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DOE OSTI2022

Ta compressibility to 20+ Mbar

Developing techniques for experimentally constraining equation of state (EOS) models for important programmatic materials under extreme conditions is vital for advancing our modeling and predictive capabilities. Tantalum is a frequently used standard material for both calibration and testing, and this report describes our work to both measure Ta compressibility to very high pressures and densities using the Ramp Compression Equation of State platform on the National Ignition Facility (NIF). Using a series of seven shots, increasing in peak pressure with each shot, we have made absolute measurements of the compressibility of Ta along the ramp compression path up to 2.3 TPa. Previous experimental measurements constrained the cold compressibility up to ~400 GPa, and there is a spread in the EOS models above that pressure. To improve communication and collaboration between the experimental team and the EOS development group, these new data, along with other experimental and theoretical constraints, were used to develop a Ta equation of state table, M73000. This report first describes the experimental measurements made at the NIF, and then discusses the construction of the EOS model. The ramp compression data can be found in tabular form in Appendix A. Appendix B contains some additional experimental details. In Appendix C we include some additional details on the EOS modeling. At the end of this document, we have attached a detailed report on the NIF ramp compression platform itself and in the main text referenced specific sections for additional details.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Benchmark calculations of infinite neutron matter with realistic two- and three-nucleon potentials

In this study, we present the equation of state of infinite neutron matter as obtained from highly realistic Hamiltonians that include nucleon-nucleon and three-nucleon coordinate-space potentials. We benchmark three independent many-body methods: Brueckner-Bethe-Goldstone (BBG), Fermi hypernetted chain/single-operator chain (FHNC/SOC), and auxiliary-field diffusion Monte Carlo (AFDMC). We find them to provide similar equations of state when the Argonne v 18 and the Argonne v' 6 nucleon-nucleon potentials are used in combination with the Urbana IX three-body force. Only at densities larger than about 1.5 the nuclear saturation density ( ρ 0 =0.16 fm ⁻3 ) the FHNC/SOC energies are appreciably lower than the other two approaches. The AFDMC calculations carried out with all of the Norfolk potentials fitted to reproduce the experimental trinucleon ground-state energies and nd doublet scattering length yield unphysically bound neutron matter, associated with the formation of neutron droplets. Including tritium β decay in the fitting procedure, as in the second family of Norfolk potentials, mitigates but does not completely resolve this problem. An excellent agreement between the BBG and AFDMC results is found for the subset of Norfolk interactions that do not make neutron-matter collapse, while the FHNC/SOC equations of state are moderately softer.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2024

A theoretical/computational framework to measure SiO2 and MgO viscosity at high pressure

The convection of the mantle of Earth and super-Earths is important for many terrestrial phenomena, from plate tectonics to outgassing. Rheological properties, such as viscosity, regulate the transport of thermal energy and mass. However, the viscosity of mantle-relevant materials, such as MgO, at relevant pressures (>120 GPa) are not well constrained. The objective of this work was to develop a computational platform to simulate novel experiments aiming to measure the viscosity of MgO at high pressures. Experiments performed by our collaborators at Johns Hopkins University and Lawrence Livermore National Laboratory use the OMEGA EP laser facility to shock a corrugated MgO interface to 170 GPa, with resulting velocity evolution governed by the viscous Richtmyer-Meshkov instability. We used an in-house hydrocode to simulate this process and thus provide a bound on viscosity by comparing our simulations results to these experiments, as well as to examine the physical processes at play. We simulated the experiments with different values of MgO viscosity (from inviscid to 10,000 Pa∙s) while taking into account the unsteady laser pulse, the material's equation of state, and the rate-dependent constitutive relation for MgO, and the materials' equations of state. Our results suggest that MgO at these conditions has a viscosity within an order of magnitude of 5000 Pa∙s.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

NASA NTRS1995

New model atmospheres for very cool white dwarfs with mixed H/He and pure He compositions

