First-principles study of low-index surfaces of lead

Abstract

We report a density-functional theory study for $\mathrm{Pb}(111)$, $\mathrm{Pb}(100)$, and $\mathrm{Pb}(110)$ surfaces using ab initio pseudopotentials and a plane-wave basis set. Creating the pseudopotential with the $6s$, $6p$, and $6d$ states in the valence shell is found to yield good results for the bulk lattice constant, bulk modulus, and cohesive energy. Convergence of the surface energies with plane-wave cutoff, $\mathbf{k}$-mesh, vacuum and slab thickness was carefully checked, as was the effect of the nonlinearity of the core-valence exchange-correlation interaction. Employing the local-density approximation of the exchange-correlation functional we obtain excellent agreement of the calculated surface energies and surface-energy anisotropies with recent experimental results. However, with the generalized gradient approximation the calculated surface energies are about 30% too low. For all three studied surfaces, the calculations give interlayer relaxations that are in reasonable agreement with low-energy electron diffraction analysis. The relaxations exhibit a damped oscillatory behavior away from the surface, which is typical for a metal surface.