Theory of surface segregation in metallic alloys: The generalized perturbation method

Abstract

The energetics of the surface region of metallic alloys and the surface segregation are studied in terms of an effective Ising Hamiltonian, whose parameters (often called effective cluster interactions (ECIs)) are determined from ab initio electronic structure calculations using the force theorem. The tight-binding linear muffin-tin orbital method is used in combination with the coherent potential approximation and the formalism of surface Green functions. The band term is treated within the generalized perturbation method (GPM) and the contributions to the on-site effective interactions arising from the core states, the double-counting and the Madelung terms are included. The surface concentration profile and its dependence on the temperature are studied by methods of statistical mechanics, in particular, using a Monte Carlo (MC) simulation. The electronic structure and the Ising Hamiltonian parameters are then recalculated for the new profile, and this procedure is repeated until self-consistency between the electronic structure and the segregation profile is achieved. As an illustration, we review the results for various alloys and as a case study we present and discuss in detail the Pt–Rh alloy system.