Thermophysical Properties of Materials

445 Pages·1999·5.124 MB·English

by  G. Grimvall

THERMOPHYSICAL PROPERTIES
OF MATERIALS
This Page Intentionally Left Blank
THERMOPHYSICAL PROPERTIES
OF MATERIALS
Enlarged and revised edition
GORAN GRIMVALL
The Royal Institute of Technology
Stockholm, Sweden
1999
ELSEVIER
Amsterdam - Lausanne - New York - Oxford - Shannon - Singapore - Tokyo
ELSEVIER SCIENCE B.V.
Sara Burgerhartstraat 25
P.O. Box 211,1000 AE Amsterdam, The Netherlands
© 1999 Elsevier Science B.V. All rights reserved.
This work is protected under copyright by Elsevier Science, and the following terms and conditions apply to its use:
Photocopying
Single photocopies of single chapters may be made for personal use as allowed by national copyright laws. Permission of the
publisher and payment of a fee is required for all other photocopying, including multiple or systematic copying, copying for
advertising or promotional purposes, resale, and all forms of document delivery. Special rates are available for educational
institutions that wish to make photocopies for non-profit educational classroom use.
Permissions may be sought directly from Elsevier Science Rights & Permissions Department, PO Box 800, Oxford OX5 1DX,
UK; phone: [phone], fax: [phone], e-mail: [email protected]. You may also contact Rights &
Permissions directly through Elsevier's home page (http://www.elsevier.nl), selecting first 'Customer Support', then 'General
Information', then 'Permissions Query Form'.
In the USA, users may clear permissions and make payments through the Copyright Clearance Center, Inc., 222 Rosewood Drive,
Danvers, MA 01923, USA; phone: [phone], fax: [phone], and in the UK through the Copyright Licensing Agency
Rapid Clearance Service (CLARCS), 90 Tottenham Court Road, London W1P 0LP, UK; phone: [phone]; fax: (+44)
171 631 5500. Other countries may have a local reprographic rights agency for payments.
Derivative Works
Tables of contents may be producd for internal circulation, but permission of Elsevier Science is required for external resale or
distribution of such material.
Permission of the publisher is required for all other derivative works, including compilations and translations.
Electronic Storage or Usage
Permission of the publisher is required to store or use electronically any material contained in this work, including any chapter or
part of a chapter.
Except as outlined above, no part of this work may be reproduced, stored in a retrieval system or transmitted in any form or by any
means, electronic, mechanical, photocopying, recording or otherwise, without prior written permission of the publisher.
Address permissions requests to: Elsevier Science Rights & Permissions Department, at the mail, fax and e-mail addresses noted
above.
Notice
No responsibility is assumed by the publisher for any injury and/or damage to persons or property as a matter of products
liability, negligence or otherwise, or from any use or operation of any methods, products, instructions or ideas contained in the
material herein. Because of rapid advances in the medical sciences, in particular, independent verification of diagnoses and drug
dosages should be made.
First edition 1999
Library of Congress Cataloging in Publication Data
A catalog record from the Library of Congress has been applied for.
ISBN: 0444 82794 3
(ro) The paper used in this publication meets the requirements of ANSI/NISO Z39.48-1992 (Permanence of Paper).
Printed in The Netherlands.
PREFACE
This is a thoroughly revised version of my earlier (1986) book with the
same title. About half the content of the previous book is kept essen-
tially unchanged, and one quarter is rewritten and updated. The rest is
replaced by completely new and extended material.
Materials science is a field with a steadily moving research front,
dealing with the most modern methods and materials. At the same
time, it rests on classical physics or elementary quantum mechanics
that was developed a long time ago. There is also a certain amount
of fashion in the choice of research problems. Many important areas
of materials science were most intensely studied in the 1960's and
1970's. For instance, the investigation of phonon spectra by inelastic
neutron scattering and the experimental study of properties of electrons
in elemental metals peaked at that time. More recent research focuses
on, e.g., new materials produced by means of "molecular engineering",
and computational materials science through ab initio electron structure
calculations. Another trend is the ever growing interdisciplinary aspect
of both basic and applied materials science. There is an obvious need
for reviews that link well established results to the modern approaches.
