COMPUTATIONAL SOLID STATE PBYSICS

Transcription

1 COMPUTATIONAL SOLID STATE PBYSICS

2 THE IBM RESEARCH SYMPOSIA SERIES 1971: Computational Methods in Band Theory Edited by P. M. Marcus, J. F. Janak, and A. R. Williams 1972: Computational Solid State Physics Edited by F. Herman, N. W. Dalton, and T. R. Koehler Sparse Matrices and Their Applications Edited by D. J. Rose and R. A. Willoughby

3 COMPUTATIONAL SOLID STATE PBYSICS Proceedings of an International Symposium Held October 6-8,1971, in Wildbad, Germany Edited by Prank Bennan, Norris W. Dalton, and Thomas B. Koehler Large-Scale Scientific Computations Department IBM Research Laboratory San Jose, California 9? PLENUM PRESS NEW!ORK-LONDON 1972

4 Library of Congress Catalog Card Number ISBN-13: e-isbn-13: DOl: / Plenum Press, New York Softcover reprint of the hardcover 1st edition 1972 A Division of Plenum Publishing Corporation 227 West 17th Street, New York, N.Y United Kingdom edition published by Plenum Press, London A Division of Plenum Publishing Corporation Davis House (4th Floor), 8 Scrubs Lane, Harlesden, NW10, 6SE, London, England All rights reserved No part of this publication may be reproduced in any form without written permission from the publisher

5 PREFACE During the past 20 years, solid state physics has become one of the major branches of physics. 1-2 Today over one-third of all scientific articles published in physics deal with solid state topics. 3 During the last two decades, there has also been ra~id growth of scientific computation in a wide variety of fields. -5 The combination of solid state physics and comp~tation may be termed computational solid state physics. This emerging field is distinguished from theoretical solid state physics only to the extent that electronic computers rather than slide rules or backs of envelopes are used to solve numerical or logical problems, test scientific hypotheses, and discover the essential physical content of formal mathematical theories. Papers in computational solid state physics are widely scattered in the literature. They can be found in the traditional physics journals and review series, such as The Physical Review and Solid State Physics; in more specialized publications, such as Journal of Computational Physics, Computer Physics Communications, and Methods in Computational Physics; and in the proceedings of a number of recent conferences and seminar courses. 6-9 Plans for holding an International Symposium on Computational Solid State Physics in early October 1971 were formulated by Dr. Gerhard Hubner, IBM Germany, Sindelfingen, and one of us (F.H.) in Copenhagen in June The location chosen was Wildbad, Germany, a picturesque health resort in the Black Forest. The objective was to bring together a small number of physicists with a view to exploring future experimental and theoretical opportunities in solid state physics, with particular emphasis on problems that lend themselves to computational investigation. It was felt that such a symposium would also serve as a means for establishing computational solid state physics as a subject of interest in its own right. In order to encourage in-depth discussions, the scope of the symposium was limited to a few key topics: electronic band structure, exchange and correlation effects, harmonic and anharmonic lattice dynamics, localized imperfections and dislocations, and solid state astrophysics. Experimentalists and theoreticians representing each v

