Modern Aspects of Solid State Chemistry

629 Pages·1970·52.436 MB·English

by  J. Mahanty (auth.), C. N. R. Rao (eds.)

Modern Aspects of
Solid State Chemistry
Modern Aspects of
Solid State Chemistry
Edited by
C. N. R. Rao
Professor of Chemistry
Indian Institute of Technology
Kanpur, India
':t?
PLENUM PRESS • NEW YORK-LONDON • 1970
This volume comprises the lectures given at a Winter School
in Solid State Chemistry, supported by the National Council for
Science Education, New Delhi (which operates in cooperation
with the U.S. National Science Foundation and the
Indian University grants commission), held at Kanpur, India,
in November and December of 1969.
Library of Congress Catalog Card Number 76-133422
SBN 306-30506-2
ISBN-13: 978-1-4684-1877-4 e-ISBN-13: 978-1-4684-1875-0
DOl: 10.1007/978-1-4684-1875-0
© 1970 Plenum Press, New York
softcover reprint ofthe hardcover 1s t edition 1970
A Division of Plenum Publishing Corporation
227 West 17th Street, New York, N. Y. 10011
United Kingdom edition published by Plenum Press, London
A Division of Plenum Publishing Corporation, Ltd.
Donington House, 30 Norfolk Street, London W. C. 2, England
All rights reserved
No part of this publication may be reproduced in any form
without written permission from the publisher
PREFACE
The three natural streams of present-day chemistry are
Structure, Dynamics and Synthesis and all these three elements
are essential for the study of materials, particularly in the
solid state. The solid state provides challenging opportunities
for illustrating and applying principles of chemistry to systems
of academic interest and technological importance. There are
several practising solid state chemists in universities and
research laboratories, but the subject has not yet become part
of the formal training program in chemistry. Being one of the
new frontiers of chemistry, Solid State Chemistry has a tremendous
future and undoubtedly demands the active involvement of many
more chemists.
A Winter School in Solid State Chemistry was organized at
the Indian Institute of Technology, Kanpur, to promote this area
and to develop curricular material. Solid State Chemistry being
lighly interdisciplinary in nature, the lecturers and participants
at the Winter School had widely different backgrounds and interests.
It was my great desire that the lecture material from the Winter
School should become available to a larger body of students,
teachers and research workers interested in the solid state and
hence this volume.
Some of the areas which have not been covered in this volume
are crystallography and crystal chemistry, materials preparation
including synthetic routes, organic solids, color centers,
spectroscopy and defect chemistry associated with impurity ions
doped in host crystals, and the role of ;;olid state chemistry in
developing devices. There were lectures on some of these topics
at the Winter School, but unfortunately we could not obtain these
contributions in time for inclusion in this volume. If the
material on some of these topics is taken from other sources, I
have a feeling that the present volume can provide much of the
basic material required for a course in Solid State Chemistry.
I have tr ied to edit the chapter s and link them up wherever
possible. In spite of this effort, the readers will undoubtedly
notice differences in language, symbols and notations as well as
the bre ad th and depth of coverage among the chapters. I fee I that
these shortcomings may not be very serious since each chapter is
a unit by itself. I sincerely hope that this volume will find
response from all those interested in the study of the solid state.
Kanpur, India C.N.R. RAO
May 7, 1970
v
CONTRIBUTORS TO THE VOLUME"
ANDERSON J. S., University of Oxford, Oxford
BHIDE V. G., National Physical Laboratory, Delhi
CHAKRA VORTY D., Indian Institute of Technology, Kanpur
HONIG J. M, Purdue University, Lafayette. Indiana
KHAN D. C., Indian Institute of Technology, Kanpur
MAHANTY J., Indian Institute of Technology, Kanpur
MENYUK N., Lincoln Laboratory, M. I. T., Lexington, Mass.
NARASIMHAN P. T., Indian Institute of Technology, Kanpur
PARASNIS A. S., Indian Institute of Technology, Kanpur
RAMAKRISHNA V., Indian Institute of Technology, Delhi
RAMASASTRY C., Indian Institute of Technology, Madras
RAO C . N. R., Indian Institute of Techno,ogy, Kanpur
RA Y R. K., Indian Institute of Technology, Kanpur .
