Principal Hugoniot Research Articles

Laser-launched flyer plates for shock physics experiments

The TRIDENT laser was used to launch Cu, Ga, and NiTi flyers from poly(methylmethacrylate) (PMMA) substrates, coated with thin (∼micron) layers to absorb the laser energy, confine the plasma, and insulate the flyer. The laser pulse was ∼600ns long, and the flyers were 50 to 250μm thick and 4 mm in diameter. With an energy of 10–20 J, speeds of several hundred meters per second were obtained. Simulations were performed of the flyer launch process, using different models. The simulations reproduced the magnitude of the flyer speed and qualitative variations with drive energy and design parameters, but systematically overpredicted the flyer speed. The most likely explanation is that some of the laser energy was deposited in the transparent substrate, reducing the amount available for acceleration. The deceleration of the flyer was measured on impact with a PMMA window. Given the equation of state and optical properties of PMMA, the deceleration allowed points to be deduced on the principal Hugoniot of Cu. The points deduced were in good agreement with the published equation of state for Cu, suggesting that there was no significant preheating of the flyer or other systematic effects which might reduce the accuracy of equation of state measurements.

The shock properties of a La2O3 filled silicate glass

A survey of the shock properties of the silicate glass, LACA has been carried out using manganin stress gauges. The principal Hugoniot has been measured and found to have significantly higher values than for other common silicate glasses. Gauges mounted on the rear of the target (supported with a block of polymethylmethacrylate) show reloading signals superimposed on the main compressive shock pulse. This has been interpreted as evidence of dynamic compressive failure (the failure wave or front). Manganin gauges mounted so as to be sensitive to the lateral component of stress support this hypothesis. Finally, failure front velocities, measured using known lateral gauge separations increase with increasing shock stress, tending towards the shear wave speed.

Adiabatic release measurements in aluminum from 240-to500-GPa states on the principal Hugoniot

Adiabatic release measurements were performed on aluminum (6061-T6) from ∼240-to500-GPa(∼2.4–5Mbar) states on the principal Hugoniot. Using a magnetically accelerated flyer plate technique, capable of launching macroscopic aluminum flyer plates (approximately 12×25mm in lateral dimension and ∼300μm in thickness) to velocities in excess of 20km∕s, direct impact experiments were performed on a low shock impedance, 200-mg∕cc silica aerogel to determine the aerogel Hugoniot in the pressure range of ∼30–75GPa. Release experiments were then performed in which the aerogel was mounted onto an aluminum base plate, and the initial shock in the base plate was transmitted to the aerogel sample. Given the measured aerogel shock velocities from the release experiments and the measured aerogel Hugoniot from the direct impact experiments, release states on release adiabats of aluminum were ascertained. The results were compared to several equation of state models for aluminum, and a rigorous statistical analysis was performed. The statistical analysis enabled the suitability of these various models in describing the release response of hot, liquid states to be determined. This study enhances our understanding of the release response of aluminum for high-pressure states on the Hugoniot and lends confidence to the use of aluminum as a standard material in impedance-matching experiments.

Electrical Conductivity of Noble Gases at High Pressures

AbstractWe present experimental and theoretical results for the electrical conductivity of noble gases (He, Ne, Ar, Kr, Xe) up to high pressures where a transition from nonmetallic to metallic‐like conductivities occurs. In addition, we show the behavior of the thermal conductivity and thermopower for xenon as an example. The experiments were performed using explosively driven shock waves. Different geometries allow to probe various parameter regions up to several megabars. Besides single‐shock experiments along the principal Hugoniot curve, also multiple‐shock experiments were performed which follow almost an isentrope. The theoretical calculations were performed within a partially ionized plasma model. The composition is determined by solving a system of mass action laws. The transport coefficients are calculated within linear response theory taking into account the relevant scattering mechanisms of electrons at different ion species, atoms, and other electrons. The general trends of the experimental results can be explained within this theoretical approach. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Measurement of a release adiabat from ∼8 Mbar in lead using magnetically driven flyer impact

Using magnetically driven aluminium flyers to generate ∼8 Mbar shocks in lead, which were then transmitted into lower-impedance material samples, points on a lead release adiabat have been measured. The pressure–particle-velocity points were calculated from known sample principal Hugoniots and from shock velocities measured using arrays of fiber-optic active and passive shock breakout diagnostics, and point and line velocity interferometer for a surface of any reflectivity (VISARs). The measured points agree closely with adiabats calculated using models which do not include ionization, or do include it both with, and without, atomic shell effects. Though the data are not sufficient to discriminate between widely different models we may qualitatively identify errors within these models. This is the first attempt to measure a release adiabat from such high pressures.

