Pressure dependence of the elastic moduli of semimetallic(Ti1−xVx)2O3at 296 K. Softening of a slow shear mode and two other elastic eigenvalues whenx≈0.04

Abstract

Ultrasonic 30-MHz-wave travel times have been measured at 296 K for semimetallic, single-crystal ${({\mathrm{Ti}}_{1\ensuremath{-}x}{\mathrm{V}}_{x})}_{2}{\mathrm{O}}_{3}$ samples with $0.02\ensuremath{\le}x\ensuremath{\le}0.09$ as a function of hydrostatic pressure up to 4 kbar. The moduli of all waves except the slow transverse (ST) mode propagating in the [100] direction in the $x=0.04$ sample stiffen with increasing pressure. This ST mode is a symmetry-breaking one, and its modulus, ${\mathrm{C}}_{\mathrm{ST}}$, is an eigenvalue of the elastic constant matrix. Linear extrapolation of ${\mathrm{C}}_{\mathrm{ST}}$ implies a structural transition at very high pressure (1000 kbar using the Born criterion ${\mathrm{C}}_{\mathrm{ST}}$=0, and 275 kbar using a Demarest et al.-type criterion $\frac{{\mathrm{C}}_{\mathrm{ST}}}{B}=0.2$, where $B$ is the bulk modulus). The pressure dependences of all six independent elastic constants, ${C}_{11}$, ${C}_{12}$, ${C}_{13}$, ${C}_{14}$, ${C}_{33}$, and ${C}_{44}$ are determined for samples with $x=0.02$ and $0.04$ or $0.05$ and of all ${C}_{\mathrm{ij}}$'s except ${C}_{13}$ for $x=0.09$ samples. Comparison with data for semiconducting ${\mathrm{Ti}}_{2}$${\mathrm{O}}_{3}$ does not reveal any simple correlation between the $\frac{{\ensuremath{\Delta}C}_{\mathrm{ij}}}{\ensuremath{\Delta}P}$ values with electrical resistivity, lattice parameters, interatomic spacings, or the values of the ${C}_{\mathrm{ij}}$'s. It is found that the other eigenvalues of the ${C}_{\mathrm{ij}}$ matrix usually increase with pressure. Samples with $x=0.04$ or $0.05$ are exceptional again in that two other eigenvalues are decreased by pressure. One of them is associated with a symmetry-breaking mode and is approximately equal to ${C}_{11}\ensuremath{-}{C}_{12}$ because ${C}_{14}$ is very small.