The temperature of shock‐compressed water

Development of an analytical exponential-6 equation of state through Monte Carlo simulations

The exponential-6 (exp-6) potential is commonly used to model fluids at high densities. In this paper, I propose a new equation of state (EOS) in the form of an analytical expression for the excess Helmholtz free energy of an exp-6 fluid. The EOS is based on extensive Monte Carlo simulations and therefore combines the excellent accuracy of the simulations with the numerical efficiency of a polynomial expression. The mean relative error in compressibility factor and internal energy is 0.14% and 0.25% respectively, which is a significant improvement over statistical mechanical theories. The EOS was implemented into a thermochemical code in order to optimize gas parameters and evaluate its performance on pure gas data, shock compression and detonation properties. Predicted gas densities, heat capacities and speed of sound for pure gases were generally within experimental uncertainties at pressures up to 1 GPa and temperatures above 300 K. For polar molecules, a simple free energy correction was introduced which greatly improved accuracy at low temperature. Calculated shock Hugoniots showed excellent agreement with experimental values up to 150 GPa and 10 000 K, and the detonation performance was accurately predicted for a number of different types of explosives.

In operando measurements of high explosives

In operando studies of high explosives involve dynamic extreme conditions produced as a shock wave travels through the explosive to produce a detonation. Here, we describe a method to safely produce detonations and dynamic extreme conditions in high explosives and in inert solids and liquids on a tabletop in a high-throughput format. This method uses a shock compression microscope, a microscope with a pulsed laser that can launch a hypervelocity flyer plate along with a velocimeter, an optical pyrometer, and a nanosecond camera that together can measure pressures, densities, and temperatures with high time and space resolution (2 ns and 2 µm). We discuss how a detonation builds up in liquid nitromethane and show that we can produce and study detonations in sample volumes close to the theoretical minimum. We then discuss how a detonation builds up from a shock in a plastic-bonded explosive (PBX) based on HMX (1,3,5,7-Tetranitro-1,3,5,7-tetrazocane), where the initial steps are hotspot formation and deflagration growth in the shocked microstructure. A method is demonstrated where we can measure thermal emission from high-temperature reactions in every HMX crystal in the PBX, with the intent of determining which configurations produce the critical hot spots that grow and ignite the entire PBX.

A global equation-of-state model from mathematical interpolation between low- and high-density limits

The ideal gas equation of state (EOS) model is a well-known low-density limiting model. Recently, an ideal dense matter EOS model for the high-density limit symmetric to the ideal gas model has been developed. Here, by mathematically interpolating between the ideal gas and ideal dense matter limiting models, we establish a global model containing two EOS in the form of P-V-T and P-S-T for arbitrary ranges of densities. Different from empirical or semi-empirical EOS, the coefficients in the global EOS have a clear physical meaning and can be determined from a priori knowledge. The proposed global model is thermodynamically consistent and continuous. It reduces to the ideal gas model when approaching the low-density limit and to the ideal dense matter model when approaching the high-density limit. Verifications for ⁴He show that the global model reproduces the large-range behavior of matter well, along with providing important insight into the nature of the large-range behavior. Compared to the third-order virial EOS and the Benedict–Webb–Rubin EOS, the global P-V-T EOS has higher descriptive accuracy with fewer coefficients over a wide range of data for N₂. The global model is shown to work well in extreme applied sciences. It predicts a linear, inverse relationship between entropy and volume when the temperature-to-pressure ratio is constant, which can explain the entropy-production behavior in shock-Hugoniots.

Laser pulses into bullets: tabletop shock experiments

This article discusses tabletop high-throughput laser experiments on shock waves in solids and liquids, where the more usual laser pump pulse is replaced by a 0.5 mm diameter laser-launched bullet, a thin metal disk called a flyer plate. The hypervelocity flyer (up to 6 km s^-1 or Mach 18) can have kinetic energy (∼1 J) to briefly produce extreme conditions of temperature and pressure, thousands of K and tens of GPa (1 GPa = 10 000 bar) in a small volume with a rise time <2 ns. The experiments are performed using a "shock compression microscope", a microscope fitted with the laser flyer launcher plus an optical velocimeter, a high-speed laser interferometer that measures the motion of the flyer plate or the sample material after impact. This makes it possible to generate extreme conditions at the push of a button in an intrinsically safe environment, and probe with any of the diagnostics used in microscope experiments, such as high-speed video, optical emission, nonlinear coherent spectroscopies and so on. The barrier to entering this field is relatively low since many laser laboratories already possess much of the needed instrumentation. A brief introduction to shock waves and instrumentation is presented. Then several examples of recent applications are described, including shocked water, the photophysics of fluorescent molecules under extreme conditions, shocked protein solutions, shocked metal-organic frameworks (MOFs), shocked explosives, chemical catalysis in a shocked liquid, and molecules at shocked interfaces. Since one can shoot a bullet at practically anything, there are many emerging opportunities in chemistry, biophysics, materials science, physics and hypervelocity aerodynamics.

