Oxygen pressure dependence of $HfO2$ stoichiometry: An ab initio investigation

The oxygen pressure dependence of the formation of excess O vacancies and interstitials in monoclinic $HfO2$ was investigated by performing first principles and thermodynamic calculations. Upper and lower critical oxygen pressures are identified that heavily favor the formation of oxygen interstitials and vacancies, respectively. The ratio of these critical pressures can be specified unambiguously as the sum of the formation energies of O vacancies and interstitials at $0K$ obtained from ab initio calculations.