Experimental Equation Of State Research Articles

Stability and Metastability of Liquid Water in a Machine-Learned Coarse-Grained Model with Short-Range Interactions.

Coarse-grained water models are ∼100 times more efficient than all-atom models, enabling simulations of supercooled water and crystallization. The machine-learned monatomic model ML-BOP reproduces the experimental equation of state (EOS) and ice-liquid thermodynamics at 0.1 MPa on par with the all-atom TIP4P/2005 and TIP4P/Ice models. These all-atom models were parametrized using high-pressure experimental data and are either accurate for water's EOS (TIP4P/2005) or ice-liquid equilibrium (TIP4P/Ice). ML-BOP was parametrized from temperature-dependent ice and liquid experimental densities and melting data at 0.1 MPa; its only pressure training is from compression of TIP4P/2005 ice at 0 K. Here we investigate whether ML-BOP replicates the experimental EOS and ice-water thermodynamics along all pressures of ice I. We find that ML-BOP reproduces the temperature, enthalpy, entropy, and volume of melting of hexagonal ice up to 400 MPa and the EOS of water along the melting line with an accuracy that rivals that of both TIP4P/2005 and TIP4P/Ice. We interpret that the accuracy of ML-BOP originates from its ability to capture the shift between compact and open local structures to changes in pressure and temperature. ML-BOP reproduces the sharpening of the tetrahedral peak of the pair distribution function of water upon supercooling, and its pressure dependence. We characterize the region of metastability of liquid ML-BOP with respect to crystallization and cavitation. The accessibility of ice crystallization to simulations of ML-BOP, together with its accurate representation of the thermodynamics of water, makes it promising for investigating the interplay between anomalies, glass transition, and crystallization under conditions challenging to access through experiments.

Synthesis of molecular metallic barium superhydride: pseudocubic BaH12

Following the discovery of high-temperature superconductivity in the La–H system, we studied the formation of new chemical compounds in the barium-hydrogen system at pressures from 75 to 173 GPa. Using in situ generation of hydrogen from NH3BH3, we synthesized previously unknown superhydride BaH12 with a pseudocubic (fcc) Ba sublattice in four independent experiments. Density functional theory calculations indicate close agreement between the theoretical and experimental equations of state. In addition, we identified previously known P6/mmm-BaH2 and possibly BaH10 and BaH6 as impurities in the samples. Ab initio calculations show that newly discovered semimetallic BaH12 contains H2 and H3– molecular units and detached H12 chains which are formed as a result of a Peierls-type distortion of the cubic cage structure. Barium dodecahydride is a unique molecular hydride with metallic conductivity that demonstrates the superconducting transition around 20 K at 140 GPa.

Characterization of Ottawa Sand and Application to Blast Simulations

The present work aims at presenting consistent data both from laboratory characterization and from blast tests to see how a computer model performs when only data from mechanical tests are being fed to the constitutive model. A sand (Ottawa 20-30) that meets ASTM C778 requirements, i.e., well characterized microscopically, was tested in triaxial compression under confinement pressures ranging from 50 to 300 MPa and moisture contents of 0 to 15% as well as high strain-rates. These tests provided both the experimental equation of state (pressure vs. volume) and compaction curves as well as the strength vs. pressure properties to build a constitutive model both in LS-DYNA and CTH. Blast tests were subsequently performed by burying explosive at three different depths inside a sand pot with a rigid steel plate on top. During flight, the height of the steel plate was tracked with Phantom high-speed cameras to determine the impulse transmitted to the plate as well as the maximum jump height. Simulations were performed with both an Eulerian code (CTH) and a Lagrangian/ALE code (LS-DYNA) using the constitutive model determined during the material characterization. The predictions of both codes are as close as 7% and as far as 22%, depending on the test configuration.

Static compression of rare earth metal holmium to 282 GPa

ABSTRACT The phase transitions and equation of state measurements were carried out on rare earth metal Holmium (Ho) to 282 GPa using toroidal diamond anvils thereby doubling the pressure range to which it has been studied previously. The first set of experiment employed standard beveled diamond anvils utilizing copper as an x-ray pressure standard to 217 GPa. The second set of experiment employed toroidal diamond anvils utilizing platinum as an x-ray pressure standard to 282 GPa. The recently proposed 16-atom orthorhombic structure (oF16) appeared to be stable between 103 and 282 GPa. The scaled axial ratio (c/a) shows a narrow range of variation of 1.58 ± 0.05 for the five known crystalline phases of Ho to 282 GPa. The experimental equation of state of Ho is presented up to a threefold volume compression V/Vo = 0.322.