6 PREFACE of these topics were invited, in the expectation that this would lead to a broader exchange of information and ideas, an expectation borne out in practice. Inclusion of the section on solid state astrophysics was inspired by a paper on solid stars presented by Professor Malvin A. Ruderman of Columbia University at a Gordon Conference in the summer of A popular account of this subject has recently been published. lo Most of the papers presented at the symposium are included in this volume, which is being published as the second volume of the IBM RESEARCH SYMPOSIA SERIES. The organizers of the symposium are grateful to the contributors for their excellent lectures and their carefully prepared manuscripts. Informal presentations by Dr. John Hubbard (remarks on the exchange-correlation problem), Prof. Carl Moser (highlights report on the Menton Conference 9 ), and Prof. Lars Hedin (highlights report on the Strathclyde Conference ll ) are not included. The organizers are grateful to these three speakers for their valuable off-the-record comments. We also thank Plenum Press for their cooperation and efforts to expedite rapid publication. This volume is divided into six sections. Each has an introductory essay which sets the stage for the remaining papers in the section. All the papers contained in this volume are intended for graduate students as well as research workers in solid state physics and related disciplines. Most have extensive bibliographies which should facilitate further reading. The first section is concerned with experimental studies of the electronic structure of solids, particularly spatial dispersion (Yu and Cardona), photoemission (Eastman and Williams); synchrotron radiation (Haensel and Sonntag); and positron annihilation (Berko and Weger). As noted in the introductory lecture (Madelung), current progress in experimental band structure determination represents the culmination of nearly twenty years of fruitful interplay between theory and experiment. With the development of ever more powerful theoretical and experimental techniques, and with the growing importance of numerical studies, this subject has now reached a high level of development. However, much remains to be done on the band structure of important but as yet poorly understood materials such as magnetic semiconductors, and on materials such as the transition metal oxides where one-electron methods appear to be inadequate. All the papers in this section contain detailed illustrations of the value of strong interaction between theory and experiment. They all emphasize the importance of calculating not only the band structure, but also the physical observables that can be compared directly with experiment. There is still need for improved energy band interpolation schemes, particularly in situations involving extended energy ranges, and for refined zonal integration methods. The analysis of future experiments will undoubtedly stimulate more

7 PREFACE vii serious theoretical studies of excited electron transport and surface escape mechanisms, inner shell excitations, multiple electron excitations, and conduction electron momentum distributions. The second section is devoted to theoretical studies of the electronic structure of solids. Some of the papers emphasize the progress that has been made using empirical methods (Treusch, Schneider and Stoll, Rudge and Ortenburger), while others report progress made with first-principles methods (Dalton, Bross and Stohr, Christensen, Rossler). These two approaches appear to be complementary, and future progress will undoubtedly depend not only on continuing advances on both sides, but on cross fertilization. There is also a short contribution on atomic arrangements in amorphous semiconductors (Henderson) and a short research note (Dalton and Schreiber) showing the enormous potential of computer graphics in solid state applications. The third section is concerned with exchange and correlation effects in solids. Following a broad and highly instructive introductory survey of the correlation problem (Lowdin), there are detailed discussions of the effect of electron correlation on charge and momentum distributions in solids based on a density matrix development (March and Stoddart); and of recent progress in the theory and application of local exchange-correlation potentials in realistic solids (Lundqvist and Lundqvist, Hedin). Also included are short contributions on improved statistical exchange approximations (Herman and Schwarz) and on cohesive energy calculations for metallic lithium (Sperber and Calais). The work reported on local exchange-correlation potentials appears extremely promising, though its merits cannot be judged until such potentials are incorporated into band structure calculations which are free of numerical and physical noise (inadequate convergence, lack of self-consistency, neglect of relativistic effects, low standards of numerical accuracy, etc.). The same can be said for the work on charge and momentum distributions and on improved exchange approximations. The fourth section on solid state astrophysics (Biermann, Borner, Baym) indicates how such familiar solid state ideas as electron gas degeneracy, equation of state, crustal fracture, plastic flow, superconductivity, and superfluidity are being applied to the extreme states of matter exemplified by neutron stars and white dwarfs, and how these ideas are being used to provide models for these objects and plausible explanations for observations on pulsars. The fifth section on lattice dynamics includes an introductory survey (Koehler), a highlights report on the Rennes Conference

