Ebook: Site Symmetry in Crystals: Theory and Applications

This is the first comprehensive account of the group-theoretical aspects of the site (local) symmetry approach to the study of crystalline solids, whichis based on the concepts of simple induced and band representations of space groups. The efficiency of this approach in the physics and chemistry of solids is demonstrated by considering newly developed applications to electron surface states, point defects, symmetry analysis in lattice dynamics, the theory of second-order phase transitions, and magnetically ordered and non-rigid crystals. Owing to their importance in the theory, the induced representations of space groups and the little group method are considered in detail, including the induced representations of layer (slab) groups and induced corepresentationsof magnetic groups. Tables of simple induced representations are given for the 24 most commonly occurring space groups, allowing the rapid analysis of electron and phonon states in complex crystals with many atoms in the unit cell.

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This is the first comprehensive account of the group-theoretical aspects of the site (local) symmetry approach to the study of crystalline solids, whichis based on the concepts of simple induced and band representations of space groups. The efficiency of this approach in the physics and chemistry of solids is demonstrated by considering newly developed applications to electron surface states, point defects, symmetry analysis in lattice dynamics, the theory of second-order phase transitions, and magnetically ordered and non-rigid crystals. Owing to their importance in the theory, the induced representations of space groups and the little group method are considered in detail, including the induced representations of layer (slab) groups and induced corepresentationsof magnetic groups. Tables of simple induced representations are given for the 24 most commonly occurring space groups, allowing the rapid analysis of electron and phonon states in complex crystals with many atoms in the unit cell.
Content:
Front Matter....Pages I-XI
Introduction....Pages 1-3
Finite Groups and Their Representations....Pages 5-30
Symmetry Groups and Their Representations....Pages 31-87
Site Symmetry and Induced Representations of Symmetry Groups....Pages 89-124
Application of Induced Representations in the Electron Theory of Molecules and Crystals....Pages 125-184
Induced Representations in the Theory of Imperfect Crystals....Pages 185-203
Application of Induced Representations of Space Group to Second Order Phase Transitions....Pages 205-212
Induced Representations of Space Groups in Phonon Spectroscopy of Crystals....Pages 213-236
Site Symmetry in Magnetic Crystals and Induced Corepresentations....Pages 237-250
Site Symmetry in Permutation — Inversion Symmetry Groups of Nonrigid Crystals....Pages 251-264
Back Matter....Pages 265-276

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This is the first comprehensive account of the group-theoretical aspects of the site (local) symmetry approach to the study of crystalline solids, whichis based on the concepts of simple induced and band representations of space groups. The efficiency of this approach in the physics and chemistry of solids is demonstrated by considering newly developed applications to electron surface states, point defects, symmetry analysis in lattice dynamics, the theory of second-order phase transitions, and magnetically ordered and non-rigid crystals. Owing to their importance in the theory, the induced representations of space groups and the little group method are considered in detail, including the induced representations of layer (slab) groups and induced corepresentationsof magnetic groups. Tables of simple induced representations are given for the 24 most commonly occurring space groups, allowing the rapid analysis of electron and phonon states in complex crystals with many atoms in the unit cell.
Content:
Front Matter....Pages I-XI
Introduction....Pages 1-3
Finite Groups and Their Representations....Pages 5-30
Symmetry Groups and Their Representations....Pages 31-87
Site Symmetry and Induced Representations of Symmetry Groups....Pages 89-124
Application of Induced Representations in the Electron Theory of Molecules and Crystals....Pages 125-184
Induced Representations in the Theory of Imperfect Crystals....Pages 185-203
Application of Induced Representations of Space Group to Second Order Phase Transitions....Pages 205-212
Induced Representations of Space Groups in Phonon Spectroscopy of Crystals....Pages 213-236
Site Symmetry in Magnetic Crystals and Induced Corepresentations....Pages 237-250
Site Symmetry in Permutation — Inversion Symmetry Groups of Nonrigid Crystals....Pages 251-264
Back Matter....Pages 265-276
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