Epitaxial growth of fcc clusters

The statistics of epitaxially grown free fcc clusters is studied in a simple growth model, where the clusters have only (111) surfaces, and only one facet grows at a time. The abundance spectrum shows regular oscillations as a function of ${\mathit{N}}^{1/3}$ and as a function of ${\mathit{N}}^{2/3}$. The former corresponds to octahedral growth pattern, although only an insignificant number of the clusters are perfect octahedra. The latter is a result of the differences in the facet sizes of imperfect octahedra.