bornctein New Series lll/l9a

Bonnenberg, Hempel, Wijn

1.2.1.2.7 Fe-Co-Ni: magnetocrystalline anisotropy

210 7 .lO 3 cm! mol

-

Fe-Ni o measured

1

0 8.53 8.55 8.60 8.65 8.70 8.75 8.80 8.85 8.90 8.95 9.00 fl-

Fig. 143. High-field susceptibility z,,,- mcasurcd or cxtrapolatcd V~LICS. at 4.2 K as dcpcndcnt on the number II of outer electrons per atom of Fe Ni alloys and of FCo.~0~sNio.~~~oMno.o~,6[71 Y I]. The dotted curve is calculated according to the rigid band model [69 S 23.

1.2.1.2.7 Magnetocrystalline

anisotropy

Ni

80

1 Fe

10

20

30

10

50

60

70

80 90

co

Fig. 144. Survey of the room-tcmpcraturc magnctocrystallinc anisotropy energy of fee crystals of Fe-Co-Ni alloys. Arrows indicate the anisotropy constant K, of the various alloys. Arrow up denotes positive anisotropy. Solid circles: [63 P I],opcn circles: [37 M l].Thc lefthand and righthand arrows apply to, respcctivcly, quenched and annealed samples ofthc same composition. Solid and broken lines indicate the boundaries separating positive and negative anisotropy ticlds for quenched and annealed samples. rcspcctively [63 P I]. For earlier results. see [37 M I]. where a similar survey for room-tempcraturc values and the values at 200 “C are given.

Bonnenberg, Hempel, Wijn

[Ref. p. 274

1.2.1.2.7 Fe-Co-Ni: magnetocrystalline anisotropy

210 7 .lO 3 cm! mol

-

Fe-Ni o measured

1

0 8.53 8.55 8.60 8.65 8.70 8.75 8.80 8.85 8.90 8.95 9.00 fl-

Fig. 143. High-field susceptibility z,,,- mcasurcd or cxtrapolatcd V~LICS. at 4.2 K as dcpcndcnt on the number II of outer electrons per atom of Fe Ni alloys and of FCo.~0~sNio.~~~oMno.o~,6[71 Y I]. The dotted curve is calculated according to the rigid band model [69 S 23.

1.2.1.2.7 Magnetocrystalline

anisotropy

Ni

80

1 Fe

10

20

30

10

50

60

70

80 90

co

Fig. 144. Survey of the room-tcmpcraturc magnctocrystallinc anisotropy energy of fee crystals of Fe-Co-Ni alloys. Arrows indicate the anisotropy constant K, of the various alloys. Arrow up denotes positive anisotropy. Solid circles: [63 P I],opcn circles: [37 M l].Thc lefthand and righthand arrows apply to, respcctivcly, quenched and annealed samples ofthc same composition. Solid and broken lines indicate the boundaries separating positive and negative anisotropy ticlds for quenched and annealed samples. rcspcctively [63 P I]. For earlier results. see [37 M I]. where a similar survey for room-tempcraturc values and the values at 200 “C are given.

Bonnenberg, Hempel, Wijn

[Ref. p. 274

1.2.1.2.7 Fe-Co-Ni:

Ref. p. 2741

211

magnetocrystalline anisotropy B

5.0 IO6 ' erg cm3 _

Fe, hcp (ABAB)

4 3” e‘s c m3

Colex dhcp(~~~C)

I

8 406 !!Y cm3

0 p-i--

I g-2.5 s -5.0 -

-7.5 -

mT ,

T=XlOK

-10.0 0

I 0.5

I 1.5

1.0

a

I 2.0

2.5

x-

Fig. 145a. Room-temperature values of the magnetocrystalline anisotropy constants K, and K, for hexagonal Fe,Co,-, alloys in hcp (ABAB) and dhcp (ABAC) configuration [64 C 2,73 W 11.From the calculation ofthe anisotropy constants from the energy bands of the electrons in the dhcp configuration it is found that K 1 = -8.3. 106ergcmm3 and K,= -1.1. 106ergcme3 [74M 11. See also [83 M 11. L50 "C Fe-Co . LOO

.

t I

-12 I-12 0

‘---‘..

T-

50 .I04 I--. e'gy cm3

\.

350

.

300’1

"C LOO

300

200

100

b

fee .\ hcp

-8

I Fe bee

h, K!

Co

‘\? \

30

‘\

RT

20

5om

o quenched

-30 -

0 0 c co

0.5

1.0

1.5

2.0 at%

2.5

Fe -

Fig. 145b. Magnetocrystalline anisotropy constant K, vs. temperature T for hcp Fe-Co alloys. The inversibility with respect to the change of temperature is indicated by the arrows along the curves. Phase transitions are indicated by vertical arrows [SOT 31. Fig. 145~.Diagram showing the direction of the easy axis @A.) of magnetization for hcp Fe-Co alloys [SOT 31. Land&-Bdmstein New Series lll/l9a

/ \

. slowly cooled

\

\,/I

’

-40 -50

0 Fe

IO

20

30

40

50

60 wt% 70

co -

Fig. 146. Magnetocrystalline anisotropy constants K, and K, ofbcc Fe-Co alloys at room temperature [62 L 1, 36 S 1, 37 M 11. Symbols: results obtained by [59 H 11.

Bonnenberg, Hempel, Wijn

212

1.2.1.2.7 Fe-Co-Ni: magnetocrystalline anisotropy

[Ref. p. 274

13 (110) 120/O

.I05 erg cm3 I G

a 11

‘5.3 14.5 -53

--+q

-40

-20

0 T-

20

10 -60

40 "C 60

-20

-40

0

20

40 "C 60

I-

Fig. 147. The mqnctic anisotropy cncrgy AE,=2K, + K,Q in the (100) plane as a function of tcmpcraturc for a sit& crystal of F~,,&o,,,~ [72 N I].

Fig. 148. The magnetic anisotropy energy AE,=3K,/2$

K,/4$K,l32

in the (I IO) plant as a function oftemperaturc for a single crystal of Fc,,,&o~,~~ [72 N I].

BOO

1 600..

200 0

0

0.5

a

1.0

I

I

I

I

I

1.5

2.0

2.5

3.0

3.5

X-

Fig. 150a. Room-tcmpcraturc values of the induced uniaxial magnetic anisotropy constant K, for hcp and dhcp Fc,Co, -I alloys anncalcd at 950°C and then cooled in a magnetic ticld of 1.6kOc at a rate of 14”Cimin [76W I].

40

53

6:

70 co-

80

Co-l.Zat%Fe

90v:t % 100 co

ClOiO, RT

Fig. 149. Room-temperature values of the induced uniaxial magnetic anisotropy constant K, for polycrystallinc bee Fe Co alloys. combined vvith the equilibrium phase dinSram. Open circles: [7S T I]. samples prc-annealed at 1200“C. and cooled in a magnetic field of 4lOOc at the rate of 2OO”C,/h. Solid circles: [55 M I], samples prcannealed at a temperature below the ~-+r transition. Fig l50b. The mqnctic cnsy direction ofCo0,0RRFc0,0,2 can bc changed from the c plane to the c asis by an applied mqnctic ficld at room tcmpcraturc. The tigurc shows the relation bctvvcen the direction of the magnetic ficld in the (10iO)planc and the field strength ncccssary to induct the chan_rc in the direction of easy magnetization from the hcxnSonnl axis (solid circles) to the basal plant (open circles). The shadowed area gives the region where dhcp -+hcp transformation occurs as found from electron diffraction studies [8! TZ]. Bonnenberg,

b Hemp&

Hlc -

Wijn

Ref. p. 2741

213

1.2.1.2.7 Fe-Co-Ni: magnetocrystalline anisotropy

0 .I03 -erg cm3 -20

Fig. 151. Room-temperature values ofthe induced magnetic anisotropy constants K,, and K,, as a function of roll reduction R for a crystal of an Ni,,,Co,,, alloy. The anisotropy of rolled Ni,,,,Co,,,, crystals where lower than 10’ ergcme3. (a)(OOl) [llO] roll, (b)(llO) [OOl] roll. The roll magnetic anisotropy E, is given by E,= -$K,,cos28-$K,,cos40, where 0 is the angle between magnetization and roll direction [62 T I].

cc c

RT

0

j

-20

0.06

0.09

0.15

0.12

0.18

x-

Fig. 152. Magnetocrystalline anisotropy constant K, vs. composition for bee Fe, -,Ni, alloys at room temperature [39 T 11.

-40

-60

20 403 pro 2 cm3

tf (IlO)lOOll

0

20

60

40

roll 80

%

Fe-Ni

100

R-

1

0 -10 t g-20 -30 -40

-50

-601 30

40

50

60

70 Ni -

Cooling rate -

Fig. 154. Room-temperature value of the magnetocrystalline anisotropy constant of the fee Fe,,,,Ni,.,, alloy as dependent on the cooling rate in the temperature range from 600 to 300°C [53 B 11. LandoIl-BBmstein New Series

11~1%

80

90wt% 100 Ni

Fig, 153. Magnetocrystalline anisotropy constant K, vs. composition for fee Fe-Ni alloys at room temperature. Cooling rate between 600 and 300°C either lO’“C/h (quenched), or 2.5 “C/h (slowly cooled) [53 B 11.

Bonnenberg, Hempel, Wijn

1.2.1.2.7 Fe-Co-Ni: magnetocrystalline anisotropy 20 Xl3 L?Gl cm: 0

-I

I SC

-20

-LO

-60 -0.5 40 -erg cm3

-25

-35 0 -103 erg G3 I

-200

-100

0

100 I-

200

300 "C LOO

Fig. 155. Tempcraturc dcpcndcncc of the magnctocrystallinc anisotropy constant K, for Fe,-,Ni, alloys as derived from torque measurements on single crystals. For similar results derived from ferromagnetic resonance data, see [76B2]. Open circles: annealed, i.e. cooled from 600 to 300°C in the course of 15...20 days, solid circles: qucnchcd. i.e. heated by 700 “C and cooled in water [61 P 11.

Bonnenberg, Hempel, Wijn

[Ref. p. 274

Ref. p. 2741

1.2.1.2.7 Fe-Co-Ni: magnetocrystalline anisotropy

215

RT

I

I

-20

k?

-501 0

100

200

300

400 "C 500

a clFig. 157a. Room-temperature values of the magnitude of the magnetocrystalline anisotropy constant K, vs. annealing temperatur T, for a single crystal of FeNi,. The crystal was annealed at 900 “C and very slowly cooled to temperature, resulting in K, = -38.5 room . lo3 erg cme3. Subsequently the specimen was annealed at the various temperatures T, and rapidly cooled to room temperature for measurement [SOT 11. 0

10

20

30

Ni

40

50

60at% 70

Fe -

Fig. 156. Magnetocrystalline anisotropy constant K, vs. composition for quenched fee Fe-Ni alloys, measured at various temperatures [61 P I].

IO,

I

IO3 e's cm3 0

IO,

I

/

67 C

70

76

73

79 wt%

82

Ni-

Fig. 157~. Isothermal annealing curves of the first order magnetocrystalline anisotropy constant K, for various Ni,Fe-type alloys [83 H 21. Solid circles: [53 B2,53 B 11. 390

410

430

450

470

490

510

530°C E

70b Fig. 157b. Room-temperature first order magnetocrystalline anisotropy constant K, vs. annealing temperature T, for various FeNi,-type alloys. The samples were in the perfectly ordered state before annealing for 1 h in sequence at each T,. For T,=51O”C the samples become disordered [83 H 2-J.

Landolt-Bhmstein New Series 111/19a

Bonnenberg, Hempel, Wijn

[Ref. p. 274

1.2.1.2.7 Fe-Co-Ni: magnetocrystallinc anisotropy

a

x-

Ni

Fig. 159a. Induced uniaxial magnetic anisotropy constant K, of Fe,-,Ni, alloys due to a magnetic annealing [55 C I], or mechanical rolling. crows: [4l R I], solid circles: [55 C I]. For variations ofannealing temperature and the influcncc of neutron irradiation with curves derived from measurcmcnts on polycrystallinc samples. see also [SS F I, 74 R 21. For kinetics of the process. see [82 H I].

/

I

I

10

20

30

I

LO kOe ’

Hop:' -

Fig. 15s. The mngnctocrystallinc anisotropy constant K, 1sdepcndcnt on the magnitude of the mngnctic Iicld for Fe, -,Ni, invar alloys at 4.2 K, as derived from torque ncnsurcments on single crystals [820 I]. For room:empcrature results. see [73 0 I].

b

Fe

Ni -

Fig. l59b. Magnetic anisotropy constant K, of Fe-Ni alloys induced by magnetic cooling through y+r transformation tcmpcraturc. Cooling rate 4”C/min in a magnetic field Hap,,,=IO kOe. Solid curve after cooling to room temperature, broken curve after cooling to liquid nitrogen tempcraturc [660 I].

Bonnenberg,

Hempel,

Wijn

Ref. p. 2741

1.2.1.2.7 Fe-Co-Ni:

magnetocrystalline

217

anisotropy

Fig. 160. Induced uniaxial magnetic anisotropy constant

K, as a function of the orientation of the magnetic annealing field in an (110) ablate single crystal of FeNi, after cooling from 600 “C at various rates. The direction of the magnetic annealing field is given by the angle 0 measured with respect to the [loo] direction in the crystal plane. The first order magnetocrystalline constant K, is also given [56 C 1, 57 C 11. 1.8 t

1.2

3.9

0.6

0.3 0 0”

15”

30”

45”

A S”C/min D l”C/min I 60” 75”

90”

-0.L 0

b

. perfect order I I 80 % 60

40

1

R-

Fig. 161b. Variation of the uniaxial roll magnetic anisotropy constant K, with the progress of (001) [llO] rolling of a FeNi, crystal [64 C 11.

0 perfect order -3.2

0 a Landolt-Bbmstein New Series 111/19a

20

LO

60

80

%

100

Fig. 161a. Variation of the uniaxial roll magnetic anisotropy constant K, with the progress of (110) [loo] rolling of a FeNi, crystal [64 C 11.

R-

Bonnenberg, Hempel, Wijn

[Ref. p. 274

1.2.1.2.7 Fe-Co-Ni: magnetocrystalline. anisotropy

218

Fe ’

1

I

0.652 NhB

1.0 10-5 'C-:

I

lOOl)[llOl

cm3

roll

(I

A4

5

0.5

/ 0 I 23 4 0.5

1.0

0

10

20

b

a Fig. l62a. Uniaxial masnctic anisotropy constant K, induced by (001) [I IO] rollin! as a function ofstrain c for a at vartous quenching tcmpcraturcs samplcofFc,,,,Ni,,,, [79S I].

30 R-

40

-- 1.5

50 % 60

Fig. 162b. Roll-induced magnetic anisotropy constant K, for Fe,,,,,Ni,~,,, invar alloy as a function of roll reduction for the cast of(001) [ I lO].Furnace-cooled from 1000“C to RT [77 K I]. The diffcrcnce Ar between the linear thermal expansion coctkicnts measured parallel or pcrpcndicular to the roll reduction is also given [77 K I]. For a. see Fig. 2 I I.

2.5

0 erg

.105 .105 erg erg 3

e’s.

cm3s

cm3

-0.5

1.5 -1.0 1.0 I 0.5 s

s

0

2.0

-0.5

1.5

-1.0

1.0

-2.5

-1.5 -2.0 I 0

I 20

I 40

I I 60 % 80

0 0

100

200

300

400

500 "C 630

E-

70 -

Fig. 162~. Uniasial magnetic anisotropy constant K, induced by rolling in the (I IO) plane as a function ofstrain for a sample of Fe,, ,,Ni,,, r. Samples qucnchcd from high temperature [79S I]. 0: angle bctwccn axis of easy magctization and rolling direction.

Fig. 163.Variation ofthc uniaxial anisotropy constant K, induced by (I IO) [I IO] rolling of the sample, E= I6.5%, of Fig. 162 with annealing temperature T, [79S I]. Also indicated is the tcmpcraturc dependence of the recovery rate ofthc induced rolling anisotropy as a consequence of annealing at constant tcmpcraturc [79 S I]. set also [74S2,74S 11.

C

Bonnenberg, Hemp& Wijn

219

1.2.1.2.7 Fe-Co-Ni: magnetocrystalline anisotropy

Ref. p. 2741 2.50 *IO3 erg cm3

erg cm3

I g 2.00

I

k

1.75 1.50 100

50

150

200

0

250 "C 300

100

200

300

b

L-

a

400

500 "C 600

b-

Fig. 164. The magnitude of the compression-induced magnetic anisotropy I& vs. annealing temperature for a FeNi, alloy single crystal. After annealing at 900 “C the sample was very slowly cooled to room temperature in order to obtain a high degree of ordering. The specimen was compressed to (a) E= 14% perpendicular to its (110) surface at room temperature [76T 11, see also [77T 1, 77 T 2,78 T 3,80 T 21; (b)s = 3% and now in a wider range of annealing temperatures [83 T 11.

‘$i Fe-Ni-C cm3 1.6

1.61-1

RT

I

1.2 I s

SF 0.8

0.8

0.4

0.4

0 0 a Fe.Ni

01

0.3

0.2

0.4wt% 0.5

c-

Fig. 165. Induced uniaxial magnetic anisotropy constant K, as a function ofC content for fee FeNi polycrystalline and texture-free samples. Magnetic field annealing at 200°C measurements at room temperature. Before fieldannealing the samples had been water-quenched from about 1000“C unless otherwise stated in order to keep the C in solid solution [69 A 21. See also [68 R 1,67 A 11. For co o,osNi,.,,: K,=5. 103ergcmm3, K,=O [75W 11. Fe content (a) 2 50 wt%, (b) 2 50 wt%.

0 0 , Fe,Ni

0.2

0.6

0.8 wt % 1.0 C

c-

0

Fig. 166. Magnetocrystalline anisotropy constant K, of fee CoNi alloys at room temperature. Solid circles: [59 H 11, open circles: [36 S 11, triangles: [37 M 11. Landott-Bbrnstein New Series 111/19a

0.4

Bonnenberg, Hempel, Wijn

50 403

e’s cm3

-300I N;

I0

20

30

co -

4Owt%50

220

1.2.1.2.7 Fe-Co-Ni: magnetocrystalline anisotropy

Co-Ni

%-ye.

\

.105 erg

G-3 8 6

ZOv:t%Ni

-,

[Ref. p. 274

hcp‘1

fee

4

1 0 1 GO 1 0 1 0 0 -1 0

I I I I J 300 400 500 600 K 7130 Ia Fig. 167a. Tempcraturc dcpcndcncc of the first order minxial magnetocrystallinc anisotropy constant K, for ncp Co-Ni alloys [7S T 21. -31 0

lb1

0

-!

I

1OC

I 200

,

100

I

200

I

I

I

I

300

400

500

600

4.5 ,105 erg cm3

1.5

i Ly

0

4c -1.5

-3.0

-4.5

200

300 400 500 600 K 700 IFig. 169. Tcmpcraturc dcpcndcncc of the cubic magnctocrystallinc anisotropy constants K, and K, for the fee Co-30wt% Ni alloy. On cooling through 250K the transformation to hcp structure takes place [78 T 21. 0

100

K ;

b IFig. 167b. Tempcraturc depcndcncc of the second order uniaxial magnctocrystallinc anisotropy constant K2 for hcp Co--Ni alloys [78T2]. The tempcraturc 7;, for the phase transition from hcp to FCCis indicated. For a calculation of the anisotropy constant from the d-band model. see [83 M I].

Bonnenberg, Hempel, Wijn

1.2.1.2.7 Fe-Co-Ni: magnetocrystalline anisotropy

Ref. p. 2741 I

900

I I K Co-Ni ! 800+ &

I

xl" o erg” cm3 -

Co- Ni

0 1

221

I

T,,(300K)-

fee

400

300

,0°0<

b

0

a Co

5

IO

15

20

25

30wt% 35

NI -

30 wt% 35

Co

NI -

Fig. 169b. Relation between the temperature where the first order uniaxial anisotropy constant K, = 0 and the Ni concentration of hcp Co-Ni alloys [78 T 23.

Fig. 169a. First and second order uniaxial magnetocrystalline anisotropy constants K, and K, vs. Ni concentration in hcp Co-Ni alloys at 77 K, 300 K and at the temperature 7;,, just below the temperature of the ~(hcp) +y(fcc)phase transformation [78 T 21. For ‘I;, vs. composition, see Fig. 17. IO,

I

105 ero

6

Co-Ni

IRTl I !47-b!

4 2 t s

0

-2 -4

Fig. 170. Room-temperature values of the induced uniaxial magnetic anisotropy constant K, for polycrystalline Co-Ni alloys as a consequence of magnetic annealing. Open circles: [79T 11, solid circles: [62G 11, crosses: [60 T 11. Triangles: cold rolling [79 T 11. Landolf-Bdmstein New Series llVl9a

wt%

-I005

co

Bonnenberg, Hempel, Wijn

Ni -

1.2.1.2.8 Fe-Co-Ni: magnetostriction

0 CO-X

0.1

0.2

0.3

0.i wt%

0.5

0.3

0.4

[Ref. p. 274

0.5

0.7

0.6

c-

0.8

0.9

x-

Fig. 171. Room-temperature values of the induced uniaxial magnetic anisotropy constant K, for Co -Ni alloys containing some C. Annealing temperature 200°C [69 A2J.

1.0 Ni

Fig. 172. Room-temperature values of the induced uniaxial magnetic anisotropy constant per wt% of C conccntration, KU/c for Co-Ni and FecNi alloys. The anisotropy contribution in Co-Ni alloys is independent on C concentrations up to 0.5 wt% C [69A 21.

1.2.1.2.8 Magnetostriction Table 22~1.Linear forced magnetostriction

7-M

293 17 1.5

constants I(, of polycrystallinc

Fe, -,Co,

alloys [65 S2].

11; [lO-loOe-l] x: 0

0.054

0.164

0.262

0.303

0.35

0.503

0.145

0.925 ‘)

1.5(l) l.S( 1) 1.5( 1)

1.7(l) 1.7( 1) 1.6( 1)

1.9(l) 1.8( 1) 1.8(l)

1.4(l) 1.2(l) 1.1(l)

1.1(l) 0.8(l) 0.6( 1)

0.8(l) 0.7( 1) 0.6( 1)

OX(l) 0.7( 1) 0.8(l)

0.9(l) 0.8(l) 0.8(l)

1.7(l) 1.7(l) 1.6(l)

‘) X-ray analysis for the y-phase. Table 22b. Room-temperature values of the linear magnetostriction constants for hcp and dhcp Fe-Co alloys, defined by the equation:

i.=i~‘(Bt+PI)(r:-~)+j.S28:(~XjZ--f) +RyL{f(~:-~:)(a:-a:)+2~,~2al~2} where xi and /Ii are the direction cosines of the magnetization and of the measured change in length. respectively, set [65 C 3, 84 I 1] and also [63 C 11. The constants are only weakly dependent on composition, 106 2.;: hcp

dhcp

78 28

106. )Q ‘2 -134 - 85

106 . 1.Y’ :;

106. )Q -234 - 51

*) I.?2 gradually decreases with increasing Fe content, without appreciable change at the phase transition (see Fig. 174a).

an

Bonnenberg, Hempel, Wijn

+21,cz(~,cr, +~2~2)r3~3,

1.2.1.2.8 Fe-Co-Ni: magnetostriction

0 CO-X

0.1

0.2

0.3

0.i wt%

0.5

0.3

0.4

[Ref. p. 274

0.5

0.7

0.6

c-

0.8

0.9

x-

Fig. 171. Room-temperature values of the induced uniaxial magnetic anisotropy constant K, for Co -Ni alloys containing some C. Annealing temperature 200°C [69 A2J.

1.0 Ni

Fig. 172. Room-temperature values of the induced uniaxial magnetic anisotropy constant per wt% of C conccntration, KU/c for Co-Ni and FecNi alloys. The anisotropy contribution in Co-Ni alloys is independent on C concentrations up to 0.5 wt% C [69A 21.

1.2.1.2.8 Magnetostriction Table 22~1.Linear forced magnetostriction

7-M

293 17 1.5

constants I(, of polycrystallinc

Fe, -,Co,

alloys [65 S2].

11; [lO-loOe-l] x: 0

0.054

0.164

0.262

0.303

0.35

0.503

0.145

0.925 ‘)

1.5(l) l.S( 1) 1.5( 1)

1.7(l) 1.7( 1) 1.6( 1)

1.9(l) 1.8( 1) 1.8(l)

1.4(l) 1.2(l) 1.1(l)

1.1(l) 0.8(l) 0.6( 1)

0.8(l) 0.7( 1) 0.6( 1)

OX(l) 0.7( 1) 0.8(l)

0.9(l) 0.8(l) 0.8(l)

1.7(l) 1.7(l) 1.6(l)

‘) X-ray analysis for the y-phase. Table 22b. Room-temperature values of the linear magnetostriction constants for hcp and dhcp Fe-Co alloys, defined by the equation:

i.=i~‘(Bt+PI)(r:-~)+j.S28:(~XjZ--f) +RyL{f(~:-~:)(a:-a:)+2~,~2al~2} where xi and /Ii are the direction cosines of the magnetization and of the measured change in length. respectively, set [65 C 3, 84 I 1] and also [63 C 11. The constants are only weakly dependent on composition, 106 2.;: hcp

dhcp

78 28

106. )Q ‘2 -134 - 85

106 . 1.Y’ :;

106. )Q -234 - 51

*) I.?2 gradually decreases with increasing Fe content, without appreciable change at the phase transition (see Fig. 174a).

an

Bonnenberg, Hempel, Wijn

+21,cz(~,cr, +~2~2)r3~3,

Ref. p. 2741

1.2.1.2.8 Fe-Co-Ni: magnetostriction

223

-80

0

5

IO

15

20 kOe 25

H-

Fig. 173a...d. Room-temperature values of the magnetostriction 4 of single crystals as dependent on the magnetic field strength H for Fe-Co alloys [8411], see also [78 W 11. i indicates the direction of the measured change in length caused by a magnetic field in the j-direction. a, b, and c are the main hexagonal (or cubic) crystallographic directions. e and f represent the directions [1/1/z, 0, I@] and Cl/@, 0, - Ifi], respectively.

-. -80 ' 0

Landolt-BOrnstein New Series 111/19a

5

10

II

15

20

kOe-

Bonnenberg, Hempel, Wijn

[Ref. p. 274

1.2.1.2.8 Fe-Co-Ni: magnctostriction

224 0O .y-’ -!O -20 -3; I ti..A0 -50 -E? -70 43

0 a Co

1

2

3

4

5

6 ot% I

Fe-

Fig. 174a.Dcpcndcncc ofthc saturation magnctostriction &=i(j.,; -iJon Fe concentration in polycrystallinc Fc Co alloys at room tempcraturc, measured in an applied masnctic field of 20 kOe. i.;, and I., arc the magnctostrictions parallel and perpendicular to the field direction, respectively [S4 I I].

120

,

90

C

150

300

-20 0 -20 -100 b

100 200 300 400 500 600“C 70G 7Fig. 174b. Dependence ofthe saturation magnetostriction I., on tempcraturc for polycrystalline Fe-Co alloys, measured in an applied field of 20 kOe. h-f, d-f, h-d denote transitions between (h) hexagonal. (f) face centered cubic and (d) double hcxaeonal close oacked structures [S4I I]. x ’

m” Co-8at%Fe

-90 0

-20 0

150 I-

600

0

750 K 900

Fig. 174~. Temperature depcndcncc of the saturation ma_enetostriction constants Ai of fee Co-S at% Fc, mcasured in a field of 14 kOe [70 H I, 65 S 21. The dashed line represents data for h, [67 B 23.

-0

a Fe

0.2

0.1

x-

0.6

0.8

1.0 CO

Fig. 175a. Linear forced magnetostriction constant of polycrystallinc Fe, -,Co, alloys [65 S 23.

Bonnenberg, Hempel, Wijn

Ref. p. 2741

1.2.1.2.8 Fe-Co-Ni: magnetostriction

225

2[I .10-1’0 OF’ 1:

I

Xhl

I -3

40

-II:I 0

J

0

-1cI

l

-40 100

200

300

400 T-

500

600

700 K 800

b Fig. 175b. Temperature dependence of forced magnetostriction AAJAH,,,, as measured in saturating fields for fee Co-8 at% Fe [70 H 11.

0

2.00

400

600

800 K1000 0

20

0 Fe

40 co -

- slowly cooled I 80 wt% 100 co

Fig. 176. Magnetostriction constants 1,,,, and a, r r of fee Fe-Co alloys at room temperature [62 K 21. Open symbols: [59 H 11, solid symbols: [52U I], crosses: [62 K 21.

200

400

600

800 K 1000

Fig. 177. Temperature dependence of the spontaneous volume magnetostriction w of fee Fe-Ni alloys evaluated from observed thermal expansion data. Dashed lines: extrapolated from high temperature [73 H 21. Landolt-Biirnstein New Series 111/19a

60

Bonnenberg, Hempel, Wijn

1.2.1.2.8 Fe-Co-Ni:

226

magnetostriction

[Ref. p. 274

3I

2.4 -9.3 0.3

0.1

0.5

0.6

0.7

0.8

0.9

x-

I

I

1.0 Ni

Fip. 17%Spontaneous volume mngnetostriction (II at 0 K vs. composition for fee Fe-Ni alloys [83 N 33, SW also [74 K I]. Triangles: [73 H 21. solid circles: [7l T 21, open circles: [79 0 21. The solid line represents calculated results [Sl Y I]. we also [73 z I].

1.6

I 1.2 a 0.8

h

0.4

Olb 0

\

Y

\I 100

200

300

400

K

500

IFig. 179. Tcmpcrature dcpcndcncc of the spontaneous volume magnctostriction o for Fe-Ni invar alloys (a) Feo.7%.3 and (b) Fc,,,,Ni 0,35 at various pressure as dcrivcd from X-ray lattice constants [Sl 0 41.

2.5

0

5%

103

I

I

150

200

,-

I 250 K 31

Fig. ISO. Variation of the volume magnctostriction with applied mqnctic licld. &$~H,pp,. as a function of the temperature. (a) Obtained from mcasurcmcnts on single cq%~ls of Fe -Ni and for magnetic fields bctwccn 5 and 30 kOe. The arrows indicate the tcmpcraturc of martcnsitic transfomxltion [78 K I]. (b) Mcasurcd in a magnetic applied field up to IO kOc for Fc,,,Ni,,, [6OA I].

b

Bonnenberg, Hempel, Wijn

I-

227

1.2.1.2.8 Fe-Co-Ni: magnetostriction

Ref. p. 2741

i

o++----c 738K : 01 IO 5 0

-I-15 ” 20*

kOe

H-

C

250 .10-‘0

0 0

I 200

d

---

w

I 800 K

T-

Fig. 180d. Forced volume magnetostriction ao/aH vs. temperature T for Fe-Ni alloys. Solid circles: derived from low-field measurements, 0 < < 6 kOe, open circles: derived from higher-field measurements, 10 < H < 20 kOe. The arrows indicate the Curie temperatures derived from Arrott plots [85 I 11, see also [84Y 11.

H

50

-501 -50

n

e

600

Fig. 180~.Volume expansion w under the influence of a magnetic field H at various temperatures T for Fe 0.636%.364. The Curie temperature determined from Arrott plots is T, = 529 K [85 I 11, see also [84 Y 11.

I 150 a $100 cu

/ LOO

20

ie

Landolt-BOrnstein New

Series 111/19a

LO

60 Ni -

I 80 ot% 100 Ni

&o/aH

Fig. 180e. Forced volume magnetostriction at various temperatures for Fe-Ni alloys. The spontaneous volume magnetostriction w, is also indicated [85 I I].

Bonnenberg, Hempel, Wijn

J

[Ref. p. 274

1.2.1.2.8 Fe-Co-Ni: magnetostriction

22s 3: .!C ' Oe-

Fei-,NI, '-I

I

I

2:

2[ 1 :- t : s c \ 3 c2 li

0 Fe

0.01

0.02 x-

0.03

0.04

Fig. 182. Variation of the volume magnctostriction with applied magnetic field, &@H,,,, at room temperature for [Sl z I]. the fee alloys Fe,,, +,Ni,., - 2rMnr I A-‘m&79.5770ee1.

5.!

Table 23a. Linear forced magnetostriction constants hb as in Table 22a, but now for polycrystalline Fe, -xNi, alloys [65 S 23.

2.i

TCKI

(

0

0.1 x-

0.2

F?

0.6

1.0 Ni

0.8

Fig. ISI. Variation of the volume magnctostriction with applied mayctic fcld. &?/SH,,,,. as a function of Ni concentration of Fe-Ni alloys [SS G I], xc also [7S K I]. 1:[02Nl].2:[31h41].3:[35K1].4:[37SI].Thcsamc quantity. but derived from changes of the spontaneous mqnetizntion with prcssurc. 5: [37 E I]. 6: [53 G I], 7:

[jS G I].

293 293 234 173 77 1.5

hb [lO-loOe-l] x: 0

0.094

0.192

1.5(l)

3.3(l)

3.3(l)

1.5(l) 1.5(l)

3.1(l) 3.1(l)

3.6(l) 3.6(1)

‘) bee+ fee.

Table 23~. Influence of ordering on the linear saturation magnetostriction constant i,, of FeNi, at room temperature according to various authors.

Table 23b. Linear saturation magnetostriction constant i., of polycrystalline Fe-Ni alloys [OSH I]. wt % Ni

2, bee.

I., . IOh Ref.

2,. 10” 36 46 50 70

TT20C

-186°C

20.3 25.4 24.3 11.6

30.5 30.7 26.8 12.6

disordered

ordered

1.9 7.1 8.5

4.15 10.1 10.7

Table 24. Linear forced magnetostriction constants hbfor single crystals of Fe, Ni and Ni-Co alloys [65 S 21.

TCKI

293 77 I.5

/lb [lo-“Oe-‘I Fe

Ni

Ni-25 at% Co

Ni-50 at % Co

1.5(I) 1.5(I) 1.5(I)

0.2(l) 0.5(l) 0.4(l)

0.5(1) 0.6(1) 0.6(1)

0.6(1) 0.8(l) 0.7(l)

Bonnenberg, Hempel, Wijn

49Gl 54Tl 53Bl

0.287 56(5) ‘1 8.0(l) 2, 38(2) ‘) 2w ‘1 8.0(2)2, 8.0(2)2,

1.2.1.2.8 Fe-Co-Ni:

Ref. p. 2741

229

magnetostriction

60 .m6

3 .I@

I

FelmxNix

50 40

2

30 1

I 20 x,0

t *o

0.369 ‘1

---t-

B + 0

-1

-10 -20

-2 -30 -3

-40 1.0 Oe 1.2

0.2

HFig. 183. Room-temperature linear magnetostriction ,I in very low internal fields for Fe-Ni invar alloys [Sl B 11.

a

50

100

150

200

250 K 300

Fig. 184a. Temperature dependence of the linear magnetostriction coeffkients, A,,, and A,,,, as a function of the composition of single crystals of the FeNi invar alloys. The arrows indicate the temperature of martensitic transformation fee to bee [78 K I].

60 m6 40 I 20 z 2 0 T-z -20 -40

0.6

b

x-

0.8

0.9

1.0 Ni

Fig. 184b. Linear magnetostriction coefficients, IIOo and 3,r1 r, as a function ofthe composition for single crystals of FeeNi alloys. Crosses [78 K l] and circles [53 B 11: room temperature, triangles [78 K l] : 4.2 K. 0

1

2

3 HOPPl

4

kOe

5

-

Fig. 185. Room-temperature values of the longitudinal (long) and transversal (trans) linear magnetostriction coefficients A,,, as dependent on applied field strength for a quenched Fe,,,,Ni 0.35 crystal, showing large volume effects in high fields [53 B 11. Landolt-Bbmstein New Series 111/19a

Bonnenberg, Hempel, Wijn

[Ref. p. 274

1.2.1.2.8 Fe-Co-Ni: magnetostriction

230 10s .!I--’

75

75

,

.10-'

SCl-

1 SC T-2

1

d

2Eb-

2:

0

10

5

a

20 kOe

15

5

0

H%g>! -

20 kOe

15

10 HOPPl -

b

Fig. 186a. b. Linear magnctostriction ). as dcpcndent on applied field strength for polycrystallinc samples of (a) FC0,63Ni0,J7and (b) Fe,,,,Ni,,,, at various temperatures [5l T 11.

I

FelmxNix

13.5

I

“o-6 F’3msNi 0.36k

I P

c

0 Fe

L

I

b

9.0 7.5

I

A 293 K -0 77K o 1.5 K

bee

,

I s-z6.0 -

fee

x-

4)

_I 0.8

1.0

Ni

Fig. 186~. Linear forced magnetostriction constant of polycrystallinc Fe, -,Ni, alloys [65 S 21. Solid circles: [60 K I].

0

0.5

1.0

d

1.5

2.n

2.5

3.0

kOe 1:.o

H-

Fig. 186d. Longitudinal forced linear magnetostriction 1 mcasurcd in the field direction plotted against the internal magnetic held. Measuring sample is a single crystal sphcrcT of an KFe,,,,, temperature =555 c84yl;ljo164 invar alloy. Curie C

Bonnenberg, Hempel, Wijn

231

1.2.1.2.8 Fe-Co-Ni: magnetostriction

Ref. p, 2741

I.5 I ci 6.0 J

01 250

300

350

f 0

0.5

1.0

1.5

e

2.0 H-

2.5

3.0

kOe

;;‘O

I 450

I 400

I 500

I I 550 K 600

T-

Fig. 186f. Forced volume magnetostriction &o/aH for the sample of Figs. 186d and e [84Y 11. 1.5 m6

Fig. 186e.Longitudinal forced linear magnetostriction as in Fig. 186d, but now for temperatures just above the Curie temperature [84 Y 11.

1.0

0.5

LO .10-6

I

1 ! II

I

Co- Ni

I

//,

0

-0.5 01

I I

/I/I

//I

P

YI

I

I\

I\I

I

I

I

3 -1.0

-20

cz

-1.:

-2sI

-2.: -801 0 a Ni

20

60

40 co -

II 80 wt%

100 CO

Fig. 187a. Linear saturation magnetostriction constant of polycrystalline Co-Ni alloys at room temperature [62L 11. Open circles: [53Y I], solid circles: [Sl W 11. Dashed curve: calculated from data depicted in Fig. 188,

-3sI 0 b Ni

40

60 x-

80 wt%

100 co

Fig. 187b. Room-temperature value of the volume magnetostriction w of Co-Ni alloys [Sl B 11.

&=Wmo+341dP. Landolt-B6’mslein New Series lll/l9a

20

Bonnenberg, Hempel, Wijn

1.2.1.2.8 Fe-Co-Ni: magnetostriction

232

[Ref. p. 274

83

I 63

cz LO

20 0

a -10

-!C -IO

-20 0 *.10-f I

-60 NY

‘0

20

30

- LO

50

60 wt% 70

co

Fig. 18% Magnetostriction constants I.,,, and I., , , of fee Co-Ni alloys at room tempcraturc [62K2]. Crosses: [5SY I]. circles and triangles: [59H I], dashed line: [53 Y I].

-10

-20

-30

0

100

200

300 T-

400

500

600 “C ;

Fig. 189. Linear magnetostriction constants of co 0.2sNi,,,s single crystals as measured in an applied magnetic ficld of 6.4 kA/m (80.4Oe) at various temperatures. Open circles: measured directly after applying the magnetic field, solid circles: measured after 5000.~.20000 min after application of the magnetic fields [SOM 23. Crosses: calculated from the experimental values for the [loo] and [I 1I] direction.

Bonnenberg, Hempel, Wijn

233

1.2.1.2.9 Fe-Co-Ni: elastic moduli, sound velocity

Ref. p. 2741

1.2.1.2.9 Magnetomechanical

properties, elastic mod&, sound velocity

Table 25. Young modulus E, shear modulus G and compressibility x at room temperature for polycrystaline samples of fee Fe-Ni alloys. wt % Ni 30 31.5 33.2 33.8 35.7 37.7 39.6 42.5 44.4 50.0 60.7 70.0 78.5 89.6 100

E [Mbar] [78 s l] 1.71

1.51 1.48 15.8 1.72 1.99 2.06 2.19 2.20 2.21

[72 H 21 1.644‘) 1.608 1.532 1.492 1.445 1.445 1.458 1.500 1.556 1.712

G [Mbar] [78 S l]

II [Mbar- ‘1 [72 H 21 [78 S l]

[72 H 21 0.660 0.649 0.613 0.59 0.568 0.553 0.553 0.567 0.584 0.645

0.70

0.59 0.58 0.59 0.64 0.76 0.78 0.85 0.85 0.82

0.95

0.93 0.87 0.62 0.57 0.56 0.56 0.56 0.56 0.46

0.93 0.975 0.98 0.945 0.945 0.805 0.765 0.71 0.65 0.605

0.55 ‘)

‘) [6OA 11.

Fig. 190.For caption and Figs. (a) and (c), seenext page.

-250

-125

0

Landolt-Biirnsfein New Series 111/19a

125

250 T-

b

Bonnenberg, Hempel, Wijn

375

500 “C 625

234

1.2.1.2.9 Fe-Co-Ni: elastic moduli, sound velocity

[Ref. p. 274

Fig. 190. (a) Young’s modulus E vs. temperature T for polycrystallinc samples of fee Fe -Ni alloys. The measuremcnts wcrc taken in the process ofcooling of the samples to room temperature in a magnetic field of 1.2kOe. The arrows indicate the Curie temperature Tc. The linear extrapolation below the Curie tcmpcraturc shows values of the Young’s modulus as extrapolated from the paramagnetic region. The vertical scale is equal for all compositions and is given by the length ofthc line showing a scale of0.2 Mbar [70 T 2,78 S I]. (b) YoungTsmodulus E vs. tempcraturc T as in (a) but now for Fe-N1 invar alloys and ff,,,, = 6 kOe [72 H 21; for the influence ofannealing. see [63 T 23.

2.L Mbor 2.2 2.0 I cu

1

1.8 1.6 I

I

I

I

I

LO

50

60

'IO

80

I

I

90 w! % 1oc

Ni-

Fig. l9Oc. Young’s modulus E vs. Ni concentration for fee Fc -Ni alloys at various tcmpcraturcs. Curves arc dcrivcd from Fig. 190a [70T2, 78 S I].

a

0 0 a

0.05 x-

0.10

-0.25 0 b

0.1

Fig. 191. Rclativc change of Young’s modulus AE/E at T= - 100°C upon hydrogenation of (a) Fe,,,,Ni,,,, alloys and (b) Fe,,,,Ni,,,, alloys [83 H I].

Bonnenberg, Hempel, Wijn

0.2 x-

0.3

235

1.2.1.2.9 Fe-Co-Ni: elastic mod&, sound velocity

Ref. p. 2741

1

hd,

I

A-

I 2.4. Mbar Fe-Ni

c00.1

2.2 ----/-----T---7

. , 1.4 30

40

50

60

70

--

400°C I 90 wf% 100 Ni

80

Ni -

Fig. 193. Young’s modulus E, for a hypothetical paramagnetic state of fee FeNi alloys as a function of the composition as derived from Fig. 190a [70T2, 78 S 11. The broken curves are derived from [63 T2].

Fe-Ni

I

Mbar

0.85 0

I

I

I

100

200

300

I

I

400 "C 500

TFig. 192. Young’s modulus E vs. temperature T for polycrystalline samples of fee Fe,,, -XNi,Co,,, alloys in a magnetic field of 1.5kOe [78 S 11.

8.6

8.8

9.0

9.2

9.4

9.6

E1.8

10.0

Fig. 194. Paramagnetic Young’s modulus E, at 400 “C for (solid circles) fee Fe-Ni, (open circles) fee Fe,,, -XNi,Co,,, and (crosses) fee Fe,,,-,Ni,Co,,, alloys as a function of the number n of 4s and 3d electrons per atom [78 S 11. Landolt-Biirnstein New Series 111/19a

0.76

I 0

I

I

I

I

100

200

300

400

Ta Fig. 195a. For caption, see next page.

Bonnenberg, Hempel, Wijn

I "C 500

1.2.1.2.9 Fe-Co-Ni: elastic moduli, sound velocity

236 0.703 b!>:-

[Ref. p. 274

1

Fe-Ni

I

0.659

-2is

I

I

I

-125

II

125

I

250

500 "C 625

375

Tb Fig. 195. (a) Shear modulus G vs. temperature T for polycrystallinc samples of Fc--Ni alloys. The mcasurcments were taken in the process ofcooling the samples to room temperature in a magnetic field of 1.2kOe. The arrows indicate the Curie temperature Te. The linear extrapolation bcloa the Curie tcmpcraturc shows the G values as extrapolated from the paramagnctic region. The vertical scale is equal for all compositions and is given by the length of the lint showing a scale of 0.2 Mbar [70 T 2, 78 S l].(b) Shear modulus G vs. Tas in (a). but now for Fc-Ni invar alloys and H,,,, = 6 kOe [72 H 21.

0.8E Mboi

0.68'

0.68 -oh -

-

_

-

0.50

c3

o.571-----= Fig. 196. (a) Shcnr modulus G vs. temperature T for polycrystallinc samples offcc Fe,,,-,Ni,Co,, alloys in a mnpnetic held of I.5 kOc [7S S l].(b) Shear modulus G as dependent on the number II of 4s and 3d electrons per atom for various fee alloys, measured at H,,,, = I .5 kOc (solid triangle: Fc~,~,CO~,~~. solid circles: Fe, -,Ni,. open circles: (Fc, 61Ni0,36), -$Zrr, open triangles, up,xard (Fe,-,Ni,),,Cr,,,) and in zero ticld (open trian;lcs. downward (Fc, -xNi,),,,Co, J [72 T I].

0 a

Bonnenberg, Hempel, Wijn

I

I

I

I

100

200

300

400

I-

"C :

Ref. p. 2741

1.2.1.2.9 Fe-Co-Ni: elastic moduli, sound velocity

237

1.2 Mbor 1.0

t 0.8 Q

8.6

8.8

9.0

9.2

9.L n----c

9.6

9.8

10.0

Fig. 197. Paramagnetic shear modulus G, at 400 “C for (solid circles) fee Fe-Ni and (open circles) fee Fe,,,-,Ni,Co,,, alloys as a function ofthe number n of4s and 3d electrons per atom [78 S 1,72T 11. OL11

b

10.0

n-

Fig. 196b.

_I 11.0 p 2 Iz

2.2 0

? z -1.7

;;2

0

0

t

2 60.7

5 z 2 -3.0 0

^ 70.02

-

.

-3.2 78.5 89.6

Fig. 198. Temperature derivative of the Young’s modulus E and of the shear modulus G as a function of the temperature T for various samples of fee Fe-Ni alloys in the magnetically saturated state. Open circles: (dE/dT)/E, solid circles: (dG/dT)/G [70 T 2,78 S 11.The vertical scale is equal for all compositions and is given by the length of the line showing a scale of 4. 1O-4/“C.

-3.8

-co I

I

I

I

100

200

300 7-

Landolt-BBrnstein New Series 111/19a

Bonnenberg, Hempel, Wijn

I

LOO "C

500

[Ref. p. 274

1.2.1.2.9 Fe-Co-Ni: elastic moduli, sound velocity

238

--

70.02 ..- nc.h -

0.55'r"""""" 60.7 0.5$~-

0.016r Ryo.u

a

0

100

300

200

LOO "C

F

l-

Fig. 199a. Adiabatic compressibility x vs. temperature T for polycrystallinc fee Fe -Ni alloys. as dcrivcd from the data of Figs. 190a and 195a according to the relation x =9,‘E - 3,/G [70 T 2. 78 S I]. The vertical scale is equal for all compositions and is given by the length of the lint showing a scale of 0.2 Mbar- ‘.

0

I 0.2

0.

0.1

0.6

1RT=C2 K

I 0.8

x-

Fig. 199b. Concentration dependence ofthe bulk modulur B for Fe, -,Ni, alloys at T=O K,calculated on the basis o Libcrman-Pettifor’s virial theorem. The solid line hold! for the ferromagnetic state, the dashed curve for the paramagnetic state. The arrow means that the bulk modulus has the singular value B=O at that point [8l K 1). 1 Ry a.u.o 147.25Mbar. Measuring points ac cording to [73 H I].

Bonnenberg, Hempel, Wijn

L.andolr-Bomlcin NW Sericc 111’19a

Ref. p. 2741

1.2.1.2.9 Fe-Co-Ni: elastic moduli, sound velocity

1.60 Mbar 1.55

'1.50

1x5

l.LO l.Ml

1.35

I 1.30 Q 1.25

1.20

I.15

1.10 1.05

1.00

0.95 0.90 -250

-125

0

125 T-

250

375

500

"C 625

Fig. 200. Bulk modulus B=x-’ vs. temperature T for various polycrystalline Fe-Ni invar alloys, measured in a magnetic field of 6 kOe. [72 H 2, 78 S 11.

Landolr-Bbmstein New Series lWl9a

Bonnenberg, Hempel, Wijn

239

[Ref. p. 274

1.2.1.2.9 Fe-Co-Ni: elastic moduli, sound velocity

240

Hbar 2.0 I 6 1.6 6

.I'

--

1.2

-J

2.4 Mbar I 2.0

Tl.6 6 1.2 0.8 0

100

200

300 I-

LOO

500 K 600

Fig. 201. Bulk moduli B, and B, as a function of temperature T for Fe -Ni invar alloys, (a) Fc,,,Ni,,3 and (b) Fe,,,sNi,,,,, for both the ferromagnetic phase and the pressure-induced paramagnctic phase. I: [Sl 0 33, 2: [67G2],3:[60Al].4:[79E2],5:[73HI].

Table 26. Cubicelasticconstants Fe-Ni alloys [78 S I]. wt% Ni

Cl1

[78 Sl]

30 35 40 45 50 60 70 80 90 100

c, ,, ct2, and cd4,in [Mbar],

1.46 ‘) 1.40 1.57 1.96 2.12 2.24 2.33 2.41 2.52 2.88

at room temperature for fee

c44

Cl2

[72 H 23

1.36 1.59 1.76 2.00

2.508 ‘)

[78 S l] 0.881 1) 0.92 1.09 1.42 1.55 1.51 1.46 1.43 1.43 1.81

[72 H 23

0.9 1 1.16 1.27 1.42

1.50 ‘)

1) [60A 1-J.

Bonnenberg, Hempel, Wijn

[78 S 11 1.13 1) 1.11 0.96 0.83 0.90 1.12 1.27 1.38 1.39 1.24

[72 H 21

1.042 1.024 1.035 1.072

1.235 ‘)

Ref. p. 2741

1.2.1.2.9 Fe-Co-Ni: elastic moduli, sound velocity

O.l6lL I.14 -I

I 51.4wt%Ni

t 1.10

Cl/

I\

. 3.0 t-=1

I CL= (c,,+c,*t

I 2c,,)/2

HoppI= 6kOe

a

2.0I

I

I

-250

-125

0

I 125 T-

250

375

500 "C 625

Fig. 202a, b. Single-crystal elastic constants of fee Fe-Ni invar alloys in the magnetically saturated state. The arrows indicate the Curie temperature Tc. T, is the temperature where the martensitic transformation occurs [73 H 11. See also [68 S 1,60A 11. For Fig. 202b, see next page.

Landolt-Bbmstein New Series 111/19a

Bonnenberg, Hempel, Wijn

241

1.2.1.2.9 Fe-Co-Ni: elastic moduli, sound velocity

0

-125

-250

125

250

375

[Ref. p. 274

500 "C 625

I

b Fig. 202b.

I

i.6

u

I.2

01 3G

LO

50

70

60 Ni -

80

90wt%100 Ni

Fig. 203. Room-temperature values of the elastic constants c1,, c12,and c+, offcc FeeNi alloys in the ma_rnetitally saturated state. Solid circles: [69S3], see also [64 S I], open circles: [73 H I], squares: [64S I], triangles: [6OA I].

Bonnenberg, Hempel, Wijn

Landol!.Rornrlcin Nea Srricr 111’19~

1.2.1.2.9 Fe-Co-Ni: elastic moduli, sound velocity

Ref. p. 2741

3.5 Mbar 3.3 3.1

I u'

2.9 2.1 2.5 2.3 2.1

-

1.9 0.62

r-73

0.54 0!+6 LI 0.3 I I0.31:

022 a.14

I ~,w-Fe 1.2

2

f

II

T -l

i/

1.1

Fe

NI -

Fig. 204. Ultrasonically measured elastic constants cL =(c,,+c,,+~c,,), c’=(c,,-c,,)/2, and c=cG4 for the fee Fe-Ni alloys at various temperatures. For the invar region, see [73 H 11. Outside the invar region, see 1: [64S 11, 2: [64E 11, 3: [68 B 21, 4: E. Claridge, Thesis University of Leeds (1968) [73 H 11, 5: cl-Fe [72C 1,71 S 1,70T 1],6: Ni [60Al].

Landolt-Bbmstein New Series 111/19a

Bonnenberg, Hempel, Wijn

Ni

244

1.2.1.2.9 Fe-Co-Ni:

elastic moduli,

sound velocity

Table 27. Elastic constants of Fe0.634Ni0,366 and Fe,,,,Ni,,,, and c,=c,,+c,,+c,,. [Mbar]. cd4. c’=(c,,-c,J/2

[Ref. p. 274

at 4.2K, in

Composition

CL

c44

c’

Ref.

Fe-36.6 at% Ni Fe-36.6 at% Ni Fe-37 at% Ni

2.558 (10) 2.460 ‘) 2.37

1.005(S) 1.003 ‘) 0.992

0.169(l) 0.166 1) 0.167

76Hl 73H 1 68B2

‘) Extrapolated.

0.35 K>:.: 0.X 025 0.26 0: 5

035

0

100

2OG

300

LOO

500

600 K 700

I-

Fig. 205. Temperature depcndencc ofthc elastic constant r’=(cI, -c12)/2 as determined from neutron scattering measurements of the [l IO] acoustic shear modes of the phonon spectrum of the invar crystal Fc,,,,Ni,,,, [77E I]. The solid line represents the ultrasonic measurcmcnts of [73 H 11. For more details on diffcrcnccs betlvccn elastic constants derived from dispersion relations for acoustic phonon modes and ultrasonic mcasurcmcnts. xc [79 E 2. 79 E I] and also [83 K 33, where the phonon states of alloys arc tabulated.

0

5

10

15

20

25 kOe

HopplFig. 206. Field depcndencc of the sound velocities t’ at various temperatures for a single crystal of Fc 0.634%366C76 H Il. c,=(c,,+c,,+2c4,)/2=QI:: c = c44 = p:,

whcrc u, is the longitudinal sound velocity and c,r and c,~ refer to the velocities ofshcar waves polarized in the [ IOO]

and [I IO] direction, [60A 11.

Bonnenberg, Hempel, Wijn

respectiveI;

[76 H 11, see also

Ref. p. 2741

1.2.1.2.10 Fe-Co-Ni: thermal expansion 1.2.1.2.10 Thermomagnetic properties, thermal expansion coefficient, specific heat, Debye temperature, thermal conductivity

8.9 9 cm3

8.6 8.5

I cl0

8.4 8.3

8.2 8.1 8.0

Fig. 207a. Density Qand the linear thermal expansion coefficient LXfor Fe-Co alloys. Solid circles: [Sl B 11, open circles: [29 W I], triangles: [41 E 11.For Fig. 207b, see next page.

7.3 7.8 IO a

20

30

40

50 co -

60

70

80 co

18 t 16

8

Fig. 208. For caption and Fig. (b), see next page. a Landok-BBmstein New Series 111/19a

0 Fe

IO

20

30

40

Bonnenberg, Hempel, Wijn

50 NI -

60

70

80

90wt%100 Ni

1.2.1.2.10 Fe-Co-Ni: thermal expansion

246

0 b

300

200

[Ref. p. 274

“C !

I-

IFig. 207b. Thermal expansion of polycrystallinc Fe-Co ialloys. The arrows indicate the phase transition. The ,ja+cd lines apply to samples cooled from about 400°C I[S-l I I].

Fig. 208. (a) Linear thermal expansion coetkient tl at various tcmpcratures for Fe-Ni alloys [Sl B fl. (b. c) Temperature dependence of the linear thermal expansion coefficient c(for fee Fe, -XNi, alloys above room temperaturc(b)x~0.5(c)x~0.5[7lT2],secalso[70T1,73Z1, 17C1,28Cl].

Bonnenberg,

Hempel,

Wijn

Ref. p. 2741

1.2.1.2.10 Fe-Co-Ni: thermal expansion

247

-2 -: 25

a

50

75

100 T-

125

150

175

200 K 225

Fig. 209a. Temperature dependence of the linear thermal expansion coefficient tl of the invar alloy Fe,.,,Ni,,,, below room temperature. The solid line is according to a calculation using the itinerant electron model with contributions from lattice vibrations, spin waves and single particle excitations [79 0 11. Crosses: [65 W 21, circles: [67Z I], triangles and dashed line: [71 S 11.

-0.8

I -1.2 b

-2.41

b

0

I IO

I

20

I 30

I K 40

Fig. 209b. Low-temperature linear thermal expansion coefficient CIfor a polycrystalline invar alloy sample of approximate composition Fe,,,,Ni,,,,. I: [67 Z 11, 2: [65 W 2],3: annealed, measured without magnetic field (square) and in a magnetic field (circles) of 21.6 kOe [71 S 1],4: cold worked and measured in a magnetic field (crosses) of 21.6kOe [71 S 11. Landolt-Bijrnstein New Series 111/19a

Bonnenberg, Hempel, Wijn

1.2.1.2.10 Fe-Co-Ni: thermal expansion

248

1J

[Ref. p. 274

I

I.

I*

6

2 0 -2 -4 4 2 0 I -2 84

-1

0.369 [llOl 0.408 I1001

2

--I

-2

5u

0

I

I

I

100

150 I-

200

b

-2 4

I 250 K 300

Fig. 2lOb. Linear thermal expansion cocfkicnt z for three invar alloy Fe, -,Ni, single crystals. Measured parallel to the [IOO] direction in the (001) plane. For the alloy x =0.369 also mcasurcmcnts parallel to the [I IO] direction have been made [78 K I].

2 0 -2 6

2

3 m' K-1 2

rl

I 1

4

-2 50

a

100

150

200

250 K 300

8 0

J-

Fig. 2lOa. Temperature dcpcndcncc ofthc linear thermal expansion cocflicient r for various Fe-Ni invar alloys below room temperature [83 R I].

-1 -2 0

50

C

100

150 T-

200

250 K 300

Fig. 210~. Linear thermal expansion coefficient a as a function of tempcraturc for the invar alloy Fe,,,,Ni,,,, after diffcrcnt heat trcatmcnts: qucnchcd in oil from 1000°C (solid circles), additionally annealed for 9 h at 314°C (triangles) and for 75 h at 525°C (open circles). rcspcctivcly [72 M I].

Bonnenberg, Hempel, Wijn

249

1.2.1.2.10 Fe-Co-Ni: thermal expansion

Ref. p. 2741

15.0,

21 .'a-4

xm4

18

I

I

I

I

I

I

Ni0.33H,

k0.67

c A

12.5 .

15

. 0 a

10.0 I 12

.

.

.

&*

Yl a

A

: a9

6

3 0 -180

-150

-120

d

-90 T-

-60

-30

-180

"C 0

-150

-120

Fig. 210d. Temperature dependence ofthe linear thermal expansion Al/l for hydrogenated Feo,zsNio,,5 alloys. The thermal expansion coefficient is given by the gradient of the curves [83 H 11.

-90

-60

-30

"C 0

T-

e

Fig. 210e. Temperature dependence of the linear thermal expansion AZ/1as in Fig. 210d, but now for Fe,,,,Ni,,,,H, [83 H 11.

15 10-6 K-1 IO I 8 5

0 0

f

0.05

0.10

015

x-

Fig. 210f. Hydrogen concentration dependence of linear thermal expansion coefficient CIfor Fe,,,,Ni,,,, alloys in the temperature range on - 150 to 0 “C [83 H 11.

Fig. 211. Low-temperature value of the linear thermal expansion coefficient ccof an Fe,,,,,Ni,,,,s invar alloy single crystal as a function of roll reduction R for the case of(OO1)[ 1lo] rolling, measured parallel (open circles) and perpendicular (solid circles) to roll reduction. For the difference Act between both expansion coefficients as a function of R, see Fig. 162b [77 K 11.

Landolt-Bbmstein New Series lll/l9a

x-

g

Fig. 210g. Hydrogen concentration dependence of the linear thermal expansion coefficient c(as in Fig. 21Of,but now for Fe,,,,Ni,,,, alloys [83 H I].

0

IO

Bonnenberg, Hempel, Wijn

20

30 R-

40

50 %

60

1.2.1.2.10 Fe-Co-Ni: specific heat

2.50

[Ref. p. 274

0.50 col gK 045

O.LO

c 0.30

0.25

0.20

0.15

0.10 600

700

800

900

1000

1100

1200 K 1:

Fig. 212.Spcciticheat C, vs. tcmpcraturc T for the alloy Fe,,,Co,,,. Different symbols refer to diffcrcnt runs [7402]. I cal~4.187 J. The lower lint rcprcscnts the lattice and conduction electron contribution to C,

Table 28. The low-temperature spccitic heat of fee FeNi alloys as the sum of three terms: C,=~T+/?T3+aT3’*, electronic, lattice, and spin wave contributions, respectively [68 D 11, see also [74 C 43. at% Ni 100

95.7 90.3 86.2 81.1 68.7 59.2 55.1 50.1 45.0

Y mJmol-‘K-*

P mJmol-‘K-4

c( mJmol-LK-5/2

7.039(16)')

0.0179(7) 0.0186(12) 0.0184(13) 0.0189(17) 0.0167(10) 0.0175(8) 0.0187(6) 0.0194(9) 0.0226(g) 0.0257(20) 0.0278(12)

O.Oll(13) 0.026(22) 0.043(22) 0.074(29) 0.083(17) 0.072(14) 0.115(12) 0.165(17) 0.045(14) 0.149(35) 0.235(21)

7.028(27)‘) 6.411(26) 5.58l(35) 4.957(20) 4.418(16) 3.899(14) 3.986(20) 4.028(16) 4.429(40) 4.929(24)

‘) Values from [65 D 11.

Bonnenberg, Hempel, Wijn

251

1.2.1.2.10 Fe-Co-Ni: specific heat

Ref. p. 2741 0.25

Fig. 213. Spin wave specific heat coefficient c(offcc Fe-Ni alloys as derived from various measurements. Triangles: specific heat measurements [68 D 11,open circles: specific heat measurements of [68 D l] combined with ultrasonic measurements of the elastic constants [68 B2], solid circles and line: neutron scattering measurements [64H 11. Cross: disordered FeNi, [70 K 21.

mr& 0.20

0.15

I 0.10 8

-0.05 0 Ni

0.1

0.2

0.4

0.3 x-

0.5

0.7

0.6 -^

s.u mJ mol K2

ordered

-cc))-I-

--

--

CD= 2.286.10-2T3t3.301 T 3.0 0

2

6

4

8

12

IO T2 -

14

16

18 K2 20

Fig. 214. Low-temperature specific heat capacity C, of ordered and disordered FeNi, [70 K 21.

Fig. 215. For caption, see p. 253.

8

0

a Fig. 215a. Land&Bbmstein New Series III/I%

200

600

400 T-

800 K

IC

0

b Fig. 215b.

Bonnenberg, Hempel, Wijn

200

400

600 T-

800

K II

252

1.2.1.2.10 Fe-Co-Ni: specific heat

[Ref. p. 274 -l

12 Cii

mz’ K 10

I Fed%.:77 I

I

12 COI molK

HI P

10

8

8

I cl6

I ,6

4

4

2

2

0

200

400

600

800

200

K 1000

400

600

800

I

I

600

800

K 1030

T-

I-----

C

Fig. 21.5~-f.

1;

Ii COI mol K

CUl

mzl K

Fe0.508 Ni0.492

I

I

l[

0 e

200

400

600 I-

800

K 1000

200 f0

Bonnenberg, Hempel, Wijn

400 T-

K 1000

253

1.2.1.2.10 Fe-Co-Ni: specific heat

Ref. p. 2741

IO col mol K 8

200

600

400

800

K IC

0

200

400

800

600

K 1000

T-

h

T-

Fig. 215g-j.

IC col molK

I

FeO.662 Ni0.338 81

8

I

%I Fe0.708,i0@

I

r

cv

I

I

/

1

61

I4

u

I

i

200

600

400 T-

800

K 1000

0

200

400

j

Fig. 215a-j. Specific heat C of fee Fe-Ni alloys at high temperature. Sample annealed at 1000 “C for 25 h and cooled in the furnace. C,: derived from C, by substrating the contribution of thermal expansion, C,,: specific heat contribution from lattice vibrations, as calculated from Debye temperatures obtained from measurements of the elastic moduli, C,,: contribution from conduction electrons, supposed to be proportional to the temperature, also at higher temperatures, Cv, and Cv,: contributions from magnetic and atomic ordering, respectively [73T2]. lcal~4.1875.

Landolf-Bijrnstein New Series 111/19n

Bonnenberg, Hempel, Wijn

600 T-

800

K 1000

[Ref. p. 274

1.2.1.2.10 Fe-Co-Ni: specific heat

254

40 mJ K.* Cotom

i

JGT7-1 I

20

unFertoinly in,CvJ

2E

I

10

6

O -10

2i -20 2G

-30 ( 2000

0

Cl.1

Fe

Fig. 216. Specific heat ofdisordered FeNi, as a function of temperature. Experimental curve C, from [73 K 31. C, is derived from C, using a dilatation correction. The lattice specific heat C,., is derived from a Dcbye tempcraturc of 38-l K. C,., is the electronic specific heat. T,=872.6K is Curie temperature of the disordered alloy and Trd = 773 K is the order-disorder transition temperature [82 B I]. For specific heats ofFcNi, samples with various degree of order. see [73 K 33.

0

so

100

150 I-

200

250 K 300

0.2

0.3

0.4

0.5

0.6

0.7

X-

Fig. 217. Increment of the electronic specific heat coeflicicnt Ay per C atom in Fc,Ni, -,C, alloys [74C 23.

Fig. 218. Debye temperature 0, ofFe, -,Ni, invar alloys as derived from measurements ofintegrated intensities of X-rays at various temperatures. T, = 92 K is the temperature where the martensitic transformation starts [79 M 11.

Bonnenberg, Hempel, Wijn

Ref. p. 2741

1.2.1.2.10 Fe-Co-Ni: specific heat

255

Fig. 219a. Debye temperature On of Fe,-.Ni, alloys as derived from low-temperature elastic constants. The dash-dotted curve refers to the paramagnetic state by extrapolating the elastic constants from above the Curie temperature [75 H 11.1: [75 H 1],2: [68 B 2],3: [6OA 11, 4: cl-Fe [61 R 11. Dashed line: calculated from elastic constant data extrapolated to low temperature. For 0, derived from low-temperature specific heat measurements, see [68 D l] : Ni [at%]

@DCKI

Ni [at%]

@niw

100

477.4(62)

68.7

470.9(101)

59.2 55.1

470.6(50) 464.4(72)

441.4(52)

50.1 45.0

412.2(59)

95.7

473.2(111)

90.3

469.1(141)

86.2

488.2(98) 480.6(73)

81.1

423.0(110)

500 K 460

0.6

I,420 0

a

0.8

1.0 Ni

x-

Fe

380 v 3LO 30

40

50

70

60

80

400°C 90 wt%loo

b Ni Ni Fig. 219b. Debye temperature On of Fe-Ni alloys as derived from elastic constant at various temperatures [71 T 11. 2.5 mW cmK

40 mW cmK

4 -mW cmK

w . oc .O Ir! 0 -b Tl .O .0O

20

2

1

I ‘!

0.7 I 0.8 0.6 x'

; x 6 5

0.5

4

0.4

3

0.3

2

0.2

0.5 0.1

1 1

01 1.0

1.5

2.0

2.5

3.0

3.5

4.0

L.5 K 5.0

TFig. 220. Decrease of the low-temnerature thermal conductivity II of an Fe,,,Ni,,, alloy in various magnetic fields [70 Y 11. Landolt-Biirncfein New Series 111/19a

2

3 T-

4

5 6 7 EKIO

Fig. 221. Low-temperature total thermal conductivity x of two Fe-Ni alloys, as well as the supposed magnon part of the thermal conductivity, x,, both in absence of a magnetic field [70 Y 11.

Bonnenberg, Hempel, Wijn

1.2.1.2.10 Fe-Co-Ni: specific heat

256

[Ref. p. 274

25 molKL

mJ molK2 7.0

\ \

/

6.5

6.0 I x 5.5

5.0

1.8Ol 0.3

0.4

0.5

0.7

0.6

0.8

4.5 I Ni

0.9

X-

Fig. 222. Electronic and lattice specific heat constants, 1 and /?, rcspcctivcly, for Co, -,Ni, alloys as dcrivcd from low-tempcraturc (1.2.‘.8 K) specific heat mcasurcmcnts [74C4]. see also [59 W I].

I

400

16 >:I

D 0

A

14

0

co

- 300

0.2

0.4

x-

0.6

0.8

1.0 Ni

Fig. 223. Electronic specific heat constant y and Debyc tempcraturc 0, for Co,-,Ni, alloys [68 H I]. lcal&4.187J.

Bonnenberg,

Hempel,

Wijn

Ref. p. 2741

1.2.1.2.11 Galvanomagnetic

properties

26, p.Qcm 1

257

1.2.1.2.11 Fe-Co-Ni: resistivity, Hall coefficient, thermoelectric power

I

I

I

I

18

20

22 co -

24

I

Fe-Co

20

I Qr 18

0 16

2 30

IQn 0

IO

0 Fe

16 b

0

26 wt% ;

Fig. 224b. Electrical resistivity of Fe-Co alloys at room temperature [75 F 11.

0 2 0 2 0

Okdl 0

-200

a

T-

800 1000 "C Ii

Fig. 224a. Temperature dependence of the electrical resistivity Q for Fe-Co alloys [39 S 21.

UI

0

c Fe

20

40

co-

60

80 wt% 1’

co

Fig. 224~. Resistivity of the Fe-Co alloys, at various temperatures [74V 11.

Land&Bbrnstein New Series lll/l9a

Bonnenberg, Hempel, Wijn

258

1.2.1.2.11 Fe-Co-Ni: resistivity, Hall coefiicient, thermoelectric power

4s .?i-2

Fe-Co

[Ref. p. 274

I = -195°C

3.f

i 3.2

I sr”

2.6

60

40

2.4

20

-195°C

0

-20 0

c

20

Fe

60

40

co -

80 wt% 100 co

Fig. 225~. Concentration depcndcncc of the anomalous Hall constant R, for Fe--Co alloys at various temperatunes [74V I].

0.E

0.4

C

1

-0.i a

1

20

FE

60

Fig. 225a. Longitudinal magnctorcsistancc. i.e. the rclative change of the electrical rcsistivity, AQ ,/Q. as a conscqucncc of an applied ficld of I.5 kOc for Fc Co allow at various tempcraturcs [39 S 2).

80 wt%

co -

co

80

I d

63

40

20

0 -20 -200

-100

0

100

200

300

400

0 500 "C 601

Fig. 225b. Tcmpcraturc depcndcncc of anomalous Hall constant R, for Fc Co alloys [74V I].

b

Bonnenberg, Hempel, Wijn

I.andolr.Rornrlcin Neu Scricr III ‘19:s

Ref. p. 2741

1.2.1.2.11 Fe-Co-Ni: resistivity, Hall coefficient, thermoelectric power

n

rc-‘y’

259

29.87wt%Ni

Fe-Ni

11 p!h

IL

-F-

j

19.56

I 13 Qr

12

IO

7

-!73 -200 a

II

200

I

I

400 7-

600

I

800 “C IC

b

0 -273 -200

0

200

KIO

600

800 “C I[

7-

Fig. 226. Temperature dependence of the electrical resistivity Q for FeNi alloys. (a) 0...30wt% Ni, (b) 35 . ..lOO wt% Ni. The arrows on the curves indicate the temperature sequence of the measuring points. The vertical arrows denote the Debye temperature On as derived from the specific heat. The vertical scale is equal for all compositions and is given by the length ofthebarindexed40@2cm[39S3,60K1,71T1].

1.F pQcm

1.C I Q 0.5

Fig. 227. Electrical resistivity Q at 4.2K vs. Fe concentration in Fe,Ni,-, alloys. The straight line derived trom a least-squares fit is given by @=0,03(2)+33(1)x, p in @cm [71 S 21. Landolt-BBmstein New Series Ill/~%

0 NI

Bonnenberg, Hempel, Wijn

0.01

0.02

0.03

x-

O.OL

0

[Ref. p. 274

1.2.1.2.11 Fe-Co-Ni: resistivity, Hall coefficient, thermoelectric power

260

I quenched from1400K 2 equilibrium at 767 755 3 735 4 713 5

6

1000

1200 K 1L

Fig. 228. Electrical rcsistivity Q vs. tempcraturc T for FeNi, alloys after various heat trcatmcnts leading to rarious degrees of atomic ordering [73 K 31. See also [82 0 21. Krd: order-disorder transition tempcraturc.

0

10

20

30

LO

50

60

70 K 80

I-

Fig. 230. Tcmpcraturc dcpcndcncc of the rclativc change of the electrical rcsistivity for small incrcmcnts of the magnetic field. (Aplp,)‘A,H at high values of the magnetic licld strength H. i.e. in the range ofthc pnraproccss for Fe Ni invar alloys. 40 denotes the rcsistivity in zero magnetic licld [59 K I].

5

0

10

20

30

40 I-

50

60

70 K 80

Fig. 229. Temperature dependence of the relative change of the electrical rcsistivity under hydrostatic pressure p, (A?/+)/Ap, for an invar alloy Fe,,,,Ni,,,,. where o0 is the rcslstlvity under ambient pressure [59 K I].

0 Ni

0.1

0.2

0.3 0.1 x-

0.5

0.6

0.7

0.8

Fig. 23 1. lncrcmcnt of the residual (i.e. low temperature) rcsistivity per atom percent c of C. A.o,lc, for (Fe,Nil -,) C, alloys [74 C 23.

Bonnenberg, Hempel, Wijn

I.andolr.Bornrrcin Nea Scrim III ‘19n

1.2.1.2.11 Fe-Co-Ni: resistivity, Hall coefficient, thermoelectric power

Ref. p. 2741 110

261

I

pQcm Fe-Ni-Ti

0

u-o AT

100 0

3 4.75 at%Ti

60

30

34

38

42

46 wt%

50

0

50

100

NI -

Fig. 232. Influence of Ti additions on the roomtemperature electrical resistivity Q of Fe-Ni invar alloys [73K2].

150 200 T-

250

300 K 350

Fig. 233. Temperature dependence of the longitudinal magnetoresistance (A@/@) ,,, measured in a magnetic field of 20 kOe for various orientations of the crystal axis of an invar alloy [78 V 11. %65%35

1.6 %

8

1.2

6 ‘= G ch

I =

I

0

I

I

IO

20

I

I

I

30 Fe -

40

I

Landolt-Bdmstein New Series I11/19a

F 2 0.4

2

0

0

50 wt”/o

Fig. 234. Spontaneous resistance anisotropy (Q,,- el)/Q for fee Fe-Ni alloys as defined by the value of the difference ofthe resistance ofa sample magnetized parallel or perpendicular to the measuring current relative to the average of their values [74 C 31. Open circles: T=20K [59 E 11, solid circles: 4.2 K [74C 31.

For Fig. 235, see next page.

4s

0.8

-0.4 0 Fe

F 1M I d+AFpIANi I I I I 20 40

60 NI -

80 wt% lOi Ni

Fig. 236. Longitudinal magnetoresistance as a consequence of an applied field of 1.5kOe for FeNi alloys at various temperatures [39 S 11. F: ferrite, M: martensite, A: austenite. Dashed curves: cooling.

Bonnenberg, Hempel, Wijn

262

1.2.1.2.11 Fe-Co-Ni: resistivity, Hall coefficient, thermoelectric power

1.2 %

‘;,y Fe-Ni 0.; fee

0.8

0.5

-

0

[Ref. p. 274

Hopp, = 1.5kOe 35wl%Ri

-_)

40

0

? 0

0.1

1 0

0

0.8

1 0.1

0 I = 2 5

I 0 204 ,a G -4

z- 1

0 0.2

0

0

1

0.2

0

0

1

0.2

C

0

1

0.2

0

0

1 0

-0.4 I -203

I 200

I 0

a

I 400 I-

I 600

I 800 “C

1;

b

IIIII

0

200

400

600

800 “C

T-

Fig 235. Longitudinal magnetoresistance vs. temperature for (a) hcc Fc-Ni and @) fee Fe-Ni alloys [39 S I]. Arrows indicate hystcrcsis. 0.3 1=20K

I = G T2

0.2 o Ni -Fe Ni-Co A Ni-Cu -A Ni-Fe-k l

0.i

0

41 ) ;’ II d Ni 0.5

1.0 PO:-

0 uCob 1 Ps

2.0

Fip. 237. Longitudinal magnetoresistancc (AQ/Q,,),, at 20K as a function of the mean magnetic moment per atom. &,, for various 3d-element alloys [Sl S 1, 575 1, 64C I].

Ni

Fe -

Fig. 238. Normal Hall coefficient R, vs. Fe concentration in Fc-Ni alloys at various temperatures [7OC I]. lm3C-‘nIO-2R cmG-‘.

Bonnenberg, Hempel, Wijn

Ref. p. 2741 0 .lO"

1.2.1.2.11 Fe-Co-Ni: resistivity, Hall coefficient, thermoelectric power

263

N i _ Fe 2000III4000

I ?2

1600

-‘!b

1.2 p&m

3200

800

t 2400 z .s s K 1600~

400

800

I 1200

1.8

P-

Fig. 239. Anomalous Hall angle Q,JQ vs. the resistivity Q for Fe-Ni alloys with small concentration in the range from 0.5 up to 5at% Fe. T=4.2K. Open circles: [75 D I], solid circle: [74 J 11. can: en = R,B + eaH.

CT

0

0

-400 -200

200

0

a

400

“C

-800 600

T-

Fig. 240a. Temperature dependence of the spontaneous Hall coefficient R, for Fe-Ni alloys. The scale on the right-hand side applies to 55wt% Fe [64K I]. lm3C-1~10-ZQcmG-1.

5

0

b

4.07 3.09 . 2.44 P I.08

I t -4+. 40

80

120

160

200

240

d

280 K 320

T-

-0 0.89

Fig. 240b. Low-temperature values of the spontaneous Hall coefficients R, of Fe-Ni alloys [65S 11. 1m3C-‘~10-Z~cmG-1.

0 a -v o

-6

1 1

I I

I

F-h\\ Y\\\

u\ I\ \

1~1if

0.43 0.35 0.07 NiII

-7

Fig. 240~. Temperature dependence of the spontaneous Hall coefficient R, for small Fe concentrations in Fe-Ni alloys NQ): annealed at 105O”C, 1 h [65H I]. 1m3 C-l& 10-2ficmG-‘. The original literature gives the absolute values of R,. Landolt-BBrnsfein New Series lll/l9a

-8 c

t

-91 0 C

Bonnenberg, Hempel, Wijn

50

100

150 T-

200

250 K :

1.2.1.2.11 Fe-Co-Ni: resistivity, Hall coefficient, thermoelectric power

264

[Ref. p. 274

-0x

=a

I oe

b

c

-0.8

\ 4

1 I 15ot% Ni 0

I 0 . -0.5

--a-

-1.2 0

50

150 I-

100

d

-1.6

-2.0 200

80

250 K 300

160 I-

e

Fi_e.240d. Normal Hall coetlicicnt R, vs. temperature for small Fe concentrations in FeNi alloys [65H I]. NiI(II): annealed at 1200“C (1050 “C) for 2 h (I h). then cooled at a rate of S”C!min. The original literature gives the absolute values of R, [65 H I].

2LO

-0.E -0,s 0.5

1.0

1.5

2.0

320

Fig. 240~. Low-temperature values of the normal Hall coefftcicnts R, of Fe-Ni alloys [65S I]. n: effective number of electrons per atom, n = - l/R,Ne, where N is the number of atoms per m3 and e is the electron charge 1m3C-‘a 10-ZRcmG-‘.

-0.E

0 Ni

K

2.5 3.0 Fe,Co,Cu -

3.5

L.0

4.5

ot%

Fig. 241. Normal Hall coctlicicnt R, for alloys ofNi with Fe.Co,andCu[65Hl].lm3C-r&IO-*ficmG-’.Thc original litcraturc gives the absolute values of R,.

Bonnenberg, Hempel, Wijn

5.5

Ref. p. 2741

1.2.1.2.11 Fe-Co-Ni: resistivity, Hall coefficient, thermoelectric power

265

Fe,-, Ni, Fel-x Ni,

0

100

200

300

a

400

500

100

600 K 71

200

300

400

500

600 K

T-

I-

Fig. 242a. Temperature dependence of the anomalous Hall resistivity can extrapolated from saturation region to zero field for Fe,-,Ni, invar alloys. The vertical arrows indicate the Curie temperatures. The vertical scale is equal for all compositions and is given by the length of the vertical bar showing a scale of 0.5 @I cm. The reference levels for the ordinate are given by the figures attached to horizontal arrows [76 S 11.

Fig. 242b. Temperature dependence of the spontaneous Hall coefficient R, in Fe,-,Ni, invar alloys. The vertical scale is equal for all compositions and is given by the length of the bar showing a scale of 50.10-lo m3 C-‘. The reference level for the ordinate is given by the figure attached to horizontal arrows [76 S 11. 1m3C-‘~10-2~cmG-‘.

0 a

20

40

60 7-

80

0

K 100

2

4

6

b

Fig. 243. Temperature variation of the thermoelectric power Q of Fe-Ni and Co-Ni alloys [70F 11. (a) T=O...lOOK, (b) T=0...15K.

Landolt-Bbmstein New Series IWl9a

Bonnenberg, Hempel, Wijn

8

T-

10

12

14 K 16

1.2.1.2.11 Fe-Co-Ni: resistivity, Hall coefficient, thermoelectric power

266

-0.5 0

0.1 0.2

0.3 0.1 0.5

0.6 0.7

Iii XM Fig. 24-l. Thcrmoclcctric power Q at I K for Fc,-,Ni, alloys and tcmary FqNi, - ,C, alloys [74 C 21. G

-2

0

Ni-Co

0.8

0

200

300

LOO

500 K 600

IFig. 245. Thermoelectric power Q of a monocrystallinc. slowly cooled sample of the invar alloy Fe,,,,Ni,,,, as a function of tcmncraturc for various crvstal directions . [78Vl]. L

I

c.2

100

[Ref. p. 274

-0.3

0.4 0.6 pQcn 1.0 $= -04 4Fig. 246n. Anomalous Hall angle P,,,/Q vs. the rcsistivity -0.5 e for Ni-Co alloys with small concentration in the range from 0.5 up to 5at% Co. e depends linearly on the Co -0.6 concentration. Solid circle: [74 J I]. open circles: [75 D I]. a

- 0.8 0

50

b

100

150

200

250 K 300

I-

Fig. 246b. Temperature dcpcndencc of the normal Hall cocffkicnt R, of Ni--Co alloys [65 H I]. I m3C-‘~10-20cmG-‘. For NiII,scccaption to Fig. 240d.

. 1.01 -1 0 C

50

100

150

200

Fig. 246~. Temperature dcpcndence of the spontaneous Hall coefficient R, of Ni -Co alloys [65H I]. lm3C-‘a10-252cmG-‘.ForNiII,scecaption toFig. 250 K 300 240d

I-

Bonnenberg, Hempel, Wijn

Ref. p. 2741

1.2.1.2.12 Fe-Co-Ni:

267

Kerr effect, optical constants

1.2.1.2.12 Magneto-optical

properties

Table 29. Polar Kerr rotation angle ak for normal incident polarized light on Fe-Co and Fe-Ni alloy surfaces, seealso Fig. 247.aK= K&f, is the rotation angle between plane of polarization of incident light and major axis of the elliptically polarized reflected light. The minus sign meansthat the rotation is opposite to the circular current producing the magnetization. (s): saturated, (u): unsaturated. Composition

Fe-25 wt% Ni

5300 5670 5890

Fe-27 wt % Ni

5890

Fe0.67Ni0.33

5300 5670 5200 5740

Fe0.67COO.33

Fe-36 wt% Ni, Invar

H

EK

41tK,

kOe ‘)

min

10m4min G-r

23.3 6) 16.8(u) 14.9(u) 16.3(u) 14.4(u) 19.13(s) (4 19.8(s) 14.51(s) 13.30(s)

-27.64 - 29.94 - 15.92 - 14.32 - 17.29 - 16.45 - 15.05 - 22.55 - 13.86‘) - 13.65 - 13.66

- 11.9 x - 9.5

17Bl 18Ml 12Ll

z - 12.5

12Ll

- 13.7

17Bl 18Ml 12Fl 12Ll

- 12.9 - 20.2

‘) Ellipticity of the reflected light ak = -0.44.10 - 3. J .lO"A

6

5

--36' 4

6

5

l 2 OAV.7 I 7 .1rl'4s-'

8

Y-

Fig. 247.Polar Kerr rotation anglec~kfor normal incident polarized light on Fe-Co and Fe-Ni alloy surfacesas dependenton the frequencyof the light [62 L 1,p. l-1941. Curve I: [18M 1],2: [17B 1],3: [12L 11. Landolt-Bdmstein New Series 111/l%

Bonnenberg, Hempel, Wijn

Ref.

268

1.2.1.2.12 Fe-Co-Ni:

[Ref. p. 274

Kerr effect, optical constants

Table 30. Room-temperature magnetization, Kerr rotation at a wavelength of 633OA of Fe, -Co, alloys in a not completely magnetically saturated state of the alloy. Saturated values estimated to be less than 10% higher than the values shown [83E 11. Alloy

0 Gcm3g-’

Fe Fe,Co FeCo FeCo, co

213 234 230 200 156

% deg

I%;/4 10-3degG-1cm-3g

-0.41 -0.41 -0.54 - 0.48 -0.35

1.9 1.8 2.3 2.4 2.2

I

Fe -36wt%Ni

Fig. 248.Frcqucncy dcpcndcnccof the cllipticity Edof the polar Kerr effectof an Fe-36~1% Ni invar alloy [62 L I. 5

6

7 .lO“ s-1

8

12Fl].

iI ,_

6

I-

I-

0

-0.4

-2

0.L

0.8 pm 1.0

0.6 A-

0.6

0.8 pm 1.O

-0.E

b!

L-

Fig. 249.Equatorial Kerr effect(M, parallel to the surface of the specimen and pcrpcndicular to the plant of incidence of the light). 6=1/l,. the relative change of intensity ofrctlcctcd light polarized parallel to the plant of incidcncc. as dcpcndcnt on wavclcngth and on angle of incidcncc 0 ofthc light [73 B 21.(a) Fe,(b) Fe-45 wt% Ni, (c) Fe-EOwt% Ni. (d) Ni.

Bonnenberg, Hemp& Wijn

0.8 pm

0.6 A-

1.0

Ref. p. 2741

1.2.1.2.12 Fe-Co-Ni: Kerr effect, optical constants

269

60 .10-i 50

-40 -50

-50 0

Fe

20

40

60 Ni-

80wt%100 Ni

0 Fe

20

40

60 Ni -

80wt%100 Ni

Fig. 250. Components of the magneto-optical parameter Q = Q, -iQ, as dependent on the composition of Fe-Ni alloys for several wavelengths ofthe light, as derived from the equatorial Kerr effect. Q = is&,, (H in z direction). [73 B 21. Curve I: 6700 A, 2: 6000 A, 3: 5400 A, 4: 4700 & 5: 4400 A.

05'

1

8

0'

-05'

Fig. 251. Longitudinal Kerr rotation angles (M, parallel to surface of the specimen and plane of incident light) a, and tlP for light polarized normal or in the plane of incidence, respectively, as dependent on the angle of incidence f3for Fe,,,Ni,,, . The wavelength ofthe light is a parameter. Room-temperature measurements [68 J 1, see also 66 T 11.The sign of the Kerr angle is chosen positive when the rotation and the direction of the reflected beam form a right-handed screw. Landolt-BBmstein New Series 111/19a

-1 0'

-1 5'

-20' 0"

Bonnenberg, Hempel, Wijn

15"

30"

45"

60"

75"

90"

1.2.1.2.12 Fe-Co-Ni: Kerr effect, optical constants

270 I

I

Fe-Ni

I

[Ref. p. 274

5.

t

CT 14 3 2 J’ r

1 I 70 NI -

I 63

I 50

I 80

I I 90 wt % 100 Ni

Fig. 25%. Longitudinal Kerr rotation angle tl, (for incident angle 0 =45’)vs.composition and wavclcngth for fee Fe -Ni alloys r68 J I]. The data for Ni arc due to [61S7].

-

-

0 40 50 60 70 80 90VAO/c103 Ni Ni b Fig. 252b. Kerr rotation (xP(for incident aqle 0 =4Y) vs. composition and wavelength for fee Fe -Ni alloys [68 J I]. The data for Ni arc due to [64 S 23.

-

0

I

*lo-‘ Fe-Ni -1

I

IEot%Ni

70 75 81 84 90 95 Ni

-6 0.25

0.50 0.75 1.00 1.25 1.50 1.75 2.00$25 1.-

FYg. 253a. Wavelength dependence of the longitudinal ma_rncto-optical Kerr rotation in the visible and near infrared regions for Fe-Ni alloys mcasurcd with s polarized light at the incident angle of 60”. The 1000A films are evaporated on a glass substrate at 200 “C in a vacuum of 2. IO-‘Torr (2.7. 10e5 mbnr) and annenlcd for about 2h [69YI].

-7 0.25

I

0.50 0.75 1.00 1.25 1.50 1.75 2.ooplr;z.25

Lb Fig. 253b. Wavclcngth dependence of the longitudinal magneto-optical Kerr rotation as in Fig. 2.53a,but nou for p polarized light and an incident angle of7Y [69Y I].

Bonnenberg, Hempel, Wijn

Ref. p. 2741

1.2.1.2.12 Fe-Co-Ni: Kerr effect, optical constants

271

Fe- Ni

.lO” 14

a= 5000 A 12 IO 8

t I

-2 --•--

-41 0”

I

I

I

Fe-BOwt% Ni

I

I

IO”

20”

I

I

30” 40” Q-

6

r

I

I

I

50”

60”

70”

80”

Fig. 254. Longitudinal Kerr rotation for light polarized in the plane ofincidence, as dependent on angle of incidence, 0, of light, and the composition of Fe-Ni alloys evaporated films. Wavelength of the light 5OOOA [76 M 31. Solid circles and dashed line: [68 J 11. 0 0

2i .,o-?

IO”

20”

30”

40”

50”

60”

70”

80”

Fig. 255. Kerr ellipticity sKfor Fe-Ni films as a hmction of the angle of incidence 0. Longitudinal arrangement, light wavelength 5000& polarized in the plane of incidence [76 M 31.

I

Fe-Ni

2c

Fe-Ni’

I

4J-N

0.6

IE

14 I 0” 12

IO

8

0 n=40508, . 4590 5030 6 -v . 5490 A 5980 4 1 50

I

60

70 NI -

80

90 wt% 100 Ni

Fig. 256. Amplitude Q, of the magneto-optical parameter Q =is.&,, (H in z direction), vs. wavelength and composition for fee FeNi alloys, as derived from longitudinal Kerr-effect [68 J 11. Q = Q, expiq. Landolt-Bbmstein New Series lll/l9a

40

50

60

70 Ni -

80

90 wt% 100 Ni

Fig. 257. Phase factor of the longitudinal magnetooptical parameter, q, as a function of composition and wavelength for fee Fe-Ni alloys [68 J 11. Q=Q,expiq = isx,,/.s,, (H in z direction).

Bonnenberg, Hempel, Wijn

[Ref. p. 274

1.2.1.2.12 Fe-Co-Ni: Kerr effect, optical constants

272

IIIrFq--j-

20’ r

0”

t -20’ b

LO50 v 5550 I 3’ -film tit7

0

-Ci

20

40

60

80 wt% 100

NI -

o SOwt%Ni 1.6

Fig. 258. Phase factor (I of the longitudinal magnctooptical parameter Q = Q. expiq = ic,)./c,, (H in z direction) as a function of composition for Fe-Ni alloys [76 M 33. Circles: [76 hl33. squares: [12 F I], upward triangles: [63 R 11, crosses and open circles [68 J 11. lozcngc and downward triangles: [63 T I].

l

80

v 70 . 60 1.4I 4000

I 1500

5d30

I 5500 1 E

Fig. 2.59.Rcfractivc index n,(n = nO(1-ix)) vs. wavelength and composition for fee Fc-Ni alloys [68 J I].

1.9 1.8 1.7

I

x

1.6

1.5

1.4 4[

L500

5000 1-

5500 1 6000

Fig. 260. Imaginary part of rcfractivc index. x(n=n, .( I -ix)), as a function of wavclcngth and composition for fee FeNi alloys [68 J I].

Bonnenherg,

0 Fe

20

40

60 NI -

80 VA% 100 Li

Fig. 261. Rcfractivc index II = nO(1-ix)vs. composition of Fc-Ni alloys, measured at 5OOOA. Circles: [76M 33. triangles: [68 J I], squares: [63 R I], lozenges [06 I I].

Hempel,

Wijn

I.andol~-Rornwin Ncu

Sericq

111’19n

Ref. p. 2741

273

1.2.1.2.13 Fe-Co-Ni: ferromagnetic resonance 1.2.1.2.13 Ferromagnetic resonanceproperties

Fig. 262. Landau-Lifshitz damping parameter L for different FeNi alloys as derived from ferromagnetic resonance linewidth data obtained at frequencies of 19.5 and 26 GHz on (100) disks of bulk single crystals [76 B 11. For single crystal of Co,,,,Ni,.,,, 1=2.18. 10-8s-1 [75W 11.

10.0 w* s-1

I

Fel+ Ni, 1.5 mg s-1 5.0

1.5

~t 5.0

I c-”

2.5 2

2.5 0 0.25 Fig. 263. Landau-Lifshitz damping parameter 1 for Fe75 wt% Ni as dependent on the state of ordering [76 B 11, see also [74 B 11. For the case of small dopes with MO or Cu, see [74P 11.

Landolt-B6mstein New Series lll/l9a

0.35

0.45

0.55 x-

0.65

0.75

0 0.85

Fig. 264. Room-temperature value ofthe Landau-Lifshitz damping parameter L for fee Fe, -,Ni, alloys as derived from ferromagnetic resonance experiments at a frequency of 6.375GHz on annealed and quenched samples, and relaxation frequency l/T, after Bloch-Bloembergen [73P 11.

Bonnenberg, Hempel, Wijn

274

Refcrcnccs for 1.2.1

1.2.1.3 References for 1.2.1 1897G 1 Guillaume, SE.: CR. Acad. Sci. 125 (1897). Nagaoka. H.. Honda. K.: Philos. Msg. 4 (1902) 45. OSH 1 Honda. K.. Shimizu, S.: Philos. Msg. 10 (1905) 548. 0611 Ingersoll. L.R.: Philos. Mag. 11 (1906) 41. Pancbianco. G.: Rend. Accad. Sci. Fis. Mat. Sot. Naz. Sci. Napoli 16 (1910) 21b. lOP1 12F 1 Foote. P.D.: Phys. Rev. 34 (1912) 96. 12Ll Loria. S.: Ann. Physik 38 (1912) 889. 17Bl Barker. S.G.: Proc. Phys. Sot. (London) 29 (1917) 1. 17c 1 Chcvenard. M.P.: Rev. Met. Paris 14 (1917) 610. 18M 1 Martin. P.: Ann. Physik 55 (1918) 561. 20G 1 Guillaume. SE.: Proc. Phys. Sot. (London) 32 (1920) 374. 25P 1 Pcschard. M.: Rev. Met. Paris 8 (1925) 490. 25P2 Pcschard. M.: Rev. Met. Paris 8 (1925) 581. 27K I Kase. T.: Sci. Rept. Tohoku Univ. 16 (1927) 491. 28C1 Chevenard. P.: Rev. Met. Paris 10 (1928) 14. 28E 1 Eimen. G.W.: J. Franklin Inst. 206 (1928) 317. 29E 1 Ehnen. G.W.: J. Franklin Inst. 207 (1929) 583. 29M 1 Masumoto. H.: Sci. Rept. Tohoku Univ. 18 (1929) 195. 29Wl Weiss, P., Forrer, R.: Ann. Phys. Paris 12 (1929) 279. 31 M 1 Masiyama. Y.: Sci. Rept. Tohoku Univ. 20 (1931) 574. 3’Sl Sadron. C.: Ann. Phys. Paris 17 (1932) 371. 35K I Kornetzi, M.: Z. Phys. 98 (1935) 371. 36Fl Fallot. M.: Ann. Phys. Paris 6 (1936) 305. Shih. J.W.: Phys. Rev. 50 (1936) 376. 36Sl 37El Ebert. H., KuBmann, A.: Phys. Z. 38 (1937) 437. 37M 1 McKeehan. L.W.: Phys. Rev. 51 (1937) 136. 3701 Owen. E.A.. Yates. E.L. et al.: Proc. Phys. Sot. (London) 49 1937) 17. 3702 Own. E.A.. Yates. E.L. et al.: Proc. Phys. Sot. (London) 49 1937) 178. 3703 Owen. E.A., Yates. E.L. et al.: Proc. Phys. Sot. (London) 49 (’1937)307. Snoek. J.L.: Physica IV 9 (1937) 853. 37s1 Shirakawa. Y.: Sci. Rept. Tohoku Univ. 27 (1938) 485. 39Sl Shirakawa. Y.: Sci. Rept. Tohoku Univ. 27 (1938) 532. 3932 Sucksmith. W.: Proc. R. Sot. London Ser. A 171 (1939) 525. 39s3 39Tl Tarasov, L.P.: Phys. Rev. 56 (1939) 1245. 41 E 1 Ellis, W.C., Grciner. E.S.: Trans. Am. Sot. Met. 29 (1941) 415. Ovvcn. L.A., Sully, A.H.: Philos. Mag. 31 (1941) 314. 4101 Rathenau, G.W., Snack. J.L.: Physica VIII 6 (1941) 555. 41R1 43F 1 Fallot. M.: Metaux Corrosion-Ind. 18 (1943) 214. Barnett. S.J.: Phys. Rev. 66 (1944) 224. 44Bl Fallot, M.: J. Phys. Radium VIII 5 (1944) 153. 44Fl 49G 1 Goldman. J.E.: Phys. Rev. 76 (1949) 471. Taylor, A.: J. Inst. Metals 77 (1950) 585. 50Tl Bozorth. R.M.: Ferromagnetism, Toronto, New York, London: D. van Nostrand Comp. Inc. 1951. 51 Bl Lement. B.S., Averbach. B.L., Cohen, M.: Trans. ASME 43 (1951) 1072. 51Ll Smit. J.: Physica 16 (1951) 612. 51Sl Tsuji. T.: J. Phys. Sot. Jpn. 13 (1958) 1310. 51Tl 51Wl Went. J.J.: Physica 17 (1951) 98. 52B 1 Barnett. S.J.,Kenny, G.S.: Phys. Rev. 87 (1952) 723. 52K 1 Kondorskii, E.J., Fedotov, J.N.: Izv. Akad. Nauk. SSSR 16 (1952) 432. 52u 1 Urquhart. H.M.A., Goldman, J.E.: Phys. Rev. 87 (1952) 210. 53B 1 Bozorth, R.M., Walker, J.G.: Phys. Rev. 89 (1953) 624. Bozorth. R.M.: Rev. Mod. Phys. 25 (1953) 42. 53B2 Galpcrin, D., Larin. C., Schischkow, A.: Doklady Akad. Nauk. USSR 89 (1953) 419. 53Gl 53 w 1 Wakelin. R.J.. Yates. E.L.: Proc. Phys. Sot. (London) Sect. B66 (1953) 221. 53Y 1 Yamamoto. M., Misyasawa, R.: Sci. Rept. Tohoku Univ. A 5 (1953) 113. 54B 1 Bozorth. R.M.: Phys. Rev. 96 (1954) 311.

