Cellular Method for Wave Functions in Imperfect Metal Lattices

Abstract

A general method is proposed for constructing conduction-band wave functions in nonperiodic monovalent metals and alloys. The method is a cellular approximation in which it is assumed that the lattice potential can be considered to be spherically symmetric within ellipsoidal cells centered on the individual ions. It is shown that the resulting wave functions are correct, within this approximation, to first order in a parameter which corresponds to the wave number in a perfect crystal. In the case of a strained metal in which the strains vary slowly in space the method takes a form analogous to the deformation-potential formalism, but contains a term which is first order in the derivatives of the strain.