Size-dependent surface energy density of typically fcc metallic nanomaterials

The surface energy density of nano-sized structural elements exhibits an obvious size-dependent feature. To study this interesting phenomenon, atomistic calculations are carried out in the present paper for different face-centered-cubic (fcc) metallic nano-slabs. Lagrangian and Eulerian descriptions are adopted, respectively, in order to find the varying trends of surface energy densities in an initially un-deformed configuration and a current one. It is found that the Lagrangian surface energy density increases monotonically with an increase of the nano-slab's thickness in the former no matter what the surface orientation is; while the variation of the Eulerian one is indefinite. The surface relaxation parameters are further simulated for differently oriented surfaces, which gives a very good explanation for the differences between the Lagrangian and Eulerian surface energy densities. The results in this paper should be a useful supplement to theoretical studies on the surface/interface effect of nanomaterials.