Correlated tracer diffusion in an ordered interface structure

In this paper, we postulate a simple two-dimensional structure that attempts to capture the character of many of the qualitative findings from computer simulations of diffusion paths in grain boundaries. We postulate two types of mechanism: those where single atom jumps occur and those where multiple atom jumps occur. We derive analytical expressions for the tracer correlation factors, including those correlation factors that appear in the analysis of the diffusion isotope effect. We also carry out Monte Carlo simulations of these correlation factors. We find very good agreement between the derived expressions for the correlation factors and the simulation results. We are able to show that, in the absence of knowledge about the kinetic energy factor DeltaK, isotope effect experiments cannot differentiate between a simple atom-jump mechanism and multiple-atom-jump mechanism.