Equation‐of‐state data for molecular hydrogen and deuterium at shock pressures in the range 2–76 GPa (20–760 kbar)a)

Effect of ionic disorder on the principal shock Hugoniot

The effect of ionic disorder on the principal Hugoniot is investigated using multiple scattering theory to very high pressure (Gbar). Calculations using molecular dynamics to simulate ionic disorder are compared to those with a fixed crystal lattice, for both carbon and aluminum. For the range of conditions considered here we find that ionic disorder has a relatively minor influence. It is most important at the onset of shell ionization and we find that, at higher pressures, the subtle effect of the ionic environment is overwhelmed by the larger number of ionized electrons with higher thermal energies.

Equilibrium properties of warm dense deuterium calculated by the wave packet molecular dynamics and density functional theory method

A joint simulation method based on the wave packet molecular dynamics and density functional theory (WPMD-DFT) is applied to study warm dense deuterium (nonideal deuterium plasmas). This method was developed recently as an extension of the wave packet molecular dynamics (WPMD) in which the equations of motion are solved simultaneously for classical ions and semiclassical electrons represented as Gaussian wave packets. Compared to the classical molecular dynamics and WPMD simulations, the method of WPMD-DFT provides a more accurate representation of quantum effects such as electron-ion coupling and electron degeneracy. It allows studying nonadiabatic dynamics of electrons and ions in equilibrium and nonequilibrium states while being more accurate and efficient at high densities than WPMD and classical molecular dynamics. In the paper, we discuss particular features of the method such as special boundary conditions and the procedure of isentrope calculation as well as the results obtained by WPMD-DFT for the shock-compressed deuterium. The compression isentrope and principal Hugoniot curves obtained by WPMD-DFT are compared with available experimental data and other simulation approaches to validate the method. It opens up a possibility of further application of the method to study nonequilibrium states and relaxation processes.

A Perspective on Hydrogen Near the Liquid-Liquid Phase Transition and Metallization of Fluid H

Metallic hydrogen has been a major issue in physical chemistry since its prediction in 1935. Its predicted density implies 100 GPa (10⁶ bar = Mbar) pressures P are needed to make metallic H with the Fermi temperature T_F = 220 000 K. Temperatures T can be several 1000 K and still be "very low" with T/T_F ≪ 1. In 1996, metallic fluid H was made under dynamic compression at P = 140 GPa and calculated T ≈ 3000 K generated with a two-stage light-gas gun. Those T's place metallic H in the liquid-liquid phase transition region. The purpose of this Perspective is to place the phase curve measured in laser-heated diamond anvil cells in context with those measured electrical conductivities. That phase curve is probably caused by dissociation of H₂ to H starting near 90 GPa/1600 K. Metallic H then forms in a crossover as a semiconductor up to 140 GPa/3000 K. Dynamic quasi-isentropic pressure was tuned to make metallic H by design in those conductivity experiments.

Shock Compression of Liquid Deuterium up to 1 TPa

We present laser-driven shock compression experiments on cryogenic liquid deuterium to 550 GPa along the principal Hugoniot and reflected-shock data up to 1 TPa. High-precision interferometric Doppler velocimetry and impedance-matching analysis were used to determine the compression accurately enough to reveal a significant difference as compared to state-of-the-art ab initio calculations and thus, no single equation of state model fully matches the principal Hugoniot of deuterium over the observed pressure range. In the molecular-to-atomic transition pressure range, models based on density functional theory calculations predict the maximum compression accurately. However, beyond 250 GPa along the principal Hugoniot, first-principles models exhibit a stiffer response than the experimental data. Similarly, above 500 GPa the reflected shock data show 5%-7% higher compression than predicted by all current models.