Generation of a double shock driven by laser

The feasibility and reliability of a multiple laser shock generation to study the equation of state surface off the principal Hugoniot curve and to approach an isentropic compression has been demonstrated. The technique is based on the use of a double laser pulse. A strong shock was generated in iron targets precompressed by a first weak shock. The effect of precompression was studied. The experiment was performed at the Laboratoire pour l'Utilisation des Lasers Intenses laboratory.

Quantum molecular dynamics simulations of shocked nitrogen oxide

Using quantum molecular dynamics, we study the dissociation of nitrogen oxide along the principal and reshocked Hugoniots. We obtain good agreement with available experimental data for the first and highest second-shock Hugoniots. Reminiscent of the experimental and theoretical findings for shocked liquid nitrogen, the calculation indicates little temperature variation along the second shock as the fluid dissociates. The analysis of the concentration of molecular species along both Hugoniots indicates, as expected, that for low final shock densities molecular nitrogen is forming when nitrogen oxide dissociates. In contrast to basic assumptions used for high pressure modeling of nitrogen oxide, we find, however, that oxygen mostly stays in an atomic state for the whole density-temperature range studied.

Principal Hugoniot, reverberating wave, and mechanical reshock measurements of liquid deuterium to 400 GPa using plate impact techniques

The high-pressure response of cryogenic liquid deuterium $(L{\mathrm{D}}_{2})$ has been studied to pressures of $\ensuremath{\sim}400\mathrm{GPa}$ and densities of $\ensuremath{\sim}1.5{\mathrm{g}/\mathrm{c}\mathrm{m}}^{3}.$ Using intense magnetic pressure produced by the Sandia National Laboratories $Z$ accelerator, macroscopic aluminum or titanium flyer plates, several mm in lateral dimensions and a few hundred microns in thickness, have been launched to velocities in excess of 22 km/s, producing constant pressure drive times of approximately 30 ns in plate impact, shock wave experiments. This flyer plate technique was used to perform shock wave experiments on $L{\mathrm{D}}_{2}$ to examine its high-pressure equation of state. Using an impedance matching method, Hugoniot measurements of $L{\mathrm{D}}_{2}$ were obtained in the pressure range of $\ensuremath{\sim}22--100\mathrm{GPa}.$ Results of these experiments indicate a peak compression ratio of approximately 4.3 on the Hugoniot. In contrast, previously reported Hugoniot states inferred from laser-driven experiments indicate a peak compression ratio of approximately 5.5--6 in this same pressure range. The stiff Hugoniot response observed in the present impedance matching experiments was confirmed in simultaneous, independent measurements of the relative transit times of shock waves reverberating within the sample cell, between the front aluminum drive plate and the rear sapphire window. The relative timing was found to be sensitive to the density compression along the principal Hugoniot. Finally, mechanical reshock measurements of $L{\mathrm{D}}_{2}$ using sapphire, aluminum, and \ensuremath{\alpha}-quartz anvils were made. These results also indicate a stiff response, in agreement with the Hugoniot and reverberating wave measurements. Using simple model-independent arguments based on wave propagation, the principal Hugoniot, reverberating wave, and sapphire anvil reshock measurements are shown to be internally self-consistent, making a strong case for a Hugoniot response with a maximum compression ratio of $\ensuremath{\sim}4.3--4.5.$ The trends observed in the present data are in very good agreement with several ab initio models and a recent chemical picture model for $L{\mathrm{D}}_{2},$ but in disagreement with previously reported laser-driven shock results. Due to this disagreement, significant emphasis is placed on the discussion of uncertainties, and the potential systematic errors associated with each measurement.

Ab initiosimulations of dense liquid deuterium: Comparison with gas-gun shock-wave experiments

We present first-principles molecular-dynamics simulations of the equation of state of liquid deuterium up to eightfold compression and temperatures between 2000 and 20 000 K. We report significant technical improvements over previous density-functional calculations leading to excellent agreement with gas gun shock wave measurements, which have provided well established experimental data for the deuterium Hugoniot. The principal Hugoniot is further investigated by performing simulations with rigid deuterium molecules. We also compute the double-shock Hugoniot curve and compare calculated and measured reshock temperatures.

