Ab-initio studies of the electronic and optical properties of Al₂O₃:Ti³⁺ laser crystals

The structural and electronic properties of pure and Ti³⁺-doped α-Al₂O₃ were calculated in the present paper by using the first-principles methods. Special attention has been paid to the location of the Ti³⁺ states (3d¹ electron configuration) in the band gap; the lowest 3d states are at about 4.78 eV above the top of the valence band. The crystal field strength 10Dq at the Ti³⁺ site was estimated from the density of states diagrams to be about 17,700 cm⁻¹. The structural optimization of the unit cell was also performed at elevated hydrostatic pressure in the range from 0 to 25 GPa. By application of the Murnaghan equation to the obtained results, the bulk modulus of α-Al₂O₃ was estimated to be 225.69 GPa. In addition, from the analysis of the Ti³⁺3d density of states the distance dependence of the crystal field strength was found to be described by the following function: 10Dq=61.744/R^4.671, where R is expressed in Å and 10Dq in eV.