Shock-adiabatic to quasi-isentropic compression of warm dense helium up to 150 GPa

Multiple reverberation compression can achieve higher pressure, higher temperature, but lower entropy. It is available to provide an important validation for the elaborate and wider planetary models and simulate the inertial confinement fusion capsule implosion process. In the work, we have developed the thermodynamic and optical properties of helium from shock-adiabatic to quasi-isentropic compression by means of a multiple reverberation technique. By this technique, the initial dense gaseous helium was compressed to high pressure and high temperature and entered the warm dense matter (WDM) region. The experimental equation of state (EOS) of WDM helium in the pressure-density-temperature (P-$\ensuremath{\rho}$-T) range of $1--150\phantom{\rule{0.16em}{0ex}}\mathrm{GPa}$, $0.1--1.1\phantom{\rule{0.16em}{0ex}}\mathrm{g}\phantom{\rule{0.16em}{0ex}}\mathrm{c}{\mathrm{m}}^{\ensuremath{-}3}$, and 4600--24 000 K were measured. The optical radiations emanating from the WDM helium were recorded, and the particle velocity profiles detecting from the sample/window interface were obtained successfully up to 10 times compression. The optical radiation results imply that dense He has become rather opaque after the 2nd compression with a density of about $0.3\phantom{\rule{0.16em}{0ex}}\mathrm{g}\phantom{\rule{0.16em}{0ex}}\mathrm{c}{\mathrm{m}}^{\ensuremath{-}3}$ and a temperature of about 1 eV. The opaque states of helium under multiple compression were analyzed by the particle velocity measurements. The multiple compression technique could efficiently enhanced the density and the compressibility, and our multiple compression ratios $({\ensuremath{\eta}}_{i}={\ensuremath{\rho}}_{i}/{\ensuremath{\rho}}_{0},\phantom{\rule{0.28em}{0ex}}i=1--10)$ of helium are greatly improved from 3.5 to 43 based on initial precompressed density $({\ensuremath{\rho}}_{0})$. For the relative compression ratio $({\ensuremath{\eta}}_{i}^{\ensuremath{'}}={\ensuremath{\rho}}_{i}/{\ensuremath{\rho}}_{i\ensuremath{-}1})$, it increases with pressure in the lower density regime and reversely decreases in the higher density regime, and a turning point occurs at the 3rd and 4th compression states under the different loading conditions. This nonmonotonic evolution of the compression is controlled by two factors, where the excitation of internal degrees of freedom results in the increasing compressibility and the repulsive interactions between the particles results in the decreasing compressibility at the onset of electron excitation and ionization. In the P-$\ensuremath{\rho}$-T contour with the experiments and the calculations, our multiple compression states from insulating to semiconducting fluid (from transparent to opaque fluid) are illustrated. Our results give an elaborate validation of EOS models and have applications for planetary and stellar opaque atmospheres.

A proposed experimental platform for measuring the properties of warm dense mixtures: Testing the applicability of the linear mixing model

This paper presents a proposed experimental technique for investigating the impact of chemical interactions in warm dense liquid mixtures. It uses experimental equation of state (EOS) measurements of warm dense liquid mixtures with different compositions to determine the deviation from the linear mixing model. Statistical mechanics is used to derive the EOS of a mixture with a constant pressure linear mixing term (Amagat’s rule) and an interspecies interaction term. A ratio between the particle density of two different compositions of mixtures, K(P, T)i: ii, is defined. By comparing this ratio for a range of mixtures, the impact of interspecies interactions can be studied. Hydrodynamic simulations of mixtures with different carbon/hydrogen ratios are used to demonstrate the application of this proposed technique to multiple shock and ramp compression experiments. The limit of the pressure correction that can be measured due to interspecies interactions using this methodology is determined by the uncertainty in the density measurement.