02Nl

Bonnenberg,

Hempel,

Wijn

References for 1.2.1 54Pl 54Tl SC1 55Ml 55Sl 5582 56Cl 56Nl 56Sl 57Cl 57C2 5751 57Nl 58Al 58Fl 58Gl 58Hl 58Yl 59Al 59El 59Hl 59Kl 59Wl 60Al 6OCl 60Kl 60Tl 6OWl 61Jl 61 K 1 61 M 1 6101 61Pl 61Rl 62Cl 62C2 62Gl 62Kl 62K2 62Ll 62Sl 6282 62Tl 63Cl 63C2 63C3 63C4 6351 63Pl 63Rl 63Tl 63T2 63Wl 64Al 64Cl 64C2 64El

275

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Hempel,

Wijn

References for 1.2.1 69Nl 69Rl 69Sl 69S2 69S3 6934 69Yl 70Al 70Bl 7OCl 7OC2 70Dl 70Fl 70Gl 70Hl 70Kl 70K2 70Ml 70Tl 70T2 7OWl 7OYl 71Al 7lA2 71Bl 71El 71Hl 71H2 71Kl 71Pl 71Sl 71S2 71s3 71s4 71Tl 71T2 71T3 71Wl 71Yl 72Bl 72Cl 72Dl 72Hl 72H2 72H3 72H4 72Ll 72Ml 72M2 72M3 72Nl 72Rl 72R2 72Sl 72Tl 72T2

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12T3 73B I 73B2

Tino, Y., Arai, J.: J. Phys. Sot. Jpn. 32 (1972) 941. Brian, M.M.: C.R. Acad. Sci. Paris 277 (1973) B-695. Burlakova. R.F., Edel’man, I.S.: Phys. Met. Metallogr. (USSR) 35 (1973)200 (Fiz. Met. Metalloved. 35 (1973) 1101). 73c1 Cable J.W., Wollan. E.O.: Phys. Rev. B7 (1973) 2005. 73D 1 Dubinin. SF., Sidorov, S.K., Teploukhov, S.G., Arkhipov, V.E.: JETP Lett. 18 (1973) 324. 73Hl Hausch. G., Warlimont. H.: Acta Metal!. 21 (1973) 401. 73H2 Hayase. M., Shiga. M., Nakamura. Y.: J. Phys. Sot. Jpn. 34 (1973) 925. 73K 1 Kalinin. V.M., Beskachko, V.P.: Phys. Met. Metallogr. (USSR) 36 (1973) 65. 73K2 Kalinin. V.M., Danilov, M.A., Komarova, L.K., Tscytlin, A.M.: Phys. Met. Metallogr. (USSR) 36 (1973) 15. 73K3 Kollie. T.G., Brooks, C.R.: Phys. Status Solidi (a) 19 (1973) 545. 73M 1 Maedo, T., Yamauchi. H., Watanabe. H.: J. Phys. Sot. Jpn. 35 (1973) 1635. 73 M 2 Menshikov, A.Z., Yurchikov, E.E.: Sov. Phys. JETP 36 (1973) 100. 13 h4 3 Mook. H.A., Lynn, J.W., Nicklow, R.M.: Phys. Rev. Lett. 30 (1973) 556. 730 1 Ozone, T., Morita. H., Hiroyoshi, H., Saito, H.: J. Phys. Sot. Jpn. 35 (1973) 298. 73 P 1 Pokatilov, V.S., Puzei, I.M.: Sov. Phys. JETP 36 (1973) 108. 13R 1 Rechenberg, H., Billard, L., Chamberod, A., Natta, M.: J. Phys. Chem. Solids 34 (1973) 1251. 73v 1 Voroshilov, V.P., Zaktlarov, A.I., Kalinin, V.M., Vralov, A.S.: Fiz. Met. Metalloved. 35 (1973) 953. 73 w 1 Wakiyama. T.: AIP Conf. Proc. Mag. Magn. Mater. 2 (1973) 921. 73 w 2 Window, B.: J. Appl. Phys. 44 (1973) 2853. 732 1 Zakharov, AI., Men’shikov, A.Z., Uralov, AS.: Phys. Met. Metallogr. (USSR) 36 (1973) 170. Bastian. D., Biller, E., Chamberod, A.: Solid State Commun. 14 (1974) 73. 74Bl 74c 1 Cable. J.W., Chield. H.R.: Phys. Rev. B 10 (1974) 4607. Cadeville. M.C., Caudron, R., Costa, P., Lerner, C.: J. Phys. F 4 (1974) L 87. 74C2 Campbell. LA.: J. Phys. F4 (1974) L 181. 74c3 Caudron, R., Meunier. J.-J., Costa, P.: Solid State Commun. 14 (1974) 975. 74c4 Crowe!!. J.M.. Walker, J.C.: J. Mag. Magn. Mater. 2 (1974) 427. 74c5 74D1 Dubovka. G.T.: Phys. Status Solidi (a) 24 (1974) 375. Edwards, L.R., Bartel. L.C.: Phys. Rev. B 10 (1974) 2044. 74El Jaou!. 0.: Thesis Univ. de Paris-Slid Centre d’Orsay 1974. 745 1 74K 1 Kalinin. V.M.. Beskachko, V.P., Khomenko, O.A.: Phys. Met. Metallogr. (USSR) 37 (1974) 184. Litvinsey, V.V., Torba. G.F., Ushakov, A.I., Didovich, Yu.N., Rusov, G.I.: Fiz. Tverd. Tela 16 (1974) 74Ll 3135. 14 hl 1 Mori. N., Ukai. T., Kono, S.: J. Phys. Sot. Jpn. 37 (1974) 1278. Menzinger. F., Sacchetti, F., Leoni, F.: II Nuovo Cimento 20B (1974) 1. 74M2 74M3 Miwa. H.: Progress of Theor. Phys. 52 (1974) 1. 74Nl Nishi. M.. Nakai. Y., Kunitomi, N.: J. Phys. Sot. Jpn. 37 (1974) 570. Ono, F., Chikazumi, S.: J. Phys. Sot. Jpn. 37 (1974) 631. 7401 Orehotsky, J., Schrader, K.: J. Phys. F4 (1974) 196. 7402 Onozuka. T., Yamaguchi. S., Hirabayashi, M., Wakiyama, T.: J. Phys. Sot. Jpn. 37 (1974) 687. 7403 Puzey. M., Pokatilov, VS.: Phys. Met. Metallogr. (USSR) 37 (1974) 174. 74P1 74R 1 Rode. U.Ye.. Krynetskaya, I.B.: Phys. Met. Metallogr. (USSR) 38 (1974) 183. 14R2 Rogozyanov, A.Ya.. Lyashchenko, G.: Phys. Met. Metallogr. (USSR) 37 (1974) 87. 74s1 Sandier, L.M., Popov, V.P., Gratsianov, Yu.A.: Phys. Met. Metallogr. (USSR) 37 (1974) 76. Sandier. CM.. Popov, U.P., Naglyuk, Ya.V.: Phys. Met. Metallogr. (USSR) 37 (1974) 187. 7432 Shiga. C., Kimura, M., Fujita, F.E.: J. Jpn. Inst. Met. 38 (1974) 1037. 7483 1434 Shiga. M.. Maeda. Y., Nakamura, Y.: J. Phys. Sot. Jpn. 37 (1974) 363. Sikorska. B., Dobrzyhski. L., Maniawski, F.: Acta Phys. PO!. A45 (1974) 431. 74S5 Tino, Y., Arai, J.: J. Phys. Sot. Jpn. 36 (1974) 669. 74Tl Vasil’eva, R.P., Cheremushkina, A.V., Yazliyav, S., Kadyrov, Ya.: Fiz. Met. Metalloved. 38 (1974) 55. 74Vl 74 w 1 Window, B.: J. Phys. F4 (1974) 329. 15B 1 Billard. L.. Chamberod, A.: Solid State Commun. 17 (1975) 113. 75Dl Dorleijn. J.W.F., Miedema, A.R.: Phys. Lett. A55 (1975) 118. 75F 1 Foster, K., Thornburg. D.R.: AIP Mag. Magn. Mater. New York 24 (1975) 709. 75Gl Gonser. U., Nasu, S., Keune, W., Weis, 0.: Solid State Commun. 17 (1975) 233. 75H 1 Hausch. G.: Phys. Status Solidi (a) 30 (1975) K 57. 75H2 Hennion. M., Hennion, B., Castets, A., Tochctti, D.: Solid State Commun. 17 (1975) 899.

Bonnenberg, Hempel, Wijn

Referencesfor 1.2.1 75Kl 75Ml 75M2 75M3 75M4 75Rl 75Wl 75W2 76Bl 76B2 76El 76Hl 76H2 76Jl 76Kl 76Ml 76M2 76M3 76M4 76Pl 76Sl 76Tl 77Bl 77Cl 77Dl 77D2 77El 77Hl 77H2 7751 77Kl 77K2 77Ml 77M2 77M3 77M4 77Sl 77Tl 77T2 77Yl 78Al 78Bl 78B2 78Cl 78Hl 78Kl 78K2 78Sl 78Tl 78T2 78T3 78Vl 78Wl

279

Kalinin, V.M.: Phys. Met. Metallogr. (USSR) 39 (1975) 201. Makarov, V.A., Puzei, I.M., Sakharova, T.V., Gutovskii, LG.: Sov. Phys. JETP 40 (1975) 382. Menshikov, A.Z., Kazantsev, V.A., Kuzmin, N.N., Sidorov, S.K.: J. Mag. Magn. Mater. 1 (1975) 91. Mokhov, B.N., Goman’kov, V.I.: JETP Lett. 21 (1975) 276. Makarov, V.A., Puzey, I.M., Sakarova, T.V.: Phys. Status Solidi (a) 30 (1975) K21. Riedinger, R., Nauciel-Bloch, M.: J. Phys. F5 (1975) 732. Wu, C.Y., Quach, H.T., Yelon, A.: AIP Conf. Proc. Mag. Magn. Mater. 29 (1975) 681. Wakiyama, T., Chin, G.Y., Robbins, M., Sherwood, R.C., Bernardini, J.E.: AIP Conf. Proc. 29 (1975) 560. Bastian, D., Biller, E.: Phys. Status Solidi (a) 35 (1976) 113. Bastian, D., Biller, E.: Phys. Status Solidi (a) 35 (1976) 465. Edwards, D.M., Hill, D.J.: J. Phys. F6 (1976) 607. Hausch, G.: J. Phys. F6 (1976) 1015. Hennion, M., Hennion, B., Nauciel-Bloch, M., Riedinger, R.: J. Phys. F6 (1976) L 303. Jo, T., Miwa, H.: J. Phys. Sot. Jpn. 40 (1976) Kohgi, M., Ishikawa, Y., Wakabayashi, N.: Solid State Commun. 18 (1976) 509. Maeda, I., Yamauchi, H., Watanabe, H.: J. Phys. Sot. Jpn. 40 (1976) 1559. Mikke, K., Jankowska, J., Modrzejewski, A.: J. Phys. F 6 (1976) 631. Muyahara, T., Takahashi, M.: Jpn. J. Appl. Phys. 15 (1976) 291. Muraoka, Y., Shiga, M., Yasuoka, H., Nakamura, Y.: J. Phys. Sot. Jpn. 40 (1976) 414. Ponyatovskii, E.G., Antonov, V.E., Belash, I.T.: Sov. Phys. Solid State 18 (1976) 2131. Soumura, T.: J. Phys. Sot. Jpn. 40 (1976) 435. Takahashi, S., Ishikawa, Y.: Phys. Status Solidi (a) 33 (1976) K 141. Bessmertnyi, A.M., Mushailov, E.S., Pyn’ko, V.G., Suvorov, A.V.: Sov. Phys. Solid State 19 (11977) 1473. Cullis, I.G., Heath, M.: Solid State Commun. 23 (1977) 891. Drijver, J.W., Woude van der, F., Radelaar, S.: Phys. Rev. B 16 (1977) 985. Drijver, J.W., Woude van der, F., Radelaar, S.: Phys. Rev. B 16 (1977) 995. Endoh, Y., Noda, Y., Ishikawa, Y.: Solid State Commun. 23 (1977) 951. Hatta, S., Hayakawa, M., Chikazumi, S.: J. Phys. Sot. Jpn. 43 (1977) 451. Hesse,J., Mtiller, J.B.: Solid State Commun. 22 (1977) 637. Jo, T.: Physica 86-88B (1977) 747. Kagawa, H., Chikazumi, S.: J. Phys. Sot. Jpn. 43 (1977) 1097. Kanamori, J., Akai, H., Hamada, N., Miwa, H.: Physica 91 B (1977) 153. Makarov, V.A., Puzey, I.M., Sakharova, T.V.: Phys. Met. Metallogr. (USSR) 44 (1977) 64. Menshikov, A.Z., Shestakov, V.A.: Phys. Met. Metallogr. (USSR) 43 (1977) 38. Mikke, K., Jankowska, J., Modrzejewski, A., Frikkee, E.: Physica 86-88 B (1977) 345. Mizia, J., Kajzar, F.: Phys. Status Solidi (b) 80 (1977) K 75. Singer, V.V., Radovskiy, I.Z.: Russ. Metall. 1 (1977) 65. Takahashi, S.: Phys. Status Solidi (a) 42 (1977) 201. Takahashi, S.: Phys. Status Solidi (a) 42 (1977) 529. Yamada, O., Ono, F., Nakai, I.: Physica 91 B (1977) 298. Antonov, V.E., Belash, LT., Degtyareva, V.F., Ponomarev, B.K., Ponyatovkii, E.G., Tissen, V.G.: Sov. Phys. Solid State 20 (1978) 1548. Bansal, C.: Phys. Status Solidi (a) 48 (1978) K 119. Billard, L., Villemain, P., Chamberod, A.: J. Phys. C: Solid State Phys. 11 (1978) 2815. Campbell, C.C.M., Schaf, J., Zawislak, F.C.: J. Mag. Magn. Mater. 8 (1978) 112. Hamada, N., Miwa, H.: Progress of Theor. Phys. 59 (1978) 1045. Kim, C.-D., Matsui, M., Chikazumi, S.: J. Phys. Sot. Jpn. 44 (1978) 1152. Kitaoka, Y., Ueno, K., Asayama, K.: J. Phys. Sot. Jpn. 44 (1978) 142. Shirakawa, Y., Tanji, Y.: Phys. and Appl. of Invar Alloys. Honda Mem. SeriesMat. Science3 (1978) 137. Takahashi, M., Kono, T.: Jpn. J. of Appl. Phys. 17 (1978) 361. Takahashi, M., Kadowaki, S.,Wakiyama, T., Anayama, T., Takahashi, M.: J. Phys. Sot. Jpn. 44 (1978) 825. Takahashi, S.: Phys. Status Solidi (a) 45 (1978) 133. Vasil’eva, R.P., Puzei, I.M., Akgaev, A.: Sov. Phys. J. 21 (1978) 383. Wakiyama, T., Brooks, H.A., Gyorgy, E.M., Bachmann, K.J., Brasen, D.: J. Appl. Phys. 49(1978) 4158.

Landolt-BOrnstein New Series 111/19a

Bonnenberg, Hempel, Wijn

2ao 79B 1 79c I 79C2 79Dl 79E 1 79E2 79Gl 79 G 2 79H 1 79H2 79 H 3 7911 7912 7913 79K 1 79M 1 79 M 2 79N 1 790 1 7902 79 0 3 79Rl 79Sl 79s2 7933 79s4 79Tl 79Y 1 79Y2 79 Y 3 80A 1 80Dl 80D2 80D3 80H 1 8011 8OLl 80Ml 80M2 80Nl 8OSl 80Tl SOT2 80T3 80T4 8OYl 81Hl 81 H2 81Kl 8101 8102 8103 8104 81 W 1

Referencesfor 1.2.1 Bansal. C., Chandra. G.: J. Phys. Coil. C 2, 40 (1979) C2-202. Chnmberod. A.. Laugicr. J.. Pcnissan. J.M.: J. Mag. Magn. Mater 10 (I 979) 139. Chikazumi. S.: J. Mag. Magn. Mater. 10 (1979) 113. Deen van, J.K.. Woude van der, F.: Phys. Rev. B20 (1979) 296. Endoh. Y.: J. Mag. Magn. Mater. 10 (1979) 177. Endoh. Y., Noda, Y.: J. Phys. Sot. Jpn. 46 (1979) 806. Goman’kov, V.L., Mokhov, B.N., Nogin, N.I.: Russ. Metall. 4 (1979) 97. Gonser, U., Nasu, S., Kappes, W.: J. Msg. Magn. Mater. 10 (1979) 244. Hamada. N.: J. Phys. Sot. Jpn. 47 (1979) 797. Hamada. N.: J. Phys. Sot. Jpn. 46 (1979) 1759. Hesse.J., Wiechmann. B.?Miiller, J.B.: J. Mag. Magn. Mater. 10 (1979)252. Inone. J., Yamada. H., Shimizu, M.: J. Phys. Sot. Jpn. 46 (1979) 1496. Ishikawa. Y., Onodera. S., Tajima. K.: J. Mag. Magn. Mater. 10 (1979) 183. Ito. Y., Akimitsu. J.. Matsui, M., Chikazumi, S.: J. Mag. Magn. Mater. 10 (1979) 194. Komura. S., Takeda. T.: J. Mag. Magn. Mater. 10 (1979) 191. Matsui. M.. Adachi. K.: J. Mag. Magn. Mater. 10 (1979) 152. Miwa. H.: J. Mag. Magn. Mater. 10 (1979) 223. Narayanasamy, A.. Nagarajan. T., Muthukumarasamy, P., Radhakrishnan, T.S.: J. Phys. F9 (1979) 2261. Ono, F.: J. Phys. Sot. Jpn. 47 (1979) 84. Ono, F.: J. Phys. Sot. Jpn. 47 (1979) 1480. Oomi, G., Mori, N.: J. Mag. Magn. Mater. 10 (1979) 170. Rode, V.E.: Phys. Status Solidi (a) 56 (1979) 407. Sandler. I.M.. Popov, V.P., Nagljluk, Ya.V.: Phys. Status Solidi (a) 55 (1979) 271. Shiozaki. Y., Nakai. Y., Kunitomi, N.: J. Phys. Sot. Jpn. 46 (1979) 59. Skvortsov, 1.1.:Phys. Met. Metallogr. (USSR) 45 (1979) 178. Sohmura. T., Fujita. F.E.: J. Mag. Magn. Mater. 10 (1979) 255. Takahashi. M.. Kadowaki. S.,Wakiyama, T., Anayama, A., Takahashi, M.: J. Phys. Sot. Jpn. 47 (1979) 1110. Yamada. H., Inouc. J., Shimizu, M.: J. Phys. Sot. Jpn. 47 (1979) 103. Yamada. H., Inoue. J., Shimizu, M.: J. Mag. Magn. Mater. 10 (1979) 241. Yamada, O., Nakai. I., Fujiwara, H., Ono, F.: J. Msg. Magn. Mater. 10 (1979) 155. Antonov, V.E., Belash. I.T., Pnomarev, B.K., Ponyatovskii, E.G., Thiessen, V.G.: Phys. Status Solidi (a) 57 (1980) 75. Decn van. J.K., Woude van der, F.: J. Phys. 41 (1980) C l-367. Dubovka. G.T.: Phys. Status Solidi (a) 59 (1980) K 35. Dubinin. S.F., Teplouchov, S.G., Sidorov, S.K., Izyumov, Yu.A., Syromyatnikov, V.N.: Phys. Status Solidi (a) 61 (1980) 159. Hennion. B.. Hennion. M.: J. Phys. F 10 (1980) 2289. Ishikawa. Y., Tajima. K., Noda, Y., Wakabayashi, N.: J. Phys. Sot. Jpn. 48 (1980) 1097. Morin-L6pez, J.L., Falicov, L.M.: J. Phys. C: Solid State Phys. 13 (1980) 1715. Morita. H., Hiriyoshi. H., Fujimori, H., Nakagawa, Y.: J. Mag. Magn. Mater. 15-18 (1980) 1197. Masumoto, H., Takahashi, M., Nakayama, T.: Trans. Jpn. Inst. Met. 21 (1980) 515. Nakai, I., Ono, F., Yamada, 0.: J. Phys. Sot. Jpn. 48 (1980) 1105. Shimizu, M.: J. Mag. Magn. Mater. 19 (1980) 219. Takahashi. S.: Phys. Lett. 78A (1980) 485. Takahashi. S.: Phys. Status Solidi (a) 59 (1980) K 135. Takahashi, M., Kadowaki, S.: J. Phys. Sot. Jpn. 48 (1980) 1391. Tino, Y., Nakaya, Y.: J. Phys. Sot. Jpn. 49 (1980) 2198. Yamada, O., Pauthenet, R., Picoche, J.-C.: C.R. Acad. Sci. Paris, t 291 (1980) SCr.B-223. Harada. S., Sohmura, T., Fujita, F.E.: J. Phys. Sot. Jpn. 50 (1981) 2909. Hayashi. K., Mori, N.: Solid State Commun. 38 (1981) 1057. Kakehashi. Y.: J. Phys. Sot. Jpn. 50 (1981) 2236. Ono. F.: J. Phys. Sot. Jpn. 50 (1981) 2231. Onodera, S.. Ishikawa, Y., Tajima, K.: J. Phys. Sot. Jpn. 50 (1981) 1513. Oomi. G.. Mori, N.: J. Phys. Sot. Jpn. 50 (1981) 2917. Oomi, G.. Mori, N.: J. Phys. Sot. Jpn. 50 (1981) 2924. Wagner. D., Wohlfarth. E.P.: J. Phys. F 11 (1981) 2417.

Bonnenberg, Hempel, Wijn

References for 1.2.1 81Yl 8121 82Bl 82Cl 82Hl 82Kl 8201 8202 82Wl 83Dl 83El 83Fl 83Hl 83H2 8311 83Kl 83K2 83K3 83Ml 83M2 83Nl 83N2 83N3 83Pl 83P2 83Rl 83Tl 83T2 83Yl 8411 84Kl 84Pl 84Vl 84Yl 8511

Land&-B6mstein New Series lll/l9a

281

Yamada, O., Nakai, I.: J. Phys. Sot. Jpn. 50 (1981) 823. Zolotarevskiy, I.V., Snezhnoy, V.L., Georgiyeva, I.Ya., Matyushenko, L.A.: Phys. Met. 51(1981) 191. Brooks, C.R., Meschter, P.J., Kollie, T.G.: Phys. Status Solidi (a) 73 (1982) 189. Cable, J.W., Brundage, W.E.: J. Appl. Phys. 53 (1982) 8085. Ho, K.-Y.: J. Appl. Phys. 53 (1982) 7831. Kakehashi, Y.: J. Phys. Sot. Jpn. 51 (1982) 3183. Ono, F., Yamada, 0.: Solid State Commun. 43 (1982) 873. Orehotsky, J., Sousa, J.B., Pinheiro, M.F.: J. Appl. Phys. 53 (1982)7939 Weissman, J., Levin, L.: J. Mag. Magn. Mater. 27 (1982) 347. Davies, M., Heath, M.: J. Mag. Magn. Mater. 31-34 (1983) 661. Eugen van, P.G.: Thesis, Delft 1983. Fujika, S.: J. Mag. Magn. Mater. 31-34 (1983) 101. Harada, S.: J. Phys. Sot. Jpn. 52 (1983) 1306. Hatafuku, H., Takahashi, S., Sasaki, T., Ichinohe, H.: J. Mag. Magn. Mater. 31-34 (1983) 847. Iida, S., Nakai, Y., Kunitomi, N.: J. Mag. Magn. Mater. 31-34 (1983) 129. Kakahashi, Y.: J. Mag. Magn. Mater. 31-34 (1983) 53. Kakehashi, Y.: J. Mag. Magn. Mater. 37 (1983) 189. Kress, W., in: Landolt-Bornstein, NS, (Hellwege, K.-H., Olsen, J.L., eds.), Berlin, Heidelberg, New York: Springer, vol. 111/13b(1983) 259. Mori, N., Ukai, T., Oktsuka, S.: J. Mag. Magn. Mater. 31 (1983) 43. Morita, H., Tanji, Y., Hiriyoshi, H., Nakagawa, Y.: J. Mag. Magn. Mater. 31-34 (1983) 107. Nakai, I., Yamada, 0.: J. Mag. Magn. Mater. 31-34 (1983) 103. Nakai, I.: J. Phys. Sot. Jpn. 52 (1983) 1781. Nakai, I., Ono, F., Yamada, 0.: J. Phys. Sot. Jpn. 52 (1983) 1791. Pauthenet, R., Maruyama, H.: J. Mag. Magn. Mater. 31-34 (1983) 835. Pierron-Bohnesn, V., Cadeville, M.C., Gautier, F.: J. Phys. F 13 (1983) 1689. Rode, V.E., Olszewski, J., Plevako, T.A., Kavalerov, V.G.: J. Mag. Magn. Mater. 31-34 (1983) 99. Takahashi, S.: J. Mag. Magn. Mater. 31-34 (1983) 817. Tanaka, T., Takahashi, M., Kadowaki, S., Wakiyama, T., Watanabe, D., Takahashi, M.: J. Mag. Magn. Mater. 31-34 (1983) 843. Yamada, O., Ono, F., Nakai, I., Maruyama, H., Ohta, K., Suzuki, M.: J. Mag. Magn. Mater. 31-34 (1983) 105. Ishio, S., Takahashi, M.: J. Mag. Magn. Mater. 46 (1984) 142. Koike, K., Hayakawa, K.: Jpn. J. Appl. Phys. 23 (1984) L 85. Preston, S., Johnson, G.: J. Mag. Magn. Mater. 43 (1984) 227. Victora, R.H., Falicov, L.M.: Phys. Rev. B30 (1984) 259. Yamada, O., Du Tremolet De Lacheisserie, E.: J. Phys. Sot. Jpn. 53 (1984) 729. Ishio, S., Takahashi, M.: J. Mag. Magn. Mater. 50 (1985) 271.

Bonnenberg, Hempel, Wijn

1.2.2 Alloys between Ti, V, Cr, Mn

282

[Ref. p. 480

1.2.2 Alloys between Ti, V, Cr or Mn 1.2.2.0 General remarks In this subsection magnetic properties of binary alloys between Ti, V, Cr or Mn are representedwhile in the following one, subsection 1.2.3,binary alloys of Ti, V, Cr or Mn and Fe, Co, or Ni are dealt with. The latter subsection also includes magnetic data on V-Cr-Mn and the pseudo-binary alloys ofTi, V, Cr or Mn and Fe, Co or Ni in which one the 3d transition metals is partially substituted by a third 3d metal. The data is compiled in figures and tables. Referenceshave been made to the main papers that appeared before 1975.For the time from 1975to 1983,about 80% of the relevant papers cited in the Chemical Abstracts have been selectedfor quoting important and reliable properties of the alloys under discussion. For each alloy system a chronological listing of relevant referencesprecedesthe representation of the data. These lists also include rcfcrcnces to papers not cited subsequently in the figures and tables. The complete list of referencesis provided at the end of subsection 1.2.3. The arrangement of the alloys is in the order of increasing atomic numbers of their constituent elements.Each of the following subsections is devoted to a particular binary alloy between Ti, V, Cr or Mn. For details, see Survey 1. Since figures and tables for a given material may contain also data of other alloys for comparison, information on a particular alloy may be found in the other subsections as well. The retrieval of such scattered information is facilitated by Survey 2 which provides all the figures and tables in which, for a given alloy and property. data is represented.

Survey 2. For each binary alloy between Ti, V, Cr or Mn the figures and tables are listed in which data on the properties specified is provided. Referenceis given not only to subsect. 1.2.2(Figs. 1...58 and Tables 1...12) but also to subsect.1.2.3(Figs. 59...427 and Tables 13...88). Numbers in roman and italic refer to figures and tables, respectively. Allo)

Phase diagram. lattice constants

Susceptibility, paramagnetic properties

V-Ti

1

2...4

I 311,312

11 I 3, 13, 14, 101, 102

Cr-Ti Cr-V

Mn-Ti Mn-V

25,311

Mn-Cr ‘)

35,41,311

Magnetization, average magnetic moment

Atomic magnetic moments, g-factor, spin structure

15...17

20

2, 9, 74

2,3, 74

19, 21, 47, 49, 264, 266 2, 3, 9, 10, 74

Magnetic transformation temperatures

12

6

3, 26...29 7 36,..39, 41, 101, 162, 224

‘) Young’s modulus: Fig. 39.

166, 227 6, 7 15, 40, 42, 43, 162, 166, 227 2, 6, 8, II, 12, 39, 74

30,31 20, 42.. .45 2

19, 21, 46...49, 264, 266 2, 9...12, 74

Ref. p. 4801

1.2.2 Alloys between Ti, V, Cr, Mn

283

Survey 1. The subsections devoted to the binary alloys between Ti, V, Cr or Mn are given, as well as information on atomic ordering and crystallographic phases considered. dil: dilute alloy, diso: disordered alloy, (3: 1): Cu,Au-type superlattice, (1: 1): CuAu-type super-lattice,(l/l): CsCl-type compound, (cr):o-phase, (L): Laves phase.

Ti V Cr

Mn

Ti

V

1.2.2.1 diso 1.2.2.2 dil diso (L) 1.2.2.4

1.2.2.3 dil diso

(4,(L)

High-field susceptibility

NMR, Mijssbauer effect

5, 8, 9

1.2.2.5 dil diso O/l)

Spin waves, exchange

Cr

Mn

1.2.2.6 dil diso, a-Mn bee, y-Mn

Magnetic anisotropy, magnetostriction

-

Specific heat, thermal expansion

Alloy

5...7, 10 5

V-Ti Cr-Ti

5, 8, 18, 22, 23

5, 10, 17, 24

4

5 Mn-Ti Mn-V

5, 32...34, 179 50

Landolt-Bbrnstein New Series 111/19a

5, 51.e.56, 179, 318 II

Cr-V

57, 58 5

Mn-Cr ‘)

284

[Ref. p. 480

1.2.2.1 V-Ti

“C

kl

V-Ti

1

1

( 600

\

200

II-

dhcp)’

sod ’ 0

I

I

10

a Ti

\

I

‘1 0

5

\ \

15 ot%

20

v-

0 b Ti

4

8

J 12 at% 16

v-

Fig. 1. (a) Equilibrium phase diagram for V-Ti alloys [QAI]. (b) Noncquilibrium phase diagram for V-Ti quenched from the elevated-tcmpcraturc, bee phase to the temperature indicated on the scale [53 D 1, 75C23. M, and M, indicate the start and the end of the martcnsitic transition. respectively.

3.0 .lG-'

1.95 xl 4 cm3 mol

Cm! TiT" .,

I

/

1

Ti- lSat%V

I

2.4

1.85

I

r:

2s

v a-Ti

6

1.80

1.8 1.5 0 a 11

20

40

60 v-

80 ot% 100 V

Fig. 2a. Room-tempcraturc magnetic molar susceptibility xrn for V-Ti alloys qucnchcd from about 1000“C into iced brine [75 C 23.

1 b

IO

102 h

10:

4 -

Fig. 2b. Variation of the room-temperature magnetic molar susceptibility I,,, for Ti-15 at% V as a consequence of annealing the alloy for various times t, at 300 “C (open symbols). Solid circles: various samples quenched from about 1000“C into iced brine [75 C 23.

Adachi

Ref. p. 4801

285

1.2.2.1 V-Ti

V-Mn

\ 10-3 c

104

1 4 -

10

3.0

IO3 h IO4

IO2

Fig. 2c. Variation of the room-temperature magnetic molar susceptibility x,, for Ti-19at%V [75C2]. Open symbols: aging results for four samples. Solid circles: various samples quenched from about 1000°C into iced brine. Solid square: P-Ti [72 C 11.

’

2.5

\40

2.0 0 V

5

. \I

v-co I V-Ni

IO 15 Impurity -

20 at%

25

Fig. 3. Magnetic molar susceptibility x,,, at 20 K for solid solutions of 3d elements in V [63 C 31.

.--I V-Ti

I

1

1

,k---PTi

1.4

;; 1.3 0 R Ix 1.2 -& 1.1 1.0 0.9

Fig. 4. Temperature dependence of the relative magnetic susceptibility for V-Ti alloys [62T 11. The broken line represents data of McQuillan and Evans (1960) for Ti. Landolf-BCi’msfein New Series 111/19a

Adachi

1.2.2.1 V-Ti

286

‘i 3d alloys ‘r

[Ref. p. 480

- 60 w

col

molK2 50 0 - 40 0 *b S5Plrl 5’v 0.

0 0

>

-

Y

x

-30 I x - 20

- 10 25

4

V 5

Cr 6

0 Mn 0

1

I 20

10

I 30

I 40

I 50

I I 60 K2 70

12-

t-l-

Fig. 5. Nuclear spin-lattice relaxation time 7” (expressed as its product with temperature T) for paramagnetic V-Ti. Cr-V and Mn-V alloys and antiferromagnetic Mn-Cr alloys. Also given is the electronic spccitic heat coeflicient 7 [73T I]. “Mn in (open circles) Mn-Cr [73T I] and (solid circles) Mn-V [7l M I]. “V in (crosses) hln-V [71 M I] and (triangles) V-Ti [64 M 3, 64 K 21 and Cr-V [64 B I]. Solid line: y [60 C 3,62 C I]. n: average number of 4s and 3d electrons per atom.

Fig. 6. Specific heat divided by temperature, C,/T, vs. the square of temperature, T*, for bee V-Ti alloys [62 C I].

I

I

-4.0

4.5

l-l’ Ti Fig. 7. Electronic specific heat coefticient y for bee V-Ti alloys [62 C I].

I

I

16

5.0 n-

5.5

0 6.0

Fig. 8. Nuclear spin-lattice relaxation time Tr for ‘IV in V-3d transition metal alloys and the density of states at the Fermi surface IV(&), as dependent on the average number of4s and 3d electrons per atom, n, [64 M 33; the experimental data for Cr-V alloys are from [64 B I].

Adachi

Ref. p. 4801

1.2.2.2 Cr-Ti

287 x in Ti Fe~.,Co,-

0.7 % V-Ti Cd

K*mol

0

20

Ti

LO

60

80 at%

v-

IO

100 V

Fig. 9. Knight shift K for 51V in bee V-Ti alloys at room temperature [62 V 21.

0

I V

5

1 Cr 6

I Mn 7

I Fe 8

I co 9

n-

Fig. 10. Electronic specific heat coefficient y of 3d transition metal alloys vs. the average valence electron (4s 3d) concentration per atom, n, [68 B 11. x corresponds to compositionin TiFe, $0,. Dashed line: bee Ti-V, V-Cr, Cr-Fe and Fe-Co alloys, solid line: Fe-Co-Ti and CoNi-Ti alloys [62 S 2, 60 C 2, 62 C 11.

1.2.2.2 Cr-Ti References:68 A 2, 71 C 2. 3.35 @ ‘i$ cm3 Y 9

e

Cr-Ti

330.3 K

5.8

K I

I 3.25

z

x” 3.20 3.15

3.20

3.10

3.15 t 0, 3.10H

0 a Cr 125 K

I

/

270.4 I e 221.4

e 5.6

3.30 D” -cm3 9

e 5.1 efr*

3.05

0.2

0.1, Ti -

0.6

181.3 0.8 at% 1.0

t 120 z 115

3.00 (((111112.95 0 50 100

150

200

250

300 K 350

b

T-

Fig. 11. Magnetic mass susceptibility xs vs. temperature for Cr-Ti alloys [71 C 21.

Landolt-Bornctein New Series 111/19a

Cr

Ti -

Fig. 12. Neel temperature TN(a) and spin-flip temperature T,, (b) vs. composition for Cr-Ti alloys. Cr : TN= 311 K [71 C2].

Ada&i

Ref. p. 4801

1.2.2.2 Cr-Ti

287 x in Ti Fe~.,Co,-

0.7 % V-Ti Cd

K*mol

0

20

Ti

LO

60

80 at%

v-

IO

100 V

Fig. 9. Knight shift K for 51V in bee V-Ti alloys at room temperature [62 V 21.

0

I V

5

1 Cr 6

I Mn 7

I Fe 8

I co 9

n-

Fig. 10. Electronic specific heat coefficient y of 3d transition metal alloys vs. the average valence electron (4s 3d) concentration per atom, n, [68 B 11. x corresponds to compositionin TiFe, $0,. Dashed line: bee Ti-V, V-Cr, Cr-Fe and Fe-Co alloys, solid line: Fe-Co-Ti and CoNi-Ti alloys [62 S 2, 60 C 2, 62 C 11.

1.2.2.2 Cr-Ti References:68 A 2, 71 C 2. 3.35 @ ‘i$ cm3 Y 9

e

Cr-Ti

330.3 K

5.8

K I

I 3.25

z

x” 3.20 3.15

3.20

3.10

3.15 t 0, 3.10H

0 a Cr 125 K

I

/

270.4 I e 221.4

e 5.6

3.30 D” -cm3 9

e 5.1 efr*

3.05

0.2

0.1, Ti -

0.6

181.3 0.8 at% 1.0

t 120 z 115

3.00 (((111112.95 0 50 100

150

200

250

300 K 350

b

T-

Fig. 11. Magnetic mass susceptibility xs vs. temperature for Cr-Ti alloys [71 C 21.

Landolt-Bornctein New Series 111/19a

Cr

Ti -

Fig. 12. Neel temperature TN(a) and spin-flip temperature T,, (b) vs. composition for Cr-Ti alloys. Cr : TN= 311 K [71 C2].

Ada&i

Table 1. Crystal and magnetic properties of Lavcs phase compounds. P: Pauli paramagnetism, F: ferromagnctism, AF: antiferromagnctism, x,,,: susceptibility per mole, Tc and TN:Curie and N&cl temperatures, respectively, pco: magnetic moment per Co atom, H,,,: hypcrfine magnetic field for 57Feobtained from Miissbaucr effect measurements. NiTi, and CoTi, were reported to have a cubic Laves structure [63 n I, p. 1461 but the magnetic properties are unknown. Crystal ‘) structure

a ‘)

c ‘)

A Ni,Sc co,sc Fe,Sc Mn,Sc Co,Ti co 2.13Ti0.87 Fe,Ti

MgCu, MgCuz MgNi, WW MD, MgNi, MS&

Cr,Ti ‘) [63n 1, p. 146).

xmW)

G

10-4cm3mol-’

K

6.926 6.921 4.972 5.033 6.706 4.729 4.779

16.278 8.278 15.41 7.761

P [69C l] P [69C I] F [64N I] P [70B2] AF [66A 1, 68N l] F [66A 1, 68N 13 AF [64W3]

0.76 6.95

6.493

-

P [68A2]

5.16 4.17

44

TN

pco

F,yp,F,W

PB

kOe

K)

202 [64N l] 43 0.12 273 97.3 [64Nl]

Remarks

NMR [66B2] NMR [66 B 21

InT,-,Fe,+,,AFforxO r68 N 21 resistivityC69 I 1, 71 I 1, 721 11, thermal expansion [66 G 11, specific heat [67 w l]

Ref. p. 4801

289

1.2.2.3 Cr-V

1.2.2.3 Cr-V References: 58 L 1,60 C 1,61 V 1,62 C 1,62 T 2,62 V 2,64 B 1,64 K 2,64 M 3,65 H 1,65 K 1,65 M 1,66 B 1, ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

3.2 w4 cm3 mol 2.8

1.6 I

0 1.2 0 V

20

40

60

80 at% 100 Cr

Cr-

Fig. 13.Magnetic molar susceptibility x,,, at 20 K for Cr-V alloys prepared from V and Cr originating from various sources [60 C 11. Crosses: x,,, at 100 K [58 L 11.

600,

I

I

I

I

I

I

I

I

50

100

150

200

I

I

250 K 300

Fig. 14. Magnetic mass susceptibility xs vs. temperature for Cb.95Vo.05 and (Cro.9~Vo.o~)o.99Coo.o~ alloys [77A2].

I

250 I 200 h'

I 3001 I

2001

A

I

\\I

150

\ I

100

100II

ii*0

dew

50

i;),

1 s*o \

0 -v

1.0 at%

0.5

Mn-

fr

Fig. 15. Magnetic phase diagram of Cr-V and Cr-Mn alloys [65 H 11, see also [66 B 11. To: transition temperature from incommensurate to commensurate structure (see Fig. 19), T,,: spin flip transition temperature horn longitudinal (L) to transverse (f) spin density wave (SDW) state, 6 = 0: commensurate phase, 6 $0: incommensurate phase, P : paramagnetic, AF: antiferromagnetic. Landolt-BHnstein New Series lll/l9a

0

3

v---b

Fig. 16. Neel temperature TN deduced from electrical resistivity minima for Cr-V alloys. Open circle: [64 K 21, solid circles: [62 T 21.

Adachi

[Ref. p. 480

1.2.2.3 Cr-V

290 400 K

3.0 mJ molK2

33C

2.5

I_2Of

1OC

c Cr

v-

Gg. 17.Neel temperature TNofCr-V alloys, defined as the cmperature where the rcsistivity shows a minimum. Also ,hown is the linear specific heat coefficient y [80T 21.

Fig. 18.NMRspin-echo spectra for 5’V in the spin density wave state of Cr-V alloys, obtained at 10 MHz and I .4 K [75 K 1-J.

I 0.8

g 0.6 9 (?*=m)

AF 0.4

0.2 0

a Cr

Fig. 19.Spin structure ofCr and Cr-based alloys: TSDW: transverse spin density wave (incommensurate). LSDW: longitudinal spin density wave (incommensurate), AF: ordinary antifcrromag.nctic structure (commensurate), I.: wavelerqth of SDW (/.=2x!@, cf. caption to Fig. 21.

1

2

3 4 Impurity -

5 at%

6

Fig. 20. Maximum magnetic moment per atom for Cr alloys at 77 K containing V, Mn, Fe, Co and Ni impurities C68El-J.

291

1.2.2.3 Cr-V

Ref. p. 4801

Table 2. Neel temperature TN, average magnetic moment per atom, J?,and wavevector Q of the spin density waves in Cr-V and Cr-Mn alloys at 77K [67 K 11.

1.00

v 0.99

Mn

at % Cr’) Cr-V

0.98 I co

Cr-Mn

L 0.97

0.45 1.00 -

0.70 1.85

TN

p

K

PB

QaPn

310 0.40(2) 0.9518 268(5) 0.36(3) 0.9431(25) 220(5) 0.28(3) 0.9300(25) 440(5) 545(5)

‘) [62Wl]. 0.96

0.95

0.94

3

2

1

c!

It at%

5

Impurity -

Fig. 21.Variation of 1- 6 for Cr alloys containing V, Mn, Fe, Co and Ni impurities at TN(dashedcurve) and at 0 K (solid curve) [68E 11. The satellite of the magnetic reflection appearsat 5 (1k 6,0,0), etc.The wavelengthof a

the SDW is A=~Tc//~,seeFig. 19.

Table 3. Spin density wave properties of Cr-V alloys in comparison with Cr: spin density wavevector Q, wavelength of antiferromagnetic modulation, 1, and average (rms) magnetic moment per atom, p. V at%

Cr 0.45 1 1.9

QaPn

PB

78K

197K

78K

197K

OK

0.9519 0.9431 0.93

0.9554 0.9480

20.8 ‘) 17.6(8) 13.2

22.4(8) 19.2(8)

0.40(2)“) 0.36(3)

‘) [62S3]. ‘) [62 W 11. 3, Room temperature.

Landolt-Bbmstein New Series lWl9a

Ref.

P

ala

Adachi

78K 0.35(3) 0.28(3)

197K 0.26(3)
64K2 64K2 65Hl 65Hl

[Ref. p. 480

1.2.2.3 Cr-V

292 0.35 (SKi-' 0.30

Hoppt= 61.9kOe

0.25

v =lSMHz

i

i 0

l,(o) 50

100

150

l,(o) 200

250 l-

300

350

400

450 K 500

Fig. 22. Tempcraturc dependence of the nuclear spin relaxation time T, for 53Cr in Cr,,,,VO,,,, expressed as (Tr 7) - r where T is the temperature. NMR measurements at 15.0MHz and 61.9 kOe. For comparison, the data for Cr is also given [83 K 41.

Table 4. Spin-lattice relaxation time T, for “V in Cr-V alloys at T=77.3K. Accuracy +_4%. No temperature dependence was found for TIT between 20.4 and 195K [64B 11. V at%

TT SK

100

0.795 0.991 1.13...1.20 1.17...1.42 1.42 1.93 2.65 4.44 5.69 7.63 8.48 8.00

85 75 70

60 50 40 30 25 20

10 5

1 0.651

T

0.50I a

v

I/

I

I

I 20

I I

/f

I

I 40

I 60

Cr-

\t

‘6

I 80 at%

I

I 100 Cr

Fig. 23. Knight shift K for 51V in bee Cr-V alloys at room tempcraturc [62 V 23.

Adachi

Land&Bbrncwin Neiv Scriec 111/19a

Ref. p. 4801

1.2.2.3 Cr-V

-a

molK*

2.4 2.2

2.2

2.2

2.2 ! \ z 2.0

1.8

1.6

T*-

Fig. 24. Specific heat divided by temperature, C,/T, vs. the square of temperature, T’, for Cr-V alloys. (a) O..A at% V, antiferromagnetic region [SOT 21; (b) 4.. .lO at% V, paramagnetic region [SOT 21; (c) 5’1.77 at% V [6OC3].

Landolt-BOrnstein New Series 111/19a

294

1.2.2.3 Cr-V 16

x-’ ml

Cr- V O!

[Ref. p. 480

^I^” I

6

6

Fig. 24. For caption seeprevious page. 0

2

4

6

8

12

14

16

18 K2 20

L-

Table 5. Specific heat properties for bee 3d transition metal alloys, according to the equation C,=yT+/?T3. E is the standard deviation of the data points from the leastsquaresfit. 0, is the Debye temperature [60 C 33.Over-all accuracy: y+ 2%, On+ 15K. Y 10-4calmol-1 K-’

Tio.sVo.s x22 Vo.77Cro.23 14.2 Vo.sCro.s 11.6 Vo.26Cro.74 5.31 5.15 Vo.*Cro.* 5.17 vo.1cro.9 V0.0sCro.9s 5.54 5.33 Cro.9Mno. 1 Cro.Nno., <16

Cr o.69Mno.31 Cro.61Mno.39 Cro.sMno.s Vo.deo.o, Vo.d’eo.~s Vo.sFeo.2 Vo.76Feo.24 Vo.74Feo.26 V 0.72Fe0.28 Vo.7Feo.3 V o.69Feo.31 Vo.66Feo.34 V a:s;:o.4s V 0.67

<29 <47 < 56(60.6) 16.1 12.4 9.4 - 10.0 <13 < 18.5 <21 < 22(22.9) 16.7 13.1 8.63

Adachi

P cal mol-’ Kv4

E %

@D K

0.0410 0.1507 0.0663 0.0627 0.0373 0.0469 0.0454

0.3 0.3 0.4 0.5 0.3 0.2 0.4

484 314 412 420 500 463 467

(-0.249) 0.0666 0.0397 0.0352

1.2 0.2 0.2 0.6

412 489 509

(-0.0516) 0.0867 0.0468 0.0917

0.3 0.4 0.5 0.4

377 463 369

Ref. p. 4801

1.2.2.4 Mn-Ti,

1.2.2.5 Mn-V

295

Table 5 (continued). Y 10m4calmol-l K-’

Cro.98Feo.02 Cro.&‘eo.o~ Cro.90Feo.l~ Cro.~4%l~ cro.8Peo.18 Cro.81Feo.l~ Cro.80Feo.20 Cro.70Feo.30

Cr o.63Feo.37 Cro.53Feo.47 Cro.z&o.7s Cro.15Feo.85 Cr o.06Feo.94

< 7.7 < 16.6 25.2 32.2 39.4 <41(42.4) (43.0) 37:3 28.4 16.4 14.3 9.87 9.36 10.2

P calmol-’ Km4

0.353 0.355 0.0405 (-0.086) (-0.123) 0.0151 0.0433 0.171 0.137 0.0768 0.0632 0.0433

E

@D

%

K

0.4 0.5 0.5

236 235 486

0.4 0.5 0.4 0.4 0.6 0.4 0.6

675 475 301 324 392 419 475

1.2.2.4 Mn-Ti Reference: 74 K 2. Table 6. Composition dependenceof the magnetic state for P-Mn-3d transition metal alloys at 4.2 K [74 K 21. The range of composition for paramagnetism (P) and antiferromagnetism (AF) is given in [at%] of the 3d metal. Ti

V

Cr

Fe

co

Ni

2...4

2...4

1 2.,.20

0.1...0.5 0.7...35

0.5.e.12

at% P AF

2

1.2.2.5 Mn-V References:63 C 3, 69 s 1, 69 V 1, 71 V 1, 74 K 2, 77 A 1, 80 M 3, 81 M 2, 83 M 1. Table 7. Magnetic susceptibility of CsCl-type compounds Ti-3d and MnV. PP: Pauli type paramagnetism, CW: Curie-Weiss type paramagnetism. NiTi ‘) CoTi FeTi MnV

PP cw cw PP

X(T)=(5.1...8.9)10-6cm3g-1 for T=77+~.823K [62Bl, 68W2] SeeFigs. 185, 186, 190 SeeFig. 69 Field-induced ferromagnetism appears, (0.061uJFe) [60 N 1, 73 A 21 x(CsC1)< X(disorder). Seealso Figs. 27, 28 [Sl M 21

‘) The CsCl-type structure is formed above ca. 380 K and transforms into a complex triclinic structure at low temperature.

Landolt-Bbmstein New Series 111/19a

Ref. p. 4801

1.2.2.4 Mn-Ti,

1.2.2.5 Mn-V

295

Table 5 (continued). Y 10m4calmol-l K-’

Cro.98Feo.02 Cro.&‘eo.o~ Cro.90Feo.l~ Cro.~4%l~ cro.8Peo.18 Cro.81Feo.l~ Cro.80Feo.20 Cro.70Feo.30

Cr o.63Feo.37 Cro.53Feo.47 Cro.z&o.7s Cro.15Feo.85 Cr o.06Feo.94

< 7.7 < 16.6 25.2 32.2 39.4 <41(42.4) (43.0) 37:3 28.4 16.4 14.3 9.87 9.36 10.2

P calmol-’ Km4

0.353 0.355 0.0405 (-0.086) (-0.123) 0.0151 0.0433 0.171 0.137 0.0768 0.0632 0.0433

E

@D

%

K

0.4 0.5 0.5

236 235 486

0.4 0.5 0.4 0.4 0.6 0.4 0.6

675 475 301 324 392 419 475

1.2.2.4 Mn-Ti Reference: 74 K 2. Table 6. Composition dependenceof the magnetic state for P-Mn-3d transition metal alloys at 4.2 K [74 K 21. The range of composition for paramagnetism (P) and antiferromagnetism (AF) is given in [at%] of the 3d metal. Ti

V

Cr

Fe

co

Ni

2...4

2...4

1 2.,.20

0.1...0.5 0.7...35

0.5.e.12

at% P AF

2

1.2.2.5 Mn-V References:63 C 3, 69 s 1, 69 V 1, 71 V 1, 74 K 2, 77 A 1, 80 M 3, 81 M 2, 83 M 1. Table 7. Magnetic susceptibility of CsCl-type compounds Ti-3d and MnV. PP: Pauli type paramagnetism, CW: Curie-Weiss type paramagnetism. NiTi ‘) CoTi FeTi MnV

PP cw cw PP

X(T)=(5.1...8.9)10-6cm3g-1 for T=77+~.823K [62Bl, 68W2] SeeFigs. 185, 186, 190 SeeFig. 69 Field-induced ferromagnetism appears, (0.061uJFe) [60 N 1, 73 A 21 x(CsC1)< X(disorder). Seealso Figs. 27, 28 [Sl M 21

‘) The CsCl-type structure is formed above ca. 380 K and transforms into a complex triclinic structure at low temperature.

Landolt-Bbmstein New Series 111/19a

296

1.2.2.5 Mn-V

[Ref. p. 480

v,Looo

,

“C

1200

m L"

10

1’

I

3n <"

rn .,"

I

v7 .Ju

I

I

rn ou

1

/

yn IU

II Mn-V

80wt%90 / I 1

-,-Mn

\ \ I

6OC1 0 Mn

IO

1 I I II 20

II 30

40

I---I I II 50 v-

60

70

80

I 90 at % 100 V

Fig. 25. Phase diagram of Mn-V alloys [69 s 11. The bee disordered Mn, -XV, alloys can be obtained by quenching from high temperature in the composition range 05x50.63.

25.0 .lOL 9 KIT!

15.0 I $12.5

Mn

2.5

0

50

0 llof%Mn . 25 I 100 150 200

0. 58 0. 68 250

300

I 350 K 400

Fig. 26. Inverse magnetic mass susceptibility xi’ vs. temperature for bee Mn-V alloys. Solid symbols: highfield extrapolation values, open triangles (downward): V,,,Mn,,,, ordered CsCl-type [71 V I].

I-

Ada&i

I andolt-Rornrrcin New Scric< lll~‘l9n

1.2.2.5 Mn-V

Ref. p. 4801 14 r I 40.' cm! (Mn0.5V0.05)xCrl-x 9 12

I

I

Y

zero-offset

1.0 0.9

3.0.lOP cm’/g 2.5

6

Cr -"

200

400

600

800

1000

1200 K

TFig. 27. Magnetic mass susceptibility xp vs. temperature alloys [Sl M2]. for Mno.5Vo.5 and (Mno,,Vo,&r,-, The vertical arrows at the curves for x = 1.O,0.9 and 0.8 signify the order-disorder transition point (bcc-CsCl), and the NCel point for x = 0,O.l and 0.2 obtained from the electrical resistivity.

Fig. 28. Magnetic mass susceptibility xs for Mn-V alloys at 130K (open symbols) and 300K (solid symbols). Circles: bee chase. trianeles: o-nhase. cross: ordered CsCl-type [7iV 11.’ A

Landolt-Bdmstein New Series 111/19a

Adachi

2.5 I 0 0 v

20

40

60 Mn -

I 80 at%

100 Mn

298

[Ref. p. 480

1.2.2.5 Mn-V 2.11

.$ 9

"2ko

Mn-V /

1.5

II

I

MnlmxVx

x =o.ot I

I

A

/

/

I

0

/_

in, .-

I

I

Y/l

57ot%Mn 68ot%Mn

I

I

I

I

0.1

0.2

0.3

0.1

I

0.5 kOe-'

Fig. 29. Magnetic mass susceptibility xp vs. the reciprocal value of the measuring field H,,,, for Mn,,5,V,,,, and Mn,,,,V,,,, alloys at various temperatures [71 VI].

H-

Fig. 30. Magnetic moment per kg, 6, as a function of magnetic field H for Mn, -XV, alloys at 4.2 K [80 M 33.

6 vsm kg I

4

b " -I

2

1

0.9

5 0.6

0

20

LO

60

80

K

Fig. 31. Magnetic moment D for Mn,-,V, alloys in an applied magnetic field of 215 kA/m as a function of temperature [80 M 31.

5.9

5.6

6.2

R-

Fig. 32. Low-temperature spin-lattice relaxation time Tr for “V and 55Mn in bee Mn-V alloys as dependent on the average 4s and 3d electron number per atom, n (T=4.2 K and 1.2K give the same results). The solid line is (T, 7) - U* as derived from the Knight shift using a generalized Korringa relation [71 M I].

Ada&i

0

0 V

299

1.2.2.5 Mn-V

Ref. p. 4801

IO

20

30

40 Mn -

50

60

at%

80

I

1.5

g K c

1.0

0.5

Fig. 33. Spin-spin relaxation rate, Tzml, for ‘IV in Mn-V alloys at low temperature (T =4.2 K and 1.2K give similar results) [71 M 11.

0 V

0

20

40

60

80 at% Mn

Mn -

50

100

200

150

250

300 K 35C

T-

Fig. 34. Knight shifts K for (a) ’ ‘V and (b) ’ ‘Mn in Mn-\ alloys at 11.4kOe and 300K. Open circles: bee phase disordered; solid circles; bee with CsCl ordering; oper triangles: pure o-phase; solid triangles: mixec a+ o-phase [71 V 11,seealso [69 V 11.(c)Knight shift fo: ‘IV in Mn,,,V,,s as a function of temperature [71 V l]

Landolt-Bbrnstein New Series IW19a

Ada&i

300

1.2.2.6 Mn-Cr

[Ref. p. 480

Mn5 10 15 20 25 30 35 10 45 50 55 60 65 70 75 80 85wt% 95

163:

c

12Oi

7 ‘C

1

9K 80[

31

‘C.

/--~

I A-

-~6OO'c --

I 10 Cr

20

30

40

50 Mn -

60

1

I

r I

I II 70

1 CY-MI

80

90 at% 100 Mn

Fig. 35. Phase diagram of MnXr alloys [58h I]. Temperature, in c”C], and composition in [at%Mn] and, in parenthcscs, in [wt%], arc given for special points of the phase diagram.

Ref. p. 4801

1.2.2.6 Mn-Cr

301

24 w6 -cm3 9

11.5

11.0

2 a-Mw5ot%Cr

I 10.5 s

5 a-Mn-Sat%Fe

10.0

9.5

0

200

400

600

800

1000 K I;

a

8.01 0 50

100

150 7-

200

250 K 300

Fig. 36. Magnetic mass susceptibility xg of Mn and Mn-based alloys [62 S 11. 3.0’ 120

150

180

210

240

K

270

7-

b

Fig. 37. Magnetic mass susceptibility xg vs. temperature for Mn-Cr alloys. (a) [79 M2], see also [62T 11; (b) [66S 11. The arrows indicate NCel temperatures determined by electrical resistivity measurements.

3.40I

300

350

400

450

K 500

Fig. 38. Magnetic mass susceptibility xp vs. reduced temperature for Cr-0.8 at% Mn. The NCel temperature, TN = 456 K, is derived from hyperfine-field measurements [Sl P 11. Landolt-BOrnstein New Series lWl9a

302

1.2.2.6 Mn-Cr

[Ref. p. 480

600 K 500 400 300 200 3.s .13-" -Ci3J 0

i H"

100 Mbor 2.9

i--I

3.3s

2.8

2.5 3.20

.! cv

A

0.5

1.0

1.5

2.0 Mn -

2.5

3.0

3.5ot% 4.0

Fig. 40. Magnetic phase diagram ofdilute Mn-Cr system [Sl P I]. Solid lines: obtained by neutron diffraction [66 K I], dotted lines: guess based on [80 H I], shaded arca: [8l P I]. P: paramagnctic phase, CAF: commensurate antiferromagnetic phase, TIAF: transverse incommcnsuratc antiferromagnetic phase, LIAF: longitudinal incommensurate antiferromagnetic phase, L: Lifshitz point.

2.7 I b 2.6

3.25

0 0 Cr

2.4

3.30 = 3.25 3.20

3.10 75

150

225

300

375

450

525 K 600

I-

Cr

Fig. 39. Magnetic mass susceptibility la vs. temperature for sin&crystal Cr-Mn alloys. Magnetic ticld pcrpcndicular to the [OOI] direction. Young’s modulus E vs. tempernturc is measured on polycrystallinc samples rcventing the transition temperatures [66 B I]. (a) CrO.l2wt% Mn. (b) Cr-0.44wt% Mn. (c) Cr-1.03wt% Mn.

Mn-

Fig. 41. Lattice parameter a of Mn-Cr alloys at room temperature and effective magnetic moment per Mn atom, perr,obtained from susceptibility measurements [79 M 21.

Table 8. N&e1temperature TNof a-Mn alloys containing 1at% 3d transition metals, as derived from the minima in the resistivity vs. temperature curves [74 M 11.AT,: shift of TNdue to alloying, relative to TN of a-Mn.

TN

AT, K

u-Mn

95

cl-Mn-1 at% Cr cr-Mn-1 at% Fe

84(l)

110(l) 118(l)

0 -12(l) +15(l) +22(l)

104(I)

+

K

u-Mn-1 at% Co a-Mn-I at% Ni

Adachi

90)

Landolr-Rornrlein Ncu Serier lll.‘l9a

1.2.2.6 Mn-Cr

Ref. p. 4801

303

80

K 710

0.0028

60

0.0024

50 40

0.0020 I 0.0016 I$

30

0.0012

20

0.0008

IO

0.0004

0 Cr

60 at% 80

Cr

Mn -

Fig. 42. Composition dependence ofNCe1 temperature TN and the average sublattice magnetic moment per atom, j& extrapolated to 0 K of Mn-Cr alloys [79 M 21. Open circles [79M 21, open squares [53 S 11, solid squares [58 K 21, solid circles [64 H 31.

5

IO

15 Mn -

20

I

3

6

9 H-

12

15

Fig. 44. Magnetic moment per gram of Mn-Cr alloys at 4.2 K, as dependent on magnetic field strength [79 M 21. Landolf-Biirnsrein New Series lll/l9a

0 25 at% 30

Fig. 43. Composition dependence of the Curie temperature Tc, the average magnetic moments j?,,,rfor the weak ferromagnetism and the spin reorientation temperature T,, of antiferromagnetism in Mn-Cr alloys [79 M 21.

b

0

Ps

Mn-Cr 1

0

Oo_IO

0.0032

I

a

Adachi

kOe

18

1.2.2.6 Mn-Cr

304 0.35 Gem! 9 0.3’;

[Ref. p. 480

Mn-Cr I Hop2,= 2.7 kOe

Noncollineor model

Collinear model 0.i C

l II

01

om

@IT

Fig. 46. Spin structure of cr-Mn [7OY I,70 Y 21. I, II, III and IV mean the lattice sites and the arrows indicate the spin direction.

0.2[

I b

0.1:

0.i 0

IO

20

30

ka I-

50

60

70 K 80

Fig. 45. Thermomagnctic curves of the weak ferromagnetism for Mn -0 alloys in H,,,,=2.7 kOe. (a) D.6,..4.5at% Mn. (b) 6.4...17.5at% Mn [79M2].

0 Kn b Re 0.90 0 CC

1

2 3 Impurity -

1

al%

5

Fig. 47. Spin density wavcvcctor Q for various dilute alloys of Cr. Q = 2 n/a corresponds to a commensurate spin structure. For each alloy system the upper of the two curves refers to data near TN, the lower to very-lowtcmpcraturc data [66 K I].

53

100

150

200 K 250

Fig. 48. Incommensurability parameter 6 of the spin density waves as a function oftempcraturc,mcasurcd for a single crystal of Cr-0.68 at% Mn. Q=(2n/a) (I -6, 0, 0) t-82G 2). I: incommensurate, C: commensurate.

Adachi

305

1.2.2.6 Mn-Cr

Ref. p. 4801

Table 9. Magnetic structure and the associatedmagnetic moment p, in [un], for Cr alloys with small additions of V and Mn, as derived from neutron diffraction experiments [65 H 11. AF,: commensurate antiferromagnetic phase, AF,: transverse incommensurate phase: magnetic moments perpendicular to spin-density wavevector, AF,: longitudinal incommensurate phase: magnetic moments parallel to spin density wavevector. T

Mn [at%]

V [at%]

Cr

1 RT 77K 21 K 4.2K

1.9

0.28(AF,) 0.28(AF,)

0.40(AF,)


0.50

0.74

2.1

0.50(AF,)

0.45(AF,)

0.47(AF,) 0.68

0.59(AF,) 0.67(AF,) 0.67(AF,)

0.54

Table 10. Spin density wave properties for Cr alloys with small additions of V and Mn [65 H 11. Q: spin density wavevector, I: wavelength of antiferromagnetic modulation, a: lattice parameter. Qa/2K

AJa

T

K 0.95 0.93 0.97 1

Cr lat%V 0.5, 0.74at% Mn >2.1 at% Mn

20.0 13.2 28.6 co

120 78 142 5...400

Table 11.Magnetic moments and hypertine magnetic fields of a-Mn for sublattice sites I, II, III and IV. For definition of the sites, see Fig. 46. Site

Land&Bbmstein New Series lll/l9a

Number of atoms

MnI MnII

1 4

MnIII

12

MnIV

12

%,,Wel

PMnClhI

(4.2 K)

collinear model (4.2K)

noncollinear model (4.4K)

[56K2] 2.5 2.5

[70 Y l] 1.90 1.78

1.7

0.60

WO

0.25

Adachi

[74 K 1-j 189.9 144.3 137.6 29.5 25.7 7.1 4.8

Table 12. Experimental data on the commensurate-incommensurate spin density wave transitions for Cr-Mn susceptibility, TE: thermal expansion, R: rcsistivity, HC: heat capacity, X: X-ray, mcasuremcnts. Mn at%

Experimental technique

0.12 0.3 0.43 0.44 0.45 0.5 0.5 0.5 0.6 0.68 0.70 0.74 0.9 0.96 1 1.03 2.1

ND, II TE TE ND, z TE, R, HC R, HC ND X TE TE, ND TE, R, HC ND TE ND TE ND, 2: ND

Hysteresis width [K]

Transition width [K]

Center of hysteresis loop CK]

15

-

-

35 31 50

50 50 x 1 100

30 30 40 80 35 40 40

50 40 % 3 100 35 10 45

260 200 197 200 250 230 175 162 170 140 120 135

alloys [82 G 21. ND: neutron diffraction, x: magnetic

Remarks

Ref.

Incommensurate for all temperatures below TN Incommensurate for all temperatures below TN No resistivity anomalies observed at T=

66Bl 78K 1 6783 66Bl 8262 77 M 6 75H4 74T1 78Kl 8262 8262 75H4 78K 1 66Kl 76H2 66Bl 75H4

Homogeneous Mn distribution No anomalies at T,

20 K between peaks Inhomogeneous Mn distribution Homogeneous Mn distribution

No anomalies for 80 < T < TN Commensurate

for all temperatures

below TN

1.2.2.6 Mn-Cr

Ref. p. 4801 -k2

0.8 0.6 OA

do d 0.6

01 0

I

II

II

0.2 I

V- Cr, Mn-Cr I

12

I

1

L

3

5

0

1 6 dO-3

0 0 Cr

5

IO

15 Mn -

20at%25

7

62 Fig. 49. Square ofthe magnetic amplitude M, vs. square of the incommensurability parameter 6 of the spin density waves of Mn-Cr and V-Cr alloys at zero temperature. The modulus of the Jacobian elliptic function describing the spin density wave is designated by k [81 N 11. Polycrystalline samples: (I) 0.25 at% Mn, (2) 0.18 at% V, (3) 0.85at% V, (4) 4.13at% V; single crystals: (5) 1.5 at% V, (6) 2.3 at% V. Open circles: [Sl N 11, solid circles: [65Hl, 67K1, 66K1, 65Kl]. Solid line: estimated, dashed line: best fit [81 N I].

Fig. 50. High-field magnetic susceptibility xHFfor Mn-Cr alloys at 4.2 K, measured at magnetic field strengths up to 18kOe [79M2].

1.i

r/r, Fig. 51. Temperature dependence of magnetic hyperfine fields measured on l1 ‘Cd probe nuclei in Cr-0.8 at% Mn. The NCel temperature is defined as the temperature where the concentration of sites with zero hyperfine field is 50% as determined from hyperfine field data. H,: maximum hyperfine field, I?, : hyperfine field averaged over half of an oscillation of the spin density wave, l!i: average hyperfine field in the commensurate-paramagnetic transition region. Circles and triangles apply to different samples of about the same composition, their NCel temperatures varying between 456K and 471 K, see caption to Fig. 52. Crosses indicate averaged hyperfine fields [Sl P 11. Ki: commensurate-incommensurate transition temperature. Landolf-Biirnstein New Series 111/19a

Adachi

30s

1.2.2.6 Mn-Cr

[Ref. p. 480

/ 1 kii Cr- 0,8at% Mn

Fig.53. Line shape ofthc spin-echo spectrum for 55Mn in bee Mno.289%.7, 1 at 1.4K. All samples with a Mn content bctwcen about 5 and 60 at% Mn show similar lint shapes [73 T I].

1 I _1 1I

0.85

0.93

70

kOe 0.95

1.00

1.05

1.10

60 1.15

I / r,, -

I 50

Fig. 52. Tempcraturc depcndcncc of magnetic hypcrfinc fields and of the concentration of sites, cp. with zero hypcrfinc field. for “‘Cd in the commcnsuratcparamrqnetic transition region of Cr-0.8 at% Mn. Sample I: Tx=461(3)K.sample 2: ‘&=456(3)K,samplc 3: rs=471 (3)K [Sl P I]. H,: maximum hypcrtinc ticld, I?: average hypcrfinc field; i7 = (I- c,)H,, rcprcscntcd by crosses [Sl P I], See also Fig. 51.

c; z 40 zE =c 30 20 10 0 0 Cr

20

40

60 Mn -

80 at% 100 Mrl

Fig. 54. Magnetic hypcrfmc field as derived from spinecho NMR spectra for “Mn in bee Mn-Cr alloys at I .4 K [73T I].

Adachi

Ref. p. 4801

1.2.2.6 Mn-Cr

a-Mn-Cr

100

110

120

130

140

150

160

190

200 MHz

V-

Fig. 55. NMR line shapes of 55Mn at site I and site II of a-Mn-Cr alloys at 1.4K [74 K 11. For site definition, see Fig. 46. Intensity scales are different for site I and site II.

I

Mn-Cr

bee

I

/

I

Cr- 0.7at%Mn

Cr- 0.45at%Mn

I

I

IO" I 20 c!

40

60 Mn -

80 at%

I

100 Mn

Fig. 56. Nuclear spin-lattice relaxation time Ti of 55Mn in bee Mn-Cr alloys, multiplied with temperature T The value of T,T is constant in the temperature range from 4.2K to 1.4K [73T 11.

I 206

I\ 210

I

if

K 21;li

178

K IEj2

TFig. 57. Latent heat dQ/dt as function of temperature for two Mn-Cr alloys as observed on heating through the transition of the incommensurate to the commensurate spin density wave state [82 G 21. Landolt-Biirnstein New Series 111/19a

Adachi

310

1.2.2.6 Mn-Cr

[Ref. p. 480

16 6 L 0

2

L

6

8

10

12

16

16

18 K2 20

12Fig. 58. Relation between specific heat C, and temperature for Mn-Cr alloys at low tempcraturcs [60 C 31.

Adachi

Ref. p. 4801

1.2.3 Alloys between Fe, Co, Ni and Ti, V, Cr, Mn

311

1.2.3 Alloys of Fe, Co or Ni and Ti, V, Cr or Mn 1.2.3.0 General remarks (Seealso subsect. 1.2.2.0,p. 282) Magnetic properties of the binary alloys of Fe, Co or Ni and Ti, V, Cr or Mn are represented, as well as magnetic properties of the respective pseudo-binary alloys in which one of the 3d transition metals is partially substituted by a third 3d metal. Surveys 3 and 5 give the subsection in which a particular alloy system is predominantly dealt with, while Surveys 4 and 6 provide a complete list of figures and tables containing data on the properties specified for the alloys under discussion. Survey 3. The subsectionsdevoted to the binary alloys of Fe, Co or Ni and Ti, V, Cr or Mn are listed, aswell as information on atomic ordering and crystallographic phases considered. dil: dilute alloy, diso: disordered alloy, (3: 1): Cu,Au-type superlattice, (1: 1): CuAu-type superlattice, (l/l): CsCl-type compound, (0): o-phase, (L): Laves phase.

Fe

co

Ni

Ti

V

Cr

Mn

1.2.3.1 dil diso U/l), (L) 1.2.3.5 diso gTy’

1.2.3.2 dil diso (4 1.2.3.6 dil diso yg$

1.2.3.4 dil diso ~1,y, c-Fe 1.2.3.8 dil diso

dil’ ’ diso (l/l)

dil’ diso (0)

1.2.3.3 dil diso (4 1.2.3.7 dil diso (0) 1.2.3.11 dil diso

1.2.3.12 dil diso (3:1), (1:l)

For survey 4, seenext page. Survey 5. The subsectionsdevoted to Mn-VCr Mn are represented.

Landolt-Bbmstein New Series II1/19a

and the pseudo-binary alloys of Fe, Co or Ni and Ti, V, Cr or

Alloy

Subsection

Mn-V-Cr Fe-VCr Fe-Cr-Mn Co-V-Cr Co-Cr-Mn Fe-Co-Ti Fe-Co-V Fe-Co-Cr Fe-Co-Mn Fe-Ni-V Fe-Ni-Cr Fe-Ni-Mn Co-Ni-Ti Co-Ni-Mn

1.2.3.13 1.2.3.14 1.2.3.15 1.2.3.16 1.2.3.17 1.2.3.18 1.2.3.19 1.2.3.20 1.2.3.21 1.2.3.22 1.2.3.23 1.2.3.24 1.2.3.25 1.2.3.26

Adachi

312

1.2.3 Alloys between Fe, Co, Ni and Ti, V, Cr, Mn

[Ref. p. 480

Survey 4. For each of the binary alloys of Fe, Co or Ni and Ti, V, Cr or Mn the figures and tables are listed in which data on the properties specified is provided. Referenceis given not only to section 1.2.3(Figs. 59. ..427 and Tables 13...88) but also to section 1.2.2(Figs. 1...58 and Tables 1. ..12). Numbers in roman and italic refer to figures and tables, respectively. For SCalloys, seeTable 1, p. 288. Alloy

Phase diagram. lattice constants

Susceptibility, paramagnctic properties

Magnetic transformation temperatures

Magnetization, average magnetic moment

Atomic magnetic moments, g-factor, spin structure

Fe-Ti

59, 60

65, 66, 332

63...69, 167, 336

70

Fe-V ‘)

1, 17 73

61...63, 65, 231, 234 13, 77 3, 74...82, 84

21,29

22...24, 29, 32

Fe-Cr ‘)

100

101...108, 208

Fe-Mn ‘)

21 156, 157, 161

23, 30. .32, 75 36, 158...163, 224, 360

7, 13...15, 17 15...17 72, 77, 80, 87...97 90...92, 96 130, 132 15, 23, 24, 32 15, 23.e.25, 32 15, 16, 25, 26, 28 109...116, 20, 21, 87, 19, 21, 131, 164 117...130, 134...139, 132...134, 145, 264, 140, 141 266, 355 15, 23, 32...34, 75 15, 23, 32, 36, 38 15,28,35...37 157, 164...166, 163,165, 167...169, 170, 171,355 227,363,400,404 363,368

363 184

42 185...189, 334

6,8, 15, 39, 42,86 195, 332

44, 45, 77 3, 198, 254

I, 7, 44 199, 200

CoCr

I, 44 197 21 206, 207

Co-Mn

21 219

50, 76 220...224, 361, 362

Co-Ti

co-v

Ni-Ti Ni-V Ni-Cr

Ni-Mn “)

83 246 1, 57 251, 252 21 256

101, 102 208.,.210, 254

253 7 21, 132, 253, 254 208, 257...259, 263

269, 270, 310

61 222...224, 271...273

67,68

69

1, 7, 13, 15, 19 82...86, 109, 164

15, 40, 42 188...195, 336

44,46 200...202 46...48 211, 261 20, 21, 132, 212...215, 217, 232 51, 76 46, 47, 52, 53 225...227, 226, 228, 229, 361, 362 232...234, 367 6,8, 39, 83 46, 47, 53, 54, 83 241, 214 249, 250 7, 55 55...57 274 132,249, 290 55 55,64 261, 274 20, 21, 132, 249, 262, 263, 265, 286, 290 51, 55, 63 55, 62...64 227, 270, 274, 275, 249, 276...284, 310,403 286, 287, 290, 310, 409.410.425 6, 8, 39, 55 55, 68, 69 67.. .69, 86

‘) Resistivity and temperature derivative of resistivity: Fig. 83.

Adachi

15, 16, 41

1 47, 48, 81 19,21,215,216, 264, 266 47, 51, 53 230, 231 47, 53, 54, 83 248, 250 57 64 19, 21, 216, 264...266 51, 64, 65 285, 287...289 67, 68, 70, 71

2, Resistivity: Figs. 103, 112.

Ref. p. 4801

High-field susceptibility

NMR, Mbssbauer effect

339

142, 143

194, 339

Specific heat, thermal expansion

Alloy

314, 341, 342 I, 15, lg...20

71, 72,332,345 77, 79

Fe-Ti

8, 93...97, 146, 173

98, 99

Fe-V ‘)

15, 20,

5

27.e.29 97, 144.**149

Spin waves, exchange

150, 151

15, 28 38 93, 172...180, 237, 238, 295, 371 13, 20,42, 43 185, 196, 314, 341, 342 45 203.. .205 49 218

176, 179, 235.. ~243,295

234

Magnetic anisotropy, magnetostriction

152, 153

5, 10, 154, 155, 345

38 181

5, 33 163, 182, 183, 420,421

217, 244

245, 332, 345, 422 46, 77, 79 245 46 245

244

46 245

co-v Co-Cr

Co-Mn

299...301

58 308...310

Ni-Mn “)

72, 73

69

60, 73

3, Resistivity and thermoelectric power: Fig. 163. Landolt-Bdmstein New Series IIl/19a

Co-Ti

59 302...307, 416, 417

267, 292

66

Fe-Mn 3,

Ni-Cr

59

173, 176, 179, 235, 237, 293...298 67, 68, 71

Fe-Cr 2,

46 268 58 255,268 58,60 260, 268

267, 292

66 291, 292

313

1.2.3 Alloys between Fe, Co, Ni and Ti, V, Cr, Mn

Adachi

4, Resistivity: Table 69.

Ni-Ti Ni-V

314

[Ref. p. 480

1.2.3 Alloys between Fe, Co, Ni and Ti, V, Cr, Mn

Survey 6. For the Mn-V-0 alloy systemas well as the pseudo-binary alloys of Fe, Co or Ni and Ti, V, Cr or Mn the figures and tables are listed in which data on the properties specified is provided. Referencesis given not only to subsect.1.2.3(Figs. 59...427 and Tables 13...88) but also to subsect.1.2.2(Figs. 1...58 and Tables 1...12). Numbers in roman and italic refer to figures and tables, respectively. Alloy

Phase diagram. lattice constants

Susceptibility paramagnetic properties

Magnetic transformation temperatures

Magnetization, average magnetic moment

Mn-V-Cr

311. 312

27, 313

312, 314, 315 74 321 75

315...317 74

36, 320 75 36, 162 14, 325 76

Fe-V-Cr ‘) Fe-Cr-Mn Co-V-Cr Co-Cr-Mn Fe-Co-Ti 2,

Fe-Co-V Fe-Co-Cr Fe-Co-Mn

423

423,424

346 359, 363, 364 83

360...362, 364, 366

Fe-Ni-V Fe-Ni-Cr

379,380

381, 382

83 394...399, 411

Fe-Ni-Mn 83

325

88

77

332...334

CoNi-Ti Co-Ni-Mn

74

76 332, 334...338 77, 78 77, 78 80 347...349,358 349...352 82 227, 361...365 363, 365...369, 373, 374 83 82,83 377 378 85 227, 380, 38I, 383, 385...389 384, 388,389 83 83 227, 398...404 396, 397, 405...411,413 83, 86, 87 87

331, 332, 334

Atomic magnetic moments, g-factor, spin structure

‘) Resistivity: Fig. 321. 2, Influence of hydrogen on magnetic properties: Table 78.

Adachi

425,426

81 355 82 355, 370 81...83 81 389,390 83 412

1.2.3 Alloys between Fe, Co, Ni and Ti, V, Cr, Mn

Ref. p. 4801

High-field susceptibility

NMR, Miissbauer effect

Spin waves, exchange

Magnetic anisotropy, magnetostriction

Specific heat, thermal expansion

318, 319

315

Alloy

Mn-V-Cr Fe-V-Cr ‘)

322.. .329

339

330 340...343

77

78

Fe-Cr-Mn Co-V-Cr

10, 332, 339, 344, 345 77, 79

77

352...354, 356

357

346, 357, 358

Co-Cr-Mn Fe-Co-Ti 2,

Fe-Co-V Fe-Co-Cr Fe-Co-Mn

371, 372, 374...376 84

Fe-Ni-V 391, 392

372,414,415

416...418

427

Landolt-Bdmstein New Series 111/19a

Fe-Ni-Cr

393

182, 419.. .421

Fe-Ni-Mn

88 10, 422 79

Co-Ni-Ti Co-Ni-Mn

Adachi

1.2.3.1 Fe-Ti

316

1700 “C

10

20

30

Ti 40 50

[Ref. p. 480

60

70

8owt%90

1600

600 500 400 0 Fe

10

20

30

40

50 Ti -

60

70

80

90ot% ’

Fig. 59. Phase diagram of Fe-Ti alloys [58h 11. Tc: [14L 11. Temperature, in c”C], and composition, in [at%Ti] and, in parentheses. in [wt%Ti], arc given for characteristic points of the phase diagram.

Adachi

Ref. p. 4801

1.2.3.1 Fe-Ti

0.45 0.45,

I

,

317

I

0.40 0.35 0.30 I 0.25 I c 0.20

Fig. 61. Magnetic molar susceptibility x,,, and its inverse value, xi ‘, as a function of temperature for Fe,,5Ti,,, [77H3].

0.15 0.10

0 30

31

32 Ti -

33

at%

34

Fig. 60. Fraction f of Fe atoms with one or more Fe neighbors on Ti sites as dependent on composition for Fe-Ti alloys [67 W 11.

-Jc& 9 40

I 30 CT 20 225 m;’ mol

IO

0 150 t 125 %oo

25

0

2

01 0

6.D6 m/A IO

4 H-l -

Fig. 62. Influence of hydrogenation on the magnetic molar susceptibility x,,, of Fe,,,Ti,,,. Curve A: before treatment with hydrogen, B: after one hydrogenation and dehydrogenation, C: after several hydrogenations and dehydrogenations [77 H 31.

Landolt-Bornstein New Series IIl/19a

I 100

I 200

I 300 T-

I 400

I 500 K 600

Fig. 63. Reciprocal magnetic mass susceptibility, xi ‘, and spontaneous magnetization crSderived from measurements in magnetic fields up to 100 kOe vs. temperature for Fe,+,Ti,-, Laves phase compounds. For an analysis of the curves, see Table 13 [70 0 11, see also [67 M 11.

Adachi

[Ref. p. 480

1.2.3.1 Fe-Ti

318

100 Gcm3 9

60 Gcmj 9 50

I 60 b 40 20 0 160 .1w6 gly 9 I x 80 e w 40

1c

0

c 2GC .lO! cm! 9 16:

2L

\

100

200

300

400

26

28

30

32

34

36

38ot%40

Fig. 65. Composition dependence of the magnetic momcnt u of Fc-Ti alloys at 44 and 500 K, Curie and Ntel tempcraturcs, Tc and TN, rcspcctivcly, and peak value of the susceptibility, xrnBx,in the antiferromagnetic region [68 N 21.

K 500

lFig. 64. hgagnetic moment 0 and the susceptibility xs mcasurcd in a magnetic field of 9.6 kOe at various tcmperaturcs for Fe-Ti Laves phase compounds [68 N 23.

Adachi

Ref. p. 4801

1.2.3.1 Fe-Ti

15

2.2: Jcrj 9 2.0[

Gcm3 9 I 5

319

5 1.7:I

1.5cI

I 1.2:, b l.OCI

0.75,

0.50I

0.25

0

8 F

I

T=$.2t

x=0.0133

Fig. 66. NCel temperature TN,Curie temperature T, and the spontaneous magnetic moment crs(&: average magnetic moment per formula unit) at OK for Fe,+,Ti,-, alloys [710 31. Solid circles: TNdefined as the temperature for the maximum in the x(T) curve, bars: TN derived from Mijssbauer experiments.

6 .I03 Ah

I

Feo.5 T' 0.5

4 I x

0

0

10

15

20

25 kOe 30

15

30

45

60

75 Ad/K 90

Fig. 67. Magnetization curves at various temperatures for Laves phase compounds Fe,+,Ti,-, [710 31. (a) x= -0.0094, (b) x=0.0133.

NIT Fig. 68. Magnetization per unit ofvolume, M, vs. the ratio

H/T, i.e. the magnetic field divided by the measuring temperature, for Fe,,,Ti,,, samples hydrogenated in a hydrogen atmosphere of 130 bar at various temperatures and slowly cooled to room temperature [77 H 31.

Landolt-Bbmstein New Series lWl9a

5

H-

2

Adachi

Table 13. Magnetic properties for Fe-Ti alloys as derived from measurementsin the temperature range 1.5...578K and up to magnetic field strengths of 1OOkOe [7001]. C,: Curie-Weiss constant, perr: effective moment per formula unit, derived from Curie-Weiss curve, pm:magnetic moment per formula unit. derived from magnetization measurement. Ti at%

[Ref. p. 480

1.2.3.1 Fe-Ti

320

Tc

0

TN

C,

Table 14. Spontaneous magnetic moment es and the average magnetic moment per atom, Pa,,for bee-type Fe-Ti alloys [79K8, 68A 11. [68A 11: Accurate to f 0.2% relative to pure Fe. [79 K 81: Estimated error 0.5%. Ti at %

T

a5

Pa,

K

Gcm3g-’

pn

2.02 4.00 5.97 2.88 4.92 7.82 2.88 4.92 7.82

0 0 0 77 77 77 RT RT RT

217.31 211.09 205.05

2.167 2.099 2.033 2.086 2.022 1.922 2.063 1.981 1.897

Pcrr Pm

cm3Kmol-’ K

Pll

31.09 318 353 2.25 33.17 162 276 2.62 34.30 94 282 2.81

4.23 1.26 4.54 0.12 4.62 -

Ref. 68Al 68Al 68A 1 79K8 79K8 79K8 79 K 8 79K8 79K8

Table 15. Change dP,,/dx of the average magnetic moment per atom of the alloy, Put,due to 3d impurities (concentration x in at%) in Fe. Impurity atom magnetic moment pi, decreaseof Curie temperature for 1at% impurity, AT,, and magnetic hyperfine field at the impurity atom, II,,,.,,, as derived from neutron scattering experiments. 3d impurity

Impurity at%

dP,,/dx un/at%

Mn

-2.11 (59al]

Cr

-2.29 [59a l] -2.36 [63 N l] -2.68 [59a l] - 3.286 [63 N l] -3.28 [59a I] - 3.392(49)[68 A l]

v Ti

Pi lh

< 0.02

0 [65 C l] 0.1(5) [66 c 1) < 0.02 -0.7(4) [65 C l] 0.177...0.678 -0.9(3) [66C 1-j < 0.02 -0.4(4) [65 C l] 0.02.. .0.60 -0.9(3) [66 c l] <0.03 -0.7(3) [65 C 1-j 0.03...0.06 - 1.2(6)[66C 13

Table 16. Magnetic moments of 3d impurity atoms in Fe, pi, as derived from Miissbauer spectra and from neutron data [76 C 21. 3d impurity

TITC

Pi

0.315 0.283 0.280 0.291 0.029 0.292 0.627 0.798

-0.1 1.8 1.3 1.2 0.9 0.2

-15 [32S 1-J - 12.1 [71 s l] - 1.5 [36F l] 4.3 [71 s l] 7.5 [36F l] 11.2 [71Sl] 3.7 [59A l] 3.8 [71 S l]

Hh\.p kde - 226.97 (OK) [68sl] - 87.3 (77 K) [68 s l]

Table 17. Magnetic moment distribution for Fe-Ti alloys at room temperature [79 K 143. Ti at%

CPIJ

Mbssbauer Ti V co Ni Mn Mn Mn Mn

AT, K

neutron -0.4 -0.9 1.4 0.8 1.0 0.6 -0.1 -0.2

hi PB

0.84(l) 2.868 1.33(3) 2.869 1.73(5) 2.87

2.146(8) 2.383(9) 2.132(6) 2.383(8) 2.118(7) 2.383(11)

‘) Derived from bulk magnetization.

Adachi

- 2.08(22) - 1.42(23) - 1.38(24)

Ref. p. 4801

1.2.3.1 Fe-Ti

321

3.5 G& 9 3.0

t b

3

pe Fe-Ti bee .

2.5

t I$

2.0

Ia"

2 ::

.. A

.

RT a

1

1.5 0

1.0

Irg fi

0.5

1 -1

0 Fe

1.0: Ijcm3

\ 5.0 at%

2.5

7.5

Ti -

Fig. 70. Room-temperature magnetic moments of bee Fe-Ti alloys. &: open triangles; &, pri: circles [79 K 81, squares [76 C 23, solid triangles [65 C 11.

$75

I

b 0.50 0.25 0 0

2.5

5.0

z5

10.0 12.5 HOPPl -

15.0 kOe 20.0

Fig. 69. Magnetization curves at various temperatures for CsCl-type FeTi compound. (a) Alloys vacuum-annealed for 72 h at 1000“C, no information on the cooling rate [60N 11. Open and solid circles refer to two different samples. (b) Alloys annealed for 4 days at 900 “C, cooled to room temperature at a rate of 30 “C/h [73 A2].

Table 18. Magnetic hyperfine fields for “Fe in Fe-Ti alloys at room temperature. Seealso [64 N 1, 70 B 11. ffhyp(57W

FeTi Fe,Ti

x 100kOe 5(3)kOe

Ref.

67W2 62Kl

Table 19. Transition from ferromagnetism in Fe-rich to antiferromagnetism in Ti-rich Fe-Ti alloys [67 W 11. Isomer shift IS, relative to Fe at room temperature. Quadrupole shift dQ, Mijssbauer linewidth 6 and effective hyperfme field Hefffor “Fe, TN:NCel temperature. TN K Ti-rich: Fe0.66%.34 Fe-rich: Fe0.69%31 ‘) ‘) 3, “) ‘)

275

T K

ZS(RT) ‘) mms-’

RT 20.4

-0.286(5) -0.17(l) 1)

298 20.4

CO.254) 5)

mms-’

6 mms-l

0.404(5) 0.40(1)2)

0.29 0.27...0.29

H hyp,&'F4 kOe

97 “) 247 4,

For Fe on 6h and 2a sites. For Fe on 2a site. For Fe on 6h site. For excessFe on Ti sites. Relative to a-Fe at 20K.

Landolt-Bbmsfein New Seriec 111/19a

dQ(RV

Adachi

322

1.2.3.1 Fe-Ti

[Ref. p. 480

Table 20. Change of hypcrfine magnetic field of 57Fe due to the neighboring impurities in Fe-Mn, Fe-V and Fe-Ti alloys (bee phase) [64 W 11.The hyperfine field of “Fe is assumed to be Hhyp.Fd) = x x NC, ’ N%, ’ H(n, m, ” Ill with H(n m) = H,,,,re(0) (1 + Kx) (I+ on + bm) , where n and m mean impurity numbers in the nearest neighbor atoms N and those in the second-nearest neighbor atoms N’, respectively, with frequency Nc, (0) is the hypertine field of pure Fe; K, and N’c,. f&y,,. r=e a and b are constants; IS is the isomer shift, in [cm s- ‘1, per nearest-neighbor impurity atom. Impurity l K IS

Mn

V

-0.0685 -0.011 0.11 0.0001

Ti

-0.0765 -0.0645 0.31 -0.0061

-0.0655 -0.061 0.055 0.000I

mJ molK2 6 t k 3

2

Fig. 71. Specific heat C, vs. tempcraturc for FcTi. Solid line: best fit to the data of the form C,IT=/?T’+C’/T \vith /?=0.035~10-4cal Ke4 mol-’ and C’=21.5 . 10m4cal K-’ mol-’ [6OS I].

-0

25

50

75

100

125

150 K2 175

12 -

Fig. 72. Tempcraturc dcpcndcncc of the molar specific heat C, of Fc,,,Ti,,, and Fe,,,gTi,,,, alloys, plotted as C,/T vs. T2 [77 H 31.

Adachi

323

1.2.3.2 Fe-V

Ref. p. 4801

1.2.3.2 Fe-V References: 34E1, 36F1, 38S1, 47W1, 50K1, Slbl, 54T1, SSNl, 56k1, 56K1, 58h1, 59a1, 6OP1, 62A1,62C2, 62V1, 63J1, 63L2, 63n1,63Nl, 64K1, 64W1, 64W3, 65C1, 66C1,66C2,66Rl, 67M2, ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 78H3,7901,80Kl, 80Kl1, 82B1, 82C4, 82L1, 82M3, 83D2, 83L1, 83Yl.

600 500 400 3001 0 Fe

I IO

20

I

II

30

40 v-

II 50

60

II at%

80

Fig. 73. Phase diagram ofF*V alloys [58 h 1,p. 7301.For reliable data of T,, see Figs. 84 and 85. Temperatures, in rC], and composition, in [at% V] and, in parentheses, in [wt% V], are given for characteristic points of the phase diagram.

Landolt-Bbmstein New Series 111/19a

Adachi

324

1.2.3.2 Fe-V

[Ref. p. 480

Table 21. Lattice constant and magnetic properties of o-phase M,M; -I alloys. M: Fe, Co, Ni and M’: Cr, V. M-M’

Lattice constants [A] 2,

Magnetism

X

a

Fe-V

0.455...0.61

ferromagnetic ‘)

Fe-Cr

0.50...0.565

ferromagnetic

co-v

0.32...0.594

Pauli paramagnetism

Co-Cr

0.37...0.41

Pauli paramagnetism

Ni-V

0.29...0.455

Pauli

x =0.399: 9.015 x =o.so: 8.799 x=0.565: 8.843

C

4.642 4.544 4.586

x = 0.477: 8.743

4.536

x=0.383: 8.98

4.64

‘) Curie temperature changes by annealing process. 2, For crystal structure and the stability of o-phase, see [63 n l] and [67p 11,

”

I 0 0

Fe

A-._-x.... 5

_1150 ^ IOK ^ ^ ---=--.a.10

15

v-

0 20

25

at% 30

Fig. 74. Paramagnctic mass susceptibility xB of Fe-V alloys at various temperatures[62A I].

1.2.3.2 Fe-V

Ref. p. 4801

325 2.60 40-2 cm3K 9

s

cm3

‘;rpxi’; 1000

1100

1200

1300

1400 K 1500

T-

0

Fig. 75. Inverse paramagnetic mass susceptibility, xi ’ vs. temperature for Fe-V alloys. Broken line: Fe [62A 11.

Fe

5

10

15

v-

20

Fig. 76. Paramagnetic and ferromagnetic Curie temperatures, 0 and Tc, respectively, and the Curie constant per gram, C,, for Fe-V alloys. I: [38 S 11, 2: [34E 11, 3: [62Al].

Table 22. Effective magnetic moment per Fe atom, perr,re,in the paramagnetic state and paramagnetic Curie temperature 0 foro-phase Fe-V alloys [69 M 2-J.

Landolf-BOrnstein New Series Ill/ I 9a

V at%

&ff,Fe

0

PB

K

40 43 46 49 51 53 55 89 44.5 46.2 47.8 52.8 53.5

1.78 1.42 1.18 0.90 0.77 0.65 0.59 1.82 1.43 1.09 0.98 0.72 0.69

185(5) 140(5) lOO(5) WJ) 44(5) W) O(5) 240(5) 188(5) 165(5) 125(5) 18(5) O(5)

25 at% 30

Heat treatment quenched into water from 1000“C

650 “C!, 350h annealed

Adachi

326

1.2.3.2 Fe-V

[Ref. p. 480

IF

I-

i-

li I ?7 1C

5

100

200

300

400

K

!

5

I-

50 F

, 6-k-v

40

36.2 at%V

I

2

H,,,,=BkOe I

20. .lO -5

cm

30

b

15.0 20

I 12.5 10

LIO. 0 s d

0

1.l5

5s

2.5 II b

0

100

200

300

400

K 500

I-

ig. 77a. b. Marqctic moment D in a magnetic ticld of kOe and the mvcrse magnetic susceptibility xi’ as zpcndcnt on tempcraturc for o-phase Fe--V alloys. ig. (a) [67 M 21, Fig. (b) [73 S 21.

0I 0

50

100

150 T-

200

250 K 3

Fig. 78. (a) Magnetic mass susceptibility zs and (b)inverse value ofX,-XO, whcrc 1, is the tempcraturc-independent part of x8. for o-phase Fe-V alloys [69 M 21.

327

1.2.3.2 Fe-V

Ref. p. 4801

25 -IO3 9

cm3

15

I 10 -2 5 0 30

100

0 35

40

45 v-

50

200

250

225

II 300 K 325

7-

55 at% 60

Fig. 79. Effective paramagnetic moment per Fe atom, PenFe, obtained from l/&,-x,) vs. T curves for o-phase Fe-V alloys [69M2]. Open circles: quenched from 1000 “C, solid circles: annealed at 650 “C. x0: temperatureindependent part of xg.

275

Fig. 80. Magnetic moment 0 in a magnetic field of20 kOe, remanence err and inverse magnetic mass susceptibility, x;‘, vs. temperature for a-phase Fe,,,,V,,,6 [77M 11. Similar behavior is found for 29...35 at% Fe, seeTable 24.

35 .10-'

1.0

cm: s 3c

0.E 25

I 3 0.E .z 2 z 20.4

I 20 G-7 15

0.2

IO

3

9

6

12

K

7--.

5

I

I

I

I ^ ^ P

I

405 9 i? I

I

I

I

3

6

9

.-

12

J

K

15

r, -

Fig. 82. (a) Relative ac susceptibility xac vs. temperature T for Fe 0.285V 0.715 samples quenched from various temperatures T,,. (b) Relative height of susceptibility maximum xmalr vs. its characteristic temperature T,

7-

Fig. 81. (a) Paramagnetic mass susceptibility xg and (b) its inverse, xi ‘, vs. temperature for Fe-V alloys m magnetic fields of 10 kOe [63 L2]. Landolt-Bbmstein New Series 111/19a

[78 C3].

Adachi

[Ref. p. 480

1.2.3.2 Fe-V

328 125 jL!x 12G 115 110 I ,105 103 95 90

a

8;55 .d 1050

1100 1150 1200 1250 K 1301

I-

I 0.25

6

2 0.20 OI - 0.15

0.35 @g

010

0.3Ko

O.Oi

0.25.!

0

830

12

16

16 at%

v-

Fig. 84. Ferromagnetic and paramagnetic Curie temperatures, Tc and 0, respectively, for Fe-V alloys. Open circles: [34 E I], triangles: [69 S 31, squares: [62A I], solid circles: [76T I].

0.20 y % 0.15

b

10

8

850

903

0.10 1000 1050 11OOK1150

950

300 K

I

Fe-V

I G-phase

I-

Fig. 83. (a) Electrical resistivity Q and (b) its temperature dcrivativc do/d7 for Fe-V alloys near the Curie tempcrature [76T I].

35

LO

45 v-

50 at%

Fig. 85. Curie temperature T, as dependent on composition and on heat treatment for a-phase Fe-V alloys. I: quenched from 1000°C [69 M 2],2: annealed at 650 ‘C for 350h [69M2], 3: annealed at 1000°C for 120h [63nl,p. 101],4:annealedat 1050°Cfor4days[60P I].

1.2.3.2 Fe-V

Ref. p. 4801 60 K

329

I

Fe-V

u-phase

30

i 20 l-2

10

0 f

71

73 at%

v-

Fig. 86.CharacteristictemperatureT, for the maximum in the x(T) curvesasdependenton composition for a-phase Fe-V alloys quenchedfrom 1200“C [78 C 31.

Table 23. Ferromagnetic and paramagnetic Curie temperatures, Tc and 0, respectively, effective magnetic moment per atom, pefh and the average magnetic moment per atom, &,, as derived from the Curie constant and the spontaneous magnetization, respectively, for o-phase Fe-V and Fe-Cr alloys [68 R 1, 67 M 21. Peff

Fe56.1V 43.9 Fe54.2 V 45.8 Fe55.5 V 44.5 Fe61.0 V 39,0 Fe56.5Cr43.5 Fe55.1Cr44.9 Fe53.4Cr46.6 Fe51.4Cr4,.,

@

J-4,

PB

K

0.205 0.180 0.222 0.320 0.125 0.096 0.070 0.041

95 140 165 230 60 53 33 9

0.866 1.017 1.139 1.227 0.967 0.788 0.729 0.716

Ref.

T,

K

PB

68Rl 67M2 67M2 67M2 68Rl 68Rl 68Rl 68Rl

~160 x210 47 29 15.5 9

Table 24. Ferromagnetic Curie temperature T,, extrapolated spontaneous magnetization crS at 0 K and the Curie constant C, for a-Fe-V alloys. N/N,: percentage of atoms carrying a magnetic moment and p: magnetic moment of the clusters as derived from C, and a, [77 M 11. Fe [at %]

29

30

31

32

T, I31

25.4 4.5 0.093 0.24 18

6.0 0.121 0.33 17

74 8.7 0.153 0.55 15

11.5 0.180 0.81 13

o,(OK) [G cm3g- ‘1 C, [cm3 K g-‘1

N/No WI P bBl

Landolf-Bbmsfein New Series 111/19a

Adachi

33 119 14.6 0.185 1.12 12

34 151 17.7 0.230 1.50 11

330

1.2.3.2 Fe-V

40 Gcm3 ~9

I T=OK

[Ref. p. 480

0.4 Gcm3 9

Fe-V

I

I cl.295"0.705 tr-phase I I

0.2

b

0 49

..3 0 I 52

55

6001% 64

Fe-

Fig. 87. Spontaneous magnetic moment extrapolated to OK for o-phase Fe-V and Fe-0 alloys. I: [6OP 11, 2: [63 N I]. 3: [67 h4 21. 4: [66 R I]. corrcctcd for cc-phase impurity

10" 0

5

10

15

20

K

25

I-

I 1:

2.5 Pa

-

2.0

-

1.5

-

1.0

-

0.5

-

0 10

20

30

LO v-

50

60

70 at% 80

Fig. 89. Average magnetic moment per atom, ji,,, for r-Fe-V alloys. as dcrtvcd from magnetization mcasurcments extrapolated to 0 K. Open ctrcles: [63 N I], solid :ircles: [36F I].

Fig. 88. (a) Magnetic moment G vs. temperature in a magnetic field of 300e for u-phase Fe,,,g5V0.,05. Solid circles: cooled in a field of 30e, open circles: heating after zero-field cooling to 4.2 K, dashed line: ac susceptibility, in relative units, in a ficld of 0.1 Oe. (b) Isothermal remanence err vs. temperature for z-phase Fe,,295V0.705and Fe,,,,,V,,,,, samples cooled in zero field. At each temperature a field of 2000e was subsequcntly applied. The low-field ac susceptibility shows a sharp peak at T, [75C I]. Inset: magnetic isotherm at 5SK for u-phase Fe,,,,,V,,,,s for increasing and decreasing magnetic field strength, respectively. The cx-phase samples were annealed at 1200°C for 4 days. then water quenched.

331

1.2.3.2 Fe-V

Ref. p. 4801 2.5 I-‘s 2.0 I 1.5 Y 4 1.0 0.5

‘$

b

0”

I

0.6 0.5

1: 0.4 0 Fe

10

20

30

40 v-

50

60

70at%80

Fig. 90. (a) Atomic magnetic moment per Fe atom, PFe,at OK for FeV alloys under the assumption that the V atoms do not have a magnetic moment. Open circles: a-phase, magnetization measurement [63 N 11; solid circles: cl’-phase (ordered CsCl-type), magnetization measurement [63 N l] ; triangles: a/-phase, neutron ditfraction [62 C 21. (b) Average magnetic moment per Fe atom jFe at 0 K as derived from magnetization measurements for a-phase and o-phase Fe-V alloys [73 S 21.1: [6OP 11, 2:[63N1],3:[67M2],4:[73S2].

Fig. 92. Average magnetic moments of the Fe and the V atoms, PFeand j!v, respectively, for Fe-V alloys [82 M 31. Full curves: CPA calculations [78 H 31.1: neutron scattering [82 M 3],2: neutron scattering [65 C 1],3: neutron scattering [76 C 11, 4: polarized neutron scattering [8OK 11.

LandobB6mstein New Series III/I%

0.3

AmV. experimental no v. calculated Olb 35

41

38

47 at% 50

44 v-

Fig. 91. Average magnetic moment per Fe atom, &, for o-phase Fe-V, (a) obtained from the saturation magnetization,I:[60P1],2:[63N1],3:[66R1],4:[69M2]and (b) for the sites III, IV and V ofthe five kinds oflattice sites, as derived from an analysis of the Mijssbauer spectra at 77K (closed symbols) and as result of a calculation applying the Pauling valence theory (open symbols) [73 S 21. jFe for site I is nearly zero. Site II is occupied by V atoms only. 2.4 PB -#He-- +I 2.0 IQ2 1.6 2 I PB 0 I

Adachi

-41 -4 0

Fe

5

! Fe-V

-

I I I

I

I

I

IO

15

20

l 4 25 at% 30

v-

I

1.2.3.2 Fe-V

332

[Ref. p. 480

Table 25. Magnetization data of the disordered cl-phase,the ordered cr’-phaseand the o-phase of Fe-V alloys. a,(OK) and cr,(OK) are the spontaneous magnetization at OK obtained by extrapolation ofmeasurementsaccording to H-0 or H+oo, respectively. &,: averagemagnetic moment per atom, pFc: average magnetic moment per Fe atom, both derived from a,(OK) [63 N 11. Composition at% V Fe 2.1 4.4 5.3 10.2 12.9 20.2 25.2 40.0 40.0 40.0 47.0 47.0 47.0 54.9 54.9 61.8 61.8 62.3 66.0 67.8 69.6

Crystal structure

40 K)

a,(0 K)

Gcm”g-’ 215.81 210.51 206.63 191.16 178.66 163.18 143.17 94.56 77.57 29.24 61.44 so.99 14.83‘) 43.03 35.63 23.58 19.98

97.9 95.6 94.7 89.8 87.1 79.8 74.8 60.0 60.0 60.0 53.0 53.0 53.0 45.1 45.1 38.2 38.2 37.7 34.0 32.2 30.4

A, PB

217.50 211.50 207.13 191.86 179.05 163.52 144.35 94.47 77.57 29.96 62.22 50.99 15.59‘) 43.03 35.63 23.58 19.98 18.93 14.39 8.34 ‘) 5.04 ‘)

2.171 2.106 2.061 1.901 1.770 1.606 1.411 0.911 0.748 0.289 0.597 0.489 0.150 ‘) 0.410 0.339 0.223 0.189 0.179 0.136 0.078 ‘) 0.047 ‘)

‘) At T=6K

Table 26. Magnetic moment distribution in Fe-V alloys as derived from neutron diffuse scattering measurements at 6 K [82 M 31, see also [8OK 1, 65C 11. AD: difference between average magnetic moments of Fe and V atoms, pa,,:average magnetic moment per atom [72A2], fiFp, pv: average magnetic moment of Fe and V atoms, respectively. V at%

AF

Pa,

PFC

2.187(5) 2.163(7) 2.14(l) 2.10(2) 2.04(3) 1.89(3) 1.74(3) 1.54(4)

2.217(l) 2.223(8) 2.226(10) 2.232(13) 2.236(23) 2.201(34) 2.177(35) 2.058(35) 1.900(49)

PV

PB

Fe ‘) 1.10 1.95 2.72 3.93 5.84 10.09 14.74 20.56

-3.26(12) -3.21(7) - 3.40(5) - 3.45(4) - 2.76(4) - 2.84(3) -2.16(3) - 1.75(4)

1) [71 c 33.

