Thermodynamic and elastic properties of pyrope at high pressure and high temperature by first-principles calculations

Pyrope is an Mg end-member garnet, which constitutes up to ~15% of the upper mantle. Thermodynamic and thermoelastic properties of garnet at high pressure and high temperature are important for understanding the composition and structure of the Earth. Here we report the first-principles calculations of vibrational properties, thermodynamic properties, and elasticity of pyrope over a wide pressure and temperature range. The calculated results exhibit good consistency with the available experimental results and provide values up to the pressure and temperature range that are challenging for experiments to achieve and measure. Pyrope is almost isotropic at high pressure. The elastic moduli, especially the shear modulus of pyrope, exhibit nonlinear pressure and temperature dependences. Density and seismic velocities of pyrope along with piclogite, pyrolite, and eclogite are compared with seismic models along the normal upper mantle and the cold subducting lithospheric plate geotherms. Pyrope has the highest density and seismic velocities among the major minerals of the upper mantle along these geotherms. Eclogite with 30% pyrope and 70% clinopyroxene is denser than the surrounding mantle even along the normal upper mantle geotherm and becomes still denser along the cold slab geotherm. Seismic velocities of eclogite with 30% pyrope along the normal upper mantle geotherm are slower than the surrounding mantle but along the cold slab geotherm are faster than the surrounding mantle.