Long-wavelength normal mode vibrations of infinite, ionic crystal lattices. II

Abstract

In an earlier paper [J. Math. Phys. 16, 1156 (1975)] we presented a mathematical theory of the long-wavelength normal mode vibrations of infinite crystal lattices whose particles interact with Coulomb forces. (Retardation was neglected.) The paper showed how the eigenvalues and eigenvectors of the complete long-wavelength dynamical matrix are related to the eigenvalues and eigenvectors of the dynamical matrix obtained by neglecting the contribution of the macroscopic electric field. Rules were obtained for determining whether or not the various branches of the dispersion relations for a lattice approach definite frequencies in the long-wavelength limit. The paper was restricted to the rigid ion approximation. In this paper we show that the above treatment can be easily extended to include lattices with polarizable and deformable atoms.