Work functions and surface charges at metallic facet edges

The electronic charge densities and work functions at sharp metallic facet edges are determined from {\em ab initio} calculations, combined with macroscopic averaging techniques. In particular, we examine how two different work functions coexist at close range near edges between inequivalent facets. The surface ionic relaxation at facet edges is shown to influence appreciably the local electrostatic potential in the vacuum. Various edges between Al(100) and Al(111) facets are studied, as well as between Na(110) facets. We also develop a model of electronic surface dipoles, which accounts for the surface charge transfer between inequivalent facets, and which allows us to predict the influence of the shape and size of a macroscopic crystal on its work functions.