<i>Ab initio</i> determination of iron melting at terapascal pressures and Super-Earths core crystallization
Felipe González‐Cataldo, Burkhard Militzer
Abstract
We performed ab initio molecular dynamics simulations for pressures and temperatures from 300--5000 GPa and 3000--30 000 K in order to determine the equation of state of solid and liquid iron. By employing a thermodynamic integration technique, we derive the ab initio entropy and Gibbs free energy of both phases, which allows us to construct solid and liquid adiabats and discuss implications for shock experiments. We derive the melting line by equating solid and liquid Gibbs free energies and represent it by a Simon fit $6469\phantom{\rule{0.16em}{0ex}}\mathrm{K}(1+(P/\mathrm{GPa}\ensuremath{-}300)/434.82{)}^{0.54369}$. Near 300 GPa, our melting line is higher than extrapolations of previous melting laws that were obtained with simulations at lower pressures but is in very good agreement with the most recent experiments by Kraus et al. Science 375, 202 (2022), that reached TPa pressures. The slope of our melting line is consistently steeper than that of our adiabats, which implies that the crystallization of iron in the cores of terrestrial planets always starts from their centers, like on Earth. We also construct models for Super-Earth interiors and compare with temperature profiles from published evolution models. These temperatures in many earlier publications are rather low, so that our melting line would imply completely frozen cores. Only later models by Stamenkovi\ifmmode \acute{c}\else \'{c}\fi{} et al. [Astrophys. J. 748, 41 (2012)] and Boujibar et al. [J. Geophys. Res. Planets 125, e2019JE006124 (2020)] consider a much wider range of interior temperatures, which imply that the core of Super-Earths may remain in a state with a partially molten core for a long time and the resulting buoyancy force will contribute to convection and the magnetic field generation.