Cluster motion on surfaces: A stochastic model

Abstract

A stochastic model of the diffusion of clusters on crystalline surfaces is presented. The cluster configurations are mapped onto a periodic lattice with internal states. The formulation is capable of treating complex kinetics, cluster structures, and surface topologies. A detailed analysis of dimers with two and three allowable states in one and two dimensions is given. These correspond to recent observations of the diffusion of atomic clusters on surfaces by field-ion microscopy techniques. Expressions for the transition rates between spatial configurations involved in the motion of the clusters are derived in terms of experimental observables. It is demonstrated that for a complete determination of the parameters characterizing the various cluster configurations (i.e., activation energies and frequency factors) full use of the field-ion microscope data (moments of the cluster centroid displacement and equilibrium-state occupation probabilities) is required. The effect of a bias field is included in our analysis, and shown to be essential in certain cases for a complete determination of the transition rates. The effect of periodically placed defects on the diffusion on surfaces is investigated.