Adachi

PFC

- 1.04(13) -0.98(8) - 1.17(6) - 1.21(6) - 0.56(7) -0.66(6) -0.10(6) + 0.15(7)

2.217 2.203 2.176 2.116 2.032 2.012 1.888 1.519 1.247 0.481 1.126 0.922 0.284 ‘) 0.909 0.752 0.584 0.495 0.475 0.399 0.243 ‘) 0.155 ‘)

Ref. p. 4801

1.2.3.2 Fe-V

333

MHz - 225 kOe -200 1 -P r -17s;e a

_;A

-150

- 125 125 -100 kOe

I 7

-75 4 G

501 0

I 200

I 400 I-

I 600

- 50 K 800

: 86

Fig. 93. NMR frequencies Y, and internal fields Hhyp for 51V and 55Mn in Fe,,,,V,,,, and Fe,,,,,Mn,,,,, alloys, respectively, as a function of temperature [64K 11. At T=77 K, for 51V v,= 97.7(3)MHz, HhyP= 87,3(3)kOe and for 55Mn v,=238,0(5)MHz, H,,,=225,5(5)kOe.

88

90

kOe

92

Hhyp-

Fig. 94. Spin-echo spectra for ‘lV in Fe-V alloys at 4.2 K. Only the main line is shown, a strong satellite appears at Hhyp= 73 kOe for the larger V concentrations [82 L 11.

Fe0.98V0.02

70

80

90 V-

100

Fig. 95. NMR spectra for 51V in Fe,,,sV,,,,, 77 and at 290 K [83 Y 11.

Land&-Bdmsfein New Series llVl9a

Adachi

MHz 1

observed at

[Ref. p. 480

1.2.3.2 Fe-V

334 Table 27. Hyperline magnetic field HhrF and full line width at half maximum, AH,,,. of the main NMR line for “V in Fe-V alloys at 4.2 K [82 L 11. V at%

AHtw

Hhrp

Table 28. Magnetic hyperline field Hhrpat Fe atoms and the magnetic moment pFefor various sites of the crystal structure for Fe-V and Fe-Cr o-phase alloys, as derived from Mijssbauer spectra at T= 77 K. jFc is the averageFe moment derived from magnetic saturation measurements [73 S 21.

kOe 0.055 0.102 0.22 0.57 1.59 2.89 8.7 ‘) 18.4‘)

X

87.3 87.3 87.4 87.4 87.6 87.9 88.0 85.0

0.25 0.3 0.4 0.8 1.7 2.4 7.0 11.0

h -xVx

Fe, -xVx

‘) [7l D 11.

Site

0.457

I III IV V 0.411 I III IV V 0.382 I III IV V 0.362 I III IV V 0.468 I III IV

Hhs$‘Fe)

PFe

~Fc

kOe

PB

p’n

0 61 16 38 0 86 31 65 0 119 47 86 0 135 65 103 0 39 15

0 0.76 0.19 0.49 0 0.81 0.29 0.61 0 0.86 0.35 0.63 0 0.93 0.45 0.72 0 0.25 0.10

0.33

0.43

0.49

0.58

0.14

Table 29. Paramagnetic susceptibility xr, Knight shift K for “V, NMR line width AH,,, at 7.545MHz (measured between derivative maxima) and lattice parameter o for Fe-V alloys [63 L 21. For < 20 at% Fe, xp is independent of the measuring field up to H,,,, = 11kOe. Fe at %

298 K V 2 7 9.9 15.5 20.2 22.9 27.2 27.7 30.1 30.4 31.0 32.2 34.0

K (“V) %

AHh Oe

17K

298 K

298 K

298 K

10.5(10) 10.7(6) 11.1(6) 11.2(6) 11.3(6) 11.5(6) 12.4(12) 15.1(12)

3.029(1)

5.15 4.55 4.60 6.09 23.00

0.567(6) 0.567(6) 0.584(6) 0.586(6) 0.596(6) 0.593(6) 0.584(10) 0.536(10)

76.00

0.481(16)

18.0(19)

%P 10-6cm3g-1

5.63 5.45 5.30 5.05 4.30 4.20 4.35 5.75 6.00 7.60 8.35 10.20 11.30 18.30

Adachi

3.004(1) 2.970(1)

2.947(1)

I.andolr.Rnrnctcin War Series III ‘19a

Ref. p. 4801

335

1.2.3.2 Fe-V 0.5 II PB

I

I

I

0

-0.5

t -1.0 6

-l.F:

-2s

-2: -3s -70 kOe

I -80 Fig. 96. Magnetic hyperfine field H,, of the main line in 2 *. -_ n the NMR spectra for ‘IV in Fe-V alloys at 4.2K, solid -, circles: [SZL 11, open circles: [71 D 11, and average Z-90. magnetic moment ofa V atom, jiv, squares: [65 C 11,open -100 triangle: [76 C 21, crosses: [77 Y 11, lozenges: [SOK 11, 5 0 solid triangles: [82 M 33.

Fig. 97. Room-temperature magnetic hyperfine field Hhyp as derived from Miissbauer spectra for 57Fe in Fe-V and Fe-Cr alloys [63 J 11.

Landolr-Bbmstein New Seriec IWl9a

Adachi

I

I

-100I 0

I

v-

z

ot% 3

I Hh,&4.ZK1

-H

Fe

IO

15 v-

Fe

V,Cr -

20

25 at%

[Ref. p. 480

1.2.3.2 Fe-V

336 20 mJ mo!K!

6

0

30

60

90

120 K'

150

a

6 12

18 mJ m;! K*

6

15

I 12 z 2

9

6

3 C

0

1 30

60

90

120

6 0

K2 150

I*-

Fig. 9s. Molar specific heat C, shown in graphs where C&T is plotted vs. the square of the temperature T for (aec)Fe, -,V,H,and(d)Fc, -,V,alloys.(e)Analysisofthc low-temperature spccitic heat C, for Fc,,,,V,,,, alloy.

b

30

120

60

150 K2 180

192O-

Top figure: measured (mcas.) and magnetically corrected (mcas.-magn.)values. Bottom ligurc: electronic (I). lattice (2) and magnetic (3) contribution [79 0 I].

Ref. p. 4801

331

1.2.3.2 Fe-V

9

24 40" c[1[ molKi 20

-!!L

mol K* 3 9

oo,,

”

” - Fe-V

69 at%V

6 I 16 =. LY

3 15 12

12

9 Ii I 12 : c3" 9

3; 404 CO1

molK2 28

6 12 9

2L 70 at%V -

I ? 20 s

'72

12

.2L 16

9 6 0

30

60

90

120 T2-

d

150

180

210 K2 280 12 76 ze 80

Fe0.29 V0.71 ’

I

I

8

I

0

8

16

2cI

K2

T2-

Fig. 99. Relation between specific heat C, and temperature for Fe-V alloys at low temperatures [60 C 31. (a) 33,..69at%V, (b) 70...92at%V.

0

150

100

50

200

K

250

15

K

18

60 mJ mol K 40 I 2 20

0 e

Landolt-BOrnstein New Series 111/19a

3

6

9 T-

12

1.2.3.3 Fe-Cr

338

[Ref. p. 480

Cr -

Fe-Cr

1

I

I

60

80 at%

LOO

203

0 20

Fe

LO

Cr-

Cr

Fig. lOO.PhasediagramofFe-Cralloys[58 h l,p.527]. Tc shows the Curie tempcraturc of qucnchcd samples(disorder) [IS M 1, 31A I]. Tempcraturc, in [“Cl, and composition. in [at% Cr] and, in parcnthcscs,in [wt% Cr], arc given for characteristic points of the phasediagram.

Adachi

Ref. p. 4801

1.2.3.3 Fe-Cr

339

7” pncrn Fe- ’ Cr

325 .10-f -cm3 mol

I

I

I

I

I

I

275

I 250 x' 225

200

175 150 0 Cr

5

IO

15 Solute -

20

25 ot% 30

Fig. 101. Magnetic molar susceptibility x,,, at room temperature (and at 66 K for V) as dependent on composition for alloys of Cr with V, Mn, Fe, Co [60 C 11.

270 w -cm3 mol 250

230 220 0

I 210 x'

190 180 170 160

50

100

150

200

250 K 300

Fig. 102.Magnetic molar susceptibility x,,,vs. temperature T for alloys of Cr with V, Fe, Co [SS L 11. Land&Bdmstein New Series 111/19a

100

150 200 T-

250

300 K 350

Fig. 103. Temperature dependence of the resistivity Qand the reciprocal of the magnetic mass susceptibility, xg.re = xp - xg.cr,for Fe-Cr alloys. xB,cr is the Cr susceptibility; ?g,FeIS considered to be the contribution to the susceptibility of the alloys due to Fe [75H2]. See also Fig. 104.

200

150 0

50

Adachi

340

[Ref. p. 480

1.2.3.3 Fe-Cr 7-

2c w

cm? T 16

i j-

I-

I 12 SF” 8

100

50

150

200

250

K :

IFig. 105. Low-field (Hnppl= 1 kOe) paramagnetic mass susceptibility xg vs. temperature for Fe,,,,Cr,,,, and FCo.142Cro.~~~alloys PO B 11.

t < 3, 0

100 150 200 250 300 K : T

3.91 .10-;

Fig. 101. Inverse mass susceptibility contribution I,:,. originating from the Fc atoms in Fe-Cr alloys as a function of temperature T [65 I I].

F 3.89

40 .lO’ -5

3.88 3.87 .~ 4.700

CiX!

4.675

I

I

I

4.650

x”

-

\

Ii I

L.625

/ / 2,22at%Fe I I

5.85 5.80

0

50

100

150 I-

200

250 K : I

Fig 106. Invcrsc mass susceptibility x; ’ vs. tcmpcraturc for o-phase Fe--Cr alloys. corrected for the influence of minor impurities of cr-phase (less than 0.1%) [68 R I].

5.65 230

240

250

260

270 I-

280 290

300 K 310

Fig. 107. Magnetic mass susceptibility xs vs. temperature at the magnetic transitions in dilute Fe-0 alloys [82 B I].

Ada&i

341

1.2.3.3 Fe-Cr

Ref. p. 4801

250

Table 30. Effective magnetic moPeff and paramagnetic Curie temperatures 0 of Fe impurities in Cr. Paramagnetic susceptibility of the alloy x =xcr +Ax, where Ax is attributed to the impurity, Ax = C,/( T- 0) [66S 11.

K

mm

200

Fe at%

Cr

Peff PB

-72 -29 -20 -3 27

Fe -

Fig. 108.ParamagneticCurie point 0 and effectiveBohr magnetonpeff,obtained from the magneticsusceptibility, vs. composition for Fe-Cr alloys. The notations, (l) and (h), indicate data obtained from low- and hightemperature parts of the susceptibility, respectively [65 I 11.Dashed lines: calculated.

Table 31. Effective magnetic moment peff, Curie constants per unit of mass, C,, and paramagnetic Curie temperature 0 for FeCr alloys [8OB 11. Fe at%

0 K

c, Gcm”Kg-’

12 14.2

96 102

0.03565

3.1(2)

0.05349

4.0(2)

Peff PB

Table 32. Ferromagnetic and paramagnetic Curie temperatures, T, and 0, respectively, ofo-phase Fe-Cr and Fe-V alloys. Average magnetic moment per atom, pa,,derived from the spontaneous magnetization and effective magnetic moment per atom, peff, derived from the Curie constant [68 R 1, 67 M 21. Cr

V

at %

Land&Bbmstein New Series HI/I%

0

“C

T,

Pat

0

Peff

K

PB

K

PB

43.5

-

47

0.125

60

0.967

44.9

-

46.6 48.6 -

43.9 45.8

29 15.5

0.096 0.070 0.041 0.205

53 33 9 95

0.788 0.729 0.716 0.866

-

44.5 39.0

0.180 0.222 0.320

140 165 230

1.017 1.139 1.227

9

x160 x210

Adachi

1.2.3.3 Fe-Cr

[Ref. p. 480

Table 33. Magnetic transition temperatures and latent heats for Fe-0 alloys in the low Fe concentration part of the phase diagram [82B I]. For latent heats, see also [79 K 2, 76 S 31. I: incommensurate spin density wave, C: commensurate spin density wave, P: paramagnetic.

0

10

20

30

Fe

40 50 Solute -

60

1OX

Transition

TN K

Latent heat Jmol-’

Cr 1.20 2.22 2.22 3.35

I-P I-P I-P C-I C-P

311 292 254 248 252

1.1 1) 1.3 1.2 0.4 12.6

‘) [75B I].

I

K, 1w I

70 at%80

Fe at%

Fe- Sn

"

o ‘

c 1033 0

2.5

5.0

7.5

Fe

10.0 12.5 15.0 at% Solute -

liC3 .__ K -9::

20.0 Table 34. Ferromagnetic Curie temperature for Fe-Cr

alloys, determined by neutron critical scattering and by low-field magnetization measurements[83 B 21.

l ---

Fe- Si

--s.yy; -

Fe at%

7X

25 24 21.7 20.8 19.9 19.5

0 Fe

5

10

15

20 25 Solute -

30

T, WI critical scattering

magnetization

148 122 84 72 55(5) 45(5)

145(3) 70(3) 55(5) 44(3)

35ot%40

Fig. 109. Ferromagnetic Curie tempcraturc as a function of composition for alloys of Fe with V, Cr and other clemcnts [36 F I].

350,

I

K I Fe,Crl-,

I

I

I

I

I

I

J

P Fi_r. 110. h4a_cnctic phase diagram for Fe-Cr alloys [83 B 21. Fcrroma_rnctic boundary: Solid circles: [83 B 23. open circles: [75 L 21. triangles (upward): [7.5S 21. triangles (downward): [77A 51. Antiferromagnctic boundary: solid circles: [78 B I]. other symbols: data compiled in [78 B I]. Spin-glass alloys: characterized by tcmpcraturc ‘& ofsusceptibility peak [83 B I, 83 B 21. Complex magnctic properties in the hatched region [83 B 21. The broken cun~ rcprcscnts the spin-flip temperature T,,. I(L): transverse (longitudinal) incommensurate spin density wave state. C: commensurate spin density wave state.

0.05 0.10

Adachi

4

0.15" QO.20 0.25 C-

I

I LI

I

I

Ref. p. 4801

1.2.3.3 Fe-Cr

KIFe-Crl I I IPI

I I

343

KIFe-CrI I I I I A I P

300 250

I k

200

! 200

I

I

I

d

x I 02

150 100 50

y\ \

0 0 Cr

0.5

1.0

1.5

2.0 Fe -

2.5 3.0

3.5at%4.0

Fig. 111. Low Fe-concentration part of the magnetic phase diagram ofFe-Cr alloys [82 B 11,seealso [76 M 21. Open circles: [82B 11, solid circles: [67Al], squares: [76 M 21, P : paramagnetic state, I: transverse incommensurate spin density wave state, L: longitudinal spin density wave state, C: commensurate spin density wave

60 p&cm 50 I

40

2 a.

30 20 10 0 0 Cr

5

IO

15

20 Fe -

25

30

35 at% 40

Fig. 112. NCel and Curie temperatures, TN and Tc, respectively, as well as the extrapolated resistivity Q at OK vs. Fe concentration for Fe-Cr alloys f75 L2]. I: [60R1],2:[63N1],3:[6511],4:[66A3j,.5:[67Ii],6: [71Al], 7: [75L2].

0 Cr

Land&Bbmstein New Series 111/19a

0.5

1.0

1.5 Fe -

2.0

2.5 at% 3.0

Fig. 113. NCel temperature TN of Fe-Cr alloys. I: [79K13], 2: [76M2], 3: [67Al], 4: [6511].

Adachi

[Ref. p. 480

1.2.3.3 Fe-G

344

6 kOe

t

10 I

I

I !

I

I

0

C-

Gg. 114. Spin-glass freezing tcmpcraturc Tr vs. compoition for Fe-Cr alloys [83 B 11. The broken lint is the ntifcrromagnctic phase boundary [78 B I]. Open circle: 79sq.

2

6 I-

8

10 K 12

Fig. 115.Temperature-magnetic field phase diagram for Fe o.16(=ro.84.The border line between the paramagnetic state (P) and the spin-glass state (SC) is derived from irrcvcrsiblc relaxations in the magnetization curves [83P I]. Different symbols indicate different extrapolation procedures. Solid line (calculated): H = A( 1- T/T,)B with T,= 12SK, fi=2.3(4).

Fe,Cr,-,

Fig. 116. Schematic tempcraturc - magnetic tieldcomposition phase diagram for Fe-Cr alloys as derived from irrcversiblc relaxations in the magnetization curves [83P 13. P: paramagnctic; F: ferromagnetic, AF: antiferromagnetic, SC: spin glass.

Adachi

Ref. p. 4801

1.2.3.3 Fe-Q

I.!

0.1251

-Gem 9 IS I b 0.t

[ 4s Gem 9 O.025b

3s

t b 2s

0.16 PB

IS

10: Gem: 9

0.12

Cr- 9at%Fe

1

t 0.08 1:

I I

T =I.2 K

1.5

0.04

bI 5s

0 0

IO

20

30

40 kOe 50

HOPPl-

Fig. 118. Average magnetic moment per atom, &,vs. applied field H,,, for (a) Fe,,,&,,, and (,b) Fe 0,142Cr0,s58alloys at various temperatures [SOB 11.

2.5

2: Gem: s

Cr-15at”/ Fe InI

I

r-onir

IF:

I IO b

5

10

15

20

kOe

Fig. 117. Magnetization curves for various Fe-Cr alloys at different temperatures: (a) 4.7 at% Fe, (b) 6 at% Fe, (c) 9 at% Fe, (d) 15 at% Fe. The remanence found for two specimens is attributed to a small Fe contamination [65 I 11.

Landolt-Bdmstein New Series 111/19a

346

1.2.3.3 Fe-Cr

2?

7 Gem 9

101 Gem 9

I

h.35

3

71

[Ref. p. 480

Cr0.65

-!

10; ! -

o-;‘& si------

-

1 ” 1 -

-

_

-

6t3 d--e

;

j

_ _

.

’ !

335.9 '11.7 4 51.4 a 061.3

6t

- j 0 lU.6 4

-a.--&

I

9E

117.2 121.9 128.6 133.4 138.9 wt.5 149.6 155.1 161.1

62

6:!

182.6

I b

197.5 94

212.3226.2

58

90

I

I

I

I

3

6

9

12 kOe

55 I

0

3

--+-I

168.1

I b 6:

151 Gem' g 151

-

. 86 I

3

6

b 205 Gcm3 g

14:

-

‘293.0H

----9

12 kOe

9

12

HI ,n teo.92 Lro.08

1LE 2041Ll 117

145

--

199.9

145

14L

200

lL3

199

lL?

198

1Ll 110 I:

I

197 0 d 3

6

9

12

kOe 15

Fig. 119a...d

3

6 H-

kOe 15

1.2.3.3 Fe-Cr

Ref. p. 4801

347 -

80

4

Fig. 119. Field dependence of the magnetic moment per unit of mass, c, for Fe-Cr alloys at various temperatures

FecCrl_,

y

r60

C76A41:(a)Fe,,,,Cr,.,,,(b)Fe,,,Cr,.,,(c)Fe,,,Cr,.,,(d) Feo.92%.08.

I b” 40

20

,’ I

I

0.OE

0

30---I

0.20

0.25

0.30

0.35

0.40

C-

Fig. 120. Extrapolated zero-field saturation magnetization of Fe-Cr alloys at various temperatures [75 L 23. T=4K: crosses: [63N 11, squares: [6511], triangles: [75L2]; T=77K and 300K: [75L2].

1.1 IT

0.1 3-

I 0.EIe, $

ox

0.1,-

[ ISia

0.tI-

I

0.tj-

F YI x

O!;

0;!-

cII!

0

0.2

0.4

0.6

U.8

l.u

7/r, -

Fig. 121. Temperature dependence of the normalized saturation magnetization M, for Fe-Cr alloys. M,, is the magnetization extrapolated to T= 0. The measurements were carried out between 4.2K and 300K and either with (a) steady magnetic fields up to 40 kOe or (b) pulsed fields up to 150kOe [83 R 11. Landolt-Bdmstein New Series HI/l%

01 0

0 %a OB,,O,

150

300

450

~~

600

o

750 “C 900

Fig. 122. Magnetic moment vs. temperature for Fe-Cr alloys. Solid circles : annealed for 150h at 500 “C, open circles: quenched in water from 1100“C [64 Y 11.

Adachi

[Ref. p. 480

1.2.3.3 Fe-Cr 2.25

3.5 3.0 I b

0.25

0

IO

20

30

LO

50

60 K 70

a 2

I 0

5

10

15

20

25

30 K 35

l-

a

;; f

'

-I

F

b

. I: ...bon.. . : . .. I . .

. : :

b0

. .

.

I 50

l

l

.

: .

1,

25ol%Fe

l

. : 20.8 ol%Fe

l *5

l -

l .

.

'

-*.. 0..

, 00.

100

150

.

-0.l ,** . . . . m.. 200

1

10

min 10'

f-

Fig. 124 (a). Magnetization vs. temperature for Fe,,,,,Cr,,,,,. ZFC: zero-Iicld cooled, FC: field cooled (H npp,= 30 Oe), TRM : thcrmoremanent magnetization. Fig. 124 (b) shows ZFC magnetization at 4.2K as dependent on the time t for an applied field of 350e [83 B 21.

HOPl,= 10 Oe

.

I: lo-'

K 2

lFig. 123a. Low-field magnetic moment of Fe-Cr alloys as a function oftempcraturc [83 B I]. Applied magnetic field is indicated. Open circles: cooled in magnetic ticld, solid circles: zero-field cooled. The data have been scaled by different factors as indicated. Fig. 123b. Magnetization vs. tcmpcraturc for the fcrromqnctic Fe-Cr alloys mcasurcd in an applied magnctic field of IO Oe. The ferromagxtic Curie tcmpcraturcs dcrivcd from small-angle neutron scattering arc indicated by arrows [83 B 21.

Adachi

Ref. p. 4801

1.2.3.3 Fe-Cr

0.1

I

-Gem 9

I

I

I

349

t b

I

a.:

I b 0.;

0

0.4

0.8kOe

O

0.5

kOe 1

0.l

//

///

0

a

100 Oe 1

50

HFig. 125. Hysteresis loops for Fe-Cr alloys at 4.2K [83B2]. (a) 17.5at%Fe, zero-field cooled (ZFC) and field cooled (FC), (h) 17.5at% Fe, ZFC for higher fields, (c) 25 at% Fe, ferromagnetic ZFC alloy.

!j!$ 9

56.5chFe \

Fe- Cr I

b-phase I

141

I

I

H,,,1=8.5 kOe 12

I 54.1,

IO\-I

b 8

0

'

I

h

IO

20

I\ u

30

I ’\I

40

I

50

60

70 K 80

Fig. 126. Magnetic moment g per gram vs. temperature for o-phase Fe-Cr alloys in a magnetic field of 8.5 kOe [66Rl]. Landolt-BOrnstein New Series 111/19a

Ada&i

[Ref. p. 480

1.2.3.3 Fe-Cr

350 12 G:i+ 9 11

I Feo.5L4Cr0.456 U-Phase

I=5K 0.8

1C

I ; 0.6 z Lo $ 0.4

F 0.2

i I E b

0

0.2

0.6

0.4

0.8

1

7/r, -

c

Fig. 129. Reduced magnetic moments from Fig. 128 for o-phase Fe-Cr alloys compared with the Brillouin function B, for .I= l/2 [66 R I].

2

4

6

8

kOe 10

H-

Fig. 127. Magnetization curves at low tempcraturcs for [66 R I].

o-phase Fe,,,,,Cr,,,,,

45

50

55 Fe -

60

at%

65

Fig. 130. Spontaneous magnetic moment for a-phase Fc-Cr and Fe-V alloys extrapolated to 0 K. I: [6OP I]. 2: [63N 1],3:[66Rl].

0

10

20

30

40

K

50

I-

Fig. 128.Spontaneous magnetic moment per unit ofmass. (T,,as a function of temperature for o-phase FeCr alloys [66 R I].

Adachi

1.2.3.3 Fe-Cr

Ref. p. 4801 50

351

2.25 2.256 0 PE PE 8% Fe-Cr 2.00 O<,

I

K Fe-Cr c-phase

I

1.75 1.50

I 19” 1.25

I

19" 1.00

0.75 I

I

I

I

I

I

I

IO

20

30

LO Cr -

50

60

I

I

0.50

01 50

52

56

5L

58

0.25

at% 60

0

Fe -

Fig. 131.Ferromagnetic Curie temperature Tc for o-phase Fe-Cr alloys [66 R 11. Open circles: extrapolation from high-field measurements, solid circles: extrapolation from low-field measurements.

0 Fe

Fig. 133. Average magnetic moment per atom, pat, for Fe-Cr alloys, as derived from low-temperature magnetization measurements [76A4]. Open circles: [76 A4], solid circles: [36 F 11.

0 Mn 25

:‘,

47

2”;

Fig. 132. Average saturation magnetic moment per atom for alloys of 3d elements [Sl b 11. Z: average number of electrons per atom.

Landolt-Bdmstein New Series 111/19a

70 at%80

Adachi

cu 29

[Ref. p. 480

1.2.3.3 Fe-Cr

352

3

Ps

Fe-b

1

2 1

0

1.0

I -=I -1

I p 0.5

-2

-3 -4 0 Fe

-1.51 -1.5 00 Fe

20

60

LO

80 80

Cr -

al% al% Cr

Fig. 134. Average Fe and Cr atomic magnetic moments obtained from neutron scattering experiments and the average atomic moment j,, of Fe-Cr alloys at 4.2K [76 A3]. Solid curves represent calculated values based upon the local environment model [80 S 23.

10

20

30

1.0

0.8

I 0.6 x B 9 0.4

0.2

0 0

4

50

60

70 owo80

Fig. 135. Magnetic moment distribution for Fe-Cr alloys [SOK 11. Solid lines: coherent potential approximation (CAP)calculations [75 F 23.1: [80 K I], 2: [71 L I] and 3: [55 S I] at room tempcraturc; 4: [76A 3) and 5: [66 C I]. jcr and bFE:individual average magnetic moment of Cr and Fe atoms, respectively; pO: diffuse magnetic moment seen in polarized neutron Bragg scattering measurements. For Fe, p0 = -0.21 pH [63 S I].

PB

Cr

40

Cr -

8

12

16 ot% 20

Fe -

Fig. 136. Variation of the maximum ordered magnetic moment pmnrwith composition for Fe-Cr alloys at 4.2 K, calculated from the results of neutron Bragg scattering experiments. The moments corresponding to the maximum amplitude of both the incommensurate (I) and the commcnsuratc (C) spin density waves are shown [78 B I]. Circles: [78 B I], open triangles: [67A I], solid triangles: [6712].

Ada&i

353

1.2.3.3 Fe-Cr

Ref. p. 4801

01 0

0.6

Fe

PB

Itat% 5 1 2 3 FeCr Fig. 138. Maximum magneticmoment pmaxofincommensurate (circles) and commensurate (triangles) spin density waves as derived from neutron diffraction in Cr-Fe single crystals. Square: (Cr-1.7at% Fe): sum of pmaxfor both states. Solid triangle: derived from powder diffraction [6712]. See also Fig. 137.

0 Cr

1

2

3

4 at% 5

Fe -

Fig. 139. Spin density wavevector Q for Fe-Cr alloys al T=OK [6712]. a: lattice constant.

Cr-4.9at”/ bFe

I I 7 250

New Series lll/l9a

3

-ii-!

Fig. 137. Temperature dependence of the maximum spin density wave amplitude pmaXfor (a) the transverse incommensurate state ofCr-0.4 at% Fe derived from singlecrystal neutron diffraction spectra, (b) the incommensurate (I) and the commensurate (C) antiferromagnetic state of Cr-1.7 at% Fe single crystal and for the commensurate antiferromagnetic state of(c) Cr-3.76 at% Fe and (d) Cr4.9 at% Fe [67 121.

Adachi

354

1.2.3.3 Fe-Cr

[Ref. p. 480

,g 0.03

I

0.02 0.01 0

0

50

100

150

200

250

a

300kOe350

Hop:' -

Fig. 140. Average magnetic moment per atom, p,,. vs. applied field H,,,, for various Fc-Cr alloys at 4.2K [8OB I]. (a) 1.0~..5.3at% Fc. (b) 12 and 14.2at% Fc.

Fig. 141. Magnetization curves in pulsed magnetic fields at 4.2K for Fe-Cr alloys with a minimum of o-phase precipitation [83 K 21.

300 kOe 1

1.2.3.3 Fe-Cr

Ref. p. 4801

355

Table 35. Average magnetic moment @rFe of the Fe atoms at 4.2 K in disordered, bee-type Cr-Fe alloys, as derived from magnetization measurements.The estimated error is fO.l pn [8OB 11. Fe [at%]

2.4

5.3

12

14.2

PFeCkll

1.4

1.5

1.8

1.8

Table 36. Magnetic moments pFeand per of, respectively, Fe and Cr atoms in FeCr alloys, obtained from analysis of magnetic diffuse neutron scattering cross sections, and average magnetic moment per atom, j&,, derived from bulk magnetization measurements.All magnetic moments in [us]. Cr at% 1.04 1.46 2 15 30 50 73

PO--PFe

- 5.88(33) -4.30(18) - 3.40 -3.15 -2.60 -2.10 - 1.80

Per

PFe

2.424(3) 2.416(2) 2.24 2.31 2.25 2.05 1.80

-3.46(33) - 1.88(18) -1.16 -0.84 -0.35 - 0.05 -

Pat

Ref.

2.153 2.143 2.174 ‘) 1.837 1.467 0.995 0.475

80Kl 80Kl 76A3 76A3 76A3 76A3 76A3

I) [76A4].

Table 37. Room-temperature value of the g-factor measured at 35.6GHz for Fe-Cr polycrystalline alloys [6OA 11. at% Cr 0.0 2.5 4.8 8.0 12.5 20.0

9 2.09 2.08 2.08 2.08 2.07 2.08

2.0 m5 cm: 9 t 1.5

;- 1.0

Ffd l=CZK

i

0.5

0 Cr

Fe-

Fig. 142.High-field magneticsusceptibility xHFfor Fe-Cr alloys at T=4.2K [8OB2].

Landolt-B6mstein New Series 111/19a

Ada&i

356

1.2.3.3 Fe-Cr

[Ref. p. 480

0,25ot%Cr 0.25ot%Cr

c Cr

10

20

30

at%

LO

Fe-

Fig. 143.High-field magnetic susceptibility xk,r (mcasurcd in pulsed mqnctic fields up to 360 kOe)at 4.2 K for Fc-Cr alloys with a minimum of the a-phase [83 C I], see also [82C3].

10,

I

I

I

I

,

0

60

63

66

a

69

72

kOe 75

HW -

Fe-Cr

-et 1 -90 d 0

Fe

-3.0 5

10

15 Cr -

20

25 at% 30

.) z

Fig. 145. Hyperfinc field H,,, for S3Cr and the Cr magnetic moment pc, in Fe-C; alloys at I .2 K [82 L I]. Solid circles: [82 L I]. open circles: [76A3], crosses: [55S I], triangle: [7l L I], lozcngc: [80 K I].

Fig. 144a. Spin-echo spectra for s3Cr in Fe-Cr alloys at 1.2K. showing the distribution in the magnetic hypcrtinc field H,,, at Cr sites [82C I].

2 5 e is r” Y .E =: 2 A

Fig. l44b. Spin-echo spectra for the main lint of “Fe in Fe-0 alloys at 4.2K. showing the distribution in the maznctic hypcrlinc field H,,, at Fc sites [83 L I].

330

b

Adachi

335

3LO

345 HWP-

350

355 kOe 363

Fe-V

Fe41

. center of gravity A center of gravity -0 peak position

I T=CZK 1

Fe

357

1.2.3.3 Fe-Cr

Ref. p. 4803

I, .

Fe-Cr R”“4

T=5K

GOot%Cr

A peak position

I

/

I LA

I/

I

I

I

0.5

1.0

1.5

I

2.0 at%

2

V,Cr -

Fig. 146.Hyperfine field H,,, for 57Fe in Fe-V and Fe-Cr alloys at 4.2 K [83 L 11.

35c Oe 250 kOe 31

Hhyp( 57Fe)-

3oc I z z- 250 s a 200

150

Fe

20

LO

60 Cr -

80 wt% 100 Cr

Fig. 147. Magnetic hyperfine field HhyPfor 57Fe in Fe-Cr alloys at room temperature. Solid circles: annealed for 150 h at 500 “C, open circles: quenched in water from 1100°C [64Y 11. Solid line: [63 J 11.

0

40

80

120

160 kOe 2[

ihyp(57Fe)Fig. 148. Magnetic hyperfine field distribution curves and histograms derived from 57Fe Mijssbauer spectra of Fe-Cr alloys at 5K. The dashed curves represent calculated hyperfine field distributions based upon the local environment model [SOS 21. Land&BBmstein New Series III/l%3

Adachi

1.2.3.3 Fe-Cr

[Ref. p. 480

Fig. 149. Hypcrfinc field Hhyp for “Fc in Fc-Cr alloys at various temperatures. (a) [63 J I], (b) 1...3: [77 K 11. 4: [63 J I] and 5: [72 H I].

350 meVF t 4

a

0

20

Fe

40

60

80 al%

Cr -

100 Cr

250 t

lo

6

T=bOK 4. RT L.2 K 5a l=L.ZK

100 -

O0 Fe

0

b

0.4

Fe

x-

0.6

0.8

10

20

30

40

50

600% I

Fig. 150. Spin wave stiffkss constants D, and D, for Fe-Cr alloys. Circles: D, and D, derived from loatemperature magnetization curves according to the 1.0 equation D=Do-D,T2 [76A4]. Triangles: D, Cr derived from neutron scattering experiments [65 L I].

Table 38. Results of various least-squares Iits of magnetization data for Fe-Cr alloys to a modified spin-wave equation D = D, -D, T*. Details of the different fits are given in [76 A 43. Average magnetic moment per atom, p,,, is calculated from a,(0 K). K,: first order anisotropy constant. Cr at%

QW Gcm”g-’

Pa, pa

DO meV A2

2.0 4 6 8 10 I2 15 20 25 30 35 40 45 50 55 60 65 70

217.72(l) 212.72(2) 208.33(2) 203.50(2) 198.36(3) 193.24(2) 185.69(2) 173.34(l) 161.38(3) 149.81(3) 138.05(3) 126.52(4) 115.03(3) 103.06(2) 92.56(3) 8 1.52(2) 70.05(l) 57.58(5)

2.174 2.121 2.074 2.023 1.969 1.916 1.837 1.709 1.586 1.467 1.347 1.230 1.114 0.995 0.890 0.781 0.669 0.548

301(3) 297(S) 296(6) 282(6) 266(4) 260(3) 249( 3) 227(2) 189(l) 183(l) 163(l) 147(l) 128(l) 113(l) 97.9(5) 83.1(3) 67.1(2) 45.7(l)

D, 10-4meVA2K-2 5.12(37) 4.59(54) 5.54(64) 5.28(63) 4.45(47) 4.59(30) 3.98(40) 3.88(19) 1.61(16) 2.42( 16) 1.90(16) 1.24(10) 1.03(7) 0.85(3) 0.43(7) -0.12(6) - 1.38(6) -5.46(1 I)

K,(OW 105ergcmm3 4.40( 14) 4.88(7) 4.27(5) 4.08( 10) 4.14(4) 3.32(9) 3.55( 11) 3.75(17) 3.25(45) 1.54(54) 1.80(52) 2.04(77) 1.60(69) 2.40(35) 1.30(21) 1.12(18)

359

1.2.3.3 Fe-Cr

Ref. p. 4801 100 100 WA2 80 70

2.5

I 50 60 Q LO

0 I 8 -2.5

30 20

-5s l-

IO

n 55

60

65

70

at%

-7.E,-

80

Cr -

Fig. 151. Composition dependence of the spin wave stiffness constant D for Fe-Cr alloys measured within the ferromagnetic phase [8 1 S 11. Circles: from neutron scattering measurements at about 50 K [Sl S I], triangles: from low-temperature magnetization measurements [76A4].

-1OS 15.c a’ K-1 12.:

10sl-

7.Fj-

50

I ~ 5sl-

I 25 2

2!j-

Fe

Cr II-

Fig. 152. Linear longitudinal saturation magnetostriction constant 1, for Fe-Cr alloys at room temperature for the easy direction of magnetization. Derived from measurements on polycrystalline samples [47 W 11.

-2.!s-5.1I-

O

I

50

100

150

200

250 K 300

Fig. 153.Linear thermal expansion coefficient c(measured for Fe,,,,Cr,,,, and Fe,,,Cr,,, as a function of temperature. The lattice contribution c(,is calculated from lattice properties, tl, = tleXP- c+ is considered to be due to the magnetic contribution. e~,,r:experimental value [83 R 11.

Landolt-BOrnstein New Series 111/19a

Ada&i

360

[Ref. p. 480

1.2.3.3 Fe-Q

0

8

I

16

I 12 ;P

8c 0

L

8

12

16

I K' 21

Fig. 154a..x. Specific heat C, for bee Fe-0 alloys at low temperatures [6OC 3-J. Squares: specific heat measurements in a magnetic field of 1 kOe.

Adachi

12

16

K2

Ref. p. 4801

1.2.3.3 Fe-Cr

130 .lom3 Fe0.559 Cr0.441 I I J Kmol 110

I 100 90 2 80 70 60

,

.I

/

/

50b 1.0

3

1.5

2.0

6

2.5

3.0 T-

9

3.5

12

4.0

4.5 K 5.0

15

K*

18

T*-

Fig. 155. Molar specific heat C, of Fe,.,,,Cr,,,,,. (a) In the a-phase. Electronic specific heat constant: y=5.02 . 10m3J Km2 mol-’ and Debye temperature: 0, =400 K. [58 H2]. The full line represents results for pure Fe [39K 11. (b) AtIer transformation of the sample to the o-phase by annealing at 700 “C [58 H 23. Solid and open circles refer to He and H, as exchange gases in the experiments, respectively. (c) Replot of the points of(b) from which an estimate of the electronic specific heat can be made: y=26.8~10-2JK-2mol-1[58H2].

Landolt-Biirnstein New Series IIl/l9a

Ada&i

362

[Ref. p. 480

1.2.3.4 Fe-Mn

1.2.3.4 Fe-Mn References: 32S1, 37M1, 5lb1, 57M1, 58A1, 58h1, 59a1, 62A1, 62S1, 62V1, 63J1, 64G1, 6451, ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 81 V 1, 82 M 2, 83 M 1, 83Y 1. FP

Mn

Mn-

1033

,

:I

1102

Y

-he

0

/

1 I

1

I

I

I

I

1100°C’

Brn

727’C

535 -cc:, 400 , I 300 1 0 10 Fe

%”

1 ‘I \ 20

30

I I

I 40

50

60

70

80

at%

Mn -

Fig. 156. Phase diagram of FeeMn alloys [SS h I]. In the low-tempcraturc phase boundary bctwccn a and y, the c-phase appears with fee structure [58 h 1, p. 6651.

100 Mn

550 K

500 I h

L50 400

Fig. 157. Part of the phase diagram for FeMn alloys. Beginning of e-y transformation on heating: solid circles [66U I]. dashed line [SS h I]. End of s-y transformation on heating: triangles [66 U I], thin solid line [58 h I]. Beginning of Y+E transformation on cooling: crosses [66 U I]. dashed-dotted line [SS h I]. Open circles: TN [66 u I].

Adachi

350

0 Fe

10

20

30 Mn -

40

50 at% 60

363

1.2.3.4 Fe-Mn

Ref. p. 4801

a.5 0

0 0

150

300

450

7 0

100

600

750

900

1050 K 1200

Fig. 159a, b. Magnetic mass susceptibility xp vs. temperature for Fe-Mn alloys [66U 11. Data of the samples: Sample No.

at% Mn

Phase at 25 “C

TN of y-phase [K]

1 2 3 4 5 6 7

20.1 21.8 25.9 28.1 32.7 39.5 49.2

YTE Y>E YaE Y Y Y Y

360 390 401 420 450 465 502

200

300

Fig. 158. Magnetic mass susceptibility xp vs. temperature for y-Fe-Mn alloys [71 E 11, see also [66U 11. (a) %.s~Mno,49, Fed%.~ and ~e,Mnl-,h.d-%o~~ 0 5 x 5 0.4. Cu has been added to stabilize the y structure. (b) (Fe,Mn,-,),,96C0,0,. 0.75x50.93. C has been added to stabilize the y structure.

0 b

Land&BOrnstein New Series 111/19a

Adachi

400

500

600 K 700

7-

a

50

100

150

200

T-

250

300

350 K 400

1.2.3.4 Fe-Mn

364

[Ref. p. 480

12.5 .m6 cm3 s. 1 a-Mn 23 Mb.qs /3-Mn-5ot%Si Cro.oj 4 a-Mn0.qFeo.ojCro.c , 5 cx-Mn,,gjFeg.cS -

I

10.5

01 0

10

20

30 Mn -

FE

40

0 x 10.0

5Oot% 600

Fig. 160. Masnctic mass susceptibility xs at 800K [66 U I] and electronic specific heat coefficient 7 [64G l] vs.composition ofFeMn alloys. For data ofthc samples. see caption to Fig. 159.

9.5 . . 9.0

8.5 8.01 0

‘h

50

100

150

200

250 K 300

300

K LOO

a Lb!:,

20 .m6 cm3 9 15

8 3.6!0 I 3.6:s 3.610 3.635 -53

I -10 H 0

50

100

150 I-

200

250

300 "C 350 5

Fig. 161.Top:Magneticmasssusccptibility~,vs.tcmpcraturc for y-phase Fc,,,,,Mn,,,,. Bottom: lattice constant o vs. temperature for y-phase Fe,,,,,Mn,,,,, [66U I].

0

b

1

100

200

Fig. 162a. Magnetic mass susceptibility zg vs. temperature for (1) a-Mn. (2) Mn,,,, Cr,,,,, u+o-phase. (3) B-Mn (with 5at% Si), (4) a-Mn,,,Fe,,,sCr,,,, and (5) ~-Mno.9sFco,os [62 S 11. Fig. 162b. Magnetic mass susceptibility za vs. temperature for hcp and fee alloys Fe,,,,,Mn,,,,, and Fe,,,,,Mn,,,,, [710

70

480

490 I

L.

I*

500

510

I

I

520 K 5:

I].

Fig. 163. Temperature variations of some physical properties ofy-Fc,,,Mn,,, [75 c I, p. 4003. x9: static susceptibility, l(S,>1*: square of sublattice magnetization. TEP: thermoelectric power, e: electrical reststtvity, C,: specific heat.

365

1.2.3.4 Fe-Mn

Ref. p. 4801

600 K 1 K 500

Fe-Mn 500 400

I

~I 300

i

h"

720

200

680

100 0

640 Ps 2.0 600 Cr

1.6

560

I 1.2 1:

520 liEP& 0 IO Fe

20 30 at% 1 V, Cr,Mn -

0.8 ",

Fig. 164. Curie temperature Tc of Fe-V, FeeCr and Fe-Mn alloys (bee phase) [Sl b 1, p. 7221.

00

o-O 0 Mn

Fe -

Fe

Fig. 165. NCel temperature TN and average magnetic moment per atom, &,, vs. composition of FeeMn alloys. ‘I;, represents the fee-fct transition temperature [68 S 11.

15c K 125

Table 39. Ntel temperature TN of a-Mn alloys containing 1 at% 3d elements, as derived from the minima in the resistivity vs. temperature curves [74M 11. ATN: shift of TN due to alloying, relative to TN of a-Mn.

IOC t 65 75 5c

25 0 I I

25

a

0 Impurity

2.5at% 5.0

500 K 400 -

I 600 h' 200

0 IO

Landolt-Bbmstein New Series 111/19a

I

at% at% at% at%

Cr Fe Co Ni

95 84(l) 110(l) 118(l) 104(l)

Fig. 166a. Ntel temperature TN of a-Mn alloys as a function of impurity concentration [74K 11. Fe,: annealed at 620 “C, Fe,: heated to 900 “C and then annealed at 620°C. I: [73 W 1],2: [71 W 11.

100

b

a-Mn a-Mn-1 a-Mn-1 cl-Mn-1 a-Mn-1

20

30 Mn -

4Oat%50

Fig. 166b. NCel temperature TN of hcp and fee Fe-Mn alloys as derived from Mijssbauer experiments [710 11.

Adachi

-L(l) 15(l) 23(l) 9(l)

[Ref. p. 480

1.2.3.4 Fe-Mn

366

Fe

I

li.Kn -

Fig. 167. Saturation magnetization M, for Fc- Ti and Fe-Mn alloys at OK. Broken lint shows M, for simple dilution [59a I. p. 851.

I

I\\

I

I

I g

0.6

5 2

0.4

Fig 168.Relative average magnetic moment per atom as a function of temperature for (a) y-Fe,,,,Mn,,, and (b) y-Fe,,,Mn,,, alloys. The Brillouin curves for spin l/2 and I arc given by the solid lines. B,,, and B,, respectively. The magnetic moments have been derived from neutron diffraction spectra [7l E I].

I Y 0 OF 7 I$ 12 OL

Table ment y-Mn, Sat% tron [71 E

0.2 Ob 0

0.2

0.4

/ 4=115K 1 jo,(OK)=0.60(5)p, I I 1.0 0.8 0.6

X

1.2

T/I,, Fig. 169. Tempcraturc variation of the avcragc magnetic moment per atom. fi,,. as dcrivcd from neutron diffraction experiments for two y-FeMn alloys stabilized with 4at% C. The open circles and the dots refer to calculations based on peak and intcgratcd intcnsitics of the (I IO) reflection. respcctivcly [7l E I].

Adachi

0.0 0.03 0.1 0.2 0.3 0.4

40. Average magnetic mofor atom, L,, per stabilized - rFer with Cu, as derived from neuexperiments diffraction 11.

Pa,Chl 293 K

OK

1.78(20) 1.85(20) 1.81(20) 1.54(50) 1.10(50) 1.23(20)

2.1 2.15 2.05 1.78 1.48 1.60 Landoh-Bornswin NW Scrier 111’19a

1.2.3.4 Fe-Mn

Ref. p. 4801 3

367

I

PB Fe-Mn

he+PO

(

2

I 9

1

0 1 -1

J’

-2 Foe

a

X

2

4

Mn 6 -

8

s y-Fe-Mn type direction of spins II
IO at% 12

Fig. 170. Magnetic moment distribution at room temperature for Fe-Mn alloys [SOK 11. pMnand pre: individual average magnetic moments of Mn and Fe atoms, respectively. p,,: diffuse magnetic moment seen in polarkd neutron Bragg scattering measurements; for Fe: p,,= -0.21 pa [63 S 11. Solid lines: coherent potential approximation calculations [72 H 21. Crosses : [SOK 11; solid circles: [75 N2]; open circles: [78 RI]; solid triangles : [76 C 21; square : [66 C I] ; open triangles : [76 M 11.

C

1’ ?I 0 4 0

,,

-----.-a/ 1’

‘y? a

’

y- Mn- type c/a<1

b

Fig. 171. Spin structure of Fe-Mn alloys. (a) y-Fe-Mn type [66U 11, (b) y-Mn type [57 M 11.

Table 41. Individual magnetic moments PFeand &, as derived from diffuse scattering cross sections of polarized neutrons, and average magnetic moment per atom, pa,, for a-Fe-Mn alloys at room temperature. Mn at %

PFe-&n

Pat

PFe

PMn

Ref.

PB

Land&BBmstein New Series lll/l9a

0.79 1.85 3.15

1.39(11)

5.89 8.83

1.25(12) 1.38(16)

2.160

2.395(2)

2.138 2.12(l) 2.05( 1) 2.00( 1)

2.397(2) 2.16(l) 2.124(12) 2.12(15)

Ada&i

-0.82(23) - 0.23(9) 0.77(12) 0.87(13) 0.74(16)

80Kl 80Kl 78Rl 78Rl 78Rl

[Ref. p. 480

1.2.3.4 Fe-Mn

368

Fe-Mn

7=17K

--em-

5ot%Mn 3

-+-

1.5

0.70

210

220

230 -0 -

210

0 . 55Mn in Ni,,,gMn,,O, A A 55Mn in Feo.sssMno.015 o v "V in Feo,sBV0.02

0.65 _

250 MHz 260

0.600 0

Fig. 172.Nuclear magnetic rcsonancc spectra for “Mn in Fe-hln alloys at 17 K [83 Y I].

200

100

300

K

LOO

I-

Fig. 173. Temperature dependence of the main (open symbols) and satellite (solid symbols) reduced NMR frcquencics for “Mn and “V in Fc,,,,,Mn,,,,,. alloys. Also given is the Fe0.98V 0.02 and %.9&fno.ol reduced magnetization a/cr(OK) of pure Fe and Ni C83Yl-J.

or-Mn-Fe

l= 1.2 K

IX- Mn-Fe

I= L.2K

30 19:

a

I 200

I 210

220

Y-

230

240 MHz

I 140

b

Adachi

150

160

170

Y-

180

190

200 MHz210

1.2.3.4 Fe-Mn

Ref. p. 4801

:-">n

siteIII

7= UK

T = 42 K site IY

r\

1 at% Fe

I

20

30

40

50

60

70 MHz

IO

5

15

Y-

180

I

I

25

30 MHz

/

I

t I

20 Y-----c

r sitelI

50

site Ill I + = s

40

P

P

* 30 fl 20 a e Mn

5

III

15 Fe,Ru -

Fig. 174. (a.. .d) Line shapes of NMR spin-echo spectra of 55Mn in a-Mn-Fe alloys at 4.2K on the four different crystallographic sites (I...IV) of Mn [74K 11. For their definition, see Fig. 46. See also Table Il. (e) Magnetic hyperfine field Hhyp of 55Mn at 4.2K for the crystallographic sites I, II and III derived from sublattice NMR spectra for a-Mn-Fe and wMn-Ru alloys [74 K 11.

Landolt-BBmstein New Series 111/19a

Adachi

cc-Mn-Ru 0 a-Mn-Fe I I 20 25 at% 30

l

[Ref. p. 480

1.2.3.4 Fe-Mn

p-Mn-Fe I I

I

Fe -

&r

Fig. 175. Average hypcrfinc field f7,,, at site I for “Fc in P-hln-Fe alloys [77 N I]. T=4.2 K: Fig. 176. Magnetic hypcrfinc field Hhgp derived from “Mn Miissbaucr expcrimcnts, as dependent on impurity concentration for b-Mn alloys with Fe, Co and Ni impurities. The quantity An, is the impurity concentration, multiplied by the difference in the number of 3d electrons between the impurity atom and Mn [74K2]. T= 1.4K.

240 MHz

53 r

kCle

220

ul -

200

I a 30 f

-

2 20 10

0

50

100

150

200

250

300

1\ 350 K 400

I-

180 1 c 5 160 s lb0 120 100

Fig. 177.Temperature depcndcncc ofthc magnetic hypcrtine fields Hhjp as derived from Miissbaucr resonance experiments on “Fe in hcp and fee Fe-Mn alloys [7lO I,

80 0

68121.

100

200

300

LOO 500 I-

600

Fig. 178.Temperature dependence ofthe NMR v, in zero applied magnetic field for Fe o.996Mno.oo4. vJ4.2 K)= 239.42 MHz Hhyp=225.5(5)kOe at “Mn in Fe,.,,,Mn,,,,,

Adachi

700 K I390

frequency “Mn in [74 K 33. [64K I].

371

1.2.3.4 Fe-Mn

Ref. p. 4801

0

y

Fe-Mn

zI -0.1 c; 2

-0.2 ,’

/

/' /. 0 ,/

-0.3 0.2 I -mm s

-----_

0

2% 0.1 c, Q E3

0 0 Fe

20 at% 30

10 Mn -

Fig. 180.Electric quadrupole shift dQ and isomershift IS, relative to bee Fe, for “Fe in hcp and feeFe-Mn alloys [710 11.Seealso Table 42. 3 at% 2

1 0 -Impurity-

1

2

3

4 at% 5

Fig. 179.Shift Av ofthe NMRfrequency for 55Mn at site I asdependenton impurity concentration of a-Mn alloys at 4.2K [74K 11.

Table 42. Magnetic properties of hcp and fee Fe-Mn alloys [710 11. Isomer shift IS, relative to bee Fe, quadrupole shift dQ and hyperfine magnetic field H,,,,r for 57Fe, extrapolated to OK. p: average sublattice magnetic moment per atom, TN: NCel temperatur, x,. . magnetic molar susceptibility at RT. Mn at%

Lattice structure

TN K

17.8 25.9 28.6 25.9 28.6

hcp hcp hcp fee fee

230 230 230 400 420

P PB

0.25 2.0 ‘)

Xm 1Om6cm3mol-l

KJ5’W kOe

dQ

556 528 734 930

1613) 16(3) 16(3) 38(3) 41(3)‘1

0.12 0.13 0.15 0.0

‘) [6711].

Landolt-BOrnstein New Series 111/19a

Adachi

mms-’

IS mms-’ - 0.05 -0.05 -0.01 -0.03

[Ref. p. 480

1.2.3.4 Fe-Mn

372

Table 43. Average magnetic hyperfine fields I?,,, derived from Miissbauer spectra for “Fe and “‘Sn in P-Fe-Mn-Sn alloys at 4.2 K [77 N 11. R,,,(57Fe)

X

A,,,(’ ’ gSn)

kOe Fe,Mn,-,

0.02 0.05 0.10 0.15 0.20

<3 10.8(10) 10.6(10) 10.5(10) 10.3(10)

Fe 0.005Mn0.g95-xSnr

0.005 0.02 0.035 0.05

<2 1W) 13(l) 15(l)

15(7) 41(2) 46(2) 48(2)

1l(l)

36(2) 36(2) W2)

0.005 0.01 0.02 0.035 0.05

12(l) 13(l) 15(l) 17(l)

4W ‘W) 50(2)

100 .103

70 .lil 6 cai K'mz!

z I 60 c, 40

0 0 Fe

2

4

6 Mn -

8 at%

Fig. 181. Magnetization energy E at room temperature measured for polycrystalline samples of Fe-Mn alloys. E is a measure for the magnetocrystallinc energy [49 W I].

Fig. 182. Coefficient of electronic spccitic heat, y, plotted against average number n of 4s and 3d electrons per atom for Fe based alloys. FeO,ss(Mn,Ni,-X)o,Xs: [72K I]. (Fe,Ni,-,),,,,Mn,,z,: [65 W I]. Fe-Mn and Fe Ni: [64G I].

Fig. 183. (a, b, c) Specific heat per gram, C,, vs. temperaturc for y-Fe-Mn alloys. Open circles: experimental results; solid curves: calculated using various Debye temperatures 0, [67 H I]. (d) Magnetic specific heat per gram, Lag. vs. temperature for y-Fe-Mn alloys. The N&cl temperatures are indicated by arrows [67 H I]. 0, is the Debye temperature, y is the electronic specific heat cochicicnt and c( is a parameter for the solid curves in (a,b,c) according to the equation C,=yT+Cr(l +rT).

Adachi

Ref. p. 4801

373

1.2.3.4 Fe-Mn

J ,

0.05

0 -a 0.20 -CO1 YKg

I

I

I

'

I Oo=425K L7

/.?c, K T4.A I\

3

450 K

b1.6 Mno.4

0.15

I *o.lo 0.05 0

0.201

I

I

I

300

400

I

I

500

600

Cal - Kg

Y-Fe;o.,Mn,,~

0.05 - Y-

hl.5 Mno.5

Od 100

200

7w

Fig. 183.

Landolt-Bornstein New Series 111/19a

Adachi

700 K 800

1.2.3.5 Co-Ti

314

[Ref. p. 480

1.2.3.5 Co-Ti ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 70N 1.70s 1, 73A2, 79B 1, 80G 1, 81 S2.

wn I ! ’ : ’

! ’

co

Ti -

li

Fig. 184. Phase diagram of Cog-Ti alloys [68 I I].

1.6 I 2.0 1.2 -!g

1.0

I

Ia

0.4

0.8

0.2

0.4

0 4.0 oi

0 80 70 60

I

2.5 * 2.0

50 I 40 -L 4

1.5

30

1.0

20

0.5

10

00

100 200 300 400 500 600 700 K 80: I--,

Fig. 185. Paramagnetic mass susceptibility xp and the Knight shift K of 5gCo as a function oftemperature T for CsCI-type Co,,,Ti,,, [8l S 21, see also [67 W 1, 68 W I]. See Fig. 196 for K vs. za.

Ada&i

375

1.2.3.5 Co-Ti

Ref. p. 4801

I

Co- Ti I

Fig. 186.Paramagnetic mass susceptibility xp vs. temperature for CsCl-type Co-Ti alloys in a magnetic field of 6.65 kOe [69A 11.

50

0

100

150 7-

16 10” s

I

‘yz 9 I

x;’

coO.666Ti0.334 I I

01 0

I

I

100

200

300

400

500

600

700

I

800 K 900’

7-

Fig. 187. Magnetic mass susceptibility xg vs. temperature T for cubic Laves phase, MgCu,-type, Co0.666Ti0.334. Ntel temperature TN=45 K. An analysis of the hightemperature behavior according to xs = x0 + C$( T- 0) parameters: x”=6.99.W6cm3/g, the gives C~=0.302~10-3cm3K/g,0=25K,p,,,=0.45~B[68N1].

8

8 Gcm3

rn--. ~“U./‘I

LYk#--L I 4

404

Tim-.. “U.LY,/

II

1 I

I

I

I

I

I

X,’

1 I

I

I

I

b

2

7-

Fig. 188. Inverse of the magnetic mass susceptibility, xi’, and the magnetic moment per gram, a, measured in a magnetic field H,,,, =9.60 kOe for MgNi,-type co 0,71Ti0,29[66A1]. 7’,,=44K.

Landolt-BBmstein New Series 111/19a

Ada&i

lcm3

200

250 K 300

[Ref. p. 480

1.2.3.5 Co-Ti

376

l"o.0

12.5 .lOL 9 Fi?

1.5

1.5

12.5 Gcm3

I 7, 5.0 =

I 6 5.0

2.5

2.5

0

r 10.0 Xl' I 9 cm3 Tg 5.0 2.5 0 0

50

100

150

200

250 K 300

Fig. 189. Inverse of the magnetic mass susceptibility, ,Y; I, and the spontaneous magnetic moment per gram, or, for Cu,Au-type Co-Ti alloys. (a) 21.4at% Ti, @) 23.0 and 23.9at% Ti [69A2].

Table 44. Magnetic data of the hexagonal Laves phasecompounds Co-Ti. x0 is a temperatureindependent paramagnetic susceptibility [70N 11. Ti

Structure

at% 28.0 29.0 30.0 30.I 31.3 32.8

MgNi, + Cu,Au MgNi, MgNi, MgNi, MgNi, MgNi, + MgCu,

d4K)

T,

xo

Gcm3g-’

K

10-6cm3g-1

4.90 8.50 6.20 5.60 2.77 2.80

42 44 38 33 18 17

12.71 13.83 13.09 9.35 -

Adachi

c,

10-4cm3Kg-’

16.24 9.77 9.77 8.76 -

1.2.3.5 Co-Ti

Ref. p. 4801

311

9.0rGem: 9

7.5

6.0

I b 4.5 3

0

6

a

9

12

kOe

Noppl-

0.20 I

035

b

20

40

60

80

K

100

T-

0.10

Fig. 192.Magnetic moment per gram in an applied field of 9.6 kOe as a function of temperature for hexagonal Laves phase Co-Ti alloys [70 N 11. I “0

I 3

6

b

9 HWPl

12 kOe 15

-

Fig. 190a. Magnetic moment vs. applied magnetic field for CsCl-type Co-Ti alloys at 4.2K [69A 11. Fig. 190b. Magnetization curves at low temperatures for Co,.,Ti,,, [73 A2].

9.0 Gem: 9

Co- Ti lovesphase

I

I

I-

r

6

8

I 29 ot%Ti

1.5

6.0 I b 4.5

Hoppl= 9.6 kOe

3.0

1.5

b

0.8

@’ 0

2

I 4

HOPPl

I

0

I

I

I

I

20

LO

60

80

I

K

100

T-

Fig. 191.Magnetic moment per gram in an applied field of 9.6 kOe as a function of temperature for cubic Laves phase, MgCu,-type, CoTi alloys [68 N 11. Landolt-BOrnstein New Series III/l9a

c 0 33.4

I

IO kOe

-

Fig. 193. Magnetic moment u as dependent on magnetic field strength H,,,, for hexagonal Laves phase CoTi alloys at 4.2 K [70 N 11.

378

1.2.3.5 Co-Ti

[Ref. p. 480

2s G:ir’ 9

100

I 1.5

80

b 1.0

60

K

I 2 40

0.5

20 0

60

120 kOe 150

Fig. 194.High-field magnetization Gvs. applied field H,,,, for Co,,Ti, 5 [79 B I]. Inset: reciprocal value ofthc highIicld magnetic susceptibility, I,;~.

28

0.3

30

31

32 at% 33

Ti Fig. 195. Spontaneous magnetization or at 4.2K and Curie temperature Tc for hexagonal Laves face Co-Ti alloys [70 N I J.

I

U

29

0.6

0.9

I

I

1.2 cm3/g1.5

Fig. 196. Knight shift K of 59Co vs. magnetic susceptibility xp, with the tempcraturc as an implicit parameter, for CsCI-type Co,,,Ti,,,. Magnetic hyperfine field per Co moment: H,,.,/pco = + 140 kOe/l,, when it is assumed that Ti does not contribute appreciably to xg [81 S 23. Set Fig. 185 for K vs. T and xn vs. ‘I:

Adachi

Ref. p. 4801

1.2.3.5 Co-Ti

379

Table 45. NMR and magnetic susceptibility properties for Co-Ti alloys [68 W 1, 67 W 11. v,, Av: frequency and width of NMR line, respectively, K: Knight shift of “Co, relative to K,Co(CN),. T K

Av

V,

K %

Zcm3mol-’

kHz

Co,1Ti4, Co50Ti50 Co4gTi5l Co46Ti54

295 77 295 77 295 77 295 77

5462 5510 5459.5 5505 5458.5 5502 5458.5 5502

11 50 7 22 6 6 6 8

2.30 3.26 2.26 3.12 2.24 3.05 2.24 3.05

10 13 10 12.5 10 13

Table 46. Low-temperature specific heats for Co-3d transition metal alloys, fitted to the equation C,=yT+jT3+xT-’ in the temperature range 1...4K. crmis the lowtemperature molar magnetic moment obtained by extrapolating 0, vs. l/H plots in the magnetic field range lO.e.30kOe to H+co, [80 G 11.

Col-xMnx

Co, -J!rX

co1 -xv,

Co, -,Ti,

co

Land&BOrnstein New Series 111/19a

X

Y pJ/mol K2

P f.tJ/molK4

x u.Lrnmol-‘K

g’m Gcm3mol-’

0.01

4527(2) 4725(2) 5192(2) 6311(3) 7258(3) 4404(2) 4556(2) 4815(3) 5289(2) 5917(3) 6447(3) 6990(2) 4437(2) 4735(2) 5250(3) 6138(3) 5101(2) 5832(4) 6540(5) 4361(2)

20.1(2) 20.0(2) 18.9(2) 16.7(3) 15.4(2) 19.9(2) 19.5(2) 18.7(2) 18.5(2) 18.8(2) 18.6(2) 18.5(2) 19.0(2) 19.8(2) 20.6(3) 10.2(3) 21.8(2) 22.7(3) 23.8(5) 20.2(2)

4622(6) 4506(7) 4217(7) 3758(10) 3403(8) 4568(6) 4185(8) 3761(11) 3265(8) 2841(8) 2366(8) 1945(7) 4474(10) 4271(7) 3915(9) 3459(9) 4313(8) 3895(12) 3498(14) 4833(7)

9250 9090

0.02 0.03 0.05 0.07 0.01 0.02 0.04 0.06 0.08 0.10 0.12 0.01 0.02 0.04 0.06 0.02 0.04 0.06

Ada&i

8770 8320 7780 9140 8770 8040 7460 6880 6180 5570 9120 8840 8460 7660 9110 8770 8260 9470

[Ref. p. 480

1.2.3.6 Co-V

380

1.2.3.6 Co-V

CO

V

v-

10

20

30

LO

5,

""

I"

vu

WI IO

"C 1LOO 1300 1200

600 500 LOO 300 200 100 0

0 co

I 1,5 10

L5.6 IL201

2L.l 31.0 12151 I28.01

pm

20

30

I

LO

50 v-

93.0 19201

66.3 163.01

60

70

80

at%

Fig. 197. Phase diagram of Co-V alloys [SS h 1, p. 5171. Temperature, in [“Cl, and composition, in [at%V] and, in parentheses. in [wt% V], arc given for characteristic points of the phase diagram.

Adachi

1 V

Ref. p. 4801

1.2.3.6 Co-V

*g$ co-v I 9

381

H,,,l=122 kOe I

0

12

16 v-

20 at% 24

Fig. 199. Ferromagnetic Curie temperature Tc for (triangles) the low-temperature phase and (circles) the hightemperature phase of Co-V alloys [78Al], see also [76A2]. Dashed line: [37K 11, solide line: [55K 11.

0 0

50

100

150 T-

200

250 K 300

Fig. 198. Magnetic mass susceptibility xp vs. temperature for Co-V alloys and H,,,,=7.22 kOe [74A 11.

600

100 & 9 80

I 60 b 0.6 40 t 02 20 0

0.3

01 14

16

. I 18 v-

20 at% 22

Fig. 200. Ferromagnetic Curie temperature T, and average magnetic moment per atom, pa,, for Co-V alloys at 4.2 K [SOA 11. au-phase: high-temperature phase, quenched from 1200 “C, a,-phase: intermediate phase, obtained by heat treatment between 700 and 860 “C.

Landolt-Bdmstein New Series 111/19a

2

4

6 HWPl

8

IO kOe 12

-

Fig. 201. Magnetic moment r~vs. applied magnetic field strength I&,, at 4.2 K for ice-water-quenched specimen of Co-V alloys. (a): [76 A2]. The samples with 4.51,7.88 and 9.89at% V are a mixture offcc and hcp structures, the other samples retain the high-temperature phase fee structure. (b) ice-water-quenched as in (a) and afterwards annealed at 600 “C for 168 h in vacuum, generating the fee Cu,Au-type structure [78 A 11.

Adachi

382

1.2.3.6 Co-V

1.6 I I-laco-v

I 1.2 ,c 0.8

[Ref. p. 480

Fig. 202. Average magnetic moment per atom. j,,. for Co-V alloys at 4.2K. Open circles: low-temperature phase q, solid circles: high-temperature phase aH [78 A I], see also [76H 21.

* f l=UK o * i

: 0.1

I .

0 8

12

20at% 2L

16

v-

Table 47. Change of the average magnetic moment per atom, &,, in dilute Co-3d transition metal alloys. x: impurity concentration, pi: magnetic moment of impurity atom. Impurity

dL,ldx p,/at% -4.5 - 5.2(9) -6.4 -6.8(18) -6.8(13)

Mn

Cr v

X

Pi

at%

PB

<0.16 0.05 < 0.0585 0.05 0.05

Ref. 57Cl 7OC2 57Cl 7OC2 57Cl 7OC2

-0.97(70) 0.45(70)

Table 48. Magnetic moment distribution for Co-V alloys [82 C 23. &,: average magnetic moment per atom derived from magnetization measurements at T= 4.2 K and Harp,= 32 kOe, pc,,,PC,,pv: atomic magnetic moments derived from polarizedneutron diffuse scattering at T= 4.2 K and Harp,= 20 kOe. V

Phase

Pat

PC0

F”

PC,

at% PB

fcc+20% hcp fee fee, ordered Cu,Au-type

10 15 20

1.21 0.871 0.237

1.38(l) -0.26(8) 1.05(l) -0.1 l(3) 0.28 ‘) 1.3*)

‘) For Co atoms on Co sites in ordered structure. ‘) For Co atoms on V sites in ordered structure.

Table 49. Analysesfor Co-V alloys of the spin-echo NMR spectra of Fig. 203 for 5gCo with 3, 2 and 1 nearest neighbor (nn) of V atoms [8OK9]. Phase

5gCo-3nnV

“Co-2nnV

Hhro %I

a1 UL

LHZ

kOe

~Hz

137 138 142

136 137 141

157 167 170 Ada&i

5gCo-lnnV

HW, kOe

;Hz

155 165 168

176 195 203

Hhw kOe 174 193 201

383

1.2.3.6 Co-V

Ref. p. 4801

I co-v

2.5 SK

=L.ZK

2.0

1.5

$

! CT

f

1.0I-

f

rf

+-

0.5 a

-19.8

,

I

I I ti 0

L

1

5 at%

6

Fig. 204. Nuclear spin-lattice relaxation time TI for 51V and 5gCo in Co-V alloys at 4.2 K [75 W 11.

0.6 ms 04 I e 0.2

Fig. 205. Nuclear spin-spin relaxation time T, of “Co in Co-V alloys at 4.2 K [75 W 11.

//I

1

\

\

15.0 \

I

I-:

125

I

150

175 Y-

Fig.

200

I

225 MHz 250

V at%

Fig. 203. Spin-echo spectra for 5gCo in Co-V alloys at 4.2K in zero applied magnetic field. 100MHz corresponds to 101kOe for the magnetic hyperfine field [80 K 91. See also Table 49.

Phase

Heat treatment “C

t

11.4...18.2 7.7...19.8

CI~,Cu,Au c~u, disordered, structure fee

i

14.3...21.8 18.2

cl,, Cu,Au CQ, Cu,Au-like structure

*) w.q.: ice-water-quenched; EC.:furnace cooled. Landok-Bdmrtein New Series lll/l9a

Ada&i

1200 600 750...800 600

h

*I 243

168

w.q. EC. w.q. f.c.

[Ref. p. 480

1.2.3.7 Co-G

(10 0 1900 “C

lo

20

10

20

30

Cr LO

CC 50

60

70 wi%

90

1800 1700

EO!

501

0 co

30

40

50 Cr -

Fig. 206. Phase diagram of Co-0

60

70

80

90ot% 100 Cr

alloys [58 h 1, p. 4671.

a: fee, B: bee, E: hcp. Temperature, in PC], and composi-

tion, in [at% Cr], are given for special points of the phase diagram.

Adachi

385

1.2.3.7 Co-Cr

Ref. p. 4801

800

! 600

400

200

0

\ ‘1

-200 0 co

5

IO

15

20

at% 25

Cr -

Fig. 207. Partial phase diagram ofCc&r alloys. Curve A: @p)+a(fcc) transformation upon heating. Curve B: ~-+a transformation upon cooling. Open triangles: Tc vs. composition for the cubic phase, open circles: Tc vs. composition for the hexagonal phase [83 B 43.

Landolt-BOrnstein New Series lll/l9a

[Ref. p. 480

1.2.3.7 Co-Cr

386

Fig. 208. (a) Magnetic mass susceptibility xn and (b) inverse magnetic mass susceptibility xi1 vs. temperature for Cr-3d transition metal alloys. Inset: the anomaly temperature TN vs. Co concentration [66 B 31, see also [75 A23.

6.5

;

6.0

j I .

5.5 I

4.8’

I

9.3ot% co I I

4.5 i 4.4 i-7 4.2

0,98ot%Fe 0.97ot%Co 3.1 3.2

2.8 26 a -200 -10:

0

100

200 300

I 400

I 500

I 600

co I 700

I 800 “C 900

Fig. 209a,..f. Inverse magnetic mass susceptibility vs. temperature for Co-Cr alloys with Cr-concentration just above the critical concentration for long-range magnetic order. Open circles: cooled in the magnetic (measuring) field H,,,,, solid circles: cooled in zero field, dashed line: Curie-Weiss-type behavior extrapolated 0 -20’.

[82 G I]. 43

0

100

200

300

400

500

600

700

Adachi

800 K 900

1.2.3.7 Co-Cr

Ref. p. 4801

-

,P

I

cm3

HoppI= 40 Oe

300 201

a

c

50

do

101:

50

100

150 T-

200

150

200

250 K 300

I

I

I

120

150 K 180

32

40

T-

2.50 .I03 9 cm3

250 K :

100

I

I

Coo.703 Cr0.297 I \

d d

1.50 i 1.25 2 1.00

0.25 0

50

100

150

200

250 K 300

b

0

e

2.5 .lO" 9 cm3

30

60

~ 90

3.5-

I -g 210

Landolt-BBmstein New Series 111/19a

K 300

Ada&i

f

0.5I 0

8

16

TL

K 48

10 w,"

I coo.;5cress ^,- - -

---r-Px"

[Ref. p. 480

1.2.3.7 Co-Cr

388

T

-

_

co0.sCro.5

0

50

100

200

150 I-

Fig. 210. Paramagnctic mass susceptibility zp vs. temperaturc for o-phase Co,,,sCr,,,, and Co,,,Cr,,, alloys [69 M 23.

250 K 300

Table 50. High-temperature paramagnetic mass susceptibility of the C&r alloys of Fig. 208b, expressed by the equation: x,=C$(T--O)+,y’+jT, where x0 is the background susceptibility of the host at OK and /I is the temperature variation of the susceptibility of unalloyed Cr above its TN (i.e. B =4.62. 10” cm3 g- 1 K-‘. P~~~,,-~:effective paramagnetic moment of the Co atoms in Cr [66 B 33, see also [75A 21.

co

Pcff.Co

at %

PB

2.79 1.90 0.97

1.7(3) 1.9(4) 2.1S(60)

x0 10-6cm3g-’

27(40) - 6(60) - 17(100)

3.14(10) 3.08( 15) 2.99(25)

a 1 0 2 .3 *v5 4

.

I 225 250

0 K

z 32i K

300 275 250 225 0 Cr

12

1,

3

5

6 ot% 7

Fig. 211. N&l tempcraturc TN for Co-Cr alloys [83 A I]. Top figure: (I) minima in resistivity vs. 7; (2) inflection points in bulk modulus B vs. 7; (3) inflection points in linear thermal expansion coefficient, (4) neutron diffraction [78 K I], (5) neutron diffraction [68 E 11. Bottom ligurc: (I) inflection points in resistivity vs. 7; (2) minima in bulk modulus vs. 7; (3) minima in linear thermal expansion coefficient, (4) and (5) as in top figure.

co -

Ada&i

Landolr-Bornwin Nor Swim 111’19a

2oi

y

389

1.2.3.7 Co-Cr

Ref. p. 4801 I

Co-Cr

I

160

16

120 I 13"

g 12 80 8

0-4

-250

0

250

500 T-

\I! \I\! I 750 1000 "C 1250 Cr-

Fig. 212. Saturation magnetic moment B, vs. temperature T for Cc&r alloys. The measurements were made for increasing temperatures. For Co-8 at% Cr also measurements were made when decreasing the temperature from T, [82G 1-J.

Fig. 213. Saturation magnetic moment gsvs. Cr content as obtained from magnetization measurements on Co-Cr alloys at 4.2 K [82 G I], see also [57 C 1J.

1.2

0.6 Gem' 9

I 0.9

0.4 y" 0.6 ,4 Q

0.2

I b

0.3

c 1.2 @Jn 9

HappIA0 Oe

Fig. 215. Relative sublattice magnetic moment, p/p(O K), vs. normalized temperature, T/T,, for Co-Cr alloys [68 E 11. Solid line: calculated from Brillouin function Bl/z.

0.6

0.1

[ 50

100

150

200

K 250

Fig. 214. Magnetization vs. temperature for Co-Cr alloys in magnetic fields of 30 and 40 Oe, respectively [82 G I]. Solid line: increasing temperature after cooling in zero field, dashed line: decreasing temperature in nonzero magnetic field.

Landolt-Bbmstein New Series 111/19a

Adachi

1.2.3.7 Co-Cr

[Ref. p. 480

Fig. 216.Temperaturedependcnccofthc wavevectorQ of the spin density wave in Cr-3d transition metal alloys [68 E I].

0

0.25 0.50 0.75

1.00

r/7, -

Table 51.Magnetic properties ofthe spin density wave in Co-Cr and Ni-Cr alloys. pmnr: maximum amplitude, Q: wavevector, 7”‘: Ntel temperature derived from neutron diffraction (ND) and thermal expansion (TE) [68 E 1-J. X

Co,Crt --r 0.0080(S) 0.0215 0.0532 Ni,Cr r -I 0.0048 0.0098

TNWI ND

TE

283 298 298 232 202

290(2) 300(2) 297(2) 240(2) 209(2)

PllLlX

Qd2~

PB

(0 K)

(TN)

0.584(I5 K) 0.579(60K) ‘) 0.460(70K) ‘) 0.504(77K) 0.452(4.2K)

0.960(3)

0.981(5)

0.948(3) 0.949(3)

0.969(5) 0.972(5)

‘) Commensurate antiferromagnetic structure. Table 52. Saturation magnetic moment o, and average moment per atom, p,,, for Co-Cr alloys at 0 K [37 F 23. The critical concentration for ferromagnetism is estimatedto be 27(l) at % Cr. Cr [at%]

5.6

10.6

16.7

22.1

CT,[Gcm3g-‘1

136 1.42

103 1.07

62 0.64

23 0.24

PMcib1

Table 53. Average magnetic moment per atom, P,,, and atomic magnetic moments of the constituing atoms as obtained from neutron diffuse scattering at room temperature for Co,~,,Cr,~,, and Co,~,,Mn,~,, [7OC2]. Pa,

Per

PM”

7

PB

Coo.9sCro.05

co o.9sMno.os

1.40 1.50

PC”

0.45(70) -

-0.97(70)

‘) According to various analyses, see [70 C 21.

1.45(4) 1.63(4)

1.41(6) 1.58(3)

391

1.2.3.8 Co-Mn

Ref. p. 4801 LU

kG

0 co

5

15

10

20 at%

25

Cr -

Fig. 217. Magnetic anisotropy field strength H, at 77 K and room temperature as derived by the singular-point detection technique on polycrystalline samples of Co-Cr alloys. Also the saturation induction 4nM, at room temperature is given [83 B4].

10

20

30

40

50 V-

60

1.2.3.8 Co-Mn

co 10

20

30

Mn 40

Mn 60

50 II

I \

400 -=

\n 10

20

70

80WY/~90

I ,111

I

I

\

01 0 co

30

50 Mn -

60

70

80

JJgMnl1

90 at% 100 Mn

Fig. 219. Phase diagram ofCoMn alloys [SS h 1,~. 481. y: fee, E: hcp. Temperature, in PC], and composition in [at% Mn], are given for special points of the phase diagram. Land&-Bbmstein New Series III/l9a

Adachi

I

II

I I I

:

‘4 40

80 MHz90

Fig. 218. Spin-echo NMR spectra of “Co in Co-Cr alloys. The signals at about 66, 44 and 24MHz correspond to Co atoms having, respectively, zero, one and two Co atoms as their nearest neighbors [75 K I]. T= 1.4K,

H=O.

1600~

70

391

1.2.3.8 Co-Mn

Ref. p. 4801 LU

kG

0 co

5

15

10

20 at%

25

Cr -

Fig. 217. Magnetic anisotropy field strength H, at 77 K and room temperature as derived by the singular-point detection technique on polycrystalline samples of Co-Cr alloys. Also the saturation induction 4nM, at room temperature is given [83 B4].

10

20

30

40

50 V-

60

1.2.3.8 Co-Mn

co 10

20

30

Mn 40

Mn 60

50 II

I \

400 -=

\n 10

20

70

80WY/~90

I ,111

I

I

\

01 0 co

30

50 Mn -

60

70

80

JJgMnl1

90 at% 100 Mn

Fig. 219. Phase diagram ofCoMn alloys [SS h 1,~. 481. y: fee, E: hcp. Temperature, in PC], and composition in [at% Mn], are given for special points of the phase diagram. Land&-Bbmstein New Series III/l9a

Adachi

I

II

I I I

:

‘4 40

80 MHz90

Fig. 218. Spin-echo NMR spectra of “Co in Co-Cr alloys. The signals at about 66, 44 and 24MHz correspond to Co atoms having, respectively, zero, one and two Co atoms as their nearest neighbors [75 K I]. T= 1.4K,

H=O.

1600~

70

[Ref. p. 480

1.2.3.8 Co-Mn

392

t. 1200

'\ \

1000

\

\,.Co-Mn

\

800 ,A

600

0

I 50

100

150

200

250

300

350 K 4

---:

I

i'-fw,N-Mn -I-. I.

I 400

a

‘\

\o

200

30 .lOf cm! TI

-600 0

50

100

b

150 T-

200

250 K 300

-800 I 0

Fig. 220. Magnetic mass susceptibility xs vs. temperature for CoMn alloys. (a) 35,..50at% Mn co) 60...85 at% Mn [75 H I]. Arrows indicate the temperature T, of the susceptibility maximum.

co

5

IO

15

20 Mn -

25

30

at%

LO

Fig. 222. Paramagnetic Curie temperature 0 vs. Mn concentration of Co-Mn and Ni-Mn alloys. Circles: [60K I], triangles: [57 C I].

2.5

0

J / I I/l 100

200

I 2.0 = a" 300

400 I

500

600

1.5

700 K 800

Fig. 221. Inverse magnetic volume susceptibility, x; *, vs. temperature for Co-Mn alloys [60 K I].

0 0

5

10

15

20 Mn-

25

30

35ot%10

Fig. 223. Effective paramagnetic moment per atom, pefr, for Co-Mn and Ni-Mn alloys. Circles: [60K 11, triangles: [57 C I].

Ada&i

Ref. p. 4801

1.2.3.8 Co-Mn

393

11.0 .lO-" cm: s

600 K

500 1o.c

400 t 9.E: x"

I 300 6.

9.c

200

8.E

8.C 50

100

150 I-

200

100

250 K 300

Fig. 224. Magnetic mass susceptibility, xs, vs. temperature for c1-and O-Mn containing 1 at% ofa 3d transition metal [74 M 11.

/ 30

01 20

/

1 40 ato/0 50

Mn -

Fig. 225. Co-Mn magnetic phase diagram. Solid curves separate (F) ferro-, (AF) antiferro- and (P) paramagnetic phases [70 M 11.The open circles are considered to be the keezing temperature of the antiferromagnetic clusters [8ORl].

1800,

I

I

150 -1

KI Chx in, I KI ‘i+ I II

12001

i

9.0

I

I

8.8

I i/r

I

I

8.6

8.4

H2.0

I

8.2

I

8.0

Fig. 226. Curie and NCel temperatures, Tc and TN, and average magnetic moment per atom, j&,(OK), of Co,-,Mn, alloys [70Ml, 73A1, 73MlJ n: average number of 4s and 3d electrons per atom.

Landolt-BOrnstein New Series 111/19a

Adachi

394

1.2.3.8 Co-Mn

[Ref. p. 480

4OC G

2oc I z

O

10

-200

I 5

Cl

-4oc -10

G( co0.6UMn0.313(

-20

/

2

1,

20

-30 V

a

/

40

Cr

Mn

Fe

Co

Ni

60[

I

P O

K

50[ 4oc

-40

~I 3oc

-60 1 6

I

I

G coo.627Mno.373

200 100

Y.56

b

3.58

3.60 u-

3.62 1 3.6L

Fig. 227a. Change of N&l temperature AT’ ofu-Mn as a consequence of alloying with 1 at% of a 3d transition element [74M I]. Solid circles: [74M 11; open circles: [73 W I], triangles: [71 W I]. Fig. 227b. Relationship between Ntel temperature and lattice parameter of Co--Mn alloys and other y-Fe type alloys [73A I].

-6 -8

-6

-4

-2

0

6 kOe 8

Fig. 228. Hysteresis loops of the magnetization M of various Co-Mn samples at 4.2 K. Solid lines: cooled in a field of HZ,,,,,= + 5 kOe, dashed line: zero-field cooling [60 K I].

Ref. p. 4801

1.2.3.8 Co-Mn

395 ;P 1.5

Co-Mn 1 0

c

0 0

I 1.0 c 19; D la" 0.5

PC0

0

I

-PM”

I

0 -0 co

IO

20 at%

30

Mn -

Fig. 230. Average ferromagnetic moments for the Co and the Mn atoms, jc,, and jiMn,respectively, in Co-Mn alloys. Note that the Mn moments are negative. See also Table 54 [82 C 11, see also [78 N I].

IO

50

G 4

3 2 1

0 0

100

In-!--+ 200 300

400 500

I600

I 700 K 800

T-

Fig. 229. Magnetization M vs. temperature for Co-Mn alloys in various magnetic field strengths H, which was slowly cycled between k 8 kOe. For H =4 kOe, the open and the solid points represent the descending and ascending field branches of the hysteresis loops, respectively [60K 11.

Fig. 23 1. Antiferromagnetic structure of Co-Mn (fee).The spin direction is indicated by angles 0 and 4 [73 A 11.

1.8, Ps

7

1.7

Land&-Bdmstein New Series 111/19a

1.52 1.36 1.18 0.88 0.58

1.63 1.54 1.44 1.18 0.80( 1)

-0.53(12) - 0.30(9) -0.33(9) -0.33(6) -0.11(4)

I

I I

t - 1.6 z

Table 54. Average magnetic moment per atom, &, of CeMn alloys, derived from magnetization values at H app,=40 kOe, and average magnetic moment of Co and Mn atoms, PC0and P,,, respectively, derived from polarized neutron diffuse scattering [82 C 11, see also [70 c 21.

5.0 9.7 14.7 19.8 24.4

I

lc;1.5

co

6 Cr, Mn -

Fig. 232. Average magnetic moment per atom, p,,(OK), of Co-Mn and Co-Cr alloys [57C 11. For pure Co, jc0=1.715uB.

Adachi

396

1.2.3.8 Co-Mn 161 Gcm3 9

[Ref. p. 480

1.75 1.50

3.5 AD-5 cm3 -c

1.25

2.5

PC!

15C

I 1.00

2.0 I

,c 0.75

1.5 ,=

0.50

1.0

0.25

0.5

0 0 Co

10

20

30 Mn -

40

0 50 at% 60

Fig. 234. Avcragc magnetic moment per atom. j,,. as derived from magnetization measurements in pulsed magnetic fields up to 400 kOe and high-field susceptibility xHF for Co-Mn alloys at 4.2 K [83 K 23. see also [60 K I]. 90

I b a'

60

100

200

300

kOe 4

Fig. 233. Magnetization curves for Co-Mn alloys measured in pulsed magnetic fields at 4.2 K [83 K 21, see also [80 K 3).

HO??l -

Adachi

Ref. p. 4801

1.2.3.8 Co-Mn

a-Mn-M

cz-Mn-M

site I

9at%Ru

Sat%Ru I 200

220

210

site II

3at% Ru

3ot%Ru

I

391

230

MHz 2

Y-

9at%Ru I 20

Landolt-Bbmstein New Series 111/19a

30

40 v-

50

Fig. 235. NMR line shapes for “Mn at crystallographic sites (I...III) for Mn in a-Mn-transition metal alloys.For 60 MHz 70 definition of the lattice sites, see Fig. 46 [74 K 11.

Adachi

[Ref. p. 480

1.2.3.8 Co-Mn

39s

/3-Mn-Co

175 kOe

T=l.kK

I 150

P-Cb-Mn I T=k2K -if

3 125 22 I, > s" 100

p

YP

AL

A

75 50 10

a

A

Mn

20 co -

30 ot% 40

20

300~% 10

35 kOe 3c T= L.2K

I

30

60 90 1' -

120

150 MHz180

Fig. 236. Line shapes of “Mn and 59Co NMR rcsonancc spectra for fl-Mn--Co alloys at 1.4K. The scales of the intensities arc different for both nuclei [74 K 21.

0 b

Impurity-

Fig, 237. Magnetic hypcrfinc field, Hhyp, at 4.2 K derived from NMR experiments [74K 23. (a) For s9Co in fi-Co--Mn alloys, (b) for “Mn in p-Mn-based alloys.

1.0

I

10

0.8

2 0.6 z x ‘;10.4 t 0.2 . fee Co-O.Eot%Mn 0 bee Fe-O.4ot% Mn

0

0.2

0.4 7/r, -

0.6

0.8

Fig. 238. NMR frequency v, normalized to the frequency at 4.2 K for 55Mn in fee Co-O.8at% Mn and bee Fe0.4at% Mn. Also are shown the temperature dependcnccs of the reduced spontaneous magnetizations uJu(OK) of fee Co and bee Fe [74 K 33.

Ref. p. 4801

1.2.3.8 Co-Mn

399

-340 kOe I -350 c 25 w 12-360

-370 0 co

2.5

5.0 Mn-

7.5at%lO.O -

Fig. 240. Mean hyperfine field Hhypfor 55Mn in Co-Mn alloys at 1.6K [73 Y 11. 320

330

X0

350

360

370

380

Fig. 239. Spin-echo NMR spectra for “Mn alloys at 1.6K [73 Y 11.

MHz J+

in Co-Mn

375.0 MHz

I’

372.5 t 370.0 c z 367.5 w x 365.0 362.5 360.0 357.5

0 5

10

15 kOe 20

HOPPl -

Fig. 241. Spin-echo NMR frequency for “Mn in co 0,95Mn,,,, at 1.6K as dependent on an applied field. The straight line is drawn according to the relation: WAK,,, = - 1.05MHz/kOe [73 Y 11.

New Series lll/l9a

50

100

150 T-

200

250 K

Fig. 242. Temperature dependence of the NMR tiequency v, for 55Mn in fee Co-O.8at% Mn in zero applied magnetic field. HhYP=- 358.3(5)kOe at 4.2K [74K 31. Hhyp= - 357.52(15)kOe for 52Mn in fee Co at 1OmK [78Z 11.

Adachi

[Ref. p. 480

1.2.3.8 Co-Mn

400 80

I

P

PS p-Co-Mn 70.

I

I

l=l.bK 60

I

50

2 LO CT P 30

20

10

0 Mn

10

20 co -

3Ool%

LO

Fig. 243. Transverse or spin-spin relaxation time T, of “Co in P-Co--Mn alloys at 1.4K [74K 21.

1.5

JO” erg

mJ

cm?

K2%

5 I1

6.5

I 6.0 x 5.5

5.0

LO

80

120

160 rw

200

260

280 K 320

4.5 4.0

Hexagonal first order magnctocrystallinc anisotropy constant K, vs. tempcraturc for Co alloyed with small amounts of 3d transition elements. Measuring field strcncgth H,,,, =32kOe [64C I]. Fig.

244.

2

I

6 Impurity-

8

10 ot%

12

Fig. 245. Electronic specific heat coefficient 7 for Co alloyed with 3d transition elements [80G I].

Ref. p. 4801

1.2.3.9 Ni-Ti

Ti

Ni IO I

1800° “C

20 11

30 I

40 ,

Ni 50 I

60 I

70 I

80 wt% 90 I I

Ni -Ti

1720°C

1600

I 500 1153'C

1400 4

1300 a7.5)

1200

lot% 1100

800

600 500 0 Ti

IO

20

30

40

50 Ni -

60

70

80

90 at% 100 Ni

Fig. 246. Phase diagram of Ni-Ti alloys [SSh 1, p. lOSO]. Temperatures, in PC], and composition, in [at% Nil, and, in parentheses, in [wt% Nil, are given for special points of the phase diagram.

Landolt-BOrnstein New Series 111/19a

Ada&i

402

[Ref. p. 480

1.2.3.9 Ni-Ti 635 K 620

I 605 L-Y 590

560 0

0.5

1.0 Ti -

1.5 ot% 2.0

Fig. 247. Fcrromagnctic Curie tempcraturc Tc of NipTi alloys. derived from resistivity measurements[78 Y I]. Open circles:maximum in dc/dTand solid circles:“kinkpoint” technique.

Table 55.Change of the averagemagnetic moment per atom: pat,and of the Curie temperature Tc of Ni-3d transition metal alloys. x: impurity concentration. Impurity

Table 56. Mean magnetic moment per atom. j,,. for Ni-Ti alloys, as derived from saturation magnetization measurements at 4.2 K in fields up to 30kOe [75 G 11.

Mn

o... 5

Cr

o... 10

V Ti

O...lO 0...15

0.616 ‘) 0.528 0.404 0.329 0.271 0.203 0.149 0.103

dTc/dx K

dL,ldx PB

f2.4 +2.8 -4.4 -6.0 -5.2 -4.0

[32 S l] [62V l] [32 S l] [62V 1) [32S l] [32 S l]

- 11.0(5)[37 M l] -35

[37 M l]

-55(3) -21

[37 M l] [37 M l]

Table 57. Magnetic moment distribution for Ni-Ti alloys. P,,: average magnetic moment per atom derived from magnetization measurements in a field of 13kOe. PNiand pri: averagemagnetic moments of the Ni and Ti atoms, respectively, as derived from elastic diffuse scattering of polarized neutrons at room temperature [79 K 141.Magnetic moments in

Ni 2 4.8 6.1 8 10 12 14

x at%

bB1.

Ti at%

3.87 7.72

Pat

Ph’i

hi

RT

1

3.537 3.551

‘) [71 c43.

Adachi

RT

4.2 K

RT

0.383(5) 0.185(S)

0.444(5) 0.267(6)

0.402(7) 0.21(l)

- 0.08(2) -0.09(4)

403

1.2.3.9 Ni-Ti

Ref. p. 4801

0 i

nucleus Ni

nucleus Ni

:fi nucleus Ni

b

a

Fig. 248. Magnetic moment distribution in (a) the (100) plane and (b) the (110) plane of y-phase Ni,.,,Ti,,,,, obtained from polarized neutron diffraction scattering. At room temperature the average magnetic moment per atom is: &,=0.505(5)pr,. Localized 3d-moment of Ni atoms: pNi 3dx 0.595(3) un. Localized 3d-moment of Ti atoms : p:p z 0.05(20) us. Nonlocalized moment per atom : PnlN - -O.O78(8)un. Proportion of electron spins in E, orbitals: y = 0.203(5) [76 L 11.

-0.2 0 Ni

2

4

6 Ti -

8

10 at%

12

Fig. 249. Mean atomic moment per atom for Ni-3d transition metal alloys at 4.2 K as derived from magnetization measurements in magnetic fields up to 30 kOe [75 G 11.

0

4

8 Impurity

12 -

Eat%0

Fig. 250. Magnetic moment distribution for Ni-Ti alloys

at room temperature [79K 141. Open circles: magnetization measurements [37 M 11, open triangles: [79K 141, solid circles and open squares: neutron measurements: [79 K 141, solid triangle: [66 M 11.

Landolt-Bbmstein New Series lWl9a

Adachi

404

[Ref. p. 480

1.2.3.9 Ni-Ti Table 58. Electronic and lattice contributions, y and /?,respectively, to the molar specific heat of Ni-3d transition metal alloys in the temperature range 1...4 K [75 G 1). X

Ni, -$rr

Ni, -IV,

Ni, -,Ti,

Ni

0.005 0.01 0.02 0.035 0.17 0.30 0.005 0.0115 0.02 0.035 0.0507 0.0511 0.0685 0.073 0.08 0.09 0.094 0.10 0.11 0.116 0.15 0.18 0.02 0.048 0.067 0.08 0.10 0.12 0.14

Y

P

mJmol-’ Km2

mJ mol-’ Km4

7.287(2) 7.544(2) 7.989(2) 8.585(2) 7.389(2) 6.950(2) 7.203(2) 7.404(2) 7.641(2) 8.033(1) 8.277(2) 8.288(2) 8.390(2) 8.405(2) 8.652(3) 8.996(2) 9.344(2) 9.967(8) 9.992(9) 8.065(13) 4.789(1) 3.867(1) 7.453(2) 7.853(2) 7.972(2) 7.975(2) 8.154(2) 8.183(2) 8.219(10) 7.034(3)

Ada&i

0.0202(2) 0.0204(2) 0.0207(3) 0.021l(2) 0.0178(2) 0.0173(2) 0.0203(2) 0.0208(3) 0.0208(2) 0.0212(2) 0.0247(2) 0.0242(2) 0.0270(3) 0.0268(3) 0.0254(3) 0.0230(3) 0.0179(2) 0.0053(5) -0.0104(5) 0.0033(6) 0.0169(2) 0.0161(2) 0.0195(2) 0.0224(2) 0.0226(2) 0.0257(3) 0.0264(3) 0.0181(2) 0.0157(5) 0.0222(3)

405

1.2.3.10 Ni-V

Ref. p. 4801

Ni I.. 2ooo”

"'

V

v-

I’!

20 I

30 I

40 I

50 I

60 I

70 I

1900125)"1

Ni-V

1800

L--. .--

I

P

.g--._N

1600

=-

1453°C

1400

80wt%90 I I

z > 1

-J

1 / / +/

/

’

//

/:

I

I

?-

/’ x127OT /-47nj/UY.bl

Ni

?

141.31 151,5wt”/o/.)V

I 890 ‘C i.21 ’

\ I

1

17

Iv

6’ \ %:7

?I

I ?? I

I

1

1

0 Ni

IO

20

1

I

I

?

1 I i i/ II

30

40

50 v-

60

70

80

90at % 100 V

Fig. 251. Phase diagram ofNi-V alloys [58 h 1, p. 10561. Temperature, in c”C], and composition, in [at% V], and, in parentheses, in [wt% V], are given for characteristic points of the phase diagram.

I C

Fig. 252. Crystal structure of o-phase materials [54 B 11. The unit cell is composed of 30 atoms with five kinds of sites. Elements V, Cr and Mn prefer to occupy position M’,while Fe, Co and Ni prefer position M. M or M’means sites of mixed occupation.

Landolt-Biirnstein New Series 111/19a

Adachi

I I/

406

1.2.3.10 Ni-V

[Ref. p. 480

H”

.

1,

c-phase

.

co-v 00 co-v

2

. Co-Cr A Ni-V

0 6.0

I

6.3

6.6

6.9

I.2

1.5

Fig. 254. Paramagnetic susceptibility vs. average number n of4s and 3d electrons ncr atom for o-chase NT-V. Co-V and Co-0 alloys at room tempcratuie [69 M 21.’

J

6% K

11.0 mJ K2mol 10.5

550

I 153 Q 10.0

9.0

253 Ni

1i.V -

8.5

Fig. 253. Efkctive paramagnctic moment per atom. pcrr, and the paramngnctic Curie tcmpcraturc 0 for Ni alloys with small V and Ti concentrations [36 M I].

8.01 0

3

6

,L+

12

15 K2 18

Fig. 255. Tcmperaturc dcpcndencc ofthe specific heat C, of Ni ,,ssaV,,, t6 for various magnetic fields H,,,,. Since C,/T is plotted vs. T2 the curves can give an indication of the magnitude of the electronic specific heat coefficient [77 B 11.

Table 59. First-order magnetocrystalline anisotropy constant K,, and linear magnetostriction constants i.,,, and I., , I for Ni-Cr and Ni-V alloys [60 W 11. X

Ni Ni, -&rx 0.0147 0.0252 0.0408 Ni,-,V, 0.0128 0.0295 0.0393

K, 104ergcmm3

16100 10-6

300 K

300 K

-4.9 -1.1 -0.38 0 - 2.4 -0.73 -0.28

77K -73 -27 -17 - 6.5 -36 -18 -13

-55.8 -44.6 - 34.8 -20.6 -43.0 - 29.6 - 19.1

Adachi

1bill 10-6

3‘100

10-6

1 ‘1 11

10-6

77K -29.5 - 19.6 - 14.2 - 7.9 -21.0 - 13.4 - 6.5

-58 -46 -43 -35 -51 -39 -34

-37 -26 -21 -17 -29 -22 -15

Ref. p. 4801

1.2.3.10 Ni-V

407

Table 60. Specific heat parameters for fee Ni-Mn and fee Ni-V alloys, according to the equation C, = A + yT. Also the Debye temperature On is given [64G 11. X

Ni, -xMnx 0.20 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.30 0.40 0.60 0.75 Ni, -xV,

0.09 0.18 0.28 0.35 0.35 0.40

Landolt-Bbmstein New Series IIl/19a

Heat treatment

quenched from 11oo”c quenched from 11oo”c quenched from 11oo”c quenched from 1100“C quenched from 1100“C quenched from 1000“C and 2 h at 485°C quenched from 1000“C and 2 h at 485 “C quenched from 1000“C and 2 h at 485 “C quenched from 1100“C and 2.5 h at 535°C quenched from 11oo”c quenched from 1000“C quenched from 980 “C quenched from 1000“C quenched from 1150°C quenched from 1150°C quenched from 1150°C quenched from 1150°C quenched from 1150°C quenched from 1150°C

Magnetic field

y

rms dev.

A

@D

K

10-4calmol-1K-2

low4 cal mol-‘K-r

none

22.1

2.09

373

none

23.1

1.67

329

cooling to 1.4K

20.7

5.26

261

cooling and measurement none

21.5

3.80

266

22.7

3.02

279

none

18.5

3.80

313

cooling to 1.4K

18.1

3.65

291

cooling and measurement

18.3

3.14

315

none

23.5

0.36

422

none

16.7

2.81

356

none

8.0

4.74

312

none

9.9

3.34

311

none

15.9

3.99

307

none

19.3

7.05

398

none

9.5

3.22

479

none

10.2

0.40

388

none

10.7

0.50

422

none

10.7

0.40

421

none

11.5

1.00

419

Ada&i

0.30

0.50

[Ref. p. 480

1.2.3.11 Ni-Cr

408

1.2.3.11 Ni-Cr

cr -. 2ooo0 “.-

10 / I’C

20 /

Ni -Cr

30 I

40 4

Ni 50 I

Ni 80wt% 90 I I

70 I

60 I

o liauids

1600

j 5CO’C

\ \

Y-Y,

\ I I

Cr

50 Ni -

60

70

80

Fig. 256. Phase diagram ofNi-Cr alloys [SS h 1, p. 5421. Temperature, in [“C], and composition, in [at% Nil, and, in parentheses, in [wt% Ni], are given for characteristic points of the phase diagram.

