  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 favour of the
(111)-faceted step, in excellent agreement with experiment; the equilibrium
shape of islands should therefore clearly be non-hexagonal. 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.
