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At least 55 records · Page 3
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

The equations of state of statically compressed palladium and rhodium

Here, the pressure–volume equations of state of palladium and rhodium statically compressed in neon are presented. Vinet fits give parameters for palladium: V0=58.678(73) Å 3 , B 0 =189.3(30) GPa, B' 0 =5.473(63), and rhodium: V 0 =55.062(63) Å3, B 0 =241.3(65) GPa, B' 0 =5.34(24). Both metals are observed to react with hydrocarbons under pressure to form hydrides. Existing equations of state are discussed with regard to potential inadvertent hydrogen contamination as a source for discrepancies and anomalous fitted parameters.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Robust second-order approximation of the compressible Euler equations with an arbitrary equation of state

Here, this paper is concerned with the approximation of the compressible Euler equations supplemented with an arbitrary or tabulated equation of state. The proposed approximation technique is robust, formally second-order accurate in space, invariant-domain preserving, and works for every equation of state, tabulated or analytic, provided the pressure is nonnegative. An entropy surrogate functional that grows across shocks is proposed. The numerical method is verified with novel analytical solutions and then validated with several computational benchmarks seen in the literature including problems with composite waves.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

P-V-T equation of state of boron carbide

We report the P-V-T equation of state measurements of B 4 C to 50 GPa and approximately 2500 K in laser-heated diamond anvil cells. We obtain an ambient temperature, third-order Birch–Murnaghan fit to the P-V data that yields a bulk modulus K 0 of 221(2) GPa and derivative, (dK/dP) 0 of 3.3(1). These were used in fits with both a Mie–Grüneisen–Debye model and a temperature-dependent, Birch–Murnaghan equation of state that includes thermal pressure estimated by thermal expansion (α) and a temperature-dependent bulk modulus (dK 0 /dT). The ambient pressure thermal expansion coefficient (α 0 + α 1 T), Grüneisen γ(V) = γ 0 (V/V 0 ) q and volume-dependent Debye temperature, were used as input parameters for these fits and found to be sufficient to describe the data in the whole P-T range of this study.

36 MATERIALS SCIENCE↗
DOE OSTI2026

Platform for 100 s Mbar equation of state measurements on the National Ignition Facility

Equation of state (EOS) measurements in the 100 s Mbar range are needed to underwrite models employed in the simulation of high energy density plasmas. To this end, a platform has been developed for fielding on the National Ignition Facility, capable of producing high-quality impedance match EOS data, wherein a planar, high-pressure, steady shock is driven into a sample package, and sample and reference standard shock velocities are measured. This platform, dubbed planar high pressure, or PHP, was fielded with an initial proof-of-concept shot in January 2023. The first PHP shot, aiming to study gold, demonstrated a pressure close to 400 Mbar, two orders of magnitude higher than previously reported gold EOS data.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Equation of state of boron carbide B 4 ⁢C

We present the results of recent experiments conducted on the Sandia Z machine and a new tabular equation of state for B 4 ⁢C. The equation of state was calibrated to a combination of density functional calculations reported here and fits to preexisting data. It was constructed partly to recover the effects of a shock-driven, polymorphic phase transition of unknown character beginning at particle velocities of just under 3 km/s (shock pressures of 95 GPa). Some of the Z experiments included sound speeds determined by the overtaking rarefaction method, from which we calculate the Grüneisen parameter and compare with previous experiments conducted at the OMEGA laser [Fratanduono et al ., Phys. Rev. B 94 , 184107 (2016)], our own first principles calculations, and another recent tabular equation of state [Zhang et al ., Phys. Rev. E 102 , 053203 (2020)]. We also compare our results with previous static compression, thermophysical, and melt studies, finding mixed consistency. We predict the onset and completion of shock melting at 225 and 265 GPa, respectively, and predict a melt curve that is largely flat to pressures of several hundred GPa.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Experimental thermal equation of state of B 2–KCl

The alkali halides are often used as optically-transparent pressure-transmitting media and thermal insulators in laser-heated diamond anvil cell experiments. High P-T equations of state for these materials would allow them to be used simultaneously as sensitive in situ pressure markers, making sample preparation and data analysis simpler. KCl is especially useful for this application because its high melting point, crystallographic simplicity, and low electron density are ideal for use in high-temperature X-ray diffraction experiments. However, the high-temperature static equation of state data for this material is limited in pressure to 8 GPa. As experiments routinely exceed 100 GPa in pressure and thousands of Kelvin, it is necessary for the equation of state of KCl to be determined experimentally at these conditions if it is to be used as an equation of state calibrant in the future. This work combines new high-pressure, high-temperature data of the B2 phase of KCl (up to 167 GPa and 2400 K) with the previously published room-temperature data of Dewaele et al. (2012) to produce a Mie-Gruneisen-Debye thermal equation of state for this material. The room temperature equation of state parameters are similar to those reported previously: V 0 = 32.0(3) cm 3 /mole, K 0 = 24(1) GPa and $K$$^{'}_{0}$ = 4.56(5). The thermal parameters, 0 and q, are 2.9(4) and 1.0(1), respectively. While a q of 1 is expected, the 0 is higher than expected from previous calculations, lower pressure experimental data, and the available shockwave data. Here, previously-reported equations of state underestimate the pressure of KCl at high temperatures.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

