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At least 235 records · Page 13
All sourcesNASA NTRSDOE OSTI
NASA NTRS1988

The equation of state for stellar envelopes. I - An occupation probability formalism for the truncation of internal partition functions

An equation of state for material in stellar envelopes, subject to the limits of temperature less than about 10 to the 7th K and density less than about .01 g/cu cm is presented. The equation makes it possible to express free energy as the sum of several terms representing effects such as partial degeneracy of the electron, Coulomb interactions among charged particles, finite-volume, hard sphere repulsion, and van der Waals attraction. An occupation probability formalism is used to represent the effects of the plasma in establishing a finite partition function. It is shown that the use of the static screened Coulomb potential to calculate level shifts and to estimate the cutoff of the internal partition function is invalid. For most of the parameter space relevant to stellar envelopes, perturbations arising from the plasma ions are shown to be dominant in establishing the internal partition function.

Hummer, D. G.↗
DOE OSTI2023

Equation of state within the EPOS3 model

Transitions between different states of matter and their thermodynamic properties are described by the Equation of State (EoS). A universal representation of the EoS of quantum chromodynamics for the wide range of phase diagrams has yet to be determined. The expectation of the systems to undergo various types of transitions depending on the temperature (T), the chemical potential (μ B ), and other thermodynamic features make solving that puzzle challenging. Furthermore, it needs to be apparent which experimentally measurable observables could provide helpful information for determining EoS. The application of different EoS for hydrodynamical evolution was introduced in the EPOS3 generator, which allows one to study its changing effect on the experimental observables. The family of EoS proposed by the BEST Collaboration was implemented. The critical point location and the strength of criticality variations were investigated with particle yield, transverse momentum spectra, flow, and moments of the net-proton distributions.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

A New Constraint on the Nuclear Equation of State from Statistical Distributions of Compact Remnants of Supernovae

Abstract Understanding how matter behaves at the highest densities and temperatures is a major open problem in both nuclear physics and relativistic astrophysics. Our understanding of such behavior is often encapsulated in the so-called high-temperature nuclear equation of state (EOS), which influences compact binary mergers, core-collapse supernovae, and other phenomena. Our focus is on the type (either black hole or neutron star) and mass of the remnant of the core collapse of a massive star. For each six candidates of equations of state, we use a very large suite of spherically symmetric supernova models to generate a sample of synthetic populations of such remnants. We then compare these synthetic populations to the observed remnant population. Our study provides a novel constraint on the high-temperature nuclear EOS and describes which EOS candidates are more or less favored by an information-theoretic metric.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2026

High Pressure X-ray Diffraction and Equation of State of Hydrazine

Synchrotron X-ray diffraction has been used to investigate the structure and equation of state (EOS) of hydrazine (N 2 H 4 ) up to 54.3 GPa at 298 K. The diffraction patterns could be fit to a monoclinic unit-cell structure and put strong constraints on previously reported phase transitions documented by vibrational spectroscopy over this pressure range. Pressure–volume ( P–V ) data were fit using a Vinet EOS, yielding parameters: V 0 = 45.2 Å 3 /molecule (fixed), K 0 = 11.8(7) GPa, and K 0 ′ = 6.5(2). Previously measured high-pressure vibrational frequency shifts were used to estimate the vibrational free energy and model P–V–T isotherms from 0 to 1200 K. The results of the P–V–T isotherms are compared to existing shock Hugoniot data on hydrazine and 298 K isotherms for assemblages of possible decomposition products. This comparison suggests dissociation at high density under shock loading. Good correspondence was found between the static lattice EOS as calculated by the model and the previously reported EOS as calculated by density functional theory. Finally, these results resolve existing uncertainties about the EOS and crystal symmetry of hydrazine at high pressure and provide valuable baseline information on this important energetic material.

diffraction↗
DOE OSTI2024

Improving equations of state calibrations in the toroidal DAC—The case study of molybdenum