Fig. 257. Magnetic mass susceptibility xp for Ni-Cr alloys at room temperature. I: quenched from 900 “C, II: annealed at 425 “C [57 K 11.

Adachi

Ni

Ref. p. 4801

1.2.3.11 Ni-Cr

409

Table 61. Paramagnetic properties of Ni-Cr alloys derived from the susceptibility vs. temperature curves given in Fig. 259, according to the equation: xp = x0 + C$( T- 0) [72 B 11. Cr [at%] C, [10M4cm3 Kg-‘]

@ CKI x0 [10e6cm3 g-i]

44

.I!" Y

11.0 22.2 96 4.09

11.5 17.6 89 3.92

12.0 14.7 51 4.70

12.5 12.2 48 4.37

13.1 9.9 2.5 4.85

13.5 11.2 -21 4.74

15.3 15.6 - 248 4.44

I

Ni-Cr

cm3

28 I 24 7 s20

0

16

250

500

750

1000 K 1250

T-

Fig. 259. Reciprocal mass susceptibility xi’ vs. temperature for Ni-Cr alloys. For the drawn curves, see Table 6 1 [72B 11.

00 Fig. 258. Inverse of the magnetic mass susceptibility, xi ‘, vs. temperature for Ni-Cr alloys. From the curves labelled a for 6 and 14wt% Cr the curves labelled b are obtained by correcting for a temperature-independent paramagnetic susceptibility x0 of 2.07. 10m6 and 3.82. 10m6gcmm3, respectively [36 M 11.

350 K 300

250

For Fig. 260, see page 413.

200 1 150

100

Fig. 261. Magnetic phase diagram of dilute Ni-Cr (dashed lines) and Cc&r (solid line) alloys. T-IC and L-IC denote transverse and longitudinal spin density wave states, respectively. AF means commensurate antiferromagnetic state. Circles: [68 E l] and triangles: [66 B 31.

Landolt-Bdmstein New Series 111/19a

Adachi

5c C 0 Cr

1

2

3 Co,Ni -

4

5 at%

410

1.2.3.11 Ni-Cr

3[ Gem 9

[Ref. p. 480

I

Ni - 5.6ot%Cr

2:

169

0

3

Cy

6

a

9

12 kOe 15

I

1=1.56K

9

12 kOe 15

H6

V

b

0

Ni

0

I

3

6

8

12 ot% 16

Cr -

Fig. 263. Average magnetic moment per atom. j,,. for NiCr alloys as determined from the magnetization in magnetic ticlds up to 30 kOe [72B I], see also [71 C 1, 32 S 1, 62 V I]. Bottom figure: extrapolated zero-field magnetic mass susceptibility xB at 0 K [72 B I].

I hli-91nt0/~~r

4

Hllat%Cr

1

0 C

5

10

15

20

25 kOe 30

Fig. 262. Magnetic moment per gram, o, as dependent on temperature and field strength [62 V I] : (a) Ni-5.6 at% Cr and (b) Ni-9.1 at% Cr.(c) Magnetic moment per gram: G, at 4.2 K, as dependent on composition and field strength [72B I].

H-

Adachi

Table 62. Saturation magnetic moment csand average magnetic moment per atom, pat, for Ni-Cr alloys at various temperatures [59 T 1-j. Cr at%

40 K) Gcm3g-’

1.70 3.28 6.74 8.75 11.2

50.9 43.7 29.0 21.9 15

0,(150K) Gcm3g-l 49.75 42.40 25.40 16.3

Ed0 K) uB 0.53 0.46 0.30 0.23 0.16

Table 64. Atomic magnetic moments as determined by polarized-neutron diffuse scattering measurementson Ni-Cr and Ni-V alloys [76 C l] and averagemagnetic moment per atom, P,, [72B 1, 71 C 1, 32s 11. T= 4.2 K, H = 57.3kOe. Cr

1 5 10 -

PB

5

0.570 0.375 0.100 0.346

Table 63. Average magnetic moment per atom, j&,,,and Curie temperature Tc for NiXr alloys [72 B 11,seealso [32S1,37M1,62Vl].T=4.2K. Cr at%

Pat PB

K

Ni 2.6 5.1 7.7 9.4 10.5 11.0 11.5 12.0 12.5

0.6155 0.4742 0.3487 0.2161 0.1268 0.0766 0.0548 0.0375 0.0221 0.0091

518 390 235 130 80 43 30 19 11

-0.20(6) -0.02(12) 0.05(6)

-0.065(48)

0.562 0.355 0.095 0.325

9 Ni Ni-1.7 at% Cr Ni-3.3 at% Cr Ni-5.0 at% Cr

Impurity-

Fig. 264.Amplitude ofthe spin density wave,p,, ofCr with various small additions of other 3d elements,as derived from neutron diffraction measurements[68 E 11.

Landolt-BOrnstein New Series 111/19a

T,

Table 65. g-factor of polycrystalline NiCr alloys, measured at room temperature and 35.6GHz [60A 11.

V

at%

411

1.2.3.11 Ni-Cr

Ref. p. 4801

Adachi

2.18 2.18 2.18 2.20

[Ref. p. 480

1.2.3.11 Ni-Cr

412

5 .w4 -cm3 mol

I

0 \\,

Ni - Cr I

L

3 I hk x 2

I I 0.2

. OAB at%Ni o Cl.98of% Ni

0.4

I

I

I

0.6

0.8

1.0

1

r/T& -

Fig. 265. Tempcraturc dependence of the relative sublatticc magnetic moment p,lp,(O K)for Ni-Cr alloys [68 E I].

0 a

Ni 12

d

3

F 10

8 I $6

0.9E I < a97 s

o Ni-Cu

0.9:

20

b NI

60

60 V. Cr. Cu -

80 ot% 100

Fig. 267. High-field magnetic susceptibility, xHF,at 4.2 K, (a)mcasured in magnetic fields up to 69 kOe for Ni-V and Ni-Cr alloys [75A I], and (b) measured in pulsed magnetic fields up to 300 kOe for Ni-Cr, Ni--V and Ni-Cu alloys [82S 21. 1

2 3 Impurity -

1 ot%

5

Fig. 266. Wavevector Q of the spin density waves in Cr with various small amounts ofothcr 3d elements [68 E I].

Ref. p. 4801

1.2.3.11 Ni-Cr

413

Table 66. High-field magnetic mass susceptibility xHF of Ni-Cr and Ni-Mn measured for field strengths up to 13 kOe [62 V 11. Cr

Mn

alloys at various temperatures and

XHF

10ms cm3 g-l at% 1.2...1.6K 0.9 5.6 9.1 2.1 -

-

2.8 0.5 0.9 12.5

5.6 11.3

20.0

2.5...3.2K

4.2 K 2.8 0.5 7.0 5.8 18.0 4.0

8.0

15K

20K

2.0 5.0

0 0 5.2

0 25.0

0 4.0

65K

0 9.2 0 140

77K

169K

300 K

0 1.5 7.0 0 0 150

0.7 2.0 2.6 6.2 3.7 140

1.4 4.0 1.5 7.5 4.0 12.0

3 .10-c 0 I -3 3 -6

-12 150

175

200

225

250 T-

275

300

325 K 350

Fig. 260. Linear thermal expansion coefficient tl= Al/l vs. temperature for Ni-Cr alloys. The arrows give the NCel temperature as determined by neutron diffraction. Measurements were made on single crystals [68 E I]. Fig. 268. Electronic specific heat coefficient y for Ni-3d transition metal alloys in the temperature range 1...4 K. The open and solid symbols reflect different analyses of the measuring results [75 G 11.

Landolt-Bbmsfein New Series lWl9a

1.2.3.12 Ni-Mn

Mn

[Ref. p. 480

Ni -

Ni

I

60

I /

I

II

60

I \i-. ,

50 J CL!.!.

LOO ’ II!

i I

i I

70

8owt% 90

q&! T

I I

\

!ji I 1 II

‘\: \moonPlic

353’

i

301 200 100 0

0 Mn

10

20

30

10

50 Ni -

60

70

80

90 ot% 100 Ni

Fig. 269.Phasediagram and crystal structuresof Mn -Ni alloys [SSh 1,p. 9393.yNi:fee,yhrn:fee-fct (Mn side),Phln: B-Mn structure.czhln: a-Mn structure, MnNi,: feeCu,Autype. MnNi (L): fct CuAu-type.Tempcraturc,in [“Cl, and composition, in [at%Ni] and, in parcnthcscs, in [wt%Ni], arc given for characteristic points of the phasediagram.

Adachi

Ref. p. 4801

1.2.3.12 Ni-Mn

415

100

60 Ni

65

70

75

80 Mn -

85

90

95at%100 Mn

200

300

400

500

600 K 700

Fig. 272. Reciprocal value of the paramagnetic volume susceptibility, x; ‘, vs. temperature T for Ni-Mn alloys, 21.6...35.9at% Mn [60K 11. See also Fig. 271.

Fig. 270. Tetragonal transition temperature ‘I; and NCel temperature TN of y-phase Ni-Mn alloys. t, : c/a > 1, t, : c/a< 1 [71 U 11, see also [7OU 11.

650 K K

Ni-Ag

1

600 61

550

I 51 500 Q L50

Ni

I

350

L50

550

T-

650

“C

750

\

Impurity -

Fig. 273. Paramagnetic Curie temperature 0 for various Ni alloys [36 M 11.

Fig. 271. Reciprocal value of the paramagnetic mass susceptibility, 1; ‘, vs. temperature for Ni-Mn alloys, 0...17.89at% Mn [36M 11. See also Fig. 272.

Landolt-Bbrnstein New Series 111/19a

.

Ada&i

416

1.2.3.12 Ni-Mn 8

[Ref. p. 480 I

kG Ni-Mn 7

j

6

/ a\

,I

'\ \

20 Mn -

25

onneoled

3 2 1 0 0 NI

a 14

N:

5

10

15

30

35w1%10

I

kG 13.

T=OK

0 b Ni

5

/

I

,'I

I

Impurity -

Fig. 274. Curie temperature T, of Ni-based 3d transition metal alloys [32 S 1. 37 M I].

10

15

20 Mn -

25

3d

4 35";;

:Ii

Fig. 276a. Saturation magnetization 4nM, for Ni-Mn alloys at room tempcraturc as a hmction ofcomposition. Open circles: quenched from 9OO”C, closed circles: anncalcd at 430°C. After [31 K I], from [51 b I]. Fig. 276b. Composition depcndencc of the saturation magnetization for Ni-Mn alloys at OK after various annealing proccsscs [53P I]. Heat treatment A: 2 h at 800 “C, then water-quenched; B: one week at 420 “C, one week cooling; C: I6 h at 550°C 250 h at 490°C 260 h at 420°C and 260 h cooling.

5

10

15 Mn -

20

25 at% 30

Fig. 275. Curie temperature vs. Mn concentration in disordered NiLMn alloys. I: [3l K I], 2: [37M I], 3: [58 K I], 4: [78 T I].

Adachi

Landoh-Aornclein Ke\r Sciirr 111’19a

Ref. p. 4801

1.2.3.12 Ni-Mn

50 Gcm3 9

417

Fig. 278a. Magnetization curves for disordered Ni o.7sMno.22 after cooling in zero magnetic field. No hysteresis is found for 4.2 and 40 K. For the intermediate temneratures the hvsteresis is similar to the one for 8 K [82kl]. -

I 30 b 20

I4

b

0

150

300

450 H-

a

600

750 Oe 900

0

150

300

450 H-

600

750 Oe 900

Fig. 277. Magnetic moment per gram, (r, vs. magnetic The isofield strength H for disordered Ni,,,,Mn,,,,. therms below T= 80 K (dashed lines) were obtained after cooling in zero field and are time-dependent [82A 11.

b -10

-40

b

H-

Fig. 278b. Hysteresis loops for disordered Ni-Mn alloys at 1.8K. Solid lines: specimens cooled in a magnetic field of 5 kOe applied parallel (left figures) and perpendicular (right figures) to the axis of measurement. Dashed lines: specimens cooled in zero field [59 K 21.

Land&-Bbmstein New Series lll/l9a

-50 -600

I

-400

-200

0

200

400 Oe fioo

HFig. 279. Hysteresis loops for the magnetization of disordered Ni,,,,Mn,,,, after cooling to 4.2 K in various magnetic fields Hcoo,[82A I], see also [59 K 21.

Adachi

418

1.2.3.12 Ni-Mn

[Ref. p. 480

l( k[ c 600

t1

,

I

I

RT

/I

I

\I

I

OrUeiPd

7 E I F I 3 2 1 0I 16

E;

I, = 275h

F

Ni-26.6at%Mn

600 I 18

I 20

I 22

I 21 b!n -

I 26

I 28

I

I I 30 OR32

Fig. 280. Effect of fast-neutron irradiation of initially ordersd Ni Mn alloys at room tcmpcraturc (neutron energy in excess of 0.5 MeV) on the magnetization 4rr.U in a magnetic field of 20 kOc. Maximum tempcrature of the specimen during radiation is 50 “C [54A I]. The integrated neutron flux during irradiation is indicated. Dashed lint: 4n1W for thermally disordcrcd Ni Mn alloy (annealing tempcraturc 1000°C). 0

150

300

150

600

K

750

Fig. 281. Temperature variations of the saturation magnetization of(a) Ni-24.6 at% Mn and (b) Ni-26.6 at% Mn alloys. The numbers in the figures indicate annealing time t, for (a) 427°C and (b) 445°C [SS H I].

100

200

300

100

500

600 K

I-

Fig. 282. Spontaneous magnetization 47cM, vs. tempcraturc for various homogeneous states of order of Ni,Mn alloys. The long-range order parameter S gives the ratio of the integrated intcnsitics of a fundamental and a superlattice reflection observed by neutron diffraction. S=O and S= 1 mean complete disorder and complete order, rcspcctivcly [66P I], see also [6l M I] and [SS K I].

Adachi

700

Ref. p. 4801

1.2.3.12 Ni-Mn

419

Table 67. Magnetic properties of stoichiometric NiMn. Phln,pNiand Hhyprefer to 0 K. For spin arrangement in the antiferromagnetic phase, see Fig. 288. Crystal structure fct CuAu-type I)

Magnetism

AF

TN K 1073(40) [68 K l]

PMn

PNi

fby,i5

5Mn)

PB

kOe

3.8(3) <0.6 [68 K 11 [68 K l]

235 “) [67 P 11

‘) a=3.74& c=3.52k “) Long-range order parameter S=O.9.

Table 68. Magnetic properties of stoichiometric Ni,Mn. j& PM,,,pNi and Hhyp refer to OK. Order-disorder transition temperature: 510 “C!. Crystal structure ordered disordered

fee Cu,Au-type fee

Magnetism

F

T,

Pai

PMn

K

PB

PB

753 [48 K l] 132 [58 K l]

F

PNi

kOe

3.83 ‘) [63 P 21

0.47‘) [63 P 21

0.73 [58 K l]

‘) Determined from an ordered sample having the long-range order parameter of 0.74.

Table 69. Electric and magnetic properties of Ni,Mn at room temperature after different heat treatments [54 T 1-J.The respective quenching temperature is indicated. Q: resistivity, M: magnetization, T,: Curie temperature, x0: initial susceptibility, 1,: saturation magnetostriction.

disordered 530 “C 510°C 500 “C 480 “C 460 “C 400 “c! 360 “C ordered

Landolt-Bdmsfein New Series III/l9a

@O “C) Pfi

M(lOOOe) G

T, “C

73.8 69.1 63.7 60.8 50.8 44.4 28.1 25.0 22.2

90 287 335 347 583 743 745 745

363 383 415 458 476 488 486

Adachi

x0

3 7 19 46 92 101 87 87

ffhyp(5‘MN

4 10-6

0.2 -0.8 - 1.0

334.5 [67 P l] 258.7 [67P l]

[Ref. p. 480

1.2.3.12 Ni-Mn

420 1.0 Ps

7

Ni -in

0.9

/'

I

1

1.5

0.8

2 1.0

il.7

f

.

0.5 I“‘--

0.6

01 0 Mn

I 0.5 12

10

20

30

1

Klot% 50

NI -

Fig. 284. Avcragc ordered magnetic moment per atom. pal. for y-Mn-Ni alloys, as derived from neutron polarization analysis of diffuse neutron scattering. Extrapolation to pure antiferromagnetic y-Mn gives pbln= 2.4 un [8 I M I]. T=4.2 K.

0.4 0.3 0.2 -

al A2 0.1 -• 3 -2-L 1 0 5 0

I

1

Ni-Mn I DT 10

Ni

15 Mn-

20

25 at%

Fig. 283. Average magnetic moment per atom, j,,, as derived from magnetization mcasurcmcnts at low tempcrature for disordered Ni-Mn alloys, 1: [31 K I], 2: [32 S 11, 3: [53P I]. 4: [78T I].

6” 1.0 P? Ni-Mn Ni-Cr

v A

VJ c

I 0.5

,h

0 27.0

27.5

28.0 n-

28.5

Fig. 2S6. Average magnetic moment per atom. &, for disordered Ni-M alloys as a function of the average number n of 3d and 4s electrons per atom, as derived from magnetization measurements at 4.2 K [S3 S 21.

61b 0 Ni

i 5

15

10

20 at%

Mn -

Fig. 285. Magnetic moment distribution in Ni-Mn alloys. (a) Room-temperature measurements. Derived from (solid circles) polarized neutron Bragg scattering [79K l] and (open circles) polarized neutron diffuse scattering [SOK I]. Open triangle: [66 M 11, squares: [74 C I], solid triangle: [55 S I] for ordered MnNi, alloy. (b) Mcasurcmcnts at 4.2 K. Solid circles: [79 K I], open circles: [74C I], squares: [SOK I]. See also [7ST I].

Adachi

421

1.2.3.12 Ni-Mn

Ref. p. 4801

NiMn

2.5 Ps

ordered

2.0 1.5 I 4 1.0 0.5 0 Mn

0 Ni -

Fig. 287. Composition dependence of the average magnetic moment per atom, pat, and of the Mn moment pr,,” for y-Mn-Ni alloys, derived from neutron Bragg scattering experiments at 4 K. The Ni moment is 0.1(l) pg. The solid curves are extrapolated to & = 2.4 pn for pure antiferromagnetic y-Mn [81 M 1, 82M 11,

Mn

0

Ni

Fig. 288. Spin structure of ordered NiMn [59K 11. The black and white circles denote Mn and Ni atoms, respectively. The moments are determined to be phln=4.0(1) and Pni=O.6un. The other possible spin structure is discussed in [59 K 11. 0.25 PB

100

0

200 H-

300

kOe

LOO

Fig. 290. Magnetization curves of disordered Ni-3d alloys at 4.2 K [83 S 21. The magnetization is expressed as an average magnetic moment per atom. Table 70. g-factors derived from ferromagnetic sonance experiments for polycrystalline Ni-Mn loys. 24.59 GHz [55 S 21, 34.88 GHz [SS B 11.

TWI

X

at% Mn 0 1.2 Fig. 289. Magnetic structure of y-Mn alloys derived from neutron diffraction spectra for c/a< 1 and cfa> 1 [71Ul].

5.1 10.1 13.5

Landolf-Bbmstein New Series II1/19a

Adachi

20 20

200 20 200 20 200 20 150 175

real-

9 24.59 GHz

34.88 GHz

2.17 2.17 2.19 2.14 2.15 2.13 2.12 2.12 2.10 2.11

2.19 2.21 2.18 2.14 2.13

1.2.3.12 Ni-Mn

Ni

[Ref. p. 480

Mn-

Fig. 291. High-field magnetic masssusceptibility ,y,,r>of Ni -Mn alloys at 4.2 K mcasurcd in pulsed magnetic ticlds up to 300 k0e [83 K 23.

0

0.5

1.0 x/x, -

1.5

2.0

Fig. 292.High-field magneticsusceptibility of disordered Ni ,-,Mn,.Ni,-,Cr,,Ni,-,V,andNi,-,Cu,alloys as a function of x/x,, where x, is the critical concentration for which the spontaneous magnetization of the alloy bccomcs zero. [83 S 21.

Table 71. Effective magnetic hyperfine field Hhyp,errfor “Mn and magnetic moment data for the Mn-Ni alloys, T=0.3...4K [67P 11. Alloy

y-Mn MnNi ordered MnNi, disordered partly ordered ordered Mn dilute in Ni ‘1 *) 3, 4, ‘)

PM”

~h,,,,ff(55Mn)

~h,.,,cd55MnYphln

Number of nearest neighbors of the Mn atoms

PB

kOe

kOe pi1

Mn

Ni

57 1) 235 259 318 335 295 “)

24(t) 59(2) g(7) lOO(8) 105(8) 123(5)

f4,18 5, 14.2 13 11.5 10.3 0

-

2.4 4.0 2) 3.183, 2.4

Assuming H,,,,,,, to be negative in y-Mn [64H 11. [59K 11. C55.5I]. [63C2]. 11 indicates moment parallel or antiparallel to host atom moment.

Adachi

7.8

0 0.3

fE.5

0.3

Ill.7 t12

0.3 0.6

1.2.3.12 Ni-Mn

Ref. p. 4801

250

260

270

260

270

280

280

290 MHz 300 300

310

330

320

340

MHz 350

MHz 290

T= 210K

T= 4.2 K l 0.5at% Mn 02 a3

l

345

350

355 Y-

Fig. 293a, b. Line shapes of NMR spin-echo spectra of 55Mn in Ni-Mn alloys at various temperatures [81 Y 11.

Land&Bbrnstein New Series 111/19a

Ada&i

360

0,5at%Mn

365 MHz 370

[Ref. p. 480

1.2.3.12 Ni-Mn

325

225

201,

175 375 b!H:

I

I

I

I

NIo.9iMn0.03

I

I

I

300

LOO

353 - I 325 2 z 5 303

275 253 b 100

200

500 K E

Fig. 293. Temperatures dependence of NMR frequency vr for “Mn in (a) Ni,,,,Mn,,,, and (b) Ni,,,,Mn,,,,. Solid line: main resonance frequency, dashed line: satellite 1, dashed-dotted line: satellite 2 [Sl Y I].

0.2 I 0

I 100

200

300

100

500

600 K 700

TFig. 295. NMR frequency v, of the main resonance. normalized to the frequency at 0 K, for “Mn in Mn-3d transition metal alloys. Also shown are the temperature depcndences of the reduced spontaneous magnetizations oJos(OK) of Ni and Fe [8l Y I].

425

1.2.3.12 Ni-Mn

Ref. p. 4801

Ni-Mn T= 1.4 K

0.4-

1

Sat%Mn

I

0

I

I

I

lOat%Mn

4x10

2-

I

0

25at%Mn

4-

125

x500

xl0

0.2 -

150

175

200

225

250

275

300

325

350MHz375

Y-

Fig. 296. Spin-echo NMR spectra for 55Mn in Ni-Mn alloys at 1.4K. The dashed curves show the line shape in an applied field of 15 kOe [78 K 11, see also [68 S4, 63 K2].

Landolt-Biirnstein New Series 111/19a

Adachi

426

[Ref. p. 480

1.2.3.12 Ni-Mn

Ni0.685 Mn 0.315 T = 1.8K

Ni3.685 M”

T = 1.8K

0.315 2.1

H: = 9.2 kF 5.7

slou:ly cooled

0

150

200

250

300

350

400 t4Hz L

Y-

1

-?!

I

I

I

I

I

-8

-4

0

4

8 kG 12

J

Fig. 298. NMR spin-echo spectra for “Mn in Ni o.6s5Mno.3~5at 1.8K and without applied magnetic field. The sample is cooled from room temperature to 1.8K in a field H, = 12kOc. (a) Slowly cooled from 900°C to room temperature, (b,c,d) quenched from TAQ= 600,700 and 900 “C, respectively, to room temperature. H, is considered to be the unidirectional anisotropy field [83 S I].

if,;-: Fig. 297a. hqaximum of the NMR spin-echo signal along a hysteresis cycle for “Mn in disordered Ni,,,Mn,,, cooled to 1.8K in a freezing field of 12kOe. set subscript Fig. 297b. The spectrum has a width of ~30 MHz and a maximum at about 200 MHz [83 S 11. Fig. 297b. Masimum of the NMR spin-echo signal for “Mn in Ni,,,,,Mn 0,3,5 at 1.8K as a function of an applied field H,,,,. The samples were furnace-cooled from 900 to 50 “C in 2 h. Afterwards all but one sample wcrc heated to &. qucnchcd to room temperature and cooled to 1.8K in a freezing field H, = 12 kOe. A positive value of H app, means H,,,,\IH,. H, is considered to be the unidirectional anisotropy field [83 Sl].

Adachi

427

1.2.3.12 Ni-Mn

Ref. p. 4801 200 meV

I

I

I

Y-Mn0.73Ni0.27

150

I $100 rc:

50

5

0 Ni 9-

75

0

I

n

ti

fee

5

IO

15

20 at%

25

Mn-

Fig. 301. Values of the effective exchange integrals J,,, for fee Ni-Mn alloys, derived from the spin wave stiffness constants shown in Fig. 300. Open circles and triangle: [77 H 11, solid circles: [75 M I].

Table 72. Values of the pair exchange integrals Jij for Ni-Mn alloys, as derived from the stiffness constants D

of Fig. 300,taking into account the room-temperature experimentalmagneticmoments of Fig. 285a [77 H 11.

JNi-Ni

JNi-Mn

JM”-M~

Ref.

13.4(12) 44(5)

- 120.1(18) - 285(30)

77Hl 75Ml

meV 50.7(2) 52(5)

Landolt-Bdmstein New Series 111/19a

20 at%

25

Mn -

Fig. 300. Spin wave stitfness constant D for fee Ni-Mn alloys, at room temperature. Curve 1: inelastic neutron scattering on single crystals [77 H 11,curve 2: small-angle neutron scattering [75 M 11.

Fig. 299. Spin wave dispersion curve for y-Mn,,,,Ni,,,,, at room temperature [76 H 1J.

meV- Ni-Mn

15

10

Adachi

428

[Ref. p. 480

1.2.3.12 Ni-Mn 12.5 kG

30 .lO? Gt Cl+

10.0 20 I <

1.5 I s

10

5.0

2.5c Hon1 -

Fig. 302. First-order magnctocrystallinc anisotropy constant K, derived from torque mcawrcmcnts on a single crystal of Ni,Mn in various states of atomic order. Crosses: [IOO] mag,netic field cooling, triangles: [OIO] magnetic field coolmg. circles: zero-field cooling. The specimen was annealed at 420 “C for 230 h [67 S 21.

0 20

25

30

01% 35

Mn-

Fig. 303. Unidirectional magnetic anisotropy field H, for disordered Ni-Mn alloys at 1.8K. Samples cooled from room tempcraturc to 1.8K in a magnetic field of 20 kOe. Open circles: NMR measurement [83 S I], solid circles: magnetization measurement [59 K 23.

0 .10-' 4

I -8 ci

-12 -16 ,

150

100

200

250

K

300

Fig. 305. Temperature dependence of the magnetostriction constants I.,,, and 1, I, in an ordered Ni,Mn allo) [62Yl].

77K G

I. Er

I 5

I 10

I 15

I 20 ot%

I

25

Mn -

i ‘100

-13.5.10-6

I 11,

-

2.5.10-6

RT -3.7.10-6 -0.5'10-6

Fig. 304. Composition dcpcndcncc of the linear magnetostriction constants I.,,, and I., , , of disordcrcd NiMn alloys [62 Y I].

Adachi

I.andoll-Rnrnrrcin Ncu Sericr III ‘198

20 ;',o"'f

-2

0

429

1.2.3.12 Ni-Mn

Ref. p. 4801

100

I Ni-Mn

A quenched from L8O"C I I 300 400 "C 500

200 7-

Fig. 306. Linear saturation magnetostriction A, vs. temperature T for Ni,Mn in various states of atomic order [54T 1J.

-201 0

0.2

0.4

0.6

0.8

1.0

1.2

7/7, Fig. 307. Temperature dependence of the forced volume magnetostriction dw/dH for disordered Ni-Mn alloys, as derived from strain-gauge linear magnetostriction measurements [SOT 11. 25,

I

I

I

I

I

I

0.5

1.0

1.5

2.0 T-

2.5

3.0

( (

0

I

1

3.5 K

LO

( (

Fig. 308. Specific heat C, of Ni,Mn and NiMn [67P 11. A,...&: Ni,Mn disordered, (A,) annealed for 2h at 900 “C and then quenched to room temperature, (AZ) after annealing for 100h at 465 “C, (A3) after a further anneal for 900 h at 400 “C, producing a high degree oflong-range order. NiMn, ordered. Land&Bornstein New Series 111/19a

Adachi

430

1.2.3.12 Ni-Mn 10

3.75 a

mJ K!V3!

3.70

8

c? o 3.65

6

3.60 0.2 &I I gK 2 0.1

I x L

0 100

2

0 0 II 43

[Ref. p. 480

200

300

LOO K

500

I-

20

10

60

80 at% 100

NI -

Ni

Fig. 309. Electronic spccitic heat cocffcient 7 for Mn Ni alloys. Open circles: [64G I]. solid circles: [67P I]. For A,...A, see caption to Fig. 308.

Fig. 310. Tcmpcraturc dcpcndcnces of the lattice paramctcrs a and c, the intensity of (I 10) neutron diffraction line and the spccilic heat C, of y-Ni,,,Mn,,2. 7;: tetragonal transition tcmpcraturc, TN:N&l temperature [71 u I].

Table 73. Specific heat parameters for MnNi and MnNi, according to the equation C,=yT+flT3+x7-*, where ;‘is the electronic, /I the lattice and x the nuclear specific heat coefficient. Also given is the effective magnetic hyperfme field Hh!p,clr for “Mn derived from the Schottky specific heat anomaly [67P 11.

MnNi MnNi,

Ordering

Y mJK-*mol-’

P mJK-4mol-’

x mJKmol-’

ffh,.,.,rX5SW kOe

ordered disordered ‘) A,

1.244(25)

0.0199(16)

1.728(28)

234.8(24)

8.845(50) 5.348(76)

A3

3.923(8)

0.152(27) 0.149(27) 0.052(2)

1.034(20) 1.559(46) 1.731(2)

258.7(27)

A2

‘) For A, . ..A.. seecaption to Fig. 308.

Adachi

317.7(62) 334.5(62)

Ref. p. 4801

1.2.3.13 Mn-Cr-V

431

1.2.3.13 Mn-V-Cr References:67 K 1, 73 T 1, 75 K 1, 76 A 5, 77 A 1, 79 M 3, 80 M 1, 80 M 3, 81 M 2.

Cr

-g Al! v

VMn

Mn

Fig. 311. Contours of the lattice constant, in [A], for disordered bee V-Cr-Mn alloys [SOM 31.

0 0

0.05 0.10 0.15 0.20 0.25 x-

Fig. 312. Lattice constant a and NCel temperature TNfor V~.dCrl-Pn,h,9~

Landolt-BOrnstein New Series 111/19a

alloys WM31.

Adachi

432

1.2.3.13 Mn-0-V

I

I

3[ 40' Hrnl F3 2:

[Ref. p. 480

I (VII.25 Mn0.75)x

Crl-x

?LrT-l-li

2[ I sl:

1C

c

t

C 21 .10-l Hm -6 18

I

15

12 I a? 9

6

I

t 0

t

t

1

t

x zero

0.5 0.7 0.8 0.9 1.0 x = 0.6

2.5 3.0 1.5 2.0 1.0 1.25

x = 0.L 0.1 0.3 Cr 0.2

0.75 0.05 0.5 -

800

1000

I I

200

600

400 r-

Fig. 313. Magnetic mass susceptibility xs vs. temperature for (a) CIo.25Mno.75)~Crl --I and Co) (Vo.sMno.5Kr~ -I alloys. Vertical arrows indicate the N&cl temperature as determined from electrical resistivity measurements. while horizontal arrows indicate increasing or decreasing temperature [80 M 33. xp: 10-‘4Hm2kg-1;(10/4~)2~ 10-6cm3g-‘.

K

1200

Ref. p. 4801

1.2.3.13 Mn-Cr-V

Cr

v

Mn

VMn

V

Fig. 314. Magnetic phase diagram of V-Cr-Mn alloys in the bee phase. BP and BPA mean the band (Pauli) paramagnetic and antiferromagnetic phases, respectively. CWP is the Curie-Weiss-type paramagnetism [SOM 33. The broken curve is the boundary for the appearance ofa localized magnetic moment. The numbers give TNin [K].

VMn

Mn

a Cr

Fig. 315a. Curie temperature Tcw ofthe weak ferromagnetism in V-Cr-Mn alloys (bee). [SOM 31. Fig. 3 15b. Average magnetic moment per atom, &,, of the weak ferromagnetism of V-Cr-Mn alloys [SOM 31.

VMn

Table 74. NCel temperature TN, average magnetic moment per atom, p, and wavevector Q of the spin density wave for V-Cr-Mn alloys [67 K 11. T = 77 K.

K

at% Cr Cr-V Cr-Mn Cr-V-Mn

Land&Bornctein New Series 111/19a

0 0.45 1.00 0 0 0.40 0.54 0.51 0.59 0.54 0.57 0.52

0

0 0 0.70 1.85 0.34 0.86 1.07 1.18 1.66 2.47 3.60

310 268(5) 220(5) 440(5) 545(5) 290(5) 360(10) 410(10) 430(10) 470(5) 526(5) 600(5)

Ada&i

VB

0.40(2) 0.36(3) 0.28(3)

0.9518 0.9431(25) 0.9300(25)

0.38(2) 0.39(2) 0.44(2) 0.65(2) 0.69(2) 0.67(2)

0.9450(25) 0.5550(25) 0.9575(25) 1.0000 1.0000 1.0000

Mn

434

1.2.3.13 Mn-Cr-V

[Ref. p. 480

1.5 *lo-' Wbm kg 5.0 I

b 2.5

0 'I.5 .lO-' Wbm kg 5.0 I b

2.5

II 0

20

40

60

80

K 100

Fig. 317. Magnetic moment u vs. temperature for (Vo.5Mno.5LCr, --I alloys in a magnetic field of H=215kA/m [80M3].

I 6

b 4

300

6

L -I LL 900

f k 1200 kA/ml!

H-

Fig. 316. Magnetic moment 0 vs. magnetic licld strength H for (Vo,sMn,,),Cr, -I alloys at 4.2K [8OM 33.

V0.075 cr0.721 Mn0.2~3

Fig. 318. NMR spin-echo spectra of 55Mn and “V in antiferromagnetic V-Cr-Mn alloys at 1.4K and zero applied field [75 K I].

Adachi

Ref. p. 4801

435

1.2.3.14 Fe-V-Cr 70 kOe 60

Fig. 319. Hyperfine magnetic fields at 55Mn and ‘lV in V-Cr-Mn alloys as dependent on the number n of4s and 3d electrons per atom [75K 11. Solid line: 55Mn in Cr-Mn [73T 11, crosses: samples of Fig. 318, circles: %889Mno.lll; Vo.020Cro.881Mno.099 and V o.~31Cro.s75Mno.094 [73 T 11. T= 1.4K.

1.2.3.14 Fe-V-0 References: 77 A 3, 78 H 1. 75 40-f gJ 9

45 I m x 30

15

0

50

100

150 T-

200

250

I---l 300 K 350

Fig. 320. Magnetic mass susceptibility xs of Feo,030V,,,,,Cr,,,,, vs. temperature, measured at HaPP,= 5.2 kOe. There is no field dependence found up to about 6 kOe [77A3].

101 0

50

100

law

TN K

A

0

250 162 108

3.34 3.20 3.16

692.0 695.4 693.3

- 16.9 - 14.8 - 14.3

4.29 3.98 3.74

335.90 519.2 580.7

-

0 0.5 1.0

Landolt-Bbmstein New Series 111/19a

Curie-Weiss

V at%

0.5 1.0

T
200

250 K 300

Fig. 321. Electrical resistivity QofFe,,,,V,Cr,.,,-, alloys vs. temperature. The arrows indicate the Ntel temperatures defined as the temperature for minimum de/dT [77A3].

Table 75. Susceptibility data fitted to the modified xa=A+C,/(T-O) for Fe,,e3Cr,,97-xVx alloys [77A3].

T>T,

150 T-

10F6 cm3 g-r

Adachi

0

c,

10-6Kcm3g-’

K

3.7 6.6 7.2

Ref. p. 4801

435

1.2.3.14 Fe-V-Cr 70 kOe 60

Fig. 319. Hyperfine magnetic fields at 55Mn and ‘lV in V-Cr-Mn alloys as dependent on the number n of4s and 3d electrons per atom [75K 11. Solid line: 55Mn in Cr-Mn [73T 11, crosses: samples of Fig. 318, circles: %889Mno.lll; Vo.020Cro.881Mno.099 and V o.~31Cro.s75Mno.094 [73 T 11. T= 1.4K.

1.2.3.14 Fe-V-0 References: 77 A 3, 78 H 1. 75 40-f gJ 9

45 I m x 30

15

0

50

100

150 T-

200

250

I---l 300 K 350

Fig. 320. Magnetic mass susceptibility xs of Feo,030V,,,,,Cr,,,,, vs. temperature, measured at HaPP,= 5.2 kOe. There is no field dependence found up to about 6 kOe [77A3].

101 0

50

100

law

TN K

A

0

250 162 108

3.34 3.20 3.16

692.0 695.4 693.3

- 16.9 - 14.8 - 14.3

4.29 3.98 3.74

335.90 519.2 580.7

-

0 0.5 1.0

Landolt-Bbmstein New Series 111/19a

Curie-Weiss

V at%

0.5 1.0

T
200

250 K 300

Fig. 321. Electrical resistivity QofFe,,,,V,Cr,.,,-, alloys vs. temperature. The arrows indicate the Ntel temperatures defined as the temperature for minimum de/dT [77A3].

Table 75. Susceptibility data fitted to the modified xa=A+C,/(T-O) for Fe,,e3Cr,,97-xVx alloys [77A3].

T>T,

150 T-

10F6 cm3 g-r

Adachi

0

c,

10-6Kcm3g-’

K

3.7 6.6 7.2

436

1.2.3.15 Fe-Cr-Mn

[Ref. p. 480

1.2.3.15 Fe-Cr-Mn References: 62 S 1, 82 R I, 83 E 2.

Fig. 323. NMR spin-echo spectrum for “Mn in disordered (Fe, -,Cr,),,,,Mn,,,, alloys at I .7 K [83 E 23. MHz Fig. 322. NMR spin-echo spectrum for “Fc in disordcrcd (Fc, -,Cr,)o,9sh4no,o, alloys at 1.7K [83 E2].

26f

kOt

I

-1

I

1

~hxCrxh.99Mno.ol

r’

P

I

I = 1.7K -1

251

- 1)

31.

‘i,.

-0

Fig. 324. “Mn hyperfinc magnetic field. I?,,,. corrcspending to the center ofgravity ofthc spectra ofFig. 323 and the Mn average magnetic moment. j$,,“, for disordcrcd (Fe, -rCrr)0,99Mn0,0, alloys at I .7 K [83 E 21.

0.05

0.10

0.15 x-

0.20

0.25

13.3;

437

1.2.3.16 Co-V-Cr

Ref. p. 4801

1.2.3.16 Co-V-Cr References:77 A2, 77 M 5. Table 76. Magnetic properties of Co impurities derived from measurementsof the Co contribution xi to the magnetic susceptibility of Co,,,,(Cr, -xVx),,99 alloys, xi =x0 + C,/( T- 0). perr: effective magnetic moment derived from the Curie constant C,, 0: paramagnetic Curie temperature, TN: Ntel temperature; see also Fig. 14 [77 A2]. 0

0.1

0.2 x-

OY3

0.4

Fig. 325. Effective magnetic moment, perr,for Co in CO~,~,(V,C~,-x)o,99 alloys, derived (open circles) from susceptibility vs. temperaturemeasurements[77 A21 and (solid circles) from 5gCoNMR spectra [77 M 51.

X

X0

10-6cm3g-1 0 0.03

0.05 0.10 0.15 0.20 0.25 0.30

O.OO(5) 0.05(S) 0.02(l)

O.OO( 1) 0.15(5) 0.08(5)

0.29(8) -

0 K

Peff

pa

K

O(5) 26(5) 25(5) 5(5) lO(5) 5(5) ll(5)

3.0(l) 2.8(l) 2.6(l) 2.4(l) 2.2(l) 1.5(l) 0.8(2)

300 70 25

-

T-4

-

0.0(l)

I --L-,- ’

P-__~_qC00.01(VxCrl-x)0.99 T=l.2K

4,

\ \ ‘4

I 0 V

0.2

0.4

0.6 x-

0.8

1.0 Cr

Fig. 327. Knight shift K of 5gCo vs. V content in the paramagnetic state of Co,,,,(V,Cr, -&a9 at 1.2K [77 M 51.

0.05 , 0.06

, 2 30

LandobB6mstein New Series III/I%

40

50

60

70 MHz

Fig. 326.Spin-echoNMR spectraof “Co in the antiferromagneticstateof (dashedline) Coo,o,(V,Cr, -x)o,ggand (solid line) Co,,,,(V,Cr, -x)o,g7alloys [77 M 51.

Adachi

438

1.2.3.17 Co-Cr-Mn 1.00 % by(VxCh-x 0.75

I

--.

h-y -

T

p. 480

Ll.ZK

_

l x=0.25

-i

[Ref.

--

-7

4

025

' x=0.2 i

0

1-q 1 0.50 0.25 Il.25 Y-

0.75 % 1.00

.

.

Fig. 328. Knight shift K of 59Co vs. Co content in the pnramagnctic state of Co,(V,,,,Cr,,,,), -y and CO~(V~.~C~~.~), -y alloys at 1.2K [77 M 51.

0 0

P 0.2

0.4

V

0.6 x-

0.8

1.0

Cr

Fig. 329. Nuclear spin-lattice relaxation time T,, (expressed as its product with tcmpcraturc 7’) of “V and ‘“Co in Co,,,,(V, -rCrX)0,99alloys, measured at 77 K and 1.2K, rcspcctivcly [77 M 5-J.

1.2.3.17 Co-Cr-Mn Reference: 74 K 1.

a-Mn I =1.4 K

coQ.D192 Cr0.n3 b,gso6 J I

190

200

MHz 210

Y-

Fig. 330. Spin-echo NMR spectra of “Mn cr-CoCrMn alloys at I .4 K [74 K I].

Adachi

at site I in

I nndoll.Rnrnrrrin Sea Scricr III

192

438

1.2.3.17 Co-Cr-Mn 1.00 % by(VxCh-x 0.75

I

--.

h-y -

T

p. 480

Ll.ZK

_

l x=0.25

-i

[Ref.

--

-7

4

025

' x=0.2 i

0

1-q 1 0.50 0.25 Il.25 Y-

0.75 % 1.00

.

.

Fig. 328. Knight shift K of 59Co vs. Co content in the pnramagnctic state of Co,(V,,,,Cr,,,,), -y and CO~(V~.~C~~.~), -y alloys at 1.2K [77 M 51.

0 0

P 0.2

0.4

V

0.6 x-

0.8

1.0

Cr

Fig. 329. Nuclear spin-lattice relaxation time T,, (expressed as its product with tcmpcraturc 7’) of “V and ‘“Co in Co,,,,(V, -rCrX)0,99alloys, measured at 77 K and 1.2K, rcspcctivcly [77 M 5-J.

1.2.3.17 Co-Cr-Mn Reference: 74 K 1.

a-Mn I =1.4 K

coQ.D192 Cr0.n3 b,gso6 J I

190

200

MHz 210

Y-

Fig. 330. Spin-echo NMR spectra of “Mn cr-CoCrMn alloys at I .4 K [74 K I].

Adachi

at site I in

I nndoll.Rnrnrrrin Sea Scricr III

192

Ref. p. 4801

1.2.3.18 Fe-Co-Ti

1.2.3.18 Fe-Co-Ti References: 6232, 67D1, 67D2, 68B1, 68G1, 68P2, 68S3, 7OS1, 73A2, 78B3, 78B4, 79B1, 79B2, 80B3, 81B2, 81H1, 83A2.

.I04

9

FexCol.,Ti

cm3

Fig. 331. Inverse magnetic mass susceptibility, xi ‘, of Fe,Co,-,Ti alloys vs. temperature [73A2], see also [67 D 21.

For Fig. 332, see next page.

Fig. 333. Relative pressure derivative T,-%T&@ of the Curie temperature T, for stoichiometric (Fe, -,Co,)Ti, (solid circles: Co-rich, open circles: Fe-rich) and offstoichiometric (Fe,,,Co,,,), --yTiy compounds [Sl B 21.

Land&B6mstein New Series III/l9a

0

25

50

75 K 100

[Ref. p. 480

1.2.3.18 Fe-Co-Ti 10 G& 9

Fig. 332a. Fcrro- and paramagnctic Curie tcmpcraturcs. Tc and 0, respectively, spontaneous magnetic moment at 0 K, a,(O),and the electronic specific heat coeflicicnt 7 of Fc, -,Co,Ti alloys [73 A2].

8 1 2L

Fig. 332b. Curie temperatures T, of Fe, -,Co,Ti alloys [79B2].

6 ;

mJ K2mo!

Fig. 332~. Curie temperatures Tc of (Fe,,,Co,,,),-,Ti, alloys. Open circles: single phase, solid circles: second phase present [79 B 21.

\I 4

20

2

16

I 12

60 K

X8

10 I 0 20 ,75 K

0

0 Fe6

a

EC-

0.2

G.4

0.6

0.8

x-

,20 1.0 Coli

1

SC

L-’

/

K Fe,.,Co,Ti

25

60 0 1ooc Gem’ mol

I 40 LF i/i

\

1 z

-0

0.2

b FeTi

0.6

0.4

l=OK

0.8

x-

5oc

1.0 CoTi 0 20 .m3 -cm3 mol

103 K 80

I 10 3s

60 I LY

0 -0 Coli

40

0

0.4

0.6 x-

0.8

1.0 Feli

Fig. 334. Curie temperature Tc. spontaneous magnetic moment at 0 K, D,(O),and the magnetic molar susceptibility x,, at 4.2 K in a magnetic field of lOkOe for Fe,Co, -,Ti alloys. Open circles: [78 B 31, solid circles: 0.4 c

FeLo

0.5

0.6

0.7

[73 A2].

Y-

Adachi

Ref. p. 4801

1.2.3.18 Fe-Co-Ti

441

Table 77. Effective paramagnetic moment peffand averagemagnetic moment per atom, pat,of (Fe,Co, -x)0,5Ti,,5 alloys, as derived from, respectively, the Curie-Weiss constant and the spontaneous magnetic moment 6, at low temperature [78 B 3,78 B 4,73 A 21. 0: paramagnetic Curie temperature, T,: ferromagnetic Curie temperature, y: electronic specific heat coefficient, ~nr: high-field magnetic susceptibility, p: hydrostatic pressure, M,(O K): spontaneous magnetization at low temperature, D: spin-wave stiffness constant.

X

0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00

Peff

0

PB

K

1.87 1.16 1.14 1.00 0.97 1.06 0.78 0.42 0.28 0.33 0.35

-440 -140 - 42 8 38 56 58 37 14 - 13 - 22

T, ‘) K

X

0.405 0.43 0.5 0.55 0.67 0.73 0.78

13.9 33.9 55 39.2 8.4

d T,ldp K kbar-l - 1.92 - 1.21 -0.66 -0.63 -0.16

T,

K

16.5 46.0 57.0 36.0 10.5

40 K)

Pat

Gcm3 g-r

PB

3.60 8.52 6.00 3.16 1.38

s,,sK’K) Gcm3 mol-l 317 686 993 683 435 178 113

Y

mJmol-1K-2 18.8 20.2 22.5 22.1 20.4 17.9 14.8 10.3 7.42 4.22 0.92

0.069 0.16 0.11 0.059 0.026

dW(O Wdp G kbar-’ - 13.3 - 13.7 - 3.75 - 1.6 - 1.3

XHF

D

1O-3 cm3mol-’

meV A2

2.6 2.2 2.1 1.6 1.0 0.74 -

‘Q(5) 66(7) W)

132(15) 53(5) -

‘) From Arrot plots.

Table 78. Influence of hydrogen H on the magnetic properties of a-phase (Fe, -,Co,)Ti alloys. Curie temperature T,, spontaneous magnetic moment at low temperature, o,(O),Mijssbauer linewidth r and isomer shift IS for “Fe at 4.2 K [Sl H 11.

‘W’eo.74%.26) Ti(Fe,.7,Co,.,,)H,.,,, TW%&od TWo.6Coo.4)Ho.os4 Wb.5Coo.5) TiFeo.5Coo.s)Ho.092 Whdh6) Ti(%.4Coo.6)Ho.o18

Landolt-Biirnsrein New Series lW19a

T, K

4 K) Am2 kg-’

r mms-l

36 43 57 89 56 54 22 0

4.18 6.50 7.10 9.78 8.48 6.87 4.44 0

0.42 0.44 0.56 0.48 0.58 0.56 0.57 0.51

Adachi

IS mms-’ 0.00 +0.01 -0.01 0.00 -0.01 -0.01 -0.02 -0.01

[Ref. p. 480

1.2.3.18 Fe-Co-Ti

a

0

3

9

6

12 kOe 15

Fig. 335. Magnetic moment per gram, c, vs. applied magnetic ticld Hap,,, for (a) Fe,,,CoO,,Ti and (b) Fe,,,Co,,3Ti alloys at various temperatures [73 A2].

Ho;:!IL --Gcm3 9 12

I ” b 6

HOPPl

-

Fig. 336. Magnetic moment per gram, cr, vs. applied magnetic field H,,,, for F&o, -,Ti alloys at 4.2K [78B4].

Adachi

Ref. p. 4801

1.2.3.18 Fe-Co-Ti

443

14 @ kg /

I

12

kbor

IO

1

8 0 k -10.0

" b" 6

I -12.5

I .~(Fe,.,Co,)Ti A ( Feo,sCoo.s),.yTi, I

I

4 -15.0 0

I,

I 50

25

I 75 K 100

T, -

2

0 8.2

8.3

8.4

8.5

8.6

8.7

8.8

“3d -

I

0.25

u-

I

0.50

0.75

I

I

I

0.52

0.50

0.48

Fig. 338. Relative pressure derivative o;‘(O)&rJO)/ap of the spontaneous magnetic moment crs(0) at OK for stoichiometric (Fe1 -,Co,)Ti (solid circles: Co-rich, open circles : Fe-rich) and off-stoichiometric @e,.,Co,,,), -yTiy compounds [Sl B 21.

Fe,Co,-,Ti

-Y

Fig. 337. Spontaneous magnetic moment cr,(O) extrapolated to T= 0 and H = 0, as dependent on the number nad of 3d electrons per formula unit in stoichiometric (Fe1 -.$o,) and off-stoichiometric Ti(n,, = 8 +x), (Fe,,,Co,,,),-,Ti, @ad= 13-9~) compounds [81 B2]. 16

/

@ cm3 Fe,Co,_,Ti mol

I

I

I

I

Al

HOPPl 0.2 CoTi

0.4

0.6 X-

0.8

1.0 FeTi

Fig. 339. High-field magnetic susceptibility xHF [79 B l] and the electronic specific heat coefficient y [73 A21 for Fe,Co, -,Ti alloys at 4.2 K. Landolt-Bdmstein New Series III/l%

-

Fig. 340. Typical line profiles for the NMR of 5gCo in Fe,Co, -,Ti alloys at room temperature. Shown are the dispersion derivatives at a fixed frequency of 8 MHz. The zero for the Knight shift (y/271= 1.0103kHz Oe-‘) is marked with an arrow [68 S 31.

Adachi

[Ref. p. 480

1.2.3.18 Fe-Co-Ti

444

Coli

x-

Feli

Feli

x-

Co?

3.5

%

(7;’

I 3.0

9.15 6.C

6.1

6.2

6.3

6.L

6.5

Fig. 341. Miisshaucr effect isomer shift IS of Fc, -,Co,Ti alloys relative to pure Fe [68 B I]. set also [81 H I]. II: average number of 4s and 3d electrons per atom. Q =0.529 A. The error bar for n = 6.35 is also typical for smaller rr KlluCs.

0.5

C 6

6.0

6.2

6.L

6.6

6.8

/7-

Fig. 342. Knight shift K for “Co in Fe, -,Co,Ti alloys at room temperature for (left scale) ;‘/2~ = 1.0054kHz/Oe and (right scale) y/2rr = I .0103 kHz/Oe, respectively [68 B I]. II: avcragc number of 4s and 3d electrons per atom.

I-

Fe;,zjCOo,pjTi --

2 . I ” -

L

00 %

)-

60 1-

10 I CI

I-

0 0 Feli

I-

I,

8

16

12

K’

20

I?-

Fig. 344. Tempcraturc depcndcncc ofthc spccitic hcnt C, plotted as (I) C,/T vs. T’ and (2) (C,-A)/T vs. T’ for (Fe,-,Co,)Ti alloys. The quantity A is the magnetic cluster specific heat [62 S 21: x

314

w

114

A[10-4calmol-‘K-‘]

11.4

10.0

1.5

0.2

0.L

0.6 x-

0.8

1.0 Co?

Fig. 343. Magnetic hypcrtinc field Hhyp for “Fe in Fc, -,Co,Ti alloys at 4.2K as determined from Mossbaucr spectra. The spectrum being analyzed under the assumption of the existence of a sextet plus a single lint. The zero hypcrfinc field is obtained for a fraction c of the Fc nuclei [Sl H I].

Adachi

Ref. p. 4801

1.2.3.18 Fe-Co-Ti

6.0

6.2

6X fl-

6.6

6.8

Fig. 345.Electronic specificheat coefficient y vs. average number n of4s and 3d electronsper atom for Fe,Co, -,Ti alloys. Circles: Co,,,,NiO,,l Ti, dashedcurve: beeCr-Fe alloys [62 S21.

Table 79. Parameters derived from fitting low-temperature specific heat data for Fe-Co-Ti and Co-Ni-Ti alloys to the equation C,= A +yT+/X3 [62 S 21. A: magnetic cluster specific heat, y: electronic specific heat coefficient, fi: lattice specific heat, On: Debye temperature. Y 10-4calmol-’ TiFe Ti,Fe,Co Ti,FeCo Ti,FeCo, TiCo Ti,Co,Ni

Land&-Bbmstein New Series lWl9a

- 0.2 11.6 22.3 31.0 25.0 16.8

P K-’

10-4calmol-’ 0.038 0.053 0.037 0.048 0.135 0.207

Km4

On

A

K

10-4calmol-’

495 444 502 459 325 282

21.9 7.5 10.0 11.4 2.7 5.5

Standard deviation K-r 0.036 0.015 0.067 0.045 0.025 0.047

[Ref. p. 480

1.2.3.19 Fe-Co-V

446

1.2.3.19 Fe-Co-V Reference:83 C 2.

Table 80. Average magnetic moment per atom, fixI. in [.tJ, as derived from neutron Bragg scattering analysis of various hkl lines, and from (bulk) magnetization measurements for ordered and disordered (Fe,,,,Co,,,,),V in magnetic fields up to 54kOe at 1.5 to 75K [83 C 21. hkl

111 200 220 311 bulk

ordered

disordered

0.015(5) 0.008(6) 0.010

0.090(5) 0.076(60) 0.050(21) 0.137(26) 0.054

Table 81. Average magnetic moments &, PC0and pv, of, respectively, Fe, Co and V atoms in ordered and disordered (Fe,,,Ni,,,),V and (Fe,,,,Co,,,,),V alloys and in Co-V alloys, as derived from neutron diffuse scattering at 4.2 K [83 C 23.

(Fe,,,Ni,,,),V, ordered disordered (Feo.22Coo,,8)3V,ordered disordered coo.9vo. 1 co 0.85 v 0.15

1.14(l) 0.95(3) 0.06(1) 0.23(5) -

‘) Assumed. ‘) [82C2].

Adachi

(0) ‘1 0.03(2) 1.38(1)‘) 1.05(1)2)

-0.31(2) -0.14(5) 0.005(4) (0) ‘1 -0.26(8) ‘) -0.11(3)2)

447

1.2.3.20 Fe-Co-Cr

Ref. p. 4803

Cr

320

I z 300

280

260 0.4

0.2

Fig. 346. Phase diagram (dashed lines) [32 K l] and (solid lines) linear thermal expansion coefficient GL[34 M l] of Fe-Cc&r alloys.

1.0

0.8

0.6 x-

CO

Fe

Fig. 347. NCel temperature TN of Fe-Co-Cr alloys as derived from the minima ofthe resistivity vs. temperatures curves [79 F 21.

3.0,

900lK

Ps

800I-

2.5

I

I

I

I

I

1500 K

7ocII 2.0 ,z 1.5

I 601: Ie

1cm I hy

1.0 I501:

500 0.5

401I0Cl 0 301 A.5

0.6

0.8

0.7

0.9

Fig. 348. Ferromagnetic Curie temperature Tc of as determined from magnetization Fe1 -xC40,s9%l~ measurements [70 S 31.

Landolt-Bornstein New Series llVl9a

0.4

0.6

0.8

0 1.0

x-

1

X----r

0.2

Fig. 349. Composition dependence of the average magnetic moment per atom jja, and the Curie temperature Tc and Fe,-$0, alloys [70F 11. for Fe1 -xCo,h.s9%~l The arrow below q,, maxindicates the composition giving the maximum volume magnetostriction.

Adachi

448

1.2.3.20 Fe-Co-0

[Ref. p. 480 1

1203 G

(Fei-xW0.fi9Cr0.11 I

0

150

300

750

600

Fig. 3.50. Magnetization M vs. tcmperaturc for (Fe, -XC~,)O,ROCr,,,, alloys. mcasurcd in a magnetic ticld of 100~~~2000e[70 F 11.

Fig. 351. Average magnetic moment per atom, j,,, of bee Fc-Co-Cr alloys at room tempcraturc. mcasurcd in a magnetic field of 20 kOe. AI 77K. b,, is less than 3% higher, which is within the measuring accuracy [770 I].

Table 82. Magnetic moments for Fe-Co-0 and Fe-Co-Mn average magnetic moment per atom derived from magnetization ments pFe.pco. per. phln: magnetic moments of Fe, Co, Cr and derived from diffuse scattering of polarized neutrons at RT [78

Feo.9Coo.067Cro.033 Feo,7%.2%.l Feo.9Coo.oJJno.~~ Feo..&oo.IMno.l

0.E 0

OS

0.2 0.3 x-

04

&t

PFc

PC0

2.14 2.02 2.18 2.06

2.30(2) 2.37(3) 2.30( 1) 2.21(l)

1.80 1.80 1.80 1.80

0.5

Per

alloys. P,,: measureMn atoms K 23. Phln

- 1.56(52) 0.03(20) -0.41(22) -1.11(8)

Fig. 352. Normalized avcragc magnetic moment per atom, j,,, and normalized magnetic hypcrfmc field H,,!,, for “Fe in Fc, -I(Co,,,,7Cr 0,333)ralloys at room tcmpcrature. pFe= 2.2 pa and H,,J’Fe)= 330 kOe for pure Fe arc taken as standards. Bars for @,,indicate the expcrimental errors. Bars for Hhyp indicate the values obtained from the distance between the centers of full width at half maximum of the Miissbauer spectra [77 0 I].

Ref. p. 4801

1.2.3.20 Fe-Co-Cr

449

Fe

I

b-x

1

I

( COO.667cro.333 )

T=77K

I

’

0.3

0.4

I 0.1

I

Cr

Fig. 353. Magnetic hyperfine field H,,, at Fe sites as derived from Miissbauer spectra for 57Fe in bee Fe-CoCr alloys at room temperature [770 I].

0.2 x-

0.5

Fig. 354. Normalized hyperfine field Hhyp for 5gCo in Fe, .JCo,,,,,Cr,.,,,), alloys at 77 K. The hyperfine field for x = 0.1 is taken as standard. For the bars, seecaption to Fig. 352 [770 11.

2 Ps

Feo.29Co0.62Cr0.09

fee

T= L.2 K

1

0 I 4 -1

-2

I

Feo.375c”o.53cro.095

0 Fe,-J,Co&-x l Fe,.,Cr,

bee

T=b2K

-3 0

0.05

0.10

0.15

0.20

0.25

0.30

xFig. 355. Magnetic moments ofCr and Mn atoms, perand pMn,respectively, as determined from polarized neutron scattering experiments on Fe-Co-Cr and Fe-Co-Mn alloys at RT [78 K 21. Fe, _ 3XCozXCrX,Fe, -&o,Mn, [78K2], Fe,-,Cr, [76A3], Fe,-,Mn, [75N2].

300

200 Hhyp (57k)

kOe L

-

Fig. 356. Distribution function P(H,,,,J for the magnetic hyperfine field at 57Fe derived from Mossbauer spectra for Fe-Co-Cr alloys at 4.2 K [79 H 11.

Landolt-Bornstein New Series lll/l9a

Adachi

1.2.3.20 Fe-Co-Cr

[Ref. p. 480

15.0 10-3

8

16

135

11

12.0

12

10.5 1

10

9.0;

8

7.5

6

6.0 6.5

2

0950 0.55 0.60 0.65 0.70 0.75 0.80 0.85 0.90

xFig. 357. Spontaneous volume magnctostriction q(0) at T=O K. linear thermal expansion cocficicnt c( at 800 K and minimum thermal expansion cocficicnt amin for Fc, -rcor)0.89cr0.11

alloys c7os

31.

8.0 - COI

molK I 7.0 9 6.5 6.0 100

150

200

250

300

350

LOO 450°C 500

Fig. 358. Molar specific heat C, for Fe-Co-Cr alloys [79 H I]. Arrows indicate the Curie tcmpcraturc T,.

Ref. p. 4801

1.2.3.21 Fe-Co-Mn

451

1.2.3.21 Fe-Co-Mn References: 63C5, 64G1, 64M2,

72A1, 73A1, 73M1,

co I 9.0

CoMn I 8.0

I 8.5

a

74Y1, 75N2, 7701,

I 1.5

Mn I 7.0

en

Fe

co 9.0

b

CoMn 8.0

8.5

Mn 1.5

7.0

-/T

Fig. 359. Crystallographic phase diagrams for Fe-Co-Mn alloys [73 M 11. (a) Samples (indicated by circles) cooled slowly from 1000 “C to room temperature during one day. @) Samples quenched from 1000°C into water. An indication of the magnetic state is given. The thin curves give the lattice constant a, in [A], for the fee lattice. n: number of 4s and 3d electrons per atom.

Landolf-BOrnstein New Series 111/19a

Adachi

78K1, 78K2, 78K4.

1.2.3.21 Fe-Co-Mn

[Ref. p. 480

IV

-cm3 9 2.2

-

I

-

I_ I

0.667 1 0.70

0.80

s

0.90 FeMn

0.5I 0

200

400

600 T-

800

1000

K

1200

I

Fe

I

-

lo lob’” Mn x = 0.5

Fig. 360. Magnetic mass susceptibility xe vs. tempcraturc in the antifcrromagnctic y-phase of (FcMn)$o,-, alloys. Vertical arrows indicate N&l tempcraturc TN and E+Y transformation temperature, horizontal arrows indicate decreasing or increasing tempcraturc [73 M I].

-2.1 c,

I

I

I

A

-

N

‘-

1.2

0.8I 0

200

LOO

600

800

1000

K

Fig. 361. Magnetic mass susceptibility xg vs. tempcraturc for Fc,(CoMn), -I alloys. Vertical arrows indicate N&l tempcraturc TN,horizontal arrows indicate decreasing or increasing tempcraturc [73 M I]. II: number of4s and 3d electrons per atom.

1200

453

1.2.3.21 Fe-Co-Mn

Ref. p. 4801

K Fe,(CoMn)l-,

1 n=8

/

A 2.0 c-z I 200

I

1.6 x

t

100

1.2

0 -0 CoMn

0.2

0.4

0.6

0.8

x-

0.8 1.0 Fe

3.64 H

Fig. 362. The NCel temperature TN and the magnetic mass susceptibility xp at 78 and 1000 K vs. composition for the alloys Fe,(CoMn), -x. Average number of 4s and 3d electrons per atom, n = 8 [72 A 1,73 M 11.

I 3.60 0 3.56

3.52 0

0.2

0.4

0.6

0.8

I 9.0

I 8.7

I 8.4 -n

, 8.1

I 7.8

co

4s .10-!

1000 K

cm 9 3.:

800

2.1

I

600 I z

N” l.E

x-

1.0 FeMn I 7.5

Fig. 363. Curie temperature Tc, NCel temperature TN, spontaneous magnetic moment per gram es at OK and lattice parameter a at room temperature vs. composition for the alloys (FeMn)xCo,-x, see phase diagram Fig. 359a [72A 1,73 M 1). n: average number of 4s and 3d electrons per atom.

400

200

0 IRT I 3.61 D 3.5:I-

Fig. 364. Ntel temperature TN,lattice parameter a at room temperature and the magnetic mass susceptibility xg at 77.3 K for the alloys y-(FeCo), -=Mn,, see phase diagram Fig. 359a [73 M 11.

phase CI I 3.570 co Fe

Landolt-BBmstein New Series 111/19a

0.2

0.4

0.6 x-

0.8

1.0 Mn

Ada&i

1.2.3.21 Fe-Co-Mn

[Ref. p. 480

co

CoMn 1

I

I

8.5

9.0

8.0

Mn I

1.5

I

7.0

-/I Fig. 365. Fcrromngnctic Curie tcmpcraturc T, and N&l tcmperaturc T,, in [K]. for the y-phases of Fc Co-Mn alloys [73 M I]. )I: number of 4s and 3d electrons per atom.

Fig. 366. Saturation magnetic moment at 0 K. p(OK), in the ferroma_cnetic state and magnetic mass susceptibilit) xr at the Nccl tcmpcraturc TN in the antiferromagnetic state of Fe-Co-Mn alloys. Dashed-dotted curve: composition at which d%JdTchangcs sign. The shadowed area is the region for the coexistence of ferro- and antiferromagnetic phases [73M I]. n: number of 4s and 3d electrons per atom.

Table 83. Antiferromagnetic and structural parameters of y-Fe-like alloys with sameaverage number of 4s and 3d electrons per atom, II = 8. 0 and 4 denote polar and azimuthal angle, respectively, of the spin direction. For spin structure, see Fig. 231. ii,,: average magnetic moment per atom, Th.:N&l temperature, n: lattice parameter [73A 11.

y-Fe Fe0.70Cr,.,sNi0.,s. stainless F~o.~~(N~o.~~Mno.~~)o.~s co o.s2Mno.4s F~o.2s(CoWo.7s

8 8 8 8 8

18.7’ 4’(4) 9.1”(5) 6.7’(7)

‘) Extrapolated.

Adachi

0.7(l) 0.40(3) 45’ 45’

0.6(2) 0.7(1)

67 21(l) 270 343(2) 259(1)

3.57 ‘) 3.58 3.594 3.606(3) 3.590(3)

Ref. p. 4801

1.2.3.21 Fe-Co-Mn

455

0.5 d 0.4

k

I 0.3

241

0.2

240

0.1

239

0

100

300

200

400

K

500

I b 238

T224

Fig. 367. Square of the average magnetic moment of the sublattice magnetization, p, vs. temperature for Fe,,,,(CoMn),,,, and Co,,,,Mn,,,,, as derived from neutron scattering intensities [73A 11. The magnetic hyperfine field determined from Miissbauer spectra is H,,,(57Fe)=30(10)kOe at 77.3 K.

223

.I

221

Fey0.50t% Mn 35 kOe 40 HOPPl -

1.5

I

IQ (Fel_,Co,),.,Mn, 1.0

I”

”

-

’ -

’

a

t o.5-

I

I

Fig. 368. High-field magnetization curves for Fe-Co-Mn alloys [78 K 41.

A

I

I pB1(Fel-YCoY)~-rMnr I 3.0

1;' " '

-

I

I

I

I

0.5

0.6

0.7

0.8

' *

I

T= 4.2 K 2.5 2.0 -2.0 ill 0

0.1

0.2

0.3

0.4 x-

0.5

0.6

0.7

0.8

I ,,; 1.5 1.0

Fig. 369. Rate ofchange ofthe magnetic moment per atom with Mn concentration c, d&,/dc, for (Fer -$o,)r -,Mn, alloys [78 K 41. Circles: T=4.2 K, [78 K4], triangles: T=20"C

0.5

C63C5-J.

01 0

0.1

0.2

0.3

0.4 X-

L

I

I

I

8.0

83

8.2

8.3

I

8.4 f?-

I

I

I

I

8.5

8.6

8.7

8.8

Fig. 370. Magnetic moment of Mn at 4.2K, &,, in Fe, -$o, alloys with small concentrations of Mn, open circles: [78 K4], solid circle: [74Y 11, square: [75N2]. Triangles: &,” at 20 “C [63 C 51.

Land&Bbmstein New Series II1/19a

Adachi

456

1.2.3.21 Fe-Co-Mn 130 MHz

[Ref. p. 480

-p\

l=L2K f\ 55Mn

410

\

I & 3%

.E

=:2 6g

l-

fl-

0 2-

Fig. 372. Resonance frequencies defined as the frequency of the maximum of the 55Mn NMR spectra at 4.2K as dcpcndcnt on the number n of 4s and 3d electrons per atom in Fe, -.$o, and Fe, -,Ni, alloys containing 3 at% Mn [78K4].

0.3

lo 210

I 220

I 230

I 2LO

I 250

MHz 2'

Mn

co

Fig. 373. Average magnetic moment per atom, ii,,, for bee Fe-Co-Mn alloys, measured in a magnetic field of20 kOe at room temperature. At 77 K, fi,, is less than 3% higher. which is within the measuring accuracy [770 I]. 55Mn Fig. 371. Spin-echo SpCCtKl for (Fe1 _,Co,), 9,Mn,,,3 alloys at 4.2 K [78 K 41.

in

Adachi

1.2.3.21 Fe-Co-Mn

Ref. p. 4801

Fe

0

0.1

0.2

0.3

I

Fig. 374. Normalized average magnetic moment per atom, &, and normalized magnetic hyperfine field Hhyp for 57Fe in Fe,-,(Co,,,Mn,,,), alloys at room temperature. pFe= 2.2 ur, and H,,,(57Fe)= 330 kOe for pure Fe are taken as standards. Bars for p,, indicate the experimental errors. Bars for Hhypindicate the values obtained from the distance between the centers of full width at half maximum of the Mijssbauer spectra [77 0 11.

~a

co

Fig. 375. Magnetic hyperfine field Hhyp at Fe sites as derived from Miissbauer spectra for 57Fe in bee Fe-CoMn alloys at room temperature [77 0 11.

1.2 I y 1.1 .-2 F . 1.0 E c 2 0.9

Fig. 376. Normalized hyperfine field, Hhyp, for “Co in Fe, -X(Co,,,Mn,,,)X alloys at 77 K. The hyperfine field for x = 0.075 is taken as standard. For the bars, see Fig. 374 [77 0 I].

Table 84. Electronic specific heat coefficient y and Debye temperature On for fee Fe-Co-Mn alloys quenched from 1100 “C [64 G 11. rms deviation

Y

@n K

Mn o.43Feo.53Coo.04 Mn Mn Mn o.lloFe 0.854 C 0.036

Landolt-Bbmstein New Series IIl/19a

428

14.3

15.9

0.60

405

19.9 33.1

0.40 1.40

399 398

Adachi

45s

[Ref. p. 480

1.2.3.22 Fe-Ni-V

1.2.3.22 FeNi-V References:34 K 1, 51 b 1, 83 C 2.

I”

I

Fe- Ni-V

0

20

I

kG

I

LO

0

60

0

NI -

60

20

80

ot% 100

NI -

Fig. 377.Curie temperatureT, of FeNi-V alloys in the fccphasc[34Kl.51bI,p.l86].

Fig. 378. Magnetization 4xM for Fe-Ni-V alloys in a magnetic field of 1OOe[Sl b 1).

Table 85. Average magnetic moment per atom, p,,, in [&J, as derived from neutron Bragg scattering analysis of various hkl lines and from (bulk) magnetization measurements for ordered and disordered (Fe,.,Ni,,,),V alloys in magnetic fields up to 54kOe at 1.5 to 75 K [83 C 21. hkl

111 200 220 311 bulk

O%.sNiAV ordered

disordered

0.38(2) 0.42(2) 0.32(4) 0.35

0.33(1) 0.36(2) 0.35(3) 0.41(4) 0.32

Adachi

Ref. p. 4801

1.2.3.23 Fe-Ni-Cr

459

1.2.3.23 Fe-Ni-Cr References: 28 C 1, 38 J 1, 49 R 1, 51 b 1, 59 K 2, 60K 2, 63 G 1, 63 K 1, 69 F 1, 70 I 1, 70K 1, 73 A 1, 7411, ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 82M4, 82M5,82Tl, 83D3, 83M2, 83P2, 83Tl.

Ni E 40-l cm3 T

1.32 IO4 s cm3 1.24

E

I.16 I 2”

I 4 H”

2

Fe

90 ot%

70

60 -

50 Fe

40

30

20

IO

Cr

1.08

0

40

80

K

1

a

Fig. 379. Phase diagram of Fe-Ni-Cr alloys at 600°C (solid and chained lines) and at 1200°C (dashed lines) [49Rl, 51 b 1, p. 1481. Practical materials: (a) hightemperature furnace elements, (h) Cr-permalloy, (c) Nichrome, (d) low-temperature furnace elements, (e) Elinvar, (f) 25-12 stainless steel, (g) 18-12 stainless steel, (h) 18-8 stainless steel.

I

Fe-Ni-Cr

b

T-

Fig. 381. Magnetic mass susceptibility xg vs. temperature for (a) Fe-9wt% Ni-18 wt% Cr (nonmagnetic stainless steel) [60 K 21, the Ntel temperature is 40 K, the paramagnetic Curie temperature is -28(3)K, (b) Fe-14.2wt% Ni, 16.1wt% Cr (O.O5wt% C, 1.34wt% MO, 0.74wt% Nb) [70 K 11, the Ntel temperature is 21.5 K.

60[

~I 40[

200

0

-200 20

40

60

80 at% 100

Fig. 380. Curie temperature Tc and ol-y transformation temperature vs. composition for Fe-Ni-Cr alloys [Sl b 1, p. 1491. Solid lines: [28C 11, dashed lines: [38 J 11.

Ni L Land&-BOrnstein New Series 111/19a

Adachi

460

1.2.3.23 Fe-Ni-Cr 0.35

50

I

1

[Ref. p. 480

1 Fe-32wt%Ni-20wt%Cr

Fe -Ni-ZOwt%Cr

1

I

0.33

1

0.25

ZOv:t%Ni

I

;;I 0.20 0 $ OS5

0.1c

0

LO

80

0.05

120

163 K

21

7-

Fig. 382. Initial (ac) volume susceptibility z,. vs. temperature for Fc-Ni-20 wt% Cr (fee austenite) alloys [76 W I]. (a) 16. I8 and 20 wt% Ni, (b) 20, 22 and 24wt% Ni, (c) 32wt% Ni.

0 I

I

I

I

-_IdY

K Fe, Ni0,8-xCro.zI y-phase 0

10

20

30

LO

K

I----

300

I .xTX\

250

w a,

Y

200

Fig. 3S3. Magnetic phase diagram and dilfcrcntial cross section of critical neutron scattering for y-Fc,Ni,,,-,Cr,,z. P. F. AF and SG arc the paramagnctic. fcrromngnctic. antifcrromagnctic and spin glass phases. rcspcctivcly. and dg,‘dR rcprcscnts the diffcrcntial cross section for neutron scnttcring in rclativc units. Open circles and crosses: [82 ht 41. trinnglcs: [76 W I] and solid circles: [70 K I].

150

Ii

A I\

’

I I \n \I I

100 50 0 0

0.1

0.2

0.3

0.1 x-

0.5

0.6

0.7

0.8

461

1.2.3.23 Fe-Ni-Cr

Ref. p. 4801

250

$

I

I

I 28wt%Ni

I

Fe-Ni- ZOwt%Cr

e 3uu 0

0

0.04

0.08

0.12

I

150

P 0.16

0.20

x-

x

100

Fig. 384. Ferromagnetic Curie temperature Tc derived from Mijssbauer spectra for stable disordered fee (Fe,,,Ni,,,),-,Cr, alloys, x5 0.15 [76B 11. 50

0

12

3

4

6 MA/ml

5

H-

Fig. 385. Effect of Ni concentration in Fe-Ni-20 wt% Cr (fee austenite) alloys on the field dependence of the magnetization A4 at 10 K [76 W 11. See also [76 W l] for detailed magnetization curves in the temperature range 10...300K.

-150 -300 -900

-600

-300

a 30 G

0 HOQQl-

300

600 Oe 900 91

I

I

-7

I 0 H-

I

I

I

20 1 IO

r:

0 -10 -20 -30 -12 I

-800

-400

0

400

800 Oe 1200

HOQQl-

b 1.2 G

-14

H7

45 kQe 60

I 14 kOe 21

Fig. 386. Hysteresis loop ofthe magnetic moment measured for an [OOl] axis of a single crystal of fee Feo.70%15Cro.ls at 4.2K. When cooling through the NCel temperature, T,=21(1)K, to T=4.2K, no shill of the hysteresis loop is observed [70 I 11.

I 0.6

2

-91 -21

O -0.6 -1.2 -600

C

Land&BCmstein New Series IIl/l9a

-400

-200

0 HOQQ’ -

200

400 Oe 600

Fig. 387. Hysteresis loops ofmagnetization A4 vs. applied alloys field %,I for samples of Fe,,&Ni,-,Cr&,,, cooled from 60K to 4.2K in a magnetic field of 1 kOe [76R2].

Adachi

462

1.2.3.23 Fe-Ni-Cr

[Ref. p. 480

x125?

0.1 / / 0.2 / 0.3 ,I

0.1 I / 0.5 I ,

\

3.0 Gcm? 9 2.5 I 2.0

0

5

-

15 at% 20

10 Cr X-

0.1

0.2 ,

.--

1

I.6 1

0.3 c

0.5

zi 1.5 s b 1.0 0.5 0 IO 0

20

LO I-

60

K

80

Fig. 389. Magnetic moment 0 in an [OOI] direction vs. tcmpcraturc T for a single crystal of fee FC~.dJi0.L5C~0.15r with the applied magnetic field as a parameter. The arrow indicates the N&l temperature TX [7011-J.

p

I

1

. -IL 5

10 Cr -

15 at% 20

Fig. 388. (a) Spontaneous magnetization M, of alloys at 4.2 K and &I) the Curie %I &Ji, -$rrh5 temperature Tc [76 R 23. Fig. 390. Magnetic structure of fee Fe,,,,,Ni,,,,Cr,,, derived from neutron scattering. The long-range antiferromagnctic order is shown. The sublatticc magnetic moment, j,, =0.3(l)p, at 4.2 K is aligned along the [OOI] direction. The spin components pcrpcndicular to [OOI] have only a short-range correlation [75 12). see also [7OI I].

Y0 iI00 I I

1.05 E z z i%

463

1.2.3.23 Fe-Ni-Cr

Ref. p. 4801

0.95

I1 T

z ‘Z P

100

I - 0.3

T i

2 0.85 ; 1.15

\

\

OA I

,

IS

- 0.5 \

0

2 ?l 2 1.05

~ UL

“hYP

200

f -100 I 0

I 0.04

I 0.08

I 0.12

I 0.16

- 0.6 mm s lo.7 0.20

Fig. 392. Average magnetic hyperfine field n,,, and 1.5 isomer shift IS at 300K for 57Fe in the ferromagnetic phase of stable disordered fee (Fe,,,Ni,,,), -.$I& alloys, x50.15. For x=0.1, the square represents IS in the Fig. 391. Mijssbauer absorption spectra for 57Fe in paramagnetic phase [76 B 11. Fe o,6sNio,ossCro,2 containing 1.2at% Mn, 1.7at% Si, 0.3at% Cu, 0.3at% C and traces of S, P and MO (304 stainless steel) in two temperature ranges. NCel temperature T,=38(2)K, estimated field hyperfine H,,,(57Fe)=21 (8)kOe at 4.2K [63 G I]. 0.85 -2.5

-2.0

-1.5

-1.0 -0.5 0 Source velocity -

0.5 mm/s

Fig. 393. Unidirectional magnetocrystalline anisotropy constant K, of Fe,,,,(Ni,-,Cr,),,,, alloys at 4.2K, as caused by cooling the alloys in a magnetic field of 1 kOe from 60K to 4.2K [76R2].

Landolt-Bdmstein New Series IWl9a

Adachi

[Ref. p. 480

1.2.3.24 Fe-Ni-Mn

464

-600 -800 0

0.1

0.2

0.3

0.4

0.5

0.6

0.8

0.7

X-

Fig. 395. Paramagnetic Curic temperature Fc,Ni 0.75-rMn0.25 alloys [65 W I].

200

400

600

800

0

of

1000 K 12oc

Fig. 393. Invcrsc magnetic mass susceptibility. xi’, FeI Ni o,Ts-xMno,zs alloys vs. temperature [65 W I].

of

Fig. 396. Invcrsc magnetic mass susceptibility, 1; ‘, and the magnetic moment 0 vs. tempcraturc for alloys. (a) 02 x 50.23, H,,,, %65(Nil -.Mnxh.ss =8.6kOc, (b) x=0.3, H,,,,=lOkOc, (c) 0.35~~~0.5. H,,,,=lOkOc and (d) 0.52x60.9, H,,,,=8.6kOe C;r, only); for comparison la of FcMn is also shown [67 S I].

Ref. p. 4801

1.2.3.24 Fe-Ni-Mn 180, Gcm3

- ,

I

I

465

I

-I 3.5 .104 s cm3

lgso 140

2.5

’

I

i 100

7, x

80 60 40 20 0

I ,

,

,

1

BI

7

I

I

.O

CC9 --iI

15

b IO

1

1

Hnnn\=lOkOe 1

= IO kOe

0

Landolt-Bdrnstein New Series 111/19a

100

200

300

400

500

600

700

800

900 K 1000

466

1.2.3.24 Fe-Ni-Mn

[Ref. p. 480

-22

h5

'

Gcm3 9

) 0.35

( %.7~Mh.2~

I I

Ho;;! =lOkOe 18 16

7 /

-GC;r’ 9

--,

6.5kOe 1000 oh N-

\

11 1 h 12 -

200

n

5 4

8 1000

I b3

6

I ;;; 800 .s

2 1 0 40

80

120

.lOP gly 4 1 9 2 0 160 K 200

; 600 -u H" 400 200

T-

Fig. 397. Temperature dependence of the mngnctic moment o of Fc,,,,(Ni,.,,Mn,,,,)~.,, in various applied matgetic liclds H,,,,. The dashed line for H,,,, = 1000Oc indicates the field-cooling effect. The ac mngnctic mass susceptibility (short-dashed curve) is mcasurcd with a mnsimum field of I Oc at 200 Hz [83S 5]. XC also [Sl s33.

0 40

80

120 160 200 T-

260 280 K 32:

Fig. 398. Tcmpcraturc dcpcndcncc of the ac magnetic mass susceptibility ,Y”~, in relative units. (a) Fe,Ni o.ss-xMno.,s: x =0.57 and 0.585. and (b) Fc,Ni,,,-,Mn,,,: x=0.4, 0.45 and 0.48. T,: transition tcmpcraturc from paramagnctic to spin-glass state. &: NCcl tempcraturc [Sl M 31. 1000 K /

800.

L-.1

600 I c,

'1 400

1.5I 5:

I 100

150

200

250

K

300

4 I F/e-M"

I

I

\

7.4

7.7

8.0

1

/-Feo.s(Ni,.,Mn,)o.j

Fig. 399. hJa_rnctic mass susccptihility la vs. tcmpcraturc n0.J,)0,,.5under hydrostatic prcssurc p Fl ~~lod%~oM 8.3 n-

8.6

8.9

9.2

9.5

Fig. 400. Magnetic phase diagram for Fe,,(Ni, -rMni)O,S alloys. The compositions arc indicated by the average number II of 4s and 3d electrons per atom [78 B 23. P: paramagnctic. F: fcrromagnctic. AF: antifcrromagnetic. The shaded area indicates coexistence of ferro- and antifcrromagnctism. Tc: Curie temperature, TV: Neel temperature.

Ref. p. 4801

467

1.2.3.24 Fe-Ni-Mn 500 K

K

I

I

I

I

Fe055( Nil-xMnxh.35

500

400 300

1 300

I

I

I l\ii

i p =‘lotm

200

I

I

A / 5.0 K kbor I 2.5 s

/’

100

100

?

- dTN/dp 1-h

r

01

0

0

500

0.2

0.4

0.6

,=-c

IO

0.8

1.0

x-

K

Fig. 402. Magnetic phase diagram for %.65Wl -xMnxh.ss alloys at atmospheric pressure and the variation with pressure of the Curie and the Ntel temperature, dTJdp and dT,ldp, respectively, as measured for pressures up to 25 kbar [75D 11, see also [71 B 1, 71 N 11.

400 I 300 h 200 100 0 20

30

40

50

60

70

80 at% 90

FeK

Fig. 401. Magnetic phase diagrams for (a) Fe,Ni o.ss-xMno.ls and (b) Fe,Ni,,,-,Mn,,, alloys [81 M 31, see also [SOM 11. P : paramagnetic, F: ferromagnetic, AF: antiferromagnetic, M : metamagnetic, SG: spin-glass. Tc: Curie temperature, TN: Neel temperature.

900 800 700 600 I L-” 500 400 300 200

Fig. 403. Curie temperature Tc for Fe-Ni-Mn alloys of various compositions [75 M 11. Fe-Ni alloys: 1 [63 C 41, 2 [72M 11, 3 [69A3]. Ni-Mn alloys: 4 [31Kl], 5 [37M 11. Fe-Ni-Mn alloys: 3...20at% Mn [75M 1).

Landolt-Bornstein New Series lWl9a

Adachi

0

10

20

30 40 (Fe-Mn)-

50

60

70 ot% 80

465

1.2.3.24 Fe-Ni-Mn

[Ref. p. 480

Table 86. Curie temperature T,, N&l temperature TNand their pressure derivatives T,.,/dp for Fe,,,,(Ni, -xMnx),,35 alloys [75 D 11. x

Mn

Ni

wt% 0.000

0

0.043 0.086 0.129 0.171 0.229 0.686 0.829 1.000

1.5 3.0 4.5 6 8 24 29 35

35 33.5 32 30.5 29 27 11 6 0

T,

TN

K

K

-G,ddp

K kbar- 1

467 402 353 228 190 90

4.4(l) 5.0( 1) 4.8( 1) 4.2(4) 3.7(3) 253 341 442

0.6(Z) 0.9( 1)

Ni at% //

40

“is. 401. Curie and N&l tempcmturcs T, and TN. qxctivcly. vs. number n of4s and 3d clcctrons per atom Fe Ni and FceMn alloys n Fc, AN1 -,Mn,),,,,.

35

30

25

20

15

10

5

0

Fig. 405. Saturation magnetization 4nh4,. in [kG], of slowly cooled Fe-Ni-Mn alloys [33 K 2, 5 1b 1, p. 1823.

:67 S I].

Adachi

Ref. p. 4801

469

1.2.3.24 Fe-Ni-Mn

200

!&!f ko.65(Nip,Mn,)0.35 g,,

T = 4.2K I 3x=0 1 0.05 I

3

15o&=P =

20 10

t 100 b I b"

-10

0

5

IO

15

20

kOe 25

H-

Fig. 406. Magnetic moment 0 vs. magnetic field strength H for Fe,,,,(Ni, -XMn,)o,ss alloys at 4.2 K [67 S 11.

-401”

I

I

-15

T=l.l, K I IO 15kOe 20

6 Gcm3 9 4 I

Fig. 407. Magnetic moment crvs. magnetic field H for (a) 1.3K Fe,.,,~Ji,.,,Mn,.,3)~.3~ at and 64 Fe,,,,~i,,,,Mn,,,,)~,~~ at 1.4K. The samples are cooled in a magnetic field of 18.5kOe, leading to a thermoremanent magnetization. The hysteresis loops are displaced: for (a) the coercive forces are +500Oe and - lOOOOe, respectively. For H= $20 kOe holds (a) 6= & 34 and (h) u=+4.9 and -3.3Gcm3gw1, Gcm3g-’ respectively [67 N 11.

b

2 0 -2

-6 b -20

-10

-5

0 ,,

Table 87. Spontaneous magnetization rr’sat 0 K for Fe-Ni-Mn alloys as derived by extrapolation from measurements from - 196 “C to the Curie temperature T, and in magnetic fields up to 11.5 kOe. Also given is the average magnetic moment per atom, Is,, [69 C 21. Fe

Ni

Mn

at%

Landolt-Bbmstein New Series III/l%

20.0 19.5 19.0 18.5 18.0

80.0 78.0 76.0 74.0 72.0

-

40.0 39.0 38.0 37.0 36.0

60.0 58.5 57.0 55.5 54.0

-

60.0 58.5 57.0 55.5 54.0

40.0 39.0 38.0 37.0 36.0

-

2.5 5.0 7.5 10.0 2.5 5.0 7.5 10.0 2.5 5.0 7.5 10.0

40 W

Pat

T,

Gcm3g-’

ps

K

102.47 105.71 105.95 104.38 99.14

1.074 1.106 1.107 1.089 1.033

840 832 786 752 672

146.69 139.64 133.47 124.97 113.89

1.522 1.447 1.382 1.292 1.176

880 852 788 710 640

182.73 163.91 148.35 127.80 99.49

1.877 1.683 1.521 1.310 1.019

648 608 548 494 396

Ada&i

5

1.2.3.24 Fe-Ni-Mn

470

[Ref. p. 480

40 Gem’ 9 35 30 62.5

25

I

I 533 b

20

b

375

15 10

12.5

5

0

0 20.0 Gem) A.5 15.0

i

b

25

b "t

12.5 I 10.0

20

b

li 10

5 0 0

53

I

200

150

I-

250

300 K :

01 0

50

100

150

I-

Fig. 408. Magnetic moment u of Fe,,,,(Ni, -,Mn,)o,ss alloys in a ma!nctic field H= 8.9 kOc as a function of tcmpcraturc, wth the applied hydrostatic prcssurc p as a parameter [71 N I].

200

250

300 K 350

Ref. p. 4801

1.2.3.24 Fe-Ni-Mn

471

1.8

L.U I

"

Fe-Ni-Mn

I

PB

I

1.5

0.6

n 40 (Fe-Mn)-

60

at%

80

0 0

200

125 I

Landolf-BBmsrein New Series lW19a

10

15 Mn -

20

25 at% 30

Fig. 410. Average magnetic moment per atom, j&, as derived from the spontaneous magnetic moment obtained from extrapolations to H =0 and T=O [75 M I]. (a) FeNi alloys: open circles [63 C 41, lozenges [63 B 11, solid circles [69A 31. Ni-Mn alloys: [31 K 11. Fe-Ni-Mn alloys: 3...20at% Mn [75 M 1],25 at% Mn [59K 11. (b) Fe-Ni-Mn alloys: 0...50at% Fe [75M 11, 65at% Fe [67S I]. (c) Fe-Ni-Mn alloys: 75at% Ni, 1: [75M l] and2:[67F1];50at%Ni,3:[70Dl]and4:[75Ml]; 30 and 35 at% Ni [75 M 11.

Gcm3 9 175

0

5

12

3

4kbar5

Fig. 409. Spontaneous magnetic moment (TVextrapolated to H=O for Fe,,,@-,Mn,),,,, alloys at 4.2 and 77K as a function of applied hydrostatic pressure p [71 N I].

Adachi

[Ref. p. 480

1.2.3.24 Fe-Ni-Mn

472 -x

- L

Fig. 412. Proposed spin configuration magnetic Fc,.,,(Ni,.,Mn,.,),.,, 0.E

- 1..6

0.1

-0 1.8 0.

[ 2

of antiferro-

Il.

Fe5.t~(Ni,.,Mn,)o.35 Few (Ni,.,Mn,)o.~

8.6 fl-

8.1

a

[69N

8.8

9.:

-X

0.1 0.2 2,5 0.: 1 Pt ,, +-Y. . . ,

0 I

\

0.6

0.7

0.8

0.9

1.G

X-

Fig. 413. Average sublattice magnetic moment per atom. p, ofantiferromagnetic Fe,,,,@, -IMnJ,3s at 77 K and extrapolated to 0 K [69 N I].

Fig. 41 I. (a) Effective magnetic moment pcrr as derived from the paramagnetic susceptibility and (a, b) avcragc magnetic moment per atom. p,,. at 0 K as derived from the spontaneous magnetization for Fc,,,,(Ni, -XMnl)o,,s alloys. II: average number of4s and 3d clcctrons per atom. For comparison j,, is also shown for Fe-Ni alloys. (a) [67 S I]. (b) [67 N I]. Fc,,,,(Ni, -,Mn,)o,~s: [67 S I], Fc Ni (fee): [64 C 2. 64 B I]. Fe -Ni (kc): [64 C 23.

Adachi

473

1.2.3.24 Fe-Ni-Mn

Ref. p. 4801

1.0

6

I

I

I

(FexNi,-,)0.995Mn0.005

x=0.2

I 0.5 lu .> E 0

0 330

340

350

360

370

380

390

MHz 410

Y-----r

a

4

I

6

I

(

Feo.9 Ni0.l ) 0.97 M"o.03 es ; 2 -T=CZK .? HB ‘; EO 230 220 .=h 210

I

4 240

250 MHz 260

2

Y-

c

390

b

400

420

410

50

100

150 Y-

300

I I Fe0.d Nil-xMnxh.35 I I

43U MHz 4

Y-

Fig. 415. Spin-echo NMR spectra for (a) 55Mn in Fe,Ni0.9s -xMn,,,, alloys at 4.2 K [73 Y 11, (b) 55Mn in (Fe,.9Ni,.l),.97Mn,.,, and ~e,.,Ni,.z)o.9,Mn,.,3 alloys at 4.2K [78 K4] and (c) (Fe,Ni,-3,,,,,Mn,,,os alloys (solid lines) at 1.4 and 4.2 K for frequencies below 200 MHz and above 300 MHz, respectively, and 61Ni in Fe,Ni,-, alloys (shaded) at 1.4K [78 K3]. In (c) the and for resonances observed above 300MHz 80.. ,160 MHz are attributed to ’ 5Mn atoms with magnetic moments coupled ferromagnetically and antiferromagnetically to the host magnetization, respectively. The dashed curve shows the low-frequency 55Mn resonance. The dotted curve for x=0.3 is the spectrum (arbitrary scale) for an applied field of 15 kOe.

25C

I 2oc z K &C

101

Fig. 414. Magnetic hyperfine field Hhyp as determined from the Miissbauer spectra of 57Fe in ferro- and antiferromagnetic FeO,&Ii, -xMnx)0,35 alloys [69 N 11.

Landolf-Bornstein New Series 111/19a

EiE! x10

n .o

Adachi

0 0

350 MHz400

[Ref. p. 480

1.2.3.24 Fe-Ni-Mn 601

-0 0

10

30 10 (FetMnl-

20

50

60

7Oot% 80

Fig. 416. Spin-wave dispersion cocflicicnt D dcrivcd from small-angle inelastic neutron scattering experiments on Fe Ni -Mn alloys at various tempcraturcs and in various magnetic liclds. Fe-Ni alloys: [64 H I]. Ni--Mn and Fc-Nip hln, 3,..20at% Mn. alloys: [75 M I].

\

; 1.0 ------A

,

I

10

20

/

30 (FetMnl-

I

I

I

40

50 ot% 60

Fig. 417. Effective exchange integral J,,, for various compositions of Fc--Ni-Mn alloys as derived from the spin-wave dispersion coefficients (Fig. 416). the lattice constants and the magnetic moments (Fig. 410) [75 M I]. Fe Ni alloys: [64H I], Ni -Mn and Fe- NikMn. 3...20 at% Mn, alloys: [75 M I]. Pair exchange integrals dcrivcd from the data of this figure: JXi,,=52(5)meV, JNiFe=38(4)mcV, JNiSln=44(5)mcV, JFeUn= 17(2)mcV, JFcFc= -8(l)meV, JMnYn= -285(30)meV.

\

o.li \

0.5

a o-

'I

l.Sr

I

0

1oc

0.22 /

200

I

300

I-

400

I

I

500 K 600

Fig. 418. Spontaneous volume magnctostriction cc)vs. tempcraturc for (a) fcrromagnctic Fc,,,,(Ni, -IMnl)oss alloys, the arrows indicating the Curie temperature, and (b) antifcrromagnetic Fe,,,,(Ni, -,MrQo,ss alloys. the arrows indicating the N&cl temperature [71 H I]. The quantity 01is defmcd as the relative difkrcncc bctwcen the volume in the magnetically ordered state and in the paramagnctic state.

Ref. p. 4801

1.2.3.24 Fe-Ni-Mn

475

32 J molK 28

28

-300

400

500

600

700 T-

800

900

1000

1100 K1200

Fig. 419. Specific heat C, in the paramagnetic region of alloys [78 B2]. Dashed lines: Feo.5(NLMn,h5 calculated.

Table 88. Electronic specific heat coefficient y, Debye temperature On derived from specific heat measurements(seeFig. 420), and paramagnetic Curie temperature 0 (derived from Fig. 395), for disordered fee Fe,,,,-,Ni,Mn,.,, alloys. II denotes the average number of 4s and 3d electrons per atom [65 W 11. X

n

0

K 0.15 0.30 0.45

0.6

Landolt-Biirnstein New Series 111/19a

8.06 8.35 8.65 8.97

-600(100) 20 240 290

Y

10-4calmol-’ 25 31 28 14

Km2

@D

K

359 177 222 224

1.2.3.24 Fe-Ni-Mn

[Ref. p. 480

70 mL &

molK2

40 I

x 30 I

I

\,‘y(NiFeliMn 20

01

7.0

I

I

7.5

8.0

I n-

8.5

9.0

J

9.5

Fig. 421. Electronic specific heat coefficient 7 of Fc,,,,(Ni, -xMnr)0.35 alloys [72 K I]. )I is the average number of4s and 3d electrons per atom. For comparison also the data for (NiFc),Mn [65 W I], Fc Mn and fee Fe Ni alloys [64G I] arc given.

0.1

57 33 27 0

1

b

8

12

16

K2 20

r2-

Fig. 470. Low-tempcraturc specific heat C,. exprcsscd as the relation bctwccn C,IT and T', whcrc T is the temperature. for (a) Fe ~Ni Mn alloys containing 25at%

Mn and (b) Fc,.,,(Ni,-,Mn,),,,, Table 86 [65 ‘A’ I].

alloys. See also

Ref. p. 4801

1.2.3.26 Co-Ni-Mn

1.2.3.25 Co-Ni-Ti,

477

1.2.3.25 Co-Ni-Ti References: 62 S 2, 67 D 2, 68 G 1, 68 P 2, 68 S 3, 68 W 1.

3c .10-G JIJ molK 2E

I ? e

Fig. 422. Temperature dependence of the specific heat C, of CoTi and Co,,,,Ni o,zsTi alloys, plotted as (I) C,/T vs. T2 and (2) (C,- A)/T vs. T’. A is the magnetic cluster specific heat, being 2.7 and 5.5. 10-4calmol-’ K-’ for these alloys, respectively [62 S 21.

22

IE

14

I

8

4

12

16

0.6

0.8

K*

20

12-

1.2.3.26 Co-Ni-Mn References: 54 K 1, 73 Y 1, 74A 2, 79 S 3.

800

K (Coo.5Mno.5)1-xNi, 600

Fig. 423. Magnetic phase diagram of (Co,,,Mn,,,), -,Ni, alloys as a function ofcomposition and average number n of 4s and 3d electrons per atom. T’,, 0 and TN are ferromagnetic Curie temperature, paramagnetic Curie temperature and Ntel temperature, respectively [74A2]. See also Fig. 424.

Landolt-Bbmstein New Series lWl9a

Ada&i

0

CoMn

8.0

0.2

0.4 8.5

x----r 9.0 /J-

1.0 Ni

9.5

10.0

478

[Ref. p. 480

1.2.3.26 Co-Ni-Mn 2.0 PB

I

Co-Ni-Mn

I

1.8

1.6 1.1 1.2 I 1.C 1: 0.E Mn

CoMn

CoilL%h)

Of

Fig. 424. Magnetic phase diagram of ternary Co -Ni -Mn alloys. The variation of Curie and N&cl tcmpcraturcs. T, and TV. rcspcctivcly. arc shown. Both ferromagnctism and antiferromagnetism coexist in the shaded region. [y-Mn] and [y-Fe] mean the spin arrangcmcnt of y-Mn and y-Fe types. respectively [74A2]. For y-Mn and y-Fe. see Fig. 171.

0.6 0.2 [: 8.0 CoMn

8.1

8.8

Y.2 /I-

Y.b Ni

Fig. 425. Magnetic moment per atom at 0 K as a function of the averagc number PIof 4s and 3d electrons per atom for Co--Ni -Mn alloys compared with those for Ni-Mn, Ni-Co and Ni-Fc alloys [74A 21. Triang!es: (Co,.,,sMn,.,,,), -xNi,. open ctrclcs: (Co,,,,Mn,,,,), .’ crrclcs.. (Co Mn ) _ diNi” sohd 05 0.51 I I and squares: (Co,,,,Mn,,,,), -xNi,. Ni

CO I

9.0

Mn

COMll I

8.5

-/i

8.0

I

1.5

7.0

Fig. 426. Ferromagnetic moment at 0 K, &,(O K), of NiCo-Mn alloys. The broken lines show compositions with constant numbers n of 4s and 3d electrons per atom [74A2].

Adachi

I nndolr-Ihrnrtein Ncn Scrim 111,‘19n

Ref. p. 4801

1.2.3.26 Co-Ni-Mn 1.0

0.5 0 1.0

0.5 0 1.0

0.5 0 1 1.0 a, .> 2 2 0.5 x .-r 2 @J 0 2 1.0 2 u 0.5 ‘aA In c w =o 1.0

0.5 0 1.0

0.5 0 1.0

0.5 0 330

340

350

360

370 Y-

380

390

itOOMHz410

Fig. 427. Normalized spin-echo NMR spectra for 5‘Mn in Co,Ni,.,, -xMn,,,, alloys at 4.2 K [73 Y 11.

