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=0c_i alpha _iY_i when alpha _i are the usual Cowley short-range order parameters of the c_i atoms in the ith shell at distance R_i.Y_i is an integral which may either be positive or negative depending on R_i 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 Y_i. 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.