New model atmosphere calculations for very cool white dwarfs with mixed H/He and pure He compositions are presented. The hydrogen-rich models incorporate improved cross section calculations of the collision-induced absorption by molecular hydrogen due to collisions with H2, H, and He. The effects associated with variations in the effective temperature (T(sub eff) greater than or equal to 4000 and less than or equal to 10,000 K), the surface gravity (log g greater than or equal to 7.5 and less than or equal to 9.5), and the chemical composition (N(He)/N(H) greater than or equal to O and less than or equal to 100) are investigated. Results from earlier calculations are confirmed qualitatively, but a more detailed comparison reveals large quantitative deviations. Cool white dwarfs with mixed H/He chemical compositions are shown to be easily recognizable from their predicted strong infrared flux deficiency. Pure helium model calculations are described as well. These include a modified version of the recently developed equation of state of D. Saumon and G. Chabrier. Nonideal effects brought about by various equations of state are explored in detail. For the purpose of this analysis, a model of pressure ionization based on an accurate description of the interactions in a mostly atomic helium fluid is developed. The effects of pressure ionization are shown to be the most important issue in the model calculations. A critical discussion of previous generations of pure helium model calculations is presented. Finally, broadband color indices are provided for the complete model grid.

Bergeron, P.↗

NASA NTRS1980

An alternative approach to the numerical simulation of steady inviscid flow

A numerical procedure for the efficient simulation of steady inviscid flow is described and its utility demonstrated. Application of the surrogate equation technique allows the formulation of stable, fully conservative, type dependent finite difference equations for use in obtaining numerical solutions to systems of first order partial differential equations, such as the steady state Euler equations or their various approximations. Computational results are presented for the full Euler equations and for the transonic disturbance equations. For the latter case, a computational efficiency greater than that obtained by means of the standard perturbation potential approach is indicated.

Johnson, G. M.↗

NASA NTRS1980

A mathematical model for Vertical Attitude Takeoff and Landing (VATOL) aircraft simulation. Volume 2: Model equations and base aircraft data

Equations incorporated in a VATOL six degree of freedom off-line digital simulation program and data for the Vought SF-121 VATOL aircraft concept which served as the baseline for the development of this program are presented. The equations and data are intended to facilitate the development of a piloted VATOL simulation. The equation presentation format is to state the equations which define a particular model segment. Listings of constants required to quantify the model segment, input variables required to exercise the model segment, and output variables required by other model segments are included. In several instances a series of input or output variables are followed by a section number in parentheses which identifies the model segment of origination or termination of those variables.

Fortenbaugh, R. L.↗

NASA NTRS1981

Surrogate-equation technique for simulation of steady inviscid flow

A numerical procedure for the iterative solution of inviscid flow problems is described, and its utility for the calculation of steady subsonic and transonic flow fields is demonstrated. Application of the surrogate equation technique defined herein allows the formulation of stable, fully conservative, type dependent finite difference equations for use in obtaining numerical solutions to systems of first order partial differential equations, such as the steady state Euler equations. Steady, two dimensional solutions to the Euler equations for both subsonic, rotational flow and supersonic flow and to the small disturbance equations for transonic flow are presented.

Johnson, G. M.↗

DOE OSTI2022

Confronting a set of Skyrme and $\chi _{EFT}$ predictions for the crust of neutron stars

With the improved accuracy of neutron star observational data, it is necessary to derive new equation of state where the crust and the core are consistently calculated within a unified approach. For this purpose we describe non-uniform matter in the crust of neutron stars employing a compressible liquid-drop model, where the bulk and the neutron fluid terms are given from the same model as the one describing uniform matter present in the core. We then generate a set of fifteen unified equations of state for cold catalyzed neutron stars built on realistic modelings of the nuclear interaction, which belongs to two main groups: the first one derives from the phenomenological Skyrme interaction and the second one from χEFT Hamiltonians. The confrontation of these model predictions allows us to investigate the model dependence for the crust properties, and in particular the effect of neutron matter at low density. Here, the new set of unified equations of state is available at the CompOSE repository.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2022

