Surface segregation and ordering of alloy surfaces in the presence of adsorbates

We argue that surface segregation can be substantially modified by the presence of adsorbates and present a first-principles method that allows us to equilibrate segregation and adsorption simultaneously on surfaces with fixed topology. The method is based on a cluster expansion theory to write the state of the system in terms of adsorbate and surface layer occupation variables. This model can be parametrized with density functional theory calculations and equilibrated at finite temperature with Monte Carlo simulation. The method is applied to surface ordering and segregation at a (111) surface of ${\mathrm{Pt}}_{(1\ensuremath{-}x)}{\mathrm{Ru}}_{x}$ alloys in the presence of adsorbing oxygen. While Pt segregates under vacuum conditions, the strong binding between oxygen and Ru couples the segregation energy of the Ru to the oxygen chemical potential. As a result, we find that variations in oxygen chemical potential can dramatically alter the segregation and surface ordering tendency of dilute Ru in Pt.