Gesina C Carter.

Metallic shifts in NMR : a review of the theory and comprehensive critical data compilation of metallic materials (Volume 20) online

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Carter, Gesina C.
Metallic shifts in NMR



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METALLIC SHIFTS IN NMR

A review of the theory and comprehensive
critical data compilation of metallic materials



(A National Bureau of Standards Office of Standard Reference Data Product)

In Four Parts

Part II

Evaluated Knight Shifts in Alloys with other
Solid State Properties



Ag-Cs



PROGRESS IN MATERIALS SCIENCE
Volume 20

The complete volume in four parts is supplied to subscribers to Progress in

Materials Science as volume 20 (an additional volume for 1977) of that series

at a 33 '/j'Vo reduction of the regular price.



PROGRESS IN MATERIALS SCIENCE

{■'.(lilor.s
B.CHALMERS

Division of Hiii^inccrin^ and Applied Pliwic.s ,
Harvard i'nivcrsily. Cambridge. Mays.. L.S.A.



J. W.CHRISTIAN

Department of Metallurgy.
L 'niversity of Oxford

and



T. B. MASSALSKI

.Mellon Institute of Seience.
Carnegie-Mellon University. Pillshurgh. Pa.. L .S..4.



METALLIC SHIFTS
INNMR



A review of the theory and comprehensive
critical data compilation of metallic materials



by

G. C. CARTER, L. H. BENNETT and D. J. KAHAN

Insiiiuti' jor Malcrlal.s Research

National Biirenii of Standards

Washington. D.C. 20234



Part II

u Stiifls in A
I Slate Prope

Ag-Cs



Evalutiled Kniahl Sfiifis in Alloys with other
Solid Slate Properties




PERGAMON PRESS

Oxford • New York • Toronto • Sydney • Paris • Tranklurt



U.K. Perganion Press Ltd., Headington Hill Hall,

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Copyright © 1977 by the Secretary of Commerce on behalf of the United States
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All Rights Reserved. No part of this publication may be

reproduced, stored in a retrieval system or transmitted in

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publishers

First edition 1977



/n order to make this volume available as economically and rapidly as possible the
author's typescripts have been reproduced in their orifiinal form. This method
unfortunately has its typographical limitaiions hut it is hoped that they in no way
dislruci the reader.



Library of Congress Cataloging in Publication Data

Carter, Gesina C.
Metallic shifts in NMR.

(Progress in materials science; v. 20)

Bibliography: p.

Includes index.

1. Knight shift. 2. Nuclear magnetic resonance

spectroscopy. L Bennett, Lawrence Herman, 1930-

joint author. IL Kahan, D. J., joint author.

HL Title. IV. Series.

QC1.P884 vol. 20 (QC7621 620.1'1208s [669 .94)

