Optical Spectra of Orientationally Disordered Crystals. I. Theory for Translational Lattice Vibrations

Abstract

There is a class of crystals in which the molecules are arranged on or near regular positions in space, but are irregularly oriented. The irregular orientation of the molecules frequently perturbs only slightly the translational lattice vibrations of the crystal, that would be perfectly periodic if the irregular orientation were absent. For a first approximation, then, the crystal can be considered to have mechanically regular vibrations. In particular, any normal vibration can be described in terms of a wave vector k that is the wave vector of the dominant Fourier component of the vibration. The irregular orientation of the molecules will cause the dipole-moment change due to a displacement of a particular molecule to depend in magnitude and direction upon its own orientation and upon the orientation of its neighbors. The crystal is thus in a sense electrically irregular. The theory of the optical spectra due to the translational lattice vibrations of these mechanically regular, electrically irregular crystals is discussed assuming that the translational and rotational vibrations are not coupled. All the vibrations are active in both infrared and Raman spectra, and to a first approximation, for a crystal with only one nearest-neighbor central interaction, the intensity of absorption or of Raman scattering by any particular normal vibration of the crystal that is active only because of the irregularity of the orientations (there may, of course, be vibrations that are active in the absence of electrical irregularity) is proportional to the square of its frequency. For more realistic models, the relationship is more complicated. The optical spectra of these crystals provides, therefore, information about the spectrum of lattice vibrations. In particular, features in the optical spectrum probably arise mainly from features in the vibrational spectrum, and it may be possible to identify corresponding features. In addition, these crystals are intermediate between perfect crystals, which are mechanically and electrically regular, and vitreous solids, which are mechanically and electrically irregular. The study of their spectra should therefore provide an approach to understanding the spectra of vitreous phases.