Laser-driven shock compression of "synthetic planetary mixtures" of water, ethanol, and ammonia

Water, methane, and ammonia are commonly considered to be the key components of the interiors of Uranus and Neptune. Modelling the planets' internal structure, evolution, and dynamo heavily relies on the properties of the complex mixtures with uncertain exact composition in their deep interiors. Therefore, characterising icy mixtures with varying composition at planetary conditions of several hundred gigapascal and a few thousand Kelvin is crucial to improve our understanding of the ice giants. In this work, pure water, a water-ethanol mixture, and a water-ethanol-ammonia "synthetic planetary mixture" (SPM) have been compressed through laser-driven decaying shocks along their principal Hugoniot curves up to 270, 280, and 260 GPa, respectively. Measured temperatures spanned from 4000 to 25000 K, just above the coldest predicted adiabatic Uranus and Neptune profiles (3000-4000 K) but more similar to those predicted by more recent models including a thermal boundary layer (7000-14000 K). The experiments were performed at the GEKKO XII and LULI2000 laser facilities using standard optical diagnostics (Doppler velocimetry and optical pyrometry) to measure the thermodynamic state and the shock-front reflectivity at two different wavelengths. The results show that water and the mixtures undergo a similar compression path under single shock loading in agreement with Density Functional Theory Molecular Dynamics (DFT-MD) calculations using the Linear Mixing Approximation (LMA). On the contrary, their shock-front reflectivities behave differently by what concerns both the onset pressures and the saturation values, with possible impact on planetary dynamos.

Ab initio calculation of thermodynamic potentials and entropies for superionic water

We construct thermodynamic potentials for two superionic phases of water [with body-centered cubic (bcc) and face-centered cubic (fcc) oxygen lattice] using a combination of density functional theory (DFT) and molecular dynamics simulations (MD). For this purpose, a generic expression for the free energy of warm dense matter is developed and parametrized with equation of state data from the DFT-MD simulations. A second central aspect is the accurate determination of the entropy, which is done using an approximate two-phase method based on the frequency spectra of the nuclear motion. The boundary between the bcc superionic phase and the ices VII and X calculated with thermodynamic potentials from DFT-MD is consistent with that directly derived from the simulations. Differences in the physical properties of the bcc and fcc superionic phases and their impact on interior modeling of water-rich giant planets are discussed.

P-ρ-T measurements of H2O up to 260 GPa under laser-driven shock loading

Pressure, density, and temperature data for H2O were obtained up to 260 GPa by using laser-driven shock compression technique. The shock compression technique combined with the diamond anvil cell was used to assess the equation of state models for the P-ρ-T conditions for both the principal Hugoniot and the off-Hugoniot states. The contrast between the models allowed for a clear assessment of the equation of state models. Our P-ρ-T data totally agree with those of the model based on quantum molecular dynamics calculations. These facts indicate that this model is adopted as the standard for modeling interior structures of Neptune, Uranus, and exoplanets in the liquid phase in the multi-Mbar range.

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.

Raman spectra from symmetric hydrogen bonds in water by high-intensity laser-induced breakdown

Raman spectra of ice VII and X were investigated using strong plasma shockwave generated by laser-induced breakdown (LIB) in liquid water. Simultaneously, the occurrence of the hydrogen emission lines of 656 nm (Hα), 486 nm (Hβ), 434 nm (Hγ) and 410 nm (Hδ) was observed. At 5 × 10(12) W/cm(2) optical power density, the O-H symmetric stretching, translational and librational modes of ice VII and a single peak at 785 cm(-1) appeared in the spectra. The band was assigned to the Raman-active O-O mode of the monomolecular phase, which was the symmetric hydrogen bond of cuprite ice X. The spectra indicated that ice VII and X structure were formed, as the trajectory of the strong plasma shockwave passes through the stable Pressure-Temperature range of ice VII and X. The shockwave temperature and pressure were calculated by the Grüneisen model.

Estimating the quantum effects from molecular vibrations of water under high pressures and temperatures

We present a simple model which estimates the influence of quantum effects from molecular vibrations on the equation of state of water under high pressures and temperatures. This model is combined with an ab initio equation of state of water generated by quantum molecular dynamics (QMD) simulations employing density functional theory for the electrons and a classical algorithm for the ions. We calculate the specific heat capacity as well as the principal Hugoniot curve, especially the Hugoniot temperature, in accordance with experiments.

A time-resolved single-pass technique for measuring optical absorption coefficients of window materials under 100 GPa shock pressures

An experimental method was developed to perform time-resolved, single-pass optical absorption measurements and to determine absorption coefficients of window materials under strong shock compression up to approximately 200 GPa. Experimental details are described of (i) a configuration to generate an in situ dynamic, bright, optical source and (ii) a sample assembly with a lithium fluoride plate to essentially eliminate heat transfer from the hot radiator into the specimen and to maintain a constant optical source within the duration of the experiment. Examples of measurements of optical absorption coefficients of several initially transparent single crystal materials at high shock pressures are presented.