Landolt-Bbmstein New Series llVl9a

Adachi

480

References for 1.2.2 and 1.2.3

1.2.3.27 References for 1.2.2 and 1.2.3 General references

Slbl 56k 1 5Sh 1 59al 63nl 63n2 67~1 67)~ 1 68~1 69s 1 75cl 75il

Bozorth. R.M.: Ferromagnetism, New York: D. Van Nostrand 1951. Kasper, J.S.: Theory of Alloy Phase, American Society of Metals, 1956, p. 1163. Hansen. M., Anderko, K.: Constitution of Binary Alloys, New York: McGraw Hill Inc. 1958. Arrott. A.. Noakes. J.E.: Iron and Its Dilute Solid Solutions (Spencer,C.W., Werner, F.E., eds.).New York: J. Wiley&Sons Ltd. 1959, p. 85. Nevitt. M.V.: Electronic Structure and Alloy Chemistry of the Transition Elements (Beck. P.A., ed.), New York: Interscience 1963, p. 101. Nevitt, M.V.: Electronic Structure and Alloy Chemistry of the Transition Elements (Beck, P.A., ed.), New York: Interscicncc 19’63,p. 146. Pearson. W.B.: Handbook of Lattice Spacings and Structure of Metals, Vol. 2, Oxford: Pergamon Press 1967. Wallace, W.E., Craig, R.S.: Phase Stability in Metals and Alloys (Rudman, P.S., ed.), New York: McGraw Hill Inc. 1967, p. 225. Shirley, D.A.: Hyperfine Structure and Nuclear Radiations, (Mathias, E., Shirley, D.E., eds.), Amsterdam: North Holland Pub!. Co. 1968, p. 979. Shunk. F.A.: Constitution of Binary Alloys, 2nd Suppl., New York: McGraw Hill Inc. 1969,p. 512. Ishikawa. Y., Endoh. Y.: Handbook of Magnetic Materials, (Chikazumi, S., ed.), Tokyo: Asakura Shoten 1975, (Jap). Ishikawa. Y.: Sci. Rept. Tohoku Univ., Ser. 1, 58 (1975) 151.

Special references

14Ll 18M 1 28Cl 29Wl 30 w 1 31Al 31Kl 31Ml 32Kl 32s 1 33Kl 33K2 34El 34K 1 34M 1 36Fl 36Ml 37Fl 37Kl 37Ml 3SJl 3SSl 39Kl 47Wl 4SKl 49R 1 50K 1 52Al 53P 1

Lamort, J.: Ferrium 11 (1914) 256. Murakami. T.: Sci. Rept. Tohoku Imp. Univ. 7 (1918) 224, 264. Chevenard. P.: Rev. Metall. (Paris) 25 (1928) 14. Wever. F., Haschimoto, U.: Mitt. Kaiser Wilhelm-Inst. Eisenforsch. Diisseldorf 11 (1929) 293. Wever. F., Lange, H.: Mitt. Kaiser Wilhelm-Inst. Eisenforsch. Diisseldorf 12 (1930) 353. Adcock. F.: J. Iron Steel Inst. 124 (1931) 99. Kaya. S.. Kussmann, A.: Z. Phys. 72 (1931) 293. Matsunaga. Y.: Kinzoku-no-Kenkyu 8 (1931) 549 (Jpn.). Kiister. W.: Arch. Eisenhiittenw. 6 (1932) 113. Sadron. C.: Ann. Phys. 17 (1932) 371. Kiister. W., Schmidt. W.: Arch. Eisenhiittenw. 7 (1933-1934) 121. Kussmann. A., Scharnow, B., Stainhaus. W.: Heraeus Vacuumschmeltz, Abertis Hanau 1934,p. 310. Edlund. D.L.: Ph.D. Thesis. Massachusetts Inst. of Techn., Cambridge, Mass. 1934. Kuhlewein. H.: Z. Anorg. Allg. Chem. 218 (1934) 65. Masumoto, H.: Sci. Rept. Tohoku Imp. Univ. 23 (1934) 265. Fallot, M.: Ann. Phys. (Paris) 6 (1936) 305. Manders. C.: Ann. Phys. 5 (1936) 167. Farcas. T.: Ann. Phys. 8 (1937) 146. Ktister. W., Wagner, E.: Z. Metallkd. 29 (1937) 230. Marian. V.: Ann. Phys. 7 (1937) 459. Jackson, L.R.. Russell, H.W.: Instruments 11 (1938) 280. Sucksmith. W., Pearce. R.R.: Proc. R. Sot. London Ser.A 167 (1938) 189. Keesom. W.H.. Kurrelmcyer, B.: Physica 6 (1939) 633. Went. J.J..in: New Developments in Ferromagnetic Materials (Snoek,J.L., ed.).Elsevier Publ. Comp. Amsterdam 1947, p. 14. Kiister, W., Rauschcr, W.: Z. Metallkd. 39 (1948) 178. Rees.W.P., Burns. B.D., Cook, A.J.: J. Iron Steel Inst. (London) 162 (1949) 325. Kussmann. A.. Gratin v. Rittberg. G.: Ann. Physik (Leipzig) 7 (1950) 173. Adenstedt. H.K.. Pequignot. J.R., Raymer, J.M.: Am. Sot. Met. 44 (1952) 990. Piercy, G.R.. Morgan, E.R.: Can. J. Phys. 31 (1953) 529.

References for 1.2.2 and 1.2.3 53Sl 54Al 54Bl 54Gl 54Kl 54Tl 55Kl 55Nl 55Sl 5582 56Kl 56K2 56Tl 57Al 57Bl 57Cl 57Kl 57Ml 58Al 58Bl 58Hl 58H2 58Kl 58K2 58Ll 59Al 59Kl 59K2 59 K3 59Tl 60Al 6OCl 6OC2 60Kl 60K2 60Nl 6OPl 60Rl 6OSl 6OWl 61Kl 61Ll 61 M 1 62Al 62Bl 62Cl 62C2 62Dl 62Kl 62Sl 6232 6283 62Tl 62T2 62Vl 62V2 62Wl 62Yl

Shull, C.G., Wilkinson, M.K.: Rev. Mod. Phys. 25 (1953) 100. Aronin, L.R.: J. Appl. Phys. 25 (1954) 344. Bergman, G., Shoemaker, D.P.: Acta Crystallogr. 7 (1954) 857. Greenfield, P., Beck, P.A.: Trans. AIME 200 (1954) 253. Kiister, W., Rittner, H.: Z. Metallkd. 45 (1954) 639. Taoka, T., Ohtsuka, T.: J. Phys. Sot. Jpn. 9 (1954) 723. Kiister, W., Schmidt, H.: Z. Metallkd. 46 (1955) 195. Nevitt, M.V., Beck, P.A.: Trans. AIME 203 (1955) 669. Shull, C.G., Wilkinson, M.K.: Phys. Rev. 97 (1955) 304. Standley, K.J., Reich, K.H.: Proc. Phys. Sot. (London) Sect. B68 (1955) 713. Kasper, J.S., Waterstrat, R.M.: Acta Crystallogr. 9 (1956) 289. Kasper, J.S., Roberts, B.W.: Phys. Rev. 101 (1956) 537. Taoka, T.: J. Phys. Sot. Jpn. 11 (1956) 537. Abragams, SC., Gutman, L., Kasper, J.S.: Phys. Rev. 105 (1957) 130. Bacon, G.E.: Proc. R. Sot. London Ser. A241 (1957) 273. Crangle, J.: Philos. Mag. 2 (1957) 659. Kiister, W., Rocholl, P.: Z. Metallkd. 48 (1957) 485. Meneghetti, D., Sidhu, S.S.: Phys. Rev. 105 (1957) 130. Ahern, S.A., Martin, M.J.C., Sucksmith, W.: Proc. R. Sot. London Ser. A248 (1958) 145. Barlow, G.S., Standley, K.J.: Proc. Phys. Sot. (London) 71 (1958) 45. Hahn, R., Kneller, E.: Z. Metallkd. 49 (1958) 426. Hoare, F.E., Matthews, J.C.: Proc. Phys. Sot. (London) 71 (1958) 220. Kouvel, J.S., Graham, CD., Jr., Becker, J.J.: J. Appl. Phys. 29 (1958) 518. Kasper, J.S., Waterstrat, R.M.: Phys. Rev. 109 (1958) 1551. Lingelbach, R.: Z. Phys. Chem. (Neue Folge) 14 (1958) 7. Arrott, A., Noakes, J.E.: J. Appl. Phys. 30 (1959) 97s. Kasper, J.S., Kouvel, J.S.: J. Phys. Chem. Solids 11 (1959) 231. Kondorsky, E.I., Sedov, V.L.: Soviet Phys. JETP 35 ( 1959) 586. Kouvel, J.S., Graham, CD., Jr.: J. Phys. Chem. Solids 11 (1959) 220. Takano, Y., Chikazumi, S.: Kobayashi Rigaku Kenkyusho Hokoku 9 (1959) 12 (Jap). Asch, G.: Thesis Strasbourg 1960. Childs, B.G., Gardner, W.E., Penfold, J.: Philos. Mag. 5 (1960) 1267. Cheng, C.H., Wei, CT., Beck, P.A.: Phys. Rev. 120 (1960) 426. Kouvel, J.S.: J. Phys. Chem. Solids 16 (1960) 107. Kondorsky, E.I., Sedov, V.L.: J. Appl. Phys. 31 (1960) 331 S. Nevitt, M.V.: J. Appl. Phys. 31 (1960) 155. Parsons, D.: Nature 185 (1960) 840. Rajan, N.S., Waterstrat, R.M., Beck, P.A.: J. Appl. Phys. 31 (1960) 731. Schrbder, K., Cheng, C.H.: J. Appl. Phys. 31 (1960) 2154. Wakiyama, T., Chikazumi, S.: J. Phys. Sot. Jpn. 15 (1960) 1975. Koi, Y., Tsujimura, A., Hihara, T., Kushida, T.: J. Phys. Sot. Jpn. 16 (1961) 574. LaForce, R.C., Ravitz, S.R., Day, G.F.: Phys. Rev. Lett. 6 (1961) 226. Marcinkowski, M., Brown, N.: J. Appl. Phys. 32 (1961) 375. Arajs, S., Colvin, R.V., Chessin, H., Peck, J.M.: J. Appl. Phys. 33 (1962) 1353. Bueller, W.J., Wiley, R.C.: Trans. Quart. 55 (1962) 269. Cheng, C.H., Gupta, K.P., Van Reuth, EC., Beck, P.A.: Phys. Rev. 126 (1962) 2030. Chandross, R.J., Shoemaker, D.P.: J. Phys. Sot. Jpn. 17, Suppl. B-III (1962) 16. Dekhtyar, M.V.: Sov. Phys. Solid State 4 (1962) 441. Kocher, C.W., Brown, P.J.: J. Appl. Phys. 33 (1962) 1091. Sato, H., Arrott, A.: J. Phys. Sot. Jpn. 17, Suppl. B-I (1962) 147. Starke, E.A., Jr., Cheng, C.H., Beck, P.A.: Phys. Rev. 126 (1962) 1746. Shirane, G., Takei, W.J.: J. Phys. Sot. Jpn. 17, B-III (1962) 35. Taniguchi, S., Tebble, R.S., Williams, D.E.G.: Proc. R. Sot. London Ser. A265 (1962) 502. Taylor, M.A.: J. Less-Common Met. 4 (1962) 476. Van Elst, H.C., Lubach, B., Van Den Berg, G.J.: Physica 28 (1962) 1297. Van Ostenburg, D.O., Lam, D.J., Trapp, H.D., MacLeod, D.E.: Phys. Rev. 128 (1962) 1550. Wilkinson, M.K., Wollan, E.O., Koehler, W.C., Cable, J.W.: Phys. Rev. 127 (1962) 2080. Yamamoto, M., Nakamichi, T.: J. Phys. Sot. Jpn. 17 (1962) 588.

Landolt-Bbmsfein New Series 111/19a

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481

482 63B 1 63C 1 63C2 63C3 63C4 63C5 63D 1 63D2 63Gl 6351 63Kl 63K2 63L 1 63L2 63M 1 63Nl 63NZ 63 P 1 63P2 63s 1 64A 1 64B 1 64 B 2 64Cl 64C2 64G 1 64H 1 64 H 2 64H3 645 1 64Kl 64K2 64K3 64Ll 64 M 1 64 M 2 64 M 3 64N 1 64 W 1 64W2 64 W 3 64Y 1 6421 65B 1 65Cl 65Dl 6SHl 6511 65Kl 65 L 1 65M 1

References for 1.2.2 and 1.2.3 Bando. Y.: J. Phys. Sot. Jpn. 19 (1963) 273. Collins, M.F., Forsyth. J.B.: Philos. Mag. 8 (1963) 401. Cameron. J.A., Lines. R.A.G., Turrell, B.G., Wilson, P.J.: Phys. Lett. 6 (1963) 167. Childs. B.G., Gardner. W.E., Penfold, J.: Philos. Mag. 8 (1963) 419. Crangle. G., Hallam. G.: Proc. R. Sot. London 272 (1963) 119. Chen. C.W.: Philos. Mag. 7 (1963) 1753; J. Appl. Phys. 34 (1963) 1374. Dekhtyar. M.V.: Sov. Phys. Solid State 5 (1963) 918. Doroschenko. A.V.: Fiz. Met. Metalloved. 15 (1963) 936 (Russ.). Gonser. U., Meechnn. C.J., Muir, A.H., Wiedersich, H.: J. Appl. Phys. 34 (1963) 2373. Johnson, C.E.. Ridout. MS.. Cranshaw, T.E.: Proc. Phys. Sot. (London) 81 (1963) 1079. Kouvel. J.S.. Kasper, J.S.: J. Phys. Chem. Solids 24 (1963) 529. Kdi, Y., Tsujimara. A.: J. Phys. Sot. Jpn. 18 (1963) 1347. Low. G.G.. Collins, M.F.: J. Appl. Phys. 34 (1963) 1195. Lam. D.J..Van Ostenburg. D.O., Nevitt, M.V.,Trapp, H.D., Pracht, D.W.: Phys. Rev. 131(1963)1428. Marcinkowsky, M.J.. Poliak, R.M.: Philos. Mag. 8 (1963) 1023. Nevitt, M.V., Aldrcd. A.T.: J. Appl. Phys. 34 (1963) 463. Nakamichi. T., Yamamoto, M.: J. Phys. Sot. Jpn. 18 (1963) 758. Piegger. E.. Craig. R.S.: J. Chem. Phys. 39 (1963) 137. Paoletti. A., Ricci. F.P.: J. Appl. Phys. 34 (1963) 1571. Shull. G.: Electronic Structure and Alloy Chemistry of Transition Elements (Beck, P.A., ed.), Interscience. New York 1963, p. 69. Antonini. B.. Felchcr, G.P., Menzinger, F., Paoletti, A., Ricci, F.P., Passari,L.: J. Phys. (Paris) 25 (1964) 604. Bando. Y.: J. Phys. Sot. Jpn. 19 (1964) 237. Butterworth. J.: Proc. Phys. Sot. (London) 83 (1964) 71. Chikazumi. S., Wakiyama, T., Yosida. K.: Proc. Int. Conf. Magn., Nottingham. London: Inst. Phys. and Phys. Sot. 1964, p. 756. Crangle. J., Hallam. C.: Proc. R. Sot. London Ser. A272 (1964) 237. Gupta. K.P., Cheng. C.H., Beck, P.A.: J. Phys. Chem. Solids 25 (1964) 73. Ho, J.C., Phillips. N.E.: Phys. Lett. 10 (1964) 34. Hatherly, M., Hirakawa, K., Lowde, R.D., Mallet, J.F., Stringfellow, M.F.: Proc. Phys. Sot. (London) 84 (1964) 55. Hamaguchi, Y., Kunitomi, N.: J. Phys. Sot. Jpn. 19 (1964) 1849. Jaccarino. V., Walker. L.R.. Wertheim, G.K.: Phys. Rev. Lett. 13 (1964) 752. Koi, Y., Tsujimura. A.. Hihara, T.: J. Phys. Sot. Jpn. 19 (1964) 1493. Komura. S., Kunitomi. N.: J. Phys. Sot. Jpn. 20 (1964) 103. Kume, K., Fujita. T.: J. Phys. Sot. Jpn. 19 (1964) 1245. Loshmanov, A.A.: Fiz. Met. Metalloved. 18 (1964) 178 (Russ.). Marcone. N.J., Coil. J.A.: Acta Metall. 12 (1964) 743. Masumoto, H.. Saito, H., Sugai, T.: Nippon Kinzoku Gakkaishi 28 (1964) 96 (Jap.). Masuda. Y., Okamura. K.: J. Phys. Sot. Jpn. 19 (1964) 1249. Nevitt, M.V., Kimball, C.W., Preston, R.S.: Proc. Int. Conf. Magn., Nottingham, London: Inst. Phys. and Phys. Sot. 1964, p. 137. Wertheim, G.K., Jaccarino, V., Wernick, J.H., Buchanan, D.N.E.: Phys. Rev. Lett. 12 (1964) 24. West. G.W.: Philos. Mag. 9 (1964) 979. Wallace. W.E., Skrabek, E.A.: Proc. 3rd Rare Earth Conf. (Vorres, K.S., ed.), New York: Gordon & Breech 1964, p. 43 1. Yamamoto. H.: Jpn. J. Appl. Phys. 3 (1964) 745. Zimmerman. J.E.. Arrott. A., Sate, H., Shinozaki, S.: J. Appl. Phys. 35 (1964) 942. Blanchard. A.. Tutovan. V.: CR. Acad. Sci. (Paris) 261 (1965) 2852. Collins, M.F., Low, G.G.: Proc. Phys. Sot. 86 (1965) 535. Drain, L.E., West, G.W.: Philos. Mag. 12 (1965) 1061. Hamnguchi. Y., Wollan. E.O., Kochler, W.C.: Phys. Rev. 138 (1965) A 737. Ishikawa, Y., Tournier. R., Fillipi, J.: J. Phys. Chem. Solids 26 (1965) 1727. Komura. S., Kunitomi. N.: J. Phys. Sot. Jpn. 20 (1965) 103. Lowde. R.D., Shimizu. M., Stringfcllow, M.W., Torric, B.H.: Phys. Rev. Lett. 14 (1965)698. Moller, H.B., Trego. A.R., Mackintosh. A.R.: Solid State Commun. 3 (1965) 137.

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References for 1.2.2 and 1.2.3 65Wl 66Al 66A2 66A3 66Bl 66B2 66B3 66Cl 66Gl 66Kl 66Ml 66Pl 66Rl 66Sl 66Ul 67Al 67Bl 67Dl 67D2 67Fl 67Hl 6711 6712 67Kl 67Ml 67M2 67Nl 67Pl 67P2 67Sl 6782 6733 67Wl 67W2 68Al 68A2 68Bl 68Cl 68C2 68El 68Fl 68Gl 6811 6812 68 K 1 68 L 1 68L2 68Nl 68N2 68Pl 68P2 68Rl 68Sl 68S2 6883 68S4 68Wl Land&Biirnstein New Series lll/l9a

483

Watanabe, H., Ehara, K., Fukuroi, T., Muto, Y., Yamamoto, H.: Sci. Rept. Res. Inst. Tohoku Univ. A 17 (1965) 300. Aoki, Y., Nakamichi, T., Yamamoto, M.: J. Phys. Sot. Jpn. 21 (1966) 565. Algie, S.H., Hall, E.O.: Acta Crystallogr. 20 (1966) 142. Arajs, S., Durmyre, G.R.: J. Appl. Phys. 37 (1966) 1017. Bastow, T.J.: Proc. Phys. Sot. 88 (1966) 935. Barnes, R.G., Beaudry, B.J., Lecander, R.G.: J. Appl. Phys. 37 (1966) 1248. Booth, J.G.: J. Phys. Chem. Solids 27 (1966) 1639. Campbell, I.A.: Proc. Phys. Sot. 89 (1966) 71. Giegengack, H., Schott, H., Schulze, G.E.R., Ullrich, H.-J.: Phys. Status Solidi 14 (1966) K 189. Koehler, W.C., Moon, R.M., Trego, A.L., Mackintosh, A.R.: Phys. Rev. 151 (1966) 405. Mook, H.A.: Phys. Rev. 148 (1966) 495. Paoletti, A., Ricci, F.P., Passari, L.: J. Appl. Phys. 37 (1966) 3236. Read, D.A., Thomas, E.H.: IEEE Trans. Magn. MAG-2 (1966) 415. Suzuki, T.: J. Phys. Sot. Jpn. 21 (1966) 442. Umebayashi, H., Ishikawa, Y.: J. Phys. Sot. Jpn. 21 (1966) 1281. Arrott, A., Werner, S.A.: Phys. Rev. 153 (1967) 624. Bucher, E., Brinkman, W.F., Maita, J.P., Williams, H.J.: Phys. Rev. Lett. 18 (1967) 1125. Dalagalme, A.: Solid State Commun. 5 (1967) 769. DeSavage, B.F., Goff, J.F.: J. Appl. Phys. 38 (1967) 1337. Fadin, V.P., Nazhalov, A.I., Panin, V.E.: Izv. Vuzov Fizika 7 (1967) 45. Hashimoto, T., Ishikawa, Y.: J. Phys. Sot. Jpn. 23 (1967) 213. Ishikawa, Y., Endoh, Y.: J. Phys. Sot. Jpn. 23 (1967) 205. Ishikawa, Y., Hoshino, S., Endoh, Y.: J. Phys. Sot. Jpn. 22 (1967) 1221. Komura, S., Kunitomi, N., Hamaguchi, Y.: J. Phys. Sot. Jpn. 23 (1967) 171. Marei, S.A., Craig, R.S., Wallace, W.E., Tsuchida, T.: J. Less-Common Met. 13 (1967) 391. Mori, N., Mitsui, T.: J. Phys. Sot. Jpn. 22 (1967) 931. Nakamura, Y., Miyata, N.: J. Phys. Sot. Jpn. 23 (1967) 223. Proctor, W., Scurlock, R.G., Wray, E.M.: Proc. Phys. Sot. 90 (1967) 697. Paoletti, A., Ricci, F.P.: Phys. Lett. A24 (1967) 371. Shiga, M.: J. Phys. Sot. Jpn. 22 (1967) 539. Satoh, T., Yokoyama, Y., Nagashima, T.: J. Phys. Sot. Jpn. 22 (1967) 1296. Syono, Y., Ishikawa, Y.: Phys. Rev. Lett. 19 (1967) 747. West, G.W.: Philos. Mag. 15 (1967) 855. Wertheim, G.K., Wernick, J.H.: Acta Metall. 15 (1967) 297. Aldred, A.T.: J. Phys. C 1 (1968) 244. Abel, A.W., Craig, R.S.: J. Less-Common Met. 16 (1968) 77. Bennett, L.H., Swartzendruber, L.J., Watson, R.E.: Phys. Rev. 165 (1968) 500. Comly, J.B., Holden, T.M., Low, G.G.: J. Phys. Cl (1968) 458. Chikazumi, S., Mizoguchi, T., Yamaguchi, N., Beckwith, P.: J. Appl. Phys. 39 (1968) 939. Endoh, Y., Ishikawa, Y., Ohno, H.: J. Phys. Sot. Jpn. 24 (1968) 263. Feinstein, L.G., Shoemaker, D.P.: J. Phys. Chem. Solids 29 (1968) 184. Goff, J.F.: J. Appl. Phys. 39 (1968) 2208. Iannucci, A., Johnson, A.A., Hughes, E.J., Barton, P.W.: J. Appl. Phys. 39 (1968) 2222. Ishikawa, Y., Endoh, Y.: J. Appl. Phys. 39 (1968) 1318. KrCn, E., Nagy, E., Nagy, I., Pal, L., Szabo, P.: J. Phys. Chem. Solids 29 (1968) 101. Low, G.G.: J. Appl. Phys. 39 (1968) 1174. Low, G.G.: Adv. Phys. XVIII (1968) 371. Nakamichi, T., Aoki, Y., Yamamoto, M.: J. Phys. Sot. Jpn. 25 (1968) 77. Nakamichi, T.: J. Phys. Sot. Jpn. 25 (1968) 1189. Pal, L., KrCn, E., Kadar, G., Szabb, P., Tarnbczi, T.: J. Appl. Phys. 39 (1968) 538. Pickart, S.J.,Nathans, R., Menzinger, F.: J. Appl. Phys. 39 (1968) 2221. Read, D.A., Thomas, E.H., Forsythe, J.B.: J. Phys. Chem. Solids 29 (1968) 1569. Smith, J.H.: J. Appl. Phys. 39 (1968) 675. Salamon, M.B., Feigl, F.J.: J. Phys. Chem. Solids 29 (1968) 1443. Swartzendruber, L.J., Bennett, L.H.: J. Appl. Phys. 39 (1968) 2215. Streever, R.L.: Phys. Rev. 173 (1968) 591. West, G.W.: J. Appll Phys. 39 (1968) 2213.

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484 65 W 2 69A1 69A2 69A3 69Cl 69C2 69E 1 69 F 1 6911 69 M 1 69 M 2 69Nl 69Sl 69S2 69S3 69V 1 69 W 1 70Bl 70B2 7OCl 7oc2 70Dl 70Fl 7011 7051 70K 1 70M 1 70N 1 7001 70s 1 7OS2 7os3 7ou 1 7OVl 7OYl 7OYZ 702 1 71Al 71 B 1 71Cl 71C2 71c3 71D1 71El 71Fl 71Hl 7111 71Ll 71Nl 7101 7102 7103 71Sl 71s2 71Tl 71Ul 71Vl

References for 1.2.2 and 1.2.3 Wang. F.E.. DeSavagc. B.F., Buchler, W.J.: J. Appl. Phys. 39 (1968) 2166. Aoki. Y., Nakamichi, T., Yamamoto, M.: J. Phys. Sot. Jpn. 27 (1969) 257. Aoki. Y.: J. Phys. Sot. Jpn. 27 (1969) 258. Asano. H.: J. Phys. Sot. Jpn. 27 (1969) 542. Callings. E.W., Smith. R.D., Lecander, R.G.: J. Less-Common Met. 18 (1969) 251. Colling. D.A.: J. Appl. Phys. 40 (1969) 1379. Endoh. Y., Ishikawa. Y., Shinjo, T.: Phys. Lett. A29 (1969) 310. Fujimori, H.. Saito. H.: Nippon Kinzoku Gakkaishi 33 (1969) 375 (Jap.). Ikeda. K.. Nakamichi, T., Yamamoto, M.: J. Phys. Sot. Jpn. 27 (1969) 1361. Menden. G.T., Rao. K.V., Loo, H.Y.: Phys. Rev. Lett. 23 (1969) 475. Mori. N., Mitsui. T.: J. Phys. Sot. Jpn. 26 (1969) 1087. Nakamura. Y., Shiga. M., Takeda, Y.: J. Phys. Sot. Jpn. 27 (1969) 1470. Shiga. M.. Nakamura, Y.: J. Phys. Sot. Jpn. 26 (1969) 24. Saito, H., Fujimori. H., Saito, T.: Nippon Kinzoku Gakkaishi 33 (1969) 231 (Jap.). Sueda. N., Fujiwara. Y., Fujiwara, H.: J. Sci. Hiroshima Univ. Ser. A-II, 33 (1969) 267. Von Meetwall. E., Schreiber. D.S.: Phys. Lett. A28 (1969) 495. Wertheim, G.K., Wernick, J.H., Sherwood, R.C.: Solid State Commun. 7 (1969) 1399. Briickncr, W., Kleinstuck, K., Schulze, G.E.R.: Phys. Status Solidi A 1 (1970) K 1. Barnes. R.G.. Lunde, B.K.: J. Phys. Sot. Jpn. 28 (1970) 408. Cable, J.W., Child. H.R.: J. Phys. (Paris) 32 (1970) Cl-67. Cable, J.W., Hicks. T.J.: Phys. Rev. B2 (1970) 176. Doroshenko. A.V., Sidorov, S.K.: JETP 58 (1970) 124. Fujimori. H., Saito, H.: Trans. Jpn. Inst. Met. 11 (1970) 72. Ishikawa. Y., Endoh, Y., Takimoto, T.: J. Phys. Chcm. Solids 31 (1970) 1225. Johanson, G.J.. McGirr, M.B., Wheeler, D.A.: Phys. Rev. Bl (1970) 3208. Kohlhaas. R.. Raiblc, A.A., Rocker, W.: Z. Angew. Phys. 30 (1970) 254. Matsui. M.. Ido, T., Sato, K., Adachi, K.: J. Phys. Sot. Jpn. 28 (1970) 791. Nakamichi. T., Aoki. Y., Yamamoto, M.: J. Phys. Sot. Jpn. 28 (1970) 590. Okazaki. M.: C. R. Acad. Sci. Ser. B270 (1970) 254. Swartz. J.C.. Swartzendruber. L.J., Bennet, L.H.: Phys. Rev. B 1 (1970) 146. Satoh. T., Shimura. T.: J. Phys. Sot. Jpn. 29 (1970) 517. Saito, H., Fujimori, H., Saito, T.: Trans. Jpn. Inst. Met. 11 (1970) 68. Uchishiba. H., Hori, T., Nakagawa. Y.: J. Phys. Sot. Jpn. 28 (1970) 792. Volkenshtein. N.V., Zotov, T.D., Savchenkova, SF., Tsiovkin, Yu.N.: Fiz. Tverd. Tela 12 (1970) 1845 (Russ). Yamada. T., Kunitomi. N., Nakai. Y., Cox, D.E., Shiranc, G.: J. Phys. Sot. Jpn. 28 (1970) 615. Yamada. T.: J. Phys. Sot. Jpn. 28 (1970) 596. Zotov, T.D., Pronina. A.P.: Fiz. Tvcrd. Tela 12 (1970) 2184 (Russ). Arajs. S., Anderson E.E.: Physica 54 (1971) 617. Bartel, L.C., Edwards, L.R., Samara, G.A.: AIP Conf. Proc. 5 (1971) 482. Chiffey, R.. Hicks. T.J.: Phys. Lett. A34 (1971) 267. Chiu. C.H.. Jericho. M.H., March, R.H.: Can. J. Phys. 49 (1971) 3010. Crangle. J.. Goodman. G.M.: Proc. R. Sot. London Ser. A321 (1971) 477. Dean. R.H.. Furley, R.J., Seurlock. R.G.: J. Phys. Fl (1971) 78. Endoh, Y., Ishikawa. Y.: J. Phys. Sot. Jpn. 30 (1971) 1614. Filip. D.P.: Phys. Status Solidi A7 (1971) K 35. Hayase. M., Shiga. M., Nakamura, Y.: J. Phys. Sot. Jpn. 30 (1971) 729. Ikeda. K.. Nakamichi. T., Yamamoto, M.: J. Phys. Sot. Jpn. 30 (1971) 1504. Lander. G.H.. Heaton, L.: J. Phys. Chem. Solids 32 (1971) 427. Nakamura. Y., Hayase, M., Shiga, M., Miyamoto, Y., Kawai, N.: J. Phys. Sot. Jpn. 30 (1971) 720. Ohno. H.. Mekata. M.: J. Phys. Sot. Jpn. 31 (1971) 102. Ohno. H.: J. Phys. Sot. Jpn. 31 (1971) 92. Okazaki, M.: J. Phys. (Paris) 32 (1971) C l-874. Stoclinga. S.J.M.: J. Phys. (Paris) 32 (1971) C l-330. Shalaev, A.M.. Krulikovskaya, M.P.: Fiz. Met. Metalloved. 32 (1971) 193 (Russ). Tutovan. V., Chiriac. M.: J. Phys. (Paris) 32 (1971) C l-872. Uchishiba. H.: J. Phys. Sot. Jpn. 31 (1971) 436. Von Meerwall. E., Schrciber, D.S.: Phys. Rev. B3 (1971) 1.

References for 1.2.2 and 1.2.3 71Wl 72Al 72A2 72Bl 72Cl 72Hl 72H2 7211 72Kl 72Ml 73Al 73A2 7311 73Ml 73 s 1 7382 73Tl 73Wl 73Yl 74Al 74A2 74A3 74Cl 74Fl 7411 74Kl 74K2 74K3 74Ml 74Pl 74P2 74P3 74P4 74Sl 74Vl 74Yl 75Al 75A2 75Bl 75Cl 75C2 75c3 75Dl 75El 75Fl 75F2 75Gl 75Hl 75H2 75H3 75H4 Landolt-BOrnstein New Series 111/19a

485

Whittaker, K.C., Dziwornooh, P.A., Riggs, R.J.: J. Low Temp. Phys. 5 (1971) 461. Adachi, K., Sato, K., Matsui, M., Mitani, S.: IEEE Trans. Magn. MAG-8 (1972) 693. Aldred, A.T.: Int. J. Magn. 2 (1972) 223. Besnus, M.J., Gottehrer, Y., Munschy, G.: Phys. Status Solidi b 49 (1972) 597. Callings, E.W., Ho, J.C., Jaffee,R.I.: Phys. Rev. 5 (1972) 4435. Herbert, I.R., Clark, P.E., Wilson, G.V.H.: J. Phys. Chem. Solids 33 (1972) 979. Hasegawa, M., Kanamori, J.: J. Phys. Sot. Jpn. 33 (1972) 1607. Ikeda, K., Nakamichi, T., Yamamoto, M.: Phys. Status Solidi (a) 12 (1972) 595. Kawarazaki, S., Shiga, M., Nakamura, Y.: Phys. Status Solidi (b) 50 (1972) 359. Men’shikov, A.Z., Yurtchikov, E.E.: Izv. Akad. Nauk SSSR Ser. Fiz. 36 (1972) 1463. Adachi, K., Matsui, M., Mitani, S.: J. Phys. Sot. Jpn. 35 (1973) 426. Asada, Y., Nose, H.: J. Phys. Sot. Jpn. 35 (1973) 409. Ishikawa, Y., Endoh, Y., Ikeda, S.: J. Phys. Sot. Jpn. 35 (1973) 1616. Matsui, M., Sato, K., Adachi, K.: J. Phys. Sot. Jpn. 35 (1973) 419. Sumiyama, K., Shiga, M., Nakamura, Y.: J. Phys. Sot. Jpn. 35 (1973) 469. Sumitomo, Y., Moriya, T., Ino, H., Fujita, E.: J. Phys. Sot. Jpn. 35 (1973) 461. Takenaka, H., Asayama, K.: J. Phys. Sot. Jpn. 35 (1973) 740. Williams, W., Jr., Stanford, J.L.: Phys. Rev. B 7 (1973) 3244. Yasuoka, H., Hoshinouchi, S., Nakamura, Y.: J. Phys. Sot. Jpn. 34 (1973) 1192. Aoki, Y., Yamamoto, M.: Phys. Status. Solidi (a) 26 (1974) K 137. Adachi, K., Sato, K., Katata, A., Mori, M.: Proc. Int. Conf. Magn. Moscow, 1973, l(2) (1974) 256. Aoki, Y., Asami, K., Yamamoto, M.: Phys. Status Solidi (a) 23 (1974) K 167. Cable, J.W., Child, H.R.: Phys. Rev. B 10 (1974) 4607. Fukamichi, K., Saito, H.: Nippon Kinzoku Gakkaishi 38 (1974) 1083 (Jap). Ishikawa, Y., Kohgi, M., Noda, Y., Tajima, K.: Proc. Int. Conf. Magn., Moscow, 1973,4 (1974) 567. Kohara, T., Asayama, K.: J. Phys. Sot. Jpn. 37 (1974) 393. Kohara, T., Asayama, K.: J. Phys. Sot. Jpn. 37 (1974) 401. Kawakami, M., Koi, Y.: J. Phys. Sot. Jpn. 37 (1974) 1257. Mekata, M., Nakahashi, Y., Yamamoto, T.: J. Phys. Sot. Jpn. 37 (1974) 1509. Panin, V.E., Lotkov, A.I., Kolubaev, A.V.: Tezisy Dokl-Vses. Konf. Kristallokhim. Intermet. Soedin., 2nd 1974, p. 23 (Russ). Panin, V.E., Lotkov, AI., Gaidikova, L.I.: Tezisy Dokl.-Vses. Konf. Kristallokhim. Intermet. Soedin., 2nd 1974, p. 24 (Russ). Pop, I., Iusan, V., Giurgiu, A.: Phys. Lett. A49 (1974) 439. Pop, I., Iusan, V., Giurgiu, A.: Stud. Univ. Babes-Balyai, Ser. Phys. 19 (1974) 68. Shinjo, T., Okada, K., Takada, T., Ishikawa, Y.: J. Phys. Sot. Jpn. 37 (1974) 877. Valiev, E.Z., Doroshenko, A.V., Sidorov, S.K., Nikulin, Yu.M., Teploukhov, S.G.: Fiz. Met. Metalloved. 38 (1974) 993 (Russ.) Yamaguchi, H., Watanabe, H., Suzuki, Y., Saito, H.: J. Phys. Sot. Jpn. 36 (1974) 971. Acker, F., Huguenin, R.: Phys. Lett. A53 (1975) 167. Arajs, S., Anderson, E.E., Kelly, J.R., Rao, K.V.: AIP Conf. Proc. 1974, 24 (1975) 412. Benediktsson, G., Astrom, H.U., Rao, K.V.: J. Phys. F5 (1975) 1966. Claus, H.: Phys. Rev. Lett. 34 (1975) 26. Collings, E.W.: J. Less-Common Met. 39 (1975) 63. Chandra, G., Ray, J., Bansal, C.: Proc. Int. Conf. Low Temp. Phys., 14th, 3 (1975) 358 (Krusius, M., Vuorio, M., eds.),Amsterdam: North-Holland Publ. Co. Dubovka, G.T., Ponyatovskii, E.G., Georgieva, I.Ya., Antonov, V.E.: Phys. Status Solidi A32 (1975) 301. Edwards, L.R., Fritz, I.J.: AIP Conf. Proc. 1974, 24 (1975) 414. Fukamichi, K., Suzuki, Y., Saito, H.: Trans. Jpn. Inst. Met. 16 (1975) 133. Frollani, G., Menzinger, F., Sacchetti, F.: Phys. Rev. B 11 (1975) 2030. Gregory, I.P., Moody, D.E.: J. Phys. F5 (1975) 36. Hori, T.: J. Phys. Sot. Jpn. 38 (1975) 1780. Hedgcock, F.T., Strom-Olsen, J.O., Wilford, D.: Proc. Int. Conf. Low Temp. Phys., 14th, 3 (1975)298 (Krusius, M., Vuorio, M., eds.),Amsterdam: North-Holland Publ. Co. Ho, J.C.,Collings, E.W.: Proc. Int. Conf. Low Temp. Phys., 14th, 2 (1975)273 (Krusius, M., Vuorio, M., eds.),Amsterdam: North-Holland Publ. Co. Hamaguchi, Y., Wollan, E.O., Koehler, W.C.: Phys. Rev. A138 (1975) 737.

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486

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Ikeda. S.. Ishikawa. Y.: J. Phys. Sot. Jpn. 39 (1975) 332. Ishikawa. Y., Kohgi. M., Noda, Y.: J. Phys. Sot. Jpn. 39 (1975) 675. Ishikawa, Y.: Sci. Rept. Tohoku Univ., Ser. I, 58 (1975) 151. Kohara. T., Asayama. K.: J. Phys. Sot. Jpn. 39 (1975) 1263. Kirillova. M.M.. Nomerovannava. L.V.: Fiz. Met. Metalloved. 40 (1975) 983 (Russ). Lynch. D.W., Rosei. R.. Weaver. J.H.: Phys. Status Solidi A 27 (1975) 515. Loegcl. B.: J. Phys. F5 (1975) 497. Loegel. B.. Friedt. J.M., Poinsot, R.: J. Phys. F5 (1975) L 54. Men’shikov, A.Z.. Kazantsev, V.A., Kuz’min, N.N., Sidorov, SK.: J. Mag. Magn. Mater. 1 (1975)91. Men’shikov, A.Z.. Kuz’min, N.N., Kazantsev, V.A., Sidorov, S.K., Kalinin, V.M.: Fiz. Met. Metalloved. 40 (1975) 647 (Russ). 75N 1 Nagasawa. H., Senbn. M.: J. Phys. Sot. Japn. 39 (1975) 70. Nakai. Y., Kunitomi. N.: J. Phys. Sot. Jpn. 39 (1975) 1257. 75N2 75P 1 Patton. C.E., Vardeman. M., Baker, G.L.: Dig. Intermag. Conf. 1975, 31.4. Rode. V.E.. Deryabin, A.V., Pislar, I.G.: Fiz. Met. Mctalloved. 40 (1975) 1110 (Russ). 75Rl Smith. T.F., Tainsh. R.J., Shelton, R.N., Gardner, W.E.: J. Phys. F5 (1975) L96. 75s 1 Shull. R.D., Beck. P.A.: AIP Conf. Proc. 1974, 24 (1975) 95. 75s’ Stetsenko. P.N.. Surikov, V.V.: Fiz. Tverd. Tela (Leningrad) 17 (1975) 590 (Russ). 75S3 75W 1 Wada. S.. Asayama. K.: J. Phys. Sot. Jpn. 39 (1975) 352. Acker. F., Huguenin. R.: J. Phys. F6 (1976) L 147. 76Al Aoki. Y., Yamamoto, M.: Phys. Status Solidi A33 (1976) 625. 76A2 Aldred. A.T., Rainford, B.D., Kouvel, J.S., Hicks, T.J.: Phys. Rev. B14 (1976) 228. 76A3 Aldrcd. A.T.: Phys. Rev. B 14 (1976) 219. 76A4 Adachi. K., Maki. S.: Toyoda Kenkyu Hokoku 29 (1976) 4 (Jap). 76A5 Bansal. C.. Chandra. G.: Solid State Commun. 19 (1976) 107. 76Bl 76C 1 Cable. J.W.. Medina. R.A.: Phys. Rev. B13 (1976) 4868. Child. H.R.. Cable. J.W.: Phys. Rev. B 13 (1976) 227. 76C2 Goman’lov, V.I.. Mokhov, B.N., Mal’tscv, E.I.: Pis’ma Zh. Eksp. Teor. Fiz. 23 (1976) 97 (Russ). 76G I Hennion. B., Hutchings. M.T., Lowde, R.D., Stringfellow, M.W., Tocchetti, D.: Proc. Conf. Neutron 76Hl Scattering 2 (CONF-760601) 1976, p. 825 (ed. by Moon, R.M., NTIS, Springfield. Va.). Hausch. G., Shiga. M., Nakamura. Y.: J. Phys. Sot. Jpn. 40 (1976) 903. 76H2 Livet. F., Radhakrishna, P.: Solid State Commun. 18 (1976) 331. 76Ll Mezei. F.: Proc. Conf. Neutron Scattering 2 (CONF-760601) 1976,670 (ed. by Moon, R.M.. NTIS, 76MI Springfield. Va.). Mori. M.. Tsunoda. Y., Kunitomi, N.: Solid State Commun. 18 (1976) 1103. 76hl2 Mcn’shikov, A.Z., Kazantsev, V.A., Kuz’min, N.N.: Zh. Eksp. Teor. Fiz. 71 (1976) 648 (Russ). 76M3 McCallum. R.W.. Johnston, D.C., Maple, M.B., Matthias, B.T.: Mater. Res. Bull. 11 (1976) 781. 76M4 76R 1 Rode. V.E.. Finkel’bcrg, S.A., Pankova. O.A.: Fiz. Met. Metalloved. 42 (1976) 895 (Russ). Rode. V.E., Deryabin, A.V., Damashke, G.: IEEE Trans. Magn. MAC-2 (1976) 404. 76R2 Satoh. T.. Patton. C.E., Goldfarb, R.B.: AIP Conf. Proc., 1976,p. 34 (Mag. Magn. Mater., Jt. MMM 76Sl Intermag Conf.. 1976)p. 361. Singer, V.V., Dovgopol, M.P., Dovgopol, S.P., Radovskii, I.Z., Gel’d, P.V., Zorin, A.I.: Izv. Vyssh. 76S2 Uchebn. Zaved.. Fiz. 19 (1976) 69 (Russ). Suzuki. T.: J. Phys. Sot. Jpn. 41 (1976) 1187. 76S3 Shiga. M.. Nakamura. Y.: Phys. Status Solidi A 37 (1976)K 89. 76S4 Teoh. W., Arajs. S., Abukay, D., Anderson, E.E.: J. Mag. Magn. Mater. 3 (1976) 260. 76Tl 76W 1 Warncs. L.A.A.. King. H.W.: Cryogenics 16 (1976) 473, 659. 77A 1 Adachi. K.. Maki. S.: Physica B+C 86-88 (1977) 263. Akoh. H., Matsumura. M., Asayama. K., Tasaki, A.: J. Phys. Sot. Jpn. 43 (1977) 1857. 77A2 Astrom. H.U., Gudmundsson, H., Hedman, L., Rao, K.V.: Physica B+C 86-88 (1977) 332. 77A3 Aoki, Y., Gotoh. Y.: Phys. Status Solidi A42 (1977) 42. 77A4 Aldred. A.T., Kouvel. J.S.: Physica B 86-88 (1977) 329. 77A5 77B 1 Bienias. J.A.. Moody, D.E.: Physica B +C 8&88 (1977) 541. 77H 1 Hcnnion. M.. Hennion. B., Kajzar. F.: Solid State Commun. 21 (1977) 231. Hausch. G., Torok. E.: Intern. Frict. Ultrason. Attenuation Solids. Proc. Int. Conf., 6th (1977)731.(Ed. 77H2 by Hasiguti R.R., Mikoshiba. N., Tokyo: Univ. Tokyo Press). Hedgcock, F.T., Strom-Olsen. J.O., Wilford, D.F.: J. Phys. F7 (1977) 855. 77H3 Hempelmann, R.. Wicke, E.: Ber. Bunsen Gesellsch. 81 (1977) 425. 77H4

7.511 75 12 7513 75K 1 75K2 75L I 75L2 75L3 75h? 1 75 hf 2

Adachi

Referencesfor 1.2.2 and 1.2.3 77Kl 77Ml 77M2 77M3 77M4 77M5 77M6 77Nl 77N2 7701 77Yl 78Al 78Bl 78B2 78B3 78B4 78Cl 78C2 78C3 78Dl 78Hl 78H2 78H3 78H4 7811 78Kl 78K2 78K3 78K4 78Ml 78M2 78Nl 78N2 78Pl 78Rl 78R2 78R3 78Tl 78Yl 7821 79Al 79Bl 79B2 79Cl 79c2 79Fl 79F2 79Gl 79Hl 79Kl 79K2

487

Kuwano, H., Ono, K.: J. Phys. Sot. Jpn. 42 (1977) 72. Mustaffa, A., Read, D.A.: J. Mag. Magn. Mater. 5 (1977) 349. Mokhov, B.N., Goman’kov, V.I., Makarov, V.A., Sakharova, T.V., Nogin, N.I.: Zh. Eksp. Teor. Fiz. 72 (1977) 1833 (Russ). Mokhov, B.N., Goman’kov, V.I., Puzei, I.M.: Pis’ma Zh. Eksp. Teor. Fiz. 25 (1977) 299 (Russ). Men’shikov, A.Z., Teplykh, A.E.: Fiz. Met. Metalloved. 44 (1977) 1215 (Russ). Matsumura, M., Asayama, K.: J. Phys. Sot. Jpn. 43 (1977) 1861. Maystrenko, L.G., Polovov, V.M.: Fiz. Met. Metalloved. 43 (1977) 991. Nishihara, Y., Ogawa, S., Waki, S.: J. Phys. Sot. Jpn. 42 (1977) 845. Narayanasamy, A., Ericsson, T., Nagarajan, T., Muthukumarasamy, P.: Phys. Status Solidi A42 (1977) K 65. Ohara, S., Komura, S., Takeda, T., Hihara, T., Komura, Y.: J. Phys. Sot. Jpn. 42 (1977) 1881. Yamashita, O., Yamaguchi, Y., Watanabe, M.: JAERI Report M (1977) 56. Aoki, Y., Fukamichi, K.: Phys. Status Solidi A50 (1978) 263. Burke, S.K., Rainford, B.D.: J. Phys. FS (1978) L239. Bendick, W., Ettwig, H.H., Pepperhoff, W.: J. Phys. F8 (1978) 2525. Beille, J., Bloch, D., Towfig, F.: Solid State Commun. 25 (1978) 57. Beille, J., Towfig, F.: J. Phys. FS (1978) 1999. Caporaletti, O., Graham, G.M.: J. Appl. Phys. 49 (1978) 1519. Campbell, LA., Allsop, A.L., Stone, N.L.: J. Phys. F8 (1978) L235. Claus, H.: Solid State Commun. 27 (1978) 423. Dubiel, S.M., Campbell, C.C.M., Obuszko, Z.: Solid State Commun. 26 (1978) 593. Hedman, L.E., Rao, K.V., Astrom, H.U.: J. Phys. Colloq. (Orsay, Fr.) 6, Vol. 2 (1978) 788. Holden, T.M., Fawcett, E.: J. Phys. F8 (1978) 2609. Hamada, N., Miwa, H.: Prog. Theor. Phys. 59 (1978) 1045. Hempelmann, R., Ohlendorf, D., Wicke, E.: Proc. Int. Symp. on Hydrides, Geilo, Norway, 1977 London: Pergamon Press 1978. Il’ichev, V.Ya., Klimenko, I.N., Khats’ko, E.N.: Fiz. Nizk. Temp. (Kiev) 4 (1978) 370 (Russ). Kondorskii, E.I., Kostina, T.I., Galkin, Y.Yu.: Conf. Ser.- Inst. Phys. 39 (Transition Met., 1977)(1978) 611. Komura, S., Takeda, T., Ohara, S., Nakai, Y., Kunitomi, N.: J. Phys. Sot. Jpn. 45 (1978) 1493. Kitaoka, Y., Ueno, K., Asayama, K.: J. Phys. Sot. Jpn. 44 (1978) 142. Kawakami, M.: J. Phys. Sot. Jpn. 44 (1978) 433. Men’shikov, A.Z., Sidorov, S.K., Teplykh, A.E.: Fiz. Met. Metalloved. 45 (1978) 949 (Russ). Mikke, K., Jankowska, J.: Transition Metals 1977 (Inst. Phys. Conf. Ser. 39), 1978, p. 595. Nakai, Y., Hozaki, K., Kunitomi, N.: J. Phys. Sot. Jpn. 45 (1978) 73. Nazimov, O.P., Bin, A.A.: Izv. Vyssh, Uchebn. Zaved., Tsvetn. Metall. 5 (1978) 112 (Russ). Pop, I., Giurgiu, A., Pop, E., Iusan, V.: Phys. Status Solidi (b) 88 (1978) K 181. Radhakrishna, P., Livet, F.: Solid State Commun. 25 (1978) 597. Rode, V.E., Finkel’berg, S.A., Skurikhin, A.V.: Fiz. Met. Metalloved. 45 (1978) 433 (Russ). Reno, R.C.: Hyperfine Interact. 4 (1978) 338. Tange, H., Tokunaga, T., Goto, M.: J. Phys. Sot. Jpn. 45 (1978) 105. Yao, Y., Arajs, S.: Phys. Status Solidi (b) 89 (1978) K 201. Zech, E., Hagn, E., Ernst, H.: Hyperf. Interact. 4 (1978) 342. Aoki, Y., Hashimoto, S.: Z. Metallkd. 70 (1979) 436. Beille, J., Bloch, D., Towfiq, F., Voiron, J.: J. Mag. Magn. Mater. 10 (1979) 265. Buis, N.: Thesis Amsterdam 1979. Cowlam, N., Bacon, G.E., Gillott, L., Harmer, G.R., Self, A.G.: J. Phys. F9 (1979) 1387. Chernykh, I.V., Demidenko, V.S., Litvintsev, V.V.: Izv. Vyssh. Uchebn. Zaved., Fiz. 22 (1979)93 (Russ). Fedchenko, R.G., Onishchenko, T.N.: Metallofizika (Akad. Nauk Ukr. SSR, Inst. Metallofiz.) 75 (1979) 86 (Russ). Fukamichi, K.: Phys. Lett. A70 (1979) 235. Goldfarb, R.B., Patton, C.E.: J. Appl. Phys. 50 7358. Hausch, G., Torok, E., Mohri, T., Nakamura, Y.: J. Mag. Magn. Mater. 10 (1979) 157. Kajzar, F., Delapalme, A.: J. Mag. Magn. Mater. 14 (1979) 139. Kondorskii, EL, Kostina, T.I., Medvedchikov, V.P., Kuskova, Yu.A.: Fiz. Met. Metalloved. 48 (1979) 1158 (Russ).

Landolf-Bbrnstein New Series 111/19a

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488 79K3 79K4 79K5 79 K 6

79K7 79 K 8 79K9 79K 10 79K I1 79K 12 79K 13 79K 14 79M 1 79 M 2 79 M 3 7901 79s1 7932 7933 80A 1 80BI 80B2 80B3 8OC 1

80El 80E2 80Fl 80G 1 80G2 80H 1 80K 1 80K2 80K3 80K4 80K5 80K6 80K7 80K8 80K9 80KlO 80K 11

8OL1 8OL2 8OL3 80Ml

Refcrcncesfor 1.2.2 and 1.2.3 Khomcnko. O.A., Khil’kevich, I.F., Zvigintseva, G.E., Vaganova, L.A., Belenkova, M.M.: Fiz. Met. Metallovet ;1979) 43 1 (Russ). Katano. S., M;. N.: J. Phys. Sot. Jpn. 46 (1979) 1265. Kajzar. F., Parette. G., Babic, B.: J. Appl. Phys. 50 (1979) 7519. Kuwano. H., 8no, K.: J. Phys. Colloq. 40 (1979) C 196. Kirillova. M.M.. Nomerovannaya, L.V.: Elektron Strukt. Perekhodnykh Met.. Ikh Splavov Intermet. Soedin. Mater. Mezhdunar. Simp. ISESTM, 2nd 1977,1979,p. 57 (Russ).(ed. by Nemoshkalenko, V.V., Kiev, USSR: Izv. Naukova Dumka). Kajzar. F., Parette. G.: Solid State Commun. 29 (1979) 323. Kemeny. T., Fogarassy, B., Arajs. S., Moyer, C.A.: Phys. Rev. B 19 (1979) 2975. Klimenko. I.N., Romanov, V.P., Il’ichev, V.Ya.: Cryogenics 19 (1979) 209 (Russ). Kalinin. V.M.: Izv. Vyssh. Uchebn. Zaved., Fiz. 22 (1979) 79 (Russ). Kokotov, S.I.. Fadin. V.P.: Izv. Vyssh. Uchcbn. Zaved., Fiz. 22 (1979) 108 (Russ). Katano, S.. Mori. N.: J. Phys. Sot. Jpn. 46 (1979) 691. Kajzar, F., Parette. G.: Phys. Rev. B20 (1979) 2002. Makarov, V.A., Tret’yakov, B.N., Puzei, I.M., Kalinin, G.P., Tokmakova, V.A.: Fiz. Tverd. Tela (Leningrad) 21 (1979) 901 (Russ). Maki. S.. Adachi. K.: J. Phys. Sot. Jpn. 46 (1979) 1131. Maki. S., Adachi. K.: Toyoda Kenkyu Hokoku 32 (1979) 12 (Jap). Ohlendorf. D.. Wicke. E.. Obermann, A.: J. Phys. Chem. Solids 40 (1979) 849. Singer. V.V., Dovgopol, S.P.,Radovskii, I.Z., Gel’d, P.V.: Izv. Vyssh. Uchebn. Zaved., Fiz. 22 (1979)86 (Russ). Strom-Olsen. J.O., Wilford. D.F., Burke, S.K., Rainford, B.D.: J. Phys. F9 (1979) L95. Shiozaki. Y., Nakai. Y., Kunitomi, N.: J. Phys. Sot. Jpn. 46 (1979) 59. Aoki. Y., Hiroyoshi. H., Kawakami, M.: J. Mag. Magn. Mater 15-18 (1980) 1179. Babic. B., Kajzar. F., Parettc, G.: J. Mag. Magn. Mater. 15-18 (1980) 287. Babic. B., Kajzar. F., Parette, G.: J. Phys. Chem. Solids 41 (1980) 1303. Buis. N., Brommer. P.E., Disveld, P., Schalkwijk, MS., Franse, J.J.M.: J. Mag. Magn. Mater. 15(1980) 291. Cywinski. R.. Hicks. T.J.: J. Phys. F 10 (1980) 693. Endoh, Y., Mizuki. J., Ishikawa, Y.: J. Mag. Magn. Mater 15-18 (1980) 501. Eibschutz, M.. Mahajan, S.. Jin, S., Brasen, D.: J. Mag. Magn. Mater. lS18 (1980) 1181. Fincher. CR.. Jr., Shapiro, S.M., Palumbo, A.H., Parks, R.D.: Phys. Rev. Lett. 45 (1980) 474. Gregory, I.P., Moody, D.E.: J. Mag. Magn. Mater 15-18 (1980) 281. Gnziev. R.A., Demidenko, V.S., Panin, V.E.: Fiz. Met. Metalloved. 50 (1980) 989 (Russ). Hornreich. R.M.: J. Mag. Ma&n. Mater 15-18 (1980) 387. Kajzar. F., Parette. G.: Phys. Rev. B 22 (1980) 5471. Kuz’min. N.N., Men’shikov, A.Z.: Fiz. Met. Metalloved. 49 (1980) 433 (Russ). Kunitomi, N., Nakai, Y., Sakakibara, T., Mollymoto, H., Date, M.: J. Phys. Sot. Jpn. 48 (1980) 1777. Khimmatkulov, F., Singer, V.V.. Radovskii, I.Z., Gel’d, P.N., Mal’tsev, A.G.: Fiz. Met. Metalloved. 50 (1980) 666 (Russ). Khimmatkulov, F., Singer, V.V., Radovskii, I.Z., Dovgopol, S.P., Gel’d, P.V.: Izv. Vyssh. Uchebn. Zaved.. Fiz. 23 (1980) 118 (Russ). Khimmatkulov, F., Singer, V.V., Radovskii, I.Z., Gel’d, P.V., Mal’tsev, A.G.: Izv. Akad. Nauk SSSR, Met. No. 4 (1980) 49 (Russ). Katano. S., Mori. N., Nakayama, K.: J. Phys. Sot. Jpn. 48 (1980) 192. Kondorskii. EL, Kostina, T.I., Trubitsina, N.V.: Fiz. Met. Metalloved. 50 (1980) 205 (Russ). Kanakami. M., Aoki, Y.: J. Phys. F 10 (1980) 2067. Kokorin. V.V., Osipenko, I.A.: Fiz. Met. Metalloved. 50 (1980) 1174 (Russ). Kinnenr. R.W.N., Campbell, S.J.,Chaplin. D.H., Wilson, G.V.H.: Phys. Status Solidi A58 (1980) 507. Larikov, L.N., Takzei, G.A., Sych, 1.1.:Dopov. Akad. Nauk Ukr. SSR,Ser. A: Fiz.-Mat. Tekh. Nauki (10) 1980. p. 86 (Ukrain). Larikov, L.N., Takzei, G.A., Sych, 1.1.:Metallofizika (Akad. Nauk Ukr. SSR, Otd. Fiz.) 2 (1980) 30 (Russ). Larikov, L.N., Sych, I.I., Takzei, G.A.: Metallofizika (Akad. Nauk Ukr. SSR.Otd.Fiz.) 2 (1980) 124 (Russ). Men’shikov, A.Z., Kuzmin, N.N., Dorofeev, Yu.A., Kazantsev, V.A., Sidorov, S.K.: J. Mag. Magn. Mater. 20 (1980) 134.

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References for 1.2.2 and 1.2.3 80M 2 80M 3 8OPl 8ORl 8OSl 8OS2 8OS3 80Tl 80T2 8021 81Bl 81B2 81Cl 81Gl 81 G2 81 G 3 81 G4 81Hl 81Kl 81 K 2 81 M 1 81 M2 81 M 3 81Nl 81Pl 81Rl 81Sl 81S2 81S3 81Tl 81T2 81T3 81Vl 81Yl 82Al 82A2 82Bl 82Cl 82C2 82C3 82C4

82D1 82D2 82Gl 82 G 2 82Ll 82M 1 82 M 2 82M 3 82 M 4

489

Men’shikov, A.Z., Teplykh, A.E.: Fiz. Met. Metalloved. 50 (1980) 995 (Russ). Maki, S., Adachi, K.: Trans. Jpn. Inst. Met. 22 (1980) 182. Pecherskaya, V.I., Bol’shutkin, D.N., Il’ichev, V.Ya.: Fiz. Met. Metalloved. 50 (1980) 300 (Russ). Rhiger, D.R., Mueller, D., Beck, P.A.: J. Mag. Magn. Mater. 15-18 (1980) 165. Suprunenko, P.A., Gavrilenko, I.S., Markiv, V.Ya.: Izv. Vyssh. Uchebn. Zaved., Fiz. 23 (1980) 124 (Russ). Shiga, M., Nakamura, Y.: J. Phys. Sot. Jpn. 49 (1980) 528. Shcherbakov, A.S., Prekul, A.F., Volkenshtein, N.V.: Fiz. Tverd. Tela (Leningrad) 22 (1980) 2301 (Russ). Tange, H., Goto, M.: J. Phys. Sot. Jpn. 49 (1980) 957. Takeuchi, J., Sasakura, H., Masuda, Y.: J. Phys. Sot. Jpn. 49 (1980) 508. Zukrowski, J., Krop, K.: J. Phys. Colloq. (Orsay, Fr.) (C-l) (1980) 359. Butylenko, A.K., Nevdacha, V.V.: Ukr. Fiz. Zh. (Russ. Ed.) 26 (1981) 1390 (Russ). Buis, N., Disveld, P., Brommer, P.E., Franse, J.J.M.: J. Phys. Fll (1981) 217. Chachkhiani, Z.B., Chechernikov, V.I., Martynova, L.F., Nedel’ko, V.I., Chachkhiani, L.G., Georgadze, G.S.: Soobshch. Akad. Nauk Gruz. SSR 103 (1981) 49 (Russ). Gribov, Yu.A., Fadin, V.P.: Izv. Vyssh. Uchebn. Zaved., Fiz. 24 (1981) 56 (Russ). Goldfarb, R.B., Patton, C.E.: Phys. Rev. B 24 (1981) 1360. Geerken, B.M., Griessen, R., Van Dijk, C., Fawcett, E.: Conf. Ser. - Inst. Phys. 55 (Phys. Transition Met.) (1981) 343. Gribov, Yu.A., Fadin, V.P.: Izv. Vyssh. Uchebn. Zaved., Fiz. 24 (1981) 9 (Russ). Hilscher, G., Weisinger, G., Hempelmann, R.: J. Phys. F 11 (1981) 2161. Kajzar, F., Parette, G., Babic, B.: J. Phys. Chem. Solids 42 (1981) 501. Kondorskii, E.I., Kostina, T.I., Medvedchikov, V.P.: Vestn. Mosk. Univ., Ser.3: Fiz., Astron. 22 (1981) 22 (Russ). Moze, O., Hicks, T.J.: J. Phys. F 11 (1981) 1471. Maki, S., Adachi, K.: Trans. Jpn. Inst. Met. 22 (1981) 182. Men’shikov, A.Z., Burlet, P., Chamberod, A., Tholence, J.L.: Solid State Commun. 39 (1981) 1093. Nakai, Y., Iida, S.: J. Phys. Sot. Jpn. 50 (1981) 3637. Peretto, P., Venegas, R., Rao, G.N.: Phys. Rev. B23 (1981) 6544. Rode, V.E., Finkel’berg, S.A., Wurl, B., Lyalin, A.I.: Phys. Status Solidi A64 (1981) 603. Shapiro, S.M., Fincher, C.R., Jr., Palumbo, A.C., Parks, R.D.: Phys. Rev. B24 (1981) 6661. Shinogi, A., Endo, K., Yamada, N., Ohyama, T.: J. Phys. Sot. Jpn. 50 (1981) 731. Shiga, M., Matsuda, T., Nakamura, Y.: J. Phys. Sot. Jpn. 51 (1981) 345. Tutovan, V., Scutaru, V., Boghian, L.: An. Stiint. Univ. “Al. I. Cuza” Iasi, Sect. lb 27 (1981) 1. Takzei, G.A., Sych, I.I., Men’shikov, A.Z.: Fiz. Met. Metalloved. 52 (1981) 1157 (Russ). Takzei, G.A., Sych, I.I., Men’shikov, A.Z., Teplykh, A.E.: Fiz. Met. Metalloved. 52 (1981) 960 (Russ). Vintakin, E.Z., Udovenko, W.A., Mikke, K., Jankowska, J.: Solid State Commun. 37 (1981) 295. Yamagata, H.: J. Phys. Sot. Jpn. 50 (1981) 461. Aitken, R.G., Cheung, T.D., Kouvel, J.S., Hurdequint, H.: J. Mag. Magn. Mater. 30 (1982) L 1. Antipov, S.D., Kondrashova, L.A., Stetsenko,P.N.: Vestn. Mosk. Univ., Ser. 3: Fiz., Astron. 23 (1982) 20 (Russ). Benediktsson, G., Hedman, L., Aastroem, H.U., Rao, K.V.: J. Phys. F 12 (1982) 1439. Cable, J.W.: Phys. Rev. B 25 (1982) 4670. Cable, J.W.: J. Appl. Phys. 53 (1982) 2456. Cey, T., Kunitomi, N.: J. Phys. Sot. Jpn. 51 (1982) 3073. Crane, S., Carnegie, D.W., Jr., Claus, H.: J. Appl. Phys. 53 (1982) 2179. De Camargo, P.C., Brotzen, F.R.: J. Mag. Magn. Mater. 27 (1982) 65. Deryabin, A.V., Rimlyand, V.I., Metsik, M.S.: Metallofizika (Akad. Nauk Ukr. SSR,Otd. Fiz.) 4 (1982) 47 (Russ). Gavoille, G., Durupt, S., Hubsch, J.: J. Phys. (Les. Ulis, Fr.) 43 (1982) 773. Geerken, B.M., Grieesen,R., Benediktsson, G., Aastroem, H.U., Van Dijk, C.: J. Phys. F 12 (1982)1603. Luetgemeier, H., Dubiel, SM.: J. Mag. Magn. Mater. 28 (1982) 277. Moze, O., Hicks, T.J.: J. Phys. F 12 (1982) 1. Mushailov, ES., Baksheev,N.V., Troinin, Yu.I., Turpanov, I.A.: Fiz. Met. Metalloved. 53 (1982) 202 (Russ). Mirebeau, I., Parette, G.: J. Appl. Phys. 53 (1982) 1960. Men’shikov, A.Z., Takzei, G.A., Teplykh, A.E.: Fiz. Met. Metalloved. 54 (1982) 465 (Russ).

Landolt-Bdmstein New Series 111/19a

Adschi

490

82M5 82P 1 B2R 1 82s 1 B'S:!

B2Tl 83A 1 83 A 2 83A3 83B 1 83B2 83 B 3 83B4 83Cl 83C2 83D 1 83D2 B3D3 83E 1 83E2 83G 1 83H1 83H2 8311 83K 1 83 K 2 B3K3 83K4 83L 1 83M 1 83M2 83N 1 83 P 1 83P2 83R 1 83s 1 B3S2 83S3 8334 8335 83Tl 83Vl 83Yl 83Zl

Referencesfor 1.2.2 and 1.2.3 Mokhov, B.N.: Pis’ma Zh. Eksp. Teor. Fiz. 35 (1982) 216 (Russ). Palumbo. A.C., Parks, R.D., Yeshurun, Y.: J. Phys. Cl5 (1982) L837. Rode. V.E.. Lyalin, AI., Finkelberg, S.A.: J. Appl. Phys. 53 (1982) 8122. Shiga. M., Matsuda. T., Nakamura, Y.: J. Phys. Sot. Jpn. 51 (1982) 345. Sakakibara. T., Date. M., Okuda, K.: Proc. ICM Conference Kyoto 1982. Takzei. G.A.. Sych. 1.1..Kostyshin, A.M.: Fiz. Met. Metalloved. 53 (1982) 1102 (Russ). Alberts. H.L., Lourcns. J.A.J.: J. Phys. F 13 (1983) 873. Albcrts. H.L., Lourens. J.A.J.: J. Msg. Magn. Mater. 31-34 (1983) 289. Antipov. S.D., Kondrashova. L.A., Stetsenko, P.N.: Vestn. Mosk. Univ., Ser. 3: Fiz., Astron. 24 (1983) 96 (Russ). Burke. S.K.. Rainford. B.D.: J. Phys. F13 (1983) 441. Burke. S.K.. Cywinski. R., Davis, J.R., Rainford, B.D.: J. Phys. F 13 (1983) 451. Burke. S.K.. Rainford. B.D.: J. Phys. F13 (1983) 471. Bolzoni. F., Leccabue, F., Panizzicri, R., Pareti, L.: J. Mag. Magn. Mater. 31-34 (1983) 845. Cep. T., Kunitomi. N.: J. Mag. Magn. Mater. 31-34 (1983) 621. Cable. J.W., Thompson. J.R., Sekula. ST.: J. Msg. Magn. Mater 40 (1983) 147. Dorofeev, Yu.A.. Men’shikov, A.Z.. Takzei. G.A.: Fiz. Met. Metalloved. 55 (1983) 948. Dubiel. S.M., Zinn. W.: J. Mag. Magn. Mater. 31-34 (1983) 530. Deryabin, A.V., Chirkov, Yu.A.: Fiz. Tverd. Tela (Leningrad) 25 (1983) 307 (Russ). Egorushkin. V.E., Kul’kov, S.N., Kul’kova, S.E.: Zh. Eksp. Teor. Fiz. 84 (1983) 599 (Russ). Enokiya, H., Kawakami. M., Tanaka. R., Hihara, T.: J. Phys. Sot. Jpn. 52 (1983) 1434. Gschneidner. K.A., Jr., Ikeda, K.: J. Mag. Magn. Mater. 31-34 (1983) 265. Hcnnion. B., Hennion, M., Hippcrt, F., Murani, A.P.: Phys. Rev. B28 (1983) 5365. Hurdequint. H.. Kouvcl, J.S., Monod, P.: J. Mag. Magn. Mater. 31-34 (1983) 1429. Iidn. S., Nakai. Y., Kunitomi, N.: J. Mag. Magn. Mater. 31-34 (1983) 129. Kondorskii. E.I.. Kostina, T.I., Trubitsina, N.V., L’vova, I.V.: Fiz. Met. Metalloved. 56 (1983) 396 (Russ). Kunitomi. N., Tsuge. S.: Proc. Int. Symp. High Field Magn., 1982,Osaka (1983)87. (ed. by Date, M., Amsterdam: North Holland Publ. Co.). Kokorin. V.V., Osipenko. I.A., Chcrepov, S.V.,Chernenko, V.A.: Fiz. Met. Metalloved. 55 (1983) 1225 (Russ). Kontani. M.. Masuda. Y.: J. Mag. Magn. Mater. 31-34 (1983) 287. Lutgemeier. H.. Bohn, H.G., Dubicl. SM.: J. Mag. Magn. Mater. 31-34 (1983) 547. Mori. N., Takahashi, M., Oomi. G.: J. Msg. Magn. Mater. 31-34 (1983) 135. Mokhov, B.N.: Zh. Eksp. Teor. Fiz. 84 (1983) 1403 (Russ). Nikanorova. LA.. Ilyushin, A.S.: Fiz. Met. Metalloved. 55 (1983) 1215 (Russ). Palumbo. A.C., Parks, R.D., Yeshurun, Y.: J. Mag. Magn. Mater. 36 (1983) 66. Pecherskay,V.I., Bol’shutkin, D.N.: Metallofizika (Akad. Nauk Ukr. SSR,Otd. Fiz.)S (1983)34(Russ). Rode, V.E.. Finkelberg. S.A., Lyalin, A.I.: J. Msg. Magn. Mater. 31-34 (1983) 293. Schaf. J., Le Dang. K., Veillet, P.: J. Msg. Magn. Mater. 37 (1983) 297. Sakakibnra. T., Date, M.. Okuda, K.: J. Mag. Magn. Mater. 31-34 (1983) 63. Sumiyama, K.. Hashimoto, Y., Yoshitake, T., Nakamura, Y.: J. Mag. Magn. Mater. 31-34 (1983) 1495. Smits. J.W., Luitjens, S.B.. den Broeder, F.J.A., Dirks, A.G.: J. Mag. Magn. Mater 31-34 (1983) 920. Shiga. M.. Nakamura. Y.: J. Msg. Magn. Mater. 31-34 (1983) 1411. Takzei. G.A.. Sych. 1.1..Kostyshin. A.M., Rafalovskii, V.A.: Metallofizika(Akad.Nauk Ukr. SSR,Otd. Fiz.) 5 (1983) 113 (Russ). Vilar. R.. Cizcron. G.: Ser. Metall. 17 (1983) 127. Yamagata. H.. Matsumura. M.: J. Mag. Magn. Mater. 31-34 (1983) 65. Zukrowski. J., Krop. K.: Acta Phys. Pol. A63 (1983) 151.

Ref. p. 5171

491

1.3.1 4d, 5d: introduction

1.3 4d and 5d elements, alloys and compounds 1.3.1 Introduction to the paramagnetism of 4d and 5d transition metals

The 4d and 5d transition metals and their mutual alloys and compounds generally exhibit paramagnetism; the major part of their susceptibility arises from the spin paramagnetism of itinerant d electrons; paramagnetic susceptibilities xor,,and xspmorb, which arise, respectively, from the terms of the orbital angular momentum and the spin-orbit interaction, are known also to be important [Sl S 11.If the Stoner model is used to describethe system of itinerant electrons, the spin susceptibility at absolute zero, xspin,is given by W;Wd

(1)

Xspin= 1- 2p;ZD(E,) ’

where uB is the magnetic moment of one electron, i.e. the Bohr magneton, Z is the effective interaction between electrons and D(E,) is the electronic density of states at the Fermi energy E, at zero temperature. Correspondingly, the electronic specific heat coefficient y is given by y = (2n2/3)kiD(E,), where k, is Boltzmann’s constant. The factor F = (1 - 2&ZD(E,))- ‘, which denotes the degree of enhancement of the spin susceptibility over the noninteracting value because of the electron-electron interaction, is called the Stoner enhancement factor. At the time of Stoner, however, the nature of D(E,) was not definite, since his theory could not answer how the electron-electron interaction influences the density of states. This point has been clarified by Landau in his theory of the Fermi liquid [56 L 11;he has shown that xspincan be exactly written in a form similar to eq. (1); bin = I+ 2@(EF) = ~ l+Yy,

’

(2)

where y is the spin-antisymmetric part of the quasiparticle interaction function, Yy,= 2tpD(E,) is one of the socalled Landau parameters, and D(E,) is the exact density of states in which the effect of the electron-electron interaction is correctly included. Here F =(l + Y,)-l should be called the Landau (instead of Stoner) enhancement factor. One modification is needed if one considers the electron-phonon interaction, since this interaction does not substantially influence the magnetic susceptibility, while it influences the electronic specific heat. If one considers that the electron-phonon interaction can be treated asrenormalization of the electronic selfenergy, while the vertex correction due to the interaction can be neglected in view of contributing the order I/mlM, where m and M are, respectively, the electron and ion masses,the effects of the electron-electron and electron-phonon interactions on the electronic density of statescan be factorized to a good approximation; the observed electronic specific heat coefficient is thus given by ’ Yob= $

k;D(EF) (I+ a),

whereas the spin susceptibility retains the form of eq. (2).Here i is the electron-phonon interaction constant and the factor (1 + 1) denotes the effective massenhancement due to that interaction. For the enhancement factor F one obtains from eqs. (2) and (3) 1 F=(l+Y,)

+‘ki (1 +&spin =x yob .

(4)

Pauli paramagnetism ranges from the weakly paramagnetic regime, Y,,-+co and F+O, to the strongly paramagnetic (or nearly ferromagnetic) regime, Y, + - 1 and F-co. It is known that, at ambient pressure,all 4d and 5d transition metals and their mutual alloys and compounds presently known are paramagnetic, i.e. Yy,> - 1. However, Y, is pressure-dependent, and hence it will be possible to find substances that become ferromagnetic at higher pressures, Y,, < - 1. Landolt-Bornstein New Series 111/19a

Misawa, Kanematsu

1.3.1 4d, 5d: introduction

492

[Ref. p. 517

To estimate the Stoner (Landau) enhancement factor F for 4d and 5d transition metals, one should single out lsrin from the observed susceptibility at 0 K. z (0 K). For that purpose one needseither to evaluate theoretical!) 3r to determine expcrimcntally xorhand x,p.orh.Such a procedure is not quite we!! defined except for Knightshift experiments and causes ambiguity. Here we adopt, as a very crude estimate, 21(OK) for zrpi,; the results for F calculated from the values of yoh.x (OK) and 3,on the basis of eq. (4) are listed in Table 1. It is concluded that, within the above-mentioned uncertainty, OSand Ru are in the weakly paramagnetic region, Pd is in the nearly ferromagnetic region and others are intermediate.

Table 1. Basic constants and susceptibility data for 4d and 5d transition metals. ~~(0K) and x,(20 “C): observed magnetic susceptibility at 0 K and 20 “C, respectively 7: observed electronic specific heat coefficient i.: electron-phonon interaction constant F: Stoner (Landau) enhanccmcnt factor. Rcfcrenccto each value of I,,(20 ‘C) is found in the corresponding place in the column of references.See[82 V 1, 81 S I] for referencesto the values of 7 and i. Crystal

~(0 K)

?

I.

structure

10-42

mJ molK’

Zr

hcp

1.06

2.77

0.4

3.9

Nb

bee

2.27

7.80

0.9

4.0

MO

bee

0.82

1.83

0.4

4.6

Tc Ru Rh

hcp hcp fee

1.07 0.39 0.95

6.28 2.8 4.64

0.4 -

1.4 -

Pd

fee

7.0

9.36

0.7

9.3

Hf

hcp

0.71

2.21

0.3

3.1

Ta

bee

1.54

6.15

0.7

3.1

w

bee

0.52

0.90

0.25

5.3

Re

hcp

0.63

2.35

0.4

2.7

OS Ir Pt

hcp fee fee

0.09 1.9s 2.06

2.35 3.19 6.48

0.4 0.3 0.6

0.4 5.9 3.7

F

Ref.

x,(20 -‘cl 10-45

‘) Sin_cle-crystalspecimens.(~“,,,(20‘C)+21,,,(20”C))/3

1.14 1.18‘) 1.26 2.02 2.09 0.65 0.73 1.07 0.34 1.01 1.06 5.25 5.4

1.17‘) 1.21 1.29 2.04 2.14 0.67 0.83 1.23 0.41 1.02 5.29 5.8

5.31

0.68 0.74 ‘) 1.50 1.54 0.52 0.54 0.56 0.68 0.10 0.23 1.87 1.91

0.70 0.75 1.52 1.62 0.53 0.59 0.65 0.71 1) 0.10 ‘) 0.27 1.89 2.0

0.70

is listed.

Misaaa, Kancmatsu

1.18 1.21 2.05 2.14 0.72 0.43 1.02

1.54 0.53 0.68 0.13 1.89 2.05

55Kl 6SVl 65S2 6532 54Al 61Kl 57Al SORl 61Kl SlAl 61 K 1 51Hl 61Kl

71Cl 6lKl 65Vl 53Kl 61Kl 77Pl 53Kl 7011 7011 5lHl

41Sl 62Tl

60Bl 70Tl

63Ml

61Kl 71Cl 53Kl 6lKl 75Al 57Al 54Al 52Wl 31Gl 60Bl 7811 60Bl

64Vl 55Kl 54Al 71Kl 6lKl 53Kl 61Kl 69Vl 73Gl 61Kl 51Hl 70Tl

65Vl

76Hl 71Kl 71Kl 31Gl 60Bl

51Hl 7lKl 71Kl 67Wl 6lKl 74Wl

Ref. p. 5171

1.3.2 4d, 5d: susceptibility

vs. temperature

493

1.3.2 Magnetic susceptibility The magnetic susceptibility of 4d and 5d transition metals and their mutual alloys is generally described by the formula x = kxe

+ Sorb + &-orb

+ &pin

9

(1)

is the diamagnetic susceptibility arising from the core electrons; xorb, xspmorb, and xspin are wherexcore paramagnetic susceptibilities arising from, respectively, the orbital angular momentum, the spin-orbit interaction term and the spin angular momentum. xspinis further decomposed into three parts (2)

Xspin=Xs+Xp+Xdf

where xs,x,, and xd refer to the paramagnetic susceptibility due to s, p, and d valence electrons, respectively. In each contribution the effect of Landau diamagnetism to the susceptibility is considered to be included. These formulae are obtained in the tight-binding approximation within the single-particle model. When the electron correlation arising from the electron-electron interaction is considered, the decomposition of x according to eqs. (1) and (2) contains some ambiguity. It is generally assumed that xd is mainly responsible for the temperature dependence of x. However, it is pointed out that the temperature variation of xspTorb and xorbis also rather significant [68 M 11.General studies for the temperature dependenceof x in which the effectsof the electron correlation, the spin-orbit coupling, etc., are taken into account are not available yet. Here we restrict ourselves to the temperature dependencearising from the spin paramagnetism of itinerant d electrons. When the electron-electron interaction is ignored, the temperature dependence of the susceptibility for a system of itinerant electrons is given by ~,,(T)=2p;

[D(E)

(

-g

>

dE

in terms of the density of states curve D(E) as a function of the single-particle energy E, where f is the Fermi distribution function. When the interaction is considered in the molecular-field approximation (the Stoner model), X(T) is given by

x(T)= 1-xoG’7 ZxoU)’

(4)

where I stands for the effective interaction between electrons. For temperatures low compared with the effective degeneracy temperature, eq. (4) can be expanded in even powers of T, as is the case for the free energy in the Sommerfeld asymptotic expansion,

x(T) = x0(1+PJ2> 9

(5)

where

x: xo=l-K’

x:=Q&%%),

K = 2p;ZD(E,),

and

For D primes denote differentiation with respect to energy and E, is the Fermi energy at zero temperature. According to this model, whether x(T) is an increasing function of Tat low temperatures or not depends on the sign of fl, i.e., whether v/j> v” or not. When one calculates x(T) on the basis of the density of states curve deduced from the observed electronic specific heat coefficient, one obtains &/aT
Misawa, Kanematsu

1.3.2 4d, 5d: susceptibility

494

vs. temperature

[Ref. p. 517

interacting fermion system contains logarithmic terms with respect to temperature, magnetic field, etc., from which one can derive the logarithmic temperature dependenceof the susceptibility

where b, and T* are constants [70 M 11. Here the constant b, does not depend on the detailed form of D(E), but on the general nature of the interaction function. It follows that b, is generally negative for transition metals, and one predicts that the susceptibility exhibits a maximum at temperature T,,, = T*fi. The phenomenon of a susceptibility maximum is universal for 4d and 5d metals and other substances[70 M I, 76 M 1, 76 B 1, 77 B 1, 81 M 11.For 4d and 5d metals T,,,, ranges from 80K (Pd) to 6850K (Ir). In the case of V, old experimental data do not show the susceptibility maximum. while new data [76 H l] clearly exhibit the existence of a maximum. It may be very probable to detect also a maximum in the x(T) curve for Nb in the near future.

1.8 .10-f 3 Y

3.7 .10-h cil~ cm!

1.4

3.;

1.2

3.3 3.3 I ;-

I

1

=‘ = 1.1 2 " x" 0.t

3.1 s

2.9

2.7

OS Hf 0.1 I ?I 0

2G3

400

600 I-

800

1000

1200 K 1100

Fig. I. Temperaturedependenceofthe susceptibility ofZr [41 s 1-J.

0.; 0

4-

100

200 I-

300

K 4OU

Fig. 2. Temperature dependenceof the susceptibility of Zr and Hf for, respectively,two different specimens;for rcfercnccthe data on Ti is included [71 C I].

Misawa, Kanematsu

[Ref. p. 517

1.3.2 4d, 5d: susceptibility vs. temperature/field direction

495

1.6

0.2 360

270” -4

180”

90”

90”

0”

180” Q-

270”

360”

Angle of rotation

Fig. 3. Crystallographic angular dependence of the susceptibility of Zr and Hf measured at room temperature by the double rotation experiment which is suitable for use with a single crystal of unknown crystallographic orientation [71 C I]. The curves yield xI=xmin, and xl, = 3xav- 2x1, where xav represents the average of susceptibilities measured in three mutually perpendicular 0.8 w6 -cm3 9

I H”0.4

a

0.2 0

200

400 600

800 1000 1200 1400K 1600

1.6

0.8 0

200

400

600 7-

800

1000 K 1200

Fig. 4. Temperature dependence of the relative susceptibility of V, Zr, and Nb. xg (20 “C) is 5.30, 1.38, and 2.34 in units of [lO-‘j cm3 g-‘1 for V, Zr, and Nb, respectively [65 S 21. Landolt-Bbrnstein New Series lll/l9a

1.0 0

200 400 600 800 1000 1200 1400”C1600 7b Fig. 5. Temperature dependence of the susceptibility and relative susceptibility of Hf. (a) [54K 11, (b) [61 K 11.

Misawa, Kanematsu

[Ref. p. 517

1.3.2 4d, 5d: susceptibility vs. temperature

496 2.29 .w Cm' 2 21

2.1 m6 @ 9

I 2.26

2.2

E225 H 2.24

I 2.1 0 N 2.0

2.23

1.9

2.22

1.8

mol

221 0

50

100

150

200

1.7 0

250 K 300

400

800

1200 I-

I-

Fig. 6. Temperature dependenceof the susceptibility of Nb [76H I].

1600

2000 K 2600

Fig. 7. Temperature dependenceof the susceptibility of Nb. Solid line: [71 K 11;dots: [53 K 11.

240 .KP pJ mol

183 0

100

200

300

LOO

500 T-

600

700

800

900 K 1000

Fig. 8. Tempcraturc depcndcnccof the susceptibility of Nb. The numbers refer to listings in Table 2 [72 C I]. Table 2. Susceptibility data of Nb at room temperature for experiments listed in Fig. 8. T K

.L 10-6cm3mol-’

Material

Curve in Fig. 8

Ref.

2S9 291 291 300 300 293 293 293 298 290 293 300

211.8 199.7 204.4 203.5 208.1 222.0 213.7 204 204.4 228 217.4 198.9

Brand and Hilgcr; “spec. pure” Siemens; pulverized Nb sheet pulverized sintered-block Nb Johnson Matthey and Co.; 99.9% Nb Fanstecl Corp.; 99.99% Nb Johnson Matthey and Co. 99.6% Nb; 700ppm of Fe Johnson Matthey and Co.; zone-refined Nb zone-refined Nb 99.86% Nbf Ta; 1OOppmof Fe Johnson Matthey and Co.; 99.7% Nb Materials Research Co.; MARZ-grade 99.98%

I 2

33H 1 48Bl 48Bl 53Kl 54Al 6011 61Kl 6251 6301 65Vl 65S2 72Cl

Misawa, Kanematsu

3 4 5 6 7 8 9

Ref. p. 5171

1.3.2 4d, 5d: susceptibility vs. temperature

497

222.5 X-6 -cm3 mol t 215.0 217.5

22 212.5

207.5 205.0 5

0 7-

Fig. 9. Temperature dependenceof the susceptibility of Nb for various purities listed in Table 3 [72 C 11.

Table 3. List of experiments for Nb in Fig. 9 [72C 11. Sample designation

Experiment no.

LI-1 MRC-1 MRC-1 FS-1

Temperature range [K]

Material

78...1056

99.8%Nb, 325 mesh powder, Leico Industries, N.Y. first run on MRC ‘) VP-grade Nb second run on above specimen vacuum annealed Nb, originally beam-melted Nb from Fansteel Corp. MRC MARZ-grade Nb

I

78...412

2

78.‘.406 78...412

78...423

MRC-2

‘) Materials Research Corporation.

0.900 40-6 -cm3 I 0.8996

1.0

H" u

0.892

0.9

5 --in -5 ‘0.8

0.7 0

0.888 I 0.860 40-b -cm3 9 x" 300

600

900 7-

1200

1500 “C 1800

0.840 0

50

100

150 7-

200

250 K 300

Fig. 10.Temperaturedependenceof the relative suscepti- Fig. 11.Temperaturedependenceof the susceptibility of bility of V, Nb, and Ta [61 K 11. Ta. (a) [78 K 11,(b) [54H 11.

Land&-BOrnstein New Series 111/19a

Misawa, Kanematsu

1.3.2 4d, 5d: susceptibility vs. tcmpcraturc/ficld direction

498

[Ref. p. 517

1.00 w4

-cm3 mol

0

400

800

1200

1600

0.80

2000 K 2LOO

I-----

Fig. 12. Temperature depcndcnce of the susceptibility of l-a. Curve I: [71 K I]. 2: [53 K l-j.

0.75 0

1200

800

400

1600 K 2C

l-

Fig. 13. Tempcraturc dcpcndcncc of the susceptibility of MO. Triangles: [53 K I]. crosses: [57A I], circles: [6l K I], solid lint: [7l K I]. dashed line: [77P I].

0.9, 0.28_ 0

800

400

1200

I

I

I

I

900 I-

1200

I

I

2000 K 2400

1600

Fig. 14. Temperature dcpcndcncc of the susceptibility of N’. Solid line: [71 K I], open circles: [61 K I], solid circles: [53 K I].

. . ’. 0.5x y 7* 0 300 600 0.6

1500 K 1800

Fig. 15. Tcmperaturc dcpcndcncc of the susceptibility of Rc. Circles and crosses: [54A I]. squares: [6l K I]. solid lines I and 2: [68 W I], dashed line: [7l K I]. 0

100

50

150 7

250 K 300

200

Fig 16. Tcmpcraturc dcpcndcncc of the susceptibility of Re in two qstallographic directions. ,Y~: H,,,,lc, I,,: H,,,,llc [69V I]. I 1.9 15

u0 E 1.6

1=293K

-5 i-7 1.3

65 0”

1.0CA 0 50”

100”

150”

200”

Fig. 17. Susceptibility ofsir@ crystal of Rc as a function of the angle d,between H and the c axis at 293 K [69 V I],

I 300

600

900 T-

1200

I 1500 “C 1800

Fig. 18. Tempcraturc dependence ofthe relative susceptibility of Ru and Ir. ,Y~(20 “C) is 0.34 and 0.14 in units of [IO-6cm3/g] for Ru and Ir, respectively [6l K I].

Misawa, Kanematsu

15.0 do-" cm3 a

15.0 .lOP cm3 Kl 125

I 10.0 x’

I 10.0 .g 6.0

1.5

LO

5.0 30” 0” HOpplllC

0 0

50

100

150 T-

250 K 300

200

Fig. 19. Temperature dependence of the susceptibility of OS single crystal for two directions ofthe magnetic field at 10 kOe; xl1: H,,,,l)c and x1: Ha&z [73 G 11.

g

0.98

0 o000o

0.10 0

150”

180” H0ppllIC

C’

0

Ooo 50

100

150 T-

200

0 o

0

o

a

1300

250 K :

Fig. 23. Temperature dependence ofthe susceptibility ofIr [60 B 1-J.

-cm -5 0.96 ST 0.9L 0.92 0

90” 120” J%,,llC Field direction

0.13 doe6 Jr cm3 9

go.,1

1.02 1.00

60”

Fig. 20. Crystallographic angular dependence of the susceptibility of OS single crystal in the a plane at room temnerature -I73. G . 11. -

t-

I

499

1.3.2 4d, 5d: susceptibility vs. temperature/field direction

Ref. p. 5171

50

100

200 150 TV

250 ‘.

300 K 350

Fig. 21. Temperature dependence of the relative susceptibility of Rh. Solid circles: [81 A 11, open circles: [60 B 11.

.,& I-

cm3 9 x” 5 0 a

50

100

150 T-

200

250 K 300

1.6

0.8

jO0 b

T-

Fig. 22. Temperature dependence of the relative susceptibility of Rh. Circles: [61 K 11, xs(20”C)=1.03 . 10m6cm3/g; dashed line: [52H 11, ~$2O”C)=O.990 10m6cm3/g. Landolt-Bornstein New Series 111/19a

T-

Fig. 24. Temperature dependence of (a) the susceptibility [68 F l] and (b) the relative susceptibility of Pd. (b) Open circles: [52H 11, solid circles: [21 F 11, triangles: [31 G 11.

Misawa, Kanematsu

[Ref. p. 517

1.32 4d, 5d: susceptibility vs. temperature/pressure

500

1.53 6.5

I 1.25 G b

I 6.0

1.0X

SF 5.5

Fo7j t-7 0.53 0.25 II

800

1200

1600 K 2000

Fi_p.25. Temperature dcpcndcncc of the relative susccptibility of Pd. Circles: [61 K I]. dashed line: [52 H I].

4.5 0

50

100

150 I-

200

250 K 300

Fig. 26. Temperature dependence of the susceptibility of Pd at hydrostatic pressure of0 and 1.5GPa in a magnetic field of 56 kOe [8 1G I].

0 !Ei!!TEl Ho:, = 56kOe I =300K

0

0.5

1.0 GPO 1.5

Fig. 27. Hydrostatic pressure dependence of the susccptibility ofPd at 300 K in a magnetic field of56 kOe. Straight line is a least-squares tit [8l G I].

P-

1.15 .lO-” cm3

I 1.0

I 190

G k $$0.8

“1.05 n

T-7 0.6

1.03 0.95 0

50

100

150 I-

200

250 K 300

0.L 0

400

800

1200

1600 K 20

I-

Fig. 28. Temperature dependence of the susceptibility of Pt. Crosses: [73 D I]. open circles: [60 B I], solid circles: [7SI I].

Fig. 29. Temperature dependence of the relative susceptibility of Pt. Circles: [6l K I], dashed line: [52H I].

Misawa, Kanematsu

Ref. p. 5171

1.3.2 4d, 5d: susceptibility vs. temperature

501

,.Hf

Hf-Ta 1.4

I /I

/

g 1.2 N $1.1 1.0 0.9 0.81

0

300

600

900

1200 "C IE

1

0

300

600

900

To

1200 "C IE

7-

7-

Fig. 30. Temperature dependence of the relative susceptibility of Zr-Nb alloys [62 T 11.

Fig. 3 1. Temperature dependence of the relative susceptibility of Hf-Ta alloys [61 T 11.

1.20

Nb-Mo

75at%Mo /

1.15 /'

1.00

0.95

I

0.90

u L

E-0.85 -e H 0.80 0.75 0.70

0

I

I

I

300

600

900

I 1200 "C 151

T-

Fig. 32. Temperature dependence of the relative susceptibility of NbTa alloys [62 T 11.

Landolt-BOrnstein New Series 111/19a

0

300

600

900

1200 "C 1500

7Fig. 33. Temperature dependence of the relative susceptibility of NbMo alloys [62 T 11.

Misawa, Kanematsu

502

1.3.2 4ci, 5d susceptibility, vs. temperature

[Ref. p. 517

1.0 .?j :

0.a 2: 0.7 06 C.5 135 &km

.”

:.i -II;-&

mol 0.9

Nbc.db.la

120

0

300

600

900

1200 "C 1500

TI 0.i: s

105

0.7

90

1 Q.

0.E 0.9 .,@i gTj m2' 0.8

75 IO3 uQcm

Fig. 35. Tempcraturc dcpcndencc ofthe relative susceptibility of Ta-W and Ta-Re alloys [62 T I].

15.0 w -cm3

I

Pd,-xRh,

192.5

100

I k4

I a0 0.7

10.0

97 I I.5 x"

0.6

96

200

LOO

600

800 "C l[: 3

5.0

IFig. 34.Tcmpcraturc dcpcndcncc ofthc susceptibility and the electrical rcsistivity ofNh Ru alloys. (a) Nb, soRu,,,,. 0~) h'h.szR~~,,,.

(~1 Nb,.s,R~~,.,,

[76D

2.5

11. 0

50

100

150

200

250 K 3

Fig. 37. Temperature depcndcncc of the susceptibility of Pd, -,Rh, alloys [60 B I].

Pdl-xRhx

%

250 K :100

Fig. 36. Temperature dependence of the susceptibility of Pd, -,Rh, alloys [69 D I].

Misawa, Kanematsu

Ref. p. 5171

1.3.2 4d, 5d: susceptibility vs. temperature

a25

Fig. 38. Temuerature deuendence of the susceptibility of Pt;-Jr, allois [60 B 11.’ 1.6I

0 I

50 I

100 I

150 7I

200

250 K 300

Fig. 39. Temperature dependence of the susceptibility of Pt-based dilute alloys Pt-Ru, Pt-Rh, P&V [78 111.

Ed x 1,

3

2

I

Fig. 40. Temperature dependence of the susceptibility of Pd-Pt alloys [70 T 11.

Landolt-Bbmstein New Series 111/19a

0

I

I

I

I

100

200

300

400 7-

Misawa, Kanematsu

500

600

700 K 800

1.3.3 4d, 5d: susceptibility vs. composition

504

[Ref. p. 517

1.3.3 Magnetic susceptibility as a function of composition Table 4. Magnetic susceptibility for metals and alloys at 20°C. The values in parenthesesare obtained by extrapolation from the high-temperature bee phase region [63 T 11.

xg(20 “Cl 10m6cm3g-’

%p(20 “Cl 10e6cm’ g+ 121(163) 163(169) 176 192 214 210 154 50 83 68 130 204

Zr Zr-25 at% Nb Zr-50 at% Nb Zr-75 at% Nb Nb Nb25at% MO Nb-50 at% MO Nb-75 at% MO MO Hf Hf-50 at% Ta Hf-75 at% Ta 65 JO-’ cm3 W-OS

Ta Ta-25at% W Ta-50at% W Ta-75 at% W W Nb-25 at % Ta Nb-50at% Ta Nb-75 at% Ta Ta-12.5 at% Re Ta-25 at % Re Ta-37.5 at% Re

154 131 115 57 53 196 179 162 133 100 58

160 10-6 -cm3 mol 120

Rl

mo: I

I E 80 H 1=300K P Tc-Ru o Tc-Rh o Ru-Rh I 8.6

n 0 I'#

1

2

3

L

at%

5

OS-

Fig. 41. Concentration depcndcncc ofthc susceptibility of \h’-OS solid solutions at room tempcraturc [75A I].

7.8

8.2

Fig. 42. Susceptibility of Tc-Ru, Tc-Rh, and Ru-Rh alloys at 300 K as a function of the number of valence electrons per atom, n [70 I I].

1, -10L cm3 ii5 3

zI 2

PI

Rh -

Rh

Fig. 43. Composition dependence of the susceptibility extrapolated to 0 K of Pt-Rh alloys [74 W I].

-0 Pd

2

L

6 w-

8

10 at% 12

Fig. 44. Concentration dependence ofthe susceptibility of Pd-W alloys at 293 K. Curve I: after cold deformation by 90%, 2: after 1 h at 900°C [79 K I].

Misawa, Kanematsu

Ref. p. 5171

1.3.3 4d, 5d: susceptibility

vs. composition

6

8 at% 6 -Rh

2.5

01 100 at% 75 Rh -Rh

50

25

0 at% 25 Pd Ag-

Fig. 45. Composition dependence of the susceptibility of Pd-Kh and Pd-Ag alloys. Open circles: 20K, solid circles: 290 K [60 B 11.

4

2

0 2 at% 4 Pd Ag Fig. 46. Composition dependence of the susceptibility of Pd-Rh and Pd-Ag alloys. Solid circles: 4.2K [69D 11, open circles: 4.2 K [63 M 11, triangles: 20 K [52 H 11.

7.? .lOv gg 9

8 -1o’4 & mol 6

I 4 g

I 20

I 40

I 80 at% 100 Pt Pt Fig. 47. Composition dependence of the susceptibility of Pd-Pt alloys at OK and 290 K [70T 11. 01 0 Pd

1.25,

-_...

I

I

I I

I 60

I

1 r 0.50Is

.

n

-7.5

1 7=20K&

-0.25 100 at% Ir -Ir Landolt-Bbmstein New Series IIVl9a

Pt-Ir

50

I 25

Pi

0 Pt

‘\

Rh Ru Re MO Nb

‘\,

v

I

I

I

3.0

k.5

6.0

1.5

‘Y 4 ‘,I

‘\

‘1 “I-

I 7.5 at% !

Fig. 49. Increment ofthe susceptibility for Pt-based alloys as a function of the concentration of dissolved metals. The values are obtained by extrapolation to 0 K [78 I 11.

0.25 0

I\ Y oM=Cu’ “4,

x -4.5 . A v -6.0 .

I

//

-3.0

25

50 Au -

at % 100 Fig. 48. Composition dependence of the susceptibility of Au Pt-Ir and Pt-Au alloys [60 B 11.

Misawa, Kanematsu

506

1.3.4 4d, 5d: high-field magnetization

[Ref. p. 517

1.3.4 High-field magnetization Because of the symmetry for time inversion, the free energy of a system is an even function of the nagnetization 0. It seemsto be plausible to expand the free energy G in even powers of 0 near g=O; G=Go+~g,a2+$g2a4+... [n the presenceof a magnetic field H, H=aG/&,

.

(1)

and hence one obtains

H 1 -==g, +g,u2+ . . . . 0 x rhis can be transformed. in view of low cr and low H, into the form for the high-field magnetization, cr=LH-cH3+..., 91

s:

3r the expression for the high-field susceptibility, (4)

T.(W=XO{~ +Bdf21 >

where x0 = g; ’ and PI,= -g2/g:. If one adopts the Stoner model to describe magnetism of itinerant electrons, x(H) at the lowest temperatures takes the form of eq. (4) with

xz

x0= I-K'

, 2 ,,s_ 3,o Pff=ab (l -K)3 )

where &‘. K. V’ and 1~”are defined in sect. 1.3.2. It is to be noted that, if one treats the electron correlation correctly, the expansion of the free energy in powers of CT~ may not be permitted. since the free energy contains logarithmic terms arising from the Fermi liquid effect [71 M I, 70 K 11; G=Go+~,l,~2+~~~~41n~+..., s

(5)

where I’,. \v2,and os are constants. From this one obtains i

=x(H)=xo

l+b,,H’lng

>

(6)

for the high-field magnetization, where b,, = - v,xi and H* = e- 1/4a,/~o. This logarithmic dependenceof 0 or x(H) has been experimentally confirmed for YCo,, LuCo,, TiBe,, etc., [76 B I,78 M 2,81 M 11.Concerning 4d or 5d metals,high-field magnetization measurementswere performed for Pd and Pd-Rh alloys [69 F 1, 71 G I]; the precise form of x(H), however, has not been settled yet becauseof rather small effects for these substances.

Misawa, Kanematsu

[Ref. p. 517

1.3.4 4d, 5d: high-field

magnetization

507 ’

Re r=1.52K

1 0.09 b 0.06

0

30

60 HOPP’-

90 kOe120 0

60 K 120 T-

Fig. 50. Magnetization of Tc, (a) as a function of applied field at 4.5 K, (b) as a function of temperature at 48 and 1OOkOe [8ORl].

I

I

I

42

44

46

I

48 kOe !

HOPPl -

Fig. 51. Magnetic field dependence of the differential susceptibility of Re at 1.52K; the field is applied to the [lOiO] direction [78 M 11.

0.07 Ps 0.06

3

Gcm3 9

0

50

100

150

200 250 HOPPl -

300

350kOe, 400

30

60

90

120

150

180 kOei

HOPPl -

Fig. 52. Magnetic field dependence of the magnetization per atom of Pd and Pd-2at% Rh at 4K; dashed line denotes a straight line with the tangent of the curve at H app,=O [71 G 11.