8 viii PREFACE (Ba1kanski), discussions of experimental and theoretical studies of lattice vibrational spectra (Cowley, Bi1z, Pick), and surveys of recent progress in the theory of anharmonic lattice dynamics (Koehler, Horner). Progress in these areas has been rapid, as all these papers indicate. It is hoped that with continuing progress in electronic structure and lattice dynamical studies these two areas will be brought closer together, and a unified treatment of electrons and lattice vibrations in solids will become possible. There has been some unification at the empirical level, but much remains to be done; at the first-principles level, unification is still remote. The final section is concerned with selected topics in the defect solid state. This is a field that has already seen considerable computational effort, particularly in studies of radiation damage. Following an introductory survey (Lidiard), there are discussions of infrared and optical studies of localized vibrational modes (Ba1kanski), the properties of point defects in ionic solids (Lidiard and Norgett), computer simulation of point and line defects in metals (Bu110ugh), and the properties of dislocations in anisotropic media (Lothe). These papers place considerable emphasis on the interplay of microscopic and macroscopic concepts, and on the value of computation in sharpening our understanding of these concepts in complex physical situations. The symposium was sponsored by the IBM World Trade Corporation, witq IBM Germany serving as the regional host. On behalf of all the participants, we wish to express our appreciation to the sponsors for their generous support, particularly Dr. Gerhard Hubner, representing IBM Germany, and Dr. Gary S. Kozak, representing IBM World Trade Headquarters, New York. We are grateful to Dr. Karl Ganzhorn for his Welcoming Remarks on behalf of IBM, and to the staff of IBM Germany for making all the necessary arrangements and for insuring the success of the symposium through their untiring efforts. Finally, the editors of this volume wish to express their appreciation to Mrs. Patricia B. Rodgers for her assistance in the preparation of the final manuscript, and to Miss Gerdi M. Herold for her help with the correspondence. Frank Herman IBM San Jose Research Laboratory Symposium Chairman Paul Schweitzer "IBM Germany, Sinde1fingen Symposium Manager REFERENCES 1. "Solid-State Physics and Condensed Matter," National Research Council, National Academy of Sciences, Washington, D.C., 1966, Publication 1295A (reprinted from: Physics: Survey and Outlook Reports on the Subfie1ds of Physics).

9 PREFACE ix 2. "Research in Solid-State Sciences," National Academy of Sciences, Washington, D.C., 1968, Publication L. J. Anthony, H. East and M. J. Slater, Rep. Prog. Phys. 32, 709 (1969). 4. Computers and Their Role in the Physical Sciences, edited by S. Fernbach and A. H. Taub (Gordon and Breach, New York, 1970). 5. Computers and Computation, Readings from Scientific American. (W. H. Freeman and Co., San Francisco, 1971). 6. Computational Methods in Band Theory, Proceedings of a Conference held at IBM Thomas J. Watson Research Center, Yorktown Heights, New York, May 1970, edited by P. M. Marcus, J. F. Janak and A. R. Williams (Plenum Press, New York, 1971). 7. Computational Physics, Proceedings of the Second Annual Conference on Computation.al Physics held at Imperial College, London, September 7-9, 1970 (The Institute of Physics and The Physical Society, London, 1970). 8. Computing as a Language of Physics, Seminar Course held at the International Center for Theoretical Physics, Trieste, August 2-20, 1971 (International Atomic Energy Agency, Vienna, 1972), in press. 9. Perspectives for Computation of Electronic Structure in Ordered and Disordered Solids, International Colloquium held at Menton, France, September 20-24, 1971, to be published as special issue of Journal de Physique, Spring M. A. Ruderman, "Solid Stars," in Scientific American, February 1971, p Band Structure Spectroscopy of Metals and Alloys, Proceedings of an International Conference held at Strathclyde, Glasgow, Scotland, September 27-30, 197.1, to be published. 12. I. E. Sutherland, "Computer Displays," in Scientific American, June 1970, p Advanced Computer Graphics--Economics Techniques and Applications, edited by R. D. Parslow and R. E. Green (Plenum Press, London and New York, 1971).

