Polycrystalline surface properties from spherical crystallites: Ag, Au, Cu and Pt

Abstract

We have performed a series of atomistic simulations of nearly spherical, crystalline (fcc) clusters of Ag, Au, Cu and Pt as a function of temperature and cluster size. Since both a spherical cluster and a random polycrystal expose all possible surfaces equally, this provides a plausible approach for determining the surface properties of random (non-textured) polycrystalline metals and to find a simple expression to relate these average surface properties to the oft calculated properties of high symmetry/low index surfaces. Atomic clusters with radii greater than approximately 4a0 yield cluster average surface energies and surface stresses are within a few percent of those obtained from very large clusters. The variation of the cluster average surface properties with cluster size is dominated by a geometrical effect associated with the discrete spacing between atomic planes and that the differences associated with differences in the atomic bonding between different elements is small, at least for the four elements considered herein. Comparison of the cluster average surface free energy with those of the more commonly studied high symmetry flat {100}, {110}, and the {111} surfaces suggest two useful approximations for the average surface free energy: (1) equating it to the surface free energy of a {110} surface and (2) using a linear fit to the {100}, {110}, and the {111} surface free energies. Conversely, the first approximation provides an accurate estimate of the {110} surface energy from experimentally measured polycrystalline surface energies.