The dependence of electrical resistivity on short-range order

Abstract

The residual resistivity rho is calculated for a binary alloy in terms of the degree of short-range order, the alloy composition and the number of conduction electrons per atom. A model is considered in which only s-s scattering occurs and in which the s electrons are described by free electron wavefunctions. This leads to an expression of the form rho varies as Sigma i=0ci alpha iYi when alpha i are the usual Cowley short-range order parameters of the ci atoms in the ith shell at distance Ri.Yi is an integral which may either be positive or negative depending on Ri and the number of conduction electrons per atom. The sign of d rho /dT calculated from the above equation will thus depend on the signs of the parameters alpha i and also of the integrals Yi. In the system for which both the resistivity and the short-range order parameters alpha i have been measured, substitution of the values of alpha i into the derived equation yields results for d rho /dT in good agreement with those experimentally observed. The argument is extended to include the effects of the magnetic order-disorder phenomenon on the residual resistivity.