Singularity-EOS XCAP Report

Solving the Euler equations is a fundamental component of simulating many physical phenomena ranging from high explosives to astrophysics. An equation of state (EOS) is a required piece that relates any two thermodynamic quantities to all other thermodynamic values. The presence of multiple materials within a control volume further complicates the solution requiring additional equations to describe the interaction of materials at a sub-grid level. Equations of state themselves can also come in many forms ranging from simple algebraic relations to more complicated differential equation models that describe material interactions over a broad range of physical conditions. In the latter case, the EOS is often pre-computed at a given set of grid points and provided in a tabular form where additional properties can be derived from the interpolation functions.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS2006

MEASURING THE MASS OF 4UO900-40 DYNAMICALLY

Accurate measurements of neutron star masses are needed to constrain the equation of state of neutron star matter - of importance to both particle physics and the astrophysics of neutron stars - and to identify the evolutionary track of the progenitor stars that form neutron stars. The best measured values of the mass of 4UO900-40 (= Vela XR-l), 1.86 +/- 0.16 Msun (Barziv et al. 2001) and 1.93 +/- 0.20 Msun (Abubekerov et al. 2004), make it a leading candidate for the most massive neutron star known. The direct relationship between the maximum mass of neutron stars and the equation of state of ultra-dense matter makes 4UO900-40 an important neutron star mass to determine accurately. The confidence interval on previous mass estimates, obtained from observations that include parameters determined by non-dynamical methods, are not small enough to significantly restrict possible equations of state. We describe here a purely dynamical method for determining the mass of 4UO900-40, an X-ray pulsar, using the reprocessed UV pulses emitted by its BO.5Ib companion. One can derive the instantaneous radial velocity of each component by simultaneous X-ray and UV observations at the two quadratures of the system. The Doppler shift caused by the primary's rotational velocity and the illumination pattern of the X-rays on the primary, two of the three principal contributors to the uncertainty on the derived mass of the neutron star, almost exactly cancel by symmetry in this method. A heuristic measurement of the mass of 4UO900-40 using observations obtained previously with the High Speed Photometer on HST is given in Appendix A.

Dolan, J. F.↗

NASA NTRS1994

Storage and recycling of water and carbon dioxide in the earth

The stabilities and properties of water- and carbon-bearing phases in the earth have been determined from phase equilibrium measurements, combined with new data on the equations of state of water, carbon dioxide, carbonates and hydrates. The data have then been used to predict the fate of calcite and hydrous phases in subducting oceanic lithosphere. From the compositions of MORB's one can estimate concentrations of water and carbon of around 200 ppm and 80 ppm respectively in the upper mantle. Lower mantle estimates are very uncertain, but 1900 ppm water and 2000 ppm C are plausible concentrations. Measurements of the density of supercritical water to 3 GPa demonstrate that this phase is less compressible than anticipated from the equations of state of Haar et al. or Saul and Wagner and is closer to predictions based on molecular dynamics simulations. Conversely, fugacity measurements on carbon dioxide to 7 GPa show that this fluid is more compressible than predicted from the MRK equation of state. The results imply that hydrates are relatively more stable and carbonates less stable at pressures greater than 5 GPa than would be predicted from simple extrapolation of the low pressure data. Nevertheless, carbonates remain extremely refractory phases within both the upper and lower mantle.

Wood, Bernard J.↗

DOE OSTI2024

Static and shock compression studies of eutectic high-entropy alloy AlCoCrFeNi 2.1 to ultrahigh pressures

The high-entropy alloy with composition AlCoCrFeNi 2.1 , additively manufactured with the laser powder-bed fusion technique, has a far-from-equilibrium BCC/FCC eutectic nanolamellar structure. We studied the high-pressure response of this alloy under both static compression and high-strain rate shock compression. The response to static compression using a diamond anvil cell was studied at pressures up to 302 GPa with synchrotron x-ray diffraction at the advanced photon source. The high-pressure FCC-only phase of the EHEA previously observed by Pope et al. [AIP Adv. 13, 035124 (2023)] is found to be stable up to the highest pressure achieved in this study with a volume compression of V/V 0 = 0.587 at ambient temperature. The shock experiments were performed by using GEKKO XII lasers at the Institute of Laser Engineering, Osaka University. The principal Hugoniot equation-of-state of the EHEA was measured up to a pressure of 515 GPa and a compression of V/V 0 = 0.613. Additionally, the thermal equation of state of the EHEA was measured up to 6.2 GPa and 1623 K using a large-volume Paris–Edinburgh cell to obtain the temperature dependence of bulk modulus and thermal expansion coefficients. The melting temperature for EHEA AlCoCrFeNi 2.1 at a pressure of 5.6 GPa was measured to be 1648 ± 25 K. These results can be used to refine stochastic (or special) quasi-random structure (SQS) models for high-pressure high-temperature behavior of high-entropy alloys.

