The lattice dynamics of ionic and covalent crystal

Abstract

First-order perturbation theory is used to derive the equations governing the normal modes of vibrations of a crystal in which the atoms are polarizable. The method is based on the harmonic, electrostatic and adiabatic approximations, it is thus assumed that all phonon frequencies are much lower than the frequencies of electron transitions; the results therefore do not apply to metals. In the dipolar approximation the equations derived are found to be identical with those which have been obtained for the `shell model' of a crystal, and which are known to give results in rather good agreement with the measured dispersion relations for phonons in germanium and sodium iodide. The method is extended to include the interaction of quadrupole and higher moments of the electron distribution of an atom or ion.