Electronic Structure and Properties

451 Pages·1981·8.988 MB·English

by  FRANK Y. FRADIN (Eds.)

TREATISE EDITOR
HERBERT HERMAN
Department of Materials Science and Engineering
State University of New York at Stony Brook
Stony Brook, New York
ADVISORY BOARD
J. W. CHRISTIAN, F.R.S. P. B. HIRSCH, F.R.S.
Oxford University Oxford University
Oxford, England Oxford, England
M. E. FINE R. I. JAFFEE
Northwestern University Electric Power Research Institute
Evanston, Illinois Palo Alto, California
J. FRIEDEL E. I. SALKOVITZ
Université de Paris U.S. Office of Naval Research
Orsay, France Arlington, Virginia
A. GOLAND A. SEEGER
Department of Physics Max-Planck-Institut
Brookhaven National Laboratory Stuttgart, Germany
Upton, New York
J. J. HARWOOD J. B. WACHTMAN
Ford Motor Company National Bureau of Standards
Dearborn, Michigan Washington, D.C.
TREATISE ON MATERIALS SCIENCE
AND TECHNOLOGY
VOLUME 21
ELECTRONIC STRUCTURE AND PROPERTIES
EDITED BY
FRANK Y. FRADIN
Materials Science Division
Argonne National Laboratory
Argonne, Illinois
1981
ACADEMIC PRESS
A Subsidiary of Harcourt Brace Jovanovich, Publishers
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COPYRIGHT © 1981, BY ACADEMIC PRESS, INC.
ALL RIGHTS RESERVED.
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United Kingdom Edition published by
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Library of Congress Cataloging in Publication Data
Main entry under title:
Electronic structure and properties.
(Treatise on materials science and technology ;
v. 21)
Includes bibliographies and index.
Contents: Electronic structure of perfect and
defective solids / A. J. Freeman—Photoelectron
spectroscopy as an electronic structure probe /
B. W. Veal—Electronic structure and the electron-
phonon interaction / W. H. Butler—[etc.]
1. Electronic structure. 2. Free electron
theory of metals. I. Fradin, Frank Y. II. Series.
TA403.T74 vol. 21 [QC176.8.E4] 620.1'ls 81-2457
ISBN 0-12-341821-6 [530.4Ί] AACR2
PRINTED IN THE UNITED STATES OF AMERICA
81 82 83 84 9 8 7 6 5 4 3 2 1
List of Contributors
Numbers in parentheses indicate the pages on which the authors' contributions begin.
W. H. BUTLER (165), Metals and Ceramics Division, Oak Ridge National
Laboratory, Oak Ridge, Tennessee 37830
Z. FISK (297), Institute for Pure and Applied Physical Sciences, University
of California, San Diego, La Jolla, California 92093
E. S. FISHER (223), Materials Science Division, Argonne National Labora­
tory, Argonne, Illinois 60439
A. J. FREEMAN (1), Department of Physics and Astronomy, Northwestern
University, Evanston, Illinois 60201
P. JENA (351), Physics Department, Michigan Technological University,
Houghton, Michigan 49931
S. G. STEINEMANN (223), University of Lausanne, Lausanne, Switzerland
B. W. VEAL (99), Materials Science Division, Argonne National Laboratory,
Argonne, Illinois 60439
G. W. WEBB (297), Institute for Pure andl Applied Physical Sciences, Uni­
versity of California, San Diego, La Jolla, California 92093
VII
Foreword
Materials science has evolved to its present advanced state through
contributions from numerous facets of the solid-state sciences. Physics and
chemistry of materials, metallurgy, ceramics, and polymer science are all
merging into more clearly defined common themes. This convergence is well
exemplified by the topic to which this volume is addressed: electronic
structure and properties.
Electronic-related properties have always been central to the growth of
materials science. In recent years, new, fresh theoretical approaches and
newly developed experimental techniques have allowed more realistic de­
terminations to be made of band structure and energy states in pure systems
and in a wide variety of solid solutions. Notable progress has been made in
understanding and predicting phase stability, and this in turn has initiated
new approaches to alloy design.
Simplified interpretations of complex and cross-linked phenomena, though
required and intellectually satisfying, do not necessarily lead readily to
reasonable predictions of behavior. To a large extent, the evolution of alloy
theory had to wait for the introduction of very sensitive and high resolution
experimental probes (e.g., photoelectron spectroscopy, positron annihila­
tion), with an attendant appreciation for the theoretically based strengths
and weaknesses of these techniques.
This volume, which has been edited by Frank Y. Fradin, has come at a
propitious time, when experimental technology and electron theory are
expanding significantly in a coordinated fashion. The near future holds
great promise for studies of electronic structure of materials and for those
applications that are bound to result from these activities.
