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

The density and arrangement of oxygen vacancies (VOs) play an important role in tuning the physicochemical properties of TiO2 for different technological applications, hence motivating significant interest in the characteristics of VOs' complexes and superstructures in this material. In this work we focus on the geometries and stabilities of VOs' 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 VOs' 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 VOs are energetically favorable over disordered noninteracting vacancies in both A- and R-TiO2. However, the energetic gain upon VOs' 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.