Lattice infrared absorption and Raman scattering in finite crystals

The ir absorption and Raman scattering associated with the lattice vibrations of a solid have been calculated for a simple harmonic model in which the system is treated as a giant molecule. A number of differences occur in the optical properties of this finite system and one in which the system is regarded as infinite in extent. The main difference is the appearance of some first order absorption and scattering over the entire range of permitted lattice frequencies instead of only at a few specific frequencies predicted by the factor group selection rules of the infinite system. While such differences might be difficult to detect employing the usual ways of investigating the optical properties of solids, they might become observable by the study of small crystals. In addition to being of fundamental interest, such observations may also be of some value in revealing critical and surface mode frequencies.