The contribution of the six-jump cycle to tracer diffusion in a two-dimensional ordered structure

In this payer a two-dimensional model of a stoichiometric ordered alloy is considered where the sublattices exist a priori. The model is a natural extension to the ordered state of the well known random alloy model. Of interest is 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 has been discussed qualitatively on many occasions, it has never been calculated. Using a combination of exact expressions and Monte Carlo computer simulation we show 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 approaches unity. The rate of approach is dictated by the relative strengths of the mobilities of the atomic components. It is suggested that the numerical contribution to the tracer diffusion coefficients in real materials from the six-jump cycle at diffusion temperatures is likely to be relatively small.