Quantum molecular dynamics study on the proton exchange, ionic structures, and transport properties of warm dense hydrogen-deuterium mixtures

Comprehensive knowledge of physical properties such as equation of state (EOS), proton exchange, dynamic structures, diffusion coefficients, and viscosities of hydrogen-deuterium mixtures with densities from 0.1 to 5 g/cm^{3} and temperatures from 1 to 50 kK has been presented via quantum molecular dynamics (QMD) simulations. The existing multi-shock experimental EOS provides an important benchmark to evaluate exchange-correlation functionals. The comparison of simulations with experiments indicates that a nonlocal van der Waals density functional (vdW-DF1) produces excellent results. Fraction analysis of molecules using a weighted integral over pair distribution functions was performed. A dissociation diagram together with a boundary where the proton exchange (H_{2}+D_{2}⇌2HD) occurs was generated, which shows evidence that the HD molecules form as the H_{2} and D_{2} molecules are almost 50% dissociated. The mechanism of proton exchange can be interpreted as a process of dissociation followed by recombination. The ionic structures at extreme conditions were analyzed by the effective coordination number model. High-order cluster, circle, and chain structures can be founded in the strongly coupled warm dense regime. The present QMD diffusion coefficient and viscosity can be used to benchmark two analytical one-component plasma (OCP) models: the Coulomb and Yukawa OCP models.

Metastable ultracondensed hydrogenous materials

The primary purpose of this paper is to stimulate theoretical predictions of how to retain metastably hydrogenous materials made at high pressure P on release to ambient. Ultracondensed metallic hydrogen has been made at high pressures in the fluid and reported made probably in the solid. Because the long quest for metallic hydrogen is likely to be concluded in the relatively near future, a logical question is whether another research direction, comparable in scale to the quest for metallic H, will arise in high pressure research. One possibility is retention of metastable solid metallic hydrogen and other hydrogenous materials on release of dynamic and static high pressures P to ambient. If hydrogenous materials could be retained metastably on release, those materials would be a new class of materials for scientific investigations and technological applications. This paper is a review of the current situation with the synthesis of metallic hydrogen, potential technological applications of metastable metallic H and other hydrogenous materials at ambient, and general background of published experimental and theoretical work on what has been accomplished with metastable phases in the past and thus what might be accomplished in the future.

High-Precision Shock Wave Measurements of Deuterium: Evaluation of Exchange-Correlation Functionals at the Molecular-to-Atomic Transition

We present shock compression data for deuterium through the molecular-to-atomic transition along the principal Hugoniot with unprecedented precision, enabling discrimination between subtle differences in first-principle theoretical predictions. These observations, supported through reshock measurements, provide tight constraints in a regime directly relevant to planetary interiors. Our findings are in best agreement with density functional theory; however, no one exchange-correlation functional describes well both the onset of dissociation and the maximum compression along the Hugoniot.

Molecular-Atomic Transition along the Deuterium Hugoniot Curve with Coupled Electron-Ion Monte Carlo Simulations

We have performed simulations of the principal deuterium Hugoniot curve using coupled electron-ion Monte Carlo calculations. Using highly accurate quantum Monte Carlo methods for the electrons, we study the region of maximum compression along the Hugoniot, where the system undergoes a continuous transition from a molecular fluid to a monatomic fluid. We include all relevant physical corrections so that a direct comparison to experiment can be made. Around 50 GPa we find a maximum compression of 4.85. This compression is approximately 5.5% higher than previous theoretical predictions and 15% higher than the most accurate experimental data. Thus first-principles simulations encompassing the most advanced techniques are in disagreement with the results of the best experiments.

A density functional tight binding model with an extended basis set and three-body repulsion for hydrogen under extreme thermodynamic conditions

We present a new DFTB-p3b density functional tight binding model for hydrogen at extremely high pressures and temperatures, which includes a polarizable basis set (p) and a three-body environmentally dependent repulsive potential (3b). We find that use of an extended basis set is necessary under dissociated liquid conditions to account for the substantial p-orbital character of the electronic states around the Fermi energy. The repulsive energy is determined through comparison to cold curve pressures computed from density functional theory (DFT) for the hexagonal close-packed solid, as well as pressures from thermally equilibrated DFT-MD simulations of the liquid phase. In particular, we observe improved agreement in our DFTB-p3b model with previous theoretical and experimental results for the shock Hugoniot of hydrogen up to 100 GPa and 25000 K, compared to a standard DFTB model using pairwise interactions and an s-orbital basis set, only. The DFTB-p3b approach discussed here provides a general method to extend the DFTB method for a wide variety of materials over a significantly larger range of thermodynamic conditions than previously possible.

