Influences of the third and fourth nearest neighbouring interactions on the surface anisotropy of face-centred-cubic metals

Abstract

The structure and the anisotropic properties of the surfaces of face-centred-cubic (FCC) metals have been studied using the broken-bond model while considering the third and fourth nearest neighbouring (3rd and 4th NN) interactions. The pair potential expressions are obtained using the Rose–Vinet universal potential equation. The model is suitable for calculation of the property of a surface with arbitrary crystallographic orientations and can provide absolute unrelaxed surface energy values using three input parameters, namely the lattice constant, bulk modulus and cohesive energy. These parameters are available for the majority of FCC metals. The numerical results for 7 FCC metals have been obtained and compared with these obtained from ab initio calculations and experimental measurements. Good agreement is observed between the two. Taking into account up to the 4th NN interactions, the overall surface energy anisotropy for FCC metals was found to be between 12% to 16%, and the ratio between the surface energies at (100) and (111) planes was found to be 1.05. These values are less than those reported by conventional calculations but more similar to experimental measurements. It is found that the strength of 3rd and 4th NN interactions differs from one element to another, the Ni and Cu interactions being the most significant while the Au, Pt and Pb interactions are the least significant. This suggests that the polar diagrams of the surface energy of Ni and Cu are different from those of Au, Pt and Pb by showing cusps of the unconventional {110} and high-index {210}, {311} and possibly {135} poles. This provides explanations to the recent experimental observations of the {110}, {210}, {311} and {135} facets in equilibrated Ni and Cu crystallines.