Land&Bbrnstein New Series 111/19a

0

Fig. 53. Magnetic field dependence of the magnetization at 4.2 K [69 F 11. ofP4,.&hm

Misawa, Kanematsu

I

508

1.3.5/1.3.6 4d, 5d: magnetization density/Knight shift

[Ref. p. 517

1.3.5 Magnetization density The magnetization density induced within a unit cell in a metal by an applied magnetic field can be measured 3)’ polarized neutron diffraction. Such measurements have been done for Pd at 4.2K in an applied field of 57.2kOe [75 C 11.

Pd 00;

Fig. 54. Magnetic moment density of Pd in a (010)plant at 4.2K in a maenctic field of 57.2kOc. The dashedlines denote zero-den&y contours [75 C I].

1.3.6 Knight shift The Knight shift K and the spin-lattice relaxation time T, of metals,which give information on the electronic structure and interaction mechanisms in metals, are measured by the NMR experiment. At a fixed frequency of rf fields, the magnetic field for resonance,H,,,, of a nuclear spin in a metal is slightly different from the field for resonance.HR<,in the casethat the nuclear spin is in a diamagnetic solid. The Knight shift is then defined by K = (H,,,-H~JH~~,. The Knight shift for transition metal nuclei can be written as KU-)=Kx,+K,+fW’-),

(1)

K, = fp, xi (i = orb, s, d) , ’ h’pNAP,, where I-I&, denotes the d-orbital, s-contact and d-spin polarization hypertine field per Bohr magneton pa. respectively, and N, is Avogadro’s number. Here we have assumedthat the total susceptibility can be expressed as (2) %(T)=)[dia+X”rh+S(%s+Xp)+rYd(T)r . where xdiu.I,,~,,.1,. xp. and xd are the ion-core diamagnetic, d-orbital, s-spin, p-spin, and d-spin susceptibilities, respectively.In eqs.(1) and (2) the temperature dependenceis assumedto arise mainly from the d electrons. Using the calculated data for the hyperfine fields and observed data on K(T) and x(T), one can in principle determine various contributions to x separately on the basis of eqs.(1) and (2). The nuclear spin-lattice relaxation rate (l/T,) is also given by the sum of several terms; (3) where orb, s, d. dip, and Q refer to the nature of the relaxation rate arising from the d-orbital, s-contact, d-spin core polarization, spin-dipolar and electric quadrupole interactions, respectively. At low temperatures (l/T,),,,. (l/T,),. and (l/T,), are known to depend linearly on temperature.

Misawa, Kanematsu

1.3.6 4d, 5d: Knight shift, relaxation time

Ref. p. 5171

509

0.89 % 0.86 ~I 0.83 0.80 0.77 200 250 K 300 150 300 600 900 1200 1500 K 1800 0 TFig. 55. Temperature dependence of the change of reFig. 56. Temperature dependence of the Knight shift of sonance frequency, v,,, - v,,, in Nb single crystal, where va Nb. Open circles: [79 S 11, solid circles: NBS data. = 305 kHz is the resonance frequency at 293 K. Magnetic field (34.6 kOe) is applied to [loo] direction; the different symbols refer to three different sequences of measurements [76 H I]. 0

50

100

0.700 % 0.675 ~t 0.650 0.625

a

0.600 200

400

600

800

1000 K Ii 00

I-

-0.25

0

300

600

900

1200

b

T-

Fig. 57. Temperature dependence of (TIT)-’ of Nb. Triangles: 20 MHz, circles: 12 MHz [79 S 11, solid line: NBS data. TI : longitudinal relaxation time.

Land&-Bbmstein New Series IIl/l9a

-1.25 0

1500 K 1800

50

100

150 TT-

200

250 K 300

Fig. 58. Temperature dependence of the Knight shift of MO, (a) at a field of 78.141 kOe [77P 11, (b) at a field of 70.335 kOe, relative to the Knight shift at room temperature [77 K 11.

Misawa, Kanematsu

1.3.6 4d, 5d: Knight shift, relaxation time

[Ref. p. 517

526 kOe -cm3

mol

100

$:.177i;

t 57.0

x" 99 14.4765

56.8 0

98

50

100 I-

150

200 K 250

Fig. 60. Temperature dependence of the field for resonance of tosPd in Pd metal at 10.7MHz [82T I]. li.1755

80

120

160

200

240

96 280 K 320

I-

Fig. 59. Tempcraturc depcndcncc of the licld for rcsonancc and the susccutibilitv of Rh. to3Rh rcsonancc at I .91500 hlHz: [65 S I j; x,,,: [bO B I] 1.75

&I

0 au6

Pd

-50

1.53

I -100 2 ,450 -200

0

0.75 0

50

100

150

200

250 K 3

Fig. 61. Temperature dcpcndcncc of (T,T)- * of Pd [82 T 1-J.Tr : longitudinal rclasation time.

-250 -300 0

150

300

450

600

750 K 900

Fig. 62. Tempcraturc depcndencc of the muon Knight shift in Pd [8l G 21.

% -1.5

-2.c I k -2.5 25 -3s

0

300

600

900

1200 K 1500

0

T-

300

600

900

1200 K 1500

I-

Fig. 63. Temperature dependence ofthc Knight shift ofPt. Solid circles: [78 S I], open circles: NBS data.

Fig. 64. Tempcraturc dcpcndence of the (T,T)-’ of Pt. Solid circles: [78 S I], open circle: NBS data. 7, : longitudinal relaxation time.

Misawa, Kanematsu

[Ref. p. 517

%

1.3.6 4d, 5d: Knight shift, relaxation time

I-

0

511

m Nb-PI

-

n Nb3Pt;A15) .., _, I .I

-3

P',D

0 0 Pt

40

60 Rh-

80 at% 100 Rh

Fig. 66. Composition dependence of (TIT) -I of lo3Rh in Pt-Rh alloys [74W 11. T= 1...4K; T,: longitudinal relaxation time. -4 0

50

100

150

200

250 K 300

Fig. 65. Temperature dependence of the Knight shift of lg5Pt in Nb,Pt (A15), Nbo,GzPt,,3,(a) and pure Pt [77K2].

Table 5. NMR and susceptibility data for Pt, -XRh,, Zr, and MO. x,,,: extrapolated to OK; K, (TIT)-‘: Xm

K

10m4cm3 mol-’

%

(TIT)-l s -1K-’

K (RN

K Pt)

- 3.4(2) - 3.0(2) - 1.8(2) -0.44(10) +0.22(10) +0.27(3) +0.71(3) +0.51(3) + 0.43 ‘)

-3.54 -3.6(2) -4.5(2) -5.1(2) -3.1(2) -2.1(2) - 1.3(2) -0.64(10) -1.18(10) -

i.l(l) 0.84(7) 0.67(4) 0.39(3) 0.26(3) 0.19(2) 0.11’)

T= l...4K. Ref.

PIT)-’ (RN

Pt Pto.,,Rhom Pto.goRho.lo Pto.soRho.,o Pt o.6oRho.40 Pto.,oRho.,o Pto.zoRho.so Pt o.loRho.9, %o,Rho.,, Rh

2.05(2) 2.56(2) 3.46(3) 3.24(3) 2.52(2) 1.58(l) 1.14(l) 0.98(l) 0.96(l) 1.00(l)

Zr

1.20

K (Zr)

0.33

0.033

75Hl

MO

1.033

K (MO)

0.60

-

77Pl

‘) C71Nl-J. “) [66Nl].

Land&-Bdrnstein New Series 111/19a

Misawa, Kanematsu

74Wl

[Ref. p. 517

1.3.7 4d, Scl: magnetostriction

512

1.3.7 Magnetostriction The magnetostriction of a paramagnetic metal is a convenient measure of the volume dependenceof the nasnetic susceptibility of the metal. When a magnetic field H is applied along the axis of a cylindrical specimen of length I and radius r, the pecimen generally shows the longitudinal magnctostriction A/// and the transverse magnetostriction Ar/r. The nagnetostriction is known to be proportional to HZ, in agreementwith the change ofthc freeenergy.The volume md shape magnetostriction S,. and S, are defined by

vherc 1’ is the volume of the specimen. The volume dependence of the susceptibility is given by the volume nasnetostriction through the relation [70 F l] v ax 2v, s

Xav=X,x

"3

ahere x is the isothermal compressibility and D, is the molar volume of the metal. The magnetostriction is found to be remarkably anisotropic even in some of the cubic transition metals 183F 11. 8s; .,3‘5

I

Table 6. Magnetostriction of groupVIII transition metals and alloys [70F2]. T=4.2K. H,,,, up to 100kOe.

1=4.2K

Oe-?

Al 1 =gl

>

~ 403 P

-2o]

lo-l8 Oe-’

1 20 ot4b 15 -Rh

i

12.R.:/h.Agj

10

5

0 Pd

5 at % 10 Ag -

Fi_r. 67. Composition dcpcndcncc of the volume magnetostrictioncoeflicicnt of Pd-Rh and Pd-Ag alloys at 4.2K. Open circles: [70 K 21. solid circles: [83 F I]. 50 .,o -!O

I l= 4.2K

oe-2 0

RU Rh Pd Ir Pt Rho.soIro.so Rh o.soPdoso If o.d’do.~o W,.d’hm W,.d%cv

- 0.9(l) 7.0(3) - 25.0(5) 2.4(1) - 20.0(3) 6.0(10) 17.0(10) 8.5(10) - 11.0(5) - 50.0(30)

1

0

I

4

P

c;; -53 00 "o

',

-100 l-p, Pd.0 -1%

20

at% 15 -Rh

10

5

Pd-Ag

0 Pd

5 at% 10 Ag-

Fig. 68. Composition dcpcndcnccof the shapemagnctostriction cocficicnt of Pd -Rh and Pd- Ag alloys at 4.2K. Open circles: [70 K 21. solid circles: [83 F I].

Misawa, Kanematsu

1.3.8 4d, 5d: magnetoresistivity,

[Ref. p. 517

Hall effect

513

Table 7. Shape and volume magnetostriction and volume dependence of the magnetic susceptibility for transition metals and Pd-Rh alloys. u& for Pd-Rh alloys is assumedto be the samevalue as for Pd [83 F 11. T=4.2K. Sf

Xm 10m4cm3mol-’

VI& lOi ergmol-’

0, ait -xrn av

1.38 2.61 3.15 1.75

1.4 1.2 0.5 5.2 6.6 15.5 18.4

10-l* OeC2 V MO W Pd PhwRho.o, WmRho.o, Pdo.,,Rhm, Zr

-

0.5 4.7 3.4 90 100 80 90

16 1.9 0.4 105 200 520 680

4.8

-9.6

2.97 0.81 0.53 7.3 9.5 11.1 12.8 0.9 ‘) 1 1.492)

0.78

-2.4 ') 1 - 1.02)

‘) For x1. “1 For XII.

1.3.8 Magnetoresistance and Hall effect The magnetic field dependenceof the electrical conductivity tensor o(H) is described as follows. With the magnetic field (parallel to the z axis) along a high-symmetry direction, the conductivity tensor takes the form; c,.,(H) = a,,(H), o,,(H) = -o,,(H), and o,,(H) = a,,(H) = a,,(H) = a,,(H) = 0. These relations, coupled with the Onsager relation eij(H) = crji(-H), require that a,,(H) and a,,(H) be even and odd function of H, respectively. When the Fermi surfaceis closed,then, according to semiclassicalmagnetoresistancetheory [56 L 21,(T,, and (T,+, at high fields have the asymptotic form ax,(T) ~xxyjp

~xyN h - n&c + a,,(T) H

H3 '

where n, and n,, are the number of electrons and holes, respectively. The temperature dependenceof a,,(T) and u,,,(T) is subject to the nature of the scattering processesin metals. If the metal is compensated (n,=n,), gxy= ~x,UYH3. Inversion of the conductivity tensor gives the resistivity tensor Q(H). At high fields, 1 - xo’,,w ~uxx(T> H2 ' exx We define the magnetoresistivity e1I and the Hall resistivity ezl through the relations e~~=&~,(H>+exx(-H)l, e21

=ik?,,W)-e,x(-WI.

Observation of the magnetoresistivity of W reveals that u,,(T) is nearly proportional to T2; this shows that the scattering mechanism is mainly due to the electron-electron interaction [72 W 1-J.In the case of Re, there appears a break in the Hall resistivity vs. H curve; the break is considered to be a consequence of magnetic breakdown causing the appearance of new closed orbits [74 K 11.

Landolt-Bornstein New Series lll/l9a

Misawa, Kanematsu

1.3.8 4d, 5d: magnetoresistivity,

[Ref. p. 517

Hall effect

513

Table 7. Shape and volume magnetostriction and volume dependence of the magnetic susceptibility for transition metals and Pd-Rh alloys. u& for Pd-Rh alloys is assumedto be the samevalue as for Pd [83 F 11. T=4.2K. Sf

Xm 10m4cm3mol-’

VI& lOi ergmol-’

0, ait -xrn av

1.38 2.61 3.15 1.75

1.4 1.2 0.5 5.2 6.6 15.5 18.4

10-l* OeC2 V MO W Pd PhwRho.o, WmRho.o, Pdo.,,Rhm, Zr

-

0.5 4.7 3.4 90 100 80 90

16 1.9 0.4 105 200 520 680

4.8

-9.6

2.97 0.81 0.53 7.3 9.5 11.1 12.8 0.9 ‘) 1 1.492)

0.78

-2.4 ') 1 - 1.02)

‘) For x1. “1 For XII.

1.3.8 Magnetoresistance and Hall effect The magnetic field dependenceof the electrical conductivity tensor o(H) is described as follows. With the magnetic field (parallel to the z axis) along a high-symmetry direction, the conductivity tensor takes the form; c,.,(H) = a,,(H), o,,(H) = -o,,(H), and o,,(H) = a,,(H) = a,,(H) = a,,(H) = 0. These relations, coupled with the Onsager relation eij(H) = crji(-H), require that a,,(H) and a,,(H) be even and odd function of H, respectively. When the Fermi surfaceis closed,then, according to semiclassicalmagnetoresistancetheory [56 L 21,(T,, and (T,+, at high fields have the asymptotic form ax,(T) ~xxyjp

~xyN h - n&c + a,,(T) H

H3 '

where n, and n,, are the number of electrons and holes, respectively. The temperature dependenceof a,,(T) and u,,,(T) is subject to the nature of the scattering processesin metals. If the metal is compensated (n,=n,), gxy= ~x,UYH3. Inversion of the conductivity tensor gives the resistivity tensor Q(H). At high fields, 1 - xo’,,w ~uxx(T> H2 ' exx We define the magnetoresistivity e1I and the Hall resistivity ezl through the relations e~~=&~,(H>+exx(-H)l, e21

=ik?,,W)-e,x(-WI.

Observation of the magnetoresistivity of W reveals that u,,(T) is nearly proportional to T2; this shows that the scattering mechanism is mainly due to the electron-electron interaction [72 W 1-J.In the case of Re, there appears a break in the Hall resistivity vs. H curve; the break is considered to be a consequence of magnetic breakdown causing the appearance of new closed orbits [74 K 11.

Landolt-Bornstein New Series lll/l9a

Misawa, Kanematsu

1.3.8 4d, 5d: magnetoresistivity, Hall effect

514

[Ref. p. 517

IO2 e 6

0 I

2

108

I

z=6 s L

‘

0

0 il

2

-, 10 6-9 E Ilk

2

c

6

E

105

2

kOe4.10s

fHcp:lFig. 69. Magnetic field dcpcndence of the Hall rcsistivity of hJo for two samples; both axes are multiplied by the residual rcsistancc ratio r = R2031R,,, to produce a Kohler plot (r = 5050 in thcsc samples) [76 F I]. Fig. 70. Change in the magnctorcsistivity, A?,, =Q, ,(HApp,)--~, r(0). for two samples ofMo as a function of applied field; both axes arc multiplied by the residual reststance ratto r= Rz9, lR,, to product a Kohler plot (r = 5050). Circles: [76 F I]. solid lint: [62 F I]. 22.5 do8 Rem _

2

IO6

2

L

4 40'2 L-km Oe 3

Re

I 2

3

i

E

105

2 kOe4.

For Fig. 71, see p. 515.

17.5 I

6

f-Hopp~ -

I 2 c;

12.5

108

/q .

7.5

0”

2.5

0

a

IO

20

30

40 Hup:1-

50

60

70 kOe80

30"

60"

b @Fig. 72. (a) Magnetic field dependence ofthc Hall resistivity of Re. Curve I: Hvpp, along [lOiO] direction; 2: H,,,, along [I 1201 direction; 3: angle between H,,,, and the c axis is 45”; 4: Hllc [74K I]. (b) Hall constants of Re as a function of the angle 4 between H,,,, and the c axis: Curves I and 2 refer to field strengths below and above the break point (about 20 kOe) in (a). respectively [74K I].

Misawa, Kanematsu

Ref. p. 5171

1.3.9 4d, 5d: electronic specific heat

515

25 .I06

11

(is 23 I 22 Z F21 ,B s" 20 19 18

Fig. 71. H&, ,/err of W as a function of T2 for various values of the magnetic field [72 W 11.

6 17 0

5

IO

15

20 T2-

25

I 30

18.6 I 35 K*

1.3.9 Magnetic field dependence of the electronic specific heat coefficient The magnetic field dependence of the electronic specific heat coefficient, y(H), is related, according to thermodynamics, to the temperature dependenceof the magnetic susceptibility x(T). Since XH = - aF/aH and y= -aZF/3T2, where F(T, H) is the free energy of the system, one can obtain a thermodynamic relation:

where y is defined as the specific heat divided by temperature. If it is assumedthat x(T) behaveslike x(O)+ j3T2 at low temperatures, where /I is a constant, then, for H-0, one should expect y(H) = y(O) + fiH2 from eq. (1). As far as x(T) depends quadratically on T, the sameholds for the dependence of y(H) on H; one has

at T2 = H2 =O. By analysing the observed data on y(H) at low H and x(T) at low T one may examine the applicability of relation (2). Such a comparison has been made so far for LuCo,, Pd, and TiBe,; the results show that eq. (2) doesnot hold [82 B 1,83 M 11.This implies that the assumption that X(T) behaveslike x(0)+flT2, or, equivalently, y(H) behaveslike y(O)+ j?H2, is not valid. This difficulty may be avoided in the Fermi liquid model by considering that the temperature dependenceof x follows a T2 In T law becauseof the Fermi liquid effect [83 M 11. For 4d and 5d transition metals y(H) has been measured only for Pd; in accordance with the above statements, the observed y(H) does not follow a simple HZ law [Sl H 1, 83 M 11. 9.50 mJ molK2 9.25

I 9.00 x

Fig. 73. Magnetic field dependenceof the electronic specificheat coefficient of Pd [81 H 11.

8.50 0

30

60

90 HVP1 -

Landolt-Bbmstein New Series 111/19a

Misawa, Kanematsn

120 kOe 150

Ref. p. 5171

1.3.9 4d, 5d: electronic specific heat

515

25 .I06

11

(is 23 I 22 Z F21 ,B s" 20 19 18

Fig. 71. H&, ,/err of W as a function of T2 for various values of the magnetic field [72 W 11.

6 17 0

5

IO

15

20 T2-

25

I 30

18.6 I 35 K*

1.3.9 Magnetic field dependence of the electronic specific heat coefficient The magnetic field dependence of the electronic specific heat coefficient, y(H), is related, according to thermodynamics, to the temperature dependenceof the magnetic susceptibility x(T). Since XH = - aF/aH and y= -aZF/3T2, where F(T, H) is the free energy of the system, one can obtain a thermodynamic relation:

where y is defined as the specific heat divided by temperature. If it is assumedthat x(T) behaveslike x(O)+ j3T2 at low temperatures, where /I is a constant, then, for H-0, one should expect y(H) = y(O) + fiH2 from eq. (1). As far as x(T) depends quadratically on T, the sameholds for the dependence of y(H) on H; one has

at T2 = H2 =O. By analysing the observed data on y(H) at low H and x(T) at low T one may examine the applicability of relation (2). Such a comparison has been made so far for LuCo,, Pd, and TiBe,; the results show that eq. (2) doesnot hold [82 B 1,83 M 11.This implies that the assumption that X(T) behaveslike x(0)+flT2, or, equivalently, y(H) behaveslike y(O)+ j?H2, is not valid. This difficulty may be avoided in the Fermi liquid model by considering that the temperature dependenceof x follows a T2 In T law becauseof the Fermi liquid effect [83 M 11. For 4d and 5d transition metals y(H) has been measured only for Pd; in accordance with the above statements, the observed y(H) does not follow a simple HZ law [Sl H 1, 83 M 11. 9.50 mJ molK2 9.25

I 9.00 x

Fig. 73. Magnetic field dependenceof the electronic specificheat coefficient of Pd [81 H 11.

8.50 0

30

60

90 HVP1 -

Landolt-Bbmstein New Series 111/19a

Misawa, Kanematsn

120 kOe 150

1.3.10 4d, 5d: plastic deformation

516

[Ref. p. 517

1.3.10 Effect of plastic deformation on the susceptibility The plastic deformation alters substantially the magnetic properties of paramagnetic materials and may either increase (e.g.for V, Nb) or decreasethe susceptibility (e.g.for AI, Cu). Concerning 4d and 5d transition metals, the effect of the plastic deformation on the susceptibility has been measured for Zr, MO, Pd, W, etc.: [76D2. 80Dl. 8OSl]. When a cylindrical spccimcn oflength /is plastically dcformcd by A/along the axis, the susceptibility becomes a function of the degree of plastic deformation

~=Al/l;

the susceptibility

depends also on the direction of

deformation relative to the direction of an applied magnetic field. The plastic deformation increases the dislocation density p through which the susceptibility

changes [80 D 11.

0

0.5

1.0

1.5

1

2.0

2.5 kOe 3.0

HODD1 -

1.6 t -m ,x 51.3 1.0

0

1

2

3

6

5

6

7 kOe8

Hor4 -

Fig. 76. Susceptibility ratio of deformed and single crystal spccimcns for Pd and W as a function ofmagnetic

E-

Fig. 74. Relative variation ofthc susceptibility ofpolycrystnllinc Zr as a fimction of the degree of deformation at room tcmpcraturc: the direction of the deformation is (solid circles) pnrallcl to the magnetic field. and (open circles) pcrpcndicular to the mngnctic licld [SOS I].

0.6 10’

10”

10’

108

log

field for various values of the degreeof deformation. E, at room temperature [76 D 21.

lOlocm-210”

Fi_r. 7% x,(r)/~~ of MO as a function of dislocation density, ! at room tcmpcraturc, whcrc x,(w) is the susceptlhllity estrapolatcd to H= ~j in the zF vs. l/H curve and ,$ is the susceptibility of the undcformcd single crystal: [SOD I].

Misawa, Kanematsu

References for 1.3

1.3.11 References for 1.3 21 F 1 31Gl 33Hl 41 s 1 48Bl 51Hl 52Hl 52Wl 53Kl 54Al 54Hl 55Kl 56Ll 56L2 57Al 60Bl 6011 61 K 1 62Fl 62Jl 62Tl 63M 1 630 1 65Sl 6582 65Vl 66Nl 67Wl 68Fl 68Ml 68Vl 68Wl 69Dl 69Fl 69Vl 70Fl 70F2 7011 70Kl 70K2 70Ml 7OSl 70Tl 71Cl 71 G 1 71Kl 71Ml 71Nl 72Cl 72Wl 73Dl

Land&-Bdmstein New Series III/l%

Fo&x, G.: Ann. Phys. Paris 16 (1921) 174. Guthrie, A.N., Bourland, L.T.: Phys. Rev. 37 (1931) 303. de Haas, W.J., van Alphen, P.M.: Koninkl. Ned. Akad. Wetenschap. Proc. Ser. A36 (1933) 263. Squire, CF., Kaufmann, A.R.: J. Chem. Phys. 9 (1941) 673. Brauer, G.: Z. Anorg. Chem. 256 (1948) 10. Hoare, F.E., Walling, J.C.: Proc. Phys. Sot. (London) Sect. B64 (1951) 337. Hoare, F.E., Matthews, J.C.: Proc. R. Sot. London Ser. A212 (1952) 137. Wucher, J., Perakis, N.: C.R. Acad. Sci. 235 (1952) 419. Kriessman, C.J.: Rev. Mod. Phys. 25 (1953) 122. Asmussen, R.W., Soling, H.: Acta Chem. Stand. 8 (1954) 563. Hoare, F.E., Kouvelites, J.S.,Matthews, J.C., Preston, J.: Proc. Phys. Sot. (London) Sect. B 67 (1954) 728. Kriessman, C.J., McGuire, T.R.: Phys. Rev. 98 (1955) 936. Landau, L.D.: Zh. Eksp. Teor. Fiz. 30 (1956) 1058; Sov. Phys. JETP (English Transl.) 3 (1957) 920. Lifshitz, I.M., Azbel, M.I., Kaganov, M.I.: Zh. Eksp. Teor. Fiz. 31(1956) 63; Sov. Phys. JETP (English Transl.) 4 (1957) 41. Asmussen, R.W., Potts-Jensen, J.: Acta Chem. Stand. 11 (1957) 1271. Budworth, D.W., Hoare, F.E., Preston, J.: Proc. R. Sot. London Ser. A257 (1960) 250. van Itterbeek, A., Peelaers,W., Steffens,F.: Appl. Sci. Res. B8 (1960) 177. Kojima, H., Tebble, R.S., Williams, D.E.G.: Proc. R. Sot. London Ser. A260 (1961) 237. Fawcett, E.: Phys. Rev. 128 (1962) 154. Jones, D.W., McQuillan, A.D.: J. Phys. Chem. Solids 23 (1962) 1441. Taniguchi, S., Tebble, R.S., Williams, D.E.G.: Proc. R. Sot. London Ser. A265 (1962) 502. Manuel, A.J., St. Quinton, J.M.P.: Proc. R. Sot. London Ser. A273 (1963) 412. van Ostenburg, D.O., Lam, D.J., Shimizu, M., Katsuki, A.: J. Phys. Sot. Jpn. 18 (1963) 1744. Seitchik, J.A., Jaccarino, V., Wernick, J.H.: Phys. Rev. Al38 (1965) 148. Suzuki, H., Miyahara, S.: J. Phys. Sot. Jpn. 20 (1965) 2102. Volkenshtein, N.V., Galoshina, E.V.: Phys. Met. Metallogr. USSR (English Transl.) 20 (1965)No. 3,48. Narath, A., Fromhold, A.T., Jr., Jones, E.D.: Phys. Rev. 144 (1966) 428. Weiss, W.D., Kohlhaas, R.: Z. Angew. Phys. 23 (1967) 175. Foner, S., Doclo, R., McNiff, E.J., Jr.: J. Appl. Phys. 39 (1968) 551. Mori, N.: J. Phys. Sot. Jpn. 25 (1968) 72. Volkenshtein, N.V., Galoshina, E.V., Shchegolikhina, N.I.: Phys. Met. Metallogr. USSR (English Transl.) 25 (1968) No. 1, 166. Wunsch, K.M., Weiss, W.D., Kohlhaas, R.: Z. Naturforsch. 23a (1968) 1402. Doclo, R., Foner, S., Narath, A.: J. Appl. Phys. 40 (1969) 1206. Foner, S., McNiff, E.J., Jr.: Phys. Lett. A29 (1969) 28. Volkenshtein, N.V., Galoshina, E.V., Shchegolikhina, N.I.: Sov. Phys. JETP (English Transl.) 29 (1969) 79. Fawcett, E.: Phys. Rev. B2 (1970) 1604. Fawcett, E.: Phys. Rev. B 2 (1970) 3887. Isaacs, L.L., Lam, D.J.: J. Phys. Chem. Solids 31 (1970) 2581. Kanno, S.: Prog. Theor. Phys. 44 (1970) 813. Keller, R., Ortelli, J., Peter, M.: Phys. Lett. A31 (1970) 376. Misawa, S.: Phys. Lett. A32 (1970) 153. Shimizu, M.: Proc. 3rd IMR Symp. on Electronic Density of States,NBS Special Publ. 323 (1970)685. Treutmann, W.: Z. Angew. Phys. 30 (1970) 5. Collings, E.W., Ho, J.C.: Phys. Rev. B4 (1971) 349. Gersdorf, R., Muller, F.A.: J. Phys. Paris Suppl. C 1, 32 (1971) 995. Kohlhaas, R., Wunsch, K.M.: Z. Angew. Phys. 32 (1971) 158. Misawa, S.: Phys. Rev. Lett. 26 (1971) 1632. Narath, A., Weaver, H.T.: Phys. Rev. B3 (1971) 616. Collings, E.W., Smith, R.D.: J. Less-Common Met. 27 (1972) 389. Wagner, D.K.: Phys. Rev. B5 (1972) 336. van Dam, J.E.: Thesis, University of Leiden 1973.

Misawa, Kanematsu

518

Referencesfor 1.3

13G 1

Galoshina. E.V., Gorina, N.B., Polyakova, V.P., Savitskii, E.M., Shchcgolikhina, NJ., Volkenshtein. N.V.: Phys. Status Solidi (b) 58 (1973) K45. 74K 1 Kondorskii. E.I.. Galkina, OS., Cheremushkina, A.V., Usarov, U.T., Chuprikov, G.E.: Soviet Phys. JETP (English Transl.) 39 (1974) 1094. 14w 1 Weaver. H.T., Quinn, R.K.: Phys. Rev. BlO (1974) 1816. 75Al Alekseyeva.L.I.. Budagovskiy, S.S.,Bykov, V.N., Kondakhchan, LG., Povarova, K.P., Podolyan, N.I., Savitskiy, Ye.M.: Phys. Met. Metallogr. USSR (English Transl.) 40 (1975) No. 5, 87. EC 1 Cable. J.W., Wollan. E.O., Felcher, G.P., Brun, T.O., Hornfeldt, S.P.: Phys. Rev. Lett. 34 (1975) 278. 75H 1 Hioki. T., Kontani. M., Masuda. Y.: J. Phys. Sot. Jpn. 39 (1975) 958. 76B 1 Burzo. E., Lazar. D.P.: Solid State Commun. 18 (1976) 381. 76Dl Das. B.K., Stern. E.A., Lieberman, D.S.: Acta Metall. 24 (1976) 37. 76D 2 Deryagin. A.I., Pavlov, V.A., Vlasov, K.V., Shishmintsev, V.F.: Phys. Met. Metallogr.USSR (English Transl.) 41 (1976) No. 5, 183. 76F 1 Fletcher, R.: Phys. Rev. B 14 (1976) 4329. 76H I Hechtfischer, D.: Z. Phys. B 23 (1976) 255. 76M 1 Misawa. S., Kanematsu, K.: J. Phys. F6 (1976) 2119. 77B 1 Barnea. G.: J. Phys. F 7 (1977) 315. 77K 1 Karcher. R., Kiibler, U., Liiders, K., Sziics, Z.: Phys. Status Solidi (b) 84 (1977) 189. 77K2 Khan, H.R., Liiders, K., Raub, Ch.J., Sziics, Z.: Phys. Status Solidi (b) 84 (1977) K 33. 77P 1 Ploumbidis. D.: Z. Phys. B28 (1977) 61. Inoue. N., Sugawara, T.: J. Phys. Sot. Jpn. 44 (1978) 440. 7811 7SK 1 Kobler. U., Schober. T.: J. Less-Common Met. 60 (1978) 101. 7SM 1 Martins. J.M.V., Missell, F.P., Percira, J.R.: Phys. Rev. B 17 (1978) 4633. 7s M 2 Misawa. S.: J. Phys. F8 (1978) L263. 7ss 1 Shaham. M., El-Hanany, U., Zamir, D.: Phys. Rev. B17 (1978) 3513. 79K 1 Klyuyeva. LB., Kuranov, A.A., Chemerinskaya, L.S., Babanova, Ye.N., Bashkatov, A.N., Syutkin, P.N., Sidorenko, F.A., Gel’d, P.V.: Phys. Met. Metallogr. USSR (English Transl.) 47 (1979)No. 4, 46. 79s 1 Shaham, M.: Phys. Rev. B20 (1979) 878. SOD1 Deryagin. A.I., Nasyrov, R.Sh.: Phys. Met. Metallogr. USSR (English Transl.) 49 (1980) No. 6, 64. SOR 1 Radhakrishna. P., Brown, P.J.: J. Phys. F 10 (1980) 489. SOS1 Savin. V.I., Markin, V.Ya.. Deryavko, I.I., Yakutovich, M.V.: Phys. Met. Metallogr. USSR (English Transl.) 49 (19SO)No. 2, 170. SlAl Abart, J.?Voitlander. J.: Solid State Commun. 40 (1981) 277. SlGl Gerhardt. W., Razavi. F., Schilling. J.S., Hiiser, D., Mydosh, J.A.: Phys. Rev. B24 (1981) 6744. SlG2 Gygax, F.N., Hintermann, A., Riiegg. W., Schenck, A., Studer, W.: Solid State Commun. 38 (1981) 1245. 81 H 1 Hsiang. T.Y., Reister, J.W., Weinstock, H., Crabtree, G.W., Vuillemin, J.J.: Phys. Rev. Lett. 47 (1981) 523. SlMl Misawa, S.: J. Mag. Magn. Mater. 23 (1981) 312. SlSl Shimizu. M.: Rep. Prog. Phys. 44 (1981) 329. S2B1 Beal-Monod. M.T.: Physica 109, 1lOB (1982) 1837. 82Tl Takigawa, M.? Yasuoka. H.: J. Phys. Sot. Jpn. 51 (1982) 787. 82Vl Vonsovsky, S.V., Izyumov, Yu.A., Kurmaev, E.Z.: Superconductivity in Transition Metals, Berlin. Heidelberg. New York: Springer 1982, ch. 4. S3Fl Fawcett. E.. Pluzhnikov, V.: Physica 119B (1983) 161. S3M 1 Misawa, S.: J. Mag. Magn. Mater. 31-34 (1983) 361.

Misawa, Kanematsu

Ref. p. 5641

519

1.4.1.1 3dAd, 5d (group 4-7): introduction

1.4 Alloys and compounds of 3d elements and 4d or 5d elements 1.4.1 3d elements and Zr, Nb, MO or Hf, Ta, W, Re 1.4.1.1 Introduction a) Phase diagram and crystal structure Solubility and intermetallic compounds in binary systemsare shown in Table 1. As seenin the table, most of the 4d and 5d elements are not soluble in the 3d elements,but they can form intermetallic compounds. Among them the Laves phase compound, AB2, is the most important one. In particular, Laves phase compounds containing Fe or Co are extensively studied in respect of magnetism. Laves phases have one of the three following structure types: (i) Cl5 (cubic, MgCu, type), (ii) Cl4 (hexagonal, MgZn, type), (iii) C36 (hexagonal, MgNiz type). In the present alloy systems,Mg is replaced by one of the 4d or 5d elementsand a 3d element takesplace of Cu or Zn site. The C36 type rarely appears. In Fig. 1 the unit cells of the Cl5 and Cl4 crystals are shown. It is worthwhile to note that these AB, crystals have a close-packed structure of two kinds of atoms with different atomic sizes,ideally R, = 1.225Rn.The two types of Laves phases,Cl5 and C14, are due to a different sequenceof atom layers and hence the coordination number of each atom is the samefor both structures. The AB, compounds treated in this section have a finite range of a single phase in off-stoichiometric compositions. There is a trend that the off-stoichiometric field spreadswider to the B side. This trend may be understood as that the A atom having larger atomic size can be easily replaced by a B atom but not B by A. It should be noted that a slight deviation from the stoichiometry can give rise to significant effects on the magnetic properties. Therefore, it is likely that disagreementsin data on magnetic properties of these compounds may be due to a slight deviation from the stoichiometry introduced in their preparations.

a

0 Mg. Cu

b

Fig. 1. Crystal structure of Laves phasecompounds.(a) Cl 5 &IgCu, type, cubic, Fd3m): Both Mg and Cu have only one chemically equivalent site. It should be noted that the local symmetryof Cu is not cubic and hencethe Cu site has a non-zero electric field gradient, whose principal axis is along one of the [l 1l] directions. The asymmetryfactor q is zero. Therefore, ifa 3d atom at a Cu

Land&-Bdmstein New Series 111/19a

0

Mg 0 Zn

site is magnetized, it can take four magnetically different sites in maximum.(b) Cl4 (MgZn,, hexagonal, P6Jmmc): There are two Zn sites, 2a and 6h, respectively. The principal axis of the electric field gradient is along the c axis for the 2a site (q = 0) and in the c plane for the 6h sites

(tt$0) as shown by bold lines.

Shiga

Table 1. Equilibrium phases and solubility limits of binary alloys between 3cl and 4d or 5d elements. See [58 h I] if not otherwise noted. For intermetallic compounds, the crystal structure is given in parentheses. Hf

Zr Ti

V

Cr

Solid solution ‘) Low-temperature High-temperature V,Zr(C15) Zr in V 3at%

Cr,Hf

Eii (

Solid solution ‘) phase r (hcp) phase p (bee) V,Hf(Cl5)*)

>

z:i (

Ta

MO

Solid solution Solid solution Solid solution Martensitic transformation @-+a) on Ti-rich side Solid solution

Not soluble

Not soluble Cr,Zr

Nb

‘? 1

Miscibility gap V in Ta 36at% Ta in V lOat% ‘)

?

Ta in Cr l.Sat% Cr in Ta 9at% Cr,Ta(C15, C14)

Miscibility

W

Re

Not soluble ‘) Ti in W IOat%

Not soluble ‘) T&b4

7

V in Re 3at% Re in V 65at% VRe, ‘)

gap

Cr in Re 5at% Re in Cr 35 at% Cr,Re,o-phase ‘)

CrinW5at% WinCr2at%

Mn

Not soluble’) Mn,Zr(C14)

Mn,Hf(C14)

7

Mn,Ta(C14)

a-phase

?

Mn,,Re16’) o-phase

Fe

Not soluble Fe,Zr(ClS)

Not soluble ‘)

Fe,Nb(C14)

Fe,Ta(C14)

MO in Fe 4at% F+WD8s)

Fe,W(C14) hW2 Fe,W@8,)

Re in Fe 11 at% Fe,Re, o-phase

Co,Nb(C 15)

Co,Ta’)

COWDO,,) Co,Mo,W,)

Co,WDO

MO in Ni 13at% Ni,Mo Ni,Mo

W in Ni 12at% Ni,W

Fe,Hf(C14+ClS) co

Ni

Not soluble CoZr(CsCI) Co I *Zr,, Co,Zr CoZr,(CuAl,) Co,Zr(ClS) ‘)

Co,Hf Co,Hf(ClS) CoHf(CsC1) CoHf,(Ti,Ni)

Ni,Zr(AuBe,) Ni,Zr,, Ni,,Zr, Ni 1*Zr,, NiZr NiZr,(CuAl,)‘)

Ni,Hf Ni,Hfi, Ni,Hf, Ni,,Hf, Ni 1,Hf,,, NiHf NiHf,(AlCu,) ‘)

‘) [65e 11. ‘) [69s 11.

,cJ

Solid solution

Co7Wlm-3,)

‘) Ni,Nb NiNb

Ni,Ta(TiCu,) Ni,Ta,

Ni in Re 45 at% Re in Ni 5 at% ‘)

Ref. p. 5641

1.4.1.2 Ti, V-4d, 5d (group 4-6)

521

b) Magnetic properties Most of the alloys and the intermetallic compounds are Pauli paramagnetic except for some of the Fe alloys and intermetallic compounds which show ferro- or antiferromagnetism. However, they usually show a temperature-dependent susceptibility. In some cases,this looks like a Curie-Weiss law. This behavior may be ascribed to a high density of statesof the d band at the Fermi level. For thesecases,we use a term “nonmagnetic”, meaning a magnetic state in which no local-moment alignment, including ferro- and antiferromagnetism, takes place at the lowest temperature. c) Arrangement of substances Binary alloys and compounds are arranged in the order of increasing atomic number of the 3d element in thesesubstances.In each of the following subsections on Ti and V, Cr, Mn, Fe, Co and Ni alloys the sequenceof the 4d and 5d elements is: Zr, Hf, Nb, Ta, MO, W, Re. Ternary alloys are, in principle, placed after the binary alloys of their constituents. For example, the ternary alloy Fe-Co-Zr appears in the subsection on Co alloys after Co-Zr binary alloys. Exceptions are V-Fe-Zr and Cr-Co-Zr ternary alloys, which are found in the subsections on V and Cr alloys, respectively.

1.4.1.2 Ti and V alloys and compounds No alloys and intermetallic compounds other than nonmagnetic ones have been found so far. Most of them becomea superconductor at low temperatures. Fairly extensive studies including magnetic properties have been done becauseof the interest in superconductors, in particular, for Laves phase compounds of V,M (M = Zr, Hf, etc.). Survey Alloy

Composition

Property

Fig.

Ti, -xNb, Ti, -XM~, V, -xNbx VI -xMox V,Zr, V,Hf, V,Ta V, - ,Al,Zr V, -,Fe,Zr V, -,Fe,Hf V,Zr 1- ,Hf,

01x11.0 -O~x~1.0 OSxS1.0 -04x
2 3 4, 5 6

V, -,ZrNb, V,Zr, -XNb, V, - ,Nb,Hf

o<x10.1 -osxjo.1 06x50.25

XII&) xnka Y(X),T,(x) X”(X),K(x) h&'J xm7xs3T,,K, e2qQ x&T) x;'(T) x~'(T) x CO,K(T) &Q, T,(x),Y(X) x&O L,(T) a, T, x,,,,e2qQ x(T) K(T) L,(T)

V,Hf, - xTax

Landolt-Bdmstein New Series 111/19a

x=0.15 x=0.3 x=0.3 OSxS1.0 --

O~x~1.0

Shiga

Table

2 7 8 8 9, 10 11 12 12 3 13 14 15

Ref. p. 5641

1.4.1.2 Ti, V-4d, 5d (group 4-6)

521

b) Magnetic properties Most of the alloys and the intermetallic compounds are Pauli paramagnetic except for some of the Fe alloys and intermetallic compounds which show ferro- or antiferromagnetism. However, they usually show a temperature-dependent susceptibility. In some cases,this looks like a Curie-Weiss law. This behavior may be ascribed to a high density of statesof the d band at the Fermi level. For thesecases,we use a term “nonmagnetic”, meaning a magnetic state in which no local-moment alignment, including ferro- and antiferromagnetism, takes place at the lowest temperature. c) Arrangement of substances Binary alloys and compounds are arranged in the order of increasing atomic number of the 3d element in thesesubstances.In each of the following subsections on Ti and V, Cr, Mn, Fe, Co and Ni alloys the sequenceof the 4d and 5d elements is: Zr, Hf, Nb, Ta, MO, W, Re. Ternary alloys are, in principle, placed after the binary alloys of their constituents. For example, the ternary alloy Fe-Co-Zr appears in the subsection on Co alloys after Co-Zr binary alloys. Exceptions are V-Fe-Zr and Cr-Co-Zr ternary alloys, which are found in the subsections on V and Cr alloys, respectively.

1.4.1.2 Ti and V alloys and compounds No alloys and intermetallic compounds other than nonmagnetic ones have been found so far. Most of them becomea superconductor at low temperatures. Fairly extensive studies including magnetic properties have been done becauseof the interest in superconductors, in particular, for Laves phase compounds of V,M (M = Zr, Hf, etc.). Survey Alloy

Composition

Property

Fig.

Ti, -xNb, Ti, -XM~, V, -xNbx VI -xMox V,Zr, V,Hf, V,Ta V, - ,Al,Zr V, -,Fe,Zr V, -,Fe,Hf V,Zr 1- ,Hf,

01x11.0 -O~x~1.0 OSxS1.0 -04x
2 3 4, 5 6

V, -,ZrNb, V,Zr, -XNb, V, - ,Nb,Hf

o<x10.1 -osxjo.1 06x50.25

XII&) xnka Y(X),T,(x) X”(X),K(x) h&'J xm7xs3T,,K, e2qQ x&T) x;'(T) x~'(T) x CO,K(T) &Q, T,(x),Y(X) x&O L,(T) a, T, x,,,,e2qQ x(T) K(T) L,(T)

V,Hf, - xTax

Landolt-Bdmstein New Series 111/19a

x=0.15 x=0.3 x=0.3 OSxS1.0 --

O~x~1.0

Shiga

Table

2 7 8 8 9, 10 11 12 12 3 13 14 15

1.4.1.2 Ti, V-4d, 5d (group 4-6)

522 2.3 JO-' -cm3 Kl3! 2.1

[Ref. p. 564

2A wL &p

mol 2.0

I E 1.9 N

IE 1.6 x

1.7

1.5 0 Ti

20

LO

60

0.81"

80 at%

Nb

Nb -

Fig. 2. Composition depcndcnce ofthc room-tcmpcraturc susceptibility ofTi -Nb alloys [76C I]. Triangles: as cast, open circles: quenched from 1000°C. open squares: quenched from 135O’C. solid squares: pure Ti and Nb. Dashed lines indicate the boundary of mctastablc phases obtained by quenching from high temperatures. The crystal structures arc as follows: c(‘: hcp, u”: tetragonal mnrtcnsite. (I): comples, p: bee. [76C I].

3.0 .lO-' CiT?

rn3 2.8

2.E I ,:

-0

26

Ti

2.2

2.c 20

40

60

Nb-

80 at %

Nb

Fig. 4. Composition dcpcndcncc ofthc magnetic susccptibility at room tempcraturc of V-Nb alloys [67 L I]. The V-Nb system forms a solid solution with the bee structure over whole concentration range [54 W I]. The specimens were homogenized at 1050°C for one week and subscqucntly water quenched.

20

40

60

MD-

80 at% 100

MO

Fig3.(a)Susccptibilityat 300K,(b)clectronicspccific heat cocllicicnt y and (c)superconducting transition temperature T, of Ti-Mo alloys [72C I]. The specimens were quenched from 1300°C after 8h annealing at the same temperature. Dashed lines indicate the phase boundaries ofthc alloys thus obtained,whosc crystal structures are as follows: a’: hcp (martensitc), o: hexagonal (precipitates in p phase), p: bee.

1.4.1.2 Ti, VAd,

Ref. p. 5641

5d (group 4-6)

0

0.641

k

v

100

150 7-

200

250

K 300

Fig. 6. Susceptibility change Ax,,, = x,( 7’) - ~~(0) as a function of temperature for V,Mo, --x alloys [79 K 11. ~JO),inunits [10e6 cm3 mol-‘],is given by 308 for V,269 for Vo.sMoo,z, 225 for V,,,Mo,,,, 142 for V,,,Mo,,,, 93 for Vo.2Moo,s, and 86 for MO, respectively. Samples were subjected to heat treatment at 1300 “C for 6h. The system forms a continuous series of bee solid solution.

P 0.54 0

50

523

20

40

60 Nb -

80

at% 100 Nb

Fig. 5. Composition dependence of g3Nb and ‘lV Knight shifts at room temperature [67 L 11. The specimens were submitted to the same heat treatments as given for susceptibility measurements in Fig. 4.

Table 2. Magnetic and related properties of V,M (M = Zr, Hf, and Ta). All these materials are nonmagnetic and become a superconductor at low temperatures. The temperature dependenceof the susceptibility is given in Fig. 9 (V,Zr and V,Hf) and Fig. 15 (V,Ta).

Structure x,JRT) [10-4cm3mol-1] xJRT) [10m6cm3g-‘1

V,Zr

V,Hf

V,Ta

Cl5 10.5

Cl5

Cl5 6.0

[k?M I]

,,‘;“, 1,

$M

8.5 [80 M l] 0.51

10.6

T,CKI K (“V) at RT [%]

11

0.57 [78P 11

2.1 [78 H 11 3.6 [78 H l]

[81Vl]

eZqQ (‘lV) at RT [MHz]

1.5 [Sl V 11 4.9 .lO-" & 9 I 4.6

Fig. 7. Temperature dependence of the susceptibility of (VO,g,,Al,,,,,),Zr. The sample was heat treated at 1100 “C for 150h and has the Cl5 structure. It has a superconducting transition point at 7.4 K [78 P 21.

Land&Bbmstein New Series III/I%

s

Shiga

i.34 0

50

100

150

200

250 K 300

1.4.1.2 Ti, V-4d, 5d (group 4-6)

524

[Ref. p. 564

5sI-

I 4.5I?7 4.CI-

3.EI-

0

I

10

20

30

40

K

7r .J_Jo

50

50

100

150

200

250 K 300

I-

Fig. 8. Temperature depcndcncc of the invcrsc susccptibility of V,.,Fe, ,Zr and V,.,Fe,,,Hf. The spccimcns were heat treated at 900 ‘C for 3 days. V,,,Fc,,,Zr has the Cl5 structure with the RT lattice paramctcr of n=7.362A. V,,,Fc,,,Hfhns the Cl4 structure with the RT lattice parameters 0=517SA and c=S434A [75 D I]. 0.52

/

“” VzZrl_,Hf, 0.48

p 0.u

Fig. 9. Tcmpcraturc dcpcndcncc of the susceptibility of V,Zr, -,Hf,. The specimens with x=0 and x =0.525 were heat trcatcd at 1200°C for 120 h [SOM 11.The specimens with x = 0.6. x = 0.75, x = 0.5, and x = I were heat treated at 1100“C for 150h [Sl V I]. All the compounds have the Cl5 structure at room tempcraturc. They undergo a structural transformation at IOW temperatures. l00...200K [79K 23. whcrc the susceptibility shows a maximum.

/

0

3

I

MHzV2Zr,_,Hf,

o I D D “a,

T=300K

2

\

1 a 60 mJ molK2

I=-

;

0.55 -j 7; k 0.53

-

0

I

o 0.6

i

x

0.46 0.5c “/b

\ -

0527-4 0 0.48 0

c’

o

53

o

40

y /

20 b 11 K 0

o 0.5

Cl0

100

150 200 T-

250

300 K 350 V,lr

Fig IO. Tcmpcmturc dcpcndcncc ofthc isotropic component ofthe Knight shift, K,,,.of”V nuclcus in VzZr, -,Hf, with the Cl5 structure [SI V I].

x-

V,Hf

Fig. 1I. Composition dcpcndcncc of(a) the electric quadrupolc splitting eZqQ in NMR spectra at 300K [St V I]. (b) the electronic spccitic heat cocficicnt 7 [SOM I]. and (c) the superconducting transition tcmpcraturc 7, of V,Zr, -,Hf, [SOM I].

Shiga

525

1.4.1.2 Ti, VAd, 5d (group 4-6)

Ref. p. 5641 .-..m4

-cm3 mol 1.08

1 1.06 :: E 1.04 x 1 6. 9.25I 50

100

I 250

I 200

150

I

K 300

-s 1.02

TFig. 12. Temperature dependence of the susceptibility of and V,-,ZrNb,. (1) V,Zr, (2) V,Zr, -,Nb, (4) V2Zro.&bo.o~9 (5) V1.95ZrNb0.05~ (3) Vl.9ZrNbo,l, VzZr,,,Nb,,,. The specimens were heat treated at 900°C for 72 h and have the C 15 structure at room temperature [77 K 11.

I.00

0

0.53 %

50

100

150

200

250 K :

TFig. 13.Temperature dependence ofthe reduced magnetic susceptibility of V2 -,Nb,Hf. The susceptibility at 300 K is given in Table 3 [8OV 11.

0.51

0.49 I 2 Ok7 k R s 0.45

0

I

/ 0

n

T

x=0

0.43

Ul 0

I 50

I 100

I

I

150 T-

200

I

I

250 K 300

Fig. 14. Temperature dependence of the isotropic Knight shift of 51V in V, -,Nb,Hf [SOV 11.

Table 3. Magnetic and related properties of V,-,Nb,Hf [SO V 11. The temperature dependence of the susceptibility and of the Knight shift are given in Figs. 13 and 14, respectively.

a (Cl5 structure) at RT [A]

T,CKI x,,,(RT) [10-4cm3mol-1] (“‘V) at 300K [MHz]

e2qQ

Land&Bbmstein New Series lW19a

x=0

x = 0.05

x=0.15

x = 0.25

7.378 9.1 9.8 1.5

7.372 9.3 9.4 1.75

7.401 9.4 8.4 2.1

7.405 9.3 8.1 2.0

Shiga

1.4.1.3 Cr-4d, 5d (group 4-7)

526

[Ref. p. 564

X-L cm3 mol

51 0

50

I 100

I 150

I 200

I 250

I

K

300

Fig. 15. Tempcraturc dcpcndencc of the susceptibility of V,Hf, -XTa,. TL indicates the structural transformation tcmpcraturc. The spccimcns except for V,Ta were heat treated at 1200°C for 12h. The V,Ta sample was heat trcatcd at 1000“C for 30 days. All specimens have the C 15 structure at room tcmpcraturc [78 H 11.

1.4.1.3 Cr alloys and compounds Cr-rich alloys are in the spin density wave state or become antifcrromagnctic. seem to be nonmagnetic.

Intermetallic

compounds of Cr

Survey

Alloy

Cr2Zr. Cr,Hf &Jr, -,Co,W (Cr, -$oJ2ZrHy Cr, -xNb, Cr, -,Ta, Cr, -,Mo, Cr, -IW, Cr, -,Re,

Composition

Property

Fig.

Table 4

O~x~1.0 01x10.75 -O~x~O.75 l.lsyg4.2 0~x~0.01 0~x~0.01 o<x10.22 -Olxll.0 -osx -- 10.04 O~x~1.0 O~x50.22

16 17 18

TN(X) TN(X) TN(x), urn Ln(X)~ Y(X) TN(X), L(T) xm>Y(X) TN(X)>x,(x)~ Y(X) xm(T)

Shiga

19 19 20, 22 21 19, 23 21 24,25 26

1.4.1.3 Cr-4d, 5d (group 4-7)

526

[Ref. p. 564

X-L cm3 mol

51 0

50

I 100

I 150

I 200

I 250

I

K

300

Fig. 15. Tempcraturc dcpcndencc of the susceptibility of V,Hf, -XTa,. TL indicates the structural transformation tcmpcraturc. The spccimcns except for V,Ta were heat treated at 1200°C for 12h. The V,Ta sample was heat trcatcd at 1000“C for 30 days. All specimens have the C 15 structure at room tcmpcraturc [78 H 11.

1.4.1.3 Cr alloys and compounds Cr-rich alloys are in the spin density wave state or become antifcrromagnctic. seem to be nonmagnetic.

Intermetallic

compounds of Cr

Survey

Alloy

Cr2Zr. Cr,Hf &Jr, -,Co,W (Cr, -$oJ2ZrHy Cr, -xNb, Cr, -,Ta, Cr, -,Mo, Cr, -IW, Cr, -,Re,

Composition

Property

Fig.

Table 4

O~x~1.0 01x10.75 -O~x~O.75 l.lsyg4.2 0~x~0.01 0~x~0.01 o<x10.22 -Olxll.0 -osx -- 10.04 O~x~1.0 O~x50.22

16 17 18

TN(X) TN(X) TN(x), urn Ln(X)~ Y(X) TN(X), L(T) xm>Y(X) TN(X)>x,(x)~ Y(X) xm(T)

Shiga

19 19 20, 22 21 19, 23 21 24,25 26

Ref. p.

5641

1.4.1.3 CrAd, 5d (group 4-7)

527

Table 4. Magnetic properties of Cr,Zr and Cr,Hf. The temperature dependence of the susceptibility of Cr,Zr is given in Fig. 17. It depends on heat treatments [83 H 11. Cr,Zr Structure Magnetism x,,, (300K) [10-4cm3mol-‘] Ref.

Cr,Hf

Cl5 Cl4 Pauli paramagnetism 9.2 4.0 [83 H 11 [68A l]

0.2

0

0.L

Cl-

0.8

0.6 X-

1.0 co

Fig. 16. Composition dependence of the susceptibility of (Cr, -.$o,),Zr and their hydrides at 273 K [83 H 11.Solid circles: (Cr, -xCo,)zZr with the Cl5 structure, solid triangles: (Cr, -$o,),Zr with the Cl4 structure, open circles: hydrides with the Cl5 structure, open triangles: hydrides with the Cl4 structure.

‘i$

(Cr,-,Co, J2Zr

mfjq&&

I

PO

15

I 55

s IO

IO

0

50

100

150

200

250 K 3

Fig. 17. Temperature dependence of the susceptibility of (Cr, -$o,),Zr [83 H 11.

I

0

I

50

I

I

100

150

200

250 K 300

Fig. 18. Temperature dependence of the susceptibility of (Cr, -,Co,),ZrH, hydrides [83 H I].

Landolf-BBmstein New Series 111/19a

Shiga

1.4.1.3 Cr-4d, 5d (group 4-7)

52s

[Ref. p. 564

320 K

25C

2oc I SF 15c 1

2

Cr

5 at%

3 Nb.Ta.W -

6

Fig. 19. Variation of the N&l tcmpcraturc TX in Cr-Nb [76 F I]. Cr-Ta [76 F I] and Cr-W, squares: [76 F I], crosser: [66 K I].

lO[

5[

[ MO-

Fig. 20. Variation of the N&l temperature TX in Cr-MO alloys. Solid circles: [66H I], triangles: [68A2], open circles: [70 B l] and squares: [SOS I].

I.1

1

1=300K

-7/ mJ nlolK2 -2

Is1.80 1.75

rl I

0.8 0 Cr

0 l

20

LO

60 Mo.W w

Cr-Mo Cr-W

I b

1.70

\ \

1.651 0

I 80 at% 1oo[ Mo.W

150

I L50

I 300

I 600

I K 753

I-

Fig. 9-l Concentration dcpcndcncc ofthc susceptibility at 300 K and the clcctronic specific hcnt cocflicicnt y of Crhlo and Cr-W alloys [70 B I].

Fig. 22. Temperature dependence of the susceptibility of CrMo alloys. The arrows indicate the N&l temperature [70 B l-j.

Shiga

1.4.1.3 Crvld, 5d (group 4-7)

Ref. p. 5641 1.95 .lOP cm3 mol 1.90

800,

I

I

I

88

I

I

I 12

I I 16 ot% ot 10

600 I

I 1.85 H"

400

h'

1.8C 200 II 0

I 300

I 150

I 600

I 450

K

I 750 01 0 Cr

T-

0

Fig. 23. Temperature dependence of the susceptibility of Cr-W alloys. The arrows indicate the NCel temperature [70B 11.

”

&

I

Re -

Fig. 24. Concentration dependence of the Neel temperature of Cr-Re alloys. Solid circles: [65 B I], open circles: [70 B 11; determined by electric conductivity measurements. Solid triangles: [64 B 21, open triangles: [70 B l] ; determined by susceptibility measurements.

1.9 a4 -cm3 mol

I

Cr-Re

1.8

5

I CG

4

1.7

I a 3

1.6 1.95 .m4 cm3 mol

:: 2.0 I w cm3 mol

44

I

I

I

I

I

I

I 1.90 2;

I 1.8 ;

1.85

1.7 1.6 0 Cr

5

IO

15 Re -

20

150

300

450

600

K

T-

Fig. 25. Concentration dependence of the susceptibility at 300K and the electronic specific heat coefficient y of Cr-Re alloys [70 B 11.

Landolt-Bbmstein New Series lWl9a

1.80 0

25 at% 30

Fig. 26. Temperature dependence of the susceptibility of Cr-Re alloys. Re content (a) 1, 7, 14at%, (b) 17, 20at% [70 B 11.

Shiga

[Ref. p. 564

1.4.1.4 Mn-4d, 5d (group 4)

530

1.4.1.4 Mn alloys and compounds Mn-rich alloys are polymorphic and show complicated phase diagrams whose magnetic properties are not ,vell understood. Neither ferromagnetic nor antiferromagnetic phases have been found in intermetallic compound except their hydrides. Surq

Allo>

Composition

MnzZr. MnzHf MnzZrH, Mn?Zr, -,Ti,H,

OIx53.8 -O~x~O.5

Property

Fig.

x, ‘U-)

21 28 29

4T) 4~)~ L,(x)~ T,(X) 2.50 Gcm3 9

r

2.25

1.5c

I 1.25 b l.OC

0

150

300

450 I-

600

750 K 900

Fig. 27. Temperature dependence of the inverse susccptibility of h4n2Zr and Mn,Hf. The specimens wcrc heat treated at 8OO’C for 30 h and have the Cl4 structure [79S I]. 320 K 210

160

80

0

0

0.1

0.2

0.3

x-

0.5

50

100

150 I-

200

250 K 300

Fig. 28. Temperature depcndcnce ofthc magnetization of Mn,Zr and hydrides, Mn,ZrH, at an applied field of 12kOe. The samples were cooled to 4.2 K in zero field before starting the mcasurcmcnts. The dashed curve rcprcscnts the magnetization of a t’icld-cooled sample at 12 kOc [SOJ I]. The effects of cxccss Mn composition on magnetic propcrtics arc given in [8l P I]. Fig. 29. (a) Magnetization ofMnzZr, -,Ti,H, hydrides at 4.2K under an applied field of 21 kOc. Compositions of hydrides arc as follows: Mn,ZrH,,,, Mn,Zr,,,Ti,,,H,,,, Mn2Zro.7’%.&~.~~ Mn.Jr~.~Tid~.~, Mn2Zr0,sTi,,,H,,,. The crystal Mn2Zro,6Tid2.~. structure of these hydrides is Cl4. The critical tempcraturc T, whcrc the magnetization abruptly drops is also rcprcscntcd. The tcmpcraturc dependence of the magnetization exhibits complex features [Sl F I]. (b) Magnetic susceptibility of Mn,Zr, -,Ti, and their hydrides at 298 K. The compositions of the hydrides arc the same given in (a) [Sl F I].

Ref. p. 5641

1.4.1.5 Fe-4d, 5d (group 4-6)

1.4.1.5 Fe alloys and compounds The solubility limit of 4d and 5d elements in Fe is very small. Therefore, interests in magnetism of Fe-rich single-phase alloys are reduced to the effects of impurities on ferromagnetism of bee Fe, which are treated in sect. 1.1. On the other hand, the solubility of Fe in 4d and 5d transition metals is also low. The magnetic properties of Fe impurities in 4d and 5d metals and alloys are studied in relation to the Kondo effect,which are described in Landolt-Bbrnstein, NS, vol. III/lSa [82 f 11. Laves phase Fe,Zr and Fe,Hf are the only ferromagnetic binary stoichiometric compounds treated in this section. In particular Fe,Zr and related alloys are most extensively studied. Distinct magneto-volume effectsare observed in these materials. For instance, the Fe,Zr,,,Nb,,, alloy exhibits an Invar-like thermal expansion curve. The Fe,Hf, -XTa, system has an interesting magnetic phase diagram. At x=0.2, ferromagnetic to antiferromagnetic and antiferromagnetic to paramagnetic transitions take place with increasing temperature and metamagnetic properties are observed in the antiferromagnetic region. The (Fe, -$oJzZr system exhibits spin-glass characteristics above x=0.5. Survey Alloy

Composition

Fe,Zr

Property

Fig.

a, g,, pFe, L

Table 5

0, G,

d’TcldP, daldH> xHF, Y

Hhyp,

Is>

e2qQ

e(T)

FeZr, Fe, - XZrX Fe,Hf Fe, -,Hf, FeHf,H, Fe,Nb, Fe,Ta, Fe,W Fe, - xTax

Fe, -XNb, Fe,Mo, --x FexWl --x 0% -xA4)2Zr Fel.4A10&H, Fe,Zr, -,Ti,

x=2, x=3 0.26lx10.36 -0.28Ix10.36 -y=o, y=3 0.325Ix
0% -.VJ2Zr

O~x~O.4 x = 0.45,x = 0.5, x=1.0 O<x
(Fe1-xV,)2ZrHy

0.0425 x 5 0.33 0.33Ix
(Fe1-xGJ2Zr

x=O.8,y=O,y=4.6 O~x
IS, e2qQ 4x), T,(x) a, 0, T,, Hhyp, e2qQ e(T) 44 T,(x) a, 0, T,, IS, e2qQ a, c, x,,,, IS, e2qQ 4T)> GO O), 4H) x,(T), x;‘(T) TN(x)>H,,,(X) TN(x),

:;;;

ffhypk)

;;x;

w

ih> k&i H,,,(X) 4T), xi ‘U-1 a@)>

C(X),

T,(x),

4x), XIII(X) M(T) G1(T) 44 44 T,(x)> T,(x) PFetx)

a(T) x,(T)> x,‘(T) a(x), 44 T,(x), T,(x) PFetX)

0.05~x~0.15 0.2~~~0.75 Landolt-Bbmstein New Series 111/19a

Shiga

x&T), x,l(T)

44, c(x), T,(x) m, x,(x) a(T) xg(Th x,‘(T)

PFe

30 6 31 7 30 32 8 9 33 34 35 36 36 37 38, 39 40 41 42 43 44 45 46 47 48 49 45 46 47 50 51 52 53

continued

1.4.1.5 Fe-4d, 5d (group 4-6)

53’

[Ref. p. 564

Survey. continued Allo}

Composition

(Feo.8Cro.2hZrH, (Fe, -,Mn,W

y=o, y=3.1 a-), x, ‘(T) 05x5 -1.0 44, C(X)>T,(x), P(x) 0.1 jxjo.4 C’-) 0.4~x~O.S x u-h x, V) 0.01~x~O.3 “Mn and “Zr NMR 0.4-5 x IO.6 “Mn NMR y=o, y=3.0, y=3.5 a(T), x,‘(T) ogx~1.0 H,,,(x) ogxg 1.0 44. C(X)>T,(x) G(x)3 PFCWz,(x) 0.15~x~O.38 a(T) 0.455 x 5 0.875 x&T) O~x~O.35 AV/V(T), o,(x), dw/dH x=0.3 T,(P) O~x~O.3 H,,,(x) 0.5~x10.7 “Fe ME, P(Hhyp) 0.4 5 x 5 0.7 g3Nb NMR 05x2 1.0 1% e2rlQ -O~x~1.0 44, 44 O~x~O.5 h(x). T,(x) O~x~l.0 A I//W’-), w,(x) OSx~l.0 44, 4x) OsxsO.25 B&X T,(x) 0.1 ~x~O.75 a(T) ocx10.7 -W4 TN(x) x=0.2 a(T), x; ‘6‘7, a(H) x = 0.15, x = 0.2 magnetic phase diagram (H-T) x=0.2 a(T), c(T), ME 01x20.7 H,,.,(T) --

FchlnZrH, Fe,Zr, -,Hf, Fe,Zr, -XNb,

Fe,Zr , - ,Ta, Fe,Zr , _XMo, Fe?Hf, -,Ta,

Property

Fig. 54 55 56 51 59 59 58 60 61 62 63 64, 65 66 67 68 69 70 71 72 73, 74 75 76 71 78 79, 80 81 82, 83 84

Table 5. Magnetic and related propcrtics of Fe,Zr. 0: angle between hyperlint held and [I 1l] direction. 4.2 K Structure

RT

Ref.

Cl5

0 CA1

7.073 Ferromagnetism 88.2 80.9 1.6 630 643 1.18

Magnetism a, [Gcm3g-‘1 PFeCPnl

T, WI @WI C, [cm3mol-’ K-l] Axis of easy magnetization dTc/dp [K kbar-‘1 dtoldH [lO-‘“Oe-‘] l,,r [10-5cm3cm-3] y [ergmol-’ Km2 Hhr,,(“Fe) [kOe: O=O- site 0 = 70.3 site

Cllll -2

4.6 2 13

Hh?p(“Zr) IWe 1s (57Fe)relative to U-Fe [mm s-‘1 &e2qQ(57Fe) [mm s-‘1

206 223 125 -0.057 0.5

Shiga

7.0

200 -0.155

79M 1 79Ml 79Ml 79Ml 79M 1 79M 1 64Wl 73Bl 80M2 79Ml 79Ml 64Wl 64Wl 64 B 1 64N 1 64Wl

Table

Ref. p. 5641

1.4.1.5 Fe-4d, 5d (group 4-6)

533

200 @cm

t 100 ar

01 0

I

I

I

200

400

600

I

I

800 K 1000

T-

Fig. 30. Temperature dependence ofthe electrical resistivity of Fe,Zr and Fe,Hf. The arrows indicate the Curie temperature [75 I 11. Table 6. Room-temperature Miissbauer intermetallic compounds [Sl V2].

parameters

of certain Fe-Zr

FeZr, Structure type

NiTi,

IS (57Fe) relative to a-Fe [mms-‘1 (57Fe) [mms-‘1

-0.151 0.24

$?qQ

FeZr, Re,B (orthorhombic) -0.319 0.91

130 !i& 9 120

00

I 110

t ooe

~ 100

00

00 K

90 80 70 i

26

28

30 Zr -

32

3L at% :

Fig. 31. Composition dependence of the magnetization at 80K and the Curie temperature of Fe-Zr alloys near Fe,Zr composition [68 K 11.The stoichiometric Fe,Zr is the cubic Laves phase (C15). Relatively wide solubility range exists Tom 27...36at% Zr. Fe-rich offstoichiometric alloys have not, however, the pure Cl5 structure but change to Cl4 [68K 1] or the mixture of other complex structure was reported [67 B 11. Land&Bdmstein New Series 111/19a

Shiga

1.4.1.5 Fe-4d, 5d (group 4-6)

534

[Ref. p. 564

Table 7. Magnetic and related properties of Fe,Hf. 0: angle between hypcrtine field and [I 1I] direction. Ref. Structure

Mixture of Cl4 and Cl5 (fraction depends on heat treatment) 7.028 (Cl 5) Ferromagnetic 52.8 591 [ill] (C15)

n at RT [A] Magnetism u @OK) [Gcm3geLJ

T, WI Axis of easy magnetization Hhrp (“Fe) at 300 K [kOe] O=O site 0 = 70.3’ site Hhyp ( 181 Ta on Hf site) at RT [kOe]

176 184 130 (C15) 85 (C14) - 0.41

&?qQ (57Fe) at RT [mm s-l]

100,

I

I

I

70Nl 70Nl 76L1 76Ll 76Ll 76Ll

,680

660

600

26

28

30

32

580 34 at% 36

Hf Fig. 32. Composition depcndcnce ofthc magnetization at 80 K and 300 K under an applied field of 9.6 kOe and the Curie temperature in Lavcs phase Fc-Hf alloys. The specimens were heat treated at 1000°C for 48 h. In the composition range between 32 and 34 at% HT,alloys have the Cl5 structure with a faint Cl4 type. Outside of this range. the structure is purely of the Cl4 type [70N I].

Table 8. Magnetic and related properties of FeHf, and FeHf,H,

Structure type a at RT [A] Magnetism 0 at 4.2 K under 9 kOe [G cm3 g- ‘1

T, WI

IS (57Fe) relative to u-Fe at RT [mms-‘1 fe2qQ (“Fe) at RT [mm s- ‘1

Shiga

hydride [79 B 11.

FeHf,

FeHf,H,

Ti,Ni 12.04 Paramagnetic

Ti,Ni 12.87 Ferromagnetic 10.8 73 0.285

-0.12 0.47

1.4.1.5 FewId, 5d (group 4-6)

Ref. p. 5641

535

Table 9. Magnetic and related properties of Fe,M (M = Nb, Ta, W). Fe,Nb Structure a at RT [A] c at RT [A] Magnetism x,,, (RT) [10m3cm3mol-l] IS (57Fe)relative to a-Fe [mm s- ‘1 at 4.2 K at RT +e’qQ (57Fe) [mms-‘1 at 4.2K at RT

Fe,Ta

Fe,W

Ref.

Cl4 Cl4 4.827 4.831 7.882 7.838 Pauli paramagnetic 2.3 2.5

Cl4 4.736 7.719

58~1 58~1

-0.13 - 0.23

-0.08 -0.23

0.37 0.33

69Kl - 0.25

64Nl 64Nl

0.24

64Nl 64Nl

0.30 0.29

150 K 180

a

,I-

Gcr s

a

~ !

T = C2 K

0

30

60

90 T-

120

150 K 180

3-

I b 2-

l-

L 0

b

4

8

kOe

HUPPI -

Fig. 33. Temperature (a) and field (b) dependenceof the magnetization in Fe-Ta alloys with the Cl4 structure [70K 11.(a) Under 9.6kOe, (h) at 4.2K.

Landolt-Bbmstein New Series 111/19a

0

8

kOe

b HOPPl Fig. 34. Temperature(a) and field (h) dependenceof the magnetization in Laves phase (C14) Fe-Ta alloys [70 K 11.(a) Under 9.6kOe, (h) at 4.2K.

Shiga

1.4.1.5 FeAd, 5d (group 4-6)

536

[Ref. p. 564

E .lO.’ cm: T L I rz” 2

Fig. 35. Tcmpcraturc dcpcndcncc ofthc susceptibility and the inverse susceptibility of the p-phase Fe,,,,Ta,,,, alloy. Circles: low-field ac susccptibilitp, squares: susccptibilityat 10 kOc,lozcnges:invcrsesusccptibilityat IOkOe. The spccimcn was hcnt trcntcd at 1200“C for 8 days and then oil quenched [83A I].

6 vs 5 I g

1,

3: K

82 68

50

51 To.Nb -

52 at% 53

Fig. 36. Composition dependence ofthc NCcl temperature and the hypcrfinc field of “Fe at 4.2 K in p-phase Fe-Nb and Fe-Ta alloys. Circles: N&l tempcraturc, triangles: hypcrtinc fields ofthc magncticcomponcnt in Fc-Nb and Fe-Ta alloys, rcspcctivcly. In both systems. there arc nonmagnetic Fe atoms which hnvc an almost zero hypcrfinc field even at 4.2K in the fraction of approximately 0.3. The spccimcns were heat trcatcd at 1200“C for 8 days and then oil quenched. They have the p-phase structure [83A I].

28

160 K 1LO

2L

120

20

100

I 16 r-L

80 I 0

12

60

8

40

4

20

0 0 MO

2

16

8 Fe -

10

0 12ol% 11,

Fig. 37. Composition dependence of the spin-glass freezing tcmpcraturc T,, the paramagnctic Curie temperature 0 and the effcctivc moment per Fe atom. perr, deduced from the Curie constants of Fe-MO alloys. T, was obtained from the maximum of the susceptibility vs. temperature curves under the applied field of 60 Oe. The samples wcrc prcparcd by sintering of powder constituents under hydrogen atmosphcrc at IOOK below the melting temperature and then rapidly cooled [76A I].

537

1.4.1.5 FeAd, 5d (group 4-6)

Ref. p. 5641 5 5

Cn \A/

0

5

1

IO

15

20

25

30 K 35

Fig. 38. Temperature dependence of the susceptibility of Fe-W alloys under 0.1 kOe. The arrows indicate heating and cooling, respectively. The specimens were heat treated at 2280 “C for 3 h [SOK 11.

I

I

(Fe,-,Alx)2Zr

I

0 W

0.5

1.0

1.5 Fe-

2.0

2.5 ot% 3.0

Fig. 39. Composition dependence of the spin-glass freezing temperature Tr of Fe-W alloys deduced from the maximum of I-- T curves (see Fig. 38). The specimens were heat treated at 2280°C for 3 h [8OK 11.

700K

350 kOe

600 250

jl-

200-

j-

100-

I

0.2

a f

0.4 x-

0.6

0.8

O0 1.0 ,41 b Fe

50

0.2

0.4 0.6 x-

0.8

0 1.0 Al c Fe

Fig. 40. Composition dependence of the magnetic properties of (Fe,-.$,),Zr alloys. Dashed lines indicate phase boundaries. (a) Magnetization per formula unit at 4.2 K, extrapolated to H,,,r = 0, at 30 kOe [77 M 11, at 70 kOe [Sl G 11. (b) Curie temperature. Open circles: [Sl G 11, solid circles: [77 M 11. (c) Mean hyperfine field I?,,, at 4.2K obtained by 57Fe Miissbauer effect [81 G 11.

Landolt-Bornstein New Series 111/19a

Shiga

u.2

0.4 0.6 x-

0.8 1.0 Al

[Ref. p. 564

1.4.1.5 FeAd, 5d (group 4-6)

53s 40

160

I

gol-

‘$ (FeQ7A10,3)2ZrH,

cm3 7nnLY

-

I

k.85 Cl5

0

80

2LO

160

K

1.75 a 1.7r

, 320'

Fig. 41. Temperature dcpcndcncc of the magctization of inverse susceptibility of 21.2kOe and the (Fc,,,~AI, ,),ZrH, with the Cl4 structure [S2 F I, 82 F 23.

I

I

.-

7.70

Cl4 I

\I

1.5lb 1001

I

I

I

I

I

I

lb

1 I

17.60 1650

1450

I

163-LIIIJ

(

80T

I

\I

' C15+ClJ I I

1.6

9

17.90

A!!

mol

t

50

300K\

60 I x'

b

40

x-

Fe,Zr 0

300

200 T-

100

"C

400

Fig. 43. Temperature dependence ofthc relative magnctization of FczZr,-,Ti, above room tempcraturc. The magnetization at 300 K is given in Fig. 42 [63P I].

Fig. 42. Composition dependence of(a)latt parameters at room tcmpcraturc, (b)Curic temperature and magnetic moment per Fe atom at 4.2 K, (c)magnetization at 300 K under the applied field of 1 kOe, and the susceptibility at 4.2 K and at 300 K of Fc,Zr, -,Ti, [63P 11.

60

mol cm3 40 I YE x 20

25

50

75

100

125

Fe,5

150

175

200

225

250 K 275

Fig. 44. Temperature dependence of the inverse susccpti. bility of Fe,Zr, -,Ti, [63P I].

Ref. p. 5641

1.4.1.5 Fe-4d, 5d (group 4-6)

539

600 i K 8

I g- 7

6

5 0

0.25

Fe

0.50

0.75

x-

1.oo

v

Fig. 45. Composition dependence of the lattice parameters in (Fe,-XV,),Zr and their hydrides (Fe1 -XVX)2ZrH, at room temperature. The alloy samples were heat treated at 900...1000 “C for one week. The hydrides were formed by exposing the host alloys to highpurity H, gas at about 40 atm [85 F 11.

0

0.25

Fe

100

1.00 V

I

I

I

(Fej_xVx)2Zr 80

o ( Fe,.,V,)2Zr

0.75

Fig. 46. Composition dependence of the Curie temperature Tc and the superconducting transition temperature T, for (Fe, -XVX)sZr and their hydrides. The conditions for sample preparation are given in Fig. 45 [85 F I].

y

2.J ‘Y

0.50

x-

-k;

60 b 40

1.5 1.0

0

0.5

100

200

300

400

500

600 K 700

I-

Fig. 48. Temperature dependence of the magnetization at 8.3 kOe of (Fe, -XV,),Zr above 70 K. The specimens were heat treated at 800 “C for one week [70 K 21.

0 0 Fe

0.25

0.50 x-

0.75

1.00 V

Fig. 47. Composition dependence of the magnetization per Fe atom at 4.2 K of (Fe1 -XV,),Zr and their hydrides. The conditions for sample preparation are given in Fig. 45 [85 F 11.

Land&Bbmstein New Series 111/19a

Shiga

[Ref. p. 564

1.4.1.5 Fe-4d, 5d (group 4-6)

540 4.5 .10-f 3 T 3.5

..,

I

,

I

I

I

18.175u

I

I

I I

8.125

3.C I

./

2.F I x"

2s 6

1.E 1.1 0.i [

500 K t I-

Fig. 49. Tempcraturc dependence ofthc susceptibility and the inverse susceptibility of(Fc, -IV,)2Zr. The spccimcns were heat trcntcd at 800°C for one week [70K 21.

2.51

1

I

/

,

I

125 cm3

15 I 7, x 10

1.5 * 1.0

5

0.5

0 0

M

100

150 I-

200

0 250 K 300

Fig. 50. Temperature dcpcndence of the susceptibility of (Fc, 2V,,)zZr and its hydride. The sample was prepared by the same method as in Fig. 45 [8S F 11.

0.2

Fe,Zr

0.6

0.4

x-

0.8

1.0

Cr,Zr

Fig. 51. Composition dcpcndcnce ofvarious properties of (Fc, -,Cr,)2Zr and their hydrides. (a) Lattice parameters at room temperature [70 K 21. (b) Curie temperature. Solid circle: [79 M I]. open circles: [70K 23. open squares: [8OJ I], solid squares: hydrides [8OJ I]. (c) Magnetic moment per formula unit, solid circle: [79 M I] at 4.2 K and H-0, open circles: [70 K 23 at H = 8.3 kOe. extrapolated to T=O, open and solid squares: [SOJ I] at 4.2 K cxtrapolatcd to l/H,,,, = 0, and the susceptibility at 290K. triangles: [70K 23. open and solid lozenges: [80 J I].

Ref. p. 5641

1.4.1.5 FeAd, 5d (group 4-6)

541

80 Gcm3 9 60 t b 4o 20

4

0

500 K 600 300 400 IFig. 52. Temperature dependence of the magnetization at 8.3 kOe of (Fe1 -$&),Zr [70 K 21.

4.! JO-

I

I

100

200

I

cm' 9

3.F

I

3.1

b

I 2.5 x” 2s 1.5 1.0 0.5 0

Fig. 53. Temperature dependence ofthe susceptibility and the inverse susceptibility of (Fe,-.Cr,),Zr with the Cl4 structure [70 K 21.

Landolt-Bbmstein New Series llVl9a

Fig. 54. Temperature dependence of the magnetization 0 12kOe and the inverse susceptibility of

~edh.J2ZrH,

Shiga

W J 11.

[Ref. p. 564

1.4.1.5 Fe-4d, 5d (group 4-6)

542

I

\.

60

\

b

40

83Zr

Kl

/

e

6;;

I

I

I

I

I

I

I

I

\

of (Fe,.,Mn,),Zr

>

A

I

I

1

0

I

100

200

300

400

500 K I

Fig. 56. Tempcraturc depcndcncc ofthc magnetization at 8.4 kOe of (Fe, -rMnr)2Zr [7l K I].

(Fe,.,Mn,),ZrH,

403

-,-;k

7 40 f cm3i 9

--f

ObJ

4.0 Ps

(Fe,-xMn,)2Zr

5

5

4

4

3.0

I

II I

2.0

o A (Fe,.,Mn,),Zr A (Fe,., Mn, ),ZrH,

I 7.7 3x

I g3

16 2 1.0

I

\ 1

0

I(

0

Fe,Zr

0.2

\ 3.6 z 3.6 -T*. ‘Y 0.6 0.8

0.4 x-

II 0

1.0_

Mn,fr

Fig. 55. Composition depcndcncc ofvarious propcrtics of (Fc, _,hln,&Zr and their hydrides. (a) Lattice parameters at room tcmpcrature [71 K I], (b) Curie tcmpcrature. Circles: [71 K I]. open trinnglcs: [82 F 31, solid triangles: hydrides [82 F 33. Tc in [82 F3] was dctcrmincd by plottin: Al’ vs. T and estrapolating to M=O. (c) Magncti7ntion per formula unit. Circles: [7l K I] (mcasurcd at 21 kOc). open trian_clcs: [82F3]. solid triangles: hydrides [Q F 33 (mcasurcd at 21 kOc). The samples used in [7l K I] were heat trcatcd at 800°C for one week. The samples used in [8:! F 31 lvcrc annealed at 900...1000 “C for 5 h. The composition of hydrides in [82 F 31 arc as follow: (Fc,,?Mn,,,)2ZrI-I,,,. ~c,,,,Mn,,,s)~Zrl~I~,~, 0% sh~n,,s)JrH3.s.

100

200

I

I

300 T-

400

I

I

500 K 60:

Fig. 57. Temperature dependence ofthc susceptibility and the inverse susceptibility of (Fe, -xMn,),Zr [71 K I].

Shiga

1.4.1.5 FewId, 5d (group 4-6)

Ref. p. 5641

Fig. 58. Temperature dependence of the magnetization and the inverse susceptibility of (Fe,,,Mn,.,),Zr and its hydrides at 21 kOe [82 F 11.

55Mnin (Fe,-,Mn, ),Zr

200

160

120

MHz

l-

I error

55Mnin(Fe1-,Mn,)2Zr

I

40 c

I

40

120

80

160 MHz 200

50

I

I

70

60

80

MHz 90

Y-

Fig. 59. Zero-field NMR spin-echo spectra of (Fe, -xMn,),Zr [Sl Y 11. (a) 55Mn spin-echo spectra for x 5 0.3 at 15 K, (b) 55Mn spin-echo spectra for 0.4 5 x 50.6 at 1.5K, (c) 91Zr spin-echo spectra for xs 0.3 at 15K.

Y-----r

Landolt-Bbmsrein New Series 111/19a

n

Shiga

[Ref. p. 564

1.4.1.5 Fe-4d, 5d (group 4-6)

544

7.08,

0 Fe,Hf

0.2

0.4

0.8

0.6

I

,8.01

I

1.0

x-

Fe,Zr

Fig. 60. Composition dcpcndencc of the “‘Ta hypcrfinc field at 300K in FczZr,Hf, -I [83A2], solid circle: [76 L I]. This system is ferromagnetic for the whole composition ransc at 300 K. The crystal structure is Cl5 for st- 0.2. In this range. “Fc h4iissbaucr spectra arc quite idcntlcal to pure Fc,Zr. H,,,, being constant, namcl) H (‘1‘ l)=22OkOc and Hh!p (site 2)=204kOc at 7;:. 4),: easy mngncti7ntion axis is along [I I I].

I

I

I

I

Fe@-, Nb,

6?

1

OC

b

n

40

0

0.4 x-

I

100

I

I

200

300 T-

400

500 K 600

Fig. 62. Temperature dcpcndencc oithc magnetization of fcrromn_rnctic Fe&-,Nb, with the Cl5 structure at 9.3 kOc [69 K 21.

0.6

0.8

Fe,Elb

Fig. 61. Composition dependence ofvarious properties of Fe,Zr,_,Nb,Lavcsphascalloys.(a)Latticeparametcrsat room tempcraturc. For ~~0.35, the crystal structure is Cl5. For x>O.5, C14. For 0.35<x
Ref. p. 5641

1.4.1.5 Fe-4d, 5d (group 4-6)

545

Fe,Zr,-, Nb,

100

200

300 7-

400

500 K 600 I

Fig. 63. Temperature dependence of the susceptibility of Fe,Zr, -,Nb, with the Cl4 structure [69 K 21.

I

200

0

I

I

LOO

800 K 1000

600 7-

Fig. 64. Volume thermal expansion curves of Fe,Zr, -,Nb,. Arrows indicate the Curie temperature [79 S 21. The expansion anomalies below the Curie temperature are due to the spontaneous volume magnetostriction, whose magnitude at 0 K is given in Fig. 65.

IO 10-g OF’

I

801

I

I

I

I

I

I kbar

I 40

8 t

2 0 0 Fe,Zr

2 -601 0

0

0.1

0.2

x-

0.3

0.4

Fig. 65. Composition dependence of the spontaneous volume magnetostriction at OK, w,(O), and the forced volume magnetostriction at 77 K and at 300K of Fe,Zr, -,Nb, [79 S 21.

Landolt-Bornctein New Series 111/19a

I 5

I IO

I

I

I

I

15

20 P-

25

30

Fig. 66. Shift of the Curie temperature of Fe,Zr,,,Nb,,, with pressure [69Al]. dTJdp= -3.3Kkbar-‘. For [69Al]. Fe2-W.65Nbo.35~dTc/dp=-3.5Kkbar-’

Shiga

1.4.1.5 Fe-4d, 5d (group 4-6) 239

[Ref. p. 564

For Fig. 68, see next page.

kOeFe,Zr,-,Nb x

I= 4.2;

I

Fe+-,-, Nb, l= 1.5K

I 130 ,120

s”

110 90 83

To.7 I I I

70

60 0

030 a.15

0.05

0.20

0.25

0.30

0.35

0.40

5

IO

x-

Fe,Zr

15

I

I

20

25

I 30 MHz

Ir-

Fig. 67. Composition depcndencc ofthc hypcrlinc field at “Fe. “Zr and g3Nb nuclei in FezZr, -,Nb, alloys with hc Cl5 structure. W,,, ~‘as estimated from zero-field \IhlR spin-echo spectia measured at 4.2K. For “Fe, .hcrc arc two magnetically diffcrcnt sites. Hhypshown here s for the site where the maenetization direction makes an mgle of 70-32’ with the local symmetry axis [I 1I]

Fig. 69. Zero-field NMR spin-echo spectra of g3Nb in antifcrromagnctic Fe,Zr, -,Nb, with the C14 structure at ISK [83Y I].

:s3\i 1-J.

p -0.3 0.5

-I

c,

a

m s< -,

AT 0

0

Y 0.4 CY e %J 0.3 b 0

Fe,Zr

\

0.2

0.6

0.4

x-

0.8

1.0

0 0.2 Fe,Zr

Fe,Nb

Fig. 70. Composition dependence of 57Fe Miissbaucr parameters of Fe,Zr, -,Nb, alloys at room tcmpcrature. :a) Isomer shift. IS. relative to a-Fc. Open circles: [68 T I]. jolid circles: [64 N I]. (I-J)Eicctric quadrupolc splitting. v2qQ’2 [68T I]. The sign of qQ is ncgativc in the fcrromngnctic region (x ~0.4) [64W 11. The si!n in the lntifcrromagnetic region has not been dctcrmmed.

0.4

x-

0.6

0.8

1.0 &To

Fig. 71. Lattice parameters of Fe,Zr,-,Ta, at room temperature. Solid circles: a for the Cl5 phase. open circles: a fi and triangles: c 1/3/2 for the Cl4 phase [83 M I].

Shiga

1.4.1.5 FewId, 5d (group 4-6)

Ref. p. 5641

547

I mm/s

Fig. 68. 57Fe Miissbauer spectra of antiferromagnetic Fe,Zr, -,Nb, alloys with the Cl4 structure at 4.2 K and hyperfine field distribution curves, P(Hhyp) [SON 11.

0

100 kOe 150

50

I-

1.5

C 0 Fe,Zr

0.25 x-

0 0.50

Fig. 12. Composition dependence of the spontaneous magnetization per Fe atom at 4.2K and the Curie temperature of Fe,Zr, -,Ta, [83 M 11. Fig. 73. Volume thermal expansion of Fe,Zr,-,Ta,. Arrows indicate the Curie or the Ntel temperature. Expansion anomalies below T, are due to the spontaw neous volume magnetostriction o, [83 M 11. Landolt-Bdrnstein New Series 111/19a

O

Shiga

I

I

I

200

400 r-

600

K

I

1.4.1.5 FeAd, 5d (group 4-6)

548

H

(

[Ref. p. 564

1 Fe2Zr,-XMoX

1

7.08

8.1 1

I G; uD 7.06

s L 7.9 z

7.OL

FezTo

x-

Fe,!r

Fif. 74. Composition dcpcndcncc of the spontaneous volume magnetostriction q at 0 K [83 M I].

7.7

I

II

I

OW”

0 Fe,Zr

0.2

0.4

I

I

I s 2 0 0.6

0.8

x-

Fig. 75. Composition etcrs of Fe,Zr, -.Mo,

1.0 k,KO

dependence of the lattice paramat room temperature [74 I l]

63: K

&ppl = 10kOe

50: 4OC

1.6 I 1.2 ,g

I ,303

I

60

b

40

EC

103 0 0 Fe:Zr

&pg-qJ OS

0.2

0.3

x-

Fig. 76. Composition dcpcndcncc ture and the magnetic moment romngnctic Fe2Zr, -=Mo, with IO kOc cstrapolatcd IO T=O [74

of the Curie tcmpcraper Fe atom of fcrthe Cl5 structure at I I].

Ob 0

100

200

300

400

500 K 600

IFig. 77. Tcmpcraturc dcpcndcncc of the ma_rnctization of Fc,Zr, -xMo, at IO kOc with (a) the Cl 5 structure and (b) the Cl4 structure [741 I].

1.4.1.5 FeAd, 5d (group 4-6)

Ref. p. 5641

549

Gcm3 9

Y cm3

1.6 I

I 40

1.2Ts

b 30

0 0 Fe,Hf

0.25

0.75

0.50 x-

20

0.8

IO

0.4

0 0

1.00 FezTa

Fig. 78. Magnetic phase diagram ofFe,Hf, -xTa, with the Cl4 structure. For x=0.15 and 0.2 ferromagnetic-antiferromagnetic+paramagnetic transitions take place with increasing temperature [83N 11. T,: ferro- to antiferromagnetic transition temperature.

100

200

300 T-

0 500 K 600

400

Fig. 79. Temperature dependence ofthe magnetization at and the inverse susceptibility of Fe,Hf,,,Ta,,, [83 N 11. T,: ferro- to antiferromagnetic transition temperature.

H appl= 5 kOe

60 Gcm3 9 50

I

40

b

3o

IO

20

30

40 HVP1

Fig. 80. Magnetization curves of Fe,Hf,.,Ta,,, (C14) at various temperatures. The antiferromagnetic to ferromagnetic transition takes place above 150 K [83 N 11.

50

60

kOe 70

-

150 kOe 125

25

Fig. 81. Magnetic phase diagram (T-H diagram) of Fe,Hfe.sTa,., and Fe,Hfe,s,Ta,.,, [83 N 11.

Land&Bbmstein New Series 111/19a

Shiga

0 100

150

200

250 T-

300

350

K 400

550

1.4.1.5 Fe-4d, 5d (group 4-6)

[Ref. p. 564

8.075 c, 8.050

4.900I 0

I 100

I

200 300

400 500 600 K 700

Fig. 82. Tempcraturc dependence ofthc lattice parameters of FezHfO,,Ta,,, (Cl4). Dashed lines indicate magnetic phase boundaries [83 N I].

0

2

6 % 8 -6

-4

-2

0

2

4 mm/s 6

0

V-

1DU

200

300

K

4;O

T-

Fig. 83. Mdssbauer spectra of “Fe in Fc,Hf,,,Ta,,, at b’arious temperatures. At 80 K. the sample is fcrromagne!ic and Hh!p at the 6 h site and the 2a site are I56 kOe and 157kOc. respectively. At 200 K, the sample is antifcrromagnetic and H,,, at the 6 h and 2a sites are 96 kOe and nearly OkOe. respectively. The quadrupole splitting of both sites are about 0.36mm!s (the sign seems to be wgative) [83 N 11.

Fig. 84. Tempcraturc depcndencc of the hypcrfinc held. Hhyp at “Fe in Fe,Hf,-,Ta,. Hhrp at the 2a site in the antifcrromagnetic state is almost zero over the corrcsponding tempcraturc range [83 N I].

Shiga

Ref. p. 5641

1.4.1.6 Co, NiAd,

5d (group 4-6)

551

1.4.1.6 Co and Ni alloys and compounds Many types of intermetallic compounds are found but magnetic properties are scarcely known. Supposedly, most of them will be nonmagnetic. Among them, Laves phase compounds of Co are fairly well studied. Only offstoichiometric Co 2+,Zr is weakly ferromagnetic. Survey Alloy

Composition

Property

Fig.

Co, -xZrx

0.23Ix -- IO.34 0.25$xiO.31 0.25, 0.263 0.2832 x 5 0.337 OIx10.7 --

44 Tcc4 &i(x) 4n x, ‘UT xg(T)

8.5 85 86 87

(Fe1-xCox)2Zr

a,

c’, XHF,

T,,

0,

Tab.

