equations of state of solids for geophysics and ceramic science orson l. anderson

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OXFORD MONOGRAPHS ON GEOLOGY AND GEOPHYSICS
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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
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Copyright © 1995 by Oxford University Press, Inc.
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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
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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-