ISBN 08 021143 7 75-42466



Printed in Crcat Britain by A. Wheaton & Co.. Exeter



CONTENTS

PARTI

Preface vii

Acknowledgments viii

Glossary of Symbols and Abbreviations ix

1. General Introduction 1

2. The Knight Shift 3

2.1. The Hamiltonian 3

2.2. The Contact Interaction Term 3

2.3. Pauli Spin Susceptibility 4

2.4. Hyperfme Fields and Knight's ^ Factor 8

2.5. Spin Polarization of Closed Shells 11

2.6. The Orbital Term 12

2.7. Diamagnetic Contribution and the Total Knight Shift 13

2.8. The Korringa Relation 14

2.9. The Isotope Effect 16

2.10. Langevin Paramagnetism and Other Electron Spin— Nuclear Spin Interactions 17

3. Knight Shifts in Alloys and Intermetallic Compounds 22

3.1. Solvent Knight Shifts 22

3.2. Solute Knight Shifts 27

3.3. Knight Shifts in Concentrated Alloys 28

3.4. Effects of Magnetic Interactions on Knight Shifts 33

3.4.1. The Xvs. X relationship 33

3.4.2. Local magnetic moments 36

4. Dependence of J^'^on Temperature, Pressure and Other Parameters 42

4.1. Temperature Dependence 42

4.1.1. Within a single phase 42

4.1.2. Upon melting 43

4.1.3. Phase changes in solids and liquids 44

4.1.4. jT in superconductors 46

4.2. de Haas-van Alphen Effects 46

4.3. Effects of Pressure on .;f 50

5. Experimental Considerations for .if Measurements 54

5.1. Working Defmition of ./ 54

5.2. Chemical Shifts and i^ref ^^

5.3. Addition of Large Chemical Shifts 56

5.4. Drifts in Spectrometer Frequency or Field 56

5.5. Contributions due to Classical Magnetism 58

5.6. .j^" Measurements by Nonconventional Techniques 60



vi Contents

6. NMR Data Reduction Procedures from Observed Spectra 62

6.1. Isotropic Knight Shift 64

6.2. Orientation Dependence of .;f" 65

6.2.1. Axial symmetry 65

6.2.2. Lower than axial symmetry 68

6.3. First Order Quadrupole Effects 71

6.3.1. T? = 71

6.3.2. Tj^tO 76

6.4. Second Order Quadrupole Effects 79

6.4.1. T? = 79

6.4.2. T? =?t 84

6.5. Higher Than Second Order Quadrupole Effects 86

6.6. Axial Knight Shifts and First and Second Order Quadrupole Effects Present

Simultaneously 87

6.6.1. First order quadrupole and axial or anisotropic effects 89

6.6.2. Second order quadrupole and axial or anisotropic effects 89

6.7. Other Line Shape Effects 90

6.7.1. Asymmetry due to alloying 92

6.7.2. Satellites due to strong local behavior in alloying 92

6.7.3. Line shapes due to ordering 94

6.7.4. Skin depth effects 95

6.7.5. Resonance saturation, rapid passage effects, time constants 97

6.7.6. Modulation broadening 98

7. Review of Metallurgical Applications of NMR

7.1. Phase Changes and Sample Constitution 101

7.2. Wipeout Studies of Dislocations and Impurities 105

7.3. Diffusion 107

8. Description of the Critical Data Compilation and Tables 1 09

8. 1 . Scope 1 09

8.2. Organization and Degree of Evaluation of the Data 1 10

8.2.1. Metals HO

(a) NMR properties HO

(b) Properties of the nucleus 113

(c) Solid state properties 1 14

8.2.2. Alloys

(a) Solid state properties 115

(b) NMR properties 116

9. NMR Tables

9.1a. Periodic Chart of Jfin Metals at 4 and 300°K 120

9.1b. Periodic Chart of. # at the Melting Point 121

9.2a. Periodic Chart ofy/ln. Nuclear Spins, and Isotopic Abundances for NMR Isotopes 122

9.2b. Table ofy/ln Values in Order of Increasing Magnitude for NMR Isotopes 123

9.3. Relative Change of .Jfupon Melting for the Elemental Metals 125

9.4. Relative Change of .?f upon Alloying, P 126

9.5. Evaluated Knight Shifts in Metals together with other Solid State and Nuclear

Properties 129
PART II

9.6. Evaluated Knight Shifts in Alloys together with other Solid State Properties

Ag - Cs 379
PART III
9.6 cont.

Evaluated Knight Shifts in Alloys together with other Solid State Properties

Cu-Zn 1127
PART IV

1 0. 1 Addenda to Review Chapters and NMR Tables 2033

10.2 Resonance Index - An Alphabetical Index of Metals and Alloys in which

a particular nuclear resonance has been observed or discussed in the

evaluation 2317

10.3 Journal Abbreviations 2327

Contents of Previous Volumes in this Series 2339
A "Request for Errata to Metallic Shifts in NMR" form will be found at the end of each Part.



PREFACE



Over a decade ago, T. J. Rowland published in this series an essentially complete review of nuclear
magnetic resonance (NMR) studies in metals, alloys and intermetallic compounds. In the interim, the
literature of the field has grown so large that a single review cannot cover all aspects of it. The present
work deals almost exclusively with critically evaluated Knight shift data. Quadrupole effects and
relaxation time data, and NMR in ferromagnetic materials are considered with less completeness.

