SCIENCE OF ENGINEERING MATERIALS

Science of Engineering Materials

Volume 1 Structure of Matter

Volume 2 Materials

Volume 3 Engineering Properties

Science of Engineering Materials Volume 1

Structure of Matter

MANAS CHANDA Indian Institute of Science, Bangalore

© Manas Chanda 1979

All rights reserved. No part of this publication may be reproduced or transmitted, in any form or by any means, without permission.

First published in India 1979 by Macmillan India Ltd

First published in Great Britain 1981 by THE MACMILLAN PRESS LTD London and Basingstoke Companies alld representatives throughout the world

ISBN 978-0-333-31815-7 ISBN 978-1-349-06051-1 (eBook) DOI 10.1007/978-1-349-06051-1

The paperback edition of the book is sold subject to the condition that it shall not, by way of trade or otherwise, be lent, resold, hired out, or otherwise circulated without the publisher's prior consent in any form of binding or cover other than that in which it is published and without a similar condition including this condition being imposed on the subsequen~ purchaser.

To the memory of

Late Professor N. R. Kuloor

Foreword

Materials Science is an interdisciplinary subject of great importance. It is increasingly being recognised that a course in materials science should form an essential part of engineering science curricula in universities. This is because of the rapid progress being made in the development of sophisticated tailor-made materials of desired properties and specifications to suit specific needs. The subject is, therefore, not only of relevance to engineering but also to physical sciences, medical science, and other disciplines. Thus, modern medical practice makes use of new bio-materials while modern solid state chemistry is concerned with the synthesis of novel kinds of compounds. An introduction to materials science will un­doubtedly enable students, teachers and professionals to appreciate the problems related to materials in the modern world.

This book by Dr. Manas Chanda attempts to present an introduction to engineering materials science, which I am sur~ will be found useful by the scientific and educational community. Dr. Chanda has taken pains to work out examples and problems which will be useful to students. I recommend the book to students and teachers of materials science.

Indian Institute of Science Bangalore 22 February 1979

CNR RAO

Preface

Virtually all present-day courses in engineering include a study of the science of materials, which is perhaps a reflection of the feeling that advances in engineering and technology are intimately related to developments in engineering materials. The development of principles which relate the properties and behaviour of materials to their structures and environments has made possible a more scientific and systematic approach to the study of materials science, which not only eliminates the need for considering each of the multitude of available engineering materials individuaUy, but even permits the engineer to predict, at least qualitatively, the properties and characteristics of materials that might be developed in future.

An understanding of the nature and behaviour of materials calls for a broad spectrum of knowledge of various scientific and engineering disciplines. The integration of theoretical principles of these disciplines into a comprehensive and unified treatment of all main classes of engineering materials is the basis for the emer­gence of the relatively new subject of materials science. It was with this in mind that the present book was written.

This introductory text in engineering materials science is designed for beginner students in various disciplines of engineering and applied sciences. It, thus, builds on an elementary knowledge of chemistry and a reasonable grounding in physics, avoiding, however, the rigorous approach which is common in solid state physics books. The book will also serve professional engineers who expect to encounter materials in construction, in industrial production and in engineering design situations, and scientists who seek a basic understanding of the nature and behaviour of materials as a

x PREFACE

stepping stone for more advanced work in specific materials problems.

The book consists of sixteen chapters, organised in three volumes,. dealing respectively with structure of matter, materials of engineering,. and engineering properties. The present volume, composed of five chapters, is devoted to the study of internal structures of materials in a logical sequence that proceeds from the simple to the more· complex.

It is through a detailed understanding of the structure and inter-· actions of atoms and molecules that we can understand the complex behaviour of matter and materials around us. The atomic and molecular theory of matter is thus the starting-point of the bewilder­ing number of fields and sub-fields into which science has branched over the past century and provides a unifying theme that runs through all these apparently diverse areas of science. Chapter 1 presents the modern picture of the atom adopting the nove) approach to the teaching of basic atomic structure, in which the ideas of wave mechanics are used, in a simplified form, from the· beginning. In this treatment, however, more attention has been paid to the extranuclear electronic structure, since it is this structure dealing with the arrangement and distribution of the electrons around the nucleus that determines the chemical behaviour of that atom and influences .most of the properties of engineering interest.

The nature of interatomic and intermolecular forces is explained in Chapter 2, while Chapter 3 is devoted to the study of the different states of matter, emphasising the nature of distribution of their component atoms and molecules and how this determines their respective characteristic properties. Most of the­materials used in engineering are solids and most of the solids are partly or completely crystalline, the structure of which may vary from simple to very complex, according to the type of the bond and the geometrical arrangement of constituent atoms or molecules. The types of atomic arrangements in crystalline solids and the types of crystal structures are treated in Chapter 4.

Real crystals are rarely perfect, and the natilre and extent of crystal imp,erfection have a pronounced effect on their physical and mechanical properties. Most of Chapter 5 is devoted to the study of various types of crystal imperfections and the dependence of properties upon them. The phenomenon of atomic movements in solids, an extremely important physical process that occurs in many

PRBFACE xi

metallurgical processes and phenomena, is also treated in Chapter 5. These five chapters provide a foundation for further development of concepts necessary to understand phase equilibria, phase changes, phase characteristics (microstructures), engineering materials, and their properties, treated in Volumes 2 and 3.

