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DOE OSTI2023

Imaginary-time correlation function thermometry: A new, high-accuracy and model-free temperature analysis technique for x-ray Thomson scattering data

The accurate interpretation of experiments with matter at extreme densities and pressures is a notoriously difficult challenge. In a recent work [Dornheim et al., Nat. Commun. 13, 7911 (2022)], we have introduced a formally exact methodology that allows extracting the temperature of arbitrary complex materials without any model assumptions or simulations. Here, we provide a more detailed introduction to this approach and analyze the impact of experimental noise on the extracted temperatures. In particular, we extensively apply our method both to synthetic scattering data and to previous experimental measurements over a broad range of temperatures and wave numbers. We expect that our approach will be of high interest to a gamut of applications, including inertial confinement fusion, laboratory astrophysics, and the compilation of highly accurate equation-of-state databases.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2023

Post-detonation fireball modeling: Validation of freeze out approximations

A numerical simulation study was performed to examine the post-detonation reaction processes produced by the detonation of a 12 mm diameter hemispherical pentaerythritol tetranitrate (PETN) explosive charge. The simulations used a finite rate detailed chemical reaction model consisting of 59 species and 368 reactions to capture post-detonation reaction processes including air dissociation from Mach 19+ shock waves that initially break out of the PETN charge, reactions within the detonation products during expansion, and afterburning when the detonation products mix with the shock heated air. The multi-species and thermodynamically complete Becker-Kistiakowsky-Wilson real-gas equation of state is used for the gaseous phase to allow for the mixing of reactive species. A recent simplified reactive burn model is used to propagate the detonation through the charge and allow for detailed post-detonation reaction processes. The computed blast, shock structures, and mole fractions of species within the detonation products agree well with experimental measurements. A comparison of the simulation results to equilibrium calculations indicates that the assumption of a local equilibrium is fairly accurate until the detonation products rapidly cool to temperatures in the range of 1500-1900 K by expansion waves. Below this range, the computed results show mole fractions that are nearly chemically frozen within the detonation products for a significant portion of expansion. In conclusion, these results are consistent with the freeze out approximation used in the blast modeling community.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

Quantifying uncertainty in analysis of shockless dynamic compression experiments on platinum. II. Bayesian model calibration

Dynamic shockless compression experiments provide the ability to explore material behavior at extreme pressures but relatively low temperatures. Typically, the data from these types of experiments are interpreted through an analytic method called Lagrangian analysis. Here, in this work, alternative analysis methods are explored using modern statistical methods. Specifically, Bayesian model calibration is applied to a new set of platinum data shocklessly compressed to 570 GPa. Several platinum equation-of-state models are evaluated, including traditional parametric forms as well as a novel non-parametric model concept. The results are compared to those in Paper I obtained by inverse Lagrangian analysis. The comparisons suggest that Bayesian calibration is not only a viable framework for precise quantification of the compression path, but also reveals insights pertaining to trade-offs surrounding model form selection, sensitivities of the relevant experimental uncertainties, and assumptions and limitations within Lagrangian analysis. The non-parametric model method, in particular, is found to give precise unbiased results and is expected to be useful over a wide range of applications. The calibration results in estimates of the platinum principal isentrope over the full range of experimental pressures to a standard error of 1.6%, which extends the results from Paper I while maintaining the high precision required for the platinum pressure standard.

Brown, Justin Lee↗

DOE OSTI2023

Quantum mechanics based non-bonded force field functions for use in molecular dynamics simulations of materials and systems: The nitrogen and oxygen columns

Accurate Force Fields (FFs) are essential for Molecular Dynamics (MD) simulations of the dynamics of realistic materials in terms of atomic-level interactions. The FF parameters of short-range valence interactions can be derived through Quantum Mechanical (QM) calculations on model systems practical for QM (<300 atoms). Similarly, the dynamic electrostatic interactions can be described with methods such as QEq or PQEq that allow charges and polarization to adjust dynamically. However, accurately extracting long-range van der Waals (vdW) interactions from QM calculations poses challenges due to the absence of a definitive method to distinguish between the different energetic components of electrostatics, polarization, vdW, hydrogen bonding, and valence interactions. To do this we use the Perdew–Burke–Ernzerhof flavor of Density Functional Theory, including empirical D3 vdW corrections, to predict the Equation of State for each element (keeping any covalent bonds fixed), from which we obtain the two-body vdW nonbond potential. Here, we extend these calculations to include non-bonded parameters for the N and O columns of the periodic table so that we now describe columns 15 (N), 16 (O), 17 (F), and 18 (Ne) of the periodic table. For these 20 elements, we find that the two-body vdW potentials can all be mapped to a single universal two-body curve, with just three scaling parameters: Re, De, and L. We refer to this as the Universal NonBond (UNB) potential. We expect this to be useful for new MD simulations and a helpful starting point to obtain UNB parameters for the remainder of the periodic table.