High-temperature high-pressure phases of lithium from electron force field (eFF) quantum electron dynamics simulations

We recently developed the electron force field (eFF) method for practical nonadiabatic electron dynamics simulations of materials under extreme conditions and showed that it gave an excellent description of the shock thermodynamics of hydrogen from molecules to atoms to plasma, as well as the electron dynamics of the Auger decay in diamondoids following core electron ionization. Here we apply eFF to the shock thermodynamics of lithium metal, where we find two distinct consecutive phase changes that manifest themselves as a kink in the shock Hugoniot, previously observed experimentally, but not explained. Analyzing the atomic distribution functions, we establish that the first phase transition corresponds to (i) an fcc-to-cI16 phase transition that was observed previously in diamond anvil cell experiments at low temperature and (ii) a second phase transition that corresponds to the formation of a new amorphous phase (amor) of lithium that is distinct from normal molten lithium. The amorphous phase has enhanced valence electron-nucleus interactions due to localization of electrons into interstitial locations, along with a random connectivity distribution function. This indicates that eFF can characterize and compute the relative stability of states of matter under extreme conditions (e.g., warm dense matter).

Evidence for a first-order liquid-liquid transition in high-pressure hydrogen from ab initio simulations

Using quantum simulation techniques based on either density functional theory or quantum Monte Carlo, we find clear evidence of a first-order transition in liquid hydrogen, between a low conductivity molecular state and a high conductivity atomic state. Using the temperature dependence of the discontinuity in the electronic conductivity, we estimate the critical point of the transition at temperatures near 2,000 K and pressures near 120 GPa. Furthermore, we have determined the melting curve of molecular hydrogen up to pressures of 200 GPa, finding a reentrant melting line. The melting line crosses the metalization line at 700 K and 220 GPa using density functional energetics and at 550 K and 290 GPa using quantum Monte Carlo energetics.

Equation of State and Electrical Conductivity of Dense Fluid Hydrogen and Helium

The equation of state of fluid hydrogen, helium, and their mixtures is determined within fluid variational theory. Reactions between the constituents such as dissociation and ionization are considered. Results are given for densities and temperatures relevant for the interior of giant planets. Furthermore, the electrical conductivity is determined within linear response theory. Comparison is performed with available experiments and other theoretical work.

Excited electron dynamics modeling of warm dense matter

We present a model (the electron force field, or eFF) based on a simplified solution to the time-dependent Schrödinger equation that with a single approximate potential between nuclei and electrons correctly describes many phases relevant for warm dense hydrogen. Over a temperature range of 0 to 100,000 K and densities up to 1 g/cm(3), we find excellent agreement with experimental, path integral Monte Carlo, and linear mixing equations of state, as well as single-shock Hugoniot curves from shock compression experiments. In principle eFF should be applicable to other warm dense systems as well.

Shock wave propagation in dissociating low-Z liquids: D2

We present direct molecular dynamics simulations of shock wave propagation in liquid deuterium for a wide range of impact velocities. The calculated Hugoniot is in perfect agreement with the gas-gun data as well as with the most recent experimental data. At high impact velocities we observe a smearing of the shock wave front and propagation of fast dissociated molecules well ahead of the compressed region. This smearing occurs due to the fast deuterium dissociation at the shock wave front. The experimental results are discussed in view of this effect.

