Infrared and Raman selection rules in diperiodic three‐dimensional layers

Diperiodic three‐dimensional layers are distributed among 31 orientation classes and 80 plane groups of which 43 are symmorphic. The site symmetries of these diperiodic plane groups are tabulated. Examples of applications illustrate the determination of the first‐order selection rules for the long‐wavelength normal modes of a layer. The symmetry species of these principal modes are obtained, as in triperiodic crystals, through correlations between the reduced representation of the factor group of the layer diperiodic group and the representations of nuclear site groups, on the basis of atomic motions. Emphasis is placed on the splitting of the layer modes in a layered crystal. A procedure is described to relate a typical, quasi‐isolated layer to the real sample through a real layer in the sample, whose diperiodic group is a subgroup of both space groups corresponding to the preceding structures. The method is similar to the molecular site group analysis and provides directly, for a specific type of layer motion, the correlations between equivalent layers. The quasi‐isolated layer approximation is used to study the principal vibrations of graphite intercalation compounds and of anisotropic crystal polytypes with more than one layer per unit cell.