The elastic constants of a pyrope-grossular-almandine garnet to 20 Gpa

Laser-induced phonon spectroscopy has been applied to the determination of the elastic constants and equation of state at 25 degrees C of a natural garnet of composition Py(51.6)Al(31.7)Gr(15.8)Sp(0.9) to a pressure of 20 GPa. Moduli are linear with pressure. The adiabatic bulk modulus in GPa is given by K = 170.8 + 4.09 P and the shear modulus is mu = 94.7 + 1.76P. The derivative of the shear modulus with respect to temperature at constant density is derived from the temperature and pressure dependencies of the elastic constants. The constant pressure derivatives of the mean longitudinal (V-p) and shear (V-s) velocities are tabulated. At 298K and 1bar (partial derivative 1n V-s/partial derivative 1n rho)(p) = 1.7, (partial derivative 1n V-s/partial derivative 1n rho)(p) = 1.5 and (partial derivative 1n V-s/partial derivative 1n V-p)(p) = 0.9. The corresponding values calculated at 1000 K and 20 GPa are 1.6, 1.7 and 1.1.