The effect of a phonon on the charge density of a crystal

Abstract

The change in charge density caused by a phonon is analysed in terms of a vector field fs. The effective charges on the ions cause a macroscopic field as q to 0 and thus cause fs to have a non-analytic part. fs thus consists of the polarisation caused by the effective charges, and a part caused by neutral pseudoatoms, this part being analytic. Each pseudoatom is associated with a particular nucleus and consists of both a rigid and a deformable charge density. It is argued that when the effective charges are zero, a pseudoatom can be defined by the change in charge density caused by the movement of its associated nucleus. The dynamical matrix has a simple physical interpretation when expressed in terms of fs. It is then decomposed into five terms, involving the effective charges and the separate parts of the pseudoatom, each term having the correct symmetry properties. This expression has the correct limit as q to 0 and is valid for all q. The advantages of the formalism, both from a pictorial point of view and when performing calculations, are stressed.