Evidence for Dissociation and Ionization in Shock Compressed Nitrogen to 800 GPa.

Triple bonding in the nitrogen molecule (N_{2}) is among the strongest chemical bonds with a dissociation enthalpy of 9.8 eV/molecule. Nitrogen is therefore an excellent test bed for theoretical and numerical methods aimed at understanding how bonding evolves under the influence of the extreme pressures and temperatures of the warm dense matter regime. Here, we report laser-driven shock experiments on fluid molecular nitrogen up to 800 GPa and 4.0 g/cm^{3}. Line-imaging velocimetry measurements and impedance matching method with a quartz reference yield shock equation of state data of initially precompressed nitrogen. Comparison with numerical simulations using path integral Monte Carlo and density functional theory molecular dynamics reveals clear signatures of chemical dissociation and the onset of L-shell ionization. Combining data along multiple shock Hugoniot curves starting from densities between 0.76 and 1.29 g/cm^{3}, our study documents how pressure and density affect these changes in chemical bonding and provides benchmarks for future theoretical developments in this regime, with applications for planetary interior modeling, high energy density science, and inertial confinement fusion research.

Anharmonicity and Phase Diagram of Magnesium Oxide in the Megabar Regime.

With density functional molecular dynamics simulations, we computed the phase diagram of MgO from 50 to 2000 GPa up to 20 000 K. Via thermodynamic integration (TDI), we derive the Gibbs free energies of the B1, B2, and liquid phases and determine their phase boundaries. With TDI and a pseudo-quasi-harmonic approach, we show that anharmonic effects are important and stabilize the B1 phase in particular. As a result, the B1-B2 transition boundary in the pressure-temperature plane exhibits a steep slope. We predict the B1-B2-liquid triple point to occur at approximately T=10000 K and P=370 GPa, which is higher in pressure than was inferred with quasiharmonic methods alone. We predict the principal shock Hugoniot curve to enter the B2 phase stability domain but only over a very small range of parameters. This may render it difficult to observe this phase with shock experiments because of kinetic effects.

Prediction of chlorine and fluorine crystal structures at high pressure using symmetry driven structure search with geometric constraints.

The high-pressure properties of fluorine and chlorine are not yet well understood because both are highly reactive and volatile elements, which have made conducting diamond anvil cell and x-ray diffraction experiments a challenge. Here, we use ab initio methods to search for stable crystal structures of both elements at megabar pressures. We demonstrate how symmetry and geometric constraints can be combined to efficiently generate crystal structures that are composed of diatomic molecules. Our algorithm extends the symmetry driven structure search method [R. Domingos et al., Phys. Rev. B 98, 174107 (2018)] by adding constraints for the bond length and the number of atoms in a molecule while still maintaining generality. As a method of validation, we have tested our approach for dense hydrogen and reproduced the known molecular structures of Cmca-12 and Cmca-4. We apply our algorithm to study chlorine and fluorine in the pressure range of 10 GPa-4000 GPa while considering crystal structures with up to 40 atoms per unit cell. We predict chlorine to follow the same series of phase transformations as elemental iodine from Cmca to Immm to Fm3¯m, but at substantially higher pressures. We predict fluorine to transition from a C2/c to Cmca structure at 70 GPa, to a novel orthorhombic and metallic structure with P42/mmc symmetry at 2500 GPa, and finally to its cubic analog form with Pm3¯n symmetry at 3000 GPa.

Nonideal mixing effects in warm dense matter studied with first-principles computer simulations.

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 well 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.

Magnesium oxide at extreme temperatures and pressures studied with first-principles simulations.

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 that 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. Finally, we study how multiple shocks and ramp waves can be used to cover a large range of densities and temperatures.

Path integral Monte Carlo simulations of dense carbon-hydrogen plasmas.

