Density functional theory calculations were made of the formation energies and diffusion pathways of oxygen vacancies and Ti interstitials at and near the (101) surface and in the bulk of the anatase polymorph of TiO2. At the generalized gradient approximation level, both defects were found to be energetically more stable by about 0.5eV or more at bulk and sub-surface sites than on the surface. Moreover, the energy barriers to diffuse from the surface to the bulk were rather low, while the opposite was true for the barriers to diffuse from the bulk to the surface. This indicated that similar to Ti interstitials, also oxygen vacancies should preferentially occurred at sub-surface rather than at surface sites. To substantiate these findings, additional DFT+U calculations were performed using different values of U in the range 2.5 ≤ U ≤ 4.5eV. These showed small differences in the relative stabilities of surface and subsurface oxygen vacancies with sub-surface vacancies being more stable at low U values and a crossover in stability taking place around U ≈ 3eV. Analogous calculations for the TiO2 (110) surface of rutile showed that surface bridging oxygen vacancies were largely favored with respect to sub-surface vacancies for all values of U. Altogether, these results provided evidence of important differences between reduced anatase and rutile surfaces in agreement with experimental observations.

Energetics and Diffusion of Intrinsic Surface and Subsurface Defects on Anatase TiO2 (101). Cheng, H., Selloni, A.: Journal of Chemical Physics, 2009, 131[5], 054703