36 MATERIALS SCIENCE↗

DOE OSTI2020

Hydrodynamic simulations of shock-driven chemistry in polyimide

Here, the development for equations of state both for polyimide and its reaction products is presented along with hydrodynamic simulations linking the two EOS through an Arrhenius rate law. The equations of state compare favorably to available data, and the hydrodynamic simulations are able to qualitatively reproduce many of the features seen in both legacy shock data and more modern embedded gauge data. However, quantitative agreement is not achieved, suggesting that new rate laws are needed to fully capture the effect of the reaction over a wide range of conditions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2020

Effective viscosities in a hydrodynamically expanding boost-invariant QCD plasma

Background: The near-equilibrium properties of a QCD plasma can be encoded into transport coefficients such as bulk and shear viscosity. In QCD, the ratio of these transport coefficients to entropy density, ζ/$\textit{s}$ and η/$\textit{s}$, depends nontrivially on the plasma's temperature. This is unlike in conformal systems where they take constant values such as η/$\textit{s}$ = 1/(4π). Purpose: In this work, we show that in a (0 + 1)D boost-invariant fluid with no transverse expansion, a temperature-dependent ζ/$\textit{s(T)}$ or η/$\textit{s(T)}$ can be described by an equivalent effective viscosity $\langleζ/s\rangle_{\text{eff}}$ or $\langleη/s\rangle_{\text{eff}}$. This effective viscosity combines the actual temperature-dependent ζ/$\textit{s(T)}$ or η/$\textit{s(T)}$ with the temperature profile of the fluid. Further, we extend the concept of effective viscosity in systems with transverse expansion and discuss how effective viscosities can be used to identify families of ζ/$\textit{s(T)}$ and η /$\textit{s(T)}$ that lead to similar hydrodynamic evolution. Methods: The Navier-Stokes relativistic hydrodynamic equations are used to provide a first definition of effective viscosity, in (0 + 1)D and (1 + 1)D. In the (0 + 1)D case, the analysis is extended to Israel-Stewart-type second-order hydrodynamics to clarify the effect of higher-order hydrodynamics corrections on the effective viscosity. Results: In a boost-invariant fluid with no transverse expansion [(0 + 1)D], the effective viscosity is expressed as a simple integral of ζ/$\textit{s(T)}$ or η/$\textit{s(T)}$ over temperature, with a weight determined by the speed of sound of the fluid. The result is general for any equation of state with a moderate temperature dependence of the speed of sound, including the QCD equation of state. This definition of effective viscosity can be used to identify infinite families of ζ/$\textit{s(T)}$ or η/$\textit{s(T)}$ that produce essentially indistinguishable temperature profiles. In a boost-invariant cylindrical system [(1 + 1)D], a similar definition of effective viscosity is obtained in terms of characteristic trajectories in time and transverse direction. This leads to an infinite number of constraints on an infinite functional space for ζ/$\textit{s(T)}$ and η/$\textit{s(T)}$. Realistic examples are presented by using a finite number of constraints on a finite functional space. Conclusions: The definition of effective viscosity in a (0 + 1)D system clarifies how infinite families of ζ/$\textit{s(T)}$ and η/$\textit{s(T)}$ can result in nearly identical hydrodynamic temperature profiles. By extending the study to a boost-invariant cylindrical [(1 + 1)D] fluid, we identify an approximate but more general definition of effective viscosity that highlights the potential and limits of the concept of effective viscosity in fluids with limited symmetries.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2021

On the Nature of GW190814 and Its Impact on the Understanding of Supranuclear Matter

