On the Inconsistencies of Axially Symmetric Force Models for Noncubic Solids

Abstract

AbstractThe origin of the elastic inconsistency of a modified axially symmetric force model, proposed by Lehman, Wolfram, and De Wames, for noncubic solids and the circumstances under which its phonon frequencies become imaginary are analysed by making use of this model in the lattice dynamical study of face centred tetragonal indium. It is shown that the arbitrary differences in the tangential force constants along x and z directions destroy the compatibility between off‐diagonal and diagonal matrix elements, relatively stronger off‐diagonal elements give rise to imaginary frequencies at certain wave vectors along nonsymmetry directions while the failure of this model to comply with the rotational invariance conditions manifests itself as the elastic inconsistency. The distortions introduced by the deficiencies of this model into the phonon dispersion curves of f.c.t. indium, consequences of imposing additional invariance conditions on this model as well as its apparent equivalence with central and general tensor force models, are discussed.