Temperature measurements and dissociation of shock-compressed liquid deuterium and hydrogen

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.

Molecular dynamics simulation of strong shock waves propagating in dense deuterium, taking into consideration effects of excited electrons

We present a molecular dynamics simulation of shock waves propagating in dense deuterium with the electron force field method [J. T. Su and W. A. Goddard, Phys. Rev. Lett. 99, 185003 (2007)PRLTAO0031-900710.1103/PhysRevLett.99.185003], which explicitly takes the excitation of electrons into consideration. Nonequilibrium features associated with the excitation of electrons are systematically investigated. We show that chemical bonds in D_{2} molecules lead to a more complicated shock wave structure near the shock front, compared with the results of classical molecular dynamics simulation. Charge separation can bring about accumulation of net charges on large scales, instead of the formation of a localized dipole layer, which might cause extra energy for the shock wave to propagate. In addition, the simulations also display that molecular dissociation at the shock front is the major factor that accounts for the "bump" structure in the principal Hugoniot. These results could help to build a more realistic picture of shock wave propagation in fuel materials commonly used in the inertial confinement fusion.

Contributed Review: Absolute spectral radiance calibration of fiber-optic shock-temperature pyrometers using a coiled-coil irradiance standard lamp

We describe an accurate and precise calibration procedure for multichannel optical pyrometers such as the 6-channel, 3-ns temporal resolution instrument used in the Caltech experimental geophysics laboratory. We begin with a review of calibration sources for shock temperatures in the 3000-30,000 K range. High-power, coiled tungsten halogen standards of spectral irradiance appear to be the only practical alternative to NIST-traceable tungsten ribbon lamps, which are no longer available with large enough calibrated area. However, non-uniform radiance complicates the use of such coiled lamps for reliable and reproducible calibration of pyrometers that employ imaging or relay optics. Careful analysis of documented methods of shock pyrometer calibration to coiled irradiance standard lamps shows that only one technique, not directly applicable in our case, is free of major radiometric errors. We provide a detailed description of the modified Caltech pyrometer instrument and a procedure for its absolute spectral radiance calibration, accurate to ±5%. We employ a designated central area of a 0.7× demagnified image of a coiled-coil tungsten halogen lamp filament, cross-calibrated against a NIST-traceable tungsten ribbon lamp. We give the results of the cross-calibration along with descriptions of the optical arrangement, data acquisition, and processing. We describe a procedure to characterize the difference between the static and dynamic response of amplified photodetectors, allowing time-dependent photodiode correction factors for spectral radiance histories from shock experiments. We validate correct operation of the modified Caltech pyrometer with actual shock temperature experiments on single-crystal NaCl and MgO and obtain very good agreement with the literature data for these substances. We conclude with a summary of the most essential requirements for error-free calibration of a fiber-optic shock-temperature pyrometer using a high-power coiled tungsten halogen irradiance standard lamp.

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.

Delocalization of Electrons in Strong Insulators at High Dynamic Pressures

Systematics of material responses to shock flows at high dynamic pressures are discussed. Dissipation in shock flows drives structural and electronic transitions or crossovers, such as used to synthesize metallic liquid hydrogen and most probably Al₂O₃ metallic glass. The term “metal” here means electrical conduction in a degenerate system, which occurs by band overlap in degenerate condensed matter, rather than by thermal ionization in a non-degenerate plasma. Since H₂ and probably disordered Al₂O₃ become poor metals with minimum metallic conductivity (MMC) virtually all insulators with intermediate strengths do so as well under dynamic compression. That is, the magnitude of strength determines the split between thermal energy and disorder, which determines material response. These crossovers occur via a transition from insulators with electrons localized in chemical bonds to poor metals with electron energy bands. For example, radial extents of outermost electrons of Al and O atoms are 7 a₀ and 4 a₀, respectively, much greater than 1.7 a₀ needed for onset of hybridization at 300 GPa. All such insulators are Mott insulators, provided the term “correlated electrons” includes chemical bonds.

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.

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.

Simple analytic equations of state for hard-core single and double Yukawa fluids and mixtures based on second-order Barker-Henderson perturbation theory

A simple analytic expression with high precision for the radial distribution function of hard spheres is proposed. The form of the expression has been carefully selected to combine the well-known Camahan-Starling equation of state in it and satisfy the limit condition at low density, its simplicity and precision is superior to the well-known Percus-Yevick expression. The coefficients contained in the expression have been determined by fitting the Monte Carlo data for the first coordination shell, and by fitting both the Monte Carlo data and the numerical results of the Percus-Yevick expression for the second coordination shell. The expression has been applied to develop simple analytic equations of state for the hard-core single, double Yukawa fluids, and the hard-core Yukawa mixtures. The comparisons show that the agreement of our model with the computer simulation data is slightly better than the mean spherical approximation and other analytic models.

