Genetic-algorithms search for global minima of aluminum clusters using a Sutton-Chen potential

Abstract

The results of a genetic-algorithms search for the structures of the global total-energy minima for aluminum clusters with up to 58 atoms are presented. A Sutton-Chen potential has been used in describing the interatomic interactions. Energetic and structural properties---and especially their size dependence---are investigated, including the point groups, the radial atomic distributions, the bond lengths, the moments of inertia, and a stability function. Three so-called similarity functions have been defined to analyze the growth of the clusters. For clusters with somewhat more than ten atoms, the clusters consist of two atomic shells, and the structural properties of these depend mainly on the symmetry and size of the inner shell whereas the outer shell arranges around the inner one. Surprisingly, we find that ${\mathrm{Al}}_{13}$ is particularly unstable although it is of icosahedral symmetry and that ${\mathrm{Al}}_{55}$ is not of icosahedral shape but has a very low symmetry.