10 Search Results

The melting behavior and transport properties of MgSiO₃ at multi-megabar pressures remain poorly constrained despite their importance for high-pressure silicate physics. Here we report the first direct measurements of temperature and optical reflectivity in shock-compressed bridgmanite (MgSiO₃) using laser-driven decaying shock compression combined with velocimetry and optical pyrometry. Temperature and reflectivity data spanning approximately 4000–60 000 K were used to constrain the MgSiO₃ melting curve and to infer its electrical conductivity. We find that the MgSiO₃ melting curve becomes shallower than that of iron above 400 GPa, yielding lower melting temperatures in planetary mantles than predicted by several previous theoreticalmore » estimates. Across the solid-liquid transition, the inferred electrical conductivity increases significantly, reaching ∼2000 Ω cm⁻¹. These results provide experimental benchmarks for theoretical models of silicate melting and transport under extreme pressure-temperature conditions.« less

Ramp compression experiments characterize high-pressure states of matter at temperatures well below those present in shock compression. However, because temperature is typically not directly measured during ramp compression, it is uncertain how much heating occurs under these shock-free conditions. Here, we performed a series of ab initio simulations on carbon in order to match the density-stress measurements of Smith et al. [Smith et al., Nature (London) 511, 330 (2014)]. We considered isotropically as well as uniaxially compressed solid carbon in the diamond and BC8 phases, with and without defects, as well as liquid carbon. Our idealized model ascribes heating duringmore » ramp compression to an initially uniaxially compressed cell transforming isochorically into an isotropically (hydrostatic equivalent) compressed state having lower internal energy, hence higher temperature so as to conserve energy. Multiple such heating events can occur during a single ramp experiment, leading to higher temperatures than with isentropic compression. Comparison with experiments shows that heating alone does not explain the equation of state measurements on diamond, instead implying that a significant uniaxial stress component remains present at high compression. The temperature predictions of our ramp compression model remain to be verified with future laboratory measurements.« less

In this report 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 K [1 + P/(15.6032 GPa)]^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 transitionmore » 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 ~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.« less

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 $\mathrm{LiF},{\mathrm{B}}_4\mathrm{C},\mathrm{BN},{\mathrm{CH}}_4,{\mathrm{CH}}_2,{\mathrm{C}}_2{\mathrm{H}}_3,\mathrm{CH},{\mathrm{C}}_2\mathrm{H},\mathrm{MgO},\mathrm{and}{\mathrm{MgSiO}}_{3}more »$ . For all these materials, we provide the pressure and internal energy over a density-temperature range from $~0.5$ to 50 g ${\mathrm{cm}}^{-3}$ and from $~{10}^4$ to ${10}^9$ K, which are based on $~5000$ 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. Furthermore, 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.« less

Here, we study nonideal mixing effects in the regime of warm dense matter (WDM) by computing the shock Hugoniot curves of BN, MgO, and MgSiO₃. First, we derive these curves from the equations of state (EOS) of the fully interacting systems, which were obtained using a combination of path integral Monte Carlo calculations at high temperature and density functional molecular dynamics simulations at lower temperatures. We then use the ideal mixing approximation at constant pressure and temperature to rederive these Hugoniot curves from the EOS tables of the individual elements. We find that the linear mixing approximation works remarkably wellmore » at temperatures above ~2 × 10⁵ K, where the shock compression ratio exceeds ~3.2. The shape of the Hugoniot curve of each compound is well reproduced. Regions of increased shock compression, which emerge because of the ionization of L and K shell electrons, are well represented, and the maximum compression ratio of the Hugoniot curves is reproduced with high precision. Some deviations are seen near the onset of the L shell ionization regime, where ionization equilibrium in the fully interacting system cannot be well reproduced by the ideal mixing approximation. This approximation also breaks down at lower temperatures, where chemical bonds play an increasingly important role. However, the results imply that the equilibrium properties of binary and ternary mixtures in the regime of WDM can be derived from the EOS tables of the individual elements. This significantly simplifies the characterization of binary and ternary mixtures in the WDM and plasma phases, which otherwise requires large numbers of more computationally expensive first-principles computer simulations.« less

Using two first-principles computer simulation techniques, path integral Monte Carlo and density functional theory molecular dynamics, we derive the equation of state of magnesium in the regime of warm dense matter, with densities ranging from 0.43 to 86.11 g cm^–3 and temperatures from 20,000 K to 5×10⁸ K. These conditions are relevant for the interiors of giant planets and stars as well as for shock compression measurements and inertial confinement fusion experiments. Here, we study ionization mechanisms and the electronic structure of magnesium as a function of density and temperature. We show that the L shell electrons, 2s and 2pmore » energy bands, merge at high densities. This results in gradual ionization of the L-shell with increasing density and temperature. In this regard, Mg differs from MgO, which is also reflected in the shape of its principal shock Hugoniot curve. For Mg, we predict a single broad pressure-temperature region, where the shock compression ratio is approximately 4.9. Mg thus differs from Si and Al plasmas that exhibit two well-separated compression maxima on the Hugoniot curve for L and K shell ionizations. Finally, we study multiple shocks and effects of preheat and precompression.« less

In order to provide a comprehensive theoretical description of MgSiO₃ at extreme conditions, we combine results from path integral Monte Carlo and density functional molecular dynamics simulations and generate a consistent equation of state for this material. We consider a wide range of temperature and density conditions from 10⁴ to 10⁸ K and from 0.321 to 64.2 g/cm^-3 (0.1- to 20-fold the ambient density). We study how the L and K shell electrons are ionized with increasing temperature and pressure. We derive the shock Hugoniot curve and compare with experimental results. Our Hugoniot curve is in good agreement with themore » experiments, and we predict a broad compression maximum that is dominated by the K shell ionization of all three nuclei while the peak compression ratio of 4.70 is obtained when the Si and Mg nuclei are ionized. To conclude, we analyze the heat capacity and structural properties of the liquid.« less

We combine two first-principles computer simulation techniques, path integral Monte Carlo and density functional theory molecular dynamics, to determine the equation of state of magnesium oxide in the regime of warm dense matter, with densities ranging from 0.35 to 71 g cm^-3 and temperatures ranging from 10 000 K to 5 × 10⁸ K. These conditions are relevant for the interiors of giant planets and stars as well as for shock wave compression measurements and inertial confinement fusion experiments. We study the electronic structure of MgO and the ionization mechanisms as a function of density and temperature. We show thatmore » the L-shell orbitals of magnesium and oxygen hybridize at high density. This results in a gradual ionization of the L-shell with increasing density and temperature. In this regard, MgO behaves differently from pure oxygen, which is reflected in the shape of the MgO principal shock Hugoniot curve. The curve of oxygen shows two compression maxima, while that of MgO shows only one. We predict a maximum compression ratio of 4.66 to occur for a temperature of 6.73 × 10⁷ K. Lastly, we research how multiple shocks and ramp waves can be used to cover a large range of densities and temperatures.« less