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 ext ension to the ordered state of the well known random alloy model. Of intere st is the apparent contribution of the six-jump cycle to the tracer and vac ancy diffusion coefficients as a function of long-range order. Although thi s contribution has been discussed qualitatively on many occasions, it has n ever been calculated. Using a combination of exact expressions and Monte Ca rlo computer simulation we show that the diffusion coefficients (tracer and vacancy) by purely six-jump cycles approach the respective diffusion coeff icients (tracer and vacancy) by a simple vacancy mechanism as the long-rang e order parameter approaches unity. The rate of approach is dictated by the relative strengths of the mobilities of the atomic components. It is sugge sted that the numerical contribution to the tracer diffusion coefficients i n real materials from the six-jump cycle at diffusion temperatures is likel y to be relatively small.