Density-functional calculations of the liquid deuterium Hugoniot, reshock, and reverberation timing

The principal Hugoniot of liquid deuterium is calculated with density-functional methods. Particular attention is paid to the convergence of thermodynamic quantities with respect to the plane-wave cutoff energy and other simulation constraints. In contrast to earlier density-functional calculations, it is found that the principal Hugoniot results are in very good agreement with gas-gun data at lower pressures and compression ratios. The results at higher pressures are in very good agreement with data from magnetically launched flyer plates and show slightly less compression than earlier density-functional calculations. In addition to the principal Hugoniot, reshock states from a sapphire anvil and third-shock reverberation timings are also calculated. The latter are found to be in very good agreement with recently published results from magnetically launched flyer-plate experiments.

Quantum molecular-dynamics study of the electrical and optical properties of shocked liquid nitrogen

Using quantum molecular-dynamics simulations, we show that the electrical and optical properties of shocked liquid nitrogen change drastically as the density increases along the principal and second-shock Hugoniots. Initially, a nonmetal molecular fluid at normal conditions, we find that nitrogen becomes a metal for pressures of 60 GPa and higher. This nonmetal-metal transition for fluid nitrogen can be directly associated to the continuous dissociation occurring along the Hugoniots, and is analogous to the high-pressure nonmetal-metal transition observed experimentally for two other homonuclear diatomic fluids, hydrogen and oxygen.

LiH under high pressure and high temperature: A first‐principles study

AbstractThe behaviours of LiH under high pressure and high temperature are studied using first‐principles calculation. We have studied the pressure dependence of the electronic energy band gap as well as possible insulator‐metal phase transition. We have calculated temperature, heat capacity, and equation‐of‐state along the principal Hugoniot. The calculated results agree well with the experiments.

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.

Equation-of-state measurements for aluminum, copper, and tantalum in the pressure range 80–440 GPa (0.8–4.4 Mbar)

Off-Hugoniot equation-of-state (EOS) measurements were performed on Al, Cu, and Ta shocked to pressures in the range 62–430 GPa and double-shocked or released isentropically to pressures in the range 80–440 GPa. Calculated temperatures of the off-Hugoniot states are in the range 2 400–14 500 K. All these off-Hugoniot data are in good agreement with approximating the double-shock and isentropic release curves with the mirror reflection in P−up space of the principal Hugoniot about the vertical axis through particle velocity up1 of the first-shock state. Effective Grüneisen γ’s of Al are in good agreement with the scaling relationship γ=γ0(V/V0). The high accuracy of EOS data of Al, Cu, and Ta, both on and off the principal Hugoniot, and their simple behaviors, including the absence of any observed phase transitions, qualifies these metals as EOS standards for use as anvils in shock-compression experiments.

Reduction of shock-wave data with mean-field potential approach

Based on ab initio calculated 0 K results for the assumed face- or body-centered-cubic ground state, the thermal volume expansion of the principal Hugoniot relative to the 300 K isotherm is calculated using the recently developed mean-field potential approach for Cu, Ta, Mo, Pt, and Au. Neglecting shock melting and phase dependence of the high-temperature equation of state, shock-reduced 300 K isotherms at pressures up to 1 TPa (10 Mbar) are derived for these metals by substracting the calculated thermal volume expansion from the experimental shock-wave data. This approach does not invoke any empirical assumptions regarding the Grüneisen parameters or heat capacities. The excellent agreement between such shock-reduced data and the normal standards or empirical reductions by other authors shows that the reduced results can be used as pressure standards for the widely employed static diamond-anvil-cell experiments.

Measurement of the lead principal Hugoniot at ∼800 kbar by indirect laser drive

We have measured points on the principal Hugoniot of lead, using the impedance-match method, at pressures of ∼800 kbar using indirect laser drive. The experiments used laser-heated hohlraums to drive shocks into stepped targets. An active shock breakout diagnostic consisting of a ruby probe laser and optical streak camera detection system monitored target reflectivity—expected to vanish at shock breakout—and shock velocities were calculated from the target step heights and the measured shock transit times. Hugoniot point parameters were calculated from these shock velocities using the known equation-of-state (EOS) of the aluminium base and one step.Our results agree well with previous measurements made using gas-guns or explosively driven shocks, indicating that there are no intrinsic errors in laser-driven EOS experiments, such as those from using non-bulk material or spatial and temporal shock non-uniformity, and so supporting laser-driven EOS measurements at higher pressures.

