THE DIELECTRIC TENSOR IN INCOMMENSURATELY MODULATED CRYSTAL PHASES

A characterization of the dielectric properties in incommensurately modulated phases is presented. First a microscopic description is adopted. It takes into account the structural restrictions imposed on a microscopic scale by the superspace group. The macroscopic optical properties are derived from it. The optical activity as observed in the incommensurate phases of several compounds cannot be explained within a plain microscopic approximation. Therefore, a mesoscopic level is considered, implying averaging distances large with respect to the basic unit cell parameters or even the modulation wavelength, but small with respect to the size of the finite crystal. The phenomenological approach presented is compatible both with the microscopic description based on a superspace group symmetry, as well as with the macroscopic one involving the point group of the average structure. In the case considered here (one-dimensional incommensurate modulation) the optical properties of the dielectric medium are analysed in terms of subperiodic groups, periodic along the direction of the modulation wave and homogeneous along the other two directions. It is shown that the optical properties are affected by the incommensurability and that small changes in symmetry related to boundary conditions can lead to macroscopic effects. To interpret the experimental data more quantitatively a Jones model is applied, which describes the mesoscopic spatial dispersion of the modulated dielectric tensor to vary periodically along the modulation and being constant in the plane perpendicular to it. This model is compared with the experimental results for the ellipticity angle-chi of (N(CH3)4)2ZnCl4 obtained for light propagating along the modulation.