Site Symmetry in Crystals

1. Introduction.- 2. Finite Groups and Their Representations.- 2.1 Elements of Group Theory.- 2.2 Elements of Group Representation Theory.- 2.3 Generation of Representations.- 3. Symmetry Groups and Their Representations.- 3.1 The Euclidean Group and Its Subgroups.- 3.2 Point Symmetry Groups.- 3.3 Space Groups.- 3.4 Site Symmetry in Space Groups.- 3.5 Symmetry Operations in Quantum Mechanics.- 3.6 Irreducible Representations of Rotation and Full Orthogonal Groups.- 3.7 Representations of Point Groups.- 3.8 Representations of Space Groups.- 4. Site Symmetry and Induced Representations of Symmetry Groups.- 4.1 Induced Representations of Point Groups. Correlation Tables.- 4.2 Induced Representations of Space Groups.- 4.3 Double-Valued Induced Representations.- 4.4 Generation of the Simple Induced Representations of the Space Group D4h14.- 4.5 The Twenty-Four Most Common Space Groups: Crystal Structures and Tables of Simple Induced Representations.- 5. Application of Induced Representations in the Electron Theory of Molecules and Crystals.- 5.1 Adiabatic and One-Electron Approximations.- 5.2 Induced Representations in the Electron Theory of Molecules.- 5.3 One-Electron Approximation for Crystals.- 5.4 Induced Representations and the Theory of Chemical Bonding in Crystals.- 5.5 Energy Bands and Localized States.- 5.6 Localized Orbitals in Molecular Models of Crystals.- 6. Induced Representations in the Theory of Imperfect Crystals.- 6.1 Point Defects in Crystals.- 6.2 Diperiodic Space Groups. Surface Electron States.- 7. Application of Induced Representations of Space Groups to Second Order Phase Transitions.- 7.1 Symmetry Rules in the Landau Theory of Second Order Phase Transitions.- 7.2 Tensor Fields in Crystals and Induced Representations of Space Groups. Tensor Fields for Space Group D4h14.- 7.3 Vibrational Field Representation and Phase Transitions in High-Temperature Superconductors.- 8. Induced Representations of Space Groups in Phonon Spectroscopy of Crystals.- 8.1 Phonon Symmetry Analysis.- 8.2 Infrared and Raman Spectra Selection Rules.- 8.3 Phonon Symmetry and Optical Spectra Selection Rules in Semiconductor Superlattices.- 8.4 Phonon Symmetry in High-Temperature Superconductors.- 8.5 Phonon Symmetry in Diperiodic Systems.- 9. Site Symmetry in Magnetic Crystals and Induced Corepresentations.- 9.1 Shubnikov Space Groups of Symmetry of Magnetic Crystals.- 9.2 Site Symmetry in Magnetic Crystals.- 9.3 Corepresentations of Shubnikov Space Groups.- 9.4 Induced Corepresentations of Magnetic Space Groups.- 9.5 Corepresentations of the Space Groups of Antiferromagnetic La2CuO4.- 10. Site Symmetry in Permutation - Inversion Symmetry Groups of Nonrigid Crystals.- 10.1 Symmetry Groups of Nonrigid Crystals.- 10.2 Irreducible Representations of a Nonrigid Crystal Symmetry Group.- 10.3 Generalized Symmetry of High-Temperature Phase of Fullerite C60.- References.