Monte Carlo results for the hydrogen Hugoniot

We propose a theoretical Hugoniot relation obtained by combining results for the equation of state from the direct path integral Monte Carlo technique (DPIMC) and those from reaction ensemble Monte Carlo (REMC) simulations. The main idea of this proposal is based on the fact that the DPMIC technique provides first-principle results for a wide range of densities and temperatures including the region of partially ionized plasmas. On the other hand, for lower temperatures where the formation of molecules becomes dominant, DPIMC simulations become cumbersome and inefficient. For this region it is possible to use accurate REMC simulations where bound states (molecules) are treated on the Born-Oppenheimer level. The remaining interaction is then reduced to the scattering between neutral particles which is reliably treated classically by applying effective potentials. The resulting Hugoniot is located between the experimental values of Knudson et al. [Phys. Rev. Lett. 87, 225501 (2001)] and Collins et al. [Science 281, 1178 (1998)].

Reaction ensemble Monte Carlo technique and hypernetted chain approximation study of dense hydrogen

In spite of the simple structure of hydrogen, up to now there is no unified theoretical and experimental description of hydrogen at high pressures. Recent results of Z-pinch experiments show a large deviation from those obtained by laser driven ones. Theoretical investigations including ab initio computer simulations show considerable differences at such extreme conditions from each other and from experimental values. We apply the reaction ensemble Monte Carlo technique on one hand and a combination of the hypernetted chain approximation with the mass action law on the other to study the behavior of dense hydrogen at such conditions. The agreement between both methods for the equation of state and for the Hugoniot curve is excellent. Comparison to other methods and experimental results is also performed.

Use of a wave reverberation technique to infer the density compression of shocked liquid deuterium to 75 GPa

A novel approach was developed to probe density compression of liquid deuterium (L-D2) along the principal Hugoniot. Relative transit times of shock waves reverberating within the sample are shown to be sensitive to the compression due to the first shock. This technique has proven to be more sensitive than the conventional method of inferring density from the shock and mass velocity, at least in this high-pressure regime. Results in the range of 22-75 GPa indicate an approximately fourfold density compression, and provide data to differentiate between proposed theories for hydrogen and its isotopes.

Shock compression of deuterium near 100 GPa pressures

The shock-compression curve (Hugoniot) of D2 near 100 GPa pressures (1 Mbar) has been contro-versial because the two published measurements have limiting compressions of fourfold and sixfold. Our purpose is to examine published experimental results to decide which, if either, is probably correct. The published Hugoniot data of low-Z diatomic molecules have a universal behavior. The deuterium data of Knudson et al. (fourfold limiting compression) have this universal behavior, which suggests that Knudson et al. are correct and shows that deuterium behaves as other low-Z elements at high tem-peratures. In D2, H2, N2, CO, and O2, dissociation completes and average kinetic energy dominates average potential energy above approximately 60 GPa. Below approximately 30 GPa, D2, H2, N2, CO, and O2 are diatomic. D2 dissociation is accompanied by a temperature-driven nonmetal-metal transition at approximately 50 GPa.

Temperature measurements of shock compressed liquid deuterium up to 230 GPa

Pyrometric measurements of single-shock-compressed liquid deuterium reveal that shock front temperatures T increase from 0.47 to 4.4 eV as the pressure P increases from 31 to 230 GPa. Where deuterium becomes both conducting and highly compressible, 30< or =P< or =50 GPa, T is lower than most models predict and T<<T(Fermi), proving that deuterium is a degenerate Fermi-liquid metal. At P>50 Gpa, where the optical reflectivity is saturated, there is an increase in the rate that T increases with P.

Path integral monte carlo calculation of the deuterium hugoniot

Restricted path integral Monte Carlo simulations have been used to calculate the equilibrium properties of deuterium for two densities: 0.674 and 0.838 g cm(-3) ( r(s) = 2.00 and 1.86) in the temperature range of 10(5)</=T</=10(6) K. We carefully assess size effects and dependence on the time step of the path integral. Further, we compare the results obtained with a free particle nodal restriction with those from a self-consistent variational principle, which includes interactions and bound states. By using the calculated internal energies and pressures, we determine the shock Hugoniot and compare with recent laser shock wave experiments as well as other theories.

