The embedded-atom model applied to vacancy formation in bulk aluminium and lithium

The embedded-atom model (EAM) is applied to the study of vacancy formation in bulk aluminium and lithium. A systematic study is undertaken into the sensitivity of the EAM potentials and embedding energy functionals as a function of the unrelaxed vacancy formation energy which is normally obtained via ab initio density functional calculations. The effect of this `empirical' input parameter on the vacancy relaxation energy, formation volume and structural relaxation is also investigated using super-cell sizes not normally accessible in orbital-based ab initio relaxation studies. We find that for aluminium, for which at most a fifth-nearest-neighbour model is required, the vacancy relaxation energy and formation volume are not sensitive functions of the unrelaxed vacancy formation energy. For lithium, for which at least a ninth-nearest-neighbour model is needed, the situation is somewhat different: both the vacancy relaxation energy and the formation volume are found to be a noticeably related to the unrelaxed vacancy formation energy. For both solids, the structural relaxation was found to be largely insensitive to the unrelaxed vacancy formation energy, agreeing well with previous ab initio calculations. In particular for aluminium, the EAM result agrees extremely well with recent orbital-free density functional calculations which use super-cell sizes approaching those used here. Finally, we find that for lithium, the embedding energy functional has negligible curvature for a wide range of local electronic densities, justifying the use of a simpler pair potential description for lithium in mildly inhomogeneous systems.