SASTRI M. V. C., Indian Institute of Technology, Madras
SHARA N R., Indian Institute of Technology, Kanpur
SINGRU R. M., Indian Institute of Technology, Kanpur
SUBBARAO E. C., Indian Institute of Technology, Kanpur
VUAYARAGHAVAN R., Tata Institute of Fundamental Research, Bombay
YOGANARASIMHAN S. R., Indian Institute of Technology, Delhi
• Onl y Winter School Lecturers have been listed.
vi
ACKNOWLEDGEMENTS
The Winter School in Solid State Chemistry, held at the Indian
Institute of Technology, Kanpur, between November 25 and December 15,
1969, was supported and sponsored by the National Council for Soience
Educa.tion (NCSE), New Delhi. I am most grateful to Professor D.S.
Kothari, Chairman, University Grants Commission and NCSE, Dr. R.D.
De shpande , Chief Executive of the NCSE and members of the NCSE
Chemistry Panel, partioularly Professor T.R. Seshadri and Prof. N.~.
Subba Rao, for their generous support. But for the grant from the
NCSE it would not have been possible to support the travel and stay
of a majority of the participants and lecturers.
The travel of the visiting professors from abroad, Professors
J.S. Anderson, J.M. Honig and N. Menyuk was supported by the Kanpur
Indo-American Program and I am highly thankful to Mr. Gilbert
Oakley, Jr., the Leader of the Program. The Winter School would
not have been the same without these visiting professors.
The Winter School received considerable support from
Dr. P.K. Kelkar, Director, and Dr. M.S. Muthana, Deputy Director,
of this Institute, to whom my thanks are due. The cooperation and
assistance of the Department of Chemistry of this Institute, in
particular from the Department Head, Professor M.V. George, are
gratefully acknowledged.
I would like to express my sincere thanks to all the lecturers
at the Winter School for their enthusiastic collaboration; most of
them have put in considerable effort in writing the chapters in
this volume. Some of the lecturers who could not contribute to
this volume, but contributed to the Winter School significantly
are Professor S. Ramaseshan and Dr. A.K. Singh of the National
Aeronautical Laboratory, Bangalore, Dr. J. Shankar and Dr. M.D.
Karkhanavala of the Bhabha Atomio Research Centre, Bombay,
Dr. A.K. Sridhar of the Solid State Physics Laboratory, New Delhi,
and Dr. T.M. Srinivasan and Dr. M.M. Chaudhri of this Institute.
vii
viii ACKNOWLEDGEMENTS
The Winter School was lively and had high intellectual
content. There was an average of 100 participants in a lecture.
I am thankful to the participants from the various universities
and research laboratories of this country for their participation.
The members of my research group, particularly IIf.r. M. Natarajan,
Mr. S. Ramdas and Dr. G.V. Subba Rao, have assisted me greatly in
organizing the Winter School and in bringing out this volume; to
these gentlemen, I offer my thanks. I am thankful to Mr. M. Natu
who has provided considerable help in the office of the Winter
School and in the preparation of the manuscript and to Messrs. N.
Ahmad, R.D. Tripathi and R.D. Singh who have devoted several hours
in typing the manuscripts.
I am most thankful to Mr. Robert Ubell and the Plenum
Publishing Corporation, New York, for their enthusiastic
cooperation in bringing out this volume.
Finally, I would like to tbank my wife, Indu, and my
children, Suchitra and Sanjay Srinivas, who have sacrificed
considerably in allowing me to fully devote my time and efforts
to my profession.
C.N.R. RAO
Director
Kanpur, India Winter School in Solid State Chemistry
CONTENTS
Page No.
