Correlation Factors for Diffusion in Nondilute Alloys

Abstract

Correlation factors for diffusion in binary and multicomponent alloys are calculated for a random-alloy model with diffusion by a vacancy mechanism. This model, which should apply best for nondilute alloys, assumes that atoms and vacancies are randomly distributed and that suitable average values can be used to represent the actual atom and vacancy jump frequencies in the crystal. In alloys, both atoms and vacancies follow correlated walks. Also, the atom correlation factors are influenced by the nonrandom motion of the vacancies. Thus, in order to treat correlation effects in concentrated alloys properly, one must consider not only the correlation factors ${f}_{i}$ for diffusion of atoms but also the correlation factor ${f}_{v}$ for diffusion of vacancies. In specific calculations, one also must find the partial correlation factors ${f}_{v}^{i}$ for diffusion of vacancies by exchange with atoms of the particular species $i$. Analytic expressions for all of these correlation factors are calculated. These equations can be expressed directly in terms of the measureable tracer-diffusion-coefficient ratios $\frac{{D}_{i}^{*}}{{D}_{k}^{*}}$ with no unknown jump frequencies appearing. The calculations also yield a forbidden region in the plot of diffusion-coefficient ratio as a function of alloy composition, with correlation factors going to zero at the boundary of this region. Specific applications to binary alloys are discussed.