Abstract
We develop a cluster-expansion (CE) formalism for the first-principles study of substrate-adsorbate interaction in order to study adsorbate-induced segregation. The simulation lattice, the configuration space, and the basis functions of the CE are bisected into separate but interacting subsystems. The method is applied to the C-contaminated Pt${}_{25}$Rh${}_{75}$$(100)$ surface. For such catalytic surfaces, it is essential to understand the change in the segregation profile of the substrate due to the presence of adsorbates. In accordance with experiments, we find that even a small amount of C impurities leads to a considerable decrease in the Pt segregation to the topmost substrate layer. We discuss the coupling of the substrate with the adsorbate layers in the CE Hamiltonian, the $T=0\phantom{\rule{4pt}{0ex}}\mathrm{K}$ stability diagram of C/Pt${}_{25}$Rh${}_{75}$$(100)$, and our prediction of the temperature-dependent segregation profile for different C contaminations.
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