Carbon-hydrogen plasmas and hydrocarbon materials are of broad interest to laser shock experimentalists, high energy density physicists, and astrophysicists. Accurate equations of state (EOSs) of hydrocarbons are valuable for various studies from inertial confinement fusion to planetary science. By combining path integral Monte Carlo (PIMC) results at high temperatures and density functional theory molecular dynamics results at lower temperatures, we compute the EOSs for hydrocarbons from simulations performed at 1473 separate (ρ, T)-points distributed over a range of compositions. These methods accurately treat electronic excitation effects with neither adjustable parameter nor experimental input. PIMC is also an accurate simulation method that is capable of treating many-body interaction and nuclear quantum effects at finite temperatures. These methods therefore provide a benchmark-quality EOS that surpasses that of semi-empirical and Thomas-Fermi-based methods in the warm dense matter regime. By comparing our first-principles EOS to the LEOS 5112 model for CH, we validate the specific heat assumptions in this model but suggest that the Grüneisen parameter is too large at low temperatures. Based on our first-principles EOSs, we predict the principal Hugoniot curve of polystyrene to be 2%-5% softer at maximum shock compression than that predicted by orbital-free density functional theory and SESAME 7593. By investigating the atomic structure and chemical bonding of hydrocarbons, we show a drastic decrease in the lifetime of chemical bonds in the pressure interval from 0.4 to 4 megabar. We find the assumption of linear mixing to be valid for describing the EOS and the shock Hugoniot curve of hydrocarbons in the regime of partially ionized atomic liquids. We make predictions of the shock compression of glow-discharge polymers and investigate the effects of oxygen content and C:H ratio on its Hugoniot curve. Our full suite of first-principles simulation results may be used to benchmark future theoretical investigations pertaining to hydrocarbon EOSs and should be helpful in guiding the design of future experiments on hydrocarbons in the gigabar regime.

Equation of state and shock compression of warm dense sodium-A first-principles study.

As one of the simple alkali metals, sodium has been of fundamental interest for shock physics experiments, but knowledge of its equation of state (EOS) in hot, dense regimes is not well known. By combining path integral Monte Carlo (PIMC) results for partially ionized states [B. Militzer and K. P. Driver, Phys. Rev. Lett. 115, 176403 (2015)] at high temperatures and density functional theory molecular dynamics (DFT-MD) results at lower temperatures, we have constructed a coherent equation of state for sodium over a wide density-temperature range of 1.93-11.60 g/cm3 and 103-1.29×108 K. We find that a localized, Hartree-Fock nodal structure in PIMC yields pressures and internal energies that are consistent with DFT-MD at intermediate temperatures of 2×106 K. Since PIMC and DFT-MD provide a first-principles treatment of electron shell and excitation effects, we are able to identify two compression maxima in the shock Hugoniot curve corresponding to K-shell and L-shell ionization. Our Hugoniot curves provide a benchmark for widely used EOS models: SESAME, LEOS, and Purgatorio. Due to the low ambient density, sodium has an unusually high first compression maximum along the shock Hugoniot curve. At beyond 107 K, we show that the radiation effect leads to very high compression along the Hugoniot curve, surpassing relativistic corrections, and observe an increasing deviation of the shock and particle velocities from a linear relation. We also compute the temperature-density dependence of thermal and pressure ionization processes.

Development of Path Integral Monte Carlo Simulations with Localized Nodal Surfaces for Second-Row Elements.

We extend the applicability range of fermionic path integral Monte Carlo simulations to heavier elements and lower temperatures by introducing various localized nodal surfaces. Hartree-Fock nodes yield the most accurate prediction for pressure and internal energy, which we combine with the results from density functional molecular dynamics simulations to obtain a consistent equation of state for hot, dense silicon under plasma conditions and in the regime of warm dense matter (2.3-18.6 g cm(-3), 5.0×10(5)-1.3×10(8) K). The shock Hugoniot curve is derived and the structure of the fluid is characterized with various pair correlation functions.

Superconductivity in Dilute Hydrides of Ammonia under Pressure.

The past decade has witnessed great progress in predicting and synthesizing polyhydrides that exhibit superconductivity under pressure. Dopants allow these compounds to become metals at pressures lower than those required to metallize elemental hydrogen. Here, we show that by combining the fundamental planetary building blocks of molecular hydrogen and ammonia, conventional superconducting compounds can be formed at high pressure. Through extensive theoretical calculations, we predict metallic metastable structures with NHn (n = 10, 11, 24) stoichiometries that are based on NH4+ superalkali cations and complex hydrogenic lattices. The hydrogen atoms in the molecular cation contribute to the superconducting mechanism, and the estimated superconducting critical temperatures, Tc's, are comparable to the highest values computed for the alkali metal polyhydrides. The largest calculated (isotropic Eliashberg) Tc is ∼180 K for Pnma-NH10 at 300 GPa. Our results suggest that other molecular cations can be mixed with hydrogen under pressure, yielding superconducting compounds.

