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At least 325 records · Page 18
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Shock equation of state experiments in MgO up to 1.5 TPa and the effects of optical depth on temperature determination

Laser-driven shock compression enables an experimental study of phase transitions at unprecedented pressures and temperatures. One example is the shock Hugoniot of magnesium oxide (MgO), which crosses the B1–B2-liquid triple point at 400–600 GPa, 10 000–13 000 K (0.86–1.12 eV). MgO is a major component within the mantles of terrestrial planets and has long been a focus of high-pressure research. Here, we combine time-resolved velocimetry and pyrometry measurements with a decaying shock platform to obtain pressure–temperature data on MgO from 300 to 1500 GPa and 9000 to 50 000 K. Pressure–temperature–density Hugoniot data are reported at 1500 GPa. These data represent the near-instantaneous response of an MgO [100] single crystal to shock compression. We report on a prominent temperature anomaly between 400 and 460 GPa, in general agreement with previous shock studies, and draw comparison with equation-of-state models. We provide a detailed analysis of the decaying shock compression platform, including a treatment of a pressure-dependent optical depth near the shock front. We show that if the optical depth of the shocked material is larger than 1 μm, treating the shock front as an optically thick gray body will lead to a noticeable overestimation of the shock temperature.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Multi-fidelity equations of state and transport coefficient datasets for pulsed-power applications

Reliably simulating experiments relevant to the National Nuclear Security Administration (NNSA) requires a detailed description of material properties across a wide range of conditions. Such properties include the equations of state, charged-particle transport coefficients, and optical properties like the opacity. Together, these properties make up the material models used in radiation-magnetohydrodynamic simulations of nuclear fusion experiments. Many of these models do not incorporate uncertainties in the data used to produce them. It is unknown whether these uncertainties significantly impact the interpretation of simulation results and diagnostics. The purpose of this work is to quantify how such uncertainties impact simulations of pulsed-power experiments. We accomplished this task by first assessing discrepancies between approaches used to generate the data. This included bringing together members of the high-energy-density community spanning the three NNSA laboratories and multiple universities. Then, using these data, we developed a general framework that systematically incorporates physical uncertainties within the material models suitable for uncertainty quantification analyses. The framework utilizes machine learning, Bayesian inference, and incorporates multi-fidelity datasets. We demonstrated the framework by quantifying the impact that material model uncertainties have on simulations of pulsed-power experiments underway on Z at Sandia National Laboratories. As a result of this work, we discovered that modest uncertainties in material models (roughly 20%) correspond to significant uncertainties in the outputs from simulations. Our framework has enabled rapid construction of material models through an automated procedure and allows for the generation of material models of interest to the NNSA.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Structure and equation of state of Bi 2 Sr 2 Ca n-1 Cu n O 2n+4+δ from x-ray diffraction to megabar pressures

Pressure is a unique tuning parameter for probing the properties of materials, and it has been particularly useful for studies of electronic materials such as high-temperature cuprate superconductors. In this work we report the effects of quasihydrostatic compression produced by a neon pressure medium on the structures of bismuth-based high-T c cuprate superconductors with the nominal composition Bi 2 Sr 2 Ca n-1 Cu n O 2n+4+δ (n=1, 2, 3) up to 155 GPa. The structures of all three compositions obtained by synchrotron x-ray diffraction can be described as pseudotetragonal over the entire pressure range studied. We show that previously reported pressure-induced distortions and structural changes arise from the large strains that can be induced in these layered materials by nonhydrostatic stresses. The pressure-volume equations of state (EOS) measured under these quasihydrostatic conditions cannot be fit to single phenomenological formulation over the pressure ranges studied, starting below 20 GPa. This intrinsic anomalous compression as well as the sensitivity of Bi 2 Sr 2 Ca n-1 Cu n O 2n+4+δ to deviatoric stresses provide explanations for the numerous inconsistencies in reported EOS parameters for these materials. We conclude that the anomalous compressional behavior of all three compositions is a manifestation of the changes in electronic properties that are also responsible for the remarkable nonmonotonic dependence of T c with pressure, including the increase in T c at the highest pressures studied so far for each. Transport and spectroscopic measurements up to megabar pressures are needed to fully characterize these cuprates and explore higher possible critical temperatures in these materials.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Pressure-temperature equation of state of Al 2 ⁢O 3 up to 14 Mbar and 40 kK