Neutron stars and the dense matter equation of state

The past two decades have witnessed tremendous progress in understanding the properties of neutron stars, their maximum mass and radii, and the properties of the dense matter in their cores, made possible by electromagnetic observations of neutron stars and the detection of gravitational waves from their mergers. These observations have provided novel constraints on neutron-star structure that are intimately related to the properties of dense neutron-rich matter described by the nuclear equation of state. Nevertheless, constraining the equation of state over the wide range of densities probed by astrophysical observations is still challenging, as the physics involved is broad and the system spans many orders of magnitude in density. Here, theoretical approaches to calculate and model the neutron-star equation of state in various regimes of densities are reviewed, and the related consequent properties of neutron stars are discussed. How the equation of state at low densities can be calculated from nuclear interactions that are constrained and benchmarked by nuclear experiments is described. Neutron-star observations, with a particular emphasis on information provided by gravitational-wave signals and electromagnetic observations, are reviewed. Finally, future challenges and opportunities in the field are discussed.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

The high-density equation of state in heavy-ion collisions: constraints from proton flow

Abstract A set of different equations of state is implemented in the molecular dynamics part of a non-equilibrium transport simulation (UrQMD) of heavy-ion collisions. It is shown how different flow observables are affected by the density dependence of the equation of state. In particular, the effects of a phase transition at high density are explored, including an expected reduction in mean $$m_T$$ m T . We also show that an increase in $$v_2$$ v 2 is characteristic for a strong softening of the equation of state. The phase transitions with a low coexistence density, $$n_{\text {CE}}<4 n_0$$ n CE < 4 n 0 , show a distinct minimum in the slope of the directed flow as a function of the beam energy, which would be a clear experimental signal. By comparing our results with experimental data, we can exclude any strong phase transition at densities below $$4n_0$$ 4 n 0 .

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2020

Inelastic equation of state for solids

In this study, a complete inelastic equation of state (IEOS) for solids is developed based on a superposition of thermodynamic energy potentials. The IEOS allows for a tensorial stress state by including an isochoric hyperelastic Helmholtz potential in addition to the zero-kelvin isotherm and lattice vibration energy contributions. Inelasticity is introduced through the nonlinear equations of finite strain plasticity which utilize the temperature dependent Johnson–Cook yield model. Material failure is incorporated into the model by a coupling of the damage history variable to the energy potentials. The numerical evaluation of the IEOS requires a nonlinear solution of stress, temperature and history variables associated with elastic trial states for stress and temperature. The model is implemented into the ALEGRA shock and multi-physics code and the applications presented include single element deformation paths, the Taylor anvil problem and an energetically driven thermo-mechanical problem.

42 ENGINEERING↗
DOE OSTI2020

The shock physics of giant impacts: Key requirements for the equations of state

We discuss major challenges in modeling giant impacts between planetary bodies, focusing on the equations of state (EOS). During the giant impact stage of planet formation, rocky planets are melted and partially vaporized. However, most EOS models fail to reproduce experimental constraints on the thermodynamic properties of the major minerals over the required phase space. Here, we present an updated version of the widely-used ANEOS model that includes a user-defined heat capacity limit in the thermal free energy term. Our revised model for forsterite (Mg 2 SiO 4 ), a common proxy for the mantles of rocky planets, provides a better fit to material data over most of the phase space of giant impacts. We discuss the limitations of this model and the Tillotson equation of state, a commonly used alternative model.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Strangeness-neutral equation of state for QCD with a critical point

We present a strangeness-neutral equation of state for QCD that exhibits critical behavior and matches lattice QCD results for the Taylor-expanded thermodynamic variables up to fourth-order in µ B /T. It is compatible with the SMASH hadronic transport approach and has a range of temperatures and baryonic chemical potentials relevant for phase II of the Beam Energy Scan at RHIC. We provide an updated version of the software BES-EoS, which produces an equation of state for QCD that includes a critical point in the 3D Ising model universality class. This new version also includes isentropic trejectories and the critical contribution to the correlation length. Since heavy-ion collisions have zero global net-strangeness density and a fixed ratio of electric charge to baryon number, the BES-EoS is more suitable to describe this system. Comparison with the previous version of the EoS is thoroughly discussed.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2023

Phase transition phenomenology with nonparametric representations of the neutron star equation of state

Astrophysical observations of neutron stars probe the structure of dense nuclear matter and have the potential to reveal phase transitions at high densities. Most recent analyses are based on parametrized models of the equation of state with a finite number of parameters and occasionally include extra parameters intended to capture phase-transition phenomenology. However, such models restrict the types of behavior allowed and may not match the true equation of state. We introduce a complementary approach that extracts phase transitions directly from the equation of state without relying on, and thus being restricted by, an underlying parametrization. We then constrain the presence of phase transitions in neutron stars with astrophysical data. Current pulsar mass, tidal deformability, and mass-radius measurements disfavor only the strongest of possible phase transitions (latent energy per particle ≳ 100 MeV). Weaker phase transitions are consistent with observations. Here we further investigate the prospects for measuring phase transitions with future gravitational-wave observations and find that catalogs of O (100) events will (at best) yield Bayes factors of ~ 10 : 1 in favor of phase transitions even when the true equation of state contains very strong phase transitions. Our results reinforce the idea that neutron star observations will primarily constrain trends in macroscopic properties rather than detailed microscopic behavior. Fine-tuned equation of state models will likely remain unconstrained in the near future.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Equation-of-state, sound speed, and reshock of shock-compressed fluid carbon dioxide

