Diffusion of small clusters on metal (100) surfaces: Exact master-equation analysis for lattice-gas models

Abstract

Exact results are presented for the surface diffusion of small two-dimensional clusters, the constituent atoms of which are commensurate with a square lattice of adsorption sites. Cluster motion is due to the hopping of atoms along the cluster perimeter with various rates. We apply the formalism of Titulaer and Deutch [J. Chem. Phys. {bold 77}, 472 (1982)], which describes evolution in reciprocal space via a linear master equation with dimension equal to the number of cluster configurations. We focus on the regime of rapid hopping of atoms along straight close-packed edges, where certain subsets of configurations cycle rapidly between each other. Each such subset is treated as a single quasiconfiguration, thereby reducing the dimension of the evolution equation, simplifying the analysis, and elucidating limiting behavior. We also discuss the influence of concerted atom motions on the diffusion of tetramers and larger clusters. {copyright} {ital 1999} {ital The American Physical Society}