A semi-analytical method to compute surface elastic properties

In this paper, a semi-analytic method is developed to compute the surface elastic properties of crystalline materials. Using this method, surface elastic properties, such as the intrinsic surface energy density, intrinsic surface stress and surface elastic stiffness, are given analytically in terms of the inter-atomic potentials of the material. To evaluate these analytical expressions, one needs to know only the equilibrium (or relaxed) positions of the atoms near the free surface. The relaxed positions of the atoms near the free surface can be obtained by conducting a standard molecular simulation of a free surface. In comparison with existing methods, the semi-analytical method developed here reduces the amount of computation significantly. More importantly, because of the analytical nature of the method, it can provide us with a much better understanding of the surface characteristics. To illustrate the methodology, low-index surfaces (1 1 1), (1 0 0) and (1 1 0) of face-centered cubic metals Cu, Ni, Ag, and Pd are considered. A full set of data on surface elastic properties including the intrinsic surface energy, the intrinsic surface stress tensor, and the surface elastic stiffness tensor have been computed and are reported here for these materials. It is believed that such a complete set of surface property data for these materials are new to the literature.