10 CONTENTS 1. Experimental Studies of the Electronic Structure of Crystals INTRODUCTORY REMARKS Otfried Madelung SPATIAL DISPERSION INDUCED BIREFRINGENCE IN CUBIC SEMICONDUCTORS Peter Y. Yu and Manuel Cardona PHOTOEMISSION STUDIES OF THE ELECTRONIC STRUCTURE OF SOLIDS Dean E. Eastman and Arthur R. Williams INVESTIGATION OF INNER SHELL EXCITATIONS IN SOLIDS BY SYNCHROTRON RADIATION Ruprecht Haensel and Bernd Sonntag POSITRON ANNIHILATION EXPERIMENTS AND THE BAND STRUCTURE OF V3Si Stephan Berko and Meir Weger Theoretical Studies of the Electronic Structure of Crystals INTRODUCTORY REMARKS Norris W. Dalton EMPIRICAL BAND CALCULATIONS Joachim Treusch ON THE THEORY OF METALLIC LITHIUM Toni Schneider and Eric Stoll GENERALIZATIONS OF THE RELATIVISTIC OPW METHOD INCLUDING OVERLAPPING AND NON-OVERLAPPING ATOMIC ORBITALS Norris W. Dalton

11 xii MAPW-CALCULATIONS WITH SCREENED EXCHANGE APPLICATION TO COPPER Helmut Bross and Herbert Stohr CONTENTS 143 SOME REMARKS ON CURRENT RAPW CALCULATIONS FOR SILVER, MOLYBDENUM, AND VANADIUM Niels Egede Christensen RECENT KKR BAND CALCULATIONS Ulrich Rossler THE ATOMIC ARRANGEMENTS AND RADIAL DISTRIBUTION FUNCTIONS OF AMORPHOUS SILICON AND GERMANIUM Douglas Henderson OPTICAL PROPERTIES OF POLYTYPES OF GERMANIUM William E. Rudge and Irene B. Ortenburger CHARGE DENSITY IN THE GALLIUM ARSENIDE CRYSTAL Norris W. Dalton and Donald E. Schreiber Treatment of Exchange and Correlation Effects in Crystals INTRODUCTORY REMARKS Per-Olov Lowdin 191 EFFECTS OF ELECTRON CORRELATION WITH PARTICULAR 205 REFERENCE TO CHARGE AND MOMENTUM DENSITIES IN CRYSTALS Norman H. March and J. Colin Stoddart LOCAL EXCHANGE-CORRELATION POTENTIALS Bengt I. Lundqvist and Stig Lundqvist EXCHANGE-CORRELATION POTENTIALS Lars Hedin AN IMPROVED STATISTICAL EXCHANGE APPROXIMATION Frank Herman and Karlheinz Schwarz COHESIVE ENERGY OF THE LITHIUM METAL BY THE AMO METHOD Gunnar Sperber and Jean-Louis Calais Solid State Astrophysics INTRODUCTORY REMARKS Ludwig Biermann 257

12 CONTENTS OBSERVATIONAL EVIDENCE FOR SOLID STATE PHENOMENA IN PULSARS Gerhard Borner NEUTRON STARS AND WHITE DWARFS Gordon Baym xiii 5. Lattice Dynamics INTRODUCTORY REMARKS Thomas R. Koehler NOTE ON THE RENNES CONFERENCE ON PHONONS Minko Balkanski NEUTRON AND X-RAY INELASTIC SCATTERING BY LATTICE VIBRATIONS Roger A. Cowley PHONON DISPERSION RELATIONS Heinz Bilz MICROSCOPIC THEORY OF PHONONS IN SOLIDS Robert M. Pick COMPUTATIONAL ASPECTS OF ANHARMONIC LATTICE DYNAMICS 339 Thomas R. Koehler ANHARMONIC LATTICE DYNAMICS: Heinz Horner RENORMALIZED THEORY Localized Imperfections and Dislocations INTRODUCTORY REMARKS Alan B. Lidiard LOCALIZED VIBRATIONAL MODES IN CRYSTALS Minko Balkanski POINT DEFECTS IN IONIC CRYSTALS Alan B. Lidiard and Michael J. Norgett COMPUTER SIMULATION OF POINT AND LINE DEFECTS IN IRON AND COPPER Ronald Bullough DISLOCATIONS IN ANISOTROPIC MEDIA Jens Lothe

13 xiv List of Contributors Subject Index CONTENTS