Superionic to superionic phase change in water: consequences for the interiors of uranus and neptune.

Using density functional molecular dynamics free energy calculations, we show that the body centered cubic (bcc) phase of superionic ice previously believed to be the only phase is, in fact, thermodynamically unstable compared to a novel phase with oxygen positions in face centered cubic lattice sites. The novel phase has a lower proton mobility than the bcc phase and may exhibit a higher melting temperature. We predict a transition between the two phases at a pressure of 1±0.5 Mbar, with potential consequences for the interiors of ice giants such as Uranus and Neptune.

Double superionicity in icy compounds at planetary interior conditions.

The elements hydrogen, carbon, nitrogen and oxygen are assumed to comprise the bulk of the interiors of the ice giant planets Uranus, Neptune, and sub-Neptune exoplanets. The details of their interior structures have remained largely unknown because it is not understood how the compounds H2O, NH3 and CH4 behave and react once they have been accreted and exposed to high pressures and temperatures. Here we study thirteen H-C-N-O compounds with ab initio computer simulations and demonstrate that they assume a superionic state at elevated temperatures, in which the hydrogen ions diffuse through a stable sublattice that is provided by the larger nuclei. At yet higher temperatures, four of the thirteen compounds undergo a second transition to a novel doubly superionic state, in which the smallest of the heavy nuclei diffuse simultaneously with hydrogen ions through the remaining sublattice. Since this transition and the melting transition at yet higher temperatures are both of first order, this may introduce additional layers in the mantle of ice giant planets and alter their convective patterns.

Rocky core solubility in Jupiter and giant exoplanets.

Gas giants are believed to form by the accretion of hydrogen-helium gas around an initial protocore of rock and ice. The question of whether the rocky parts of the core dissolve into the fluid H-He layers following formation has significant implications for planetary structure and evolution. Here we use ab initio calculations to study rock solubility in fluid hydrogen, choosing MgO as a representative example of planetary rocky materials, and find MgO to be highly soluble in H for temperatures in excess of approximately 10,000 K, implying the potential for significant redistribution of rocky core material in Jupiter and larger exoplanets.

Path integral Monte Carlo approach to the structural properties and collective excitations of liquid [Formula: see text] without fixed nodes.

Due to its nature as a strongly correlated quantum liquid, ultracold helium is characterized by the nontrivial interplay of different physical effects. Bosonic [Formula: see text] exhibits superfluidity and Bose-Einstein condensation. Its physical properties have been accurately determined on the basis of ab initio path integral Monte Carlo (PIMC) simulations. In contrast, the corresponding theoretical description of fermionic [Formula: see text] is severely hampered by the notorious fermion sign problem, and previous PIMC results have been derived by introducing the uncontrolled fixed-node approximation. In this work, we present extensive new PIMC simulations of normal liquid [Formula: see text] without any nodal constraints. This allows us to to unambiguously quantify the impact of Fermi statistics and to study the effects of temperature on different physical properties like the static structure factor [Formula: see text], the momentum distribution [Formula: see text], and the static density response function [Formula: see text]. In addition, the dynamic structure factor [Formula: see text] is rigorously reconstructed from imaginary-time PIMC data. From simulations of [Formula: see text], we derived the familiar phonon-maxon-roton dispersion function that is well-known for [Formula: see text] and has been reported previously for two-dimensional [Formula: see text] films (Nature 483:576-579 (2012)). The comparison of our new results for both [Formula: see text] and [Formula: see text] with neutron scattering measurements reveals an excellent agreement between theory and experiment.

The phase diagrams of beryllium and magnesium oxide at megabar pressures.

