A version of the vacancy mediated tracer diffusion model was developed which follows the properties of the physical system of In atoms diffusing within the top layer of Cu(001) terraces. This model differed from the classical tracer diffusion problem in that (i) the lattice was finite, (ii) the boundary was a trap for the vacancy, and (iii) the diffusion rate of the vacancy was different (here markedly enhanced) in the neighborhood of the tracer atom. A simple continuum solution was formulated for this problem, which together with the numerical solution of the discrete model compared well with the experimental results.

Vacancy Diffusion in the Cu(001) Surface - Random Walk Theory. E.Somfai, R.van Gastel, S.B.van Albada, W.van Saarloos, J.W.M.Frenken: Surface Science, 2002, 521[1-2], 26-33