Island morphology and adatom self-diffusion on Pt(111)

The results of a density-functional-theory study of the formation energies of (100)- and (111)-faceted steps on the Pt(111) surface, as well as of the barrier for diffusion of an adatom on the flat surface, are presented. The step formation energies are found to be in a ratio of 0.88 in favor of the (111)-faceted step, in excellent agreement with experiment; the equilibrium shape of islands should, therefore, clearly be nonhexagonal. The origin of the difference between the two steps is discussed in terms of the release of stress at the surface through relaxation. For the diffusion barrier, we also find relaxation to be important, leading to a $20\%$ decrease of its energy. The value we obtain, 0.33 eV, however, remains higher than available experimental data; possible reasons for this discrepancy are discussed. We find the ratio of step formation energies and the diffusion barrier to be the same whether using the local-density approximation or the generalized-gradient approximation for the exchange-and-correlation energy.