Direct enumeration of the geometrical characteristics of clusters

The geometrical characteristics of cubo-octahedral, icosahedral, body-centered cubic, and simple cubic clusters are systematically studied and enumerated as a function of the number of sites in the cluster. The various types of sites and the number of first nearest-neighbors for each one of the structures are analyzed. One-parameter analytic expressions, to calculate the total number of sites in the cluster, those at the surface, the number of sites of the various kinds, the dispersion, the number of bonds, and the average coordination number, are presented. In the dispersion relationships, we studied the contributions arising from the face, vertex, and edge sites. The average coordination number of the core, the one of the surface and between the core and the surface are also calculated. (C) 1997 Acta Metallurgica Inc.