Percolative aspects of diffusion in binary alloys

We discuss the diffusion of a species C in an A-B, disordered, substitutional, binary alloy. When the diffusivity of C in one pure phase is much larger than that in the other pure phase, the problem can take on percolative aspects. We construct a simple model of diffusion in the alloy for this case, and treat it both analytically in an approximate effective-medium theory, and numerically using a random-resistor-network approach. This work was prompted by recent experiments on the substitutional alloy GeₓSi_1-x, and detailed comparisons to that system are made throughout. The model is surprisingly successful in explaining the detailed behavior of the activation energy for diffusion and the exponential prefactor as a function of composition in the Ge-Si binary.