Laser-driven shock experiments on precompressed water: Implications for “icy” giant planets

Laser-driven shock compression of samples precompressed to 1 GPa produces high-pressure-temperature conditions inducing two significant changes in the optical properties of water: the onset of opacity followed by enhanced reflectivity in the initially transparent water. The onset of reflectivity at infrared wavelengths can be interpreted as a semiconductor<-->electronic conductor transition in water, and is found at pressures above approximately 130 GPa for single-shocked samples precompressed to 1 GPa. Our results indicate that conductivity in the deep interior of "icy" giant planets is greater than realized previously because of an additional contribution from electrons.

Submicrosecond temperature measurement in liquid water with laser-induced thermal acoustics

Using laser-induced thermal acoustics, we demonstrate nonintrusive and remote sound-speed and temperature measurements in liquid water. Unsteady thermal gradients in the water sample produce fast, random laser beam misalignments, which are the primary source of uncertainty in these measurements. For water temperatures over the range 10 degrees C to 45 degrees C, the precision of a single 300-ns-duration measurement varies from +/-1 to +/-16.5 m/s for sound speed and from +/-0.3 degrees C to +/-9.5 degrees C for temperature. Averaging over 10 s (100 laser pulses) yields accuracies of +/-0.64 m/s and +/-0.45 degrees C for sound speed and temperature, respectively.

Supercritical Water as a Solvent

Water is not restricted to moderate temperatures and low pressures, but can exist up to very high temperatures, far above its critical point at 647 K. In this supercritical regime, water can be gradually compressed from gas-like to liquid-like densities. The resulting dense supercritical states have extraordinary properties which can be tuned by temperature and pressure, and form the basis for innovative technologies. This Review covers the current knowledge of the major properties of supercritical water and its solutions with nonpolar, polar, and ionic compounds, and of the underlying molecular processes.

Cometary impacts into ocean: Thermodynamical equilibrium calculations of high-temperature O2 generation on the early Earth

The early Earth?s atmosphere apparently differed from the present atmosphere mainly in its lack of free O2, and this absence is believed to have been indispensable for the origin of early anaerobic life forms. One of the central problems in Earth science is to explain the apparent transition from the primitive atmosphere (free of O2) to the present atmosphere which contains 21% of the gas. Theoretical models suggest that the initial form of O2 in the Earth?s atmosphere may have been H2O, which was converted into atmospheric O2 mainly through photosynthesis. We have investigated an alternative (abiotic) method for the conversion of H2O to O2: a high-temperature shock generated during a cometary impact into an ocean (or on land). The calculations presented here show that 1% of the present level of O2 could have resulted from an icy 1.3x1016 kg comet entering the early (pre-oxygenic) Earth with a velocity of between about 11 and 30 km s-1.

Dissociation of water under pressure

The dissociation of water under pressure is investigated with a series of ab initio molecular dynamics simulations at thermodynamic conditions close to those obtained in shock wave experiments. We find that molecular dissociation occurs via a bimolecular process similar to ambient conditions, leading to the formation of short-lived hydronium ions. Up to twofold compression and 2000 K, the oxygen diffusion coefficient is characteristic of a fluid. Our findings do not support models used to estimate the liquid electrical conductivity and interpret Raman spectra that assume the presence of free protons.

APPLICATIONS OF IMPULSIVE STIMULATED SCATTERING IN THE EARTH AND PLANETARY SCIENCES

▪ Abstract  The elastic, thermodynamic, and transport properties of crystals and fluids at high temperature and pressure play a central role in the earth and planetary sciences as well as in a variety of technologies. These properties also constitute a principal experimental constraint on the description of intermolecular interactions at short distances. Aspects of “impulsive stimulated scattering,” when adapted to measurements in the diamond-anvil high-pressure cell, provide an approach to the determination of a subset of equilibrium and dynamic properties at high density.

The Nature of the Interior of Uranus Based on Studies of Planetary Ices at High Dynamic Pressure

Data from the Voyager II spacecraft showed that Uranus has a large magnetic field with geometry similar to an offset tilted dipole. To interpret the origin of the magnetic field, measurements were made of electrical conductivity and equation-of-state data of the planetary "ices" ammonia, methane, and "synthetic Uranus" at shock pressures and temperatures up to 75 gigapascals and 5000 K. These pressures and temperatures correspond to conditions at the depths at which the surface magnetic field is generated. Above 40 gigapascals the conductivities of synthetic Uranus, water, and ammonia plateau at about 20(ohm-cm)(-1), providing an upper limit for the electrical conductivity used in kinematic or dynamo calculations. The nature of materials at the extreme conditions in the interior is discussed.

Propagation of laser breakdown and detonation waves in transparent droplets

A computer model is used to study recent experiments investigating laser-induced plasma formation and explosion of single liquid aerosol droplets. The model accounts for the formation and evolution of the plasma and the resulting fluid flow; it does not account for the initial breakdown. The model shows all the qualitative features of the experiment, including laser-supported detonation waves, which at high laser intensities rapidly convert the whole droplet into a plasma. In addition, quantitative agreement with measured velocities has been obtained to within approximately 50%.