Site Symmetry in Crystals Theory and Applications [Paperback]

Site Symmetry in Crystals is the first comprehensive account of the group-theoretical aspects of the site (local) symmetry approach to the study of crystalline solids. The efficiency of this approach, which is based on the concepts of simple induced and band representations of space groups, 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. Tables of simple induced respresentations are given for the 24 most common space groups, allowing the rapid analysis of electron and phonon states in complex crystals with many atoms in the unit cell.Site Symmetry in Crystals is the first comprehensive account of the group-theoretical aspects of the site (local) symmetry approach to the study of crystalline solids. The efficiency of this approach, which is based on the concepts of simple induced and band representations of space groups, 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. Tables of simple induced respresentations are given for the 24 most common space groups, allowing the rapid analysis of electron and phonon states in complex crystals with many atoms in the unit cell.1. Introduction.- 2. Finite Groups and Their Representations.- 2.1 Elements of Group Theory.- 2.1.1 Groups. Generators and Generating Relations. Subgroups. Cosets. Invariant Subgroups. The Factor Group.- 2.1.2 Conjugate Elements and Classes. Factorization of Groups.- 2.1.3 Homomorphism and Isomorphism of Groups.- 2.2 Elements of Group Representation Theory.- 2.2.1 Representations of a Group. Equivalent, Reducible and Irreducible Representations. Orthogonality Relations. Representation Characters.- 2lÓÍ