Exploring stereographic surface energy maps of cubic metals via an effective pair-potential approach

A fast and efficient way to calculate and generate an accurate surface energy database (of more than several million surface energy data points) for all bcc and fcc metals is proposed based on an effective pair-wise-potential model. The accuracy of this model is rigorously tested and verified by employing density functional theory calculations, which shows good agreement within a mean absolute error of 0.03 eV/atom. The surface energy database generated by this model is then visualized and mapped in various ways; namely, the surface energy as a function of relative orientation, a orientation-dependent stereographic projection (the so-called Wulff net), and Gibbs--Wulff construction of the equilibrium crystal shape, for comparison and analysis. The Wulff nets (drawn with several million surface energy data points) provide us with characteristic surface energy maps of these cubic metals. In an attempt to explain the surface energy anomaly in bcc Li, we demonstrate how our effective-pair-potential-derived Wulff net can clearly discriminate the strong influence of the second- and third-nearest-neighbor bonds on the high-Miller-index surface energetics of bcc Li.