Thermodynamics of oxygen defective Magnéli phases in rutile: A first-principles study

Ab initio thermodynamics has been used to calculate the formation energies, in different environmental conditions, for a number of oxygen-defective structures in rutile. In addition to the Ti_nO_2n-1 (3⩽n⩽5) Magnéli phases, the two fundamental points defects, Ti interstitials and neutral oxygen vacancies, were also considered. The predicted phase stability is compared to available experimental data and there is reasonable agreement between the calculated phase boundaries and those observed. These results are used to discuss a mechanism that has been proposed as an explanation for the formation of the crystallographic shear planes in rutile.