We report an updated isothermal equation of state (EoS) of molybdenum (Mo) obtained by compression in beveled and toroidal diamond-anvil cells (DACs). For an improved compression environment, we developed a copper (Cu) pressure-transmitting medium (PTM) for the toroidal diamond-anvil cell samples, as it is a soft metal compared to Mo with a well calibrated EoS. A Ne PTM was used for the conventional beveled DAC samples. The unit-cell volumes of Mo were measured to 336(1) GPa in the Cu PTM and 231.2(6) GPa in the Ne PTM at room temperature. We additionally calculated elastic stiffness and compliance constants and evaluated the uniaxial stress of Mo and Cu with pressure. A new EoS for Mo is presented from data collected in all sample environments and compared to our theoretical predictions as well as previous compression studies of Mo. The (200) lattice plane of Mo produced the lowest volumes across the pressure range of this study for all compression environments, suggesting that it is less affected by nonhydrostatic stresses in the DAC compared to the other observed diffraction planes. The presented Mo EoS is compatible with extrapolations of EoS fits of Mo in helium (He) within ~1% at 330 GPa. Results from this work demonstrate that compressing a sample in a softer metal in the toroidal DAC can improve the compression environment and result in measured sample volumes comparable to those collected in noble-gas media at multi-megabar conditions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Simulating neutron stars with a flexible enthalpy-based equation of state parametrization in sp ECTRE

Numerical simulations of neutron star mergers represent an essential step toward interpreting the full complexity of multimessenger observations and constraining the properties of supranuclear matter. Currently, simulations are limited by an array of factors, including computational performance and input physics uncertainties, such as the neutron star equation of state. In this work, we expand the range of nuclear phenomenology efficiently available to simulations by introducing a new analytic parametrization of cold, beta-equilibrated matter that is based on the relativistic enthalpy. Here we show that the new enthalpy parametrization can capture a range of nuclear behavior, including strong phase transitions. We implement the enthalpy parametrization in the spectre code, simulate isolated neutron stars, and compare performance to the commonly used spectral and polytropic parametrizations. We find comparable computational performance for nuclear models that are well represented by either parametrization, such as simple hadronic equations of state. We show that the enthalpy parametrization further allows us to simulate more complicated hadronic models or models with phase transitions that are inaccessible to current parametrizations.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Radiation drive designed to extend the pressure ranges measured in Gbar equation of state experiments at the National Ignition Facility

We present the design and demonstration of a Shock-Strengthening hohlraum radiation temperature drive in the Gbar experimental platform at the National Ignition Facility intended to increase the pressure range measured in a single experiment. Previously published experiments by Döppner et al. measured the equation of state in polystyrene from 25 to 60 Mbar. Recent experimental data of the Shock-Strengthening drive initially demonstrated a much larger pressure range from 15 to 110 Mbar using the same peak radiation temperature and experimental platform. The Shock-Strengthening drive starts with a low temperature foot that launches a weak shock into the sample and is followed by a continuous increase in radiation temperature to strengthen the leading shock. The additional strengthening increases the pressure within the sample beyond what is achievable by convergence alone. Design features of the Shock-Strengthening drive and accompanying radiation hydrodynamics simulations are used to illustrate the method by which the pressure range is increased from previous experiments. This method of modifying the radiation temperature drive can be used on the Gbar platform to significantly increase the range for equation of state data collected in a single experiment for many materials.

Physics - Plasma physics↗
DOE OSTI2023

Equation of state, phase transitions, and band-gap closure in Pb Cl 2 and Sn Cl 2

The equations of state and band-gap closures for Pb Cl 2 and Sn Cl 2 were studied using both experimental and theoretical methods. Here we measured the volume of both materials to a maximum pressure of 70 GPa using synchrotron-based angle-dispersive powder x-ray diffraction. The lattice parameters for both compounds showed anomalous changes between 16–32 GPa, providing evidence of a phase transition from the cotunnite structure to the related Co 2 Si structure, in contrast to the postcotunnite structure as previously suggested. First-principles calculations confirm this finding and predict a second phase transition to a Co 2 Si-like structure between 75– 110 GPa in Pb Cl 2 and 60–75 GPa in Sn Cl 2 . Band gaps were measured under compression to ~70 GPa for Pb Cl 2 and ~66 GPa for Sn Cl 2 and calculated up to 200 GPa for Pb CI 2 and 120 GPa for Sn Cl 2 . We find an excellent agreement between our experimental and theoretical results when using the Heyd-Scuseria-Ernzerhof (HSE06) hybrid functional, which suggests that this functional could reliably be used to calculate the band gap of similar AX 2 compounds. Experimental and calculated band-gap results show discontinuous decreases in the band gap corresponding to phase changes to higher-coordinated crystal structures, giving insight into the relationship between interatomic geometry and metallicity.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Efficient and Accurate Pre-Inversion of Equation of State Data

