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.

💡 Research Summary

This paper presents a comprehensive first‑principles investigation of the intrinsic defect chemistry of orthorhombic Ba₂In₂O₅ (BIO), a brownmillerite‑type oxide that has attracted attention as a mixed ionic‑electronic conductor for solid‑oxide fuel cells. The authors combine density‑functional theory (DFT) calculations using the generalized‑gradient approximation (PBE) for structural relaxations with hybrid‑functional (HSE06) calculations to obtain an accurate electronic structure and to correct the well‑known band‑gap underestimation of semilocal functionals. The HSE06 band gap of 2.82 eV is in close agreement with the experimental value (~2.94 eV), providing reliable valence‑band‑maximum (VBM) and conduction‑band‑minimum (CBM) reference levels for defect energetics.

A thermodynamic framework is constructed in which defect formation energies depend on the chemical potentials of Ba, In, and O. By extracting formation enthalpies of competing phases from the Materials Project database, the authors map the stability region of BIO in the μ_Ba–μ_In–μ_O space and define four representative points (A–D) spanning O‑rich to Ba‑/In‑rich conditions, plus an experimental point X corresponding to sintering at 1573 K and pO₂ = 0.21 atm (Δμ_O = ‑1.85 eV). The formation energy expression includes charge‑state terms, finite‑size electrostatic corrections (Kumagai scheme), and a band‑gap correction that rigidly shifts VBM and CBM to the HSE06 values.

The defect set examined comprises oxygen vacancies (V_O) in charge states 0, +1, and +2, a variety of oxygen interstitial configurations (O_i), and Frenkel pairs (V_O + O_i). An automated Voronoi interstitial generator identifies eleven possible O_i sites; after relaxation, two families emerge as energetically favorable. The first is an O–O “dumbbell” interstitial, analogous to that previously reported in In₂O₃. This configuration remains electrically neutral (O_i⁰) across the entire band gap; no charge‑transition levels are found, meaning it does not act as a donor or acceptor regardless of the Fermi level. The second family consists of conventional interstitials that occupy lattice‑oxygen sites; these can exist as O_i²⁻, O_i⁻, or O_i⁰ depending on the Fermi level and oxygen chemical potential.

Oxygen vacancies are most stable under O‑poor conditions, with formation energies as low as ~0.8 eV for the doubly‑charged V_O²⁺ state. Under O‑rich conditions, the neutral dumbbell interstitial and the doubly‑charged conventional interstitial (O_i²⁻) become competitive. The latter acts as an acceptor, compensating the positively charged V_O²⁺, and its formation energy drops to ~1.2 eV at high pO₂. Consequently, the dominant charge‑compensation mechanism shifts from vacancy‑driven (low pO₂) to interstitial‑driven (high pO₂).

Frenkel pairs are also evaluated; the binding energy of ~‑0.3 eV indicates that the paired state is thermodynamically favored over isolated defects. At temperatures above 1000 K, the calculated equilibrium concentrations of Frenkel pairs reach ~10¹⁸ cm⁻³, suggesting they could contribute significantly to oxygen transport.

To obtain realistic defect concentrations, the authors solve the charge‑neutrality condition self‑consistently, integrating the density of states to compute intrinsic electron and hole concentrations and iterating for the equilibrium Fermi level (μ_e). Under the experimental sintering conditions (T = 1573 K, pO₂ = 0.21 atm), the equilibrium concentrations are estimated as V_O²⁺ ≈ 10¹⁷ cm⁻³, O_i²⁻ ≈ 10¹⁶ cm⁻³, and neutral dumbbell O_i⁰ ≈ 10¹⁵ cm⁻³. These values imply that, even at moderate oxygen pressures, a substantial population of mobile oxygen vacancies exists, providing the ionic conductivity required for SOFC operation, while the neutral dumbbell interstitials do not impede electronic transport.

Overall, the study delivers a detailed thermodynamic picture of intrinsic defects in Ba₂In₂O₅, highlighting the previously unrecognized role of neutral oxygen‑dumbbell interstitials. By quantifying formation energies, charge‑transition levels, and equilibrium concentrations across a realistic range of oxygen partial pressures, the work lays a solid foundation for future investigations of defect migration pathways, dopant strategies, and the design of high‑performance brownmillerite electrolytes.