One of the aims of this book is to provide such an overview in a specific
field of materials science, namely thermophysical phenomena that are
intimately connected with the lattice vibrations of solids. This includes,
e.g., elastic properties and electrical and thermal transport.
Traditional textbooks in materials science or condensed matter
physics often quote results in special and very simplified cases. This
book attempts to present the results in such a form that the reader
can clearly see their domain of applicability, for instance if and how
they depend on crystal structure, defects, applied pressure, crystal
anisotropy, etc. The level and presentation is such that the results can
be immediately used in research. Derivations are therefore avoided.
V
VI Preface
In the selection of references one aim has been to give credit to pio-
neering papers, even though one often does give an explicit reference to
that work in today's research. Another aim has been to quote papers that
are easily accessible or of such a character that they will normally be
quoted in later works and therefore are useful as a starting point in cita-
tion searches. No doubt I have failed to identify many important papers,
and I apologize in advance to those authors for my lack of knowledge.
Many of the figures in the book, providing illustrating examples, are
taken from work done by me or in my research group. That is often
for the practical reason that I already have a computer file with those
figures, and it does not mean that the work of others has been ignored.
Finally, the reader I have in mind may be a graduate student in con-
densed matter physics, metallurgy, inorganic chemistry or geophysical
materials. S/he could also be a theoretical physicist moving in the di-
rection of applications, or a scientist in an industrial research laboratory
who has to go beyond the level of undergraduate textbooks. In fact, I
have been more or less involved in all these areas, and that reflects the
style and choice of topics in this book.
Goran Grimvall
Stockholm, December 1998
LIST OF MOST IMPORTANT SYMBOLS
c heat capacity
c phonon group velocity
g
harmonic phonon heat capacity
^har
C(q,s) sound velocity of mode (q, s)
sound velocity in the Debye model
^ sound, D
C Debye model heat capacity
D
c heat capacity at constant pressure
P
C heat capacity of constant volume
v
c concentration of impurities, etc.
CU elastic stiffness
D dynamical matrix
E energy
E Young's modulus
E Fermi energy
F
e electron charge
F Helmholtz (free) energy
F(co) phonon density of states
f Fermi-Dirac distribution function
fi volume fraction of phase /
G Gibbs (free) energy
G shear modulus
H enthalpy
K bulk modulus
K isentropic (adiabatic) bulk modulus
s
Kj isothermal bulk modulus
vii
viii List of most important symbols
Boltzmann's constant
*B
k electron wave vector
k Fermi wave number
F
I electron (or phonon) mean free path
M ion (atom) mass
m free electron mass
m electron band mass
b
m electron thermal mass
th
N total number of atoms (ions)
N Avogadro's number
A
N(E) electron density of states
N(E ) density of states at Fermi level
P
n number of electrons per unit volume
n Bose-Einstein distribution function
P pressure
q phonon wave vector
Debye wave number
GD
(q,s) label on phonon state
R position of atom (ion)
r electron density parameter
s
S entropy
s label on phonon branch
SU elastic compliance
T temperature
Tv Fermi temperature
melting temperature
Tfus
U lattice energy
u displacement vector of atom (ion)
V crystal volume
v,v electron velocity
k
V Fermi velocity
F
Z ionic charge
Z partition function
List of most important symbols
a linear expansion coefficient
a^F(co) transport coupling function
f3 cubic expansion coefficient
y electronic heat capacity coefficient
YG thermodynamic Griineisen parameter
Y (n) generalised Griineisen parameter
Y (q, s) Griineisen parameter of phonon mode (q, s)
^2(3,4) anharmonic phonon frequency shifts
£, £t electron energy
£, stj elastic strain
e(q, s) phonon eigenvector
# Debye temperature
D
9j)(n) generalised Debye temperature
OE Einstein temperature
K compressibility
K label on atom in unit cell
K thermal conductivity
K isentropic (adiabatic) compressibility
S
K isothermal compressibility
T
K\ electron part of thermal conductivity
e
/ch phonon part of thermal conductivity
p
Ai_ph electron-phonon interaction parameter
e
v Poisson ratio
p electrical resistivity
p mass density of solid
a electrical conductivity
cr,cfij elastic stress
r scattering time
r shear stress
£2 atomic volume
a
a) phonon frequency
co(n) moment frequency
COD Debye frequency
a)v(n) generalised Debye frequency
&>(q, £) phonon frequency of mode (q, s)