In this report, we evaluate the trade-offs between accuracy and performance in three equation of state interpola- tion strategies- EOSPAC, SpinerEOSDependsRhoT, and SpinerEOSDependsRhoSie-using SESAME tabular data. We also investigate ways to reduce nonlinearity in the data through invertible transformations within the SpinerEOS- DependsRhoSie class with the goal of impacting interpolation accuracy. We include a variety of benchmarking tests that vary the grid densities and how memory is accessed.

36 MATERIALS SCIENCE↗
DOE OSTI2022

First-principles equation of state of CHON resin for inertial confinement fusion applications

A wide-range (0 to 1044.0 g/ cm 3 and 0 to 10 9 K) equation-of-state (EOS) table for a CH 1.72 O 0.37 N 0.086 quaternary compound has been constructed based on density-functional theory (DFT) molecular-dynamics (MD) calculations using a combination of Kohn-Sham DFT MD, orbital-free DFT MD, and numerical extrapolation. The first-principles EOS data are compared with predictions of simple models, including the fully ionized ideal gas and the Fermi-degenerate electron gas models, to chart their temperature-density conditions of applicability. The shock Hugoniot, thermodynamic properties, and bulk sound velocities are predicted based on the EOS table and compared to those of C-H compounds. The Hugoniot results show the maximum compression ratio of the C-H-O-N resin is larger than that of CH polystyrene due to the existence of oxygen and nitrogen; while the other properties are similar between CHON and CH. Radiation hydrodynamic simulations have been performed using the table for inertial confinement fusion targets with a CHON ablator and compared with a similar design with CH. Here, the simulations show CHON outperforms CH as the ablator for laser-direct-drive target designs.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

Validation of a detonation product equation of state for an insensitive high explosive via slab geometry expansion tests

Slab expansion (SLABEX) tests are conducted to validate a process for calibrating the detonation products equation of state (EOS) of a high explosive (HE). The SLABEX tests use rectangular slabs of PBX 9502, a polymer-bonded HE formulation consisting of 95 wt.% 1,3,5-triamino-2,4,6-trinitrobenzene bound with Kel F-800, a co-polymer of chlorotrifluoroethylene and vinylidene-fluoride. Three PBX 9502 slab thicknesses are examined, each confined symmetrically by two rectangular copper (Cu) plates approximately one-tenth the thickness of the HE slab. For the duration of each experiment, the detonation flow along the central axis of the PBX 9502 slab remains two-dimensional. The lateral flow velocity component of the outer surfaces of the expanding Cu plates is measured, along with the steady axial detonation speed along the central axis of the SLABEX. Hydrodynamic simulations of the Cu plate expansion in the SLABEX geometry, driven by the energy stored in the detonation products by the detonation combustion event, are conducted using a Jones–Wilkins–Lee EOS for the detonation products. This EOS form was recently parameterized for PBX 9502 in the cylinder expansion test geometry using a newly developed calibration technique [Voelkel et al., Combust. Flame 246, 112373 (2022)]. Good agreement between the experiment and prediction is found in each SLABEX test, demonstrating that the detonation product EOS calibration technique produces EOSs that are predictive when applied to other geometries.

