Elasticity of CaSiO₃ perovskite at high pressure and high temperature

Ab initio molecular dynamic (AIMD) simulations were performed to calculate the equation of state (EOS) of CaSiO₃ perovskite at mantle pressure-temperature conditions. At temperatures above 2000 K, even though the hydrostatic crystal structure is metrically tetragonal in the pressure range of 13-123 GPa, the symmetry of the elastic moduli is consistent with cubic symmetry. Our results show that elastic constants and velocities are independent of temperature at constant volume. Referenced to room pressure and 2000 K, we find: Gru{combining double acute accent}neisen parameter is γ(V) = γ₀(V/V₀)^q with γ₀ = 1.53 and q = 1.02(5), and the Anderson Gru{combining double acute accent}neisen parameter is given by ( α / α₀ ) = ( V / V₀ )^δT in which α₀ = 2.89 × 10^-5 K^-1 and δ_T = 4.09(5). Using the third order Birch Murnaghan equation of state to fit our data, we have for ambient P and T, K₀ = 236.6(8) GPa, K^′₀ = 3.99 ( 3 ), and V₀ = 729.0(6) ų. Calculated acoustic velocities show the following P-T dependence: (∂ln V_P/∂V) _{T or P} = -1.9 × 10^-3; (∂ln V_S/∂V)_{T or P} = -1.5 × 10^-3; (∂ln V_Φ/∂V)_{T or P} = -2.4 × 10^-3; (∂ln V_S/∂ln V_P) _{T or P} = 0.79; (∂ln V_S/∂ln V_Φ)_{T or P} = 0.63, indicating that the variations in bulk modulus overpower the variations in shear modulus. The bulk modulus of CaSiO₃ perovskite is up to 10% lower than MgSiO₃ perovskite under lower mantle conditions. The difference diminishes with pressure and temperature. The shear modulus of CaSiO₃ perovskite is almost 25% lower compared with MgSiO₃ perovskite for shallow lower mantle pressures and temperatures and about 3% lower at the base of the lower mantle. The difference in density of these two perovskite is about 3-4% for all conditions. Both the density and bulk modulus differ from PREM by less than 2% throughout the lower mantle. The shear modulus is ∼10% lower at shallow depths grading to ∼5% by the core-mantle boundary. Thus, the seismic velocity of CaSiO₃ perovskite will be lower (0-6%) than PREM.