Pressure dependence of elastic constants of (${\mathrm{V}}_{1\mathrm{-}\mathrm{x}}$${\mathrm{Cr}}_{\mathrm{x}}$${)}_2$${\mathrm{O}}_3$ at 296 K

Transit times of 30-MHz ultrasonic waves in (${\mathrm{V}}_{1\mathrm{-}\mathrm{x}}$ ${\mathrm{Cr}}_{\mathrm{x}}$ ${)}_2$ ${\mathrm{O}}_3$ single crystals, with nominal (actual) x values of 0.015 (0.013) and 0.030 (0.028), were measured at 296 K using hydrostatic pressures up to 4 kbar for x=0.03 and 1.2 kbar for x=0.015. The results were used to deduce 1-bar values and pressure derivatives of the elastic constants. Two of the elastic constants, $C_{11}$ and $C_{12}$, have unusual negative pressure dependences resulting in both the ${\lambda }_4$ elastic eigenvalue and the bulk modulus B decreasing strongly with increasing pressure. The behavior of ${\lambda }_4$ indicates that pressure tends to make the lattice unstable toward a deformation which increases the c/a ratio without changing the crystal symmetry. This is consistent with the structural change at the pressure-induced, paramagnetic insulator-to-metal transition. For (${\mathrm{V}}_{0.97}$ ${\mathrm{Cr}}_{0.03}$ ${)}_2$O ${}_3{}^{}{}_{}{}^{}$, we deduce a negative elastic γ which disagrees with its positive thermal γ whereas these γ’s agree with each other in ${\mathrm{V}}_2$ ${\mathrm{O}}_3$. These results are due to the elastic γ having strong negative contributions from some acoustic modes in certain directions in (${\mathrm{V}}_{0.97}$ ${\mathrm{Cr}}_{0.03}$ ${)}_2$O ${}_3{}^{}{}_{}{}^{}$ but not in ${\mathrm{V}}_2$ ${\mathrm{O}}_3$.