45 MILITARY TECHNOLOGY, WEAPONRY, AND NATIONAL DEF↗
DOE OSTI2020

Influence of Equation-of-States on Supercritical CO2 Combustion Mixtures

Abstract Fossil fuel based direct-fired supercritical CO2 (sCO2) cycles are gaining the attention of industry, academia, and government due to their remarkable efficiency and carbon capture at high-source temperatures. Modeling plays an important role in the development of sCO2 combustors because experiments are very expensive at the designed operating conditions of these direct-fired cycles. Inaccurate density estimates are detrimental to the simulation output. Hence, this work focuses on comprehensive evaluation of the influence and applicability of various equation-of-states (EOS) which are being used in the supercritical combustion modeling literature. A state-of-the-art supercritical combustion modeling methodology is used to simulate counter-flow supercritical CO2 flames by using various equation-of-states. The results show that using the corresponding state principle to evaluate compressibility factor is not accurate. Also, van der Waal type EOSs predictions can be as accurate as complex Benedict–Webb–Rubin EOSs; hence van der Waal EOSs are more suitable to simulate sCO2 combustor simulations. Non-ideal effects are significant under the operating conditions considered in this work. The choice of EOS significantly influences the flame structure and heat release rate. Also, assuming the binary interaction parameter as zero is reasonable in sCO2 combustion simulations.

Energy & Fuels↗
DOE OSTI2022

Embedding a critical point in a hadron to quark-gluon crossover equation of state

Lattice QCD simulations have shown unequivocally that the transition from hadrons to quarks and gluons is a crossover when the baryon chemical potential is zero or small. Many model calculations predict the existence of a critical point at a value of the chemical potential where current lattice simulations are unreliable. We show how to embed a critical point in a smooth background equation of state so as to yield the critical exponents and critical amplitude ratios expected of a transition in the same universality class as the liquid-gas phase transition and the three-dimensional Ising model. There are only two independent critical exponents; the relations α + 2β + γ = 2 and β(δ-1) = γ arise automatically, as does a relation between the two critical amplitudes. The resulting equation of state has parameters that may be inferred by hydrodynamic modeling of heavy-ion collisions in the Beam Energy Scan II at the BNL Relativistic Heavy Ion Collider or in experiments at other accelerators.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2020

Quantifying uncertainties and correlations in the nuclear-matter equation of state

We perform statistically rigorous uncertainty quantification (UQ) for chiral effective field theory (χ EFT) applied to infinite nuclear matter up to twice nuclear saturation density. The equation of state (EOS) is based on high-order many-body perturbation theory calculations with nucleon-nucleon and three-nucleon interactions up to fourth order in the χ EFT expansion. From these calculations our newly developed Bayesian machine-learning approach extracts the size and smoothness properties of the correlated EFT truncation error. Furthermore, we then propose a novel extension that uses multitask machine learning to reveal correlations between the EOS at different proton fractions. The inferred in-medium χ EFT breakdown scale in pure neutron matter and symmetric nuclear matter is consistent with that from free-space nucleon-nucleon scattering. These significant advances allow us to provide posterior distributions for the nuclear saturation point and propagate theoretical uncertainties to derived quantities: the pressure and incompressibility of symmetric nuclear matter, the nuclear symmetry energy, and its derivative. Our results, which are validated by statistical diagnostics, demonstrate that an understanding of truncation-error correlations between different densities and different observables is crucial for reliable UQ. The methods developed here are publicly available as annotated Jupyter notebooks.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

Constraints on the Dense Matter Equation of State and Neutron Star Properties from NICER’s Mass–Radius Estimate of PSR J0740+6620 and Multimessenger Observations

In recent years our understanding of the dense matter equation of state (EOS) of neutron stars has significantly improved by analyzing multimessenger data from radio/X-ray pulsars, gravitational wave events, and from nuclear physics constraints. Here we study the additional impact on the EOS from the jointly estimated mass and radius of PSR J0740+6620, presented in Riley et al. by analyzing a combined data set from X-ray telescopes NICER and XMM-Newton. We employ two different high-density EOS parameterizations: a piecewise-polytropic (PP) model and a model based on the speed of sound in a neutron star (CS). Here, at nuclear densities these are connected to microscopic calculations of neutron matter based on chiral effective field theory (EFT) interactions. In addition to the new NICER data for this heavy neutron star, we separately study constraints from the radio timing mass measurement of PSR J0740+6620, the gravitational wave events of binary neutron stars GW190425 and GW170817, and for the latter the associated kilonova AT2017gfo. By combining all these, and the NICER mass-radius estimate of PSR J0030+0451, we find the radius of a 1.4 M ⊙ neutron star to be constrained to the 95% credible ranges 12.33$^{+0.76}_{–0.81}$km (PP model) and 12.18$^{+0.56}_{–0.79}$km (CS model). In addition, we explore different chiral EFT calculations and show that the new NICER results provide tight constraints for the pressure of neutron star matter at around twice saturation density, which shows the power of these observations to constrain dense matter interactions at intermediate densities.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

