Site Symmetry in Crystals

This is a detailed account of group-theoretical aspects of the site symmetry approach to the study of crystalline solids. This is based on concepts of simple, induced and band representations of space groups. The efficiency of the approach is demonstrated by way of new applications.

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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, which is 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 methods are considered in detail, including the induced representations of layer (slab) groups, co-representations of layer (slab) groups and induced co-representations of 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.