Sapphire (Al 2 ⁢O 3 ), known for its remarkable incompressibility at ambient conditions, plays a pivotal role in both static and dynamic compression research. Accurately characterizing its equation of state (EoS) is essential for these applications. Here, we present a complete Hugoniot of Al 2 ⁢ O 3 as locus of experimentally assessed, high-precision, pressure, density and temperature states up to 14 Mbar and 43 kK. The Hugoniot is established with single shock experiments using magnetically launched hyper velocity flyers on the Z Accelerator at Sandia National Laboratories. We explore principal Hugoniot states at very high shock 𝑇 and 𝑝 in the solid phase, tracking the solid-liquid boundary and culminating at 2.4-fold compression, where data provides a direct constraint on the liquid phase. Corresponding shock release data probe thermodynamic states complementary to the Hugoniot and place additional constraints on tabular EoS models. Our findings indicate a significant deviation from existing tabular EoS models for Al 2 ⁢ O 3 dictating a comprehensive overhaul. We develop two advanced EoSs for Al 2 ⁢ O 3 the SESAME 97412 model, featuring an extensive phase diagram that includes three solid phases and the liquid phase, and the updated LEOS 2200m2 model. EoS development is assisted with Quantum Molecular Dynamics simulations. Our experimental data allows for stringent testing of our EoSs. Both models accurately capture the Hugoniot of Al 2 ⁢O 3 up to the highest pressures and temperatures. Rigorous experimental determination of extreme pressures and temperatures, paired with sophisticated models, advances the frontier of EoS development beyond 1 terapascal.

Kalita, Patricia [Sandia National Laboratories (SN↗
DOE OSTI2026

An Exploration of the Equation of State Dependence of Core-collapse Supernova Explosion Outcomes and Signatures

We explore, using a state-of-the-art simulation code in 3D and late-enough times to witness final observables, the dependence of core-collapse supernova explosions on the nuclear equation of state (EOS). Going beyond questions of explodability, we compare final explosion energies, nucleosynthetic yields, recoil kicks, and gravitational-wave and neutrino signatures using the SFHo and DD2 nuclear EOSs for a 9 M ⊙ /solar-metallicity progenitor star. The DD2 EOS is stiffer and has a lower effective nucleon mass. The result is a more extended protoneutron star (PNS) and lower central densities. As a consequence, the mean neutrino energies, final explosion energy, and recoil kick speed are lower. Moreover, the evolution of PNS convection differs between the two EOS models in significant ways. This translates in part into interestingly altered neutrino “light” curves and noticeably altered gravitational-wave signal strengths and frequency characteristics that may be diagnostic. The faster exploding model (SFHo) yields slightly more neutron-rich ejecta and more species with atomic weights between 60 and 90 and a weak r-process. However, this is merely a preliminary study. The next step is a more comprehensive and multiprogenitor set of 3D supernova simulations for various EOSs to late times when the observables have asymptoted. Such a future investigation will have a direct bearing on the neutron star and black hole birth mass functions and the quest toward a fully quantitative theory of supernova observables.

Rusakov, Aleksandr [Princeton University, NJ (Unit↗
DOE OSTI2020

First-principles equations of state and structures of liquid metals in multi-megabar conditions

Liquid metals at extreme pressures and temperatures are widely interested in the high-pressure community. Based on density functional theory molecular dynamics, we conduct first-principles investigations on the equation of state ( EOS) and structures of four metals (Cu, Fe, Pb, and Sn) at 1.5–5 megabar conditions and 5 × 10 3 –4 × 10 4 K. Our first-principles EOS data enable evaluating the performance of four EOS models in predicting Hugoniot densities and temperatures of the four systems. We find the melting temperature of Cu is 1000–2000 K higher and shows a similar Clapeyron slope, in comparison to those of Fe. Our structure, coordination number, and diffusivity analysis indicates all the four liquid metals form similar simple close-packed structures. Our results set theoretical benchmarks for EOS development and structures of metals in their liquid states and under dynamic compression.

36 MATERIALS SCIENCE↗
NASA NTRS2005

Shock Melting of Permafrost on Mars: Water Ice Multiphase Equation of State for Numerical Modeling and Its Testing

The presence of water/ice/brine in upper layers of Martian crust affects many processes of impact cratering. Modeling of these effects promises better understanding of Martian cratering records. We present here the new ANEOS-based multiphase equation of state for water/ice constructed for usage in hydrocodes and first numerical experiments on permafrost shock melting. Preliminary results show that due to multiple shock compression of ice inclusions in rocks the entropy jump in shocked ice is smaller than in pure ice for the same shock pressure. Hence previous estimates of ice melting during impact cratering on Mars should be re-evaluated. Additional information is included in the original extended abstract.

