Pub. Date:
Springer New York
Symmetry, Group Theory, and the Physical Properties of Crystals / Edition 1

Symmetry, Group Theory, and the Physical Properties of Crystals / Edition 1

by Richard C Powell


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Symmetry, Group Theory, and the Physical Properties of Crystals / Edition 1

This book demonstrates the importance of symmetry in determining the properties of solids and the power of using group theory and tensor algebra to elucidate these properties. It provides the fundamentals necessary for the reader to understand how to utilize these techniques in many different applications without becoming lost in a heavy formal treatment of the subject matter. The book begins by discussing the concepts of symmetry relevant to crystal structures. This is followed by a summary of the basics of group theory and how it applies to quantum mechanics. Next is a discussion of the description of the macroscopic properties of crystals by tensors and how symmetry determines the form of these tensors. The basic concepts covered in these early chapters are then applied to a series of different examples including crystal field theory treatment of point defects in solids, molecular orbitals, two-photon processes, the optical properties of solids, the nonlinear optical properties of solids, lattice vibrations, the Jahn-Teller effect, and the effects of translational symmetry on electronic energy bands in solids.. Emphasis is placed on showing how group theory and tensor algebra can provide important information about the properties of a system without resorting to first principal quantum mechanical calculations. The book also features a comprehensive set of relevant tables, including crystal symmetries, point group character tables, matter tensors of different rank, and other tensor properties.

Key Features:
•Serves as a textbook or reference book for solid-state physics, solid-state chemistry, and materials science and engineering
•Shows how the physical properties of solids are determined by their symmetry
•Demonstrates the applications of group theory
•Utilizes the concept of matter tensors
•Includes an extensive set of reference tables and end of chapter problems

Product Details

ISBN-13: 9781441975973
Publisher: Springer New York
Publication date: 12/10/2010
Series: Lecture Notes in Physics , #824
Edition description: 2010
Pages: 230
Product dimensions: 6.10(w) x 9.10(h) x 0.70(d)

About the Author

I. Symmetry in Solids
II. Group Theory
III. Tensor Properties of Crystals
IV. Symmetry Properties of Point Defects in Solids
V. Symmetry and the Optical Properties of Solids
VI. Nonlinear Optics
VII. Symmetry and Lattice Vibrations
VIII. Symmetry and Electron Energy Levels

Table of Contents

1 Symmetry in Solids 1

1.1 Symmetry 1

1.2 Crystal Structures 4

1.3 Symmetry in Reciprocal Space 15

1.4 Problems 24

References 24

2 Group Theory 25

2.1 Basic Concepts of Group Theory 27

2.2 Character Tables 31

2.3 Group Theory Examples 40

2.3.1 C3v Point Group 40

2.3.2 Oh Point Group 45

2.4 Group Theory in Quantum Mechanics 47

2.5 Problems 52

References 53

3 Tensor Properties of Crystals 55

3.1 First-Rank Matter Tensors 57

3.2 Second-Rank Matter Tensors 62

3.3 Third-Rank Matter Tensors 68

3.4 Fourth-Rank Matter Tensors 73

3.5 Problems 77

References 77

4 Symmetry Properties of Point Defects in Solids 79

4.1 Energy Levels of Free Ions 79

4.2 Crystal Field Symmetry 85

4.3 Energy Levels of Ions in Crystals 87

4.4 Example: d-Electrons 95

4.5 Example: f-Electrons 100

4.6 Problems 104

References 104

5 Symmetry and the Optical Properties of Crystals 105

5.1 Tensor Treatment of Polarization 105

5.2 Birefringence 114

5.3 Optical Activity 118

5.4 Electrooptical Effect 123

5.5 Photoelastic Effect 131

5.6 Problems 134

References 134

6 Nonlinear Optics 137

6.1 Basic Concepts 138

6.2 Effective Nonlinear Optical Coefficient 145

6.3 Index Matching 150

6.4 Maximizing SHG Efficiency 153

6.5 Two-Photon Absorption 157

6.6 Problems 162

References 163

7 Symmetry and Lattice Vibrations 165

7.1 Symmetry and Local Mode Vibrations 166

7.2 Symmetry and Lattice Vibrational Modes 173

7.3 Transitions Between Vibrational Energy Levels 180

7.3.1 Radiationless Transitions 181

7.3.2 Infrared Transitions 183

7.4 Raman Scattering 185

7.5 Jahn-Teller Effect 194

7.6 Problems 198

References 198

8 Symmetry and Electron Energy Levels 201

8.1 Symmetry and Molecular Bonds 201

8.2 Character Tables for Space Groups 212

8.3 Electron Energy Bands 214

8.4 Symmetry Properties of Electron Energy Bands 220

8.5 Problems 223

References 224

Index 225

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