A computational approach that integrated ab initio electronic structure and thermodynamic calculations was used to determine point defect stability in rutile over a range of temperatures, O partial pressures and stoichiometries. Both donors (Ti interstitials and O vacancies) and acceptors (Ti vacancies) were predicted to have shallow defect transition levels in the electronic-structure calculations. The resultant defect formation energies for all possible charge states were then used in thermodynamic calculations in order to predict the influence of temperature and O partial pressure upon the relative stabilities of the point defects. Their ordering was found to be the same as the temperature increased and the O partial pressure decreased: Ti vacancy → O vacancy → Ti interstitial. However, the charges on these defects were quite sensitive to the Fermi level. The combined formation energies of point defect complexes, including Schottky, Frenkel and anti-Frenkel defects, were predicted to limit the further formation of point defects.

Prediction of High-Temperature Point Defect Formation in TiO2 from Combined ab initio and Thermodynamic Calculations. He, J., Behera, R.K., Finnis, M.W., Li, X., Dickey, E.C., Phillpot, S.R., Sinnott, S.B.: Acta Materialia, 2007, 55[13], 4325-37