Self-Similar Spatial Ordering of Clusters on Surfaces during Ostwald Ripening

The concept of self-similarity during late stage phase separation on surfaces will be investigated. We present the self-similar evolution of spatial ordering as a novel feature, supplementing previous discussions in the literature on scaling power laws of cluster growth and self-similar evolution of the cluster size distribution. Based on experimental data on the ripening of three-dimensional Sn clusters on Si(111) surfaces a mechanism for the observed dynamics will be discussed which is consistent with the observation of the ordering at areal cluster coverages as low as 0.1%.