Ivanov, B. A.↗
NASA NTRS1994

Hydrodynamics of binary coalescence. 1: Polytropes with stiff equations of state

We performed a series of three-dimensional hydrodynamic calculations of binary coalescence using the smoothed particle hydrodynamics (SPH) method. The initial conditions are exact polytropic equilibrium configurations on the verge of dynamical instability. We consider synchronized equilbria only and concentrate on stiff equations of state, with adiabatic Gamma greater than 5/3. We assume that the polytropic constants (K identically equal to P/(rho(exp Gamma)) are the same for both components. These conditions apply well to models of neutron star binaries. Accordingly, we discuss our results in the context of the Laser Interferometer Gravitational-Wave Observatory (LIGO) project, and we calculate the emission of gravitational radiation in the quadruple approximation. The fully nonlinear development of the instability is followed using SPH until a new equilibrium configuration is reached by the system. We find that the properties of this final configuration depend sensitively on both the compressibility and mass ratio. An axisymmetric merged configuration is always produced when the adiabatic exponent Gamma approximately less than 2.3. As a consequence, the emission of gravitational radiation shuts off abruptly right after the onset of dynamical instability. In contrast, triaxial merged configurations are obtained when Gamma approximately greater than 2.3, and the system continues to emit gravitational waves after the final coalescence. Systems with mass ratios q not equal to 1 typically become dynamically unstable before the onset of mass transfer. Stable mass transfer from one neutron star to another in a close binary is therefore probably ruled out. For a mass ratio q approximately less than 0.5, however, dynamical mass transfer can temporarily retard the coalescence by causing a rapid reexpansion of the binary into a new, slightly eccentric but dynamically stable orbit. The maximum amplitude h(sub max) and peak luminosity L(sub max) of the gravitational waves emitted during the final coalescence are nearly independent of Gamma, but depend sensitively on the mass ratio q. The approximate scalings we find are h(sub max) varies as q(exp 2) and L(sub max) varies as q(exp 6) for q close to unity.

Rasio, Frederic A.↗
NASA NTRS1990

Dynamical effects from equation of state on topographies and geoid anomalies due to internal loading

Using a Cartesian compressible model, the effects of compressibility on geoid anomalies and of deformations on the topographic signatures caused by internal loading in the mantle are quantitatively investigated by examining different types of the equation of state. Also considered are different types of density laws with variations of thermodynamical parameters taken into play. It is shown that surface topographies are not changed much by the effects of mantle compressibility and that the deformation of bottom boundary is not significantly influenced except for long wavelengths and large viscosity contrasts between the upper and lower mantles. On the other hand, mantle compressibility can greatly affect geoid signals with horizontal wavelengths exceeding 10,000 km.

Hong, Hanjing↗
DOE OSTI2025

Accuracy of Kohn–Sham density functional theory for warm- and hot-dense matter equation of state

We study the accuracy of Kohn–Sham density functional theory (DFT) for warm- and hot-dense matter (WDM and HDM). Specifically, considering a wide range of systems, we perform accurate ab initio molecular dynamics simulations with temperature-independent local/semilocal density functionals to determine the equations of state at compression ratios of 3x–7x and temperatures near 1 MK. We find very good agreement with path integral Monte Carlo benchmarks, while having significantly smaller error bars and smoother data, demonstrating the accuracy of DFT for the study of WDM and HDM at such conditions. In addition, using a Δ-machine learned force field scheme, we confirm that the DFT results are insensitive to the choice of exchange-correlation functional, whether local, semilocal, or nonlocal.

Suryanarayana, Phanish (ORCID:0000000151720049)↗
NASA NTRS1977

Is the common definition of the Mie-Grueneisen equation of state inconsistent

Anharmonic models are used to describe the high temperatures and the electronic effects characteristic of shock wave phenomena and planetary interiors. It is found that a generalized Grueneisen function dependent on temperature and volume is necessary for the self-consistent application of the Mie-Grueneisen equation at the physical conditions encountered in shock wave phenomena or in the interior of planets. It is noted that at temperatures of a few thousand degrees Kelvin, by deriving the function in terms of anharmonic lattice dynamics, the difference between gamma and gamma(th) is of the same order of a magnitude as gamma. This leads to the conclusions that (1) gamma is not a function of temperature and (2) gamma?gamma(th) does not explain either the equation of state of planetary interiors or high-temperature shock wave phenomena.

