Formation energies of point defects in rutile (TiO2)

The formation energies for the point defect species Ti⁴⁺ interstitials, Ti_i⁴⁺, and oxygen vacancies with an effective charge of + 2e, Vo²⁺, have been calculated using the polarisable point ion shell model. The formation energy of Ti_i⁴⁺ was found to be a 10.8 eV for occupation of the (0, $\text{1}\text{2}$, $\text{1}\text{2}$) site. The energy of Ti_i⁴⁺ at other sites is somewhat higher than this figure, and allowed the migration energy of Ti_i⁴⁺ parallel to the c axis to be estimated as 2.9 eV. The formation energy of Vo²⁺ was found to be 10.1eV. The variation of these formation energies with dielectric constant was also calculated. It was found that the energy of formation of Ti_i⁴⁺ varied considerably with dielectric constant, while the formation energy of Vo²⁺ was almost independent of dielectric constant. The relevance of these results to the presence of crystallographic shear planes in reduced rutile is considered.