Mechanical equation-of-state data of initially liquid and solid CO2 shock-compressed to terapascal conditions are reported. Diamond-sapphire anvil cells were used to vary the initial density and state of CO2 samples that were then further compressed with laser-driven shock waves, resulting in a data set from which precise derivative quantities, including Grüneisen parameter and sound speed, are determined. Reshock states are measured to 800 GPa and map the same pressure-density conditions as the single shock using different thermodynamic paths. The compressibility data reported here do not support current density-functional-theory calculations, but are better represented by tabular equation-of-state models.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Multiphase equation of state for Ta 2 O 5

A new equation of state for Ta 2 O 5 is presented. The EOS is constructed using the OpenSesame software and is referred to as SESAME 3530. The EOS uses a combination of density functional theory (DFT) calculations and experimental data. DFT calculations include cold curves and phonons of the solid phases, as well as DFT-based molecular dynamics simulations of the liquid phase. Experimental data includes isobaric, diamond anvil cell, and porous shock Hugoniot data. To fit the data, we create a multiphase EOS consisting of two solid phases and the liquid. Overall agreement with experimental data is shown, and we provide some suggestions for future experiments that could improve our knowledge of the phase diagram.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Dense Nuclear Matter Equation of State from Heavy-Ion Collisions

The nuclear equation of state (EOS) is at the center of numerous theoretical and experimental efforts in nuclear physics, motivated by its crucial role in our understanding of the properties of nuclear matter found on Earth, in neutron stars, and in neutron-star mergers. With advances in microscopic theories for nuclear interactions, the availability of experiments probing nuclear matter under conditions not reached before, and the advent of multi-messenger astronomy, the next decade will bring new opportunities for determining the nuclear matter EOS.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

What Can We Learn about the Unstable Equation-of-state Branch from Neutron Star Mergers?

Abstract The equation of state (EOS) of dense strongly interacting matter can be probed by astrophysical observations of neutron stars (NS), such as X-ray detections of pulsars or the measurement of the tidal deformability of NSs during the inspiral stage of NS mergers. These observations constrain the EOS at most up to the density of the maximum-mass configuration, n TOV , which is the highest density that can be explored by stable NSs for a given EOS. However, under the right circumstances, binary neutron star (BNS) mergers can create a postmerger remnant that explores densities above n TOV . In this work, we explore whether the EOS above n TOV can be measured from gravitational-wave or electromagnetic observations of the postmerger remnant. We perform a total of 25 numerical-relativity simulations of BNS mergers for a range of EOSs and find no case in which different descriptions of the matter above n TOV have a detectable impact on postmerger observables. Hence, we conclude that the EOS above n TOV can likely not be probed through BNS merger observations for the current and next generation of detectors.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Measuring the structure and equation of state of polyethylene terephthalate at megabar pressures

Abstract We present structure and equation of state (EOS) measurements of biaxially orientated polyethylene terephthalate (PET, $$({\hbox {C}}_{10} {\hbox {H}}_8 {\hbox {O}}_4)_n$$ ( C 10 H 8 O 4 ) n , also called mylar) shock-compressed to ( $$155 \pm 20$$ 155 ± 20 ) GPa and ( $$6000 \pm 1000$$ 6000 ± 1000 ) K using in situ X-ray diffraction, Doppler velocimetry, and optical pyrometry. Comparing to density functional theory molecular dynamics (DFT-MD) simulations, we find a highly correlated liquid at conditions differing from predictions by some equations of state tables, which underlines the influence of complex chemical interactions in this regime. EOS calculations from ab initio DFT-MD simulations and shock Hugoniot measurements of density, pressure and temperature confirm the discrepancy to these tables and present an experimentally benchmarked correction to the description of PET as an exemplary material to represent the mixture of light elements at planetary interior conditions.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Mapping out the thermodynamic stability of a QCD equation of state with a critical point using active learning

The Beam Energy Scan Theory (BEST) collaboration's equation of state (EoS) incorporates a three-dimensional Ising model critical point into the quantum chromodynamics (QCD) equation of state from lattice simulations. Furthermore, it contains four free parameters related to the size and location of the critical region in the QCD phase diagram. Certain combinations of the free parameters lead to acausal or unstable realizations of the EoS that should not be considered. In this work, we use an active learning framework to rule out pathological EoS efficiently. We find that checking stability and causality for a small portion of the parameters' range is sufficient to construct algorithms that perform with > 96 % accuracy across the entire parameter space. Though in this work we focus on a specific case, our approach can be generalized to any EoS containing a parameter space-class correspondence.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