On the Equation of State of Cementitious Composites - an Experimental Study

Abstract The behavior of cementitious materials under severe loading is of particular interest, for research on ballistic impact, penetration and near distance explosions, where very high pressures are developed. Therefore it is important to investigate the behavior of such materials in the exceptionally high hydrostatic pressures range. One of the key characteristics of this behavior is the equation of state (EOS) that is the relationship between hydrostatic pressure and density (or bulk strain). However it has not been adequately investigated, and therefore the mechanisms of cementitious materials deformation and damage that are developed within that range of high pressures is at least partly obscure and far from being clearly understood. This is partly because the controlled application of extreme pressures requires special equipment and expensive experimental setups and testing is associated with a wide variety of technical problems. This paper aims at presentation of the development of an experimental setup to perform confined compression tests of mortar and concrete specimens at high pressures up to 1GPa. It presents the experimental study of different cement paste and mortar specimens and their comparison with previous results, obtained under high pressures up to 300 MPa. This allows the investigations of size effect for unsaturated samples, as well as the effect of the sand volumetric content on the loading branch of the equation of state. The experimental study shows a good repeatability for the cement paste specimens and for mortar specimens with fine sand. It also shows that decrease of water/cement ratio in the cement paste mix as well as increase of the sand volumetric contain in mortar results in monotonic increase of the secant bulk modulus of the loading branch of EOS. The comparison of the mean loading branch of the experimental EOS for unsaturated specimens having 30 mm diameter (70 mm height) and 70 mm diameter (150 mm height) clearly indicates that there is practically no size effect for all tested mixture compositions. While for the cement paste there is no difference up to 270 MPa (highest pressure level in the test in the small apparatus), the addition of sand yields an increase of the difference, which, anyway, remains small.

Measurement of the equation of state and of the index of refraction of an amorphous glow discharge polymer up to 45 GPa

We present an experimental determination of the ambient temperature equation of state, P(ρ/ρ0,293 K), up to 45 GPa, of the glow discharge polymer (GDP) used as a confining capsule for the fusible deuterium-tritium mixture in inertial confinement fusion experiments. An original method has been implemented to measure both the compression factor and the refractive index versus pressure. The data are obtained in a diamond anvil cell with two sample chambers of equal thickness containing, respectively, the GDP and a NaCl reference. This experimental equation of state is compared to numerical first principles simulations. Deviations are ascribed to the difficulty to simulate the detailed atomic structure of the polymer under moderate pressure.

Confirming a pyrolitic lower mantle using self‐consistent pressure scales and new constraints on CaSiO3 perovskite

AbstractIn this study, we have examined the lower mantle composition and mineralogy by modeling the density (ρ), bulk sound velocity (VΦ), and dlnρ/dlnVΦ profiles of candidate lower mantle minerals using literature and new experimental equation of state (EoS) results. For CaSiO3 perovskite, complimentary synchrotron X‐ray diffraction measurements in a laser‐heated diamond anvil cell were conducted up to 156 GPa between 1200 K and 2600 K to provide more reliable constraints on the thermal EoS parameters. These new experimental results as well as literature P‐V‐T data sets are systematically analyzed using an internally self‐consistent pressure scale. We have modeled ρ, VΦ, and dlnρ/dlnVΦ profiles of the lower mantle with representative pyrolitic and chondritic compositional models in which the effect of Fe spin transition in ferropericlase is also taken into account. Our modeling results show that a pyrolitic lower mantle with an aggregate mineralogy of 75 vol % bridgmanite, 17 vol % ferropericlase, and 8 vol % CaSiO3 perovskite produces ρ and VΦ profiles in better agreement with preliminary reference Earth model than a lower mantle with a chondritic composition. The modeled ρ, VΦ, and dlnρ/dlnVΦ are mainly affected by the relative ratio of bridgmanite and ferropericlase but are not sensitive to the variation of the CaSiO3 perovskite content. In addition, the spin crossover of Fe in ferropericlase can greatly raise the value of dlnρ/dlnVΦ in the middle lower mantle, which is useful in detecting the presence of ferropericlase in the region. Based on these new mineral physical constraints and radial seismic structure, our study suggests the lower mantle is pyrolitic, which is chemically indistinguishable from the upper mantle.

Numerical Analysis of the Hydrodynamic Behavior of Ion-beam-heated Uranium Targets for Equation-of-state Studies under Extreme Conditions

Abstract The equation of state (EOS) of fissile materials under extreme thermodynamic conditions is of great importance to assess the safety of nuclear energy systems related to extremely severe nuclear accidents and intentional nuclear terrorism. In this study, for a simple, safe, and precise measurement of these properties, we propose an experimental setup in which a small amount of fissile material sample is homogeneously heated by an intense short-pulsed heavy-ion beam, and subsequent hydrodynamic motion is examined. As an example, we investigated the response of a slab of uranium foam (density = 5% of solid density) to a pulsed 23 Na + beam with a duration of 2 ns and peak irradiation flux of 5 GW/mm 2 . The target thickness and incident beam energy were adjusted to 80 μm and 1.5 MeV/u, respectively, for the beam-energy deposition to occur almost at the top of the Bragg peak and inhomogeneity in the stopping power to be ±2.5%. The hydrodynamic motion of the target during and after irradiation was calculated with a one-dimensional radiation hydrodynamic code. To calculate beam-energy deposition in the target, we used density- and temperature-dependent projectile stopping data obtained with a finite-temperature Thomas-Fermi target atomic model and degeneracy-dependent dielectric response functions. The numerical results showed that the target was almost isometrically heated up to ≈ 10 5 K well before the rarefaction wave reached the center of the target, and fairly homogeneous temperature and density distributions were obtained at the end of the pulse duration. We discuss the feasibility of experimental EOS studies, such as the evaluation of pressures at off-Hugoniot conditions as a function of internal energy from the measurements of the target expansion velocity.