QCD Constraints on Isospin-Dense Matter and the Nuclear Equation of State

Understanding the behavior of dense hadronic matter is a central goal in nuclear physics as it governs the nature and dynamics of astrophysical objects such as supernovae and neutron stars. Because of the nonperturbative nature of quantum chromodynamics (QCD), little is known rigorously about hadronic matter in these extreme conditions. Here, lattice QCD calculations are used to compute thermodynamic quantities and the equation of state of QCD over a wide range of isospin chemical potentials with controlled systematic uncertainties. Agreement is seen with chiral perturbation theory when the chemical potential is small. Comparison to perturbative QCD at large chemical potential allows for an estimate of the gap in the superconducting phase, and this quantity is seen to agree with perturbative determinations. Since the partition function for an isospin chemical potential μ I bounds the partition function for a baryon chemical potential μ B = 3 μ I / 2 , these calculations also provide rigorous nonperturbative QCD bounds on the symmetric nuclear matter equation of state over a wide range of baryon densities for the first time. Published by the American Physical Society 2025

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2020

H2OI95: A Stand-Alone Fortran Code for Evaluating the IAPWS-95 Equation-of-State Model for Water (Rev. 1)

H2OI95 is a stand-alone Fortran code for evaluating the IAPWS-95 equation-of-state model for the thermodynamic properties of water. It also evaluates the corresponding thermochemical properties of water consistent with the CODATA recommendations. The IAPWS-95 model is based on a model equation for the dimensionless Helmholtz energy for which the primary variables are the inverse reduced temperature (τ = T cr /T ) and reduced density (δ = ρ/ρ cr ). Here T is the absolute temperature (K), ρ is density (kg/m³), and the subscript “ cr ” refers to the critical point of water (647.096 K and 22.064 MPa pressure in this model, for which ρ cr is 322 kg/m³). The code solves four basic types of problems, distinguished by the specified inputs: 1. Temperature (K) and density (ρ kg/m³) or reduced density (δ) 2. Temperature (K) and pressure (MPa). 3. Temperature (K) on the saturation (liquid-vapor equilibrium) curve 4. Pressure (MPa) on the saturation curve. Each type of problem is run using a corresponding input (text) file. All but the first type of problem require iteration. For example, to solve for desired temperature and pressure, the reduced density must be adjusted to give the desired pressure. Iteration is accomplished using the Newton-Raphson method, though the secant method is also used in solving the fourth type of problem. For the last three types of problems, H2OI95 has been used to conduct numerical studies of convergence and the problem of multiple numerical solutions, some of which are not physically valid. Obtaining valid results depends mainly on appropriate choice of starting values for the density. The default values used in H2OI95 appear to consistently lead to generally desired results. With modification (not addressed here), H2OI95 can be used to support SUPCRT92 and similar codes that compute chemical thermodynamic properties of species and reactions over a wide range of temperature and pressure (273.16-1273K and 0-1000 MPa). Version 1.1 of this software calculates an extended set of water properties, including some derivable solely from IAPWS-95, such as the isobaric thermal expansivity and the isothermal compressibility, and still other properties based on supplementary models sanctioned by IAPWS, including the dynamic viscosity, thermal conductivity, surface tension, and static dielectric constant, and various other properties (notably Debye-Hückel parameters) derivable from the dielectric constant and its partial derivatives with respect to temperature and pressure. A coding error in Version 1.0 was identified while testing the implementation of the viscosity model. This error is described in Appendix C. It mainly affects calculation of “higher order” properties such as compressibility and heat capacity near the critical point.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