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At least 127 records · Page 7

Equation of State for the Thermodynamic Properties of Trans-1,2-dichloroethene [R-1130(E)]

We present an empirical equation of state in terms of the Helmholtz energy for trans-1,2-dichloroethene [R-1130(E)]. The range of validity is from the triple-point temperature, 223.31 K to 525 K with pressures up to 30 MPa. It may be used to calculate all thermodynamic properties in the fluid phase, including liquid, gas, and supercritical regions. Comparisons are given with existing literature data and estimated uncertainties are provided. In addition, checks were made for correct extrapolation behavior so that the equation behaves in a physically realistic manner when used outside of its range of validity, enabling its use in mixture models. The estimated uncertainties (at a k = 2 or 95 % level of confidence) are based on comparisons with critically assessed data and are 0.25 % for vapor pressure for temperatures in the range 300 K < T < 454 K, rising to 1.5 % as the temperature decreases from 300 K to 265 K. For density in the liquid phase the estimated uncertainty is 0.14 % for temperatures 270 K < T < 410 K and for pressures up to 30 MPa. For the vapor phase the estimated uncertainty in density is 3 %. The uncertainty for liquid-phase heat capacity is 1 % at atmospheric pressure over the temperature range 268 K < T < 309 K, and the uncertainty for the speed of sound in the liquid phase is 0.25 % for temperatures 230 K < T < 420 K and for pressures up to 30 MPa. The uncertainties are larger outside of these specified ranges and in the critical region.

1,2-Dichloroethene↗

The development of thermodynamically consistent and physics-informed equation-of-state model through machine learning

Ab initio molecular dynamics (AIMD) simulations have become an important tool used in the construction of equations of state (EOS) tables for warm dense matter. Due to computational costs, only a limited number of system state conditions can be simulated, and the remaining EOS surface must be interpolated for use in radiation-hydrodynamic simulations of experiments. In this work, we develop a thermodynamically consistent EOS model that utilizes a physics-informed machine learning approach to implicitly learn the underlying Helmholtz free-energy from AIMD generated energies and pressures. The model, referred to as PIML-EOS, was trained and tested on warm dense polystyrene producing a fit within a 1% relative error for both energy and pressure and is shown to satisfy both the Maxwell and Gibbs–Duhem relations. In addition, we provide a path toward obtaining thermodynamic quantities, such as the total entropy and chemical potential (containing both ionic and electronic contributions), which are not available from current AIMD simulations.

74 ATOMIC AND MOLECULAR PHYSICS↗

On the equation of state for an electron gas in an intense magnetic field

In this paper we derive the equation of state for a relativistic electron gas imbedded in a static homogeneous magnetic field of arbitrary strength. The derivation is based on the evaluation of the energy-momentum tensor and the use of Dirac's equation for such a problem. Contrary to a derivation presented several years ago, the present derivation is completely gauge-invariant. We also show how to recover, in an exact manner, the perfect gas law for the case of weak magnetic fields.

Canuto, V.↗

Kilonova Emissions from Neutron Star Merger Remnants: Implications for the Nuclear Equation of State

Multimessenger observations of binary neutron star mergers can provide valuable information on the nuclear equation of state (EOS). Here, we investigate the extent to which electromagnetic observations of the associated kilonovae allow us to place constraints on the EOS. For this, we use state-of-the-art three-dimensional general-relativistic magnetohydrodynamics simulations and detailed nucleosynthesis modeling to connect properties of observed light curves to properties of the accretion disk, and hence, the EOS. Using our general approach, we use multimessenger observations of GW170817/AT2017gfo to study the impact of various sources of uncertainty on inferences of the EOS. We constrain the radius of a 1.4M ⊙ neutron star to lie within 10.30 ≤ R 1.4 ≤ 13.0 km and the maximum mass to be M TOV ≤ 3.06M ⊙ .

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

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.↗

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↗

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↗

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↗

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↗

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↗

Development of a multiphase equation of state for gallium with experiments and ab initio free-energy calculations

Here, we present a five-phase equation of state (EOS) for elemental gallium (Ga) that is developed using both experimental data and new theoretical predictions. Four experimentally observed solid phases (Ga-I, Ga-II, Ga-III, and Ga-IV) and one liquid phase are included. To improve our understanding of the thermal behavior of Ga and its phase boundaries under compression, we have performed ab initio density functional theory (DFT) free-energy calculations for the Ga-III and liquid phases, which enables us to determine the melt temperature to be 2214 ± 100 K at 110 GPa, extending significantly beyond the existing experimental melt data, which are limited to 25 GPa. In order to best describe the electron-thermal contribution, which dominates the liquid free energy at high temperatures, we have carried out averaged-atom-in-jellium DFT calculations to cover the entire temperature and density range of the EOS. The resulting multiphase Ga EOS is able to accurately reproduce a diverse variety of data, including known phase boundaries, the principal Hugoniot, low-pressure liquid isobars, and diamond-anvil-cell isotherm measurements at high pressures. It agrees more closely with key experimentally measured properties than other Ga EOS models targeted for high-pressure applications.