The book contains many worked out examples and problems for class assignment at the end of each chapter. Answers to numeri­cal problems are provided so that the student can check his progress. The book, in addition, features an extensive bibliography and original literature references.

I am deeply indebted to my faculty colleagues, friends, innumer­able students whom I met during my ten years of teaching experience, and associates in other universities who have aided in the preparation of the book. I regret that it is impossible to thank each person individually. I have had the good fortune to have Professor C.N.R. Rao read the manuscript and write a Foreword to the book. My gratitude is due to Messrs M.N. Chandrashekara, P. Raghavendrachar and C.C. Lakshmanan, who have performed the painstaking task of proof-reading during my stay abroad despite their busy involvement in research programmes, and to my wife, Mridula, and daughter, Amrita, who steadfastly tolerated the time devoted to the project. Finally, I should like to thank the National Book Trust of India for extending financial subsidy for the publication of the book.

Banga/ore February 1979

MANAS CHANDA

Contents

Foreword vii

Preface ix

CHAPTER 1: THE STRUCTURE OF ATOMS

1 . 1 Introduction 1 1 .2 The Atom; Constituent Parts and Definitions 2 1.3 Bohr~Rutherford Atomic Modd 6 1.4 Wave-Mechanical Model of the Atom 9

The uncertainty principle. The Schrodinger wave equation. Quantum numbers from wave-mechanical treatment. Atomic orbitals. Charg~cloud represen-tation of orbitals

I.S Four-Quantum~Number System 21 1.6 Electronic Configuration of the Atoms 22

~w n References 28 Further Reading 28 Problems 29

CHAPTER 2: INTERATOMIC AND INTERMOLECULAR FORCES

2. 1 Introduction 2.2 Ionic Bonding

Ionization potential. Electron affinity. Energetics

31 31

xiv CONTENTS

of ionic bond formation. Equilibrium spacing. Bonding force in ionic solids. Ionic radii

2.3 Covalent Bonding 46

Directional nature of covalent bonds. Covalent radii. Bond energies

2.4 Transitional Type Bonds 55 2.5 Metallic Bond 57 2.6 Secondary Bonds 59

Permanent dipole attractions. Induced dipole attrac-tions. Fluctuating dipole attractions

Notes References Further Reading Problems

CHAPTER 3: STATES OF MATTER

3.1 Introduction 3 .2 Theory of Liquids 3.3 Transitions between States of Matter

Energetics of Transitions

3.4 Structure of Solids 3.5 Crystallization

Homogeneous nucleation. Heterogeneous nucleation. Nucleation rates. Crystal growth

3.6 Polymorphism Some examples of polymorphic transformations

3 .7 Formation of Amorphous Solids Metallic glasses

3.8 Colloidal State of Matter Gels. Emulsions

3 .9 Liquid Crystals 3 . 10 The Plasma State of Matter

Notes References Further Reading Problems

66 67 68 68

71 72 75

77 79

88

90

92

97 99

102 103 104 105

CONfENTS xv

CHAPTER 4: ATOMIC ARRANGEMENTS IN CRYSTALLINE SOLIDS

4.1 Introduction 107 4.2 Space Lattice and Unit Cell 107 4.3 Crystal System and Lattice Coordinates 110 4.4 Crystal Planes and Directions 112

Atomic density of crystallographic planes and lines. Interplanar spacings. Crystal cleavag~

4.5 Packing of Atoms in Crystals 121 Body-centred cubic structures. Face-centred cubic structures. Hexagonal close-packed structures. Stac-king of closed-packed layers. Atomic packing and deformability

4.6 X-ray Crystallography 4.7 Types of Crystal Structures

Ionic structures. Covalent structures. Molecular structures

136 lSI

4.8 Crystal Structures of Compounds 158 Interstitial sites. AX-type compounds. AX2-type compounds. A2Xa-type compounds. ABmX/I·type compounds. The spinel structure

4.9 Influence of Radius Ratio on Structure Notes References Further Reading Problems

CHAPTER 5: CRYSTAL IMPERFECTIONS

167 169 169 170 170

5.1 Introduction 174 5.2 Point Defects 174

Nonstoichiometric compounds. Physical effects of defect structures

5.3 Line Defects 182 Edge dislocation. Partial dislocations. Extended dislocation. Screw dislocation. Other dislocations. Energy of a dislocation. Dislocation line tension. Interaction between dislocations

xvi CONTENTS·

5.4 Dislocation Mechanism of Slip

Dislocation multiplication. Dislocation climb and cross-slip. Jogs

5 .5 Role of Dislocations 5 . 6 Planar Defects

Stacking faults. Twinning. Grain boundaries. Grain size. Tilt boundaries

5 .7 Other Crystal Imperfections 5.8 Atomic Movements in Solids

Mechanism of diffusion in crystals. Fick's laws. Factors influencing diffusion coefficient. Self­diffusivity and intrinsic diffusivity

200

212 313

223 223

Notes 232 References 233 Further Reading 234 Problems 234

Appendix 1: Fundamental Physical Constants Appendix 2: Conversion Factors for Energy Appendix 3: Electronic Configurations of the Ground States

237 238

of the Elements 239 Index 245