Defect thermodynamics of orthorhombic Ba$_2$In$_2$O$_5$: First-principles calculations on the role of oxygen dumbbell interstitials

The brownmillerite-type barium indate (Ba$_2$In$_2$O$_5$) is a potential electrolyte for mixed ionic-electronic conduction in solid oxide fuel cells. Revealing the defect chemistry of this material is key to understanding its ionic and electronic conductivity. In this contribution, we report the existence of oxygen interstitials in a dumbbell configuration, which are also observed in In$_2$O$_3$. Using Density Functional Theory within the generalized gradient approximation, complemented by selected hybrid-functional calculations, we investigate vacancies, various oxygen interstitials, and Frenkel pairs. In doing so, we evaluate the formation energies, charge transition levels, and concentrations as a function of oxygen partial pressure. Our results show that oxygen vacancies and interstitials dominate the intrinsic defect landscape. Among the interstitials, we identify stable dumbbell configurations that remain neutral across the entire band gap. Other interstitial configurations exhibit charged states and become the prevailing compensating defects at high oxygen partial pressures, alongside oxygen vacancies. Our results provide a consistent picture of the thermodynamics of intrinsic defects in barium indate, setting the stage for future investigations of the diffusion dynamics of oxygen vacancies and interstitials.