10

peff

Y>K,yp, dT,ldp> as do/dH

0% -xCox)2+,Zrl -,,

-01X10.5 04x
Co,Hf, Co, -,Hf, (Fe1JW2Hf Co,Ta, Co, -xTa, Co,Nb, Co, -xM~, co1 -xwx Ni,Zr, Ni, -xM~, Ni, -xW,

Landolt-Biirnstein New Series 111/19a

44, C) T,(x), 44 x,(T) W) AK0 dH)> A~P’W)

88 89, 91 90 92 94 95 96

&/T

97

d4WG

XHFtX)

vs. T=

ME, PW,,,) FFec;o$~hyp’“’ ‘lZr NMR o(H)

98 99 100, 101 102 92

4~1, T,(Y), 4~)

93 11

a, pco, T,, xg

0) 4x), x,( T>

0.29l~x~O.341 osxs 1.0 --

PFe -CO(~),

0.275x50.36 0.255-2 x IO.398

a, xg 44 X&% 47

R,,,(x)

104 103 105 11 106 106 11

a, xgT PC~

05x60.6 OIx10.03 -01x10.8 -o<x
phase diagram, T,(x) &4 phase diagram, T,(x) m Xm Y, @D x,(T) x,(T) G%6OK) &4 T,(x) xg(T) W PM T,(x)

