INFRARED AND RAMAN SELECTION-RULES IN DIPERIODIC 3-DIMENSIONAL LAYERS

Diperiodic three-dimensional layers are distributed among 31 orientati on classes and 80 plane groups of which 43 are symmorphic. The site sy mmetries of these diperiodic plane groups are tabulated. Examples of a pplications illustrate the determination of the first-order selection rules for the long-wavelength normal modes of a layer. The symmetry sp ecies of these principal modes are obtained, as in triperiodic crystal s, through correlations between the reduced representation of the fact or group of the layer diperiodic group and the representations of nucl ear 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 sampl e through a real layer in the sample, whose diperiodic group is a subg roup of both space groups corresponding to the preceding structures. T he method is similar to the molecular site group analysis and provides directly, for a specific type of layer motion, the correlations betwe en equivalent layers. The quasi-isolated layer approximation is used t o study the principal vibrations of graphite intercalation compounds a nd of anisotropic crystal polytypes with more than one layer per unit cell.