Abstract
A model for predicting the surface segregation of solute in very dilute binary solid alloys is developed. The two main factors contributing to the driving force for segregation are the bond strength ratio ϵ ∗ and size ratio σ ∗ for the solute atom in the solvent matrix. These differences are accounted for implicity by considering various solid solution systems in bulk and surface configurations and by minimizing the total potential energy of the systems (0 K) through atomic relaxation consistent with the assumed long-range, pairwise interactions between the atoms. In previous studies, these two factors have been treated separately in an “ad hoc” manner and the strain energy due to the odd-size solute atom in the solvent lattice has been estimated using various continuum elasticity models. We demonstrate the short-comings of the conventional approach, in particular the failure of the simple continuum elasticity theory to accurately estimate the elastic driving force. We invent the ϵ ∗−σ ∗ representation which greatly facilitates a comparison of the various theories with one another and with experiments, the usefulness of this representation residing in the important finding that the theoretical boundary separating segregation and non-segregation regions depends only on ϵ ∗ and σ ∗. Comparison of our theory with experiment in 31 cases yields 28 correct predictions.
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