A model study of the growth of crystals consisting of a small number of metal atoms by the Hückel molecular orbital method (I). Addition of One atom to small crystals

The paper deals 1) with the regularities of the formation of ( N + 1)‐atomic clusters during the growth of N ‐atomic one‐, two‐, and three‐dimensional crystals and 2) with the distribution with respect to stability of the ( N + 1)‐atomic clusters. The N ‐atomic crystals have the structure of a hypothetical metal with a simple cubic lattice and a small number of one‐electron atoms. The binding energy (BE) of the clusters calculated by the Hückel molecular orbital method was assumed to be a measure of their stability. Interactions between nearest‐neighbours only were taken into account. The most stable ( N + 1)‐atomic cluster formed from a one‐dimensional crystal is that in which the N + 1‐st atom is bonded to the end atom of the N ‐atomic one‐dimensional crystal. For two‐dimensional crystals, the N + 1st atom forms the strongest bond with an atom from the diagonal of the square. With three‐dimensional crystals, the N + 1st atom is most strongly bonded to a corner atom of the small crystal. The inhomogeneity in the bond energy of the N + 1st atom to a surface atom of the small N ‐atomic crystal decreases with increasing N . According to earlier studies of ours, the BE per atom increases, whereas the mean energy of a nearest‐neighbour bond decreases with increasing N .