A theory of diffusion in the ordered alloy .2. Percolation and tracer diffusion

In this study, a model of a long-range ordered alloy where the sublattices exist a priori is considered. The model is a natural extension to the ordered state of the well known random alloy model. The analysis developed in Belova and Murch (1996, Phil. Mag. A, 73, 117), which was an adaptation of the ordered model of Manning's formalism for the random alloy, is considered further with emphasis on the percolative behaviour. It is shown that the percolation threshold for the mobile component in the highly ordered alloy moves from a composition given by (1 - f(0)) where f(0) is the tracer correlation factor in the lattice of a pure component (the random alloy result) to a composition given by (1 - (f(0)/2)). Expressions for the average jump frequencies are also derived. These, in combination with the analysis of tracer correlation in Belova and Murch (1996), enable the tracer diffusion coefficients to be determined.