Elastic properties of polycrystalline minerals: Comparison of theory and experiment

Literature compressional and shear wave velocities measured versus pressure and temperature on dense, isotropic polycrystals of periclase, corundum, forsterite, fayalite, alpha-quartz, rutile, germania, and cassiterite are compared with the Voigt, Reuss, and Hashin-Shtrikman bounds calculated from single-crystal elastic stiffnesses and their first pressure and temperature derivatives. The Hashin-Shtrikman bounds reduce the separation between the Voigt and Reuss bounds by factors of from 3 to 15. There is very good agreement between the Hashin-Shtrikman bounds and the experimental data when errors in the polycrystal data and in the single-crystal elastic stiffnesses are taken into account. This comparison demonstrates that the Hashin-Shtrikman bounds can be used with considerable confidence in modeling velocities in mineral assemblages, particularly mantle assemblages, and are especially useful in problems where sensitivity of the results to the uncertainties in all the input parameters is of interest.