Pressure dependence of the elastic moduli of semimetallic ${\left({\mathrm{Ti}}_{1-x}{\mathrm{V}}_x\right)}_2{\mathrm{O}}_3$ at 296 K. Softening of a slow shear mode and two other elastic eigenvalues when $x\approx 0.04$

Ultrasonic 30-MHz-wave travel times have been measured at 296 K for semimetallic, single-crystal ${\left({\mathrm{Ti}}_{1-x}{\mathrm{V}}_x\right)}_2{\mathrm{O}}_3$ samples with $0.02\le x\le 0.09$ 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 $x=0.04\mathrm{}$ 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 $\frac{{\mathrm{C}}_{\mathrm{ST}}}{B}=0.2\mathrm{}$, 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 $x=0.02\mathrm{}$ and $0.04$ or $0.05$ and of all $C_{\mathrm{ij}}$'s except $C_{13}$ for $x=0.09\mathrm{}$ samples. Comparison with data for semiconducting ${\mathrm{Ti}}_2$${\mathrm{O}}_3$ does not reveal any simple correlation between the $\frac{{\Delta C}_{\mathrm{ij}}}{\Delta P}$ 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 $x=0.04\mathrm{}$ 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 $C_{11}-C_{12}$ because $C_{14}$ is very small.