Density of configurational states from first-principles calculations: The phase diagram of Al-Na surface alloys

The structural phases of AlxNa1-x surface alloys have been investigated theoretically and experimentally. We describe the system using a lattice gas Hamiltonian, determined from density functional theory together with Monte Carlo (MC) calculations. The obtained phase diagram reproduces the experiment on a quantitative level. From calculation of the (configurational) density of states by recently introduced Wang-Landau MC algorithm, we derive thermodynamic quantities such as free energy and entropy which are not directly accessible from conventional MC simulations. We accurately reproduce the stoichiometry, as well as the temperature at which an order-disorder phase transition occurs, and demonstrate the crucial role, and magnitude of the configurational entropy.