H. HERMAN
IX
Prefoce
There has been remarkable progress in the understanding of the electronic
structure and properties of materials in the past two decades, due in large
part to impressive advances in various spectroscopies for directly measuring
the electronic structure, e.g., photoemission spectroscopy, as well as to
advances in the theoretical methods of calculating the electronic structure of
complex materials, e.g., the local density approach, supercell methods, and
the coherent potential approximation. The improved understanding of the
electronic structure has led to exciting new insights into a number of
physical properties, e.g., superconductivity, phonon and lattice instabilities,
magnetism, surface activity, energetics of point defects, and electron trans­
port in complex materials. In this volume we present these new develop­
ments in electron theory and electron spectroscopies. The approach, while
pedagogical in nature, avoids becoming bogged down in computational or
experimental detail. The contributing chapters are exemplary rather than
comprehensive, although sufficient references are given to help the inter­
ested reader find more detail. Emphasis in the chapters is on transition
metals, alloys, and intermetallic compounds, with a number of illustrative
examples from the oxides and silicates.
Although the electron theory of metals and alloys was developed by Mott
and others as early as the 1930s, quantitative success of the theory was
restricted to the simple alkali or noble metals. Of greater interest to the
materials scientist are the alloys and compounds of technological impor­
tance for their interesting physical properties. As A. J. Freeman points out
in Chapter 1, it has only been within the past 20 years that abinitio energy
band structures have developed to the point that confidence could be placed
on their predictions for highly complex structures. In his chapter on
electronic structure, Dr. Freeman introduces the local density functional
approximation and then describes the modern energy band methods. He
also introduces the supercell method for treating the case of reduced (i.e.,
surfaces) or broken (i.e., defects, impurities) translational invariance and the
XI
XU PREFACE
coherent potential approximation for treating the disordered concentrated
alloy problem. A number of illustrative examples are given in Chapter 1
that serve to relate the electronic structure calculations both to the various
electron spectroscopies and to a number of physical phenomena discussed
in the other chapters.
Photoelectron-emission spectroscopy is perhaps the most important spec-
troscopy to establish both qualitative and quantitative verification of the
electron theory of solids. In Chapter 2, B. W. Veal introduces the ultraviolet
and the x-ray photoemission techniques and describes the application of the
techniques to study both core-electron and valence-electron structures. Dr.
Veal includes illustrative examples of metals, alloys, oxides, hydrides, as
well as amorphous materials.
The electron-phonon interaction is the central theme of many exciting
phenomena in modern studies of metallic materials. In Chapter 3, W. H.
Butler introduces the theory of the electron-phonon interaction. He then
discusses the ramifications of the electron-phonon interaction for the
superconducting transition temperature, lifetimes of phonons, lattice ther­
mal resistivity, and interatomic force constants or phonon frequencies.
Specific examples are given for the free electron metals, the transition
metals, and the A-15 (e.g., VSi) type compounds.
3
The elastic properties of transition metals is the subject of Chapter 4 by
S. G. Steinemann and E. S. Fisher. In this chapter emphasis is placed on the
effect of deformation on the Fermi surface and the resultant systematic
dependence of the elastic constants on the electronic structure. A heavy
emphasis is given to the body-centered-cubic transition-metal alloys, which
have received the most exhaustive theoretical and experimental attention.
Other examples include the face-centered-cubic and the hexagonal-
close-packed transition metals and the A-15 superconductors. A short
section on the effects of interstitial hydrogen in niobium is also included.
The electrical resistivity of metals and alloys is the subject of Chapter 5
by Z. Fisk and G. W. Webb. In this chapter Drs. Fisk and Webb discuss the
nature of defect-dominated electron scattering, including concentrated al­
loys and liquid metals, as well as contributions to the electrical resistivity
due to the electron-electron interaction, the electron-phonon interaction,
and magnetic effects. A discussion of the electrical resistivity changes
occurring at various types of phase transformations is also included.
In the final chapter, P. Jena reviews the electronic structure of point
defects in metals. In this chapter Dr. Jena surveys the various theoretical
formulations for the point-defect problem. He then illustrates the theoretical
results and makes contact with experimental probes such as nuclear
quadrupole and nuclear magnetic resonance, impurity resistivity, muon spin
rotation, and positron annihilation. Specific examples include hydrogenlike
impurities in metals, including isotope effects, and vacancies in metals.
J
Electronic Structure of Perfect and Defective Solids
A. J. FREEMAN
Department of Physics and Astronomy
Northwestern University
Evanston, Illinois
I. Introduction and Historical Perspective 1
II. Theoretical Methods 2
A. Complexities and Approximations Required for Treating the Many-Body
Problem of a Solid in a Solvable, Tractable Form 3
B. Local Density and Local Spin Density Functional Theories 4
C. Energy Band Methods 6
D. LDF-Energy Band Approach 14
E. Problems of Itinerant versus Localized Electron Distributions and the
Treatment of Non-Ground-State Properties 15
F. Supercell Method for Systems Having Broken or Reduced Symmetry 17
G. Coherent Potential Approximation (CPA) and KKR-CPA 22
III. Illustrative Examples 25
A. Charge and Spin Densities 25
B. Cohesive Properties of Solids 36
C. Electronic Structure of Metals 42
D. Complex Systems 52
E. Electronically Driven Phase Transitions and Phonon Anomalies 58
F. Surfaces, Surface Magnetization, and Chemisorption in Metals 67
G. Disordered Alloys 80
H. Microstructure Materials and Their Properties 87
References 90
I. Introduction and Historical Perspective
The past decade has witnessed a coming of age of the energy band
approach to the study of materials. During this time the energy band
method has become an increasingly powerful and sophisticated tool of the
solid-state physicist and materials scientist for theoretically studying the
multitudinous and increasingly complex properties of matter in the con­
densed state. Thus today, information derived from energy band studies are
l
Copyright © 1981 by Academic Press, Inc.