Mulargia, F.↗
DOE OSTI2023

Deducing neutron star equation of state parameters directly from telescope spectra with uncertainty-aware machine learning

Neutron stars provide a unique laboratory for studying matter at extreme pressures and densities. While there is no direct way to explore their interior structure, X-rays emitted from these stars can indirectly provide clues to the equation of state (EOS) of the superdense nuclear matter through the inference of the star's mass and radius. However, inference of EOS directly from a star's X-ray spectra is extremely challenging and is complicated by systematic uncertainties. The current state of the art is to use simulation-based likelihoods in a piece-wise method which relies on certain theoretical assumptions and simplifications about the uncertainties. It first infers the star's mass and radius to reduce the dimensionality of the problem, and from those quantities infer the EOS. Here we demonstrate a series of enhancements to the state of the art, in terms of realistic uncertainty quantification and a path towards circumventing the need for theoretical assumptions to infer physical properties with machine learning. We also demonstrate novel inference of the EOS directly from the high-dimensional spectra of observed stars, avoiding the intermediate mass-radius step. Our network is conditioned on the sources of uncertainty of each star, allowing for natural and complete propagation of uncertainties to the EOS.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

Richtmyer–Meshkov instability when a shock is reflected for fluids with arbitrary equation of state

First predicted by Richtmyer in 1960 and experimentally confirmed by Meshkov in 1969, the Richtmyer–Meshkov instability (RMI) is crucial in fields such as physics, astrophysics, inertial confinement fusion and high-energy-density physics. These disciplines often deal with strong shocks moving through condensed materials or high-pressure plasmas that exhibit non-ideal equations of state (EoS), thus requiring theoretical models with realistic fluid EoS for accurate RMI simulations. Approximate formulae for asymptotic growth rates, like those proposed by Richtmyer, are helpful but rely on heuristic prescriptions for compressible materials. These prescriptions can sometimes approximate the RMI growth rate well, but their accuracy remains uncertain without exact solutions, as the fully compressible RMI growth rate is influenced by both vorticity deposited during shock refraction and multiple sonic wave refractions. This study advances previous work by presenting an analytic, fully compressible theory of RMI for reflected shocks with arbitrary EoS. It compares theoretical predictions with heuristic prescriptions using ideal gas, van der Waals gas and three-term constitutive equations for simple metals, the latter being analysed with detailed and simplified ideal-gas-like EoS. We additionally offer an alternative explicit approximate formula for the asymptotic growth rate. The comprehensive model also incorporates the effects of constant-amplitude acoustic waves at the interface, associated with the D'yakov–Kontorovich instability in shocks.

Napieralski, Mario (ORCID:0009000692344901)↗
DOE OSTI2020

Constraining the Dense Matter Equation of State with Joint Analysis of NICER and LIGO/Virgo Measurements

The Neutron Star Interior Composition Explorer collaboration recently published a joint estimate of the mass and the radius of PSR J0030+0451, derived via X-ray pulse-profile modeling. Raaijmakers et al. explored the implications of this measurement for the dense matter equation of state (EOS) using two parameterizations of the high-density EOS: a piecewise-polytropic model, and a model based on the speed of sound in neutron stars (NSs). In this work we obtain further constraints on the EOS following this approach, but we also include information about the tidal deformability of NSs from the gravitational wave signal of the compact binary merger GW170817. Further, we compare the constraints on the EOS to those set by the recent measurement of a 2.14 Me pulsar, included as a likelihood function approximated by a Gaussian, and find a small increase in information gain. To show the flexibility of our method, we also explore the possibility that GW170817 was a NS–black hole merger, which yields weaker constraints on the EOS.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

Curvature of the chiral phase transition line from the magnetic equation of state of ( 2 + 1 )-flavor QCD

