Quantum Theory of the Residual Electrical Resistivity of Disordered Alloys

Abstract

Nordheim's theory for purely random alloys and Hall's extension for nonrandom alloys in terms of Cowley parameters are further developed and applied to substitutional binary systems. The theory is valid for any degree of order, excepting perfect superlattices. Purely random alloys and nonrandom alloys are shown to possess certain analogies with normal and umklapp processes, respectively. By accounting for those Fermi volume changes with concentration arising when the two atoms are different in size and valence, it is possible to explain the experimental non-parabolic curves of resistivity versus concentration. Applications are made to the cases of the Cu-Au and the Cu-Ni systems rapidly quenched from a high temperature. Results of a limited study of the data for the slowly annealed Cu-Au system are presented, but more experimental measurements of the Cowley parameters are required to test the theory. A few new relations obeyed by the Cowley parameters are given. The work reported here meets certain independent checks carried out by Christy in unpublished calculations on ordering energy.