Large-Scale Modeling of Defects in Advanced Oxides: Oxygen Vacancies in BaZrO₃ Crystals

Abstract

Quantum mechanical simulations have proved to be an accurate tool in the description and characterization of point defects which can substantially alter the physical and chemical properties of oxides and their applications, e.g. in fuel cells and permeation membranes. Accurate simulations should take into account both the defect energetics in the real material and the thermodynamic effects at finite temperatures. We studied and compared here the structural, electronic and thermodynamic properties of the neutral $\mathrm{(v_{O}^{\times })}$ and the positively doubly charged $\mathrm{(v_{O}^{\bullet \bullet })}$ oxygen vacancies in bulk BaZrO₃; particular emphasis was given in the evaluation of the contribution of lattice vibrations on the defect thermodynamic properties. The large-scale computer calculations were performed within the linear combination of atomic orbitals (LCAO) approach and the hybrid of Hartree-Fock method and density functional theory (HF-DFT). It is shown that phonons contribute significantly to the formation energy of the charged oxygen vacancy at high temperatures ($\sim$ 1 eV at 1000 K), due to the large lattice distortion brought by this defect and thus their neglect would lead to a considerable error.