OXFORD MONOGRAPHS ON GEOLOGY AND GEOPHYSICS Series Editors H. Charnock J. F. Dewey S. Conway Morris A. Navrotsky E. R. Oxburgh R. A. Price B. J. Skinner OXFORD MONOGRAPHS ON GEOLOGY AND GEOPHYSICS 1. DeVerle P. Harris: Mineral resources appraisal: mineral endowment, resources, and potential supply: concepts, methods, and cases 2. J. J. Veevers (ed.): Phanerozoic earth history of Australia 3. Yang Zunyi, Cheng Yuqi, and Wang Hongzhen (eds.): The geology of China 4. Lin-gun Liu and William A Bassett: Elements, oxides, and silicates: high- pressure phases with implications for the Earth's interior 5. Antoni Hoffman and Matthew H. Nitccki (eds.): Problematic fossil taxa 6. S. Mahmood Naqvi and John J. W. Rogers: Precambrian geology of India 7. Chih-Pei Chang and T. N. Krishnamurti (eds.): Monsoon meteorology 8. Zvi Ben-Avraham (ed.): The evolution of the Pacific Ocean margins 9. Ian McDougall and T. Mark Harrison: Geochronology and thermochronology by the 40Ar/39Ar method 10. Walter C. Sweet: The conodonta: morphology, taxonomy, paleoecology, and evolutionary history of a long-extinct animal phylum 11. H. J. Melosh: Impact cratering: a geologic process 12. J. W. Cowie and M. D. Brasier (eds.): The Precambrian-Cambrian boundary 13. C. S. Hutchinson: Geological evolution of south-east Asia 14. Anthony J. Naldrctt: Magmatic sulfide deposits 15. D. R. Prothero and R.M. Schoch (eds.): The evolution of perissodactyls 16. M. Menzies (ed.): Continental mantle 17. R. J. Tingey (ed.): Geology of the Antarctic 18. Thomas J. Crowley and Gerald R. North: Paleoclimatology 19. Gregory J. Retallack: Miocene paleosols and ape habitats in Pakistan and Kenya 20. Kuo-Nan Liou: Radiation and cloud processes in the atmosphere: theory, observation, and modeling 21. Brian Bayley: Chemical change in deforming materials 22. A. K. Gibbs and C. N. Barron: The geology of the Guiana Shield 23. Peter J. Ortoleva: Geochemical self organization 24. Robert G. Coleman: Geologic evolution of the Red Sea 25. Richard W. Spinrad, Kendall L. Carder, and Mary Jane Perry: Ocean optics 26. Clinton M. Case: Physical principles of flow in unsaturated porous media 27. Eric B. Kraus and Joost A. Businger: Atmosphere-ocean interaction, second edition 28. M Solomon & D. I. Groves: The geology and origins of Australia's mineral deposits 29. R. L. Stanton: Ore elements in arc lavas 30. P. Wignall: Black shales 31. Orson L. Anderson: Equations of state of solids for geophysics and ceramic science EQUATIONS OF STATE OF SOLIDS FOR GEOPHYSICS AND CERAMIC SCIENCE ORSON L. ANDERSON Institute of Geophysics and Planetary Physics University of California at Los Angeles New York Oxford OXFORD UNIVERSITY PRESS 1995 Oxford University Press Oxford New York Toronto Delhi Bombay Calcutta Madras Karachi Kuala Lumpur Singapore Hong Kong Tokyo Nairobi Dar es Salaam Cape Town Melbourne Auckland Madrid and associated companies in Berlin Ibadan Copyright © 1995 by Oxford University Press, Inc. Published by Oxford University Press, Inc., 200 Madison Avenue, New York, New York 10016 Oxford is a registered trademark of Oxford University Press All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior permission of Oxford University Press. Library of Congress Cataloging-in-Publication Data Anderson, O. L. (Orson L.) Equations of state of solids for geophysics and ceramic science. Orson L. Anderson p. cm. — (Oxford monographs on geology and geophysics: 31) Includes index. ISBNO-19-505606-X 1. Geophysics. 2. Equations of state. 