Effective cluster interactions at alloy surfaces and charge self-consistency: Surface segregation in Ni–10 at. % Al and Cu-Ni

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Abstract
First-principles results are presented for the effective cluster interactions at the surface of a random Ni–10 at. % Al alloy. The derivation is based on an extension of the generalized perturbation method to semi-infinite inhomogeneous binary alloys, using a layer version of the Korringa-Kohn-Rostocker multiple-scattering approach in conjunction with the single-site coherent potential approximation to compute the self-consistent electronic structure of the system. When applied to the bulk, the method yields effective pair interactions that have the full point-group symmetry of the lattice to a very high level of numerical accuracy, despite the fact that intra- and interlayer couplings (scattering-path operators) are treated differently, and which are in perfect agreement with those of a recent three-dimensional treatment. Besides the pair terms, a selected class of triplet and quadruplet interactions are calculated, as well as the point interactions induced by the presence of the surface. The value of the latter in the first lattice plane is strongly exaggerated in our approach, leading to a complete segregation of the minority species to the surface. Using a value corresponding to the difference in the surface energies of the pure components for this term leads to the observed Al concentration of ≊25% at the surface. Possible reasons for the shortcomings of the theory are analyzed, and test calculations for the well studied Cu-Ni system show that the free energy of the semi-infinite alloy cannot be approximated by the sum over the single-particle band energies, once charge self-consistency is enforced at the surface.