Elastic constants of garnet under pressure and temperature

The elastic constants and their pressure and temperature derivatives for a single-crystal garnet (almandite-pyrope type, M/p = 23.9) have been determined by means of a pulse superposition method. The adiabatic bulk modulus BS and its pressure and temperature derivatives at 25°C were found to be BS = 1770 kb, (∂BS/∂P)T = 5.43, and (∂BS/∂T)P = −0.201 kb/deg. The value of (∂BS/∂P)T was higher than that for MgO, which has about the same bulk modulus but M/p = 20. The isotropic wave velocities, υs and υp, and their derivatives were also calculated from these single-crystal elastic constants by means of the Voigt-Reuss-Hill approximation. The values at 25°C are υs = 4.762 km/sec, υp = 8.531 km/sec; (∂υs/∂P)T = 2.17 × 10−3 km/sec kb, (∂υp/∂P)T = 7.84 × 10−3 km/sec kb; (∂υs/∂T)P = −2.18 × 10−4 km/sec deg, (∂υp/∂T)P = −3.93 × 10−4 km/sec deg; (∂T/∂P)υs = 9.7 and (∂T/∂P) υp = 20 deg/kb. These values of the critical temperature gradient are not essentially different from the values reported for MgO, Al2O3, and Mg2SiO4, although the value of M/p increases from 20 to 24.