1. LATTICE DYNAMICS by J. Mahanty 1
Introduction
Theory of Small Oscillations
Effect of Lattice Symmetry
Density of Vibrational states
Vibrational Thermodynamic Properties of Crystals
X-ray and Neutron Scattering
2. COHESIVE ENERGIES OF IONIC SOLIDS by CoN oR Rae 17
0
Born-Haber Cyole
Born Treatment of Ionic Solids
Some Related Aspects
3. DEFECT CHEMISTRY AND NON-STOICHIOME'ffiIC COMPOUNDS
by JoSo Anderson 29
Point Defect Equilibria in Crystals
The Systematics of Non-Stoichiometric Compounds
Grossly Non-Stoichiometric Compounds
Ferrous Oxide: A Case History
Strong Defect Orderingl Intermediate
Superstructure Phases
Elimination of Defectsl Crystallographic Shear
Imperfections of Ordered structures (Lattice Imaging)
Conclusions and Outstanding Problems
4. THEORY OF POINT DEFECTS IN IONIC CRYSTALS
by C.NoR. Rae and S. Ramdas 107
Introduction to Point Defects in Ionic Crystals
Experimental Studies of Point Defects
Theoretical Calculations of the Formation
Energies of Schottky Defects
Defect Interaction Energies
Migration Energies
Interstitial Defects
Concluding Remarks
ix
x CONTENTS
5. DIELECTRIC PROPERTIES by E.C. Subberao 129
Definitions and Units
Mechanisms of Polarization
Alternating Current Phenomena
Ferroelec tr ics
6. MAGNETISM by N. Menyuk 159
Non-Interacting Atoms
Magnetic Interactions
Long-Range Order
Spiral Configurations
Magnetic Atoms in a Crystal
Superexchange Interactions
Collective d-Electron Model
7. NEUTRON DIFFRACTION .AN]) SOLID·STATE PROPERTIES
by D.C. Khan 219
Introduction
Thermal Neutrons
Elastic Scattering
Inelastic Scattering
Conc lusions
8. NJ.GNETIC RESONANCE by P. T. Narasimhan 231
Introduc tion
Nuclear Moments and Nuclear Magnetic Resonance
Spin-Lattice Relaxation
Bloch Equations and Transverse Relaxation
Experimental Arrangements
NMR in Non-metallic Solids
Quadrupolar Splittings in NMR
NMR in Metals
Chemical Shift and Spin Coupling in Solids
Pure Quadrupole Resonance in Solids
Electron Paramagnetic Resonance
Concluding Remarks
9. NUCLEAR MAGNETIC RESONANCE IN SUPERCONDUCTORS ANn
DILUTE ALLOYS by R. Vijayaraghavan 261
NMR in Superconductors
NMR in Dilute Alloys
CONTENTS xi
10. MAGNETOSTRICTION IN MATERIALS by R.K. Ray 273
Introduction
Behaviour of Common Materials
Conclusions
11. MOSSBAUER EFFECT AND DYNAMICS OF ATOMIC MOTION
IN SOLIDS by V.G. Bhide 287
Resonance Fluorescence
Mossbauer's Experiment
Resonance Absorption of Gamma Rays and
Dynamics of Atomic Motion
Experimental Results
Concluding Remarks
12. POSITRON ANNIHILATION IN SOLIDS by R.M. Singru 329
Introduction
Methods and Results
13. ELEMENTS OF ORDER-DISORDER THEORY AND DIVERSE
APPLICATIONS by J.M. Honig 343
Statement of the Problem
The Zero Order Approximation (Langmuir Isotherm)
The Fermi-Dirac Distribution Function
Decomposition of the Lattice into Subfigures
The Fowler-Guggenheim Adsorption Isotherm
Thermodynamic Properties of Binary Mixtures
in the Bragg-Williams Approximation
14. DIJt'FUSION IN SOLIDS by V. Ramakr ishna 359
The Diffusion Coefficient
Intrinsic Diffusion Coefficients
Self-Diffusion Coefficients
Experimental Procedures
15. IONIC CONDUCTIVITY by C. Ramasastry, Y.V.G.S. Murti
and B. S. V• S .R. Acharyulu 377
Conduction Mechanisms in Ionic Crystals
Anisotropy of Conduction in Ionic Crystals