Many-body effects on surface stress, surface energy and surface relaxation of fcc metals

The results of an investigation aimed at isolating the role played by pair-wise and many-body contributions in determining the surface stress, surface energy and surface relaxation for clean, low-index fcc metal surfaces are presented. General expressions for surface stress and surface energy are developed for generic embedded atom method (EAM) potentials and are contrasted with results derived from central-force pair potentials. Calculations are presented for specific forms. We find that these pair-wise and many-body contributions usually act in opposition to each other. Pair potentials tend to produce compressive surface stress contributions and favor outward surface relaxations, while the many-body component produces tensile surface stress contributions and favors inward relaxations. We also bring to light certain relationships between surface and bulk thermodynamic properties within the framework of these models. It is shown how surface stress can be expressed in an approximate form involving terms proportional to the product of an elastic modulus and the neighbor spacing characteristic of the material, and constants of proportionality that depend only on surface orientation. This form provides a good fit to a set of first-principles results as well. Finally, we demonstrate how various surface properties display a strong correlation with the ratio of bulk-to-shear moduli, Beq/Geq.