We analyze the dependence of the chiral phase transition temperature on baryon number and strangeness chemical potentials by calculating the leading order curvature coefficients in the light and strange quark flavor basis as well as in the conserved charge ( B , S ) basis. Making use of scaling properties of the magnetic equation of state (MEoS) and including diagonal as well as off-diagonal contributions in the expansion of the energylike scaling variable that enters the parametrization of the MEoS, allows to explore the variation of T c ( μ B , μ S ) = T c ( 1 − ( κ 2 B μ ^ B 2 + κ 2 S μ ^ S 2 + 2 κ 11 B S μ ^ B μ ^ S ) ) along different lines in the ( μ B , μ S ) plane. On lattices with fixed cutoff in units of temperature, a T = 1 / 8 , we find κ 2 B = 0.015 ( 1 ) , κ 2 S = 0.0124 ( 5 ) and κ 11 B S = − 0.0050 ( 7 ) . We show that the chemical potential dependence along the line of vanishing strangeness chemical potential is about 10% larger than along the strangeness neutral line. The latter differs only by about 3% from the curvature on a line of vanishing strange quark chemical potential, μ s = 0 . We also show that close to the chiral limit the strange quark mass contributes like an energylike variable in scaling relations for pseudocritical temperatures. The chiral phase transition temperature decreases with decreasing strange quark mass, T c ( m s ) = T c ( m s phy ) ( 1 − 0.097 ( 2 ) ( m s − m s phys ) / m s phy + O ( ( Δ m s ) 2 ) . Published by the American Physical Society 2024

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
NASA NTRS2021

Constraining the Neutron Star Mass–Radius Relation and Dense Matter Equation of State with NICER. III. Model Description and Verification of Parameter Estimation Codes

We describe the X-ray pulse profile models we use and how we use them to analyze Neutron Star Interior Composition Explorer(NICER)observations of rotation-powered millisecond pulsars to obtain information about the mass–radius relation of neutron stars and the equation of state of the dense matter in their cores. Here we detail our modeling of the observed profile of PSR J0030+0451 that we analyzed in Miller et al. and Riley et al. and describe a cross-verification of computations of the pulse profiles of a star with R/M 3, in case stars this compact need to be considered in future analyses. We also present our early cross-verification efforts of the parameter estimation procedures used by Miller et al. and Riley et al. by analyzing two distinct synthetic data sets. Both codes yielded credible regions in the mass–radius plane that are statistically consistent with one another, and both gave posterior distributions for model parameter values consistent with the values that were used to generate the data. We also summarize the additional tests of the parameter estimation procedure of Miller et al. that used synthetic pulse profiles and the NICER pulse profile of PSR J0030+0451. We then illustrate how the precision of mass and radius estimates depends on the pulsar’s spin rate and the size of its hot spot by analyzing four different synthetic pulse profiles. Finally, we assess possible sources of systematic error in the estimates made using this technique, some of which may warrant further investigation.

Slavko Bogdanov↗
DOE OSTI2021

Implications of an improved water equation of state for water-rich planets

Water (H 2 O), in all forms, is an important constituent in planetary bodies, controlling habitability and influencing geological activity. Under conditions found in the interior of many planets, as the pressure increases, the H-bonds in water gradually weaken and are replaced by ionic bonds. Recent experimental measurements of the water equation of state (EOS) showed both a new phase of H-bonded water ice, ice-VIIt, and a relatively low transition pressure just above 30 GPa to ionic bonded ice-X, which has a bulk modulus 2.5 times larger. The higher bulk modulus of ice-X produces larger planets for a given mass, thereby either reducing the atmospheric contribution to the volume of many exoplanets or limiting their water content. We investigate the impact of the new EOS measurements on the planetary mass–radius relation and interior structure for water-rich planets. We find that the change in the planet mass–radius relation caused by the systematic differences between previous and new experimental EOS measurements is comparable to the observational uncertainties in some planet sizes – an issue that will become more important as observations continue to improve.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Correlations between the Neutron Star Mass–Radius Relation and the Equation of State of Dense Matter

We develop an analytic method of inverting the Tolman–Oppenheimer–Volkoff relations to high accuracy. In principle, a specified energy density–pressure relation gives a unique mass–radius (M–R) relation and vice versa. Our method is developed from the strong correlations that are shown to exist between the neutron star mass–radius curve and the equation of state (EOS) or pressure–energy density relation. Selecting points that have masses equal to fixed fractions of the maximum mass, we find a semi-universal power-law relation between the central energy densities, pressures, sound speeds, chemical potentials, and number densities of those stars, with the maximum mass and the radii of one or more fractional maximum mass points. Rms fitting accuracies, for EOSs without large first-order phase transitions, are typically 0.5% for all quantities at all mass points. The method also works well, although less accurately, in reconstructing the EOS of hybrid stars with first-order phase transitions. These results permit, in effect, an analytic method of inverting an arbitrary M–R curve to yield its underlying EOS. We discuss applications of this inversion technique to the inference of the dense matter EOS from measurements of neutron star masses and radii as a possible alternative to traditional Bayesian approaches.

Bayesian statistics↗