First-principles study of thermodynamic stability and the electronic properties of intrinsic vacancy defects in barium hafnate

The formation of intrinsic vacancy defects in barium hafnate, BaHfO3 and their corresponding electronic structures have been investigated using first-principles calculations. The thermodynamics of pristine and vacancy defects containing barium hafnate have been analyzed. Formation energies for neutral and fully charged Ba, Hf and O vacancies have been evaluated for determining their stability with respect to different chemical environments. From the calculated electronic structure and density of states, it is found that cation deficient barium hafnate is hole-doped, while the incorporation of oxygen vacancy retains the insulating nature of this material. The defect reaction energies for partial and full Schottky reactions are also computed, which controls the properties of non-stoichiometric barium hafnate.