3. Thermodynamics. I. Title. II. Series: Oxford monographs on geology and geophysics: no. 31 QE501.3.A53 1995 550—dc20 94-2242 Since this page cannot accommodate all the copyright notices, the two pages that follow constitute an extension of the copyright page. 987654321 Printed in the United States of America on acid-free paper Permissions Laws die, books never. —Edward Bulwer-Lytton The quotation on page ix is from The Poetry of Robert Frost, edited by Ed- ward Connery Lathem, copyright 1944 by Robert Frost; copyright 1916© 1969 by Henry Holt and Company, Inc. Reprinted by permission of Henry Holt and Company, Inc. Permission for use also granted by the Estate of Robert Frost and Jonathan Cape, Ltd., Publishers. The quotation on page 157 is from The Logic of Modern Physics, by P.W. Bridgman, copyright 1927, 1960 edition, copyright 1955, by P.W. Bridg- man. Reprinted by permission of the MacMillan Publishing Company. The quotation on page 1 by Professor Julian Schwinger has been used by him in many of his lectures and talks. It is very appropriate for Part I, because we show there that the high temperature experimental data on insulators obey the high temperature limit of the quasiharmonic approxi- mation of statistical mechanics much better than expected. Quotation used with permission of Professor Julian Schwinger. The quotation on page 221 is from American Mathematical Physicist Par Excellence, by Raymond J. Seeger, copyright 1978; copyright 1974 by Perg- amon Press, Ltd. Professor Seeger died in 1992. Quotation used with permission of Mrs. Vivian Seeger. The quotation on page 383 is from Of All Things! Classic Quotations from Hugh Nibley, compiled and edited by Gary Gillum. Salt Lake City, Deseret Books and F.A.R.M.S.: copyright 1993, p. 226. Oral permission to use granted by Deseret Books and F.A.R.M.S. Data in Table A-7, Appendix, reprinted from Anderson et al., The Reviews of Geophysics, 30, 58-63, 1992. Figures 1.1, 1.2, 2.1, 2.2, 2.3, 2.4, 2.5 constructed from data in Table A-7. Figure 2.6 redrafted from a figure in The Reviews of Geophysics, 30, 67, 1992. Figure 4.10 redrafted from a figure in The Reviews of Geophysics, 30, 86, 1992. Figure 5.18 redrafted from a figure in Kieffer Reviews of Geophysics and Space Physics, 20: 866, 1982. All in this paragraph copyright by the American Geophysical Union and used with permission of the American Geophysical Union. Figure 4.1 redrafted from a figure in Anderson et al., Geophysical Research Letters, 19: 1988, 1992, copyright by the American Geophysical Union. Used with permission of the American Geophysical Union. Figures 9.2 and 9.3 redrafted from figures in Hemley and Gordon, Journal of Geophysical Research, 90: 7808, 1985. Figures 9.4 and 9.5 redrafted from figures in Anderson and Demarest, Journal of Geophysical Research, vi 76: 1357, 1358, 1971. Figure 9.10 redrafted from a figure in D.L. Ander- son, Journal of Geophysical Research, 93: 4692, 1988. Figure 10.2 redrafted from a figure in Hardy, Journal of Geophysical Research, 85: 7013, 1980. Figures 11.7 and 11.8 redrafted from figures in Wolf and Jeanloz, Journal of Geophysical Research, 89: 7827, 7828, 1984. All in this paragraph copy- right by the American Geophysical Union and used with permission of the American Geophysical Union. Figures 2.8, 3.7, 3.8, 3.9, 3.10, 3.11, and 3.12 redrafted from figures in An- derson et al., A thermodynamic theory of the Griineisen ratio at extreme conditions: MgO as an example, Physics and Chemistry of Minerals, 19: 369-380 (371-377), 1993. Figure 5.19 redrafted from a figure in Hofmeister and Ito, Thermodynamic properties of MgSiOs ilmenite from vibrational spectra, Physics and Chemistry of Minerals, 18: 423-432 (428), 1992. Figure 10.5 (lower) redrafted from a figure in Yamamoto and Anderson, Elasticity and anharmonicity of potassium chloride at high temperature, Physics and Chemistry of Minerals, 14: 332-340 (335), 1987. Used with permission of Springer-Verlag. Figure 3.2 redrafted from a figure in Journal of Physics and Chemistry of Solids, 54, Anderson and