In observations of Brownian motion of islands of adsorbed atoms and of vacancies with a mean radius R, the cluster diffusion constant had varied as R-1 and R-2. From an analytical Langevin description of the cluster's step-like boundary, three cases, R-1, R-2 and R-3 were found, corresponding to the three microscopic surface mass-transport mechanisms of straight steps. This thus provided a unified treatment of the dynamics of steps and clusters. For corroboration, Monte Carlo simulations of simple lattice gases were performed and atomistic diffusion constants were derived.

Diffusion of Monolayer Adatom and Vacancy Clusters: Langevin Analysis and Monte Carlo Simulations of Their Brownian Motion. S.V.Khare, N.C.Bartelt, T.L.Einstein: Physical Review Letters, 1995, 75[11], 2148-51