The Knight shift, which is measured almost exclusively by the NMR technique, has far-reaching
applications in solid state physics, physical metallurgy, and other areas. For instance, it is very sensitive
to details of a metal's Fermi surface, and to changes in the Fermi surface caused by alloying, and thus
can serve as a sensitive test of models proposed to explain the electronic structure of metals. It is also an
important analytical chemical or metallurgical tool in both basic and appbed studies. For example, the
NMR of metals such as cesium is used for precise measurement of magnetic fields and applications of
NMR to phase diagram determinations.

NMR theory is reviewed in Chapters 1 through 4, data reduction techniques are discussed in
Chapters 5 and 6, and metallurgical applications of NMR are described in Chapter 7. Critical evaluation
methods and coverage are detailed in Qiapter 8, and the evaluated Knight shifts, together with many
other physical properties that have been evaluated to a lesser extent, are treated in Chapter 9. There are
summarizing tables both in Chapter 9 and in the review chapters as pertinent to the text. For example,
nuclear spin-lattice relaxation times and Korringa ratios for solid nontransition metals are given in
Table 2.4, and pressure dependence parameters of the Knight shift for elemental metals in Table 4.1 .

Addenda listing references not included with the evaluations are provided following Chapter 9, in
order to include the latest Hterature references. Thus, to be aware of the most current work in a given
alloy, the reader should look at the bibliographies both in the evaluations a/7J the Addenda.



Vll



ACKNOWLEDGMENTS



This manuscript was prepared as one of the functions of the Alloy Data Center in the Alloy Physics
Section, Metallurgy Division, histitute for Materials Research, National Bureau of Standards. The Alloy
Data Center is part of the National Standard Reference Data System (NSRDS), which is responsible for
many continuing data collection and evaluation projects. We are grateful to the Office of Standard
Reference Data for financial support of our work. In accord with the aims of the NSRDS, the
bibliographic files from which these data were extracted will be kept current.

The authors have benefited from continual interactions with R. W. Mebs, I. D. Weisman and several
other members of the Alloy Physics Section, and with R. E. Watson of Brookhaven National Laboratory,
consultant to the Section. Assistance with the preparation of various sections of this manuscript has
been gratefully received from G. H. Fuller, P. R. Locher, and F. L. Carter for reevaluation of several of
the nuclear moments, from T. Kushida in the review section on high pressure effects, from E. F. W.
Seymour, M. N. Alexander, W. van der Lugt and S. K. Joshi in the review section on paramagnetic
susceptibilities in metals and alloys, from T. J. Rowland, A. J. McAlister, and C. Berthier in reviewing
alloying effects, and from R. R. Hewitt, L. E. Drain and many others who have made valuable
suggestions towards the preparation of the review of the Knight shift in metals and alloys. Assistance was
also very gratefully received from the above-named as well as many other speciaHsts in particular topics
of interest, in detailed reviewing of the critical evaluations of Chapter 9. Without high quality
proofreading by specialists familiar with the particular materials, accurate evaluation could not have
been achieved. Specific contributions and private communications from our reviewers are referenced and
acknowledged where appropriate throughout the critical evaluations. Among the reviewers of specific
metal or alloy evaluations are T. J. Rowland, M. N. Alexander, E. F. W. Seymour, E. R. Andrew, L. 0.
Andersson, K. Asayama, P. Averbuch, R. G. Barnes, F. Borsa, K. H. J. Buschow, Y. Chabre, R. M. Cotts,
A. M. van Diepen, L E. Drain, U. El-Hanany, N. Fernelius, F. Y. Fradin, T. H. Geballe, A. C. Gossard, R.
R. Hewitt, J. Itoh, A. Kerlin, N. Karnezos, M. Kasaya, S. Kobayashi, V. Jaccarino, P. R. Locher, W. van
der Lugt, R. G. Lye, M. Minier, Y. Nakamura, A. Narath, P. Pannisod, B. Pedersen, V. H. Schmidt, D. S.
Schreiber, R. T. Schumacher, D. L R. Setty, M. B. Stearns, I. Solomon, D. R. Torgeson, R.
Vijayaraghavan, W. W. Warren, Jr., D. L Williams, D. Zamir, and O. J. Zogal.

