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Contents
Preface vii
1 Structures of Melts and Solids 1
1.1 Introduction 1
1.2 X-ray Analysis 2
1.3 The Hard Sphere Model of Atoms 10
1.4 Crystal Structure 12
1.5 Crystal Structures of Solid Metals 19
1.6 Crystal Defects in Pure Metals 24
1.7 Structures of Alloy Melts and Solids 30
Summary 39
Exercises 42
2 Theory of Atoms and Molecules 45
2.1 Introduction 46
2.2 The Bohr Model of Atomic Structure 46
2.3 The Quantum Mechanical Model of Atomic Structure 48
2.4 Solution of the Schrödinger Equation for Atoms 57
2.5 Quantum Mechanics and Probability: Selection Rules 65
2.6 The Quantum Mechanical Model of Molecular Structure 71
2.7 Diatomic Molecules 75
2.8 Polyatomic Molecules 88
Summary 89
Exercises 94
3 Theory of Solids 97
3.1 Introduction 97
3.2 Bonds in Molecules and Solids: Some Definitions 98
3.3 Bonds in Molecules and Nonmetallic Solids 100
3.4 Metallic Bonds 112
3.5 Band Theory of Solids 125
3.6 Elastic Vibrations in Solids 146
3.7 Influence of Lattice Defects on Electronic Structures in Crystals 151
Summary 157
Exercises 163
4 Properties of Gases 169
4.1 Introduction 170
4.2 Kinetic Theory of Gases 170
4.3 Energy Distribution in Particle Systems: Maxwell¨CBoltzmann Distribution Law 174
4.4 Gas Laws 178
4.5 Heat Capacity 185
4.6 Mean Free Path 192
4.7 Viscosity 196
4.8 Thermal Conduction 198
4.9 Diffusion 199
4.10 Molecular Sizes 204
4.11 Properties of Gas Mixtures 205
4.12 Plasma ¨C The Fourth State of Matter 208
Summary 213
Exercises 216
5 Transformation Kinetics: Diffusion in Solids 219
5.1 Introduction 220
5.2 Thermodynamics 220
5.3 Transformation Kinetics 236
5.4 Reaction Rates 242
5.5 Kinetics of Homogeneous Reactions in Gases 245
5.6 Diffusion in Solids 253
Summary 276
Exercises 283
6 Mechanical, Thermal and Magnetic Properties of Solids 287
6.1 Introduction 287
6.2 Total Energy of Metallic Crystals 288
6.3 Elasticity and Compressibility 290
6.4 Expansion 296
6.5 Heat Capacity 303
6.6 Magnetism 317
Summary 333
Exercises 337
7 Transport Properties of Solids. Optical Properties of Solids 341
7.1 Introduction 342
7.2 Thermal Conduction 342
7.3 Electrical Conduction 347
7.4 Metallic Conductors 350
7.5 Insulators 357
7.6 Semiconductors 362
7.7 Optical Properties of Solids 375
Summary 388
Exercises 394
8 Properties of Liquids and Melts 399
8.1 Introduction 400
8.2 X-ray Spectra of Liquids and Melts 400
8.3 Models of Pure Liquids and Melts 402
8.4 Melting Points of Solid Metals 406
8.5 Density and Volume 407
8.6 Thermal Expansion 409
8.7 Heat Capacity 412
8.8 Transport Properties of Liquids 415
8.9 Diffusion 416
8.10 Viscosity 425
8.11 Thermal Conduction 438
8.12 Electrical Conduction 439
Summary 443
Exercises 449
Answers to Exercises 455
Index 475
The basic idea and the initial aim of this book, Physics of Functional Materials, was to provide the necessary knowledge
in physics for a deeper interpretation of many of the solidification and crystallization processes that are treated in the book
Materials Processing during Casting, written for the university undergraduate level and published in March 2006. The present
book fulfils this requirement and is at such a mathematical level that a basic knowledge of mathematics at university level is
sufficient.
However, the book Physics of Functional Materials has a very wide and general character. It is by no means designed
only for the purpose described above. On the contrary, this book may be useful and suitable for students in various sciences
at the Master¡¯s and PhD level, who have not taken mathematics and physics as major subjects. Examples of such sciences
are materials science, chemistry, metallurgy and many other scientific and technical fields where a basic knowledge of the
foundations of modern physics and/or properties of materials is necessary or desirable as a basis and a background for higher
studies.
Fundamental properties of different materials such as diffusion, viscosity, heat capacity and thermal and electrical conduction
are examined more extensively in the present book than in available physics books of today. This book will fill a gap between
the demand for and supply of such knowledge.
The atomistic view of matter requires a genuine background of modern physics from atoms via molecules to solid-state
physics, primarily the modern band theory of solids, and the nature of bonds and crystal structure in solids. These topics are
treated in Chapters 1¨C3 and are applied in later chapters, particularly in Chapter 7.
The three first chapters on modern physics are followed by applications of classical physics of material properties. Basic
thermodynamics, properties of gases, including the kinetic theory of gases and the Boltzmann distributions of velocity and
energy of molecules, transformation kinetics including chemical reactions and diffusion in solids, mechanical, thermal and
magnetic properties of matter including ferromagnetism, are treated in Chapters 4¨C6.
Chapter 7 deals with thermal and electrical conduction in solids and their optical properties, particularly electrical conduction
in metals and semiconductors. Polarization phenomena in crystals and optical activity in solids and liquids are discussed. In
the last chapter, a short survey of the material properties of liquids is given.
Physics of Functional Materials contains solved examples in the text and exercises for students at the end of each chapter.
Answers to all the exercises are given at the end of the book.
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