Factor-group analysis of high-symmetry layer dynamics

The method of factor-group analysis used for molecular crystals has been extended to the case of layer crystals which usually have very high symmetry. In case of such high-symmetry layer crystals, the optically active modes are divided into compressional and shear types. It is found that there is a one-to-one correspondence between a compressional and a doubly degenerate shear mode in case of the layer crystals in which each atomic sheet contains only one atom of the unit cell. Further it is shown that for such simple layer crystals the matrix for the transformation to symmetry coordinates is the same for both compression and shear motions. This leads to considerable simplification in the numerical solution of the dynamics of these structures. The numerical calculations for the intralayer modes of Mo${\mathrm{S}}_2$, Pb${\mathrm{I}}_2$, GaS, and GaSe are presented in both the nearest- and the second-nearest-neighbor approximations.