Model of surface segregation driving forces and their coupling

Abstract

Separating the surface segregation enthalpy into three elementary contributions (cohesive, alloy, and size) has been proposed by many authors but rarely tested quantitatively. A three element separation rule has been derived from a tight-binding Hamiltonian 15 years ago. It has yielded very satisfying results for various environments (close-packed surfaces, vicinal surfaces, grain boundaries, and clusters) for the Cu-Ag system and for many other alloys. However recently this rule has stumbled over the Co-Pt system. We therefore develop an approach---the coupled three effects model (CTEM)---based on a systematic study of the properties of permutation enthalpies---both in the bulk and in the surface---as a function of the value of the mixed interaction involved in the $N$-body interatomic potentials derived from the second moment approximation of the tight-binding scheme. We show that both the disagreement previously observed for Co-Pt and the agreement mentioned above for Cu-Ag can be explained by the variation of the alloy effective pair interactions (EPIs) in the surface and by the existence of coupling coefficients between the three effects. We also show that the surface EPIs are proportional to the bulk EPIs when the difference of atomic radii of the components can be neglected, while they differ from an additive constant in the presence of a large size effect. We suggest general criteria to determine alloys where the present improvements are expected to be significant.