We are grateful to R. C. Dobbyn of the Alloy Data Center for aid with the literature search, and are
indebted to M. R. Shaver for frequent computer assistance in handling the bibliographic references. The
many diagrams and figures were drafted by L. W. Ketron and R. L. Parke.



viu



GLOSSARY OF SYMBOLS AND ABBREVIATIONS



(a) Roman Symbols

a lattice parameter.

a axial Knight shift parameter, sec defining eqn. (6.4).

<fl> hyperfine interaction parameter, see defining eqns. (2.3) and (2.5).

(flj) s-electron contribution to the hyperfine interaction parameter, see eqn. (3.10).

<fl^> <i-electron contribution to the hyperfine interaction parameter, see eqn. (3.10).

ais) atomic hyperfine coupling constant, see eqns. (2.14) and (2.15).

A number of nucleons in a given atom, or isotopic mass number, i.e. A = 1 in L\.

A component A in an alloy.

A, A' resonance parameters in the presence of isotropic and axial NMR shifts only, see defining figure.
Fig. 6.5.

A(l), A(2), . . . atom A in site 1, 2, ... in a crystal with inequivalent A sites.

AI, All, . . . high pressure phases I, II, ... of a metal, A.

A-B NMR on isotope A in A-B alloy.

b quadrupole parameter, see defining eqn. (6.9).

<6> orbital hyperfine coupling constant, see defining eqn. (2.17).

B magnetic induction field.

B component B of an alloy.

c concentration (e.g. (1 - c) A - cB, for an A-B alloy).

c lattice parameter.

c speed of Ught. In vacuum c = 2.9979246 x 10 ms""'.

Cq, cp solubility Umits of concentration for phases a, /3.

C Coulomb.

C, C excess or deficit charge as a result of an impurity added into a host, see defining eqns. (3.2) and (3.3).

e electron or proton charge, 1.60219 x lO"!^ C, 1.60219 x lO^^O emu.

eq electric field gradient (EFG).

e^qQ/h electric quadrupole coupling constant.

E energy.

AE change in electron energy; energy splitting.

Ep energy of electrons at the Fermi surface.

/ subscript referring to final state.

/ filling factor.

fa'fji fraction of a and /3 phase in two-phase alloy, by the lever rule, see eqn. (7.1).

(fe\)~ orbital degeneracy.

Eiq) hnear response function of the dynamic susceptibility of a noninteracting electron gas.

g ^-factor.

^el electronic g-facXor.

ij Landed-factor.

h Planck's constant, 6.6262 x 10 -3"* J • s, 6.6262 x 10"^"^ erg • s.

h h/2n, 1.05459 x lO-^'* J • s, 1.05459 x 10~27 erg • s.

H Hamiltonian.

.*' magnetizing field.

'^appl applied magnetizing or magnetic field.

//eff effective or hyperfine magnetic field at the nucleus, in units of magnetic field, or magnetic field
per Bohr magneton, depending on method of measurement. Other authors at times have used
magnetic field per unit spin.

f/aiom effective or hyperfine field at the nucleus for free atom.



Glossary of Symbols and Abbreviations



Roman Symbols {Continued)



Hfy^ magnetic field at resonance in a metal.

//^gf magnetic field at resonance in a reference material.

//jgj magnetic field at resonance.

A// magnetic field displacement, or shift, of resonance, for a nucleus upon changing environment.

A//* resonance parameter in the presence of isotropic and axial NMR shifts only, see defining figure,
Fig. 6.5.

I subscript referring to inital state.

/ nuclear spin quantum state, or number.

/ NMR intensity.

I{v) NMR line shape function.

If^ classical macroscopic magnetization.

/ total angular momentum quantum state, or number.

/eff effective conduction-electron conduction-electron exchange interaction parameter.

sf s-/ electron- electron exchange interaction parameter, also written T^f'^n the literature.

k, k wave vector, wave vector magnitude.

k^ Boltzmann constant, 1.3807 x 10-23 J°K-l, 1.3807 x IQ-'^ erg °K-l.

kp wave vector of an electron at the Fermi surface.

jT Knight shift, see defining eqns. (5.1) and (5.2).

JTjn anisotropic Knight shift, see defining eqns. (6.6), (6.8) and (6.20).

jTjx axial Knight shift, see defining eqns. (6.1) and (6.3) and see section 6.2.1.

