A two-dimensional model of a stoichiometric ordered alloy was considered where the sub-lattices existed a priori. The model was a natural extension to the ordered state of the well known random alloy model. Of interest was the apparent contribution of the six-jump cycle to the tracer and vacancy diffusion coefficients as a function of long-range order. Although this contribution was discussed qualitatively on many occasions, it had never been calculated. Using a combination of exact expressions and Monte Carlo computer simulation it was shown that the diffusion coefficients (tracer and vacancy) by purely six-jump cycles approach the respective diffusion coefficients (tracer and vacancy) by a simple vacancy mechanism as the long-range order parameter approached unity. The rate of approach was dictated by the relative strengths of the mobilities of the atomic components. It was suggested that the numerical contribution to the tracer diffusion coefficients in real materials from the six-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