Thermoelastic Properties of Olivine and its High Pressure Polymorphs at High Pressures and Temperatures: A First-Principles Study*

We combine density functional theory (DFT) within the local density approximation (LDA), the quasiharmonic approximation (QHA), and a model of vibrational density of states (VDoS) to calculate aggregate elastic moduli and sound velocities of olivine ($\alpha-$phase) (Fe$_x$,Mg$_{1-x}$)$_2$SiO$_4$, and its high pressure polymorphs, wadsleyite ($\beta-$phase) and ringwoodite ($\gamma-$phase), the most abundant minerals of the Earth's upper mantle (UM) and transition zone (TZ). Comparison of results with high-pressure and room-temperature data and ambient-pressure and high-temperature data shows very good agreement. Using our findings, we investigate the discontinuities in elastic moduli and velocities associated with the $\alpha$ to $\beta$ and $\beta$ to $\gamma$ transformations at pressures and temperatures relevant to seismic discontinuities near 410 km and 520 km depth. This information offers clearly defined reference values to advance understanding of the role that chemical composition and temperature play in these mantle boundary layers.