Shock-induced transformation of liquid deuterium into a metallic fluid

Simultaneous measurements of shock velocity and optical reflectance at 1064, 808, and 404 nm of a high pressure shock front propagating through liquid deuterium show a continuous increase in reflectance from below 10% and saturating at approximately (40-60)% in the range of shock velocities from 12 to 20 &mgr;m/ns (pressure range 17-50 GPa). The high optical reflectance is evidence that the shocked deuterium reaches a conducting state characteristic of a metallic fluid. Above 20 &mgr;m/ns shock velocity (50 GPa pressure) reflectance is constant indicating that the transformation is substantially complete.

Modeling hot, dense hydrogen with a classical spin dependent hamiltonian

Hot, dense hydrogen is studied with a classical model in which the interaction energy between atoms depends on their internal spins as well as their separation distance. The spins are treated as classical variables. This model is used in Monte Carlo simulations to calculate internal energies, pressures, and pair correlation functions, as well as the Hugoniot for shocked liquid deuterium. The results clearly show the transition of hot, dense hydrogen from a molecular to an atomic fluid. Our results are in reasonable agreement with far more elaborate quantum mechanical simulations.

Measurements of the equation of state of deuterium at the fluid insulator-metal transition

A high-intensity laser was used to shock-compress liquid deuterium to pressures from 22 to 340 gigapascals. In this regime deuterium is predicted to transform from an insulating molecular fluid to an atomic metallic fluid. Shock densities and pressures, determined by radiography, revealed an increase in compressibility near 100 gigapascals indicative of such a transition. Velocity interferometry measurements, obtained by reflecting a laser probe directly off the shock front in flight, demonstrated that deuterium shocked above 55 gigapascals has an electrical conductivity characteristic of a liquid metal and independently confirmed the radiography.

Temperature measurements of shock-compressed liquid hydrogen: implications for the interior of Jupiter

Shock temperatures of hydrogen up to 5200 kelvin were measured optically at pressures up to 83 gigapascals (830 kilobars). At highest pressures, the measured temperatures are substantially lower than predicted. These lower temperatures are caused by a continuous dissociative phase transition above 20 gigapascals. Because hydrogen is in thermal equilibrium in shock-compression experiments, the theory derived from the shock data can be applied to Jupiter. The planet's molecular envelope is cooler and has much less temperature variation than previously believed. The continuous dissociative phase transition suggests that there is no sharp boundary between Jupiter's molecular mantle and its metallic core. A possible convectively quiescent boundary layer might induce an additional layer in the molecular region, as has been predicted.

Sound Velocities in Dense Hydrogen and the Interior of Jupiter

Sound velocities in fluid and crystalline hydrogen were measured under pressure to 24 gigapascals by Brillouin spectroscopy in the diamond anvil cell. The results provide constraints on the intermolecular interactions of dense hydrogen and are used to construct an intermolecular potential consistent with all available data. Fluid perturbation theory calculations with the potential indicate that sound velocities in hydrogen at conditions of the molecular layer of the Jovian planets are lower than previously believed. Jovian models consistent with the present results remain discrepant with recent free oscillation spectra of the planet by 15 percent. The effect of changing interior temperatures, the metallic phase transition depth, and the fraction of high atomic number material on Jovian oscillation frequencies is also investigated with the Brillouin equation of state. The present data place strong constraints on sound velocities in the Jovian molecular layer and provide an improved basis for interpreting possible Jovian oscillations.

Dense Astrophysical Plasmas

Degenerate bodies composed primarily of dense hydrogen and helium plasmas range from giant planets to the so far hypothetical brown dwarfs. More massive objects begin their lives as nondegenerate stars and may end as white dwarfs, composed primarily of carbon and oxygen, or as neutron stars, with solid crusts of iron or heavier elements and cores of neutron matter. The physical properties of dense plasmas that are necessary to construct theoretical models of such degenerate stars include the equation of state, transport properties, and nuclear reaction rates.