Temperature dependence of the Gibbs energies of formation of point defects in B2 MoTa from ab initio calculations

Abstract

Using B2 MoTa, the strongest B2 former among group V/VI refractory binaries, as a model system, we compute temperature-dependent Gibbs energies of formation of vacancies and antisites from ab initio calculations up to 3000 K at the stoichiometric composition. We explicitly account for thermal electronic excitations, vibrational anharmonicity, and electron-vibration coupling. The key finding is that the temperature dependence of the Gibbs energies of vacancy formation exhibits a pronounced sublattice asymmetry. Specifically, the Gibbs energy of formation of a Mo-site vacancy decreases by 1.1 eV from 0 to 3000 K, whereas the decrease for a Ta-site vacancy amounts to 2.1 eV, almost a factor of two larger. Two contributions of distinct origin govern the temperature dependence of this asymmetry: a quasiharmonic contribution associated with the chemical-potential imbalance set by the two antisite structures and an anharmonic contribution associated with the local vibrational response of the vacancy structures. The asymmetry in anharmonic vibrations is traced back to an enlarged local vibrational distribution of the first-nearest neighbors around the Ta-site vacancy. In contrast to the vacancies, the Gibbs energies of antisite formation vary only weakly with temperature.