The high-pressure, single-crystal elasticity of pyrope, grossular, and andradite

High-pressure Brillouin scattering experiments were conducted on three natu ral, single-crystal garnets with near end-member compositions: pyrope (Mg3A l2Si3O12), grossular (Ca3Al2Si3O12), and andradite (Ca3Fe23+Si3O12). Acoust ic velocities of the samples were measured from the samples at pressures to 10 GPa in a diamond-anvil cell with a methanol-ethanol-water pressure medi um. Elastic stiffness constants (C-ij) and their pressure dependencies (par tial derivative C-ij/partial derivative P) were calculated, as were aggrega te elastic noduli (K-s and G) and their respective pressure derivatives. Th e Cauchy relations changed with pressure for both grossular and andradite, suggesting that assuming these are constant is not valid for extrapolation to high pressures for these and possibly other minerals. The variation in p artial derivative K-s/dP and partial derivative G/partial derivative P was sensitive to composition and required a complex mixing model for extrapolat ion of end-member elasticity values from garnets of intermediate compositio ns.