All rights of reproduction in any form reserved
ISBN-0-12-341821-6
2 A. J. FREEMAN
increasingly attracting the interest of materials scientists for solutions and/or
understanding of phenomena (including some in the more classical metal­
lurgical domain) previously thought to be too complex for theoretical
treatment.
The manifold successes of the band approach, which we now take for
granted, are all the more remarkable when one recalls that only some 20
years ago very little confidence or physical meaning was attributed to ab
initio energy band structures (i.e., eigenvalue phenomena). The status of
band theory today may be viewed as a direct result of the fact that in the
past decade new sophisticated experiments on both traditional materials
and those having complex crystallographic structures have demanded not
only theoretical descriptions of eigenvalue phenomena but also detailed and
precise wave functions with which to determine the expectation values of
different observable operators. Such a demanding test of the predictions of
one-electron theory has the additional virtue in permitting, by their com­
parison with experiment, accurate determinations of the relative magnitude
and importance of many-body effects in real solids. Thus there had devel­
oped considerable interest in the Hohenberg-Kohn-Sham (Hohenberg and
Kohn, 1964; Kohn and Sham, 1965; Sham and Kohn, 1966) local density
functional (LDF) formalism for investigation of various ground-state prop­
erties of solids, despite the usual difficulties of solving the associated
one-particle equation characterized by a multicenter nonspherical potential.
Aside from providing a rigorous basis and justification of the single-particle
energy band description of the ground-state properties of materials, it has
led to accurate, tractable, computational schemes for describing them from
first principles.
In this chapter we describe and discuss some of these developments in the
local-density theory energy band approach and indicate by means of
selected examples some of the richness and variety of properties and
pheonomena which are and can be studied. It will also give an overview of
the detailed interaction that can now be made between ab initio theoretical
calculations and experiment, it being well understood that only through this
close interplay will a more fundamental understanding of electronic struc­
ture and properties emerge.
II. Theoretical Methods
The very success of the energy band approach and its recent great
popularity (as attested to by the proliferation of such approaches and the
large growth in the number of its practitioners) make it imperative that we
ELECTRONIC STRUCTURE OF PERFECT AND DEFECTIVE SOLIDS 3
discuss the basis of the method and its underlying assumptions and ap­
proximations in order to better understand the applicability (and reliability)
of the results obtained and to assess their validity relative to experiment.
A. Complexities and Approximations Required for Treating the
Many-Body Problem of a Solid in a Solvable, Tractable Form
The energy band method for calculating electronic eigenstates in crystals
is based on a number of simplifying assumptions and approximations that
reduce the many-body problem, involving the interactions between all the
particles—electrons and nuclei—in the system, to a one-electron or in­
dependent electron model. (The reason for these approximations is clear:
the many-body problem for the crystal entails the solution of Schrödinger's
equation for 1023 nuclei and electrons and is a completely hopeless task.) It
is important to keep these approximations in mind as they are not com­
pletely justifiable and may affect seriously some of the physical results
obtained.
The first of these is the zero-order Born-Oppenheimer approximation,
which essentially amounts to neglecting the electron-phonon interaction
and reduces the problem to that of an interacting electron system in the
field of fixed nuclear potentials. Actually, as discussed at length in Chapter
3, the electron-phonon interaction plays an important role in a number of
physical phenomena, the most famous being its essential role as origin of
superconductivity in the Bardeen- Cooper- Schlief fer (BCS) theory. In nor­
mal metals it can cause an enhancement of measured electron masses,
electron velocities, g factors, the measured oscillator strength for optical
transitions, density of states at the Fermi energy as obtained from specific
heat measurements, etc. In general, it does not appear to affect measured
Fermi surface dimensions, which therefore may be directly compared with
predictions arising from the theoretical calculations.
The direct solution of the many-electron Hamiltonian with its 1023
variables is obviously not possible. Thus we must make an approximation
that separates the variables to yield an effective single-particle equation that
is the approximate Hamiltonian of the energy band model. There have been
two "justifications" of this model: one is based on the Hartree-Fock
formalism; the other arises from a more generalized many-body interacting
homogeneous electron gas approach for treating the ground state of a
system—the so-called local density functional theory.
The most recent justification of the band model is the local density
functional formalism of Hohenberg, Kohn, and Sham, which we shall
describe more fully in Section ΙΙ,Β (Hohenberg and Kohn, 1964; Kohn and