Elastic Constants and the Electrical Transition inTi2O3

Measurements have been made of the transit times of pulses of longitudinal and transverse ultrasonic waves in single-crystal samples of ${\mathrm{Ti}}_2$ ${\mathrm{O}}_3$ having appropriate orientations at various temperatures between 75 and 580 K. Sample-length-versus-temperature data were also obtained using a dilatometer. The elastic constants deduced from our measurements are found to exhibit anomalies connected with the gradual electrical transition which starts at about 400 K. Minima in $C_{11}$, $C_{33}$, and $C_{12}$ and a maximum in $C_{13}$ are accounted for semiquantitatively by means of a calculation of the contribution of $\mathrm{Ti} 3d$ electrons to the elastic constants using a deformation-potential approach and two $3d$ subbands whose separation decreases drastically with increasing temperature and becomes negative above the electrical transition. Electron-electron and/or electron-phonon interactions may be involved implicitly via the strong dependence of the energy gap on temperature. The temperature dependence of $C_{44}$ is accounted for as a lattice effect, and $C_{14}$ is so small that no attempt is made to interpret its temperature dependence. The room-temperature bulk modulus and Debye-temperature-versus-temperature results are reported.