Predicting surface-energy anisotropy of metals with geometric properties of surfaces and atoms.

Surface-energy anisotropy of metals is crucial for the stability and structure, however, its determining factors and structure-property relationship are still elusive. Herein, we identify three key factors for predicting surface-energy anisotropy of pure metals and alloys: the surface-atom density, coordination numbers and atomic radius. We find that the coupling rules of surface geometric determinants, which determining surface-energy anisotropy of face-centred-cubic (FCC), hexagonal-close-packed (HCP) and body-centred-cubic (BCC) metals, are essentially controlled by the crystal structures instead of chemical bonds, alloying or electronic structures. Furthermore, BCC metals exhibit material-dependent surface-energy anisotropy depending on the atomic radius, unlike FCC and HCP metals. The underlying mechanism can be understood from the bonding properties in the framework of the tight-binding model. Our scheme provides not only a new physical picture of surface stability but also a useful tool for material design.