Anharmonic effects in ionic crystals

Abstract

The effects of the anharmonicity of the normal modes of vibration in crystals have been studied by using thermodynamic Green's functions. It is found that for some purposes a quasiharmonic approximation can be introduced, in which the frequencies of the normal modes are those which can be measured experimentally by neutron, or infra-red spectroscopy. This approximation is particularly important for ferroelectric crystals, in which the frequencies of some of the normal modes are strongly temperature dependent. Very good descriptions, in the harmonic approximation, of the frequencies of the normal modes, which have been determined by neutron spectroscopy, were obtained by using a shell model for potassium bromide, and sodium iodide. These calculations have now been extended by making simple assumptions to obtain the third and fourth order potentials, so that the anharmonic properties can be calculated, with reasonable confidence in the frequencies and normal modes of the quasiharmonic approximation. Detailed calculations are presented of the thermal expansion, dielectric properties, and neutron scattering cross-sections of long wavelength vibrations for potassium bromide and sodium iodide.