Structure and Stability of Oxygen Vacancy Aggregates in Reduced Anatase and Rutile TiO₂

The density and arrangement of oxygen vacancies (V_Os) play an important role in tuning the physicochemical properties of TiO₂ for different technological applications, hence motivating significant interest in the characteristics of V_Os’ complexes and superstructures in this material. In this work we focus on the geometries and stabilities of V_Os’ aggregates in rutile (R-TiO₂) and anatase (A-TiO₂), the two most common TiO₂ polymorphs, using density functional theory (DFT) calculations with on-site Hubbard U repulsion. Through extensive exploration of various possible configurations, we identify the most favorable geometries of divacancies and larger V_Os’ complexes. We find that divacancies prefer to lie at second-nearest-neighbor trans positions in the same TiO₆ octahedron, and ordered chains and planar aggregates of V_Os are energetically favorable over disordered noninteracting vacancies in both A- and R-TiO₂. However, the energetic gain upon V_Os’ aggregation is much larger in R-TiO₂ than A-TiO₂. As a result, vacancy complexes are stable at and above typical sample preparation and annealing temperatures (∼1000 K) in R-TiO₂, whereas only one-dimensional chain structures are predicted to survive at those temperatures in anatase.