Thermodynamical model for hydrogen storage capacity in carbon nanostructures

A simple thermodynamical model taking into account non-ideality and inhomogeneity of absorbed hydrogen molecular gas has been proposed to calculate hydrogen storage capacity in carbon nanostructures as a function of temperature and pressure. The model utilizing the effective interaction potential of the hydrogen molecule with the atoms of the considered material, is based on the experimental equation of state and a local density approximation for molecular hydrogen. We have applied the model for the search of the optimal geometry for hydrogen storage of such promising carbon materials as a set of graphene layers and bundles of carbon nanotubes. We demonstrate that the hydrogen storage capacity depends on the geometry of material and discuss the origin of this effect.

Free Volume Approximation and Equation of State for the fcc Phase of Polydisperse Hard Spheres

Monte Carlo simulations of the fcc phase of polydisperse hard spheres near close packing are reported. An experimental equation of state (EoS) is determined numerically in the NpT ensemble with variable shape of the periodic box. The close packing volume extrapolated from the obtained data shows a good agreement with earlier experiments performed by other methods. A new theoretical EoS, based on the free volume approximation, is proposed. The modified EoS fits experimental data for polydisperse hard spheres better than the approximation used before.

Equation of state, refractive index and polarizability of compressed water to 7 GPa and 673 K

The equation of state (EoS), refractive index n, and polarizability α of water have been determined up to 673 K and 7 GPa from acoustic velocity measurements conducted in a resistively heated diamond anvil cell using Brillouin scattering spectroscopy. Measured acoustic velocities compare favorably with previous experimental studies but they are lower than velocities calculated from the extrapolation of the IAPWS95 equation of state above 3 GPa at 673 K and deviations increase up to 6% at 7 GPa. Densities calculated from the velocity data were used to propose an empirical EoS suitable in the 0.6-7 GPa and 293-673 K range with a total estimated uncertainty of 0.5% or less. The density model and thermodynamic properties derived from the experimental EoS have been compared to several EoS proposed in the literature. The IAPWS95 EoS provides good agreement, although underestimates density by up to 1.2% at 7 GPa and 673 K and the thermodynamic properties deviate greatly (10%-20%) outside the estimated uncertainties above 4 GPa. The refractive index n of liquid water increases linearly with density and do not depend intrinsically on temperature. The polarizability decreases with pressure by less than 4% within the investigated P-T range, suggesting strong intermolecular interactions in H(2)O that are consistent with the prevalence of the hydrogen bond network in the fluid. The results will allow the refinement of interaction potentials that consider polarization effects for a better understanding of solvent-solvent and ion-solvent interactions in aqueous fluids at high pressure and temperature conditions.

High-pressure–temperature phase diagram and the equation of state of beryllium

X-ray diffraction of beryllium in a laser-heated diamond anvil cell provides experimental insight into its behavior at high pressure and temperature. We measure the cold compression of Be in helium and NaCl pressure media up 192 GPa, and its thermal expansion up to 82 GPa and 2630 K. The new measurements form a $P\ensuremath{-}V\ensuremath{-}T$ data set which is fit by the Vinet-Debye form to establish a Be experimental equation of state. We compare the results to several theoretical models. The crystal structure of Be is determined up to 205 GPa and 4000 K; no evidence for the predicted high-temperature transition to a cubic phase is found. Finally, the maximum temperature stability of the solid phase along isobaric heating ramps gives a lower bound for the melting curve.

