Phase diagram of oxygen adsorbed on Ni(111) and thermodynamic properties from first-principles

Abstract

The thermodynamic properties and the surface phase diagram of O/Ni(111) have been calculated from Metropolis and Wang-Landau Monte Carlo simulations based on lateral interactions derived from density-functional theory (DFT) calculations. The DFT energies were mapped onto an Ising-like Hamiltonian according to the cluster expansion technique formalism. Both fcc and hcp adsorption sites were included in the Hamiltonian. Different criteria were used to evaluate competing parameter sets: cross-validation score CV, Mallow's ${C}_{p}$ statistics, and adjusted ${R}^{2}$ statistics. The parameter space was searched using genetic algorithms in order to find optimum parameter sets. The different parameter sets obtained from different criteria lead essentially to the same transition temperatures. Excellent agreement is found when comparing the shape and the stability regions of the theoretical and the experimental (from the literature) phase diagrams. We investigate the nature of the $p(2\ifmmode\times\else\texttimes\fi{}2)$ and $(\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3})R30\ifmmode^\circ\else\textdegree\fi{}$ phase transitions at $\ensuremath{\Theta}=1/4$ and 1/3 ML, respectively. Differences arise when comparing the values of the calculated and the experimental transition temperatures owing to imprecision in present-day DFT calculations.