The combination of density functional theory (DFT) with concepts from statistical physics is applied to construct a DFT-based phase diagram for a binary alloy surface without any empirical parameters. While treating the results of DFT calculations within a thermodynamic model reveals the stable ordered phases, application of a cluster expansion in conjunction with Monte Carlo simulations allows to treat short range order in the alloy surface.
As an example, we studied the structure and stability of the B2-CoAl(100) surface consisting of alternating Co- and Al-layers. For ideal bulk stoichiometry, the surface shows a termination by the Al-sublattice. However, a tiny surplus of Co-atoms in the bulk, equivalent to the existence of antisite atoms, i.e. Co-atoms on the Al-sublattice, leads to the segregation of such antisites to the surface. Based on DFT calculations in combination with an appropriate thermodynamic model, it is possible to construct a phase diagram for the CoAl (100) surface. While still based on the assumption of a long range ordered surface, comparison of the structural parameters of the predicted stable phases are in quantitative agreement with those retrieved from LEED structure determinations. However, with long range order assumed the model fails to describe short range order of the antisite atoms as observed for CoAl(100). The limitations of our model, which is based only on long range ordered DFT calculations, can be overcome by combination of the DFT calculations with a cluster expansion (CE) and Monte-Carlo (MC) simulations. This approach considers both layer dependent interactions and configurational entropy. Thus, we can study ordering phenomena and segregation profiles of metal alloy surfaces.

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