The equation of state, shock-induced molecule dissociation, and transparency loss for multi-compressed dense gaseous H2 + D2 mixtures

The experimental equation of state and temperature data of the dense gaseous H2 + D2 mixtures under multi-shock compression were presented in a pressure range of 2–36 GPa and a temperature range of 2300–5300 K. The strong shock wave was produced using the flyer plate impact by accelerated up to 5.1–6.2 km/s with a two-stage light-gas gun and introduced into the plenum gas sample, which was pre-compressed from environmental pressure to 30–40 MPa. Time-resolved spectral radiation histories were acquired with two sets of multi-wavelength channel pyrometers, which were used to determine the shock velocity and shock temperature in the sample. Shock pressure and particle velocity were obtained by the impedance matching method. The experimental data prove the validity of self-consistent fluid variational theory (SFVT) model in the partial dissociation region. The time-resolved spectral radiation histories along with the SFVT calculation show that the shocked gas samples lose their transparency in visible light wavelength ranges of 400–800 nm at about 12.99 GPa and 4413 K or higher.

Experimental equation of state in pp and [formula omitted] collisions and phase transition to quark gluon plasma

We deduce approximate equations of state from experimental measurements in pp and pp¯ collisions. Thermodynamic quantities are estimated combining the measure of average transverse momentum 〈pT〉 vs pseudorapidity density dNchdη with the estimation of the interaction region size from measures of Bose Einstein correlation, or from a theoretical model which relates dNchdη to the impact parameter. The results are very similar to theory predictions in case of crossover from hadron gas to quark gluon plasma. According to our analysis, the possible crossover should start at dNchdη≃6 and end at dNchdη≃24.

Measurements of the equations of state and spectrum of nonideal xenon plasma under shock compression

Experimental equations of state on generation of nonideal xenon plasma by intense shock wave compression was presented in the ranges of pressure of 2-16 GPa and temperature of 31-50 kK, and the xenon plasma with the nonideal coupling parameter Γ range from 0.6-2.1 was generated. The shock wave was produced using the flyer plate impact and accelerated up to ∼6 km/s with a two-stage light gas gun. Gaseous specimens were shocked from two initial pressures of 0.80 and 4.72 MPa at room temperature. Time-resolved spectral radiation histories were recorded by using a multiwavelength channel pyrometer. The transient spectra with the wavelength range of 460-700 nm were recorded by using a spectrometer to evaluate the shock temperature. Shock velocity was measured and particle velocity was determined by the impedance matching methods. The equations of state of xenon plasma and ionization degree have been discussed in terms of the self-consistent fluid variational theory.

Brillouin scattering studies of liquid argon at high temperatures and high pressures

Brillouin scattering measurements were performed on liquid argon in a diamond anvil cell at various solidification points up to 503 K. With the measured results from the 60 degree platelet- and 180 degree back-scattering geometries, the sound velocity, refractive index, experimental equation of state, and adiabatic bulk modulus of liquid argon as a function of pressure were determined. The discrepancy between experimental and previous calculated equation of state indicates that the many-body contribution to the density of liquid argon increases with increasing pressure and decreases with increasing temperature. By analyzing the Brillouin spectra in the coexistence of liquid and solid phase regions, the volume change and latent heat of solid-liquid transformation along the equilibrium curve have been also obtained for the first time.

Study of the high-pressure helium phase diagram using molecular dynamics

The rich occurrence of helium and hydrogen in space makes their properties highly interesting.By means of molecular dynamics (MD), we have examined two interatomic potentials for4He. Both potentials are demonstrated to reproduce high-pressure solid and liquid equation ofstate (EOS) data. The EOS, solid–solid transitions and melting at high pressures(P) were studied using a two-phase method. The Buckingham potential shows agood agreement with theoretical and experimental EOS, but does not reproduceexperimental melting data. The Aziz potential shows a perfect match with theoreticalmelting data. We conclude that there is a stable body-centred-cubic (bcc) phase for4He attemperatures (T) above 340 K and pressures above 22 GPa for the Buckingham potential,whereas no bcc phase is found for the Aziz potential in the appliedPT range.

Quantum Monte Carlo, density functional theory, and pair potential studies of solid neon

We report quantum Monte Carlo (QMC), plane-wave density-functional theory (DFT), and interatomic pair-potential calculations of the zero-temperature equation of state (EOS) of solid neon. We find that the DFT EOS depends strongly on the choice of exchange-correlation functional, whereas the QMC EOS is extremely close to both the experimental EOS and the EOS obtained using the best semiempirical pair potential in the literature. This suggests that QMC is able to give an accurate treatment of van der Waals forces in real materials, unlike DFT. We calculate the QMC EOS up to very high densities, beyond the range of values for which experimental data are currently available. At high densities the QMC EOS is more accurate than the pair-potential EOS. We generate a different pair potential for neon by a direct evaluation of the QMC energy as a function of the separation of an isolated pair of neon atoms. The resulting pair potential reproduces the EOS more accurately than the equivalent potential generated using the coupled-cluster CCSD(T) method.