Lattice Vibrations and Harmonic Forces in Solids

Abstract

A discussion is given of the interpretation in terms of harmonic forces between atoms of the phonon frequency against wave vector data which is provided by the results of both X-ray and neutron scattering experiments. A knowledge of the phonon polarization vectors is required before a calculation of the components of the interatomic harmonic force tensors between all neighbour atom pairs can be made, but for lattice waves propagating along the symmetry directions of a crystal the Fourier series expansions of the dispersion curves give directly the harmonic force constants between entire planes of atoms. The interpretation of these interplanar force constants in terms of a model with interatomic tensor harmonic forces between a limited number of atom neighbours may require that the interplanar force constants satisfy an internal consistency relation; the failure of the X-ray data for aluminium to satisfy this relation exactly suggests either that atoms beyond the fourth nearest neighbour are interacting appreciably or that the concept of static harmonic forces between atoms is breaking down.