Introduction to the Electron Theory of Metals - U.Mizutani, CUP, 2001.pdf

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INTRODUCTION TO
THE ELECTRON
THEORY OF METALS
UICHIRO MIZUTANI
CAMBRIDGE UNIVERSITY PRESS
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Introduction to the Electron Theory of Metals
The electron theory of metals describes how electrons are responsible for the bonding of metals
and subsequent physical, chemical and transport properties. This textbook gives a complete
account of electron theory in both periodic and non-periodic metallic systems.
The author presents an accessible approach to the theory of electrons, comparing it with
experimental results as much as possible. The book starts with the basics of one-electron band
theory and progresses to cover up-to-date topics such as high- T c superconductors and quasi-
crystals. The relationship between theory and potential applications is also emphasized. The
material presented assumes some knowledge of elementary quantum mechanics as well as the
principles of classical mechanics and electromagnetism.
This textbook will be of interest to advanced undergraduates and graduate students in physics,
chemistry, materials science and electrical engineering. The book contains numerous exercises
and an extensive list of references and numerical data.
Uichiro Mizutani was born in Japan on March 25, 1942. During his early career as a post-
doctoral fellow at Carnegie–Mellon University from the late 1960s to 1975, he studied the elec-
tronic structure of the Hume-Rothery alloy phases. He received a doctorate of Engineering in
this field from Nagoya University in 1971. Together with Professor Thaddeus B. Massalski, he
wrote a seminal review article on the electron theory of the Hume-Rothery alloys ( Progress in
Materials Science , 1978). From the late 1970s to the 1980s he worked on the electronic structure
and transport properties of amorphous alloys. His review article on the electronic structure of
amorphous alloys ( Progress in Materials Science , 1983) provided the first comprehensive under-
standing of electron transport in such systems. His research field has gradually broadened since
then to cover electronic structure and transport properties of quasicrystals and high- T c super-
conductors. It involves both basic and practical application-oriented science like the develop-
ment of superconducting permanent magnets and thermoelectric materials.
He became a professor of Nagoya University in 1989 and was visiting professor at the
University of Paris in 1997 and 1999. He received the Japan Society of Powder and Powder
Metallurgy award for distinguished achievement in research in 1995, the best year’s paper award
from the Japan Institute of Metals in 1997 and the award of merit for Science and Technology
of High- T c Superconductivity in 1999 from the Society of Non-Traditional Technology, Japan.
INTRODUCTION TO THE ELECTRON
THEORY OF METALS
UICHIRO MIZUTANI
Department of Crystalline Materials Science, Nagoya University
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PUBLISHED BY CAMBRIDGE UNIVERSITY PRESS (VIRTUAL PUBLISHING)
FOR AND ON BEHALF OF THE PRESS SYNDICATE OF THE UNIVERSITY OF CAMBRIDGE
The Pitt Building, Trumpington Street, Cambridge CB2 IRP
40 West 20th Street, New York, NY 10011-4211, USA
477 Williamstown Road, Port Melbourne, VIC 3207, Australia
http://www.cambridge.org
Japanese edition © Uchida Rokakuho 1995 (Vol. 1,pp. 1-260); 1996 (Vol. 2,pp.261-520)
English edition © Cambridge University Press 2001
This edition © Cambridge University Press (Virtual Publishing) 2003
First published in printed format 2001
A catalogue record for the original printed book is available
from the British Library and from the Library of Congress
Original ISBN 0 521 58334 9 hardback
Original ISBN 0 521 58709 3 paperback
ISBN 0 511 01244 6 virtual (netLibrary Edition)
Contents
Preface
page xi
1 Introduction
1
1.1 What is the electron theory of metals?
1
1.2 Historical survey of the electron theory of metals
3
1.3 Outline of this book
8
2 Bonding styles and the free-electron model
10
2.1 Prologue
10
2.2 Concept of an energy band
10
2.3 Bonding styles
13
2.4 Motion of an electron in free space
16
2.5 Free electron under the periodic boundary condition
18
2.6 Free electron in a box
20
2.7 Construction of the Fermi sphere
21
Exercises
28
3 Electrons in a metal at finite temperatures
29
3.1 Prologue
29
3.2 Fermi–Dirac distribution function (I)
29
3.3 Fermi–Dirac distribution function (II)
34
3.4 Electronic specific heat
37
3.5 Low-temperature specific heat measurement
40
3.6 Pauli paramagnetism
44
3.7 Thermionic emission
50
Exercise
53
4 Periodic lattice, and lattice vibrations in crystals
54
4.1 Prologue
54
4.2 Periodic structure and reciprocal lattice vectors
54
4.3 Periodic lattice in real space and in reciprocal space
57
4.4 Lattice vibrations in one-dimensional monatomic lattice
64
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