We present first principles predictions of the absolute entropy of a silicate liquid (CaSiO3) over a wide pressure-temperature range encompassing the Earth’s mantle (2000–6000 K, 0–270 GPa). The results are derived from molecular dynamics simulations based on density functional theory and the two-phase thermodynamic (2PT) method, which divides the vibrational density of states into solid-like and gas-like parts, and which we describe in detail. The heat capacity derived from the absolute entropy agrees well with experimental measurements at low pressure. We find that the vibrational contribution accounts for more than 75% of the total entropy over the range of our study. We find that the two-body approximation to the excess entropy (relative to the ideal gas), which is computed with knowledge only of the radial distribution function, is excellent over most of the range considered, except at the lowest pressures and temperatures. We also compute the entropy of CaSiO3 perovskite and use the entropy of liquid and solid phases to determine their absolute free energies and the melting curve. The melting curve agrees well with experiment and independent theoretical determinations based on Clausius-Clapeyron integration and the ZW method, showing a melting temperature of 5600 K at the Earth’s core-mantle boundary. We find a nearly universal scaling of the self-diffusion coefficients with the excess entropy , where D* is the self-diffusion coefficient suitably non-dimensionalized using macroscopic thermodynamic properties, and Sex is the excess entropy in units of the Boltzmann constant per atom. We use our results to estimate the temperature distribution in an isentropic, molten silicate Earth, finding 4.4 kJ/kg/K to be the lowest entropy that is completely molten, and producing a temperature at the core-mantle boundary of 6000 K.
CORE (COnnecting REpositories)
CORE (COnnecting REpositories)