Exact results were presented for the surface diffusion of small 2-dimensional clusters whose constituent atoms were commensurate with a square lattice of adsorption sites. Cluster motion was due to the hopping of atoms at various rates along the cluster perimeter. A formalism was applied which described the evolution in reciprocal space via a linear master equation with a dimension equal to the number of cluster configurations. Attention was focussed upon the rapid-hopping regime of atoms along straight close-packed edges, where certain sub-sets of configurations cycled rapidly between one another. Each sub-set was treated as a single quasi-configuration; thereby reducing the dimension of the evolution equation, simplifying the analysis and clarifying the limiting behavior. The influence of concerted atom motions upon the diffusion of tetramers and larger clusters was also considered.

Diffusion of Small Clusters on Metal (100) Surfaces: Exact Master-Equation Analysis for Lattice-Gas Models. J.R.Sanchez, J.W.Evans: Physical Review B, 1999, 59[4], 3224-33