Wu, Christine J. [Lawrence Livermore National Labo↗

Two lectures on Yang-Lee edge singularity and analytic structure of QCD equation of state

These lecture notes, prepared for the 2024 XQCD PhD, provide an introduction to the analytic structure of an equation of state near a second-order phase transition and its most prominent landmark: the Yang-Lee edge singularity. In addition to discussing general properties, the notes review recent theoretical progress in locating the QCD critical point by tracking the trajectory of the Yang-Lee edge singularity.

Skokov, Vladimir (ORCID:0000000176191796)↗

Equation of state of ammonia-water liquid - Derivation and planetological applications

The present least-squares fit calculation of the equation of state for ammonia-water liquid has yielded results for the zero-100 wt pct NH3, 170-300 K temperature, and zero-10 kb pressure parameter ranges. In conjunction with solid density and thermodynamic measurements, the present calculated and measured liquid densities are used to yield estimates of density and thermal expansion at 1 bar for the solid phases of ammonia's monohydrate, dihydrate, and hemihydrate between absolute zero and their respective melting points. Attention is given to the implications for icy satellite morphologic and tectonic forms of peritectic ammonia-water liquid that is neutrally buoyant relative to the corresponding solid phases.

Croft, S. K.↗

Rapidly rotating neutron stars in general relativity: Realistic equations of state

We construct equilibrium sequences of rotating neutron stars in general relativity. We compare results for 14 nuclear matter equations of state. We determine a number of important physical parameters for such stars, including the maximum mass and maximum spin rate. The stability of the configurations to quasi-radial perturbations is assessed. We employ a numerical scheme particularly well suited to handle rapid rotation and large departures from spherical symmetry. We provide an extensive tabulation of models for future reference. Two classes of evolutionary sequences of fixed baryon rest mass and entropy are explored: normal sequences, which behave very much like Newtonian sequences, and supramassive sequences, which exist for neutron stars solely because of general relativistic effects. Adiabatic dissipation of energy and angular momentum causes a star to evolve in quasi-stationary fashion along an evolutionary sequence. Supramassive sequences have masses exceeding the maximum mass of a nonrotating neutron star. A supramassive star evolves toward eventual catastrophic collapse to a black hole. Prior to collapse, the star actually spins up as it loses angular momentum, an effect that may provide an observable precursor to gravitational collapse to a black hole.

Cook, Gregory B.↗

From Existing and New Nuclear and Astrophysical Constraints to Stringent Limits on the Equation of State of Neutron-Rich Dense Matter

Through continuous progress in nuclear theory and experiment and an increasing number of neutron-star (NS) observations, a multitude of information about the equation of state (EOS) for matter at extreme densities is available. To constrain the EOS across its entire density range, this information needs to be combined consistently. However, the impact and model dependency of individual observations vary. Given their growing number, assessing the various methods is crucial to compare the respective effects on the EOS and discover potential biases. For this purpose, we present a broad compendium of different constraints and apply them individually to a large set of EOS candidates within a Bayesian framework. Specifically, we explore different ways of how chiral effective field theory and perturbative quantum chromodynamics can be used to place a likelihood on EOS candidates. We also investigate the impact of nuclear experimental constraints, as well as different radio and x-ray observations of NS masses and radii. This is augmented by reanalyses of the existing data from binary neutron star coalescences, in particular of GW170817, with improved models for the tidal waveform and kilonova light curves, which we also utilize to construct a tight upper limit of 2.39 M ⊙ on the TOV mass based on GW170817’s remnant. Our diverse set of constraints is eventually combined to obtain stringent limits on NS properties. We organize the combination in a way to distinguish between constraints where the systematic uncertainties are deemed small and those that rely on less conservative assumptions. For the former, we find the radius of the canonical 1.4 M ⊙ neutron star to be R 1.4 = 12.2 6 − 0.91 + 0.80 km and the TOV mass at M TOV = 2.2 5 − 0.22 + 0.42 M ⊙ (95% credibility). Including all the presented constraints yields R 1.4 = 12.2 0 − 0.48 + 0.50 km and M TOV = 2.3 0 − 0.20 + 0.07 M ⊙ . When comparing these limits to individual data points, we find that the quoted radius of HESS J1731-347 displays noticeable tension with other constraints. Constraining microphysical properties of the EOS proves more challenging. For instance, the symmetry energy slope is restricted to L sym = 48 − 25 + 21 MeV , where this constraint is mainly dominated by our reanalysis of the PREX-II and CREX experiment. Published by the American Physical Society 2025

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