The stability of vicinal surfaces and the equilibrium crystal shape of Pb by first principles theory

The orientation-dependent surface energies of fcc Pb for more than 30 vicinal orientations, distributed over the [110] and [001] zones of the stereographic triangle, have been studied by density-functional theory. For bulk-truncated structures almost all vicinal surfaces are found to be unstable and would facet into (111) and (100) orientations. However, after surface relaxation, all vicinal surfaces are stable relative to faceting into (111) and (100) orientations. There are also regions of relaxed vicinal surfaces which will facet into nearby stable vicinal surfaces. Overall, surface relaxation significantly affects the equilibrium crystal shape (ECS) of Pb. In both the [110] and [001] crystallographic zones the (110), (112), (221), and (023) facets are found on the ECS only after relaxation, in addition to (111) and (100). This result is in agreement with the experimental ECS of Pb at 353 K. Step formation energies for various vicinal orientations are estimated from facet diameters of the theoretical ECS and compared with experimental data.