An old system revisited: Al₂O₃:Ti³⁺ - Microscopic crystal field effects explored by the crystal field and first-principles calculations

The exchange charge model of crystal field has been used to analyze the microscopic crystal field in the Al₂O₃:Ti³⁺ system. The effects of lattice relaxation upon doping were treated in the framework of density functional based calculations of the optimized geometry of the doped host. The optimized Al₂O₃:Ti³⁺ structure was used as an input for the calculations of distance dependence of the crystal field parameters and crystal field splittings of the Ti³⁺ 3d states. From these calculations, the constants of the electron-vibrational interaction and the Stokes shift between the absorption and emission spectra of Ti³⁺ ions in Al₂O₃:Ti³⁺ were estimated to yield good agreement with the experimental results. In addition, four parameters of the superposition model of the crystal field (which in general are considered as the fitting parameters) were extracted from the results of the exchange charge model calculations. The proposed method of linking together two independent models of the crystal field is a reliable way of calculating the superposition model parameters (rather than allowing them to vary freely) and can be readily applied to other systems.