We put together a first-principles equation of state (FPEOS) database for matter at extreme conditions by combining results from path integral Monte Carlo and density functional molecular dynamics simulations of the elements H, He, B, C, N, O, Ne, Na, Mg, Al, and Si as well as the compounds $\mathrm{LiF}, {\mathrm{B}}_4\mathrm{C}, \mathrm{BN}, {\mathrm{CH}}_4, {\mathrm{CH}}_2, {\mathrm{C}}_2{\mathrm{H}}_3, \mathrm{CH}, {\mathrm{C}}_2\mathrm{H}, \mathrm{MgO}, \mathrm{and} {\mathrm{MgSiO}}_3$. For all these materials, we provide the pressure and internal energy over a density-temperature range from $\sim 0.5$ to 50 g ${\mathrm{cm}}^{-3}$ and from $\sim {10}^4$ to ${10}^9$ K, which are based on $\sim 5000$ different first-principles simulations. We compute isobars, adiabats, and shock Hugoniot curves in the regime of $\mathrm{L}$- and $\mathrm{K}$-shell ionization. Invoking the linear mixing approximation, we study the properties of mixtures at high density and temperature. We derive the Hugoniot curves for water and alumina as well as for carbon-oxygen, helium-neon, and CH-silicon mixtures. We predict the maximal shock compression ratios of ${\mathrm{H}}_2\mathrm{O},$ ${\mathrm{H}}_2{\mathrm{O}}_2,$ ${\mathrm{Al}}_2{\mathrm{O}}_3, \mathrm{CO}, \mathrm{and} {\mathrm{CO}}_2$ to be 4.61, 4.64, 4.64, 4.89, and 4.83, respectively. Finally we use the FPEOS database to determine the points of maximum shock compression for all available binary mixtures. We identify mixtures that reach higher shock compression ratios than their end members. We discuss trends common to all mixtures in pressure-temperature and particle-shock velocity spaces. In the Supplemental Material, we provide all FPEOS tables as well as computer codes for interpolation, Hugoniot calculations, and plots of various thermodynamic functions.

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 $6469\mathrm{K}(1+(P/\mathrm{GPa}-300)/434.82{)}^{0.54369}$. 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 Stamenković 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.

Ultrahigh-pressure phase boundary between solid and liquid SiO₂ is still quite unclear. Here we present predictions of silica melting curve for the multimegabar pressure regime, as obtained from first principles molecular dynamics simulations. We calculate the melting temperatures from three high pressure phases of silica (pyrite-, cotunnite-, and Fe₂P-type SiO₂) at different pressures using the Z method. The computed melting curve is found to rise abruptly around 330 GPa, an increase not previously reported by any melting simulations. This is in close agreement with recent experiments reporting the α-PbO₂–pyrite transition around this pressure. The predicted phase diagram indicates that silica could be one of the dominant components of the rocky cores of gas giants, as it remains solid at the core of our Solar System’s gas giants. These results are also relevant to model the interior structure and evolution of massive super-Earths.

We use first-principles molecular dynamics simulations coupled with the thermodynamic integration method to study the hexagonal close-packed (hcp) to body-centered cubic (bcc) transition and melting of beryllium up to a pressure of 1600 GPa. We derive the melting line by equating solid and liquid Gibbs free energies and represent it by a Simon-Glatzel fit $T_m=1564\text{K}{[1+P/\left(15.6032\text{GPa}\right)]}^{0.383}$, which is in good agreement with previous two-phase simulations <6000 K. We also derive the hcp-bcc solid-solid phase boundary and show that the quasiharmonic approximation underestimates the stability of the hcp structure, predicting lower transition pressures between hcp and bcc phases. Our results are consistent with the stability regime predicted by the phonon quasiparticle method. We also predict that the hcp-bcc-liquid triple point is located at 164.7 GPa and 4314 K. In addition, we compute the shock Hugoniot curve and show that it is in good agreement with experiments, intersecting our derived melting curve at $\sim 235$ GPa and 4900 K. Finally, we make predictions for future ramp compression experiments. Starting with an isentropic compression of the liquid, we predict the path to intersect the melting line at low pressure and temperature, then to continue along the melting line over a large temperature interval of 7000 K as the sample remains in the mixed solid-liquid state before it enters the solid phase.

Super-Earths and sub-Neptunes are the most common planet types in our galaxy. A subset of these planets is predicted to be water worlds, bodies that are rich in water and poor in hydrogen gas. The interior structures of water worlds have been assumed to consist of water surrounding a rocky mantle and iron core. In small planets, water and rock form distinct layers with limited incorporation of water into silicate phases, but these materials may interact differently during the growth and evolution of water worlds due to greater interior pressures and temperatures. Here, we use density functional molecular dynamics (DFT-MD) simulations to study the miscibility and interactions of enstatite (MgSiO₃), a major end-member silicate phase, and water (H₂O) at extreme conditions in water world interiors. We explore pressures ranging from 30 to 120 GPa and temperatures from 500 to 8000 K. Our results demonstrate that enstatite and water are miscible in all proportions if the temperature exceeds the melting point of MgSiO₃. Furthermore, we performed smoothed particle hydrodynamics simulations to demonstrate that the conditions necessary for rock-water miscibility are reached during giant impacts between water-rich bodies of 0.7–4.7 Earth masses. Our simulations lead to water worlds that include a mixed layer of rock and water.