First-principles plane-wave pseudopotential calculations were performed to study electronic structures, structural relaxation, and energetics of point defects in Ti-doped ${\mathrm{Al}}_2{\mathrm{O}}_3.$ Substitutional and interstitial Ti ions with charge compensating intrinsic defects were considered, and their formation energies were evaluated under various atomic chemical potentials. It was found that substitutional ${\mathrm{Ti}}^{4+}$ ions with charge compensating Al vacancies were most stable in the oxidized condition. In contrast, as oxygen chemical potentials decreased, the formation energy of substitutional ${\mathrm{Ti}}^{3+}$ decreased to have the smallest value in the relatively reduced conditions. However, in the intermediate range of oxygen potentials, substitutional ${\mathrm{Ti}}^{3+}$ and ${\mathrm{Ti}}^{4+}$ exhibited similar formation energies, indicating that these Ti defects can coexist in a particular reduction environment.

• Received 7 August 2003

DOI:https://doi.org/10.1103/PhysRevB.68.214102