Collective diffusion of adsorbed particles on stepped surfaces was studied using analytical and numerical techniques. The Langmuir lattice-gas model was used, where the distribution of adatoms on the surface was determined solely by the difference in adsorption energy of atoms on terraces and along step edges. For the system in equilibrium, the master equation approach was considered for collective diffusion across the steps within the dynamic mean-field approximation. It was demonstrated that results obtained for the collective diffusion coefficient were sensitive to the choice of relevant slow variables for inhomogeneous systems such as stepped surfaces. Diffusion across steps was then considered for situations in which the system was not in equilibrium; such as during spreading or ordering. Thus, a phenomenological theory was considered using a balance between particle fluxes across a stepped surface within the linear response theory. This permitted the derivation of expressions for effective diffusion coefficients in the limit of large and small coverages, where the results agreed well with the collective diffusion coefficient within the corresponding limits.

Theoretical Approaches to Collective Diffusion on Stepped Surfaces. Z.Chvoj, M.Masín, T.Ala-Nissila: Journal of Statistical Mechanics, 2006, 100038