We performab initiosimulations of beryllium (Be) and magnesium oxide (MgO) at megabar pressures and compare their structural and thermodynamic properties. We make a detailed comparison of our two recently derived phase diagrams of Be (Wuet al2021Phys. Rev.B104014103) and MgO (Soubiran and Militzer 2020Phys. Rev. Lett.125175701) using the thermodynamic integration technique, as they exhibit striking similarities regarding their shape. We explore whether the Lindemann criterion can explain the melting temperatures of these materials through the calculation of the Debye temperature at high pressure. From our free energy calculations, we find that the melting line of both materials is well represented by the Simon-Glazel fitTm(P) =T0(1 +P/a)1/c, whereT0= 1564 K,a= 15.8037 GPa andc= 2.4154 for Be, whileT0= 3010 K,a= 10.5797 GPa andc= 2.8683 for the MgO in the B1. For the B2 phase, we use the valuesa= 26.1163 GPa andc= 2.2426. Both materials exhibit negative Clapeyron slopes on the boundaries between the two solid phases that are strongly affected by anharmonic effects, which also influence the location of the solid-solid-liquid triple point. We find that the quasi-harmonic approximation underestimates the stability range of the low-pressure phases, namely hcp for Be and B1 for MgO. We also compute the phonon dispersion relations at low and high pressure for each of the phases of these materials, and also explore how the phonon density of states is modified by temperature. Finally, we derive secondary shock Hugoniot curves in addition to the principal Hugoniot curve for both materials, and study their offsets in pressure between solid and liquid branches.

Miscibility of rock and ice in the interiors of water worlds.

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.

Loss of a satellite could explain Saturn's obliquity and young rings.

The origin of Saturn's ~26.7° obliquity and ~100-million-year-old rings is unknown. The observed rapid outward migration of Saturn's largest satellite, Titan, could have raised Saturn's obliquity through a spin-orbit precession resonance with Neptune. We use Cassini data to refine estimates of Saturn's moment of inertia, finding that it is just outside the range required for the resonance. We propose that Saturn previously had an additional satellite, which we name Chrysalis, that caused Saturn's obliquity to increase through the Neptune resonance. Destabilization of Chrysalis's orbit ~100 million years ago can then explain the proximity of the system to the resonance and the formation of the rings through a grazing encounter with Saturn.

Momentum distribution of the uniform electron gas at finite temperature: Effects of spin polarization.

We carry out extensive direct path integral Monte Carlo (PIMC) simulations of the uniform electron gas (UEG) at finite temperature for different values of the spin-polarization ξ. This allows us to unambiguously quantify the impact of spin effects on the momentum distribution function n(k) and related properties. We find that interesting physical effects like the interaction-induced increase in the occupation of the zero-momentum state n(0) substantially depend on ξ. Our results further advance the current understanding of the UEG as a fundamental model system, and are of practical relevance for the description of transport properties of warm dense matter in an external magnetic field. All PIMC results are freely available online and can be used as a benchmark for the development of methods and applications.

First-principles equation of state database for warm dense matter computation.

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 LiF, B_{4}C, BN, CH_{4}, CH_{2}, C_{2}H_{3}, CH, C_{2}H, MgO, and MgSiO_{3}. For all these materials, we provide the pressure and internal energy over a density-temperature range from ∼0.5 to 50 g 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 L- and 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 H_{2}O, H_{2}O_{2}, Al_{2}O_{3}, CO, and 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.

New phases of water ice predicted at megabar pressures.

Based on density functional calculations we predict water ice to attain two new crystal structures with Pbca and Cmcm symmetry at 7.6 and 15.5 Mbar, respectively. The known high-pressure ice phases VII, VIII, X, and Pbcm as well as the Pbca phase are all insulating and composed of two interpenetrating hydrogen bonded networks, but the Cmcm structure is metallic and consists of corrugated sheets of H and O atoms. The H atoms are squeezed into octahedral positions between next-nearest O atoms while they occupy tetrahedral positions between nearest O atoms in the ice X, Pbcm, and Pbca phases.

Sequestration of noble gases in giant planet interiors.

The Galileo probe showed that Jupiter's atmosphere is severely depleted in neon compared to protosolar values. We show via ab initio simulations of the partitioning of neon between hydrogen-helium phases that the observed depletion can be explained by the sequestration of neon into helium-rich droplets within the postulated hydrogen-helium immiscibility layer of the planets interior. We also demonstrate that this mechanism will not affect argon explaining the observed lack of depletion of this gas. This provides strong indirect evidence for hydrogen-helium immiscibility in Jupiter.