Isaak, The dependence of the Anderson-Griineisen parameter ST upon compression at extreme conditions, 221-227 (223), Copyright (1993). Figure 10.5 (upper) redrafted from a figure in Journal of Physics and Chemistry of Solids, 48, Yamamoto et al., High temperature elasticity of sodium chloride, 143-151 (146) 1987. Both figures used with kind permission from Elsevier Science Ltd., The Boulevard, Langford Lane, Kidlington 0X5 1GB, UK. Figures 7.3 and 10.13 redrafted from figures in Anderson and Sumino, Physics of Earth and Planetary Interiors, 23, 315, 324, 1980. Used with permission of Elsevier Science Publishers B.V. Figure 11.9 redrafted from a figure in Zerr and Boehler, Science, 262: 553- 555, 1993 (p. 554), Copyright 1993 by the AAAS. Used with permission of Science and the authors. Figure 11.13 redrafted from a figure in Boehler, Nature, 363: 534-536(535), Copyright (1993) Macmillan Magazines Limited. Used with permission of Nature and the authors. Figure 12.4 redrafted from a figure in LASL Shock Hugoniot Data, (Stanley P. Marsh, Ed.), p. 89. Copyright ©1980, The Regents of the University of California. Used with permission of University of California Press. TO N. BERNEICE ANDERSON, WHO KNOWS INSTINCTIVELY WHEN A FANCY WORD IS A COVERUP, WITH LOVE AND AFFECTION This page intentionally left blank PREFACE Two roads diverged in a wood, and I— I took the one less traveled by, And that has made all the difference. —Robert Frost This book is a product of my odyssey in certain branches of materials physics and geophysics. A few years ago, while rereading Frost's poetry, I realized that his words above described very well my decisions at crossroads. My first job as a young Ph.D. physicist was in the research department of Bell Telephone Laboratories, where I was to find elastic constants of solids using physical acoustics under the mentorship of Warren Mason. For sev- eral months, I had the good fortune to be in the same corridor as many famous physicists, including Art Schawlow, Walter Bond, Brent Matthais, Phil Anderson, Conyers Herring, Gregory Wannier, William Shockley, Wal- ter Brattain, and John Bardeen. Five of these later obtained (in total) six Nobel prizes. During my temporary stay in this corridor, while my new physical acoustics laboratory was being assembled, I felt a strong impres- sion from these colleagues that the cutting edge of research was in semi- conductor physics, and it was tacitly assumed that I would apply the skills of physical acoustics to this field. But I remember thinking that doing my kind of research on semiconductors would be boring. I was fascinated with glass physics and the acoustics of low symmetry silicates, so I took the road "less traveled by." Much of my research was published in the Journal of the American Ceramic Society and Physical Review, and I was associated with great ceramicists like Jack Wachtman. I found that another market for my research results was in geophysics, and I was soon invited to build a second physical acoustics laboratory at the Lamont Geological Observa- tory of Columbia University by its famous director, Maurice Ewing. Doing physical acoustics in a geophysical institute was certainly an uncommon endeavor. In 1964, Ed Schreiber, Nahiro Soga, and I nailed a sign over our new laboratory there, proclaiming it the first "Mineral Physics Laboratory." Ed and I showed the community that precision ultrasonic measure- ments of sound velocity done under pressure (modest indeed by today's standards) could yield valid equations of state in the shock wave pressure regime. Nahiro and I demonstrated that high temperature elasticity obeyed certain fundamental laws in solid state physics first presented by Max Born and E. Griineisen in the 1920's and 1930's. Soon a number of other geo-