•^dia contribution to ,/ from diamagnetic conduction electrons.

J^iso isotropic Knight shift, see eqn. (6.5), and see section 6.1.

JT/, jfof a metal or alloy in the liquid state.

jTq temperature-independent Knight shift associated with the conduction band Pauli susceptibility,
see eqn. (3.11).

J<^orb Knight shift term associated with the electronic orbital magnetism, see defining eqns. (2.17) and
(2.18).

■^loc(^ temperature-dependent part of the Knight shift arising from the response at the nonmagnetic site
to the induced local spin moment on a magnetic site, see eqns. (3.1 1)-(3.13).

jTl, J^2, -^Xy -^Y' ■^Z anisotropic and axial Knight shift parameters, see defining eqns. (6.3), (6.6), (6.8) and (6.21).

Jf (c, T, P, . . .) Knight shift as a function of composition, temperature, pressure, . . .

J^(A) Knight shift of metal A.

AJT change of Knight shift upon changing an experimental variable.

A Jf/jf relative change of Knight shift upon changing an experimental variable.

/ orbital angular momentum quantum state, or number of an electron.

L angular momentum quantum state, or number.

L subscript referring to metal or alloy in the liquid state.

m nuclear quantum spin state, or number.

m mass of the electron, 9.1095 x 10"^^ kg.

m* band effective mass.

m*/m band effective mass ratio.

M mass of nucleon (proton, neutron).

n integer.

n wipeout number.

«,• occupied Bloch states.

«y unoccupied Bloch states.

N Avogadro's number, 6.02205 x lO^^ mol"*.

A'^ impurity doping of semiconductors.

NiEp) density of states at the Fermi surface.

P pressure.

Pji electron probability density at the nucleus for a free atom.

Pp electron probability density at the nucleus for an electron at the Fermi surface.

q see eq.

Q nuclear electric quadrupole moment, measured in units of e. In the equations, e has been
expUcitly shown, by using eQ.

r the ratio, av^jb, see Fig. 6.27.



Glossary of Symbols and Abbreviations



XI



Roman Symbols (Continued)

r distance, usually radial, such as nucleus-electron distance.

R distance, usually radial, such as impurity nucleus to host nucleus.

R NMR intensity ratio.

5 Korringa relation parameter, see defining eqn. (2.23).

S spin quantum state, or number.

T absolute temperature.

T(. superconducting transition temperature.

^Curie Curie temperature, or ferromagnetic transition temperature.

7'Neel ^t&\ temperature, or antiferromagnetic transition temperature.

Ti spin-lattice relaxation time, longitudinal relaxation time, or thermal relaxation time.

T2 spin-spin relaxation time, transverse relaxation time, or spin-phase memory time.

V volume.

^A' ^B atomic volumes for components A, B in an alloy A-B.

V{r) spherical potential.

Z valence.



(b) Greek Symbols



a.


QA-


Q^A-B


/3,


^A.


^A-B





7.


yl2n




7/27r(proton)




7',


.7eff

7el

-TCP


!■


- 7A


. 7A-B




r


r

6
6
6


t


>.6A'*A-B






A






A






A






e






TJ






n/






e






X






M






M






M













MJV



Stoner enhancement factor, see eqns (2.8a), (2.8b), (4.2), and (4.3).

Q-phase in a metal. A, or A— B alloy, i.e. a^jn-

demagnetization factor, see eqn. (5.6).

^-phase in metal. A, or A-B alloy, i.e. ^mh-

compressibility.

coefficient of classical microscopic dipole field introduced within a Lorentz cavity, see eqn. (5.6).

magnetogyric ratio, usually referred to as gyromagnetic ratio.

4.25772 kHz/G in this compilation (see p. 1 1 3).

effective gyromagnetic ratio as measured in a material, usually including electron effects of the
material.

gyromagnetic ratio for an electron.

gyromagnetic ratio for a nucleus.

electronic specific heat, or coefficient of the electronic term in the total specific heat.