Equation of state measurements in liquid deuterium to 70 GPa

Using intense magnetic pressure, a method was developed to launch flyer plates to velocities in excess of 20 km/s. This technique was used to perform plate-impact, shock wave experiments on cryogenic liquid deuterium ( L-D(2)) to examine its high-pressure equation of state. Using an impedance matching method, Hugoniot measurements were obtained in the pressure range of 30-70 GPa. The results of these experiments disagree with previously reported Hugoniot measurements of L-D(2) in the pressure range above approximately 40 GPa, but are in good agreement with first principles, ab initio models for hydrogen and its isotopes.

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.

Isentropes and Hugoniot curves for dense hydrogen and deuterium

Multiple-shock experiments with fluid hydrogen have shown that a transition from semiconducting behavior to metal-like conductivity occurs at pressures (p) of about 140 GPa and temperatures (T) near 3000 K. We model the p-T pathway by Hugoniot curves (initial shock) and isentropes (subsequent shocks). For the calculation of these curves we apply an expression for the free energy developed recently for dense hydrogen and deuterium plasma in the regions of partial dissociation and partial ionization. Furthermore, we discuss the relations between Hugoniot curves, isentropes and the coexistence line of the plasma phase transition.

Local-spin-density-approximation molecular-dynamics simulations of dense deuterium

Local-spin-density-approximation molecular-dynamics simulations of deuterium in the dissociating regime are presented, with a particular emphasis on the molecular phase of two isochores corresponding for deuterium to V=6 cm(3)/mole, rho=0.670 g/cm(3) and V=4 cm(3)/mole, rho=1 g/cm(3). It is shown that the transition from the molecular regime, well described by the local-spin-density-approximation functional, to the dissociated regime where previous local-density-approximation results are recovered, comes with a negative curvature deltaP/deltaT<0 in the isochore. We show that this effect is not enough to explain the large compressibility measured in the laser experiments [L. B. DaSilva et al., Phys. Rev. Lett. 78, 483 (1997); G. W. Collins et al., Science 281, 1178 (1998); P. Celliers et al., Phys. Rev. Lett. 84, 5564 (2000)].

Reflected shock experiments on the equation-of-state properties of liquid deuterium at 100-600 GPa (1-6 mbar)

New laser-driven shock experiments have been used to study the equation-of-state (EOS) properties of liquid deuterium. Reflected shocks are utilized to increase the shock pressure and to enhance the sensitivity to differences in compressibility. The results of these experiments differ substantially from the predictions of the Sesame EOS. EOS models showing large dissociation effects with much greater compressibility (up to a factor of 2) agree with the data. By use of independent techniques, this experiment offers the first confirmation of an earlier observation of enhanced compressibility in liquid deuterium.

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.

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.

On the Radii of Close-in Giant Planets

The recent discovery that the close-in extrasolar giant planet HD 209458b transits its star has provided a first-of-its-kind measurement of the planet's radius and mass. In addition, there is a provocative detection of the light reflected off of the giant planet tau Bootis b. Including the effects of stellar irradiation, we estimate the general behavior of radius/age trajectories for such planets and interpret the large measured radii of HD 209458b and tau Boo b in that context. We find that HD 209458b must be a hydrogen-rich gas giant. Furthermore, the large radius of a close-in gas giant is not due to the thermal expansion of its atmosphere but to the high residual entropy that remains throughout its bulk by dint of its early proximity to a luminous primary. The large stellar flux does not inflate the planet but retards its otherwise inexorable contraction from a more extended configuration at birth. This implies either that such a planet was formed near its current orbital distance or that it migrated in from larger distances (>/=0.5 AU), no later than a few times 107 yr of birth.

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.

Metallization and electrical conductivity of hydrogen in Jupiter

Electrical conductivities of molecular hydrogen in Jupiter were calculated by scaling electrical conductivities measured at shock pressures in the range of 10 to 180 gigapascals (0.1 to 1.8 megabars) and temperatures to 4000 kelvin, representative of conditions inside Jupiter. Jupiter's magnetic field is caused by convective dynamo motion of electrically conducting fluid hydrogen. The data imply that Jupiter should become metallic at 140 gigapascals in the fluid, and the electrical conductivity in the jovian molecular envelope at pressures up to metallization is about an order of magnitude larger than expected previously. The large magnetic field is produced in the molecular envelope closer to the surface than previously thought.