Theory of the Resistivity Change in a Metal due to Multiple Point Imperfections

Abstract

A unified theory is proposed for the resistivity change in a metal due to an arbitrary distribution of point imperfections and to the lattice strain around them. Mott's treatment of the scattering power of an isolated impurity atom in a free-electron metal, using the phase-shift formalism, has been generalized to apply to a complex of interacting point defects. Lattice distortion is approximated in the scattering scheme by a system of charge dipoles. The theory takes a very tractable form when the scattering potential of the assembly is very nearly a superposition of the potentials of discrete imperfections. Empirical data on the scattering power of isolated point defects can then be utilized to yield good estimates for the resistivity change due to aggregates of these defects. For illustration, the scattering power of vacancies, interstitials, divacancies, di-interstitials, Frenkel pairs, and trivacancies in copper have been evaluated.