7-phase in a metal A, or A-B alloy, i.e. 7Mn-

electron-electron exchange interaction parameter, see also under J,Jsf-

■^'^ A^/Ac, relative slope of a Jf vs. c plot, see defining eqn. (3.5); AJ^/yf'and c are in fractions.

jr~* AifJAc, for an alloy in the liquid state.

mathematical infinitesimal increment, as opposed to A, a finite change or shift.

skin depth.

resonance parameter in the presence of isotropic and axial NMR shifts only, see defining eqn.
(6.19).

6-phase in a metal, A, or A-B alloy, i.e. S^^.

small but finite difference or change in a parameter, such as -^ or c, as opposed to 6, an
infinitesimal change.

conduction electron band width.

isotope effect in .W, see defining eqn. (2.28).

asymmetry parameter of Jf', see defining eqns. (6.7), (6.8) and (6.22).

quadrupole asymmetry, see defining eqn. (6.14).

phase shift between the /th component of the incoming and scattered electron wave functions, or
partial waves, see eqn. (3.1).

angle, usually between //appi and the Z axis of the crystal.

spin-orbit interaction energy.

substituted for cose in several equations.

magnetic permeability.

magnetic moment.

nuclear magnetic moment.

nuclear magneton = 5.05050 x 10"^** erg/G, in this compilation (see p.l 13).



xii Glossary of Symbols and Abbreviations

Greek Symbols (Continued)

Mproton magnetic moment of the proton = 2.79278 m^^.

M|3 Bohr magneton, 0.92741 x 10"^^ erg/G.

V frequency.

vq true resonance center for JT deductions.

I'c.g. centroid, or center of gravity of the resonance.

"H^ VL infinities in Hne shape function of a second order central resonance in presence of axial Knight

shift effect.

Vjy^ resonance frequency in a metal.

I'ref resonance frequency in a reference material.

Vq quadrupole resonance frequency, see defining eqn. (6.1 0).

i" , v^ infinities in line shape function of a second order central resonance.

"11. ''i resonance frequencies for //gppi parallel and perpendicular to the symmetry (Z) axis of a crystal
with axial symmetry.

A" displacement or shift of resonance frequency for a nucleus upon changing environment.

% Knight's ^ factor, or fractional s character, see defining eqn. (2.13).

p electrical resistivity.

p classical molecular field enliancement factor.

p charge density.

Ap change in charge distribution.

a chemical shift.

a half-width at half maximum of a resonance; half-width at maximum slopes of a Gaussian
resonance.

a resonance width parameter in the presence of isotropic and axial NMR shifts only, see eqn.
(6.19) and following defining sentence.

wave function.

azimuthal (Eulerian) angle.

X magnetic susceptibility.

Xdia diamagnetic part of the magnetic susceptibility.

'^^dfa" contribution to the susceptibility by the diamagnetic conduction electrons.

Xd?a'^^ core electron contribution to the diamagnetic susceptibility.

'^exp experimental total susceptibihty.

'^rb orbital contribution to the susceptibility.

'^P Pauli paramagnetic susceptibility.

'^p Pauli susceptibility as derived from electronic specific heats.

"Xp Pauli free electron susceptibility.

X^ unenhanced independent particle susceptibility.

XV total volume susceptibility.

^ wave function.

\^ angle.

w angular frequency (or rf), = 2tiv.

^ angle.



(c) Other Symbols, Abbreviations, Units, Usages

* asterisk designates unstable isotope (e.g. ^^^U*).

( ) (i) used as brackets in written text, for comments, etc.

(ii) used to indicate magnitude of error in decimal(s) immediately preceding bracket, e.g.
jr= 0.12(2)% is synonymous with jr= (0.12 ± 0.02)%.

I 1 (i) used as a symbol for an average of the bracketed quantity.

(ii) used in numerical data evaluations (Chapter 9) if the statement enclosed is deduced in the
evaluation, as opposed to a value given in a report, except when employed in equations.

[o] used in graphical presentations of data evaluations (Chapter 9) if the graphical point is deduced

in the evaluation, as opposed to a value given in the report.

'^All "NaCl style to designate the resonance frequency of ^'^Al in Al metal divided by the resonance
frequency of ^^Na in NaCl.

atm atmosphere.



Glossary of Symbols and Abbreviations



XI 11



Other Symbols, Abbreviations, Units, Usages (Continued)



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