Elastic constants of single-crystal rutile under pressures to 7.5 kilobars

Abstract

The elastic constants of single-crystal rutile measured to 7.5 kb at 25°C and to 100°C at 1 bar, by the ultrasonic interferometry technique, are found to vary linearly with pressure and temperature within experimental error. The pressure and temperature derivatives of the elastic constants are:Cij dCij/dP dCij/dT, kb/degC11 6.47 −0.51C33 8.34 −0.90C44 1.10 −0.22C66 6.43 −0.78C12 9.10 −0.58C13 5.02 −0.33The value of (dKs/dP), where Ks is the isotropic adiabatic bulk modulus derived from the Voigt-Reuss-Hill (VRH) approximation, is 6.76; this value is higher than the values reported for other oxides of geophysical importance, such as MgO, Al2O3, and CaO but is close to the value for SiO2 (α quartz). The value of (dμH/dp), where μH is the isotropic shear modulus derived from the VRH approximation, is low (0.78); its geophysical implication is discussed. The values for (dKs/dT) and (dμH/dT) are −0.41 and −0.27 kb/deg, respectively. Significantly large differences between (dμv/dP) and (dμR/dP) and between (dμv/dT) and (Dμv/dT) are found in rutile because of its elastic anisotropy. The pressure and temperature dependence of the isotropic velocities are: (dνp/dP) = 7.64 × 10−3 km/sec/kb; (dνs/dP) = 5.20 × 10−4 km/sec/kb; (dνp/dT = −8.9 × 10−4 km/sec/deg; and (dνs/dT) = −3.9 × 104 km/sec/deg. The values obtained for the critical thermal gradients (∂T/∂Z)νs and (∂T/∂Z)ν s are, respectively, 4.64 and 1.74°C/km; the significance of the low (∂T/∂Z)ν s value is that no unreasonably high temperature gradient would be necessary to effect a decrease in shear velocity with depth. The reported shock-wave and X-ray data for rutile are discussed in the light of the ultrasonic equation of state.