The observation of a compact object with a mass of 2.50–2.67M ⊙ on 2019 August 14, by the LIGO Scientific and Virgo collaborations (LVC) has the potential to improve our understanding of the supranuclear equation of state. While the gravitational-wave analysis of the LVC suggests that GW190814 likely was a binary black hole system, the secondary component could also have been the heaviest neutron star observed to date. Here, we use our previously derived nuclear-physics-multimessenger astrophysics framework to address the nature of this object. Based on our findings, we determine GW190814 to be a binary black hole merger with a probability of >99.9%. Even if we weaken previously employed constraints on the maximum mass of neutron stars, the probability of a binary black hole origin is still ~81%. Furthermore, we study the impact that this observation has on our understanding of the nuclear equation of state by analyzing the allowed region in the mass–radius diagram of neutron stars for both a binary black hole or neutron star–black hole scenario. We find that the unlikely scenario in which the secondary object was a neutron star requires rather stiff equations of state with a maximum speed of sound c s ≥ $\sqrt{0.6}$ times the speed of light, while the binary black hole scenario does not offer any new insight.

79 ASTRONOMY AND ASTROPHYSICS↗

NASA NTRS1993

Thermal expansivity, bulk modulus, and melting curve of H2O-ice VII to 20 GPa

Equation of state properties of ice VII and fluid H2O at high pressures and temperatures have been studied experimentally from 6 to 20 GPa and 300-700 K. The techniques involve direct measurements of the unit-cell volume of the solid using synchrotron X-ray diffraction with an externally heated diamond-anvil cell. The pressure dependencies of the volume and bulk modulus of ice VII at room temperature are in good agreement with previous synchrotron X-ray studies. The thermal expansivity was determined as a function of pressure and the results fit to a newly proposed phenomenological relation and to a Mie-Gruneisen equation of state formalism. The onset of melting of ice VII was determined directly by X-ray diffraction at a series of pressures and found to be in accord with previous volumetric determinations. Thermodynamic calculations based on the new data are performed to evaluate the range of validity of previously proposed equations of state for fluid water derived from static and shock-wave compression experiments and from simulations.

Fei, Yingwei↗

DOE OSTI2020

Steady detonation propagation in thin channels with strong confinement

We examine asymptotically the dynamics of two-dimensional, steady detonation wave propagation and failure for a strongly confined high explosive (HE), in which the width of the explosive is small relative to the reaction zone length. An energy balance equation is derived, which shows how the longitudinal acceleration of subsonic flow behind the detonation shock is influenced both by chemical reaction and by the effects of HE boundary streamline deflection, specifically via the induced rate of change of mass flux through the detonation wave. The latter serves to either counteract or reinforce the acceleration of longitudinal flow, depending on the sign of the gradient of the boundary streamline deflection at the detonation shock. The analysis is valid for general equations of state and chemical reaction rates in the HE. The asymptotically derived form of the energy equation represents an eigenvalue problem for the determination of the steady detonation propagation speed, solved via a shooting method. We explore specific results for ideal and stiffened equations of state, along with a pressure-dependent reaction rate for which changes in the pressure exponent and reaction order are also studied. We consider the influences of both straight and curved HE boundary streamline shapes. The asymptotic analysis reveals significant physical insights into how detonation propagation and failure are affected by strong confinement.

42 ENGINEERING↗

DOE OSTI2022

Phase Transition and Criticality of Methane Confined in Nanopores

For the first time, the phase transition and criticality of methane confined in nanoporous media are measured. The measurement is performed by establishing an experimental setup utilizing a differential scanning calorimeter (DSC) capable of operating under very low temperatures as well as high pressures to detect the capillary phase transition of methane inside nanopores. By performing experiments along isochoric cooling paths, both the capillary condensation and the bulk condensation of methane are detected. Here, the pore critical point (PCP) of nanoconfined methane is also determined and then used to derive the parameters of a previously developed self-consistent equation of state based on the Generalized van der Waals (vdW) partition function. Using this parameter, the equation of state can predict the capillary-condensation curves that agree well with the experimental data.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