Reconstruction of Ross' linear-mixing model for the equation of state of deuterium

The linear mixing (LM) model proposed by Ross [Phys. Rev. B 58 (1998) 669] can accurately reproduce experimental Hugoniot data for shocked liquid deuterium at pressures up to 6 Mbar. Using a simple dissociation scheme, the model smoothly interpolates between (or linearly “mixes”) a molecular fluid equation of state (EOS) applicable at low pressures, and a metallic-like description valid under more extreme conditions, with the relative composition of the mixture determined by minimizing the total Helmholtz free energy of the system. Although the formulation of the LM model is straightforward, it nevertheless involves a series of nontrivial computations and results whose details are fragmented in the published literature. We present an explicit and self-contained reconstruction of the LM model, and correct minor typographical errors that appeared in the original publications. Limitations of Ross' approach and comparisons with popular alternate theories are also discussed, although no attempt is made to conduct a thorough survey of existing EOS models for deuterium. Listings of the Mathematica codes used to compute the principal Hugoniot curve, and equilibrium thermodynamic quantities such as the specific heat, Grüneisen coefficient, and sound speed, are provided in the appendices.

Model for assessing the melting on Hugoniots of metals: Al, Pb, Cu, Mo, Fe, and U

A shock-release model is proposed to calculate shock temperatures along the principal Hugoniot, and to relate initial shock (Hugoniot) to release melting (off-Hugoniot). Thus a melting point crossing the Hugoniot can be defined. For the shock-release model, an assumed configuration of baseplate(metal-sample)/window is modeled to formulate the initial shock and interfacial release processes, the Lindemann law is used to describe the melting behavior of metals at high pressure, and the Grüneisen equation of state is applied to express the relation between pressure and specific internal energy. The effect of melting on the Hugoniot temperature is considered in this model, so the pressure–temperature regime of solid–liquid mixed phase region can be outlined. Aluminum, lead, copper, molybdenum, iron, and uranium were chosen for modeling calculations. It was found from the comparison of calculated results with their high-pressure melting data from experimental measurements that for most investigated metals γ=γ0(ρ0/ρ) (where γ and ρ are Grüneisen parameter and density, respectively, and subscript 0 denotes ambient conditions) is a good approximation to γ at high pressure, and the melting latent heat (ΔHM) at high pressure is better estimated using ΔHM=RTM (where TM is the melting temperature, and R is the gas constant) than using ΔHM=TM⋅ΔSM0 (where ΔSM0 is the melting entropy at ambient pressure).

Impedance match equation of state experiments using indirectly laser-driven multimegabar shocks

Measurements of equation of state (EOS) points on the principal Hugoniots of Cu, Au, Pb and the plastics Parylene-C and brominated CH at multimegabar pressures have been made using the 1 TW HELEN laser at AWE. The aim was 1% accuracy in shock velocity measurement (3%–4% in pressure) in order to compare with data from gas-gun and nuclear underground test experiments and the theoretical EOS’s based on, or supported by, these data. Experiments comprised a hohlraum heated by two 500 J, 0.53 μm wavelength, 1 ns Gaussian laser pulses generating an x-ray flux which drove a shock into a target consisting of a base, with steps of a known EOS material and of the material of unknown EOS. Shock breakout from base and steps was detected by monitoring light emission from the target with optical streak cameras and shock velocities were derived from the transit times across the known-height steps.

Phase diagram of iron, revised‐core temperatures

Shock‐wave experiments on iron preheated to 1573 K from 14 to 73 GPa, yield sound velocities of the γ‐ and liquid‐phases. Melting is observed in the highest pressure (∼71 ± 2 GPa) experiments at calculated shock temperatures of 2775 ± 160 K. This single crossing of the γ‐liquid boundary agrees with the γ‐iron melting line of Boehler [1993], Saxena et al. [1993], and Jephcoat and Besedin [1997]. This γ‐iron melting curve is ∼300°C lower than that of Shen et al. [1998] at 80 GPa. In agreement with Brown [2001] the discrepancy between the diamond cell melting data and the iron shock temperatures require the occurrence of yet another sub‐solidus phase along the principal Hugoniot at ∼200 GPa. This would reconcile the static and dynamic data for iron's melting curve. Upward pressure and temperature extrapolation of the γ‐iron melting curve to 330 GPa yields 5300 ± 400 K for the inner core‐outer core boundary temperature.