A 2-dimensional model for a stoichiometric ordered alloy was considered in which the sub-lattices existed a priori. This model was a natural extension to the ordered state of the familiar random alloy model. A particular study was made of the apparent contribution which the 6-jump cycle made to the tracer and vacancy diffusion coefficients as a function of the long-range order. This contribution had not previously been calculated. By using a combination of exact expressions and Monte Carlo computer simulations, it was shown that the tracer and vacancy diffusion coefficients, as based only upon 6-jump cycles, approached the respective tracer and vacancy diffusion coefficients – for a simple vacancy mechanism - as the long-range order parameter approached unity. The rate of approach was dictated by the relative mobilities of the atomic components. It was suggested that the contribution to the tracer diffusion coefficient in real materials, which arose from the 6-jump cycle at diffusion temperatures, was likely to be relatively small.

The Contribution of the Six-Jump Cycle to Tracer Diffusion in a Two-Dimensional Ordered Structure. I.V.Belova, G.E.Murch: Philosophical Magazine A, 2000, 80[7], 1481-93