o<x
Shiga

107 108 107 108 12 109 110 111 112 113 111

[Ref. p. 564

1.4.1.6 CoP4d, 5d (group 4-6)

552 7.oc H

L

I

“, B

Co-Zr

6.95 I

7.1cI8 \

1 Fe,-, C0,)J.r

,7.OE

c

Rl

6.90 I 7.0: 0 6.85 6.9t !I.!

~~~~

601

I &= 4OI 22

28 Zr -

26

2L

32 at% 34

30

L?

Fig. 85. Composition dcpcndencc ofvarious propertics of cubic Lavcs phase Co Zr alloys. (a) Lattice parameter at room temperature [Sl F 21. (b) Curie temperature. Open circles: [81 F 21. solid circles: [72A I]. (c) Spontaneous magnetic moment per Co atom at 4.2K. Open circles: [S I F 21. solid circles: [72A I]. The samples in [S I F 21 were heat treated at l250...13OO”C for 5 h and then quenched

201

II! 121 IGem3 9

l= L2K

El I

b” 35,

/

,

4

I

1.5 loc 9

41

:m3 C

!.5 !.O

I yg

1.5 1.0 3.5

01 0

/ 50

100

150

200

3 250 K : I

Fis. 86. Temperature dcpcndencc ofthc magnetization at 21.1 kOc and the inverse susceptibility for ZrCo, with x=2.8 (26.3atX Zr) and x=3.0 (25.0at% Zr) [8l F2].

0 Fe,lr

0.2

0.4

0.6 x-

0.8

1.0

CqZr

Fig. 88. Composition dependence ofvarious properties of cubic Laves phase (Fe I -,CoJ2Zr. (a) Lattice parameter at room tcmpcrature [79 M l],(b) Curie temperature Tc and the spin-glass freezing temperature T, [79 M I]. Dashed line indicates the Curie temperature of as-cast samples [82 W I]. (c)Spontaneous magnetization at 4.2 K [79 M I. 79 M 21. The samples used in [79 M I, 79 M 23 were heat treated at 1100°C for 48 h. See also Table IO.

1.4.1.6 CoAd, 5d (group 4-6)

Ref. p. 5641

553

0.8

Fig. 87. Temperaturedependence of the magnetic susceptibility for the 28.3...33.7at% Co-Zr alloys [72A 11. Table 10. Magnetic and related properties of (Fe, -.$oJzZr

a at RT [A] CTat 4.2K [Gcm3g-‘1 xHFat 4.2K [10-6cm3g-‘]

TcWI @L-K1 Peff CPBI

y [ergmol-’ Km21 Hhyp (57Fe),mean at 4.2K [kOe] Axis of easy magnetization dTc/dp [K kbar-‘1 co,at OK [10m3] dw/dH at 4.2K [lo-”

x=0.0

x=0.2

x=0.3

x=0.4

7.074 88.2 3 630 643 3.07 13.0 212

7.052 78.6 3 504 527 3.09 17.2 192

7.037 68.8 8 422 433 3.14 23.6 174

7.026 52.9 50 275 316 3.1 40.4 146

Cl111

cw

cw

cw

- 22) 10 4.6 Oe-‘1

9.3 4.5

6.1 9.2

‘) Spin-glass freezing temperature. ‘) [73 B 11. 3, [69A 11. Landolt-BBmstein New Series 111/19a

[79 M 1, 80 M 21.

Shiga

- 6.6 3) 4.2 78

x=0.5 7.015 50 ‘)

x=0.6 7.005

x=0.7 6.993

25 ‘)

12 ‘)

72

43

3.11 94

[Ref. p. 564

1.4.1.6 CoAd, 5d (group 4-6)

554

2.0 a4 @ 9 1.5

I-1.0 H

0.5

0 250

c 50

100

150

200

K

T-

0

600

LOO T-

K

Fig 90. Temperature dependence of the susceptibility of (Fc, -$o,),Zr at 8.2 kOe [79 M I].

I

Fig. 89. Tempcraturc dependence of the magnetization of (Tel -$oJzZr at H,,,, = 9.96 kOe [79 M 21.

CC;;;3 9 LO

/’

_---

+/C-.--

/-

x = 0.5

/ 35 1=4.2K 30

1-1

b

--

(Fe,.,C0,)~2r (bCox~d-~.~7

_

I

I

I

I

0.61

10

20

30 HWI -

40

50 kOe 60

20

0

20

10 T-

60

K

0

80

Fig. 91. Temperature dependence of the magnetization of mictomagnctic (Fc,,,Co,,,)2Zr (annealed sample) [79 h4 I]. Curve I: cooled at zero field and measured at 0.3 kOe; 2: cooled and measured at 0.3 kOe; 3: after cooled at zero field. applied 10 kOe at 4.2 K and mcasurcd at 0.3 kOe; 4 and 5: zero-held cooled. mcasurcd at 1.3kOe and IO kOe, respectively.

Fig. 92. Magnetization curves of(Fe, -$o,),Zr (full lines) and (Fc, -rCox)2,03Zr,,97 (broken 1incs)at 4.2 K [79 M 1).

Shiga

1.4.1.6 CoAd, 5d (group 4-6)

Ref. p. 5641

Fig. 94. Thermal expansion curves of (Fe,-$o,),Zr. Arrows indicate the Curie temperature. Dashed curves are the estimated thermal expansion due to unharmonic lattice vibrations. The difference between solid and dashed curves corresponds to the spontaneous volume magnetostriction [80 M 21.

102r-----H

14, .lO-3

555

(I%-,Co,)2Zr I I

I

Tc 1I /

7I 8

7.00

a

t

6.98

6

0

6.96

6.94 600 K 400 I 2

0

200

150

300

450

600

750 K 900

I-

0 ^^

tL I

I

I

I

I

I

Gc; Gcm3 9 t 60

b

40

80 .1o-l’c OF’

:0 IO-5 cm3

70

ss”

3

I I I I i

60 0 - 0.08

-0.04

0

0.04 Y-

0.08

0.12

0.16

-

OAV dw/dH . XHF

30

I

Fig. 93. Composition dependence ofvarious properties of (Fe,,,Co,,,),+,Zr, -y [79 M 11. (a) Lattice parameter at room temperature, (b) Curie temperature, (c) magnetization at 4.2 K under H,,,, = 30 kOe.

25

20 I x

I I

15 T=290K/ /

Fig. 95. Composition dependence of the forced volume magnetostriction, dm/dH, at 4.2 K, 77 K and 290 K of (Fe, -$o,),Zr [SOM 23. Solid circles indicate the highfield susceptibility xHF at 4.2 K [SOM 21.

Landolt-Bdmstein New Series 11~1%

Shiga

/’ 77K/

10

5

0 F+Zr

0.1

0.2

0.3 x-

0.4

0 0.5

1.4.1.6 Co-4d, 5d (group 4-6)

556

[Ref. p. 564

70 ml molK2 60

8

0

12

kOe 16

HOPP!-

Fig. 96. (a) Volume mnyctostriclion and (b) magncli7ation of (Fe, Jo,,)& at 4.2 K. Increasing and dccrcasins mnsnctic fxlds arc indicated by solid and open circles. respcctivcly [8O M 21.

20 15

For Fig. 9S, see next pag

101 0

(FeiwxCox)2Zr x = 0.01

I

I

6

I

I L.-

I

12

15 K2 18

Fig.97. Low-temperature specific heat divided by temperature against the square of tcmpcraturc for (Fc, -xCo,),Zr [79 M I].

I error I

I

3

I

200 kOe

0.50 0.25

0.3 I

0 0.2

Fe,Zr

0.i

OX

x-

0.6

0.8

1.0 Co,Zr

Fig. 99. Composition dcpcndence for (Fc, -Jo,),Zr of 120 MHz 150 the avcragc magnetic moment &c-c0, per Fe-Co atom (triangles) and the mean hypcrfine field for “Fc (open 1' circles) at 4.2 K which was estimated from P(H,,,)curvcs -ig. 100. NMR spin-echo spectra of “Co in in Fig. 98. Solid circles indicate the mean hypcrfinc field Fe,_,Co,),Zr for x50.4 at 77K [8OY I]. for (Fe, -xCo,hZro.97 [79 M 11. I

0

30

60

90

1.4.1.6 CoAd, 5d (group 4-6)

Ref. p. 5641

557

T=4.2K x = 0.2

0.6 ;i

I

I

I

I

0.7

-5

a

I -4

I -3

I -2

I -1

I 0

V-

I 1

I 2

I t 3 mm/s 5

0

b

50

100

I 150

I 200

I 250 kOe

bp -

Fig. 98. (a) M&batter spectra and (b) hyperfine field distribution curves, P(Hhyp), for 57Fe in (Fe, -,Co,),Zr at 4.2 K. Full lines in the spectra are produced from the analyzed hyperfine field distribution where e2qQ = - l.O5mm/s and the easy magnetization axis is assumed in [loo]. The broken line for x=0.2 was fitted by assuming the easy axis being in [l 111 for comparison [79 M 11.

Landolt-B6mstein New Series 111/19a

Shiga

1.4.1.6 Co-4d, 5d (group 4-6)

558

1.0 lrIzzJ

6

v=lOMHz

1.0

2

L

1

2

0

7

8

a

9

10 H,-,! r -

11

kOe 13

0 El 0 b

1

0

20

2L

28

32

[Ref. p. 564

36

40

LL

HWP’ -0 -

50

100 MHz 150

Fig. 101. NMR spin-echo spectra of 5gCo in (Fe, -$o,),Zr for x>=0.5 at 4.2K [8OY I]. (a) At IOMHz. (b) In zero field.

Y-

Fig. 102. NMR spin-echo spectra of ‘lZr in (Fe, -$o,),Zr for x 5 0.2 at 4.2 K [81 W 11.The positions ofthe lines due to diffcrcnt Fe, Co neighborhoods of”Zr are indicated by vertical bars, labeled with the respective 48 MHz52 number of Fe and Co atom in the neighborhood.

YI.andol!-Rorncrein Ncu- Series 111/19a

1.4.1.6 CoAd, 5d (group 4-6)

Ref. p. 5641

559

Table 11. Magnetic and related properties of certain intermetallic compounds of Co-Hf, Co-Ta, and Co-Nb [82 B 11.For the compounds not showing magnetic ordering, the Pauli susceptibility is given instead of PC0and Tc Compound

Structure

a “)

Tc

Co,Hf Co,Hf C%,Hf, Co,Hf

Cl5 Cl5 Th6M%3 hexagonal

Co,Ta Co,Ta Co,Nb Co,Nb

Cl5 Cu,Au Cl5 Cl5

PC~

K

A

XP

. 10m6cm3g-l

PB

-

6.896

6.833 11.502 5.477 ‘) 8.070“) 6.761 6.788 6.773 6.717

7.8

40 499 600

0.12 0.66 1.14

-

12 10 7 0.17

‘) a, in hexagonal plane. ‘) c, along hexagonal axis. 3, RT.

7.0 8, I 6.9 D 6.8 27

28

29

30

a

31 Hf-

32

8 Oogo*Q

0

0 “&“*O

#*cl,

go@

0 .O 0.

O*“@w

4 0

b

50

100

150

33

34 at% 35

32.8 @New @.O& po*Q @ + 34.1at% Hf 200

250

TFig. 103.(a)Latticeparameterat room temperatureand(b) temperature dependenceof the susceptibility of cubic Laves phase Co-Hf alloys [73A 11. The sampleswere annealedat 1000“C for 6 days and then water quenched.

Landolt-BOrnstein New Series lll/l9a

Shiga

K

300

[Ref. p. 564

1.4.1.6 Co-4d, 5d (group 4-6)

560

__

9

I

2.5

H,;,,= 3 kOe

PB

250 kOe

I

I

( Fe,mxCox 12Hf 0

20

I

0

2.0 .

200

0 0

b

I= 4.2K 0

10 \ ‘\ 0

\

Co,Hf .’ ---___ 100 200

300

100

K 500

0

I 1.5 ” I%

I-

.

150

,)

.

I z IX

HhYP

,I .

100

1.0 4,

Fig. 103. Tcmpcraturc dcpcndcncc of the magnetization af Co,Hf (dashed line) and Coz,Hf, (solid lint) at 3 kOc [SZ B I-J.

4, -co 50

0.5 .

[

0.2

FI?,Hf

0

0.6

0.8

.O 1.0 Co,Hf

Fig. 105. Composition dependence ofthc avcragc ma_enetic moment per 3d atom and the mean hypcrfine ficld at “Fc of (Fc, -$o,),Hf with the Cl5 structure. T=4.2 K. The specimens were heat treated at I I50 “C for 2 days and at 700°C for I day [80 K 21.

For Fig. 106, see next page

co

0.4 x-

20

40 w-

60 wt% t 0

co

20

LO MO -

60 wt% 80

Fig. 107. Phase diagram and composition dcpcndcncc of the Curie temperature of Co-W and CO-MO alloys [32 K I].

Ref. p. 5641

1.4.1.6 CoAd,

5d (group 4-6)

561

6.78 A I 6.74 b

a

6.70 24

26

28

30 Ta -

32

34 at% 36

3.c gclj 9 3.c 2.E 1 2s

IO

b 1.5

I

1.0

15

H" IO

0.5

0

30

60

b

90 T-

120

150 K 180

Fig. 106. (a) Composition dependence of the lattice parameter at room temperature, (b) temperature dependence of the magnetization at 7.22 kOe and (c) the susceutibilitv at 7.22 kOe of cubic Laves phase Co-Ta alloys [74 I i].

15

IO

15

IO

5

50

1.60 t ,$.45

0

2.5

5.0 Ma,W -

7.5 at% 10.0

Fig. 108. Composition dependence of the average atomic moment of CO-MO and Co-W alloys [32 S 2,37 F 11. Landolt-Bdmvein New Series lWl9a

250 K 300

1.4.1.6 Nihld, 5d (group 4, 6)

562

[Ref. p. 564

Table 12. Magnetic and related properties of certain intermetallic compounds of Ni-Zr [82 A 11.Temperature dependenceof susceptibility is given in Figs. 109and 110. Except for Ni,Zr the susceptibility is temperature-independent. Compound

Structure type

xrn . 10e6cm3 mol- ’

Y mJmol-’ K-*

@D K

Zr NiZrz NiZr Ni, ,Zr, Ni,,Zr, Ni,,Zr, Ni,Zr NiiZr, Ni ,Zr

bee CuAlz CrB Ni, ,Zr, Ni,,Zr, Ni,,Zr, Ni,Sn Ni,Zr, AuBe,

131 95 72 79 13 19 89

2.80 4.85 2.0

291 216 270

2.5

351

1p8

5.75

485

‘) Weak ferromagnet.

10.0 4-6 3 Y I

x” 5.0 2.5

50

0

100

150 T-

200

250

Fig. 109.Tempcraturcdependenceofthc susceptibility of Ni -Zr compounds [82A I].

15 .10-6 -cm3 9 I 12

w’ H9

6 0

20

40

60

80

K 100

Fig. I IO.Tempcraturcdependenceofthc susceptibility of Ni,Zr at a high field (z60kOe) [82A I].

Shiga

K

300

1.4.1.6 NiAd, 5d (group 4, 6)

Ref. p. 5641

0.6 k

563

""600 K

0

0.4

400 Ni-W

0.2

lz

200

f

Ni

Mo.W-

Ni

Mo,W-

Fig. 111. Composition dependence of the average atomic moment and the Curie temperature of Ni-Mo and Ni-W alloys [32 S 1, 37 M 11.

Fig. 112. Temperature dependence of the susceptibility of Ni-Mo alloys with 18...lOOwt% MO for heating process. Arrows indicate phase boundary temperatures. T,: a-phase (fee) occurs. TP (x860 “C), TY (z91O”C) and T6 (c 1350 “C) correspond to the peritectic temperatures of, respectively, the P-phase (Ni,Mo), y-phase (Ni,Mo) and g-phase (NiMo). Ta (z 1350 “C) is the eutectic temperature .between aLphase -and g-phase: For alloys with less than 60 wt% MO. Axp, which is shown in the figure, has been added in order to avoid crossing curves [38 G 11.

600 meVW2

I

II

I

300

600

I

I

c

1.0 e----Mo

0.5I 0

900

1200 "C 1500

TNi

MO-

Fig. 113. Composition dependence of the spin-wave stifiess constant D at 4.2 K of Ni-Mo alloys [78 H 21. Land&BOrnstein New Series 111/19a

Shiga

Rcfcrcnces for 1.4.1

561

1.4.1.7 References for 1.4.1 General references 5Sh

I

5Spl 65el 69~1 8’fl

Hansen. M.: Constitution of Binary Alloys, New York: McGraw-Hi!! Inc. 1958. Pearson, W.B.: A Handbook of Lattice Spacings and Structures of Metals and Alloys, London: Pergnmon Press 1958. Elliott. R.P.: Constitution of Binary Alloys, 1st. supp!., New York: McGraw-Hill Inc. 1965. Shunk. F.A.: Constitution of Binary Alloys, 2nd. suppl., New York: McGraw-Hill Inc. 1969. Fischer. K.H., in: Landolt-Biirnstein. New Series(Hellwege, K.H., Olsen, J.L.. eds.),Berlin: Heidelberg. New York: Springer, vol. 1% (1982) 289.

Special references 32K 1 37Sl 37F 1 37hl 1 38G I 54 11’1 63 P 1 64B 1 64 B 2 64N 1 64 W 1 65B I 66H 1 66K 1 67B I 67L 1 68A I 65 A 2 6SK 1 68-I-l 69Al 69K 1 69 K 2 70Bl 70K 1 70K2 7ON 1 71Kl 72Al 72Cl 73Al 73B 1 741 I 7412 75D I 7511 76A I 76Cl 76F1 76L 1 77K 1

Koster. W., Tonn. W.: Z. Metallkd. 24 (1932) 296. Sadron. C.: Ann. Phys. Ser. 10, 17 (1932) 371. Farcns. T.: Ann. Phys. Ser. 11, 8 (1937) 146. Marinn. V.: Ann. Phys. Ser. 11, 7 (1937) 459. Grube. G.. Winklcr. 0.: Z. Elcctrochcm. 44 (1938) 423. Wilhelm, H.A.. Carlson. O.N.. Dickinson. J.M.: Trans. AIME 200 (1954) 915. Piqger, E.. Craig. R.S.: J. Chcm. Phys. 39 (1963) 137. Betsuyaku. H.. Komura. S., Betsuyaku, Y.: J. Phys. Sot. Jpn. 19 (1964) 1262. Booth. J.G.: Phys. Status Solidi 7 (1964) K 157. Nevitt. M.V., Kimball. C.W., Preston. R.S.: Proc. ICM, Nottingham 1964, p. 137. Werthcim. G.K.. Jaccarino, V., Wernick, J.H.: Phys. Rev. A 135 (1964) 151. Bu!yfcnko. A.K.. Gridncv, V.N.: Fiz. Met. Mctallovcd. 19 (1965) 205. Helmgcr. F.: Phys. Kondcns. Mater. 5 (1966) 285. Koehler. W.C.. Moon, R.M.. Trcgo. A.L., Mackintosh, A.R.: Phys. Rev. 151 (1966) 405. Bruckner. W.. Kleinstuck. K., Schulzc. G.E.R.: Phys. Status Solidi 23 (1967) 475. Lam. D.J.. Spokas. J.J., Van Ostenburg. D.O.: Phys. Rev. 156 (1967) 735. Abel, A.W., Craig. R.S.: J. Less-Common Met. 16 (1968) 77. Arajs, S.: J. App!. Phys. 39 (1968) 673. Kai. K.. Nakamichi. T., Yamamoto, M.: J. Phys. Sot. Jpn. 25 (1968) 1192. Tanaka, M.. Ito. N., Tokoro, T., Kanematsu, K.: J. Phys. Sot. Jpn. 25 (1968) 1541. Alfieri. G.T., Banks. E., Kanematsu, K.: J. Appl. Phys. 40 (1969) 1322. Kai, K.: Dr. Thesis. Tohoku Univ. 1969. Kancmntsu. K.: J. Phys. Sot. Jpn. 27 (1969) 849. Bender, D.. Muller. J.: Phys. Kondens Mater. 10 (1970) 342. Kai. K.. Nakamichi. T., Yamamoto, M.: J. Phys. Sot. Jpn. 29 (1970) 1094. Kanemntsu, K.. Fujita. Y.: J. Phys. Sot. Jpn. 29 (1970) 864. Nakamichi. T., Kai, K.. Aoki. Y., Ikedn, K., Yamamoto, M.: J. Phys. Sot. Jpn. 29 (1970) 794. Kancmatsu. K.: J. Phys. Sot. Jpn. 31 (1971) 1355. Aoki. Y., Nakamichi. T., Yamamoto, M.: Phys. Status Solidi (b) 53 (1972) K 137. Callings, E.W., Ho, J.C., Jaffee,R.I.: Phys. Rev. B5 (1972) 4435. Aoki. Y., Nakamichi, T., Yamamoto, M.: Phys. Status Solidi 56 (1973) K 17. Brouha. M.. Buschow, K.H.J.: J. App!. Phys. 44 (1973) 1813. Itoh. K.. Fujita. Y., Kanematsu, K.: J. Phys. Sot. Jpn. 36 (1974) 1024. Itoh. H., Aoki. Y.. Nakamichi, T., Yamamoto, M.: Z. Metallkd. 65 (1974) 149. DufTcr, P.. Sankar. S.G.. Rao. V.U.S.. Bergner, R.L., Obcrmyer, R.: Phys. Status Solidi (a) 31 (1975) 655. Ikeda. K., Nakamichi. T.: J. Phys. Sot. Jpn. 39 (1975) 963. Amamou. A., Caudron. R.. Costa. P., Friedt. J.M., Gautier, F., Loege!, B.: J. Phys. F6 (1976) 2371. Callings, E.W.. Smith. R.D.: J. Less-Common Met. 48 (1976) 187. Fukamichi. K.. Saito. H.: J. Jpn. Inst. Metals (in Japanese)40 (1976) 22. Livi, F.P., Rogers, J.D.. Viccaro, P.J.: Phys. Status Solidi (a) 37 (1976) 133. Kimura. Y.: Phys. Status Solidi (a) 43 (1977) K 141.

References for 1.4.1 77Ml 78Hl 78H2 78Pl 78P2 79Bl 79Kl 79K2 79Ml 79M2 79Sl 7982 8OJl 80Kl 80K2 80Ml 80M2 80Nl 8OSl 8OVl 8OYl 81Fl 81F2 81Gl 81Pl 81Vl 81V2 81Wl 81Yl 82Al 82Bl 82Fl 82F2 82F3 82Wl 83Al 83A2 83Hl 83Ml 83Nl 83Yl 85Fl

Muraoka, Y., Shiga, M., Nakamura, Y.: Phys.‘ Status Solidi (a) 42 (1977) 369. Hafstrom, J.W., Knapp, G.S., Aldred, A.T.: Phys. Rev. B 17 (1978) 2892. Hennion, M., Hennion, B.: J. Phys. F8 (1978) 287. Pop, I., Coldea, M., Rao, V.U.S.: Phys. Status Solidi (a) 49 (1978) 207. Pan, Y.M., Bulakh, I.Ye., Shevchenko, A.D., Latysheva, V.I.: Fiz. Met. Metalloved. 46 (1978) 741. Buschow, K.H.J., van Diepen, A.M.: Solid State Commun. 31 (1979) 469. Khan, H.R., Kobler, U., Luders, K., Raub, Ch.J., Szucs, Z.: Phys. Status Solidi (b) 94 (1979) K27. Kozhanov, V.N.,Romanov,Ye.I?, Verkhovskiy, S.V., Stepanov, A.P.: Fiz. Met. Metalloved 48 (1979) 1249. Muraoka, Y., Shiga, M., Nakamura, Y.: J. Phys. F9 (1979) 1889. Muraoka, Y.: Thesis submitted to Kyoto Univ. 1979. Shavishvili, T.M., Meskhishvili, A.I., Andriadze, T.D.: Fiz. Met. Metalloved. 47 (1979) 880. Shiga, M., Nakamura, Y.: J. Phys. Sot. Jpn. 47 (1979) 1446. Jacob, I., Davidov, D., Shaltiel, D.: J. Mag. Magn. Mater. 20 (1980) 226. Krischel, D., Thomas, L.K.: J. Phys. F 10 (1980) 115. van der Kraan, A.M., Gubbens, P.C.M., Buschow, K.H.J.: J. de Phys. 41 (1980) C 1-189. Marchenko, V.A., Polovov, V.M.: Zh. Eksp. Teor. Fiz. 78 (1980) 1062[Sov. Phys. JETP 51(1980) 535-J. Muraoka, Y., Shiga, M., Nakamura, Y.: J. Phys. F 10 (1980) 127. Nakamura, Y., Shiga, M.: J. Mag. Magn. Mater. 15-18 (1980) 629. Strom-Olsen, J.O., Wilford, D.F.: J. Phys. F 10 (1980) 1467. Verkhovskiy, S.V., Kozhanov, V.N., Stepanov, A.P., Romanow, Ye.P., Galoshina, E.V.: Fiz. Met. Metalloved. 49 (1980) 1234 [Phys. Met. Metallogr. (USSR) 49, No. 6 (1981) 941. Yamada, Y., Ohmae, H.: J. Phys. Sot. Jpn. 48 (1980) 1513. Fujii, H., Pourarian, F., Sinha. V.K., Wallace, W.E.: J. Phys. Chem. 85 (1981) 3112. Fujii, H., Pourarian, F., Wallace, W.E.: J. Mag. Magn. Mater. 24 (1981) 93. Grossinger, R., Hilscher, G., Wiesinger, G.: J. Mag. Magn. Mater. 23 (1981) 47. Pourarian, F., Fujii, H., Wallace, W.E., Sinha, V.K., Smith, H.K.: J. Phys. Chem. 85 (1981) 3105. Verkhovskiy, S.V., Kozhanov, V.N., Stepanov, A.P., Shevchenko, A.D., Pan, V.M., Bulakh, Lye.: Fiz. Met. Metalloved. 49 (1981) 553 [Phys. Met. Metallogr. (USSR) 49 No. 3 (1981) 911. Vincze, I., van der Woude, F., Scott, M.G.: Solid State Commun. 37 (1981) 567. Wiesinger, G., Oppelt, A., Buschow, K.H.J.: J. Mag. Magn. Mater. 22 (1981) 227. Yamada, Y., Ohira, K.: J. Phys. Sot. Jpn. 50 (1981) 3569. Amamou, A., Kuentzler, R., Dossmann, Y., Forey, P., Glimois, J.L., Feron, J.L.: J. Phys. F 12 (1982) 2509. Buschow, K.H.J.: J. Appl. Phys. 53 (1982) 7713. Fujii, H., Pourarian, F., Wallace, W.E.: J. Less-Common Met. 88 (1982) 187. Fujii, H., Pourarian, F., Wallace, W.E.: J. Mag. Magn. Mater. 27 (1982) 215. Fujii, H, Sinha, V.K., Pourarian, F., Wallace, W.E.: J. Less-Common Met. 85 (1982) 43. Wiesinger, G., Hilscher, G.: J. Phys. F 12 (1982) 497. Ahmed, MS., Hallam, G.C., Read, D.A.: J. Mag. Magn. Mater. 37 (1983) 101. Akselrod, Z.Z., Budzynski, M., Khazratov, T., Komissarova, B.A., Kryukova, L.N., Reiman, S.I., Ryasny, G.K., Sorokin, A.A.: Hyperfine Inter. 14 (1983) 7. Hirosawa, S., Pourarian, F., Sinha, V.K., Wallace, W.E.: J. Mag. Magn. Mater. 38 (1983) 159. Muraoka, Y., Shiga, M., Nakamura, Y.: Phys. Status Solidi (a) 78 (1983) 717. Nishihara, Y., Yamaguchi, Y.: J. Phys. Sot. Jpn. 52 (1983) 3630. Yamada, Y., Ohira, K.: J. Phys. Sot. Jpn. 52 (1983) 3646. Fujii, H., Okamoto, T., Wallace, W.E., Pourarian, F., Morisaki, T.: J. Mag. Magn. Mater. 46 (1985) 245.

Landolt-Bbrnstein New Series 111/19a

565

Shiga

1.4.2.1 3d-4d, 5d (group 8): 3d-rich alloys

[Ref. p. 648

1.4.2 3d elements and Ru, Rh, Pd or OS, Ir, Pt 1.4.2.1 3d-rich alloys Survey Alloy Cr, -,Ru,

Cr, -,Rh, Cr, -,Pd, Cr, -%os,

Cr, -Jrr

Crl -,Pt,

Mn, -xPd,

Fe, -A

co, -A Nil -A Ni, -,Ru, Ni, -IOs,

X

x
Property

Fig

x& T) TN(X) TN(X)

1, 2 3 4 5

TNk PI

magn. structure ~maxC4 TN(X)

ek T), TN(x) TN(x) TN(x) e(x>7-j TN(X) x&x, 7-1 eh T) ek 4.2 W, TN(x) e(T), x,(T) TN(x) WT) T,(x) X&T 1

6 3 7 8 3 9 10

TN(x) TN(X) x&x, T) magn. phase diagram magn. structure a, c

15 16 17 18 19 20

edx),

Table

1 l-2 3

3 11 12 13 14

4

P.1

L(x) T,(x)

21

PSOl”lC

22 23 24 25 26 27 114 (in 1.4.2.2) 28 29 30 31

5

x <0.20 x <0.30 x < 0.03 x < 0.20

&y,,(x) T,(x) Pa,(x) aiz,(x)/ax T,(x) iat

x < 0.03 x < 0.03 x
Ba,(x) PNi? ~dX) H,,gpr47-1 H,,y,v 47

Frame, Gersdorf

Ref. 75Al 64Bl 75A1 7051 81 Pl 81Pl 70A1 64B1 73Al 80M 1 64Bl 81Hl 70A 1 70Al 75Fl 75Fl 75Fl 72D 1 75A2 75A3 75A2 68Hl 68Hl 68Hl 68Hl 68H1 36Fl 71 s2 68s 1 68 s-l 6OCl 6OCl 70 L 1 6OCl 6OCl 79P2 79P2 68Sl 75Fl

I andnlr-Bornrrcin Nea Ccrie% 111’19a

Ref. p. 6481

1.4.2.1 CrAd, 5d (group 8)

567

Hardly any information is available for the 3d-rich alloys based on the paramagnetic 3d elementsSC,Ti, and v. For antiferromagnetic Cr, the Neel temperature starts to increase with Ru, Rh, OS, Ir, and Pt content, reaching maximum values at a few at%. For Cr-Pd alloys TNshows a different composition dependence(Fig. 7). The transition from incommensurate to commensurate state has been studied for Cr-Ru alloys. Magnetic phase diagrams showing the commensurate, incommensurate and paramagnetic states as a function of temperature and pressure are known for Cr + 0.3 at% Ru and Cr + 0.6 at% Ru (Fig. 5). The y-Mn phase can be stabilized by alloying Mn with small amounts of other elements (e.g. Pd) and quenching from high temperatures. In dilute Fe-(Ru, Rh, OS,Ir) alloys the Curie temperature decreaseslinearly with composition; the magnetic moment per atom initially increaseswith composition for Fe-Ir, Fe-Rh, and Fe-Pt, remains nearly constant for Fe-Ru and Fe-Pd, and decreasesfor Fe-OS (Fig. 21). The magnetic moment per atom and the Curie temperature both decreasewith composition in Co-(Ru, Rh, Pd, OS, Ir, Pt) alloys (Figs. 24 and 25). For Ni-(Ru, Rh, Pd, OS, Ir, Pt) alloys, the results of magnetic measurementsare summarized in Fig. 114 of subsect. 1.4.2.2and Fig. 28. The magnetic moment distribution in dilute Ni-Rh alloys has been investigated by diffuse neutron scattering experiments. Hyperfine fields were studied by perturbed angular correlation (PAC) experiments for Ni-Ru and Ni-0s.

3.3 I x" 3.2

0

2

4

6 Ru -

8

IO at% 12

Fig. 1.Mass susceptibility xpofCr-Ru alloys at 400K and 600K [75Al].

Landolt-Bdmstein New Series 111/19a

3.0 300

350

400

450

500

550

600 K 650

Fig. 2. Mass susceptibility xp of Cr-Ru alloys between 300K and 600K [75A 11.

Frame, Gersdorf

[Ref. p. 648

1.4.2.1 Cr-4d, 5d (group 8)

568

600 “C

K

30:

550

I 15:: 2

500

0

I F 156

LOO

-152 6 IIt% x -

12

18

Fig. 3. NCel temperature TNofthc bee alloys ofCrwith Ru. Rh. and OS [64 B I].

350

300

Fig. 4. N&cl temperature TN of Cr-Ru alloys as derived from susceptibility measurements (circles) [75A I] and from resistivity measurements (triaqles) [73 D I], see also [7OA I].

K

ioi 1 35:

30:

--. WY

2531 0

corn.

pore.

‘-.,.

I 3

I/ 6

‘7-b /

worn. I 9

\I‘

I I 12 kbor 15

Fig. 5. Magnetic phase diagram ofCr-Ru alloys, showing the commensurate (corn.) incommensurate (incorn.) and paramagnetic (para.) phases in the T-p plane [70 J I].

P-

Table 1. Antiferromagnetic phases above 4K as a function of temperature concentration for Cr-Ru alloys as derived from neutron diffraction [81 P 11.

and Ru

K 0.3 longitudinal incommensurate 1.5 5.0

114 transversal incommensurate commensurate commensurate

Franse, Gersdorf

250 commensurate

380 480 514

1.4.2.1 Cr-4d, 5d (group 8)

Ref. p. 6481

569

Table 2. Maximum magnetic moment pmar and Neel temperature for Cr-Ru [Sl P 11, see also [66 K 11 and Fig. 23 in sect. 1.1. at% Ru

0.3 1.5 5.0

Pmax PB

TN K

0.57(6) 0.69(7) 0.60(6)

[SIP11 380 480 514

TN K

Q(4.2 K) pi2 cm

@km

50 40

Ru

0.9 2.1 3.0

507 530 565

3.14 8.39 11.48

t cm30

OS

4.8 0.3

558 359

19.89 0.81

20

0.6 1.1 2.0

465 533 566

1.88 2.65 5.26

IO

0 0.3 0.5 0.8

312 301 477 512

1.1 1.4

534 547

Ir

[75A l] z350 480 550

60

Table 3. Ntel temperature and the residual electrical resistivity of Cr-Ru, Cr-0s [7OA l] and Cr-Ir [72 D l] alloys.

at%

[70 J l] 376 -

0

200

400

600

800

1000 K 1200

TFig. 6. Electrical resistivity Qof Cr-Ru alloys between 4 K and 1050 K [7OA 11.

350.

K Cr-Pd

o susceptibility 1

2 Pd -

3

at%

4

Fig. 7. NCel temperature TN of Cr-Pd alloys as derived from susceptibility measurements (circles) and from resistivity measurements (crosses) [73A 11, see also [SOM 11.

Fig. 8. Electrical resistivity Q vs. temperature of Cr-Pd alloys [80 M 11. The insert shows the residual resistivity Q,,,determined at 4.2 K, vs. x. Landolt-Bbmstein New Series IIl/l9a

0

Franse, Gersdorf

100

200

300 T-

400

500

600 K 700

1.4.2.1 CrvId, 5d (group 8)

570

[Ref. p. 648

60 p&m 50

3.4 I g 3.2

2.sl 0

I 200

I 100

I 300 I-

I 400

I I 500 K 600

Fig. 9. Mass susceptibility xp vs. temperature for various Cr--0s alloys. Arrows indtcate the N&l temperature [Sl H I].

0

200

400

600 T-

BOO

1000 K 12

Fig. 10. Electrical resistivity e vs. temperature of Cr-0s alloys [7OA 11.

x” -31 360

440

400

K 480

T-

Fig. 11. Temperature depcndencc of the mass susceptibility,%, and of the relative change Ae/e in the electrical resistivity for the Cr-0.3 at% Ir alloy [75 F I]. 0

1

2

3

4 at% 5

Ir-

Fig. 12. N&cl temperature Tn of Cr-Ir alloys as derived from susceptibility measurements. Dashed line: [73 A23, solid line: [75 F I].

I

I

I

340

393

440 I-

I

490 K !

Fig. 13.Thermal expansivity curves for dilute Cr-Ir alloys [75 F I].

Frame, Gersdorf

1.4.2.1 CrAd, 5d (group 8)

Ref. p. 6481 3.4 .1W6 -cm3 9 I

Cr-Pt . e*** 0.6at% Pt .

3.2

s3.1

30 p&cm

550 K

25

500

:08@-o

l

0

.-

o o 3.0 0

.

0

f0:6atyoPt + + +++++++w#++++ I

I

300 350

I

I

I

400 450 500

I

I

550

600

250 1.2 at% 1.8

0.6 Pt -

I

650 K 700

7-

Fig. 15. NCel temperature TN and the low-temperature electrical resistivity Q,,,determined at 4.2 K, of dilute CrPt alloys [75 A 31.

Fig. 14. Mass susceptibility xg (circles) and relative electrical resistivities Q (crosses) vs. temperature for Cr0.6 at% Pt and Cr-3 at% Pt alloys [75 A2].

650 K 600 600

550

t 500 t hz 450

400

350

30,ku 300 U

1

2

3

8

9

IO at% 11

Pt -

Fig. 16. Variation of the Ntel temperature TN derived from resistivity measurements (solid circles) and susceptibility measurements (open circles) of Cr-Pt alloys [75A2].

Landolt-Bbmstein New Series IW19a

Franse, Gersdorf

1.4.2.1 Mn--4d, 5d (group 8)

572

[Ref. p. 648

600 K -

I

I

Mn.., Ni, I

(

A’ f’ /

/’

1

/

A’ x = 0.21

/’ / /’

/’

!

300

I

I

I

\.!‘,\4 4

tetrogonol

200

I \

100 1 I

1DG

200

I

I

300 I-

LOO

500

K

E

0

/

oniiterromynetic

’

“\I

5

10

, 4

15

20

2:j

30 ot%

35

Ni, Pd -

Fig. 17. Mass susceptibility lE vs. tcmpcraturc for some y-phase Mn, -,Pd, and Mn, _,Ni, alloys [68 H I].

y-Mn-Pd

Fig. 18. Magnetic and structural phase diagram of qucnchcd Mn Pd and Mn Ni alloys as derived from anomalies in the temperature-dcpcndcnt behavior of the Young’s modulus [68 H I]. Solid and open circles: magnctic transformation for Pd and Ni alloys, rcspcctivcly. Solid and open trianglcs:crystallographic transformation for Pd and Ni alloys, rcspcctivcly.

Table 4. Average magnetic moment per atom Is,, at TzO K as derived from neutron diffraction measurements for Mn-Pd alloys [68H I], see also [83 C I]. at% Pd Fig. 19. Magnetic structure of y-phase MnPd [68 H I].

3.85

A Mno.87Pd013

0

I

alloys

0 3 9 13 1.5 21

2.30(5) 2.4( 1) 2.6(l) 2.7(l) 2.7(l) 3.0( 1)

i 3.8:: u d

Fig. 20. Lattice parameters n and c vs. temperature for Mn o.mPdo.,x. TN and 7; arc the magnetic and structural transformation tempcraturcs, respectively, xc Fig. 18 [68 H I].

Ref. p. 6481

1.4.2.1 F&d,

5d (group 8)

573

2.6 PB

2.4

1.8

I 1.6 lc? IA

Fig. 21. Average magnetic moment per atom &, in iron-rich Fe-(@, Rh, Pd, OS, Ir, Pt) alloys as a fimction of solute concentration [36 F 11.

0

IO

20at"/bl X-

3

Table 5. Influence of Ru, Rh, Pd, OS, Ir and Pt impurities on the Curie temperature of Fe [71 S 21, see also [71 S 11. c: solute concentration.

pB Fe-3d 0

2o

l-

lo

Ru Rh Pd OS Ir Pt

-1 -

-16 -2 -3 -11 -4

-2 t 1 I LI

I

I fe

0

AT,lc K/at %

I f0

i, I V

Ii I Cr

I Mn

I Fe

I Co

I Ni I

0

I,

Fig. 22. Localized moments for 3d, 4d, and 5d solutes in Fe, as derived from neutron scattering (solid circles: [65 C 31, squares: [66 C 11)and from conduction-electron and core polarization (open circles) [68 S I].

Land&-Bbmstein New Series 111/19a

Franse, Gersdorf

I

I w

I Re

I OS

I Ir

I Pt

574

1.4.2.1 Fe, Chid, 0.8 MOe 0.6

5d (group 8)

Fe-4d .

.

E s' 1.6 ' MOe 1.2 0.8

[Ref. p. 648

.

I

I

I

I

I

I

I

Nb

MO

Tc

Ru

Rh

Pd

Aa

.

Fe-5d .

.

.

.

.

.

04 0

I

I

To

W

I

I

Re OS Solute

I

I

I

Ir

Pt

Au

Fig. 23. Hypcrfinc field H,,, for various 4d and 5d solutes in Fe [68’S I].

For Fig. 24, see next page

Y cls Co-4d

1.8

0 0

-2

P'e

-4

I 1.7

I 0

-6 ,z 1.6

1.5 1.1 1.8 Ps 1 1.7

,$

1.6 0

1.5

1

-12 I

30

Fig. 25. Average magnetic moment per atom j,, ofcobaltrich fee Co-(Ru. Rh. Pd. OS, Ir, Pt) alloys as a function of composition [60 C I].

I Ht

I To

I W

I Re Solute

I OS

I Ir

I Pt

Fig. 26. Variation of the average magnetic moment of Co alloys with the concentration c of the 4d and 5d solute, $,,/ac. Open circles: measured for a field intensity of 15 kOe and c? 0.02 [60 C I]; Solid circles: measured for a field intensity of 30 kOe and c 5 0.02 [70 L I].

Frame, Gersdorf

575

1.4.2.1 Co, Ni-4d, 5d (group 8)

Ref. p. 6481 1400 K I 1300 hy

1200 1100 1000 0

2

4

6

8

IO

12

14

16

18

20at%22

xFig. 24. Composition dependence of the Curie temperature of cobalt-rich fee Co-(Ru, Rh, Pd, OS, Ir, Pt) alloys [60 C 11, see also [52 K 11.

1

18

5

20at%22

xFig. 27. Composition dependence of the Curie temperature of nickel-rich Ni-(Rh, Ir, OS) alloys [60 C 11.

I

1.g0.55

0.50

0.45 0

1

2

3

4

at%

5

Ru -

Fig. 28. Average magnetic moment per atom j?,,for Ni-Ru alloys. Solid line: OK [32 S 11,dashed line: 290 K [32 S 11, solid triangle: [71 C 31, open triangle: [71 M 21, circles: 4.2K [79P2], squares: 290K [79P2].

Landolt-Bbmstein New Series lll/l9a

Franse, Gersdorf

576

1.4.2.1 Ni-4d, 5d (group 8)

0

1

2 Ru -

3

[Ref. p. 648

at%

4

Fig. 29. Magnetic moment distribution as dcrivcd from polarized neutron scattering in Ni -Ru alloys near zero tcmpcraturc (xc also [68 C I]). ijNi: triangle [71 M 21 and solid circles [79 P 21. Is,,,: open circles [79P 21.

1.0

1.4,

I

1 Ni-0s

3.2 0 0

---

win

= l/2

-.-

spin I

= 5/z

0.2

0.4 0.6 r/r, -

0.8

0 1.0

Fig. 30. Rcduccd hypcrfinc field vs. rcduccd temperature br Ni 1 atXQ9Ru. 7”=6lOK. H,,,(4.2K)=217.2kOc. The broken cunrs arc calculated’ on the basis of a noleculnr field model [68 S I]. The solid curve represents the rcduccd spontaneous magnetization cr,l~,(O) for pure Ni.

I

I

1

I 1.0

1.0

-2 0.8 .> E; u --& 0.6 s'

0.8

0.63 11

@.I -L 0.4G-

0.4 0.2

* IO.2 i

0 0

0.2

0.4

r/r, -

0.6

0.8

PO 1.0

Fig. 3 I. Reduced hypcrfinc field on OS in Ni vs. reduced tempcraturc [75 E 11. Circles: lg20s, squares: ‘**OS. Triangles: W in Ni. The line represents the reduced spontaneous magnetization I&, for pure Ni.

Frame, Gersdorf

1.4.2.2 3d-4d, 5d (group 8): concentrated alloys and compounds

Ref. p. 6481

577

1.4.2.2 Concentrated alloys and intermetallic compounds 1.4.2.2.0 Introduction

Detailed phase diagrams for the binary constitutional alloys T-M, in which T is a 3d transition element and M a group-VIII 4d or 5d element, are available for most of the systems.The T-M alloys show a wide variety of ordered structures at room temperature. In many casesthe experimentally determined magnetic parameters strongly depend on the state of atomic ordering. For the system T-Pt this is indicated in Table 1. The different types of magnetic order and the magnetic parameters of the ordered T-Pt compounds are summarized in Table 2. Table 1.Crystallographic structure and type ofmagnetic order in atomically ordered (0) and disordered (d) T-Pt compounds [Sl K2]. T: 3d transition elements Ti...Ni; P: paramagnetic, F: ferromagnetic, AF: antiferromagnetic. T Ti

V

Cr

Mn

Fe

co

Ni

Al5 P -

Al5 P -

Cu,Au AF fee AF

Cu,Au F fee F

-

d

Al5 P -

-

Cu,Au F fee F

o

AuCd

CuAuI P

d

-

AuCd P -

CUAUI AF fee P

CuAuI AF fee P?F

CuAuI F fee F

CuAuI F fee F

CuAuI P fee F

TiAl, F fee P

Cu,Au F

Cu,Au F fee P

Cu,Au F fee P?

Cu,Au AF fee F

Cu,Au F fee F

-

T,Pt o

TPt

TPt, o

Cu,Au P -

d

-

Table 2. Magnetic moment per atom and magnetic ordering temperature of some ordered T-Pt compounds T: 3d transition elementsV...Ni; P: paramagnetic, F: ferromagnetic, AF: antiferromagnetic, FI: ferrimagnetic; T,: temperature at which a transition between two different types of magnetic order occurs. These quantities strongly depend on the atomic state of ordering; data from various authors generally disagree.The values given in this table have therefore qualitative significance only. T

T,Pt

TPt

V

Cr

Mn

Fe

P

P

AF, T,=485K PM,, = 3.0 PB ‘) T,=365K

F, Tc=400K

P

TPt,

AF kr=2.24

FI, T,=200...240K P”=l PPt =

pB4) -

‘) At 300K.

Landolr-Bbrmtein New Series IWl9a

o.3

PB “)

“) At 77K.

PB ‘1

FI, T,=481 K PO = 2.33 PB ‘) pPt= -0.27 FB ') “) At 4.2K.

Ni

co

PFe = 2.7

PB “)

PPt = o.5

kB 3,

F

AF, T,=975K hh=4.3 PB ‘) T,=715K

FI, Tc=670K

F, T,=750K

P~c~2.8 VB ‘) pp,= -0.25 pB

~~0~1.6~1~

F, Tc=395K = 3.60PB

AF, T,=170K

F, Tc=290K

PFe = 3.3

PcO=~.~~FB

PM”

“)

pPt=0.17 pB 2,

4, At 1.7K.

Franse, Gersdorf

PB

PP1=

o.25

Ppt = 0.26

PB

PB

P

1.4.2.2.1 SC,Ti, VAd, 5d (group 8)

578

[Ref. p. 648

1.4.2.2.1 SC,Ti, and V alloys and compounds Incidental experimental work has been reported for the CsCI-type of compounds ScRu and TiRu. Intermetallic compounds of Ti or V with Pd or Pt have been studied more frequently, especially VPt,, which compound orders magnetically below 240K in the atomically ordered Cu,Au structure, the spontaneous magnetic moment per cell, Pee,,,being as small as0.101pu, For the tetragonal, TiAl,-type of structure, compound VPt, different results are obtained: T,=210K; FCC,,=O.O75n,.NMR experiments on V(Ir, -XPtx)3indicate that VPt, has a ferrimagnetic structure with pv= 1 un and pp,= -0.3 un. Disordered VPt, has been reported to be paramagnetic. Experiments on VPd, down to 1.6K do not give any evidence for magnetic order in this compound. Survey Property

X

ScRu TiRu Ti 1-3’4 V, -3’4 VPd, V, -,Fe,Pd,

0.75-Ix -I 1 0.65~5 1 0.01sxso.2

Fig

x0.c,. 0 x0,Xp,c,, @

1 2 3 4 5, 6 7

L(T) L(T) zr(T) X,(T),

a(H) Pi.‘@ %o x,(T) e(T)> z,(T), 4W

VIr, vpt, W, -PtJ3

OIx-
x& T). T,(x)

Table

Ref.

3 3

73Tl 73Tl 58Gl 58G1 82Bl 82Bl

4

82Bl 77Gl 8151 77Gl 79Kl 82Al 82Al 82Al

11 8, 9, 10 11, 12, 13, 14

dx, T), ii&), PP, VPt, VPt v,pt

5 5 5

Xm Y Xm Y Xm.Y

1.25 .lO" A!-.

Table 3. Susceptibility data of ScRu and TiRu compounds with the CsCl-type of structure; )I~= ,yo+ C&T- 0). The Curie-Weiss contribution to xF is attributed to the magnetic moments of Ti atoms on Ru sites [73T 11.

cm!

X0

10-6cm3g-1 ScRu TiRu

0’

53

100

150

200

250 K 300

Fig. I. Reciprocal magnetic mass susceptibility of TiRu vs. tcmpcrature: solid curve represents the equation zS= lo + C/( T- 0) with the paramctcrs given in Table 3 [73T I].

Fransc, Gersdorf

1.10 0.90(10)

c,

0

10-6cm3Kg-’

K

0 12(l)

1.0(3)

1.4.2.2.1 SC,Ti, V--4d, 5d (group 8)

Ref. p. 6481 f 40' cm’ Kl 4

t 2 x'

I

I

I

I

I

200

400

600 T-

800

1000

I

K

1200

K

1200

Fig. 2. Temperature dependence of the molar susceptibility x,,, of Pd-Ti alloys [58 G 11.

.I$ -cm3 mol I

4

N’ 2

1000

800

600 T-

400

200

0

Fig. 3. Temperature dependence of the molar susceptibility x,,, of Pd-V alloys [58 G 11.

2.0 .I@

-cm3

l

VPd,

g l =...l

I

T

I l

’

0..

l

. .

.

.

.

.

.

.

l

.

1.0

H”

0.5

0

50

100

150 T-

200

2'513 K:

Fig. 4. Temperature dependence of the mass susceptibility xp of VPd3 [82 B I]. Landolt-BOrnstein New Series 111/19a

Frame, Gersdorf

1.4.2.2.1

580

0.12. .1rj-' .

-

cm3

I

l

0.05 .

w=

.

[Ref. p. 648

I

I

a .

SC,Ti, V-4d, 5d (group 8)

V,-,Fe, Pd3 I H = 3.2 kOe 0 x =

0.01

0

50

100

150 T-

IFig. 5. h&s susceptibility zL:vs. T for V, -,Fc,Pd, whcrc s=O.Ol and s=O.O5. respcctivcly. H=3.2 kOc [82 B I].

I

V0.83Fe0.20Pd3

X

I b'

250 K 300

Fig. 6. Mass susceptibility zr: and ac susceptibility zuc (insert, in relative unit) vs. T for V,,,,Fe,,,,Pd, [82 B I].

Table 4. Curie-Weiss [82 B I].

T=4.2K

200

0 0.01 0.05

parameters

for Fe,V, -xPd,

X0

!&ff.Fe

@

T, ‘1

10-6cm3g-’

pa

K

K

1.27 1.35 1.1

4.4 4.8

-7.5 - 2.4 2.1

2

‘) To: ordering temperature of, possibly, a magnetic cluster-glass state. 0

20

LO H-

60

kOe

80

Fig. 7. High-field magnetic moment per unit ofmass. U, for V 0.8OFeO.20 Pd, [82 B I].

.‘“g” VP& ii? i

I

01 701 0

100 53

100

r

150

200

250 K :

Fig. 8. Electrical resistivity Q of VPt, with the Cu,Austructurt‘ as a function of temperature. The arrow shows the ordering tcmpcraturc at 206 K [79 K I]. The broken lint is IO dcmnnstratc the change in slope of e( T) at the ordering tempcrnture.

A9 300

500

700

900 K 1100

IFig. 9. Mass susceptibility of ordcrcd VPt, alloys above their Curie point [8l J 1). Open circles: Cu,Au-type. solid circles: TiAl,-type. ,~~=0.471 . 10-6cm3g-1 for Cu,Autype and 1,=0.503. 10-6cm3g-’ for TN,-type VPt,.

Frame, Gersdorf

1.4.2.2.1 SC,Ti, V-4d, 5d (group 8)

Ref. p. 6481

i0 kOe 180 a 0.90 J& 9

I

0.87

581

0.6,

I

I

I

,240

h I V(Ir,_,Pt,)3

I

IL

I

lK

0.4

160 I 120*

15 0.3

-I 0.84 2 0.67

0.2

80

0.1

40

6 0.640.61 0

2-c --

0.1

0.2

0.3 luuH-* -

b

0.4

0.5(kOei‘*0.6

0.5

0.6

0.7

0.9

0 1.0

Fig. 12. Variation of the Curie temperature T, and magnetic moment per V atom, jjv, with concentration x for V(Ir, -xPtx)3 alloys [77 G 11.

01

I

200

300

400

I-

I

500

TFig. 11. Variation of the reciprocal magnetic mass susceptibility xs (x=0.50,0.55,0.69, and 0.85) and magnetic mass susceptibility (x = 0 and 0.40) with temperature for V(Ir, -.Pt,), alloys [77 G 11.

Landolt-Bbmsrein New Series 111/19a

0.8

X-

Fig. 10. Magnetic moment per unit of mass, 0, of two ordered VPt, samples at 4.2 K in the high-field domain 0 < H < 150kOe. Open circles: Cu,Au-type, solid circles: TN,-type; (a) magnetization curve against field, corrected for demagnetization; (b) approach to saturation: cr-~nrH against He2 [Sl J i], see also [8OB l] and [82 J 11. High-field susceptibility xHF= dg/dH, H>50kOe: XHF=0.9. 10-6cm3g-’ for Cu,Au-type VPt,. and xHF=l.O. 10v6 cm3 g-’ for T&-type

100

0 0.4

Frame, Gersdorf

I

K

600

1.4.2.2.2 Cr-4d, 5d (group 8)

582

[Ref. p. 648

3 Gem: 9

2 I b

0

50

100

!

i'00

150

T-

K

250

Fig. 13.Variation of the spontaneousmagneticmoment per unit mass,U,with temperaturefor V(Ir, -rPtr)3 alloys [77 G 11.

Table 5. Experimental values for the coefficient 7 of the electronic term in the specific heat, and for the susceptibility xrnof various V-Pt compounds [82A 11. Compound

y mJ mol-’ K-’

Xm 10m6cm3mol- ’

V v,pt VPt vpt, vpt, Pt

9.9 7.19 3.38 2.00 3.24 6.6

286 220...250 148 118 ordered 237

Fig. 14.EstimatedaveragemagneticmomentofV atoms, j,., and of Pt atoms. j&,. together with the observed spontaneousmagneticmoment per formula unit, j, as a function of x in V(Ir, -XPtr)3[79 K I].

1.4.2.2.2 Cr alloys and compounds Thermomagnetic measurementshave been performed on concentrated Cr-M alloys (M: group VIII 4d or 5d element) over the whole composition range (Figs. 15 and 17).The susceptibility at room temperature strongly depends on the heat treatment as is indicated for Cr-Pd in Fig. 18. Cr-Pd and Cr-Pt have been studied in more detail. The fee Cr-Pd alloys in the composition range 25...35 at% Cr show mictomagnetic behavior (Fig. 21). Neutron diffraction measurementsreveal that the magnetic structure of ordered CrPt, is ferrimagnetic with two sublattices: the Cr atoms occupy one sublattice, the Pt atoms the other one, see Table 6. An antiferromagnetic structure in which Cr spins are antiferromagnetic within each layer was detected in the ordered CrPt compound (CuAuI-structure) at room temperature (Fig. 24). For the disordered systems superparamagnetic behavior is suggested[73 B 23.

Franse, Gersdorf

1.4.2.2.2 Cr-4d, 5d (group 8)

582

[Ref. p. 648

3 Gem: 9

2 I b

0

50

100

!

i'00

150

T-

K

250

Fig. 13.Variation of the spontaneousmagneticmoment per unit mass,U,with temperaturefor V(Ir, -rPtr)3 alloys [77 G 11.

Table 5. Experimental values for the coefficient 7 of the electronic term in the specific heat, and for the susceptibility xrnof various V-Pt compounds [82A 11. Compound

y mJ mol-’ K-’

Xm 10m6cm3mol- ’

V v,pt VPt vpt, vpt, Pt

9.9 7.19 3.38 2.00 3.24 6.6

286 220...250 148 118 ordered 237

Fig. 14.EstimatedaveragemagneticmomentofV atoms, j,., and of Pt atoms. j&,. together with the observed spontaneousmagneticmoment per formula unit, j, as a function of x in V(Ir, -XPtr)3[79 K I].

1.4.2.2.2 Cr alloys and compounds Thermomagnetic measurementshave been performed on concentrated Cr-M alloys (M: group VIII 4d or 5d element) over the whole composition range (Figs. 15 and 17).The susceptibility at room temperature strongly depends on the heat treatment as is indicated for Cr-Pd in Fig. 18. Cr-Pd and Cr-Pt have been studied in more detail. The fee Cr-Pd alloys in the composition range 25...35 at% Cr show mictomagnetic behavior (Fig. 21). Neutron diffraction measurementsreveal that the magnetic structure of ordered CrPt, is ferrimagnetic with two sublattices: the Cr atoms occupy one sublattice, the Pt atoms the other one, see Table 6. An antiferromagnetic structure in which Cr spins are antiferromagnetic within each layer was detected in the ordered CrPt compound (CuAuI-structure) at room temperature (Fig. 24). For the disordered systems superparamagnetic behavior is suggested[73 B 23.

Franse, Gersdorf

Ref. p. 6481

1.4.2.2.2 Cr-4d, 5d (group

8)

583

Survey

Cr, -.Ru, Cr, -xRh, Cr, -,Pd,

Cr, -,Os, Cr, -Jrx Cr, -xPt,

CrPt %.3%7 CrPt CrPt, CrPt, CrPt, Cr, -,Mn,Pt,

X

Property

Fig.

O<x
xg(x, T) X&G T) x,(x), T,(x) XIII(X) xmk T) 6 T, w, PcrW, T X&G T> x,(x), T,(x) x,(xX T,(x) Tc(x)> P,,(x) T,(x), E&x)> Pdx) x,(T)

15, 16 15, 16 17 18 19 20, 21 15, 16 17 17 22

magnon dispersion T,, P,,(x) magnon dispersion magnon dispersion

W&ndt3

.g

Rh-Cr I

Or 0 Rh

20

I

,

I

40

60

80 at% lODo Cr

Cr -

8 8

8

Pat O<x
6

7

24 25

Ref.

68Kl 68Kl 68Kl 58Gl 58Gl 71Cl 68K 1 68Kl 68Kl 73Bl 7762 73Bl 62Pl 73B2 73B2 63Pl 83Wl 79Wl 81Wl 83Wl

23

Pat Pat, 4 c o(H, 20K)

Table

26 27 28 26

I Cr-10.5at%Ru

2 -phase

33

Cr f

t

29

z.. 30 H w'

8’ 1 -phase _ 3,7 2 w6

m3 -6

27

“” I

E /

Ru OS

I1 E

1

RuCr,

Cr

26

I OsCr3

1

(

13.2

Fig. 15. Mass susceptibility xp as a function of composition in the systems Cr-Ru, Cr-Os, and Cr-Rh [68 K 11. Fig. 16. X-Tcurves of Cr-rich two-phase alloys with weak ferromagnetic properties (upper curves) and one-phase antiferromagnetic alloys (lower curves) [68 K 11.

Land&BOrnstein New Series 111/19a

Frame, Gersdorf

[Ref. p. 648

1.4.2.2.2 Cr-4d, 5d (group 8)

584

-2001 il 105 I

/ I

I

I

Pi Pd

pd k’&‘,,h

I

I

I

Cr -

.,/

:::::

., I .

:::::-.o::;:ff

Ir “//ckT”/ /,+,AI&( lijl:

Cr

PdCr

El

111

t-1 IrCg HCr

Fig. 17.Mass susceptibility xEand Curie tempcraturc T, of annealed Cr--Pd,CrrIr,and Cr-Pt alloys (for fcrromagnctic samples ,ys rcfcrs to a ticld of 4 10’ A/m & 5.03 kOe [68 K I], for Cr-Pt alloys, set also [35 F I]; for the specific heat of thcsc alloys, SW [73 K 33. 10 do-' cm3 iia

0 0

Pd

10

20

30 Cr -

10

50 ot% 60

Fig. IS. Molar susceptibility xrn of Pd Cr alloys at room temperature for anncalcd (open symbols) and qucnchcd (closed symbols) samples: solid circles: quenched from 900K: open squares: slowly cooled from 900K; open circles: anncalcd for two hours at 500K [SC I] and [58 G 21.

’

200

LOO

600 I-

800

1000 K 1200

Fig. 19. Molar susceptibility xrn vs. temperature for different Pd-Cr alloys [58 G I].

Frame, Gersdorf

1.4.2.2.2 Cr-Ad, 5d (group 8)

Ref. p. 6481

b I 20

IO

b

5

0

IO

15

kOe 15

HWP’ Fig. 20. Magnetic moment per unit of mass, 0, vs. applied field at 4.2K for quenched Pd,,,, Cr,,,,. Open circles: cooled in a magnetic field of 12.56kOe; solid circles: cooled to 4.2 K in zero field [71 C 11, see also [70 K 11.

IO

5 0

100

200

K

300

T-

Fig. 21. Magnetic moment per unit of mass, cr, vs. temperature for quenched Pd,,,,Cr,,,, at H appl= 12.64kOe; open circles: field-cooled state, solid circles: cooled in zero field [71 C 11. Table 6. Magnetic properties of Cr-Pd alloys; the thermomagnetic remanence otr was measured at 4.2 K after cooling in an applied field of 12.64 kOe; Tr is the freezing temperature for mictomagnetism; or is the magnetic moment at Tf [71 C 11. Quenched from 1200 “C

at% Pd 75 72.6 71 67 65

Annealed at 400 “C

PC,

T

Cf

%

T

Bf

ctr

pa

K

10-2Gcm3g-1

lo-‘Gcm3g-’

K

10-2Gcm3g-1

10-2Gcm3g-1

0.48 0.61 1.23 1.25 1.27

36 42 50 70 76

11.2 17 26.5 24.8 19.5

3.5 7.5 12.4 11.2 9.2

32 34 30 14 10

11.7 80 850 910 950

3.5 35 620 550 130

1.2

1200 K

Ps

1000

1.0

I 800

t 0.8

ct-

600

,a” 0.6

400

0.4

200

0.2 0 0

0 0 a

IO

20 30 Cr-

4Oot%50 b

IO

20

30

Cr -

Fig. 22. Variation with composition ofthe Curie temperature Tc (a) and the mean magnetic moment (h) at 20 K for annealed Pt-Cr samples [73 B 11. Landolt-Bdmstein New Series 111/19a

Frame, Gersdorf

4Oot%50

[Ref. p. 648

1.4.2.2.2 Cr--4d, 5d (group 8)

586

Table 7. Summary of heat treatments, atomic long-range order parameter S, lattice parameter a and magnetic data of Cr-Pt alloys [77 G 21. (I): slow cooling, (II): quenching. per determined from saturation magnetization at 77K; T=annealing temperature. at% Pt

Time

T

s

“C

Pcrr,cr

Per

T,

1

FB

p’n

K

0.33 1.70

320 355 473

82 78

900 1400 900

2 weeks (I) 1 hour (II) 2 weeks (I)

0 0.24(5) 0.80(3)

3.892 3.889 3.885

3.20 2.45 3.45

75

1450 420 800 1100

1 hour (II) 1 day (1) 1 day (1) 2 weeks (I)

0.33(5) 0.67(5) 0.80(1) 0.90(1)

3.877

2.25

3.875

3.60

1.25 1.55 1.85 2.25

1450 1070

1 hour (II) 2 weeks (I)

0.30(6) 0.92(3)

3.866

2.76

0’) 1.68

675

65

1070

2 weeks (I)

0.98(2)

3.857

2.32

1.12

860

60

1100

2 weeks (I)

0.97(3)

3.845

1.75

0.60

990

70

500

‘) The magnetization increases linearly for magnetic fields up to 80 kOe.

3 .105

CrPt

----_

CTTi?

9 I T-7

1

0

300

600

900

1200 “C 1500

I-

0

Fig. 23. Temperature dependenceof the masssusccptibility of an ordered CrPt sample. Open circles: on hentmg: solid circles: on cooling [73 B 1-j.

Pt

0

Cr

Fig. 24. Spin structure of CrPt (CuAuI-type of structure) [63P I].

Table 8. Magnetic moment distribution in Cr-Pt alloys near the 1: 1, 1: 2 and 1 : 3 composition, from neutron diffraction experiments at 300 K.

Cro.Pb7

CrPt, CrPt

FCr

PPI

CL0

CLB

2.56(10) 2.33(10) 2.24(15)

- 0.47 -0.27(5) small

Frame, Gersdorf

Ref. 62Pl 63 P 1 63 P 1

I.andd-Bornwin Ncn Scrie\ III ‘19~3

1.4.2.2.2 CrAd, 5d (group 8)

Ref. p. 6481

587 1

$1

IO THz

CrPI,

8 I 6

P

4 2 0 IO THz 8 0

5

IO

20

15 HOPPl -

I 6

25 kOe 30

a

Fig. 25. Magnetization curves as a function of the applied field at 20 K for a powder sample of CrPt, obtained by cold work before and after various heat treatments: Curve I: ordered, 16h, 950°C; 2: 1 h, 650°C; 3: 1 h, 580°C; 4: 1 h, 510°C; 5: 1 h, 450°C; 6: disordered (cold worked)

4

[73 B2].

5Fig. 26. The acoustic branches of the [OOl] magnon dispersion curves in (a) Cr,,,Mn,,,Pt, and (b) CrPt, at 4.2K. Points: experimental data; solid curves: calculated magnon dispersion; broken curves: low-q extrapolation for “localized modes”. For small q values the magnon dispersion constants v/q2 are 37 and 100THz A’, respectively [83 W 11, see also [81 W 11. v: magnon frequency.

0.8

0.6 0

0.2 0.4 0.6

0.8

1.0

0

Fig. 27. Curie temperature and magnetic moment per atom P,, of ordered alloys with compositions Cr, -,Mn,Pt, [79 W I].

Landott-BOrnstein New Series 111/19a

0.2 0.4 0.6 0.8 x-

Fig. 28. The ratio of magnon dispersion constants D(x)/D(O) as a function of composition x for the alloy system Cr, -,Mn,Pt,. Solid circles: derived from inelastic neutron scattering at 4.2K [Sl W 11, open circles: derived from bulk magnetization measurements [79 W 11, triangle: inelastic neutron scattering at 77 K [79P I].

Franse, Gersdorf

1.4.2.2.3 Mn-4d, 5d (group 8)

588

[Ref. p. 648

1.4.2.2.3 Mn alloys and compounds Survey x

Property

Fig

Mn, -XRh, MnRh Mn,Rh MnPd,

0.35<x <0.45

4-h e(T) &u-). e(T)

29, 30 31 32

MnPd, Mn, -XPd,

disordered 0.69 <x <0.80

MnPd Mn, -rIrr

0.1 <x
Mn 0.R31r0.17 Mn, -,Pt, MnPt,

0.6 < x < 0.9

MnPt, MnPt, MnPt, MnPt MnPt,. MnPt, Mn,Pt Mn,Pt Mn, -,Pt, Mn,Pt L-%Rh,

0.1O<x
magn. structure & = - 0.2 p1,;PM”= 4.0 PI, TN= 170K magn. correlations magn. structure &4(x). PhhW z,(T), TN> magn. structure TN(X),i%,n(x) magn. structure TN(X),A&) magn. phase diagram e, M. II,(T) M,(x), T,(x) P,,,(77 K) = 3.60(9)CLB P,,(77K) = 0.17(4)ve magn. dispersion magnetization distribution PaT, xp(T), L magn. structure magn. structure, phase diagram magn. structure I$-) ma&n. phase diagram

Table

7421 63Kl 66K2 62Cl 9

79Rl 69K 1

10

68P1

33 34, 35

Ref.

71Yl 74Y2

36 37 11 38 39 40

74Yl 74Yl 50Al 62Pl

41 42

79Pl 69Al

27 34, 35

10

79Wl 68 P 1

43

68K2

32 44 45

66K2 63Yl 66K2

Different types of antiferromagnetic order have been observed in the ordered Mn-M compounds. Susceptibility and resistivity versus temperature curves for the ordered compound MnRh show a large temperature hysteresis. indicating a gradual transition from the high-temperature CsCl-type structure to the low-temperature CuAuI-type structure (Fig. 31). Tetragonal MnRh is a strong antiferromagnet with a Ntel temperature well above 200 K. Neutron diffraction experiments on Mn,Rh reveal a triangular antiferromagnetic structure below T,=850(10)K with a value for the magnetic moment per Mn atom of 3.6(4)~, (Fig. 32). The face-centeredtetragonal form of Mn can be stabilized by addition of small amounts of other elements. Neutron crosssectionsof 5,10, and 16at% Pd in antiferromagnetic y-Mn have beenmeasuredat 4.2 K. In MnPd (CuAuI-type structure) an antiferromagnetic structure with j&,,”= 44(4)p,, and T,=810(lO)K has been established by neutron diffraction. The possible magnetic structures arc given in Fig. 35. Above 870K the tetragonal structure of MnPd transforms into a CsCI-type of structure. In the stoichiometric MnPd, compound a one-dimensional. long-period superlattice basedon the Cu,Au-type of order with periodic antiphase domains has been observed. The magnetic moments in antiferromagnctic MnPd, change their direction with composition, being parallel to the c axis below 25at% Mn and perpendicular above (Fig. 33). A neutron diffraction study in disordered Mn-Ir alloys with face-centeredcubic and face-centeredtetragonal lattices reveals an increasein TNwith increasing Ir content in the composition range l0...30at% Ir. By ordering in the Cu,Au-type of structure, TN is further increased. The magnetic transition is not associated with the

Frame, Gersdorf

Ref. p. 6481

1.4.2.2.3 Mn-4d,

5d (group 8)

589

crystallographic transition fee-fct, but occurs at higher temperatures. A magnetic phase diagram of Mn-Ir is shown in Fig. 38; the magnetic structure is given in Fig. 37. Fig. 36 representsthe lattice parameter together with the average magnetic moment and the Ntel temperature as a function of composition. In the Mn-Pt systemferromagnetic order has been reported for ordered MnPt, and antiferromagnetic order for ordered MnPt and Mn,Pt. The results of magnetization studies on Mn-Pt alloys near the MnPt, composition are shown in Fig. 40. Values for the magnetic moments in MnPt, at 77K are: &=3.60(9)uB, &, =0.17(4) us [62 C 11; a slightly different value for j&t of 0.26(3)uB is reported in [69 A 11. Ordered MnPt is antiferromagnetic with &,,, = 4.3(2)uLgand TN= 970(10)K; its possible magnetic structures are given by Fig. 43a. Between 600 K and 800 K a transition from structure II to structure III occurs for the stoichiometric compound. In antiferromagnetic Mn,Pt two different magnetic structures are found; the possible magnetic structures for this compound are shown in Fig. 43b. The values for the magnetic moment at 77 K and for the NCel temperature of the stoichiometric compound are: & = 3.0(3)pa and TN= 475(10)K; the transition between the two structures D and F occurs at 365(10)K. A magnetic phase diagram of the whole Mn-Pt system is given in Fig. 43~. I( l.10-lI Qcm cIEI I "4

150

200

250

300

350 T-

400

450

500 K !

1.6 1.8 2.0 2.2W3K“ 2.6 Fig. 29. Temperature dependenceof the magnetic moment per unit of massof Mn-Rh sampleswith different l/Tcomposition, at increasing and decreasingtemperature, Fig. 30. Dependencesof the electrical resistivity Q and indicated by arrows for 42 at% Rh. The curvesreflect the magneticmoment (r ofMn,,&h,,,, on the reciprocal of P(CsCl-type)-+y(CuAuI-type)martensitictransformation the temperature.The steepincreasein resistivity is due to [74Zl]. the scattering of the electrons by superparamagnetic clusters [74 Z 11.

.?04 s cm3 3

2

pQcm 100

Fig. 31. Mass susceptibility xe (and its reciprocal) and electrical resistivity Q of equiatomic MnRh during a complete temperature cycle between 4.2K and 700K, indicated by arrows. In the ordered high-temperature cubic phase,the susceptibility is of a Curie-Weisstype. The susceptibility and resistivity of the low-temperature tetragonal (CuAuI-type) phasesuggestthat MnRh in its tetragonal form is a strong antiferromagnet [63 K 11.

Landolt-BBmstein New Series 111/19a

I

b

0

0

Frame, Gersdorf

100

200

300

400

500

600 K 700

I

3

590

1.4.2.2.3 Mn-4d, 5d (group 8)

[Ref. p. 648

Mn,Pt

l

Mn oRh.PI

b

*OS II 0

153

t -1 r,=Llo(lo)"c

300

150

I

600 “C 750

Fig. 32. Temperature dependence of magnetic intensities in neutron diffraction experiments on Mn,Rh. and Mn,Pt; possible magnetic strucM~3~hJ%., tures arc given by A, B, and C; at 77 K good agreement is obtained in all casts with model A and values for the magnetic moment per Mn atom of 3.6(4), 3.5(4). and 3.0(3)u,,. respectively; above 380 K, Mn,Pt transforms into a collinear antifcrromagnctic structure (structure C) with jhln = 2.4(3)u, [66 K 23.

7-

MnPd3

Fig. 33. Crystallographic and magnetic structures of MnPd,; the crystallographic structure can be considered as an antiphase domain structure based on a nonstoichiometric CuAuI-type of order, indicating a continuous transition to the CuAuI-type phase existing at higher Mn concentration [69 K I].

Table 9. Crystal and magnetic structure data for Mn-Pd alloys, the angle cp,is defined in Fig. 33; S is the atomic longrange order parameter .The magnetic moments have been obtained at 77 K assuming pPd=O [69 K 11. at% Pd 80.5

fl [Al c [Al

-

CIA S

1 -

PM”IM cpcCd4 Th'WI

-

3.87

77.3 3.87 15.48 :.85(5) 4.2(3)

74.7 3.87 15.48 4 0.90(5) 4.1(3)

O(2)

8(2)

205(15)

220(10)

Frame, Gersdorf

69.6 3.93 15.05 3.83 1.00(5) 4.1(3) 90(2) 235(10)

1.4.2.2.3 Mn-Ltd, 5d (group 8)

Ref. p. 6481

591

MnPt

pa” II IO011

B I--f _ /- I- ---/ F/ / fY

PPd.Pt

0

100 200 300

NO T-

500 600

700 "C 801

Fig. 34. Temperature dependence of the magnetic mass susceptibility ofequiatomic MnPd and MnPt; the hysteresis, depicted by arrows, occurring in MnPd at high temperatures indicates a first order transition between a low-temperature CuAuI-type of structure and a hightemperature CsCl-type of structure [68 P 11.

&II

-0 -

~1001

P#“II Ill01 PPd,PtIILIT01

ppdPtII [IO01 l

Mn

0 Pd,Pt

Fig. 35. Allowed magnetic structures of equiatomic MnX (CuAuI-type of structure) from neutron diffraction experiments. The Mn and X atoms are represented by open and solid circles, respectively; X=Pd, Pt; for MnPd the structure is either B or C; for MnPt structure A is found below T, and structure B between T, and TN,see Table 10 [68P 11.

Table 10. Crystal and magnetic structural data at room temperature for Pd-Mn and Pt-Mn alloys; values of the transition temperature T, between different magnetic structures, and the Ntel point TN [68 P 11, see also [66 K 31. For type of magnetic

structure, seeFig. 35.The magnetic moments of Mn are room-temperature values, with vanishing pPd and ppt. Specimen Mn 13:;3;:l.lo Mn 1.04 MnPt Mn 1.04pt0.96 Mn 1.13Pt0.87 Mno.d’4.20 Mno.d%.12 MnPd Mnl.ddo.97

Landolt-BBmstein

at% Mn

Type 1

ti

44.0 50.0

3.97 3.99 4.00 3.99 3.97 4.05 4.06 4.07

3.73 3.67 3.67 3.67 3.71 3.64 3.61 3.58

51.6

4.07

3.59

45.3 48.0 50.3 52.3 56.4

40.1

B

B A A A B B B B

Franse, Gersdorf

FMn

T,

TN

PB

“C

“C

4.2(2) 4.2(2) 4.3(2) 4.2(2) 3.9(2) 4.2(2) 4.4(3) 4.4(4) 4.3(2)

<-268 E440 a510

630(20) 680(10) 700(10) 610(20) 420(20) 340(10) 560(20) 540(10) 490(10)

592

1.4.2.2.3 Mn4d,

5d (group

8)

[Ref. p. 648

y-Mn-lr (disordered 1

e

/ :

a

8 3.78I D 3.7L

63: 553 5

15 Ir -

10

20 at% 25

Fig. 36. Antifcrromagnctic transition tcmpcraturcs TN. avcra_rcmagnetic moments per Mn atom. j&,., and lattice parameters n of fee Mn -1r alloys [71 Y I].

Fig. 37. The antifcrromagnctic two-sublattice spin structure of the disordered y-phase Mn-Ir alloys [74 Y 21.

Table 11. Neutron diffraction results for disordered y-phase Mn-Ir alloys [74Y 21. A,“: average magnetic moment per Mn atom at 0 K, assuming pIr=O Th: N&e! temperature S: atomic long range order parameter 0,: Dehye temperature at% Ir

I%!”CPnl

TsILKI 0, WI

S

12.8

17.0

20.4

25.6

2.3(3) 618(4) 300(30) O.OO(7)

2.4( 1) 648(4) 300(30) O.OO(3)

2.6(2) 682(4) 300(30) 0.00(S)

0.8(1.5) 780 300(30) 0.12(3)

lCtl1

I 0.75

1

Mn-1:

K

1.00

' ++

ontiferro

% 0.50 d 0.25 I

ontifeiro’ ‘” fct lc/a >I ) 252

0w 0 F11

I

20 at% 30

10 Ir -

Fig. 38. Magnetic phase diagram of y-phase Mn, -Jrx alloys [74Y I]. Fig. 39. Tempcraturc depcndencc of magnetic mass susceptibility )I~ and electrical resistivity e of the Mn,,,,Ir,,,, alloy (disordcrcd, y-phase). compared with the tcmpcraturc dependence ofsquarcd relative sublatticc magnetization MZ obtained from neutron diffraction. Arrows indicate the anomalies corresponding to the antifcrromagnctic transition [74Y 11.

Frame, Cersdorf

a80

6y,

Landolt-Rorn?lcin . ..

^

1.4.2.2.3 MnvId, 5d (group 8)

Ref. p. 6481 600 “C

593

16 THz

400

I *

200

0

-200 8000 G

20 THz

6000

16

t 2s 4000 #

I 12 ?

2000

0 10

8

30 at%

20

40

Mn-

Fig. 40. Saturation magnetization M, and Curie temperature Tc of Pt-Mn alloys near the 3: 1 composition [50 A 11. Fig. 41. Magnon dispersion relation of MnPt, in the three principal symmetry directions at a temperature of 80 K: (a): [loo]; (b): [llO] and (c): [ill]. The data are compared with the dispersion relation of FePd, at 4.2 K (solid curves) as measured by [77 S 11. Horizontal error bars refer to constant-E-type scanqvertical error bars refer to constant-Q-type scans [79P 11.

Landolt-Bornstein New Series 111/19a

Franse, Gersdorf

1.4.2.2.3 Mnwld, 5d (group 8)

594

Pt 0.t.t

a

b

‘

Mn0.0.0

Pi0 f.i

d

L11 2.2.2

[Ref. p. 648

f.o.0

o.+.o

e

Fig. 42. Sections of the magnetization distribution in MnPt, obtained by Fourier inversion of the polarized neutron diffraction data. Contours arc exprcsscd in [pn/A3]. Wavevector of momentum transfer: Q =4n(sinO)/%. (a) l/4 of the section on a basal plane including all reflections out to (sinO)/i.=0.75&‘, (b) l/4 ofthc section parallel to a basal plane through the center of the cell, including all rcflcctions out to (sin 0),/L=0.75 A - I, (c)same as (a), including all rcflcctions out to (sin0)/1.=0.85 A-‘, (d) same as (b), including all rcflcctions out to (sinO)j%=O.fGA-‘, (c) same as (c), integrated over a volume &Y3,where 26 is the edge of the cubic volume ccntcrcd at the point over which the avcragc is taken. 6=a/lO, and (f) same as (d), intcgratcd over a volume 8fi3 with S=a,/lO. In sections (a) to (d), the zero contour lines (dotted lines) enclose regions of ncgativc magnetic density, which rcachcs the lcvcl -0.025 pR/A3 at the center of the Pt site [69A I].

Frame, Cersdorf

Landoh-R6rnwin Nex Scrin 111’19n

Ref. p. 6481

1.4.2.2.3 Mn-4d,

MnPt

a

595

8)

Mn3Pt

b

l Mn oPt

F

E

MnP& I 70 at% Mn

G

H

Fig. 43. (a) Possible magnetic structures ofMnPt (CuAuItype of structure); the Mn and Pt atoms are represented by solid and open circles, respectively; structures II. ..IV correspond to, respectively, structures A. .C in Fig. 35; (b) possible magnetic structures of Mn,Pt (Cu,Au-type of structure); (c) magnetic phase diagram of the Mn-Pt system; the letters denote, for the ordered alloys, the stability regions of the various magnetic structures given in (a) and (b) [68 K 21, see also [74 R 11.A’: structure A in (b) with Mn on Pt-sites and vice versa. The dashed line represents TN for disordered Mn-Pt.

\ A’

c

5d (group

Pt -

IO 40-f cm3 9

120 .1o-g m3 kg 80

6 IO

120

8

100 80

hI

I 1: H" 8

120 I 100 .=g

I!

)OOD 01 0

0.2

0.4

120 80

8

0.6

0.8

1.0

x-

Fig. 45. Magnetic phase diagram of the Mn,Pt,-Jh, system; the letters denote, for the ordered alloys, the stability regions of the various magnetic structures given in Fig. 43b [68 K 21. The dashed line represents TN for disordered Mn,Pt, -,Rh,.

100

6

80

IO

120

8

100 80

6 0

200

400

600

800

1000"C 1200

i-

Fig. 44. Mass susceptibility xp vs. temperature for Mn-Pt alloys [63 Y 11. Landolt-BOrnstein New Series 111/19a

Frame, Gersdorf

1.4.2.2.4 Fe-4d, 5d (group 8)

596

[Ref. p. 648

1.4.2.2.4 Fe alloys and compounds

The FeRu and FeeOs systems,having the hcp phase boundary in the Fe-rich region, allow the study of the magnetic properties of Fe in the hcp phase. For both systemsthe internal magnetic field has been studied in the antifcrromagnetic state by means of MGssbaucr experiments (Fig. 48). Fe--Rh alloys near the equiatomic composition have the CsCI-type of structure. At low temperatures the alloys are antiferromagnctic with magnetic moments of 3.3p,, antiparallel on neighboring iron atoms. Above 320 K the magnetic structure transforms into a ferromagnetic state with magnetic moments of 3.17l.1,~ and 0.97pu on the Fe and Rh sites. respectively. The magnetic moment distribution for the nonstoichiometric Fe-rich compounds is shonn in Fig. 5 1. The antiferromagnctic-ferromagnetic and ferromagnetic-paramagnetic transition temperatures have been studied as a function of pressure for equiatomic FeRh and Fe,,,,,Rh,,,,,. The phasedia_eramof the Fc-Pd systemrevealstwo ordcrcd structures: FePd (CuAuI-type) and FePd,; both order ferromagnetically. For FePd the iron and palladium magnetic moments amount to 2.85pa and 0.35l.~a, respectively [65 C 11.Different results for the atomic magnetic moments have been reported for ordered FePd,. At 300K: &=2.37(13)p,,. &=0.51(4)p,) [62P I]; in reference [65C 11: ~re=3.10~lj. &,=0.42p11. The ironrich FeePd alloys show excellent magnetic properties after an appropriate heat treatment and cold-drawing (Fig. 64). Fe-Pd alloys around 30at% Pd, whcrc the transition from the fee to the bee structure occurs, show typical Invar properties: anomalies in the thermal expansion below T, (Fig. 65) and large forced magnetostrictions. Fe&r alloys have been investi_patedin magnetization experiments in the composition range 30,..70at% Fe. In the Fe-Pt systemseveral types ofmagnetic order have been observed.The Curie temperature as a function of composition is given in Fig. 72. In Fig. 77 the basic types of magnetic structures for this systemare shown. In the composition range 24...36 at% Fe, a change in the type of antiferromagnetic order occurs from parallel iron moments in the (110) planes to parallel moments in the (100)or (010) planes. A value of 3.3 pa has been reported for the magnetic moment per iron atom in FePt, [63 B I]. Above 32at% Fe ferromagnetism becomes predominant. The saturation magnetization for ordered and disordered alloys is shown in Fig. 78. The magnetic ordering temperatures of the ordered and disordered FePt, phasedependson composition as indicated in Fig. 75 and Table 15.In the pseudobinary scrics of Fc(Pd,Pt 1-X)3a transition from a ferromagnetic state as in FePd, to an antiferromagnetic state as in FePt, occurs near x=0.5. In the intermediate region an additional magnetic transition from a high-temperature ferromagnetic to a low-temperature canted-ferrimagnetic structure is found (Figs. 93 and 94). The ordered equiatomic FePt alloy (CuAuI-type of structure) is hard to magnetize. A value for the mean atomic magnetic moment of 0.77 pn has been reported. By disordering FePt the bulk magnetization increasesconsiderably. From theseobservations ferrimagnetic order was concluded for the ordered compound. Neutron diffraction studies. however, point to Fe magnetic moments at 300 K of 2.8(1)p,,. parallel to the c axis. whereas Pt moments could not bc determined [73 K 51. In [74 M 23 the hypothetical values pFc= 2.75pr, and ijp,= -0.25 11,~ arc mcntioncd for the ordered FePt compound. The Fc-Pt alloys near the 25 at% Pt composition show invar characteristics aswell in the Cu,Au-type ordered state asin the disordered state.At low temperature these alloys undergo a martcnsitic transformation. The results of magnetic moment and Curie temperature studies on ordcrcd and disordcrcd alloys with 20,..30at% Pt arc given in Figs. 85, 86. Anomalies in the thermal expansion arc of a similar type as those in Fe-Ni invar alloys (Fig. 87). Survey X

Fe, -.A Fe, -,Rh,

0.1 <x
FeRh Fe, -,Rh, FcRh

0.495<x
Property

Fig.

Ref.

Llw. 4w TM. H,,,(x) L(X) L(X) ILW. Pr;c.Pdx)

46, 47 48 49 49 50, 51 52 54 53 55 56, 57 58

69Fl 710 1 70V 1, 76V 1 7OV1,76Vl 64S1 69Tl

C/T(T”)

4w H,,(T) AM T) magn. phase diagr. magn. phase diagr. Frame, Gersdorf

70Ml 76V2 74Dl I nndolt-hrnrrein Kcu Serier III ‘19.1

Ref. p. 6481

1.4.2.2.4 FeAd, 5d (group 8)

Survey, continued X

Fe, -,Pd,

O<x
FePd,

Fe, -xPd, FePd, Fe, - .Pd, Fe o.mPdo.3~ Fe, -,Pd,

0.50 <x < 0.97 0.50 <x < 0.75 0.18<x
Fe, -xOs, Fe, -.Jrx Fe, -xPt,

0.315<x
FePt, Fe,Pt FePt Fe, -,Pt, Fe,Pt

0.7<x
Property

Fig.

T,(x) L(x) pFe=2.73(13)pB iipd = o.5 1c4)PB ~cell= 4.26(8)FB PFFeM PPdc4 spin wave dispersion f&,,(x) K(x), f4(4, W%,x WV, W(T) XHF(X) magnetostriction K,(x) TAP) TN>K,,,(x) xm(xb a,(T) T,(x) Pat(x) TN(x), @(4 x,(T) a(H, T, x) TN(x) H,,,(T), TN(x), T,(x) magn. structure Pa,(x) MW, 4

59 60

Hh,,(x),

TN(x),

FFe = 2.03

Fe, -,Pt,

Fe,Pt Fe, -xPt,

Fe, -,Pt, WP4 -JU

0.25<x
Landolt-Btxnstein New Series 111/19a

12, 13

14 77 78 79

t2)

17

T>

&IFtXa

T>

PB

a(H) K,(x) a(T) magn. structure hysteresis hysteresis, anisotropy T,(x)> TN(x) as(x)a

65Cl 77Sl 77R2 81W2 83Tl 83Yl 83Ml 80Kl 68Wl 710 1 70M2 50Kl 59c2 59Cl 59Cl 63B 1 63B 1 69Pl 74M2 74M2 78V2 69Vl 74Nl 75Ml 73K5 73Sl 7411

PB

T,(P), a,b> Pa,(x), A~/VT), 4~) T,(P) MO us i%,(x) T,(x)> T,(x) T, (annealing time) XHF(X~

15 16

PB

Pat7xg pol. neutron diff. PP, = OW3

36F1 59c2

61, 62 63 64 65 66 67 68 69 48 70, 71 72 60 73 74 75 76

80 81

I%+ =2.8(l)

Ref.

62Pl

T,(x)

T,(P) a(T)

Table

xHFtX)

Frame, Gersdorf

18 82, 83 69 84 19 85 86, 87 88 89 90 91 92 93 94 95 96 97 98

75A4 78Nl 68Wl 81H3 81S2 83Sl 83Sl 82H2 83Yl 83Y2 83Y2 82Yl 69K2 69K2 73K4 7782 81T2 81T2

[Ref. p. 648

1.4.2.2.4 Fe-4d, 5d (group 8)

598

12.5 w2 !ic& 9

88 .10.’ .10.!

cm! x Ei

1.5

I El* u

I b 5.0

2 0 F”,

25 20

40

60

Ru-

at%

100

0

RU

1

2

3

a

Fig. 46. Ru concentration dcpcndcncc of magnetic molar ;usccptibility zrn in E-phase Fe Ru alloys [69 F I].

4

5

6

7 kOe 8

50

60

70 kOe80

H-

50 m2 JCJJG 9

I 30

b 20 10

/ / .’

I

0

30

10

20

30

40

H-

b

kOe

,/ Hpl

Fig. 47. Low (a)and high (b) magnetic field dependence of the magnetic moment per unit of mass, o, in E-phase FeRu alloys [69 F 11.

20 rF z 10

5 m

cm3 iii3 4 Ru.OsFig. 48. (a) The hyperfine field H,,, extrapolated to 0 K, derived from Miissbauer expcrimcnts on hcp Fe-Ru and hcp Fe -0s alloys as a function of Ru. OS concentration; (b) the N&l tempcraturc in hcp Fe-Ru and hcp Fe -0s alloys as a function of Ru, OS concentration [71 0 I].

Fig. 49. Solid solutions of Fe, Co and Ni in Rh and Ru. Isothermal concentration dependence ofthc susceptibility lrn [7OVl,76Vl].

Frame, Gersdorf

20 30 Fe, Co. NI -

40 at% 50

1.4.2.2.4 FeAd, 5d (group 8)

Ref. p. 6481

2.6

3.5

I-lB

PB

2.4

3.0

I 2.2

2.5

I

2.0

,z

2.0

1.8

I$ 9 1.5 IQ

1.6

1.0

1.4 0 Fe

IO

20

30 Rh -

40

50

at% 60

Fig. 50. Average atomic moment & of Fe-Rh alloys at 300K. The values in the antiferromagnetic phase were obtained by extrapolation of the data obtained for the high-temperature phase r64 S 21. Different symbols indicate data of different authors.

599

0.5

0 0

IO

20

Fe

30 Rh -

40

50 at% 60

Fig. 51. Magnetic moment distribution in Fe-Rh alloys at room temperature, derived from neutron dilfraction experiments- Fe1 and Fe11denote iron atoms on the Fe and Rh sublattice, respectively [64 S 21. 250 kOe 200

60 t 150

t

2 100

I

0

I

I

I

4

8

12

I

16

0

K2 20

12Fig. 52. Low-temperature specific heat data for Fe (Rh, Pd) alloys plotted as C/T vs. T'. Intercepts with C/T axis give values for electronic specific heat coefficient y [69 T 11.

50

100

150

200

250

300 K 350

TFig. 53. Temperature variation of the critical field H,, required to induce the AI-F transition in Fe-61.9at%Rh. The curve represents the relation H, = Ho{1-(T/T,,)*} with H, = 236.9 kOe and To= 335K [70 M 11. 150 Gem” 9 120

90 t b 60

Fig. 54. Magnetization curves for Fe-61.2 at% Rh at two different temperatures [70 M 11.

Landolt-Bbmstein New Series 111/19a

0

Franse, Gersdorf

30

60

90 HOPPl -

120

150 kOe 180

1.4.2.2.4 FewId, 5d (group 8)

600

[Ref. p. 648

.,& 6

1 0 50

30 100

150

200

250 T-

300

350

Fig. 55. Thermal expansion of Fe-.61.2at% Rh [70M I].

7lx K K

40

50

LOO K 450

F’Jo.uo Rho.ux lro.o65

70

80 kbor

Fig. 56. p - T magnetic phase diagram for Fe-Rh alloys of various composition [76V2], see also [81 V I]. (The dashed lines serve only to guide the eye).

700, K

I

60 P-

I

I

I

I

20

40

60

80

I

I

600

633

5OC

4OGI 4OG 0

20

40

60

80 kbor 100

P-

Fig.

57. p-T magnetic phase diagram for Rh, .,nslr,,,,, alloy. Triangles: [76 V 21, circles:

3OOY 0

100 kbar 120

PFig. 58. p--T phase diagram for FeRh. Open circles: [74 D I], solid circles: [68P 23; see also [78P 11.

403

I o annealed l quenched I 2oc 0 20 Fe

’

i FePd

40

60 Pd -

I’\ FePd3 I 80 at% 100 Pd

Fig. 59. Curie temperature of Fe-Pd alloys; open circles: annealed, solid circles: quenched samples; the dashed curve represents the phase diagram [36 F 11.

Frame, Gersdorf

1.4.2.2.4 Fe&d, 5d (group 8)

Ref. p. 6481

601

Table 12. Atomic magnetic moments in Pd-Fe alloys from neutron diffraction [65 C 11. The values listed for pa, refer to zero temperature.

3 7 25 50

0.234(7) 0.457(14) LOO(3) 1.60(5)

2.92(15) 2.76(11) 2.64(15) 2.49(11)

2.9(3) 3.0(2) 2.9(2) 3.0(l)

3.07(H) 3.02(11)

2.98(15) 2.85(8)

0.15(l) 0.26(2) 0.34(5) 0.35(S)

‘) From large-angle magnetic diffuse scattering data, assuming no Pd contribution and the metallic Fe form factor.

Table 13. Summary of atomic magnetic moments for Pd-Fe and Pd-Co alloys [65 C 11. Alloy

tjFe, Co

DPd

PB

Pdo.deo.03 Pdo.93Feo.07

Pd,Fe Pd,Fe ‘) PdFe Pd,Co PdCo

3.07 3.02 2.98 3.10 2.85 1.97 1.97

0.15 0.26 0.34 0.42 0.35 0.48 0.35

-

‘.

-i-..\ Fe-Pd

b 'L \ \ \

I) Ordered.

‘f. ( \

FePd

1.6

0.6 0.4 0.:2 \

0 0 Fe

IO

20

30

40

50 Pd, Pt -

60

70

80

90 at%100 Pd Pt

Fig. 60. Magnetic moment per atom, j,,, in Fe-Pd and Fe-Pt alloys (open circles and triangles [36F 11; solid circles [59 C 21; solid triangles [SS G 11). Land&BBmstein New Series 111/19a

Franse, Gersdorf

[Ref. p. 648

1.4.2.2.4 Fe-4d, 5d (group 8)

602 10 Ttiz

16 THZ

I

FePd3

I

FePd3 I

.

.O .

8

. r=l.ZK 0 156 A 231 . 296K

2

0

0.1

0.2

0.3

0.4

-

0.5

Fig. 62. Temperature dependence of spin-wave frequcncics in the [I 1I] direction for FcPd,. Temperature is 4.2, 156, 231, and 296 K [77 S I].

b-

Fig. 61. Temperature dependence of spin-wave frequencies in the [OOI] direction for FcPd,. Temperature is 4.2, 156. 231, and 296 K [77 S I].

I

6

340

kOe

T 0.8

0.1 120 kA -iii

I 320 303

I

c!2 x 280

80

" x 40

260 210 40

1.2

50

60 Pd -

0 10

70 ot% 80

20

30

40

50 at% 60

Pd -

Fig. 63. Concentration dependence of HhVp for Fc--Pd alloys without (I) and with (2) long-range order [77 R2].

Fig. 64. Magnetic properties of Fe-Pd alloys as a function ofcomposition near the 3: I ratio; open circles: tempered at 360...45O”C after water quenching from 900... 1000“C; solid circles: tempered at 360...450 “C after water quenching from 900.. .lOOO”C and subsequent cold drawing [81 W 21. H,: coercive’forcc, B,: residual flux density, (BH),,,: maximum energy product.

Frame, Gersdorf

Ref. p. 6481

1.4.2.2.4 Fe-4d, 5d (group 8)

11 10: G

E 40: &lJ 9

7

603

Fe-id

I

H= 4OkOe110011

cI4 8 I L3

7

I x

-

<

6

A . 0 .

31.5at% Pd 31.9 34.2 37.6

2

5 1 4 0 6.I[1-4 C m3 7 :-

3 2 1

Fe-Pt I

I

I

I

I 400

I 500

I 600

0 7OO"CEOO

4-

Fig. 65. Thermal expansion and magnetization vs. temperature curves for a 31 at% Pd-Fe alloy, subject to cold-drawing and quenching, respectively; solid circles: 75% cold-drawing after annealing at 1200“C for 170 h; open circles: water-quenched after annealing at 1200 “C for 170h [83Tl].

t L x' 3-

100

200

300

500

400 r-

600

l-

180 w6

Ob 200

I I

fct

Fe -PC'1

fee

I 300

K

71

I-

Fig. 66. Temperature variation of the high-field mass susceptibility xHFfor (a) Fe-Pd and (b) Fe-Pt invar alloys

150

[83Y 11. 120

90 1 Iti 60 ' 30

0

-3q

I

I

I

33

36

39

I

I

42 at% 45

Fig. 67. Composition dependence of the mean magnetostriction constant A = 2/5& + 3151,r 1 at 4.2 K and 301 K, and the forced magnetostriction aw/aH at 4.2 K for Fe-Pd alloys. The dashed line indicates the phase boundary of fee and fct structures at 4.2 K [83 M 11.

Pd -

Landolt-Bbmsfein New Series II1/19a

Franse, Gersdorf

[Ref. p. 648

1.4.2.2.4 Fe--4d, 5d (group 8)

604 1 1, .lO" erg cm!

/

/

0

I

K kbar

-2 1

5 -3

. Pd- Ni o Pd - Fe A Pd -Co

;;;r-l$ -5

!%a

-2 0

10 20 at% Fe.Co,Ni -

. *A .

.

-6

I E5.0

0

I-

30

9 Gcmj mol I I d

8

7

0

o 0

I

= 10kOe

& A n

2.5

I

1

300 350 600 150 500 550 600 653K 70:

0

H

. Fe:.,Pt, o Fe.!.,Pd,

Fig. 69. Pressure derivative of the Curie tempcraturc as a function of T, for Fe,-,Pt, alloys (solid circles) and Fe, -xPd, alloys (open circles) [68 W 11.

0 Fe-Ir . .

I

l

Fig. 68. Plots of mn_enctocrystallinc anisotropy constant Ki at 4.2 K as a function of x for Pd-(Fe, Co. Ni) alloy ;ystems [80 K I].

10.0 40.‘ cm3 mol

x=0.250

6 0 60>

50

I

150

100

200 K 253 253

TT-

Fig. 71. Tcmpcraturc dcpcndencc of the ma_enetic moment U, of Fe-Ir alloys in an applied held of IO kOe [70 M 23. “’

0

,I
25

50 Ir -

75at% 100 Ir

Fig. 70. Composition dcpcndenccs of the molar susccptibility z, and the electronic spccilic hcnt cocflicicnt 7 for Fe Ir alloys. T=4.2 K: solid circles [70M 21. open circles [66 G I]: T = 300 K : solid triangles [70 M 21. open triangles [66 G I].

600

200 >cs onneoled i O quenched I 01 0 20

LO

60

I 80 ot"/0 19c

Pt Pt Fe Fig. 72. Curie temperature of Fe-Pt alloys; open circles: qucnchcd. crosses: annealed samples [SOK I]; solid circles: [.59C 21.

Frame, Gersdorf

1.4.2.2.4 FewId, 5d (group 8)

Ref. p. 6481 300 K

Pt-

I I FEY(annealed)

605

6nI

r I/ Tc I

0

100

200 T-

300

K 400

200

400 T-

600

K 800

15 40" s Cl%

I

t IO -5

130

5 z 110 90 70 18

0

20

22

24

26

28

30 at% 32

Fig. 74. Mass susceptibility xp of annealed Fe,,,,,Pt,,,,, alloy [59 C 11.

Fig. 73. Variation of 0 (a) and TN(b) with composition for annealed Pt-Fe alloys [59 C 11.

Pt - Fe (ordered)

I

I

b

b

I

1

@f

T=141K

29 at%Fe

I / P

I

I/d

1103

A

I

b

0

5

IO HWI -

I5 kOe 20

0

5

IO kOe 15

Hoppi -

Fig. 75. Magnetization curves at different temperatures for ordered Pt-Fe alloys, containing 26.7 and 29 (nominal) and 32.7 and 34.3 (analyzed) at% Fe. The numbers denote the temperatures in [K]. Curves drawn with open circles are for a region where magnetization increases with decreasing temperature; when solid circles are used there is a decrease of magnetization with decrease of temperature [63 B 11. Landolf-Biirnstein New Series 111/19a

Franse, Gersdorf

[Ref. p. 648

1.4.2.2.4 Fe-4d, 5d (group 8)

606

Table 14. “Fe hyperfine field Hhyp at 4.3 K and magnetic ordering temperatures of various ordered Pt-Fe alloys [69 P 11.A: antiferromagnetic; F: ferromagnetic.

28

30

32

at% Fe

Hhyp (4.3 K) kOe

T K

Order

24.0 24.5 26.7 30.0 34.5

305 305 297 288 310

212 170(l) 171(l) 145(l) 255(2)

A A A A F

311ot% 36

Fe -

Fig. 76. Variaton bvith composition of the N&cl tempcratures of ordered Pd-Fe alloys, determined from the tcmperaturc depcndencc of the neutron diffraction intensities ofthc 400. g;O reflections. rcspcctivcly [63 B I]. In a limited range of composition two magnetic structures with diErent N&cl tempcraturcs coexist at low tempcrnturcs.

Table 15. 57Fe hyperfine field of ordered and disordered Pt-Fe alloys and values for TF;and T, [69V 11. at% Fe

23.1(l) 28.0( 1) 33.1(l) 36.0( 1)

Antiferromagnetic

structure

Ferromagnetic

structure

Hhjp (77 K) kOe

TN K

H,,yp (77 K) kOe

T, K

280(5) 275(5) 260(5) -

170(2) 155(2) 131(2) -

330(5) 330(5) 330(5) 285(5) ‘) 330(5) 2,

368(2) 400(2) 458(2) 270(2) ‘) 513(2) 2,

‘) Ordered. 2, Disordered.

FePt3

W%l

I

’ 0

0 01 / %

&’ A0 --0 /

0 0 0

a

Franse, Gersdorf

?

@

i

1

Fig. 77. The basic types ofmngnctic structures in ordered Fe -Pt compounds: solid circles indicate Fe, open circles Pt atoms [74 M 21.

-

FePt 1

l

Fe 0 Pt

Fe?Pt

Ref. p. 6481

1.4.2.2.4 FeAd,

2.5

I

l-b

Pt-Fe

5d (group 8)

607

550 550, K

KP, I I Feb,Pt, I I I

/'

500 2.0 I 450

hy KJo

1.5 t 1:

350 300 250 0

0.5

IO

20

30

40

50

60

70 kbor:

P-

ov 0

1

Y 20

60

40

Pt

80 ot%

Fe -

100 Fe

Fig. 78. Concentration dependenceof the mean atomic magneticmomentof Pt-Fe alloys in the disordered(open circles) and ordered (solid circles, triangles) states [74 M 21. Solid curve: theoretical.

Fig. 80. Tc of disorderedFe, -xPt, alloys as a function of pressure: I: x=0.62, 2: 0.64, 3: 0.69, 4: 0.728, 5: 0.75 [74N 11.

Table 16. Curie temperature and its pressure derivative for disordered Pt-Fe alloys [74N 11. at% Fe 25.0 27.2 31.0 36.0 38.0

60

-I/T,.

10m3kbar-’

375(2) 405(2) 457(2) 510(2)

1.6(l) 1.7(l) 2.2(1) 2.8(l) 3.0(l)

4.3(3) 4.1(3)

529(2)

30

60

15

30

30

60 90 N-

120kOe150 0

b

30

60

H-

90

120kOe150

c

0

Fig. 79.Magnetization curvesofsingle crystalsofordered Pt-Fe alloys at 77K: (a) 25.2at% Fe; solid circles: H~~[llO];opencircles:H~~[001];solidtrianglesH~~[111]; open triangles: HI/[lOO]; (b) 28.0at% Fe; solid circles: HII[lOO]; open circles: HI/[lIO]; triangles: HII[lll];(c) 30.6at% Fe; 1: HII[lOO]; 2: Hjl[112]; 3: HII[llO]; 4: Hll[lll] [78V2]. Landolt-Bbrnstein New Series 111/19a

i3TJap

4.9(3)

5.5(2) 5.6(2)

2I

2 90

0

- dTcldp

Kkbar-’

I 120

x45 I

a

Tc

K

Franse, Gersdorf

30

60

30.6ot% Fe I I 90 120kOe1

H-

1.4.2.2.4 Fe-4d, 5d (group 8)

608

Table 17. Magnetic moment and mass susceptibility compounds at 4.2 K [73 S 11.

a, [Gcm3g-‘1

Pa,bnl xE [10w6cm3g-‘1

[Ref. p. 648 of Fe-Pt

Fe,Pt

Fe 0.72pt0.28

ordered

ordered

disordered

133.7 2.17 16.4

126.8 2.15 8.6

125.6 2.13 12.6

Table 18. Curie temperature, its pressure derivative, and the relative pressure dependence of the magnetic moment near 0 K for disordered Fe-Pt alloys [75 A 43.

at% Pt

,

F_ePt(dis

”

26.0 27.0 27.8 27.9 28.4 31.3 31.4 32.0 33.5

I

T,

- d Wdp

K

K kbar-’

390 414 445 448 462 544 543 554 583

4.0(l) 3.8(l) 3.4(l) 3.2(2)

- I/a,. aa,lap 10e2 kbar-’ 0.83(7) 0.43(3) 0.33(3) 0.19(3) 0.16(3)

2.2(l)

-

-

2.1(2) 1.9(2)

0.16(3)

Fig. 81. Temperature dcpcndencc of the magnetic moment per unit of mass measured in an applied magnetic lisld of 6kOc for ordered FePt, disordcrcd FcPt, and ordered Fc,Pt [75 M I].

‘8 0 I40-2 5; 1.1 77 3 1.0 b

21

Cl ordered . disordered

26

P

28

30

32 at% 3L

PI 0

100

200

300

LOO T-

500

600

700 K

3

Fig. 87. Fractional volume change AV/Vagainst tempcrature for the Fe,,,2 Pto,2Ralloy. The open and solid circles indicate the results for the ordered and disordcrcd states, respectively [78 N I].

Fig. 83. (a) Concentration dcpcndcnce of the magnetic moment per atom at 4.2K, and (b) concentration dependence ofthe spontaneous volume magnetostriction at OK, o,(O), for Fe-Pt alloys. The open and solid circles indicate the results for the ordered and disordered states, respectively. The full lines show the results estimated from the number of Fe atom pairs [78 N 1).

Franse, Gersdorf

FeO.72Pt 0.28 (disprdered) 1

1.00 I

609

1.4.2.2.4 Fe&d, 5d (group 8)

Ref. p. 6481

Table 19. Magnetovolume coupling constant, XC, defined as ccs=xCM2, for ordered Fe-Pt alloys [Sl S2].

T=4.2K

at% Pt

24

25

26

27

XC [10-gG-2]

10.8

8.4

7.7

6.8

0.75

XT .z

L$ 0.50

J

s

7ocI-

0.25

I

K

5

20 kbor 25

l601:

Fig. 84. Pressure dependence of the magnetization at 4.2 K and room temperature for a disordered Fec,,,Pt,,,,, invar alloy [Sl H 31.

501I-

0

15

IO

Fe- Pt

P-

+

l-

l-

a

20

22

24

26

28

310 at% 32

201 I-

Pt 2.4

101

Ps 2.3

24 t 12

. disordered, 1.9 22

24

I

I

I

26

20

30

Pi -

32 at%

ot% 32

Fig. 85. (a) Phase boundary of Fe-Pt allloys with 20...30at% Pt at 4.2 K, estimated from magnetization measurements; the hatched region indicates a two-phase region; (b) concentration dependence of the magnetic moment for Fe-Pt alloys; open circles: ordered solid circles: disordered alloys [83 S 1-j.

Fig. 87. Fractional volume change AVIV vs. temperature for FeP t alloys around the y - CIphase boundary; arrows indicate the Curie temperature Tc and the martensitic transition temperature TM, as well as increasing and decreasing C83Y3-J. temperature [83 S 11, see also [83 0 1] and

Landolt-Bornstein New Series 111/19a

30

Fig. 86. Curie temperature Tc and martensitic transition temperature TM for Fe-Pt alloys as a function of Pt content near the FePt, composition; open symbols: ordered alloys; solid symbols: disordered alloys. Different symbols refer to the results of different authors.

2.0

;

28

Pt -

2.1

b

26

2.2

I $ z2

0

Franse, Gersdorf

I I 100 200

,lh 300

,

I

I

400 T-

500

600

I 700 K 800

1.4.2.2.4 Fe&d, 5d (group 8)

610

1.0

[Ref. p. 648

3.735 A

rr, 1 0.5 I 3.730 0 0:

3.725

b auenched

10

0” s J 200 I 0.25”E 0 ( 0, 1u 1OC min 10’ 103 102 Anneoling time -

Fig. 88.Ordcr paramctcr S, Curie tcmpcrature T,, lattice constant II, half-value width of supcrlatticc line W(IO0) and half-value width of fundamental line W(l 1I), plotted against annealing time at 873 K for Fc,Pt alloy [82 H 21.

iIjI!G2

253

303

353

400 7-

450

500

550 K 600 PI -

Fig. 89. Temperature variation of the high-ftcld mass susceptibility xrrr for Fe opt invar alloys [83 Y I].

Fig. 90. High-field mass susceptibility xur of Fe-Pt disordered alloys at 4.2 K (open circles) and 77 K (solid circles) vs. concentration [83 Y 21.

Frame, Gersdorf

Ref. p. 6481

1.4.2.2.4 Fe-4d, 5d (group 8)

125.5 @ 9 125.0

erg

611

Fe- Pt

(disordered)

cm3

I

2.5

124.5 124.0

-2.5

123.5 I 123.0 1 111.5 b Gcm3

-7.51 25.0

1191.0

27.5

30.0 Pt -

32.5at% 35.0

Fig. 92. Value of the magnetocrystalline anisotropy constant K, measured at 4.2 K by extrapolating to zero field for disordered Fe-Pt alloys as a function of Pt concentration [82Y 11, see also [8OY 11.

110.5 110.0

109.5 109.0 0

5

IO B eff

15 T : -

Fig. 91. Magnetization curves of two disordered Fe-Pt alloys at 4.2 K and 77 K [83 Y 21.

I

-1

FePd1.s Pt1.4

b

15 FePd1.5Pt1.s I

IO II 25kOeJ / /I

5 ------.. I

0

----.A ---.

,---‘?2.5

\ 'A \ ‘, ‘, \. ‘\ ’ kOe ‘+;\

I

I

I

I

I

50

100

150

200

\ I

7I

250 K 300

Fig. 93. Magnetic moment per unit of mass, CT,vs. temperature curves at different fields for FePd,,,Pt,,, and the maximum at about 140K in the FeP4.5%5; curve corresponds with a change from FeP4.8b simple ferromagnetism at high temperatures to a lowtemperature ferrimagnetic state with canted Fe moments, see also Fig. 94 [69 K 2-J. Land&-Bdmstein New Series lWl9a

Fig. 94. Low-temperature canted-ferrimagnetic structure of FePd,,,Pt,,, [69 K 2-j.

Franse, Gersdorf

1.4.2.2.4 Fe-4d, 5d (group 8)

612

[Ref. p. 648

:c

I

C

b

0 kOe

H-

Fig. 95. Hystcrcsis curve at 77 K observed for the ordered W’do.,J’t ,,J,)j alloy along the [ IOO], [ 1IO], and [ 11I] axes [73 K 43. H,: coercive field. H,: anisotropy field. -1.5 0

50

100 I-

150

K

200

Fig. 96. Tempcraturc dcpcndencc of the hysteresis loop width S (curves 1,2), unidirectional anisotropy constant K, (curves 3,4), field of displacement H, (curves 5,6) for ordered Fe(Pd, -rPtr)3 alloys: solid circles: x=0.585, open circles: x = 0.625 [77 S 21.

1 1 3 x’

0.25 FePd3

0.50 x-

0.75

1.00 FePl3

Fig. 97. Phase diagram of the magnetic state of the atomically ordered Fe(Pd, -xPt,), alloys: four diffcrcnt magnetic states arc suggested in the concentration region 0.4 < x < 0.7: paramagnctic at T > T,; supcrparamagnctic in the intenal T,> T> T& ferromagnetically ordered at TG> T> T,: cocsistcncc ofintcracting fcrromagnctic and antifcrromagncticsubsystcms at T< TN[8l TZ];for T,(p) values. see [76 T I].

6 0.50 \ d 025 0 -0 Fe

2 1

0.25

0.50 x-

0 0.7501%1.00

Fig. 98. Concentration depcndcncc of the spontaneous magnetization gSand ofthc high-field susceptibility zHFin ordered Fe(Pd, -.Pt,), alloys [8l T2].

Frame, Gersdorf

1.4.2.2.5 Co-4d, 5d (group 8)

Ref. p. 6481

613

1.4.2.2.5 Co alloys and compounds

Alloys of the systemsCo-Ru, Co-Rh, CO-OS, and Co-Ir have a critical concentration for the beginning of ferromagnetism in the intermediate composition range. Phase diagrams and values of T, for these systemsare shown in Fig. 99. Magnetic moment studies on Co-Ru alloys in the fee and hcp phaseshave been performed in the composition range up to 25 at% Ru (Fig. 100). Spin-glass behavior has been investigated in Co-Rh alloys near the critical composition for ferromagnetism (Fig. 102).Co-Pd alloys show ferromagnetic order over nearly the whole range of concentration (Fig. 103),as is the casefor CoPt alloys (Fig. 107).Annealed samples of CoPd and CoPd, exhibit short-range atomic order. Magnetic moments from neutron diffraction experiments are: CoPd: &, = 1.97(7)uBLg, j& =0.35(7) un; CoPd,: PC,= 1.92(11)un, &=0.48(3) un. Two ordered phases occur in the Co-Pt system: CoPt and CoPt,. Both are ferromagnetic. In ordered CoPt (CuAuI-type of structure) the ferromagnetically coupled moments PC,= 1.6un and ppl= 0.25 uBare aligned parallel to the hexagonal axis. Co-Pt alloys near the equiatomic composition have large values for the energy product (BH),,,. By substitution of Co by Fe or Ni the energy product (BE&,,, is strongly reduced (Fig. 112).

Survey Alloy/ compound

X

Property

Fig.

co,-xxx Co, -XRu, Co, -XRh,

o<x
Co, -XPd,

O<x
T,(x) I?&) G(T) magn. phase diagram Pat(x),T,(x)

99, 113 100 101 102 103

CoPd, CoPd, Co,-,Pd,

O<x
co, -XPt,

O<x
CoPt,

-

-

PCo,

PPd

specific heat J%?(x), hl, Mx) tZt(x), T,(x)

FP, = 0.2f@)

Landolt-BOrnstein New Series lWl9a

Ref.

20

6OCl 74Fl 75Jl 75Jl 35Gl 3OCl 58Gl 65Cl

104 105, 106 107

69W2 83Fl 32Sl 40Gl 3OCl 66Ml

108 109

71 M 1 7111

pol. neutron diff. L=~W~)IJL,

CoPt, CoPt co, -XPt, (Co, Fe, Ni)Pt

Table

GWdH)

0.46<x < 0.54

PB CT>

Ho 43 won,, vs. tempering time 0s T,(x) M(x) K(x) WfLx@)

Frame, Gersdorf

21 110 111 112

75C2 75M2 75M2 75M2

1.4.2.2.5 Co4d,

614

5d (group 8)

[Ref. p. 648

Co-Rh -=.I-=y--__-----__ CL .

‘\Ik \

\ ‘CC \

0 0

20

co

E

40 0 co

Ru-

=---

20 Rh -

-.

40 0 co

-Co-Ir --‘,-- -3. ci

40

20 Pd -

Co-Pt

\ a \ ‘1.

ka \ \

\ E

\ -0

20 OS-

0

at%

20

20

at% 40 0

ot%

40

IrPtFig. 99. Phnsc diagram and Curie tcmpcraturc as a function ofcomposition for Co-rich Co-(Ru. Rh, Pd, OS. Ir, Pt) alloys: the r phase is faceccntercd cubic. the E phase hexagonal; the hrokcn lines show the variation ofthc Curie point T, for the rcspcctivc phases [60 C I]. 30I I

Pa CO,,,F%.z Ru a, w3

I

cm3 mol

2.0 R,

1

1.5

0

20 ot%

10

30

100

Ru Fig. 100. Magnetic moment per atom fi,, for the alloys CO,,,F~,,~-RLI and Co-Ru as a function of Ru concentration [74 F I].

200

K

300

Fig. 101. Magnetic moment per mol D,,,divided by H vs. tcmpcrature curves for Co,,,,Rh,,,,. The aged sample has an anomalously large magnetic moment. yet T,. the temocraturc of the maximum, remains unchanged [75j

il.

Frame, Gersdorf

I.andolt-Bornitein Sew Serier III ‘193

1.4.2.2.5 Co-4d, 5d (group 8)

Ref. p. 6481

25 K 25

615

1600

K

20

II

2.4

1200

15

I-le 1.6 I ,: 0.8

,800 I

k IO

ml

5 0 Ri

5

IO

15

co 20-

25

30

at%

LO

Fig. 102. Magnetic phase diagram of RI-Co alloys near the critical Co concentration for ferromagnetism; P, G, and F designate the paramagnetic, the magnetic glass and the ferromagnetic regions, respectively [75 J 11.

L

0 80 at% II30

0 0 CO

20

$0

60

?d

Pd -

Fig. 103. Magnetic moment per atom jat and Curie temperature for Co-Pd alloys as a function of composition. Solid circles: [35 G 11; triangles: [30 C 11; crosses and open circles: [S8 G 11.

Table 20. Atomic magnetic moments in Pd,Co and PdCo [65 C 11. Alloy

Pat

PC.‘)

fkc, -

1.9(2) 2.0(l)

1.45(12) 1.63(10)

DPd

PC,

PPd

1.92(11)

0.48(3) 0.35(7)

PB

Pd,Co PdCo

0.84(2)

1.16(3)

1.97(7)

‘) From the large-angle scattering data assuming no Pd contribution and the metallic Co form factor.

0 405 T erg 5 i I -2 E

.o co

25

50

75 at%100

Pd-

Pd

Fig. 104. The variation of the electronic specific heat

coefficient y with composition for Co-Pd alloys [69W2].

4I

0 Pd

20

40

60

co -

I co:

80 at% 1

Fig. 105. Plots of the magnetic anisotropy energy AS, [ 11l] and AS, [ 1lo] at 4.2 K as a function ofcomposition for Pd-Co alloys [83 F 11.

Land&-BOrnstein New Series 111/19a

Franse, Gersdorf

1.4.2.2.5 Co4d, 5d (group 8)

[Ref. p. 648

1600 K !

2

c 0 CT

-2

co

-4 0 Pd

20

40

60

80 at% 100 co

co -

Fig. 106.Plots ofthe magnetostriction constants h, and h, as a function of composition for Pd-Co alloys [83 F I].

61

I

I

I

I

Pt

Pt -

Fig. 107. Magnetic moment per atom & and Curie temperature for Co-Pt alloys as a function of composition. x : [32S I]; solid circles: [40G I]; open circles and + : [30 C I]. For neutron diffraction results for CePt alloys, see also [64 L I].

I w/

2000

d

n

-21 0

I 53

I 100

I 150 T-

200

I 250 K

I

300

Fig. 105. Temperature variation of the forced volume magnetostriction dw/dH of CrPt,, MnPt,, and CoPt, [7l M I].

8000 t 43 4000 n II MGOe

8 x P Table 21. Saturation magnetic moment per unit mass extrapolated to OK for three Co-Pt alloys, ordered 2 4 and disordered [75 C 21. Allo)

us [Gcm3g-‘1 Tempering time -

co0.S4PLJ.46 CoPt co 0.46pt0.54

disordered

ordered

53.5 46.6 45.0

37.8 32.1 29.3

Fig. 109. Coercive field H,, residual flux density B, and maximum energy product (BH),,, of polycrystalline specimens of CoPt as functions of tempering time at the following temperatures: curve I: 6OO”C, 2: 7OO”C, 3: 3.5 min 700 “C+600 “C; 4: 5 min 700 “C +6OO”C [7112].

Frame, Gersdorf

1.4.2.2.5 Co4d, 5d (group 8)

Ref. p. 6481 Fig. 110. Variation of Curie temperature for ordered and disordered alloys of the (Fe, Co, Ni>Pt system as a function of composition; solid circles: disordered; open circles: ordered [75 M 21; for the specific heat of Co-P& see [SOR 11.

600, “C

I

617

I

I

I

I

Fe,,Pt

0 ordered . n 0 CoPt

Fig. 111. Variation with composition of the magnetization M measured in fields up to 20 kOe for ordered and disordered alloys of the (Fe, Co, Ni>Pt system as a function of composition; solid circles: disordered; open circles: ordered [75M2].

I

0.25 x-

0.50

0.25

0.50

0.25

0.50

FePt

x-

NiPt

x-

copt

I

““Y

G

Ni,-2xCoZxPt ,

600

I = 100

0 CoPt

Fig. 112. Variation of coercive field H, and maximum energy product (BH),,, for the (Fe, Co, Ni>Pt system as a function of composition [75 M 21, see also [7112].

disordered

F kOc

0.25 x-

0.50 FePt

0.25 x-

0.50 NiPt

I

I

Co,-2xFe2xPt

Fel-2,Ni2xPt

0.25

0.50

x-

CoPt

0

MGOe

i

2

IL 0 CoPt Landolt-BBmstein New Series 111/19a

x-

FePt

Frame, Gersdorf

XW

NiPt

0.25

0 0.50

x-

copt

1.4.2.2.6 Ni4d, 5d (group 8)

618

1.4.2.2.6

Ni alloys

[Ref. p. 648

and compounds

Survey X

Ni, -XRu, Ni, -IRh,

o<x
Property

Fig. 114 115 113,114 116 117 118

Pnt(x) Wx) L

T,(x)

DNi9

PRh(X)

4H,

4

x,(x)

T,(P)>

119, 120 121 122 123 114

T,(x)

4(x) K,(x)

Ni ,-&A

Ni I -Ah Ni, -JrX Ni, -,Pt,

x=0.35 o<x
4H,

T)

L(x)

T,(x)

hi3

BldX)

H,,,(x) Hi,,,(x) UP,

T)

K,(T) K,(x) h,>

b(x)

kWdH) TM.

U-J D,,(x)

Xm,

Y(X)

T,,

Pa,(x)

Pa,(x) %,(X) Xm

Y(X)

g(H) M,

Table

7-j

L

cl(x)

!jNi,

PP,? dx)

m H,,,(x) Hi,&) 6”) Tc@)

124 125 126 127 128 129 130 131 132 113,114 133 113,114 114 134 135 136 137 138, 139 140, 141 142 126, 143 144 145 119

O), L,(P)>T,(P) u(V, xoC’)> T,(V 4x)> xo(xX T,(x) Wf) (WI) (T) AM4

146 147 148 149 150

22 22

Ref. 6OCl 80Al 6OCl 78Cl 75M3 68B1 75M3 79K3 81K3 8201 79Al 32S1, 37Ml 72Fl 78Cl 72Fl 73Gl 78P2 75F2 78Tl 78Tl 73T2 6OCl 70Bl 6OCl 6OCl 73G2 74B2 74s3 74B1 69F2 8OPl 79Al 72Fl 73Gl 78Vl 79K3 74A2 74A2 74A2 76Kl 77Fl 81Kl

Results of magnetic moment and Curie temperature studies of Ni-Ru, -Rh, -Pd, and Ni-Os, -Ir, -Pt alloys have beencollected in Figs. 113and 114.The onset of ferromagnetism in binary nickel alloys has extensively been investigated. in particular for Ni-Pt and Ni-Pd alloys. Important parametersfor the onset of ferromagnetism are the local environment of nickel atoms and the polarization clouds around local magnetic moments. The magnetic anisotropy is strongly reduced in single crystals of nickel with a few at% Ru, Rh, Pt (Fig. 115). In the Ni-Rh system the critical concentration for ferromagnetism is around 35at% Rh. The magnetic moment per atom has been studied in diffuse neutron scattering experiments (Fig. 116).

Franse, Gersdorf

Ref. p. 6481

1.4.2.2.6 Ni4d, 5d (group 8)

619

The onset of ferromagnetic order in Ni-Pd alloys near 2.3 at% Ni is ascribed to the interplay of a strongly enhanced paramagnetic matrix and the presenceof triads of nickel atoms that carry giant magnetic moments. More information on the Pd-rich nickel alloys is presented in subsect.4.2.3.Neutron scattering results for the magnetic moment per atom of concentrated Ni-Pd alloys are given in Fig. 125. For the Ni-Ir system a critical concentration for ferromagnetism has been observed at 81 at% Ni. The Ni-Pt system is subject to order-disorder transformations in two composition regions: near NiPt and near Ni,Pt. NiPt in the ordered state has a tetragonal CuAuI-type of structure whereas the disordered alloys have a fee structure. The disordered alloys show ferromagnetic order above 42.5at% Ni. The ordered NiPt compound is paramagnetic, stressing the important role of local environment effects.The magnetic properties (including magnetovolumetric effects)of the disordered alloys near the critical composition for ferromagnetism have frequently been discussed in the collective model of itinerant magnetism [74A2, 76K 1, 77 F 11. The average magnetic moments on Ni and Pt atoms in disordered Ni-Pt alloys have been determined in diffuse neutron diffraction experiments (Fig. 140).

1550 K

0.7 Pe

I 1400

0.6

~1250

t

1100 750 1 600 K

la" ox

hu

0.5

0.2 0 Ni

450

a

300 0

0.6 !JB A nr U.3

2.5

5.0

7.5

10.0 12.5 15.0 17.5 at% x-

22.5

Fig. 113.Composition dependenceof the Curie points of (a)Co-@,Rh,Pd,Os,Ir,Pt)alloysand (b)Ni-(Rh,Os,Ir) alloys [60 C 11.

I

IO

20

30

5

IO

15

40

50

60

at%

80

20

25

30

at%

40

1

,z Ok 0.3 02 i

0

“,

u. I

g

Ni-Ru I

.I05 erg c;;;3

0

b

Ni

x-

Fig. 114.Variation ofthe magneticmomentper atom with composition for Ni-(Ru, Rh, Pd, OS,Ir, Pt) alloys. Open circles: [6OC 11; solid symbols: [32 S 11, [37M 11; see also [82T I] and [83 T 21.

0.1 I 0.2

0.3

0 Ni

Landolt-Bbmstein New Series 111/19a

1

2

3

4

at%

0.4

Fig. 115. Variation of the anisotropy energy AE, =E, [l 1l] -E, [ 1001with Ru concentration in Ni-Ru alloys for different temperatures(notice the changeof scalefor T=293 K) [80A 11,seealso [78 M 11.

Ru -

Frame, Gersdorf

620

1.4.2.2.6 Ni-4d, 5d (group 8) 2.oi

[Ref. p. 648

12 Gcml g

lk 1.75 l.SC I 1.25

8 Is" 1.00 0.75 t 6 b

0.T 025 0 , Kh -

Fig. 116. Average moments at Ni and Rh sites in Ni-Rh alloys vs. concentration. The solid lint rcprcscnts 2.0~” F,?. where j,, is the fraction of Rh atoms surrounded by I2 nearest-neighbor Ni atoms [7S C I]. see also [77C 21. 10

20

30

LO

50

60 kOc

H-

Fig. 117. Magnetization curves at 4.2 K for Ni-Rh alloys [75 M 33.

0 Ni

40

60 Rh -

80 at% 100 Rh

?g. I IS. Mass susceptibility of Ni-Rh alloys at 4.2 K olid circles: [75 M 33, open circles: [68 B I].

0

200

400

600

K

800

Fig. 119. Plots of ATc/Ap as a function of Tc for Ni-(Rh. Pd, Pt) alloy systems [79 K 33, set also [75 K I]. For the composition dependence of Tc, set Figs. I I3 and 124. Open and closed triangles represent data from different authors.

Frame, Gersdorf

621

1.4.2.2.6 Ni-4d, 5d (group 8)

Ref. p. 6481 1000

I

Rh-Ni

K Pd-Ni

II Pt-’

Isp

0 t -0.4 2 -0.8 \ 2 -1.2 -1.6

-2.0 -2.4 0.l

1

IO

ot%Ni 100

Fig. 120.Plots of Tc and ATJAp as a function of(c - cF)for (Rh, Pd, Pt>Ni alloy systems; cF is the critical concentration of Ni for ferromagnetism [79 K 21, see also [SO0 11.

2 ,105 !!I cm3

I

I 1

0 Ni

I

Ni- Rh

T = 4.2 K

. E,~1101-E, [IO01 5

IO

15 Rh -

20

25 at% 30

Fig. 121. Plots of (E,[lll]-E,[lOO]) and (E,[llO] - E,[ 1001)at 4.2 K as a function of FChconcentration for Ni, -,Rh, alloys [S 1 K 31. Landolt-Bbmstein New Series 111/19a

Frame, Gersdorf

I

n

[Ref. p. 648

1.4.2.2.6 Ni-4d, 5d (group 8)

622 15 .lG' e:g cm? 12

6,

/

I

0

50

100

I

I

200

150

I

mol/cm

I

300

Fig. 123. Arrott plots (q$ vs. H/g,) at various temperaturcs and fields up to 69 kOe for the Ni-35 at% Rh alloy. Solid curvc~ and dashed curves are calculated for different cluster contributions to the magnetization [79A 11.

700,

/

,

20

40

I

I

60

80 at% 100

I

.T=OK 17 K 0.2

K’

0.1

0.6

0.8

1.0

c/c, -

Fig. 122.Concentration dcpcndcncc ofK, for Rh-Ni, Pdm Ni. and Pt-Ni alloys: cr is the critical concentration for ferromngnctism [820 I]; for Ni-Rh alloys see also [7l T I].

1.2

0 0

Ni Fig. 124. Plot of the Curie temperature vs. concentration for Pd-Ni and disordered Pt-Ni [72 F 11.

i 0.E IQ

LO

60 Pd -

80 at% 100 Pd

Fig. 125. Average moments vs. concentration for Ni-Pd alloys [78 C 11. The neutron scattering results are from [70 C 21 (open symbols) and [70 A23 (solid symbols).

Franse, Gersdorf

1.4.2.2.6 NiAd, 5d (group 8)

Ref. p. 6481

623

200 kDe 150

0 NI -

100

Fig. 126. Saturation hyperfine fields at 57Fe sites as a function of Ni concentration in Pt-Ni and Pd-Ni alloys near zero temperature [72 F 11.

50

I F x

Fig. 127. Average magnetic hyperfine fields at Ni sites (solid symbols) and Pd sites (open symbols) in the Ni-Pd alloy system. Different solid and open symbols represent data from different authors. The following equations have been used to calculate the curves [73 G 11: H&,Ni)=

0 -50

-100 -150

-76 kOe+ 125Cj-p,i)kOe/u,,

H,,,(Pd)=-180kOe+80~-~~,i)kOe/p,, where fi denotes the average magnetic moment of the sample per Ni atom, i.e. p=P,J(l-c) with c the Pd concentration. jNi is the average Ni magnetic moment. See Fig. 125 for concentration dependence of & and pm.

-200 -250

0

25

Ni

5.oc 404 9 a

3.0 .I04 9 cm3

30

93

G2cmg

2.50

I 2.0

I p 1.25

2 1.5 x 1.0

-1.25 -2.50 0

a

2.5

5.0

12.'5 7.5~102G2cm6/g2

0"2-

5

b

2.0

2.5 T2-

0 105 K2 3.5

Fig. 128. (a) Dependence H/cr=f(cr’) for the alloy Ni,,,Pd,.4 at different temperatures: (I) 420, (2) 436, (3) 450,(4)460,(5)472,(6)480,(~490,(8)500,(9)510,(10)524, (II) 540, (12) 556, (13) 570, (14) 590, and (15) 616K. 01) Initial ordinate A( T’) (open circles) and the slope B( Tz) (solid circles) of the dependences H/o = A + Ba2for the alloy Ni,,,Pd,,,, [78P 21. Landolt-Bornstein New Series 111/19a

Franse, Gersdorf

50 Pd -

75 ot% 100 Pd

1.4.2.2.6 Nilld,

[Ref. p. 648

5d (group 8) 10 405 erg cm3

I

\li - Pd

0 I s;c

-5 -1cl-15I 0 Ni

20

LO

Pd-

El0 at % 100 Pd

60

Fig. 130. Plots of K, and of the magneto-elastic contribution to K,, K, (m.e.), at OK in Ni-Pd alloys, as a function of the Pd concentration [78 T I].

0.2

0.6 0.1 r/r, -

0.8

1.0

Fig. 129. Plot of K 1 as a function of reduced tempcraturc T& for NikPd alloys [75 F 21.

I -1

r" -2 -CT

-3

-4

0 Hi

20

60 Pd -

80 at% 1 Pd

Fig. 13l.Plots ofthcmagnctostrictionconstantsh, and h, at OK in NiLPd alloys, as a function of the Pd concentration [7S T I].

0

0.2

0.1

0.6

0.8

1.0

1.2

r/r, -

Fig. 132. Plots of the forced volume magnetostriction

ho/aH vs. T/T, for Ni-Pd alloys [73T2].

Frame, Gersdorf

Ref. p. 6481 12 mJ molK2L

II I

1.4.2.2.6 Ni-4d, 5d (group 8)

625

Ir 40-6 cm3 9

,.. _.

9

60 ol x 40

8

20

I

I x

7

0t 30

35

40

45 Ni -

50

55 at%

Fig. 134. Extrapolated zero-field mass susceptibility for ordered and disordered Pt-Ni alloys [73 G 21, see also [72Gl].

Ir -

Fig. 133. Molar susceptibility x,,, and electronic specific heat coefficinet y in Ni-Ir alloys as a function of the Ir concentration [70 B I].

I

I

I/

I

I

II

20

40

\I

40-c rm3

I

I

250 200 550 100

50 02 PY

60 NI -

80 at% 100 Ni

Fig. 135. Electronic specific heat coefficient y (a) and highfield molar susceptibility x,,, (b) ofdisordered Pt-Ni alloys near zero temperature [74 B 21. Different symbols represent data of different authors. Land&Bdrnstein New Series III/l9a

Franse, Gersdorf

1.4.2.2.6 Ni-4d, 5d (group 8)

626

I I

[Ref. p. 648

I

20 I

I

1

I

I 0.a 8CI

y

9

4

1

I

I

1=77K

/ 60

/,

,51.8ot%PI

/ 57.1 P I 6

3l PI -

80 at%

100 Pt

Fig. 138. Experimental total moment per atom p,, and spin moment per atom deduced from j(sp)=2~?,,/9, in disordered Ni-Pt alloys, as a fimction of the Pt conccntration. The initial linear parts extrapolate to P,,=O.293 pn. and .&,(sp)=O.355 pr, [69 F2]. For g. see Fig. 139.

/ P

40

20

~0 Ni

I 2.3

Ni-

Pt

disordered

2.2 ” 0 c 0 0 I 2.1

JbA x &IF40

o”. ol

I

“0

‘10

20

30

0

l

50 .103a/cm3 2.0

H/rJ -

‘is. 136. ,s* vs. H/G of disordcrcd Ni-Pt alloys at 4.2 K I) and 77K (b). The curves arc labcllcd with the Pt zntent [74S 31.

1.9 - 0 1=293K . 77K t’ 1K 1.8 I I 30 0 10 20 Ni PI -

0

4Oot% 50

Fig. 139. Experimental g factors for Ni-Pt alloys [69 F 23. i 40 k 1717 -

20

0

10

20

30

40

.103g/cm1

60

Fig. 137. Arrott plots for the disordered Ni0,476Pt0,J2J alloy at various temperatures from 4.2K to 226.7K: [74Bl],seealso[76B2]and[78Bl].

Frame, Gersdorf

Landnlt-Rornriein Nea- Seriu III ‘192

627

1.4.2.2.6 Ni+Id, 5d (group 8)

Ref. p. 6481 ,

Ni- Pt

0 0 Ni

Fig. 140. Average individual moments near 4K for disordered Ni-Pt alloys [8OP 11, see also [79P 31.

IO

20

30

LO

50 at% 60

Pt -

Fig. 141. Comparison of Ni-Pt average moments &, near 4 K from neutron scattering (solid circles) and magnetization (open circles) measurements [8OP I].

I 2.0

;

-

P

1.5 I 2

1’

I

1.0

L

1

L\

’

\ !I

I

,,:

0.5 0 40 - 0.5 40

Pt 44

52

48

56 at%

80 at% 100 Ni

I

Ni -

Fig. 142. Variation of the squared spontaneous magnetic moment per mole, oS, (from Arrott plot analysis) vs. composition for disordered Pt-Ni alloys at 4.2 K [79A 11.

Landolt-Biirnstein New Series 111/19a

60 NI -

Fig. 143. Hyperfine fields at 61Ni sites as a function of composition for the Pt-Ni system [72 F 11.

Franse, Gersdorf

628

1.4.2.2.6 Ni-4d, 5d (group 8) lO! kO?

[Ref. p. 648

ml

I Ni -Pi

350 300 250 200 150 100

Fig. 144. Average magnetic hypcrtinc ticld at 4.2 K at the Ni sites as a function ofthc Pt concentration in the Ni-Pt alloy system. The solid line gives the dependence of the avcra:c moment per atom normnlizcd to the hypcrfinc field in Ni metal [73 G I].

I

50

u .?

0

z LOO a 350

250

0

I

Pt -Ni disordered

0

0

5

10

15

20

25

30

35

Fig. 145. Temperature dependence of the magnetic momcnt per unit mass ~7of two Ni-Pt alloys in a constant field of2 Oe after cooling in zero field (solid circles) and in a finite field of 20~ (open circles). To obtain absolute values of CJin [Gcm3g-‘1 multiply by 7.55. IO-’ for Ni 0.41pt0.59, and by 7.93. 10e5 for Ni0.40Pt,,,, [78 0 1-J).

c

2

I 1,

I 6

8 ot%Ni

1u

c-q Fig. 146. Experimental values for the logarithmic dcrivatives of 7,. B, and x0 with respect to volume as a ftmction oft-cr. where cr equals the critical concentration of Ni for ferromagnctism in disordcrcd PttNi alloys [74A2]. See also Table 22. o, and lo refer to zero magnetic ticld and zero tempcraturc.

Franse, Gersdorf

1.4.2.2.6 NiAd, 5d (group 8)

Ref. p. 6481

629

Table 22. Pressure dependenceof the magnetic parameters of disordered Pt-Ni alloys [74A 21.For a graphical representation of the concentration dependenceof the logarithmic derivatives of T,, 6, and x0 with respectto volume, seeFig. 146.B, and x0 refer to zero magnetic field and zero temperature. at% Ni

dddp

[Gcm3mol-l kbar-‘1 d Vdp [K kbar-I] lo5 &to/+ [cm” mol- ’ kbar - ‘1 V da, os dV --V dTc T, dV V 4x0 xo dV

42.9

45.2

47.6

50.2

- 165(l)

-11

- 8.6

- 8.1

-

- 0.7 7.4

4.2

1.5 420

23

135

44

150

29

-490

18

-43

-84

11

10-6 $V$

24

15

-39

15

18

[G2 cm6mol-‘1 1O-4 T,V$ 10-4

[K’,

8.0

x:v dX0 dV

-

2.5

8.6 -

-

1.3

1.1

-

1.6

[mol cm - 3]

For Fig. 147,seenext page. .lO-*

pt _ Ni

$l.Lat%Ni

100

.IO~,"~Pt - Ni

disordered 80 t

r

1

6

60

;: 4

a 40

I .A 2

20 0 -20 4

-4ld 0

I 5

I

I

I

IO

15

20

8

IO K 12

T-

I 25 kOe 30

HOPPl -

Fig. 148.Linear magnetostriction 1 of disorderedPt-Ni alloys as function of the applied field. The curves are labelled with the Ni concentration; T=4.2 K [76 K 11. Landolt-Bdmstein New Series III/I%

6

Fig. 149. Low-temperature thermal expansion of disordered Pt-Ni alloys as a function of temperature.The curvesare labelled with the Ni concentration; the critical concentration for ferromagnetismis about 42.5at% Ni [77 F 11,seealso [77 K 11.

Franse, Gersdorf

630

1.4.2.3 3dAd, 5d (group 8): 4d, Sd-rich alloys

0 Ni

[Ref. p. 648

30 Pt -

LO

Fig 150. Plots of (E,[lll]-EJlOO]) and(E,[l IO] -E,[lOO]) at 4.2K as a function of the Pt concentration for Ni-Pt alloys [Sl K 11,seealso [77 0 I]. NI -

Fig. 147.Variation with Ni concentration of(a) the square ofthe spontaneous magnetic moment per molt u$(b)thc square of the Curie tempcraturcs.from [72 B 21; (c) the inverseinitial susceptibility x0 for disorderedPttNi alloys near zero temperature[74 A2].

1.4.2.3 4d- and Sd-rich alloys In the dilute. 4d- and Sd-rich alloys of 3d transition metals a variety of interesting magnetic phenomena can be encountered: formation of magnetic moments, Kondo effect,local spin fluctuations, giant magnetic moments. spin-glass phenomena, etc. An introduction into these phenomena and a collection of resistivity, susceptibility, specific heat and thermopower data can be found in Landolt-Bornstein, NS, vol. III/IS, and in the review by Mydosh and Nieuwenhuys [SOM 21. The magnetic moment of 4d-Fe alloys containing 1at% Fe is shown in Fig. 1 as an example. In the 5d seriesthe critical region where iron magnetic moments appear occursjust at or to the right of Ir in the periodic table [66 G 11.Values for the Kondo (spin fluctuation) temperatures for Cr, Mn, Fe, and Co impurities in Rh, Pd. and Pt are given in Table 1. The tendency of showing spin-glass or giant moment behavior in these combinations of 3d and 4d, 5d elements is indicated in Table 2. The appearanceof ferromagnetism in dilute solutions of Fe and Co in Pd and Pt and of Ni in Pd is illustrated in Fig. 2. The critical concentrations for ferromagnetism are of the order of 0.1 and 0.2 at% Fe, Co in Pd and Pt, respectively. In theselow-concentration regions giant magnetic moments are formed around the Fe, Co atoms by polarization of the surrounding Pd, Pt matrix (Fig. 3). Below the critical concentration for ferromagnetism the interaction between the polarization clouds becomespossibly antifcrromagnetic, pointing to a RKKY-type of

Franse, Gersdorf

630

1.4.2.3 3dAd, 5d (group 8): 4d, Sd-rich alloys

0 Ni

[Ref. p. 648

30 Pt -

LO

Fig 150. Plots of (E,[lll]-EJlOO]) and(E,[l IO] -E,[lOO]) at 4.2K as a function of the Pt concentration for Ni-Pt alloys [Sl K 11,seealso [77 0 I]. NI -

Fig. 147.Variation with Ni concentration of(a) the square ofthe spontaneous magnetic moment per molt u$(b)thc square of the Curie tempcraturcs.from [72 B 21; (c) the inverseinitial susceptibility x0 for disorderedPttNi alloys near zero temperature[74 A2].

1.4.2.3 4d- and Sd-rich alloys In the dilute. 4d- and Sd-rich alloys of 3d transition metals a variety of interesting magnetic phenomena can be encountered: formation of magnetic moments, Kondo effect,local spin fluctuations, giant magnetic moments. spin-glass phenomena, etc. An introduction into these phenomena and a collection of resistivity, susceptibility, specific heat and thermopower data can be found in Landolt-Bornstein, NS, vol. III/IS, and in the review by Mydosh and Nieuwenhuys [SOM 21. The magnetic moment of 4d-Fe alloys containing 1at% Fe is shown in Fig. 1 as an example. In the 5d seriesthe critical region where iron magnetic moments appear occursjust at or to the right of Ir in the periodic table [66 G 11.Values for the Kondo (spin fluctuation) temperatures for Cr, Mn, Fe, and Co impurities in Rh, Pd. and Pt are given in Table 1. The tendency of showing spin-glass or giant moment behavior in these combinations of 3d and 4d, 5d elements is indicated in Table 2. The appearanceof ferromagnetism in dilute solutions of Fe and Co in Pd and Pt and of Ni in Pd is illustrated in Fig. 2. The critical concentrations for ferromagnetism are of the order of 0.1 and 0.2 at% Fe, Co in Pd and Pt, respectively. In theselow-concentration regions giant magnetic moments are formed around the Fe, Co atoms by polarization of the surrounding Pd, Pt matrix (Fig. 3). Below the critical concentration for ferromagnetism the interaction between the polarization clouds becomespossibly antifcrromagnetic, pointing to a RKKY-type of

Franse, Gersdorf

Ref. p. 6481

1.4.2.3 3d-4d, 5d (group 8): 4d, Sd-rich alloys

631

interaction [71 C2]. In dilute solutions of Mn in Pd a more complex situation is encountered. Besides the ferromagnetic interaction between the Mn moments by means of the polarized Pd matrix a direct antiferromagnetic interaction between neighboring Mn moments occurs. These two competing interactions give rise to spin-glass behavior in the composition range 2...10 at% Mn (seeFig. 4). By adding small amounts of Fe to Pd the transition from ferromagnetic to spin-glass behavior can be shifted to higher Mn concentrations (see Fig. 5).The critical concentration for ferromagnetism in dilute Pd-Ni alloys is around 2.3 at% Ni and is believed to be connected with a percolation among interacting magnetic clusters, nucleated by triads of Ni atoms [Sl C 11.

Survey

Alloy

Cr, -,Pt, Mn, -,Rh, Mn, -,Pd,

Mn, -XPt, Fe, -XRu, Fe, -,Rh, Fe, -,Pd,

Fe, -XOs, Fe, -Jrr

X

Property

Fig.

x=0.98 x>o.995 x = 0.982 x > 0.99 x=0.82 x>O.82 x=0.992, x =0.995 x>O.965 x=0.98 x > 0.994 x > 0.9755 x > 0.92 x = 0.902, x = 0.96 x > 0.90 x>O.89 x > 0.90 x > 0.995 x=0.99 x = 0.99 x = 0.99 x > 0.90 x > 0.999 x>O.985 x=0.985 x>o.50 x > 0.99 x>O.84 x > 0.99 x>O.84 x > 0.90 x = 0.9984 x = 0.9975 x=0.983 x=0.985 x = 0.99 x = 0.99 x > 0.50 x>O.85 x = 0.99

x&T) e(x,T ) X&O TK@) 49 T,(x) xg(T) X>) x&T) X>>

6 7 8 9 10 11 12 13 14 15 16 17 18 19 4 20 21

09 XHF,

E&T

HI

xLFCO Pso,u,e(B) PM”(X) Tc(x)>

T,(x)

Aa, AC(T) X&G T) Paat, 0, T,(x) Daat> 0, T,(x) Pm 0, T,(x) L(x) 4ff) 4H) @f, T> tjFe>

3 22 23 24 5

PPd

25 26 27 28 29 30

T>

T,(x),

@(x)

T,(x) T,(P) AC(H) T,,

9,

M,

K,,

K,

T,,

g,

M,

K,,

K,

spin waves L,(T) xg(T), $7 4x, T) C/W PFe,

3

4 4 4

44 4x,

Table

@cx)

6 6 31 32 33 34 35 36

Ref. 70Nl 75Sl 7812 72Sl 79Cl 79Cl 70Nl 69Nl 7111 72Cl 7532 7721 79Ml 79Sl 82Hl 81Bl 77Tl 62C2 62C2 62C2 80M2 71C2 70M3 70M3 65Cl 71C2 6OC2 71C2 6OC2 74Ml 75Nl 74B3 74B3 82Ll 66Gl 66Gl 66Gl 66Gl 66Gl continued

Landolt-BOrnstein New Series Il1/19a

Franse, Gersdorf

632

1.4.2.3 3d-4d, 5d (group 8): 4d, Sd-rich alloys

[Ref. p. 648

Survey, continued Alloy Fe, -,Pt, Co, -,Pd,

co, -,pt,

Ni, -,Pd,

X

x>O.85 x > 0.83 x =0.955 x>o.90 x>O.98 x = 0.9976 o<x
Property

Fig.

P,,(x)

3 37

L(x), T,(x) T,, gt M> K,, K, Pa,(x) T,(x) C,(H) Hh,, T,(P) P&4 0, c,, ii&) T,, os, Em PC,

x > 0.90 x>o.991 x > 0.80 x=0.961 x>o.995

T,, gt M, K,, K, C"(H) T,(P) x,(x, T) 4x> 4 C”(X) x, Tc. CAY(X) Tc, OS>fk PNi

x > 0.97 x > 0.97 x>O.85 x > 0.965 x>O.88 x=0.95

Table

6 3 38 39 7 29 3 8 9 6 40 29 41 42 43 44 9 6

T,, g. M>K,> K,

Table 1. Isolated-impurity Kondo (spin fluctuation) temperatures for Cr, Mn, Fe, and Co impurities in Rh, Pd, Pt [SOM 23.

Rh Pd Pt

Cr

Mn

Fe

co

1OOK 200 K

IOK 1OmK 0.1 K

50K 20 mK 0.3K

lOOOK 0.1 K 1K

Table 2. Spin-glass and giant moment combinations of transition metals [80M 21. SG and GM represent favorable combinations for spin-glass or giant-moment behavior, respectively; XT meansthat a too high Kondo temperature limits the appearance of both the spin-glass or giant-moment states.

Rh Pd Pt

Cr

Mn

Fe

co

XT XT XT

SG SG+GM SG

XT GM GM

XT GM SG

Franse, Gersdorf

Ref. 80M2 7901 74B3 80M2 72Nl 70B2 62Nl 74Ml 80M2 72Tl 65C2 74B3 73Nl 74Ml 81 Cl 81Cl 68C2 74M3 65C2 74B3

Ref. p. 6481

1.4.2.3 3d-4d,

5d (group 8): 4d, Sd-rich alloys

633

IO 1 8 I&

6

0 Pd

4 2r

5 Nb

6 MO

7

8

Re

RU

9 Rh

IO Pd

11 4

Fig. 1. Magnetic moment per Fe atom in 4d metals and alloys containing 1 at% Fe [62 C 21. The crystallographic structure as well as the number per atom of 4d and 5s electrons are indicated.

0 Pd,Pt

2

L

6

8

at%

IO

C0.k -

Fig. 3. Magnetic moment per solute atom as a function of concentration in alloys of Pd, Pt with Fe, Co [80 M 21; other references: Pd-Fe: [68 M 11, [67M 11; Pt-Fe: [74S2], [67Ml], C65Tl-J; Pd-Co: [61Bl]; Pt-Co: [75 S 33, [65 T I]. M: Mijssbauer experiment.

Landolt-Bbmstein New Series lWl9a

1

2

3 Co,Fe,Ni -

L

at%

5

Fig. 2. Curie temperature as a function of concentration for Pd, Pt alloys with Fe, Co, Ni [62 B l] ; other references: Pd-Fe: [70K2], [69K3], [69Cl], [68M 11, [68B2], [67Tl]; Pt-Fe: [75K2], [70K2]; Pd-Co: [76Ml], [71 L l], [69 W I], [68 A 11, [61 B 11; Pt-Co: [76 RI].

0 Pd

2

6 Mn -

8

at% IO

Fig. 4. Suggested phase diagram for the Pd-Mn system, showing the transition temperature as kmction of Mn concentration; F: predominantly ferromagnetic; M: mixed ordering; SG: spin-glass [82H 11, see also the references:[67S1],[69R1],[69W1],[70N2],[72Bl], [73 B 31, [75C 11, [75 Z 11, [79 G l] for the effect of pressure, and [Sl H 21.

Frame, Gersdorf

[Ref. p. 648

1.4.2.3 V-4d, 5d (group 8)

634

7 40'6

cm3 T

5

I x"

1,

3

-0

50

100

150

200

250 K 300

TFig. 6. Temperature dependcncc of mass susceptibility xg of Pd-2.0 at% V alloy [70 N I].

8

6

2

at%

nsi,

10

Mi; 047

Fig. 5. Magnetic phnsc diagram for (Pd,,,,,,Fc,,,,,,~ Mn showing the ferromngnctic transition (open circles) and the spin-glass transition (solid circles) tcmpcraturcs: open triangles dcnotc intermediate transitions; the .inshcd line rcprcscnts the fcrromngnctic transition tcmpcmturc in binary Pd-Mn alloys [78V I], set also: [79 \\‘2] and [80 F I] for the prcssurc effect. and [S I S I]. The dotted line for Tc represents the result of a calculation. The upper figure shows the concentration dependence determined from experiment of the relative strength J’,ll of ferromagnetic to spin-glass interaction parameter.

0.u

0.39 1.80

I 1.76 1.12 d" 1.68 1.6L 12 40-7 cm’ I- 9 k

1.60

8 6 0

50

100

150

200

250 K 300

0

50

100

150

200

250 K :

T-

IFig. 8. Tempcraturc dcpcndence of mass susceptibility xn of Pt (open circles) and a 1.80at% V alloy (solid circles) [78I I].

Fig. 7. Incremental resistivity AQ= ealloy--ehos,of the PdO.lSat%V and the Pd-O.5at%V alloys plotted up to 300 K. The lines arc the predictions of the localized-spinfluctuation theory. The error bars represent shape-factor unccrtaintics [75 S I], see also [73 K I].

Franse, Gersdorf

1.4.2.3 Cr-4d, 5d (group 8)

Ref. p. 6481

635

0.5 10" icm3 9 9.5

I b

9.0

5.00 .lO" Gcm3 9 100 0 Pd

8.5

0.75d% 1.00

0.50 Cr -

Fig. 9. Kondo temperature Tx vs. Cr concentration in b 4.25 dilute Pd-Cr alloys [72 S 11, see also [68 G 11, [69 S 11, and [73K2]. Tx determined from the nominal (open circles) and the analyzed (closed circles) Cr concentration. The solid lines show Tx as calculated for different electron density of states. c in [at% Cr].

5

IO

15 T-

20

25 K :

Fig. 10. Magnetization data for a Pd-18 at% Cr sample. Open triangles: cooled in zero applied magnetic field and then warmed in 1 kOe; solid triangles: cooled and warmed in 1 kOe; open circles: cooled in zero field, and warmed in 0.5 kOe; solid circles: cooled and warmed in 0.5 kOe [79 C 11. 30 K

Pd-Cr

20

2

I t-z

/

P’ IO

0

0 Pd

/ ,d

A

/ IO

15

20 at%

Cr -

Fig. 11.Temperatures T, ofthe susceptibility maximum in Pd-Cr alloys, plotted against the Cr concentration [79 c 11.

cm3 s

Fig. 12. (a) Temperature dependence of mass susceptibility xg of Pd-Cr alloys. (b) Temperature dependence of incremental mass susceptibility Axp = xhos,- xallo,, for 0.8 at% Cr and 0.5 at% Cr in Pd. For the 0.5 at% Cr alloy, the susceptibility was normalized to the susceptibility of the 0.8 at% Cr solution [70 N 11.

Landolf-Bbmstein New Series 111/19a

I

x" a 1.5

1.0 0

Franse, Gersdorf

50

100

150 T-

200

250 K 300

1.4.2.3 Cr, Mn-4d, Sd (group 8)

636

[Ref. p. 648

1X .10-b cm! s

1.2 I x" 1.1

1.0

0.9 50

100

150

200

250 K :

II

I

0

I

50

I

150

100

200

K

250

TFig. 13. Reciprocals of incrcmcntal mass susceptibility Ax,= x~,,~,!-xholr for Cr in Pt [69 N I], see also [77 R I].

1.8 W5 cm’ 9

Fig. 14. Tempcraturc dcpcndcncc of mass susccptibilit) xp of a Pt-Cr alloy containing 2.0at% Cr. and of Pt metal [71 I I].

4

LO

Gcm3 9

1.4 1 x”

I b

;crnl 5-l

3

1.5

2

I 1.0 b

1.2 3.5

1.0 08 0

100

200

300

400

500

600

3 0.4 cm? 9 9.6

700 K 800

I-

Fig. 15. Mass susceptibility temperature [72 C I].

xg of Rh Mn alloys vs.

8.8

8.0 bI

I.2

Fit. 16. Field dependence of the magnetic moment per umt mass. a,of(a)Pd -0.08at% Mn and Pd-0.49 at% Mn, and @) Pdm0.96at% Mn and Pd -2.45at% Mn at T=4.2K. The slope of the straight lines rcprcscnts the high-field susceptibility z,,r [75 S 21.

6.4

5.6 0

Frame, Gersdorf

40

80

120 HOpQl -

160 kOe 200

Ref. p. 6481

1.4.2.3 Mn4d,

5d (group 8)

637

Table 3. High-field magnetization data of Pd-Mn [75 S 21. xHFis the slope do/dH in the region of saturated solute magnetization. When saturation was not achieved (asindicated in the columns for xHFand J&J do/dH at maximum applied field is reported. osis obtained from the intersections of thesehigh-field tangents with the rr axis (Fig. 16). j& is the saturation moment per solute atom as obtained from os, For g-factor data, see [64 S l] and [74A 11. Inelastic neutron scattering data are reported in [78 V 31.

T

at% Mn

H mm

K

0.05

1.38 1.36 4.2 4.2 4.2 4.2 4.2 4.2

0.054 0.08 0.23 0.49 0.96 1.35 2.45

XHF

PM”

kOe

10-6cm3g-1

2cm3g-’

54 54 210 210 210 210 210 210

6.9

0.181 0.222 0.33 0.90 1.72 3.48 4.75 7.4

6.9 6.8 6.8 6.8 5 6.5 ~6.3 <8.5

PB

6.9 7.8 7.8 7.4 6.7 266.9 >6.7 > 5.7

320

280

240

I 200 a, .> 2 160 -

1 P IQ 2.5

2 120

0 0 0 0 0 0 0c I. 3

80

40

. l -. .

1.5 0 Pd- 4at%Mn . Pd-6at%Mn A Pd 8ot%Mn

A*

2

1.0 0.5

A-b,~~A

A-----n.

0

4

T-

6

.A

8

a.

K

IO

0

3

6

9 8 WPl

Fig. 17. Temperature dependenceof the low-field ac susceptibility xLF for Pd-Mn alloys containing 4at%, 6 at% and 8 at% Mn. The position of the sharp peaksin xLFdefinesthe freezing temperature T, [77 Z 11.

Land&BCmctein NW Serier 111/19a

1

0%

!-n

0.35ot%Fe

2.0

nor?+--

l

/'/ fiSot%Mn.

12

15

T

18

-

Fig. 18. High-field magnetization, expressedas average magneticmomentper solute atom,jsolute,for Pd-Mn and Pd-@In, Fe)vs.applied flux density [79 M 1] at 1.5K and 4.2K, respectively.

Franse, Gersdorf

1.4.2.3 Mn4d, 5d (group 8)

638

[Ref. p. 648

I

Pd-Mn

I_

0 PJ

6

2

8 at%

10

E:n -

Fig. 19. Saturation magnetic moment j& as function of Mn concentration for Pd ~Mn alloys [79S I], see also [73 B 3, 75 D 1. 77C I]. and [78 F I]. Diffcrcnt symbols rcprcscnt data ofdifTcrcnt authors for PDFMn (lower solid line). For comparison the upper solid line shows jpc VS.Fe concentration for Pd Fc.

L50 mJ molK

LOO

150 100 50 0 0

3

9

6

12

15 K

18

TFig. 20. (a) Diffcrcncc Aa in the thermal expansion cocflicicnt bctwccn various Pd-Mn alloys and pure Pd. The ferromagnetic and spin-glass transition temperatures arc indicated by T, and T,, rcspcctivcly. (b) Excess specific heat AC = C,,,,, - Ghostof various Pd--Mn alloys. The broken curve represents the ferromagnetic contribution to AC for the Pd -2 at% Mn alloy, whcrcas the solid curve shows the antiferromagnetic cluster part [S 1 B I], seealso [Sl T I].

Ref. p. 6481

1.4.2.3 Mn, Fe-4d, 5d (group 8)

.10’5

639

Pt-Mn I

-cm3 9 ,

a

2.5 0

50

100

150

200

250

300

350

400

450

0

500

0.25

b

0.50 at% Mn c-

Fig. 21. (a) Impurity contribution Axp to the mass susceptibility as measured in low field vs. normalized temperature T/c for Pt-Mn alloys. (b) Paramagnetic Curie temperature 0 as function of impurity concentration c [77 T I], see also [69 M 11; for the specific heat data, see [74 S 11.

Table 4. Magnetic moment and Curie temperature for 1 at% solutions of Fe in 4d alloys from Ru to Pd [62 C 21. pFe: Fe magnetic moment calculated from the

relation p,“,,= pFe(PFe + gla) with g = 2. & : average Fe magnetic moment derived from saturation magnetization. Alloy

Ru RU o.,dWm km%,, Rudho., Ru o.zsRh,,,, Rh Rho.+&., Rhd%.ax bd’do., Rhd%.s Rho.,Pdo., Rbd’4,.,, Pd Pdo.,,Ag,.,,

Structure

hcp hcp hcp hcp

fee fee fee fee fee fee fee fee fee fee

PFe

0

PFe

T,

PB

K

PB

K

0.0 0.0 0.8 1.3 1.7 2.2 4.5 5.9 ') 7.1 ') 9.6')

-21(2) -13(2) -17(2) -14(2) -2 -2 1

11.4‘)

E(2)

7.1 9.5

12.7') 11.3 ') 8.3 1)

49(6)

10.8

55(3) 12

9.7 6.3

i) Determined by relating the magnetic susceptibility near T = 100 K.

Landolt-Bbrnstein New Series 111/19a

Frame, Gersdorf

11 27 39 39

11

to a Curie-Weiss law

1.00

[Ref. p. 648

1.4.2.3 Fe-4d, 5d (group 8)

640

1.0 Crm3

I

I

I

0.6

b

OX

Pd.T=l.ZgK / 0.i

8 15

10

5

0

20

kOe ;

H-o;?

=ig. 22. hJngnctization curvzs for various conccnlrations If Pd Fc alloys at 1.25K and 0.05 K. rcspcctivcly. The ron conrcntrntion is _pivenin ppm [71 C 21.

16 kOe 20

12

Fig. 23. Magnctizntion curves of high-purity Pd-Fc alloys at low tcmpcratuics [70 M 31. 25.0 ,103 9

I

I

I

0.1

0.2

0.3

Pd and

I

I

I

I

0.L

0.5

0.6(Gcm3/g)’

cm3 2o.c

17.5

15.c I b 12.: \ x 0

0.0’

0.02

0.03 at%

0.05

1O.I

Fe -

Pd

5 Gcir’ Pd-Fe 9 i 1

I

3

6

2

7.:

5.1

2!

CT2-

1 I 0.75

c c

PC

0.25

0.50

Fe-

I 1.00 ot% 1.25

Fe -

Fi_r.25. Saturation mayctic moment per unit mass o, and Curie constant C, of Pd Fc alloys [7 1C 2).

Fig. 24. H/a against ~7’ for Pd-O.l5at% Fe. The highfield points (I . ..I&5 kOc) arc marked with symbols denoting the tcmpcraturc of mcasurcmcnt. For the lowfield points (0...1.25 kOe) the tcmpcraturcs are marked on the figure. The straight lines making intcrccpts on the G* axis arc drawn through isothermal points for liclds above IOkOc [70M3].

Frame, Gersdorf

641

1.4.2.3 FewId, 5d (group 8)

Ref. p. 6481

Table 5. Atomic magnetic moments in Pd-Fe alloys [65 C 11.

3 7 25 50

0.234(7) 0.457(14) 1.00(3) 1.60(5)

2.92(H) 2.76(11) 2.64(H) 2.49(11)

2.9(3) 3.0(2) 2.9(2) 3.0(l)

3.07(U) 3.02(11) 2.98(15) 2.85(8)

0.15(l) 0.26(2) 0.34(5) 0.35(8)

‘) From large-angle neutron scattering data assuming no Pd contribution and the metallic Fe form factor.

0

200 T-

-100

300

K

400

Fig. 26. Variation of spontaneous magnetization gSwith temperature for Pd-Fe alloys; the iron content is given in the figure [60 C 21. K ox I Q 0.2

I

0 c*-

hy

0.6 K I 0.4 I-Y 0.2

0

0.2

Il.kot%Fe 0.6

0

IO

20

30

m%t%Fe)*50

c*-

C-

Fig. 27. Ferromagnetic Curie temperature ‘Kcand paramagnetic Curie temperature 0 for Pd-Fe alloys as function of Fe concentration c [7 1 C 21. Landolt-Bdmstein New Series lWl9a

Franse, Gersdorf

[Ref. p. 648

1.4.2.3 Fe-4d, 5d (group 8)

642

8 Fe -

4 PO6

12 at% 16

Fig. 28.Variation ofthc Curie point with iron content for Pd-Fe alloys [60 C 23.seealso [70 C I].

/

Pd- O.l6at%Fe

1

(

1

50

100

I

150

200

250 K 300

‘C -

2

1

6

8 7-

10

12

11 K 16

Fig. 30. Excessspecific hcnt AC= C’~llny-Chos, VS. T Pd O.l6at% Fc. Curve I: H ~%%~]?~ 3: H,,,,= I .8kOc, and 4: H,,,zt=?k& also [61 V I].

Fig. 29. Volume derivative of the Curie temperaturefor Pd-Co, Fc (a) and Pt-Co, Fe (b) alloys plotted vs. the Curie tcmpcraturc of the respectivealloy [74 M I]. Diffcrcnt size of the symbols indicates different authors.

for

Table 6. Alloy compositions and magnetic parameters for dilute Pd
Alloy (at% solute)

Tc K

g

M(O) G

Pd-Co( 1.O) Pd-Co(l.5) Pt-Co(3.9) Pd-Ni(5.0) Pd-Fe(0.25) Pd-Fe( 1.7) Pt-Fe(4.5)

70 85 67 160 20 89 85

2.30 2.33 2.29 2.45 2.17 2.16 2.15

60 69 62 120 20 112 140

K ,(0)/M(O) G - 950 - 950 200 1200 0 - 65 700

Frame, Gersdorf

K,WM(O) G - 500 - 500 0 550 0 0 0

Easy axis

Cl111 Cl111 Cl001 cw

isotropic

Cl111 Cl001

1.4.2.3 FewId, 5d (group 8)

Ref. p. 6481

%!!$k Pd -1.5at%Fe

2c .m4 -cm3 mol

1=50K Q =0.12w-’

\

643

\ \ \ \

12

\

I .I0 H

\

8 6

I

.-F

I

I

I

I

I

80 k =o- counts s h

I

l= 4OK

1

601

60

80 at% 100 Ir Ir -

0~0.4 Ir0.6

20

40

60 Pt -

80 at% 100 Pt

Fig. 32. Susceptibility per mole x,,, for 5d alloys containing 1% Fe, at three different temperatures [66 G 11.

0 I

-1.0

I

I

I-

-0.5

0

I

I

-I

0.5

meV

?

E-

Fig. 3 1. Net scattering intensity of neutrons at a momentum transfer Q of 0.12A-‘, after subtraction of the nonmagnetic background. The spin waves are seento shift to smaller energies with increasing temperature [82 L 11. Ei: energy of incident neutrons, E: energy transfer.

Fig. 33. Magnetic moment per unit of mass, CJ,in an applied magnetic field of1 5.3 kOe,and H/(0-- a,) vs. Tfor samples of lat%Fe in Ir,,,Pt,,, (c, =0.0041)Gcm3g-‘) and Os,,,Ir,,,Pt,,, (cm =0.0031 Gcm3g-‘) showing almost identical behavior for ~r~=(a-crJH. pre: Fe magnetic moment derived Tom p& = pFe(pFe + gpB) with g = 2. Landolt-Bbmsrein New Series 111/19a

Franse, Gersdorf

1.4.2.3 Fe-4d, 5d (group 8)

644

1 Hoppr =k2L kOe 1

[Ref. p. 648

GUI

K2mot

I

1 2 LO LD

.Alr0.95Fe0.05

I

30 20 P-

so

0

=i

100

150

200

250 K 300

10

7-

.

Fig. 34. hlagnetic moment per unit of mass vs. tempcrature for more conccntratcd solutions of Fe in Ir [66 G I].

II

50

100

10kG I I 150 200 250 300 350 K LOO T-

Fig. 35. Heat capacity curves for more concentrated solutions of Fe in Ir, and, for comparison. of a dilute solution of Fe in Rh [66 G I]. 21: k

‘I

lx-----/‘.2

16’ I Y

7r

I

I

pfi lr- Pt t lat%Fe

E!

I

I

I

I

60

I I80 at% lOi

I

Al

1.0 I

I 1

0.8 I 4 0.6

I

04

0.2

0

3

6

9

12

0 15 ot% 18

Fe PI Fig. 37. Concentration dcpendcncc ofthc Curie tcmpcraturc Tc and the saturation magnetization. p,, for Pt-Fe alloys [790 I]. Data points for Tc arc from: crosses: [6S C 21. solid circles: [67S2]. open circles: [70K 33, solid squares: [790 I], open square: [790 I] unhomogcni7cd Pt.-l5 at% Fe alloy. The insert shows that extrapolation from high-tempcraturc data gives too large a value for the critical concentration for ferromagnetism. Data points for j,, arc from: solid triangle upward: [59 C 21. solid triangle downward: [63 B I],open triangle:

01 O

Ir

20

I LO

Pt Pt Fig. 36. Magnetic moment per Fe atom, pFc.derived from pzrf= pFe(pFe+ gua) with g = 2, and paramagnetic ordering temperature 0 for solutions of I at% Fe dissolved in Ir-Pt alloys [66G I].

[65C2].

Frame, Gersdorf

1.4.2.3 Co-4d, 5d (group 8)

Ref. p. 6481

645

12 mJ Kmol

I

’ ” cTc=75404c~

2. 4 1.0 0.8

0.6 0.1, 0.01 0.02 0.01,0.06 0.1

0.2

d%Co 1

2 I

Fig. 38. Transition temperatures of Pd-Co alloys as a function of Co concentration c. Open circles: resistivity measurements [70 W 11, triangles: Miissbauer experiments [67 D I]. Temperatures at which the excess specific heat attains its maximum are shown by solid circles [72Nl].

4

8

12

100 30 15 8 3

T, K

T K

1404 673 423 275 130

297 80 4 4 4

H hw kOe

PC,

-312(5) -305(10) -296(g) -315(4) - 310(9)

1.7 2.6 4.1 5.5 7.4

PB

Table 8. Magnetic parameters of dilute Pt-Co alloys [72 T 11. rk: temperature of the maximum of the initial susceptibility; S: spin deduced from the Curie constant C,, assuming g = 2. at% Co

0.0414 0.0807 0.163 0.271 0.312 0.662 0.878 Landolt-Bbmstein New Series III/l9a

0 K - 1.6 - 1.45 -1 0 0.6 5.15 10.2

Trk K

0.065 0.14 0.22 1.0(l)

K

20

TFig. 39. Excess specific heat AC vs. T for Pd-0.24at% Co. Curve 2: H,,,r=O, 3:H,,,,=4.5 kOe,4: II,,,,=9 kOe, 5: H app,=27 kOe. Curve 1 represents results obtained at 18 kOe; points have been omitted for clarity [70 B 23.

Table 7. 57Fe hyperhne field HhYp in Co-Pd alloys at low temperatures [62 N 11. at% Co

16

c, 10-‘cm3Kg-r

Peff

0.689 1.36 2.92 5.02 6.13 13.65 18.65

5.11 5.14 5.3 5.38 5.56 5.68 5.78

Frame, Gersdorf

s

PB

2.10 2.12 2.19 2.24 2.32 2.38 2.43

1.4.2.3 Co, NibId, 5d (group 8)

646 Table 9. Curie temperature Pd-Ni alloys [65 623.

saturation magnetization

and magnetic moments for Pd-Fe, Pt-Fe, Pt-Co, and

Pt-Fe

PDF-Fe Solute content [at%]

C WI os [Gcm3g-‘1 Pat bnl

i%eCPnl

[Ref. p. 648

0.15 4.3 0.76 0.0145 9.5

0.28 9.5 1.82 0.0346 12.2

0.53 23 3.06 0.0581 10.9

0.99 6.8 0.84 0.029 2.9

2.60 39 2.56 0.087 3.4

3.33 27 2.88 0.054 1.6

4.29 59 5.40 0.10 2.4

0.45 3.3

0.87 5.4 1.56 0.0541 6.2

2.30 21.5 3.25 0.112 4.9

4.07 59 5.87 0.199 4.9

6.30 104 9.85 0.329 5.2

Pt-Co Solute content [at%]

T, CKI CT>[Gcm3g-‘1 Pa, CPBI t% Ccd

0.51 2.7 0.36 0.013 2.5

5.17 104 5.30 0.18 3.5

10.2 218 10.52 0.34 3.4

15.2 315 15.37 0.48 3.2

20.1 19.6 0.59 3.0

Pd-Ni Solute content [at%]

T,CKl

2.5 12

os [Gcm3g-‘1 L, Cd

Psi bnl

5.55 88 7.37 0.14 2.5

11.78 177 14.50 0.26 2.2

18

mJ Krr:? 15

12 1 sg 6 .5% lolcl h?:t copxily

3

0

3

6

12

15

K 18

Fig. 40. Excess spccitic heat AC vs. T for Pt-0.5 at% Co. Curve I: H,,,,=O, 2: H,,,,=4.5 kOe. 3: Ha,,,=9 kOe, 4: H,,,,=18kOe,5: H,,,,=27kOe [73Nl].

Fig. 41. Inverse initial mass susceptibility 10 ’ vs. temperature for various Pd-Ni alloys. Solid circles [81 C I], open circles [78 S 11.

Frame, Gersdorf

Ref. p. 6481

1.4.2.3 Ni-4d, 5d (group 8)

647

Fig. 42. Magnetization curve at 2.4 K for various Pd-Ni alloys and for pure Pd. Solid circles [S 1 C 11; open circles [78 S 11; see also [74 C I] and [76 C 11. For pressure effect, see [75 B 1] and [76 B 11; for magnetostriction, see [SOH I].

0

1.00

IO

20

30

40

I

30 K

0

Pd-Ni

t

50 kOe 60

0.16 mJ K"mol I 0.12 a 0.10 0.08

Qcm ai% 7.5

r\

I 8000 'I z 6000 7 2 4000 4

D/I

1

j/-

5.0 I ? : 2.5 '

\ \I

AdI/\

.g -2

2

4

6

8 NI -

10

12

14at% 16

Fig. 43. The coefficients y and /I of the low-temperature specific heat, C,=yT+ pT3, of Pd-Ni alloys, plotted vs. Ni concentration [68 C 23, see also [83 Ill. For the de Haas-van Alphen effect, see [82 R 11;for spin fluctuations, see [83 B 11.

I

2000

I

0.06 0

0

0 24

20

4 16 0

Landolt-BOrnstein New Series ill/19a

1

2 NI -

3

at%

4

Fig. 44. (a) Inverse susceptibility &lNi of Pd-Ni alloys relative to xpdl of pure Pd as a function of Ni concentration: on the right Tc as a function of Ni concentration; (b) resistivity data for Pd-Ni alloys, plotted as l/cAA/A,, and AQ/Cvs. c; A is the coefficient of the T2 term in Q(T); AA and AQ are defined with respect to pure Pd; (c) incremental electronic specific heat vs. c [74M 31, see also [82B2].

Franse, Gersdorf

648

Rcfcrcnccs for 1.4.2

1.4.2.4 References for 1.4.2 3oc 1 32Sl 35Fl 35Gl 36F1 37M 1 40Gl 50Al 50K 1 52Kl 5SG1 5SG2 59Cl 59C2 60C 1 6OC2 61 B I 62B I 62Cl 62C2

Constant, F.W.: Phys. Rev. 36 (1930) 1654. Sadron. C.: Ann. Phys. Paris 17 (1932) 371. Friederich. E.. Kussmann. A.: Phys. Z. 36 (1935) 185. Grubc. G.. Winklcr. 0.: Z. Elektrochem. 41 (1935) 52. Fallot, M.: Ann. Phys. 6 (1936) 305; 7 (1937) 420; 10 (1938) 29. Marian. V.: Ann. Phys. Paris 7 (1937) 459. Gebhardt, E., Kbster, W.: Z. Mctallkd. 32 (1940) 252. Auwgrter. M., Kussmann. A.: Ann. Phys. 7 (1950) 169. Kussmann. A.. Rittbcrg. G. v.: Ann. Phys. 7 (1950) 173. Kiister. W., Horn. E.: Z. Mctallkd. 43 (1952) 444. Gerstenbcrg. D.: Ann. Phys. Leipzig 2 (1958) 236. Gerstenberg. D.: Z. Metallkd. 49 (1958) 476. Corliss. L.M., Hastings, J.M., Weiss, R.J.: Phys. Rev. Lett. 3 (1959) 211. Crangle. J.: J. Phys. Paris 20 (1959) 435. Crangle. J.. Parsons. D.: Proc. R. Sot. 255 (1960) 509. Crangle. J.: Philos. Mag. 5 (1960) 335. Bozorth. R.M.. Wolff. P.A., Davis, D.D., Compton, V.B., Wernick, J.H.: Phys. Rev. 122 (1961) 1157. Bozorth. R.M.. Davis. D.D., Wernick, J.H.: J. Phys. Sot. Jpn. 17, B-I (1962) 112. Cable. J.W., Wollan. E.D., Koehler, W.C., Child, H.R.: Phys. Rev. 128 (1962) 2118. Clogston. A.M., Matthias, B.T., Peter, M., Williams, H.J., Corenzwit, E., Sherwood, R.C.: Phys. Rev. 125 (1963) 541. Nagle. D.E.. Craig. P.P., Barrett, P., Cochran, D.F.R., Olsen, C.E., Taylor, R.B.: Phys. Rev. 125(1962) 62Nl 490. 62P 1 Pickart, S.J..Nathans. R.: J. Appl. Phys. 33 (1962) 1336. 63B 1 Bacon. G.E., Crangle. J.: Proc. R. Sot. London A272 (1963) 387. 63K 1 Kouvel, J.S.. Hart&us. C.C., Osika, L.M.: J. Appl. Phys. 34 (1963) 1095. 63 P 1 Pickart. S.J..Nathans. R.: J. Appl. Phys. 34 (1963) 1203. Yokoyama. T., Wuttig, M.: Z. Metallkd. 54 (1963) 308. 63Y1 Booth. J.G.: Phys. Status Solidi 7 (1964) K 157. 64B I Laar. B. van: J. Phys. Paris 25 (1964) 600. 64L1 Shaltiel. D., Wernick. J.H., Williams, H.J., Peter, M.: Phys. Rev. 135 (1964) A 1346. 64s 1 Shnltiel. D., Wernick. J.H.: Phys. Rev. 136 (1964) A 245. Shirane. G., Nathans, R., Chen, C.W.: Phys. Rev. 134 (1964) A 1547. 64S2 64V 1 Veal. B.W., Raync. J.A.: Phys. Rev. 135 (1964) A 442. Cable. J.W., Wollan. E.O., Koehler, WC.: Phys. Rev. 138 (1965) A755. 65Cl Crangle. J., Scott. W.R.: J. Appl. Phys. 38 (1965) 921. 65C2 Collins. M.F., Low, G.G.: Proc. Phys. Sot. (London) 86 (1965) 535. 65C3 Tsiovkin. Yu.N., Volkenstheyn. N.V.: Phys. Met. Metallogr. (USSR) 19, 3 (1965) 45. 65Tl 66C 1 Campbell. LA.: Proc. Phys. Sot. (London) 89 (1966) 71. 66G 1 Geballe. T.H., Matthias. B.T., Clogston, A.M., Williams, H.J., Sherwood, R.C., Maita, J.P.: J. Appl. Phys. 37 (1966) 1181. Koehler. W.C., Moon, R.M., Trego, A.L., Mackintosh, A.R.: Phys. Rev. 151 (1966) 405. 66K I 66K2 Krin, E.. KLdir. G., Pil. L., %lyom, J., Szab6, P.: Phys. Lett. 20 (1966) 331. 66K3 Krt-n. E.. S6lyom. J.: Phys. Lett. 22 (1966) 273. 66M I Menzinger. F., Paoletti. A.: Phys. Rev. 143 (1966) 365. 67Dl Dunlap, B.D., Dash. J.G.: Phys. Rev. 155 (1967) A460. 67M 1 Maley. M.P., Taylor. R.D.. Thompson, J.L.: J. Appl. Phys. 38 (1967) 1249. 67s 1 Sarachik. M.P., Shaltiel. D.: J. Appl. Phys. 38 (1967) 1155. 67S2 Segnan. R.: Phys. Rev. 160 (1967) A404. 67Tl Trousdale. W.L., Longworth, G., Kitchens, T.A.: J. Appl. Phys. 38 (1967) 922. 6SA 1 Alekseevskii. N.E., Samerskii, Yu.A., Kir’yanov, A.P., Tsebro, V.I.: JETP Lett. 8 (1968) 403. 6SB 1 Brinkman. W.F., Bucher, E., Williams, H.J., Matia, J.P.: J. Appl. Phys. 39 (1968) 547. 6SB2 Baggurley, D.M.S.. Robertson, J.A.: Phys. Lett. 27 A (1968) 516. 6SC 1 Comly, J.C.. Holden. T.M.. Low, G.G.: J. Phys. C 1 (1968) 458. 6SC2 Chouteau. G., Fourneaux. R.. Tournier, R., Lederer, P.: Phys. Rev. Lett. 21 (1968) 1082. 6SG 1 Gainon. D.. Sierra. J.: Phys. Lett. 26 A (1968) 601. Frame, Gersdorf

Referencesfor 1.4.2 68Hl 68Kl 68K2 68Ml 68Pl 68P2 68s 1 68Wl 69Al 69Cl 69Fl 69F2 69Kl 69K2 69K3 69Ml 69Nl 69Pl 69Rl 69Sl 69Tl 69Vl 69Wl 69W2 70Al 70A2 70Bl 70B2 7OCl 7OC2 7OJl 70Kl 70K2 70K3 7OLl 70Ml 70M2 70M3 70Nl 70N2 7OVl 7OWl 71 c 1 71C2 71c3 7111 7112 71Ll 71Ml 71M2 7101 71Sl 71S2 71s3 71Tl Land&B6msrein New Series 111/19a

649

Hicks, T.J., Pepper, A.R., Smith, J.H.: J. Phys. Cl (1968) 1683. Kussmann, A., Miiller, K., Raub, E.: Z. Metallkd. 59 (1968) 859. KrCn, E., Kadar, G., Pal, L., Sblyom, J., Szabo, P., Tarnoczi, T.: Phys. Rev. 171 (1968) 574. McDougal, M., Manuel, A.J.: J. Appl. Phys. 39 (1968) 961. Pal, L., KrCn, E., Kadar, G., Szabb, P., Tarnoczi, T.: J. Appl. Phys. 39 (1968) 538. Ponyatovskii, E.G., Kutsar, A.R., Dubovka, G.T.: Kristallografiya 12 (1967) 79 (Sov. Phys. Crystallogr. 12 (1968)). Shirley, D.A., Rosenblum, S.S.,Matthias, E.: Phys. Rev. 170 (1968) 363. Wayne, R.C., Bartell, L.C.: Phys. Lett. 28A (1968) 196. Antonini, B., Lucari, F., Menzinger, F., Paoletti, A.: Phys. Rev. 187 (1969) 611. Calow, J.S., Meads, R.E.: J. Phys. C2 (1969) 2120. Fujimori, H., Saito, H.: J. Phys. Sot. Jpn. 26 (1969) 1115. Fischer, G., Besnus, M.J.: Solid State Commun. 7 (1969) 1527. KrCn, E., KBdLr, G.: Phys. Lett. 29A (1969) 340. Kouvel, J.S., Forsyth, J.B.: J. Appl. Phys. 40 (1969) 1359. Kawatra, M.P., Skalski, S., Mydosh, J.A., Budnick, J.I.: J. Appl. Phys. 40 (1969) 1202. Miyaka, Y., Morishita, H., Watanabe, T.: J. Phys. Sot. Jpn. 27 (1969) 1071. Nagasawa, H.: J. Phys. Sot. Jpn. 27 (1969) 787. Palaith, D., Kimball, C.W., Preston, R.S., Crangle, J.: Phys. Rev. 178 (1969) 795. Rault, J., Burger, J.P.: C.R. Acad. Sci., Ser. B 269 (1969) 1085. Star, W.M., Nieuwenhuys, G.J.: Phys. Lett. 30A (1969) 22. Tu, P., Heeger, A.J., Kouvel, J.S., Comley, J.B.: J. Appl. Phys. 40 (1969) 1368. Vinokurova, L.I., Nikolayev, I.N., Mel’nikov, Ye.V., Adis’yevich, I.K., Reutov, Yu.B.: Phys. Met. Metallogr. (USSR) 28, 6 (1969) 147. Williams, G., Loram, J.W.: Solid State Commun. 7 (1969) 1261 and J. Phys. Chem. Solids 30 (1969) 1827. Wheeler, J.C.G.: J. Phys. C2 (1969) 135. Arajs, S., De Young, T.F., Anderson, E.E.: J. Appl. Phys. 41 (1970) 1426. Aldred, A.T., Rainford, B.D., Stringfellow, M.W.: Phys. Rev. Lett. 24 (1970) 897. Bucher, E., Brinkman, W., Maita, J.P., Cooper, A.S.: Phys. Rev. B 1 (1970) 274. Boerstoel, B.M., Baarle, C. van: J. Appl. Phys. 41 (1970) 1079. Clark, P.E., Meads, R.E.: J. Phys. C 3 (1970) S 308. Cable, J.W., Child, H.R.: Phys. Rev. B 1 (1970) 3809. Jayaraman, A., Rice, T.M., Bucher, E.: J. Appl. Phys. 41 (1970) 869. Kaneko, T., Fujimori, H.: J. Phys. Sot. Jpn. 28 (1970) 1373. Kawatra, M.P., Budnick, J.I.: Int. J. Magn. 1 (1970) 61. Kawatra, M.P., Mydosh, J.A., Budnick, J.A., Madden, B.: Proc. Low.Temp. (Kyoto) 12 (1970) 773. Loegel, B.: J. Phys. C3 (1970) S 355. McKinnon, J.B., Melville, D., Lee E.W.: J. Phys. C 3 (1970) S 46. Mizoguchi, T., Sasaki, T.: J. Phys. Sot. Jpn. 28 (1970) 532. McDougal, M., Manuel, A.J.: J. Phys. C3 (1970) 147. Nagasawa, H.: J. Phys. Sot. Jpn. 28 (1970) 1171. Nieuwenhuys, G.J., Boerstoel, B.M.: Phys. Lett. 33A (1970) 147. Vogt, E., Biilling, F., Treutmann, W.: Ann. Phys. 25 (1970) 280. Williams, G.: J. Phys. Chem. Solids 31 (1970) 529. Chakravorty, S., Panigrahy, P., Beck, P.A.: J. Appl. Phys. 42 (1971) 1698. Chouteau, G., Tournier, R.: J. Phys. Paris 32 (1971) C l-1002. Crangle, J., Goodman, G.M.: Proc. R. Sot. (London) A321 (1971) 477. Inoue, N., Nagasawa, H.: J. Phys. Sot. Jpn. 31 (1971) 477. Ivanova, G.V., Magat, L.M., Solina, L.V., Shur, Ya.S.: Phys. Met. Metallogr. (USSR) 32,3 (1971)92. Loram, J.W., Williams, G., Swallow, G.A.: Phys. Rev. B3 (1971) 3060. Matsumoto, M., Goto, T., Kaneko, T.: J. Phys. Paris 32 (1971) C 1419. Moon, R.M.: Int. J. Magnetism 1 (1971) 219. Ohno, H.: J. Phys. Sot. Jpn. 31 (1971) 92. Star, W.M.: Thesis, University of Leiden, Netherlands 1971. Stoelinga, S.J.M., Grimberg, A.J.T., Gersdorf, R., Vries, G. de: J. Phys. Paris 32 (1971) Cl-330. Swallow, G.A., Williams, G., Grassie, A.D.C., Loram, J.W.: J. Phys. Fl (1971) 511. Ttriplett, B.B., Phillips, N.E.: Phys. Lett. 37A (1971) 443. Frame, Gersdorf

650 71Vl 71Y 1 72B 1 72B2 72Cl 72Dl 72Fl 72Gl 72Ml 72Nl 72Sl 72Tl 73 Al 73A2 73Bl 73B2 73B3 73Dl 73Gl 7362 73Kl 73K2 73K3 73K4 73K5 73Nl 73s1 73Tl 73T2 74A1 74A2 74Bl 74B2 74B3 74C 1 74Dl 74Fl 7411 74Ml 74M2 74M3 74Nl 74Rl 74Sl 74S2 74s3 74Yl 74Y2 7421 75Al 75A2 75A3

Referencesfor 1.4.2 Vinokurova, L., Pardavi-Horvath, M.: Phys. Status Solidi (b) 48 (1971) K 31. Yamaoka. T., Mekata. M., Takaki, H.: J. Phys. Sot. Jpn. 31 (1971) 301. Boerstoel. B.M., Zwart, J.J., Hansen, J.: Physica 57 (1972) 397. Besnus. M.J., Herr, A.: Phys. Lett. 39 A (1972) 83. Claus, H.: Phys. Rev. B5 (1972) 1134. DeYoung. T.F., Arajs, S., Anderson, E.E.: AIP Conf. Proc. 5 (1972) 517. Ferrando, W.A., Segnan, R., Schindler, AI.: Phys. Rev. B5 (1972) 4657. Gillespie, D.J., Schindler, AI.: AIP Conf. Proc. 5 (1972) 461. Menzinger, F., Romanazzo, M., Sacchetti, F.: Phys. Rev. B5 (1972) 3778. Nieuwenhuys, G.J., Boerstoel, B.M., Zwart, J.J., Dokter, H.D., Berg, G.J. van den: Physica 62 (1972) 278. Star, W.M., Vroede, E. de, Baarle, C. van: Physica 59 (1972) 128. Tissier, B., Tournier, R.: Solid State Commun. 11 (1972) 895. Abdul-Noor, S.S.,Booth, J.G.: Phys. Lett. 43 A (1973) 381. Arajs, S., Rao, K.V., Astrom, H.U., DeYoung, T.F.: Physica Scripta 8 (1973) 109. Besnus. M.J., Meyer, A.J.P.: Phys. Status Solidi (b) 58 (1973) 533. Besnus. M.J., Meyer, A.J.P.: Phys. Status Solidi (b) 55 (1973) 521. Burger, J.P., McLachlan, D.S.: Solid State Commun. 13 (1973) 1563. DeYoung. T.F., Arajs, S., Anderson, E.E.: J. Less-Common Met. 32 (1973) 165. Goring, J.: Phys. Status Solidi (b) 57 (1973) K 7. Gillespie, D.J., Mackliet, C.A., Schindler, AI.: Amorphous Magnetism (Hooper, H., Graaf, A.M., de, eds.).New York: Plenum Press 1973, 343. Kao, F.C.C., Colp, M.E., Williams, G.: Phys. Rev. B8 (1973) 1228. Kao, F.C.C., Williams, G.: Phys. Rev. B7 (1973) 267. Kuentzler, R., Meyer, A.J.P.: Phys. Lett. 43 A (1973) 3. Kadomatsu, H., Fujii, H., Okamoto, T.: J. Phys. Sot. Jpn. 34 (1973) 1417. Kelarev, V.V., Vokhmyanin, A.P., Dorofeyev, Yu.A., Sidorov, S.K.: Phys. Met. Metallogr. (USSR) 35, 6 (1973) 1302. Nieuwenhuys, G.J., Pikart, M.F., Zwart, J.J., Boerstoel, B.M., Berg, G.J. van den: Physica 69 (1973) 119. Sumiyama, K., Graham, G.M., Nakamura, Y.: J. Phys. Sot. Jpn. 35 (1973) 1255. Tamminga. Y., Barkman, B., Boer, F.R. de: Solid State Commun. 12 (1973) 731. Tokunaga. T., Tange, H., Goto, M.: J. Phys. Sot. Jpn. 34 (1973) 1103. Alquit. G., Kreisler, A., Sadoc, G., Burger, J.P.: J. Phys. Paris Lett. 35 (1974) L69. Alberts, H.L., Beille, J., Bloch, D., Wohlfarth, E.P.: Phys. Rev. B9 (1974) 2233. Beille. J., Bloch. D., Besnus, M.J.: J. Phys. F4 (1974) 1275. Beille, J., Bloch, D., Kuentzler, R.: Solid State Commun. 14 (1974) 963. Baggurley, D.M.S., Robertson, J.A.: J. Phys. F4 (1974) 2282. Chouteau, G., Tournier, R., Mallard, P.: J. Phys. Paris 35 (1974) C4-185. Dubovka, G.T.: Sov. Phys. JETP 38 (1974) 1140. Fujimori, H., Hiroyoshi, H.: Solid State Commun. 15 (1974) 1287. Ito, Y., Sasaki, T., Mizoguchi, T.: Solid State Commun. 15 (1974) 807. Meier, J.S., Christoe, C.W., Wortmann, G., Holzapfel, W.B.: Solid State Commun. 15 (1974) 485. Men’shikov, A.Z., Dorofeyev, Yu.A., Kazantsev,V.A., Sidorov, S.K.: Phys. Met. Metallogr. (USSR)38, 3 (1974) 47. Murani, A.P., Tari, A., Coles, B.R.: J. Phys. F4 (1974) 1769. Nikolayev, I.N., Vinogradov, B.V., Pavlynkov, L.S.: Phys. Met. Metallogr. (USSR) 38, 1 (1974) 85. Ricodeau, J.A.: J. Phys. F4 (1974) 1285. Sacli, O.A., Emerson, D.J., Brewer, D.F.: J. Low Temp. Phys. 17 (1974) 425. Scherg. M., Seidel, E.R., Litterst, F.J., Gierish, W., Kalvius, G.M.: J. Phys. Paris 35 (1974) C6527. Schinkel, C.J., in: Physique sous Champs Magnttiques Intenses, Colloque du CNRS, Grenoble 1974, 25. Yamaoka, T.: J. Phys. Sot. Jpn. 36 (1974) 445. Yamaoka, T., Mekata, M., Takaki, H.: J. Phys. Sot. Jpn. 36 (1974) 438. Zavadskii, E.A., Medvedeva, L.I.: Sov. Phys. Solid State 15 (1974) 1595. Arajs, S., Moyer, CA., Kelly, J.R., Rao, K.V.: Phys. Rev. B 12 (1975) 2747. Abdul-Noor, S.S.,Booth, J.G.: J. Phys. F5 (1975) L 11. Arajs, S., Rao, K.V., Anderson, E.E.: Solid State Commun. 16 (1975) 331.

Frame, Gersdorf

References for 1.4.2 75A4 75Bl 75Cl 75C2 75Dl 75El 75Fl 75F2 7551 75Kl 75K2 75Ml 75M2 75M3 75Nl 75Sl 75S2 7583 7521 76Bl 76B2 76Cl 76Kl 76Ml 76Rl 76Tl 76Vl 76V2 77Cl 77C2 77Fl 77Gl 7762 77Kl 7701 77Rl 77R2 77Sl 7782 77Tl 7721 78Bl 78Cl 78Fl 7811 78Ml 78Nl 7801 78Pl 78P2 78Sl 78Tl 78Vl 78V2

651

Antonov, V.Ye., Dubovka, G.T.: Phys. Met. Metallogr. (USSR) 40, 3 (1975) 171. Beille, J., Chouteau, G.: J. Phys. F5 (1975) 721. Coles, B.R., Jamieson, H.C., Taylor, R.H., Tari, A.: J. Phys. F5 (1975) 565. Chen, C.W., Buttry, R.W.: AIP Conf. Proc. 24 (1975) 437. De Pater, C.J., Dijk, C. van, Nieuwenhuis, G.J.: J. Phys. F5 (1975) L 58. Eytel, L., Raghavan, P., Munnick, D.E., Raghavan, R.S.: Phys. Rev. B 11 (1975) 1160. Fukamichi, K., Saito, H.: J. Less-Common Met. 40 (1975) 357. Fujiwara, H., Tokunaga, T.: J. Phys. Sot. Jpn. 39 (1975) 927. Jamieson, H.C.: J. Phys. F5 (1975) 1021. Kadomatsu, H., Fujiwara, H., Ohishi, K., Yamamoto, Y.: J. Phys. Sot. Jpn. 38 (1975) 1211. Koon, N.C., Gubser, D.U.: AIP Conf. Proc. 24 (1975) 94. Menshikov, A., Tarnoczi, T., KrCn, E.: Phys. Status Solidi (a) 28 (1975) K 85. Martin, D.C.: J. Phys. F5 (1975) 1031. Muellner, W.C., Kouvel, J.S.: Phys. Rev. Bll (1975) 4552. Nieuwknhuys, G.J.: Adv. Phys. 24 (1975) 515. Strom-Olsen, J.O., Williams, G.: Phys. Rev. B 12 (1975) 1986. Star, W.M., Foner, S., McNiff Jr., E.J.: Phys. Rev. B 12 (1975) 2690. Swallow, G.A., Williams, G., Grassie, A.D.C., Loram, J.W.: Phys. Rev. Bll (1975) 337. Zweers, H.A., Berg, G.J. van den: J. Phys. F5 (1975) 555. Beille, J., Tournier, R.: J. Phys. F6 (1976) 621. Beille, J., Pataud, P., Radhakrishna, P.: Solid State Commun. 18 (1976) 1291. Chouteau, G.: Physica 84 B (1976) 25. Kortekaas, T.F.M., Franse, J.J.M.: J. Phys. F6 (1976) 1161. Maartense, I., Williams, G.: J. Phys. F6 (1976) L 121. Rao, K.V., Rapp, O., Johannesson, Ch., Budnick, J.I., Burch, T.J., Canella, V.: AIP Conf. Proc. 29 (1976) 346. Tsiovkin, Yu.N., Kourov, N.I., Volkenshteyn, N.V.: Phys. Met. Metallogr. (USSR) 42,2 (1976) 157. Vogt, E.: Phys. Status Solidi (a) 34 (1976) 11. Vinokurova, L., Vlasov, A.V., Pardavi-Horvath, M.: Phys. Status Solidi (b) 78 (1976) 353. Cable, J.W., David, L.: Phys. Rev. B 16 (1977) 297. Cable, J.W.: Phys. Rev. B 15 (1977) 3477. Franse, J.J.M.: Physica 86-88 B (1977) 283. Goto, T., Yamauchi, H.: J. Phys. Sot. Jpn. 43 (1977) 339. Goto, T.: J. Phys. Sot. Jpn. 43 (1977) 1848. Kortekaas, T.F.M., Franse, J.J.M.: Phys. Status Solidi (a) 40 (1977) 479. Oishi, K.: J. Sci. Hiroshima Univ. Ser. A41 (1977) 1. Roshko, R.M., Maartense, I., Williams, G.: J. Phys. F7 (1977) 1811; Physica 86-88B (1977) 829. Ryshenko, B.V., Sidorenko, F.A., Karpov, Yu.G., Gel’d, P.V.: Sov. Phys. JETP 46 (1977) 547. Smith, A.J., Stirling, W.G., Holden, T.M.: J. Phys. F7 (1977) 2411; Physica 86-88B (1977) 349. Savchenkova, S.F., Tsiovkin, Yu.N., Zolov, T.D., Volkenshteyn, N.V.: Phys. Met. Metallogr. (USSR) 43, 1 (1977) 188. Tholence, J.L., Wasserman, E.F.: Physica 86-88 B (1977) 875. Zweers, H.A., Pelt, W., Nieuwenhuys, G.J., Mydosh, J.A.: Physica 86-88 B (1977) 837. Beille, J., Bloch, D., Voiron, J.: J. Mag. Magn. Mater. 7 (1978) 271. Cable, J.W.: J. Appl. Phys. 49 (1978) 1527. Flouquet, J., Ribault, M., Taurian, V., Sanchez, J., Tholence, J.L.: Phys. Rev. B 18 (1978) 54. Inoue, N., Sugawara, T.: J. Phys. Sot. Jpn. 44 (1978) 440. Michelluti, B., Perrier de la Bathie, R., du Tremolet de Lacheisserie,E.: Solid State Commun. 28 (1978) 879. Nakamura, Y., Sumiyama, K., Shiga, M.: Inst. Phys. Conf. Proc. 39 (1978) 522. Ododo, J.C., Horvath, W.: Solid State Commun. 26 (1978) 39. Pardavi-Horvath, M., Vinokurova, L.I., Vlasov, A.V.: Inst. Phys. Conf. Proc. 39 (1978) 603. Ponomarev, B.K., Tiessen, V.G.: Phys. Status Solidi (b) 88 (1978) K 139. Sain, D., Kouvel, J.S.: Phys. Rev. B 17 (1978) 2257. Tokunaga, T., Fujiwara, H.: J. Phys. Sot. Jpn. 45 (1978) 1232. Verbeek, B.H., Nieuwenhuys, G.J., Stocker, H., Mydosh, J.A.: Phys. Rev. Lett. 40 (1978) 586. Vinokurova, L.I., Ivanov, V.Yu., Sagoyan, L.I., Rodionov, D.P.: Phys’Met. Metallogr. (USSR) 45,4, (1978) 869.

Land&-Biirnsfein New Series 111/19a

Frame, Gersdorf

652 7sv3 79Al 79Cl 79Gl 79K 1 79K2 79K3 79Ml 7901 79 P 1 79P2 79P3 79Rl 79Sl 79Wl 79w2 80Al 80B1 80Fl 80H 1 80Kl 80M 1 80M2 8001 8OPl 80R 1 8OYl 81Bl 81Cl 81 H 1 81 H2 81H3 8151 81Kl 81K2 81K3 81Pl 81Sl 81S2 81Tl 81 T2 81 v 1 81Wl 81 W2 82Al 82Bl 82B2 82H 1 82H2 82Jl 82Ll 8201 82Rl 82Tl 82Yl

Referencesfor 1.4.2 Verbeek, B.H., van Dijk, C., Nieuwenhuys, G.J., Mydosh, J.A.: J. Phys. Paris 39 (1978) C&918. Acker. F., Huguenin. R.: J. Mag. Magn. Mater. 12 (1979) 58. Cochrane, R.W., Strom-Olsen, J.O., Williams, G.: J. Phys. F9 (1979) 1165. Guy. C.N., Strom-Olsen. J.O.: J. Appl. Phys. 50 (1979) 7353. Kaaakami, M., Goto, T.: J. Phys. Sot. Jpn. 46 (1979) 1492. Kelly, J.R.. Moyer, C.A., Arajs, S.: Phys. Rev. B20 (1979) 1099. Kadomatsu, H., Fujiwara, H.: Solid State Commun. 29 (1979) 255. Mydosh, J.A., Roth, S.: Phys. Lett. 69A (1979) 350. Ododo. J.C.: J. Phys. F9 (1979) 1441. Paul, D.M., Stirling, W.G.: J. Phys. F9 (1979) 2439. Parette, G., Kajzar, F.: J. Phys. F9 (1979) 1867. Parra, R.E., Cable, J.W.: J. Appl. Phys. 50 (1979) 7522. Rainford, B.D.: J. Mag. Magn. Mater. 14 (1979) 197. Smit, J.J., Nieuwenhuys, G.J., Jongh, L.J. de: Solid State Commun. 30 (1979) 243. Williams, D.E.G., Lewin, B.G.: Z. Metallkd. 70 (1979) 441. Wu? M.K., Aitken, R.G., Chu, C.W., Huang, C.Y., Olsen, C.E.: J. Appl. Phys. 50 (1979) 7356. Aubert, G., Michelluti, B.: J. Mag. Magn. Mater. 15-18 (1980) 575. Bieber. A.?Charaki. A., Kuentzler, R.: J. Mag. Magn. Mater. 15-18 (1980) 1161. Franse, J.J.M., Hiilscher, H., Mydosh, J.A.: J. Mag. Magn. Mater. 15-18 (1980) 179. Hiilscher. H., Franse, J.J.M.: J. Mag. Magn. Mater. 15-18 (1980) 605. Kadomatsu. H., Kamimori, T., Tokunaga, T., Fujiwara, H.: J. Phys. Sot. Jpn. 49 (1980) 1189. Moyer, CA., Arajs, S., Eroglu, A.: Phys. Rev. B 22 (1977) 3277. Mydosh. J.A., Nieuwenhuys, G.J., in: Ferromagnetic Materials I (Wohlfarth, E.P., ed.), Amsterdam: North-Holland Publishing Company 1980, p. 71. Ododo, J.C.: J. Phys. F 10 (1980) 2515. Parra. R.E., Cable, J.W.: Phys. Rev. B21 (1980) 5494. Rouchy, J., du Tremolet de Lacheisserie, E., Genna, J.C.: J. Mag. Magn. Mater. 21 (1980) 69. Yamada. O., Ono, F., Arae, F., Arimune, H.: J. Mag. Magn. Mater. 15-18 (1980) 569. Brommer, P.E.. Franse,J.J.M., Geerken, B.M., Griessen,R., Holscher, H., Kragtwijk, J.A.M., Mydosh, J.A., Nieuwenhuys, G.J.: Inst. Phys. Conf. Ser. 55 (1981) 253. Cheung, T.D., Kouvel, J.S., Garland, J.W.: Phys. Rev. B23 (1981) 1245. Hedman. L., Moyer, CA., Kelly, J.R., Arajs, S., Kote, G., Garbe, K.: J. Appl. Phys. 52 (1981) 1643. Ho, SC., Maartense, I., Williams, G.: J. Phys. Fll (1981) 699, 1107. Hayashi. K., Mori, N.: Solid State Commun. 38 (1981) 1057. Jesser.R., Bieber. A., Kuentzler, R.: J. Phys. Paris 42 (1981) 1157. Kadomatsu, H., Tokunaga. T., Fujiwara, H.: J. Phys. Sot. Jpn. 50 (1981) 3. Kuentzler, R.: Inst. Phys. Conf. Ser. 55 (1981) 397. Kadomatsu, H., Tokunaga, T., Fujiwara, H.: J. Phys. Sot. Jpn. 50 (1981) 1409. Papoular, R., Debray, D.: J. Mag. Magn. Mater. 24 (1981) 106. Sate, T., Miyako, Y.: J. Phys. Sot. Jpn. 51 (1981) 1394. Sumiyama, K., Emoto, Y., Shiga, M., Nakamura, Y.: J. Phys. Sot. Jpn. 50 (1981) 3296. Thomson, J.O., Thompson, J.R.: J. Phys. Fll (1981) 247. Tsiovkin. Yu.N., Kourov, N.I., Volkenshtein, N.V.: Sov. Phys. Solid State 23 (1981) 1534. Vinokurova. L.I.. Vlasov, A.V., Kulikov, N.I., Pardavi-Horvath, M.: Hungarian Acad. Sci. Budapest 1981. Williams. D.E.G., Ziebeck, K.R.A., Hukin, D.A., Kollmar, A.: J. Phys. Fll (1981) 1119. Watanabe, K.: Phys. Status Solidi (a) 40 (1981) 697. Amamou, A., Kuentzler, R.: Solid State Commun. 43 (1982) 423. Burmester, W.L.. Sellmyer, D.J.: J. Appl. Phys. 53 (1982) 2024. Burke, SK., Cywinski, R., Lindley, E.J., Rainford, B.D.: J. Phys. Sot. Jpn. 53 (1982) 8079. Ho, S.C., Maartense, I., Williams, G.: J. Appl. Phys. 53 (1982) 2235. Hiroyoshi, H., Hoshi, A., Nakagawa, Y.: J. Appl. Phys. 53 (1982) 2453. Jesser,R., Kuentzler, R.: J. Appl. Phys. 53 (1982) 2726. Lynn. J.W., Rhyne, J.J., Budnick, J.I.: J. Appl. Phys. 53 (1982) 1982. Oishi. K., Asai. A., Fujiwara, H.: J. Phys. Sot. Jpn. 51 (1982) 3504. Roeland, L.W., Wolfrat, J.C., Mak, D.K., Springford, M.: J. Phys. F 12 (1982) L267. Takahashi, Y., Jacobs, R.L.: J. Phys. F12 (1982) 517. Yamada. O., Ono. F., Nakai, I., Maruyama, H., Arae, F., Ohta, K.: Solid State Commun. 42 (1982)473.

Franse, Gersdorf

References for 1.4.2 83Bl 83Cl 83Fl 8311 83Ml 8301 83Sl 83Tl 83T2 83Wl 83Yl 83Y2 83Y3

Land&Bbmstein New Series IW19a

653

Burke, S.K., Rainford, B.D., Lindley, E.J., Maze, 0.: J. Mag. Magn. Mater. 31-34 (1983) 545. Campbell, S.J., Hicks, T.J., Wells, P.: J. Mag. Magn. Mater. 31-34 (1983) 625. Fujiwara, H., Kadomatsu, H., Tokunaga, T.: J. Mag. Magn. Mater. 31-34 (1983) 809. Ikeda, K., Gschneider, Jr., K.A., Schindler, A.I.: Phys. Rev. B28 (1983) 1457. Matsui, M., Adachi, K.: J. Mag. Magn. Mater. 31-34 (1983) 115. Ono, F., Maeta, H., Kittaka, T.: J. Mag. Magn. Mater. 31-34 (1983) 113. Sumiyama, K., Shiga, M., Nakamura, Y.: J. Mag. Magn. Mater. 31-34 (1983) 111. Tino, Y., Iguchi, Y.: J. Mag. Magn. Mater. 31-34 (1983) 117. Takahashi, Y., Jacobs, R.L.: J. Mag. Magn. Mater. 31-34 (1983) 49. Williams, D.E.G., Ziebeck, K.R.A., Jezierski, A.: J. Mag. Magn. Mater. 31-34 (1983) 611. Yamada, O., Ono, F., Nakai, I., Maruyama, H., Ohta, K., Suzuki, M.: J. Mag. Magn. Mater. 31-34 (1983) 105. Yamada, O., Maruyama, H., Pauthenet, R., in: High Field Magnetism (Date, M., ed.), Amsterdam: North-Holland Publishing Company, 1983, p. 97. Yamada, 0.: Physica 119B (1983) 90.

Franse, Gersdorf