Chemistry↗

DOE OSTI2023

Externally Heated Diamond ANvil Cell Experimentation (EH-DANCE) for studying materials and processes under extreme conditions

Externally heated diamond anvil cells provide a stable and uniform thermal environment, making them a versatile device to simultaneously generate high-pressure and high-temperature conditions in various fields of research, such as condensed matter physics, materials science, chemistry, and geosciences. The present study features the Externally Heated Diamond ANvil Cell Experimentation (EH-DANCE) system, a versatile configuration consisting of a diamond anvil cell with a customized microheater for stable resistive heating, bidirectional pressure control facilitated by compression and decompression membranes, and a water-cooled enclosure suitable for vacuum and controlled atmospheres. This integrated system excels with its precise control of both pressure and temperature for mineral and materials science research under extreme conditions. Here, we showcase the capabilities of the system through its successful application in the investigation of the melting temperature and thermal equation of state of high-pressure ice-VII at temperatures up to 1400 K. The system was also used to measure the elastic properties of solid ice-VII and liquid H 2 O using Brillouin scattering and Raman spectra of carbonates using Raman spectroscopy, highlighting the potential of the EH-DANCE system in high-pressure research.

Instruments & Instrumentation↗

DOE OSTI2024

Sound speed determination in copper shock compressed to 190 GPa

Sound speed measurements in shock compressed solids have long been valuable for the development of equations of state at extreme conditions, shock-induced phase transformations, and a comprehensive characterization of the thermophysical response of high-pressure standards. We present results from plate impact experiments to 190 GPa to determine the longitudinal sound speed in copper—an important high-pressure standard. Surprisingly, the sound speeds determined using the two most common experimental techniques—the front surface impact (FSI) approach and the release wave overtake (RWO) approach—diverge significantly for stresses greater than ~100 GPa. Further analyses, including numerical simulations, show that the FSI experiments provide the correct sound speeds and that fundamental assumptions underlying the RWO method are likely violated due to the complex release response of shock compressed copper. The sound speeds determined using the FSI approach provide for a more accurate high-pressure description of copper in dynamic compression experiments. The present findings are in contrast to the results for shock compressed silver [Wallace et al., Phys. Rev. B 104, 214106 (2021)], where both methods provided consistent sound speed results. Thus, the findings presented here demonstrate the need to experimentally verify the validity of the RWO method on a case-by-case basis. Finally, we note that even at the high stresses in the present work, the copper unloading response shows a time-dependent, quasielastic response often observed in metals at lower stresses.

36 MATERIALS SCIENCE↗

DOE OSTI2024

Study of ablation and shock generation across three orders of magnitude of laser intensity with 100 ps laser pulses

The laser ablation and subsequent shock generation in solid targets plays an important role in a variety of research topics from equation of state models for materials to inertial confinement fusion. One of the long-standing issues is the knowledge of ablation depth in the picosecond time regime. Here, we report on a direct technique for determining the ablation depth in aluminum using x-ray diffraction data from Linac Coherent Light Source at the Stanford Linear Accelerator Center. This technique gives a direct measurement of the shock wave propagation in the bulk target, enabling an ability to discern early timescale physics from late timescale effects not available in postmortem analysis. We find that the ablation depths only vary by 0.2 μm across three orders of magnitude of laser intensity, while the pressure increased by a factor of 10 following a square root dependence on laser pulse energy. We further observe that the ablation depth in this intensity range (10 11 –10 13 W/cm 2 in intensity, corresponding to 0.8–80 J/cm 2 in fluence) cannot be modeled by a universal scaling law, given the complexity of the mechanisms governing laser ablation in this intensity regime.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2025

Fluid-like shock compression of dilute polymer nanocomposites

The shock Hugoniot of heterogenous mixtures of discrete particles has been experimentally investigated for porous agglomerates and fluids, while the study of full-density solids has been primarily limited to compressed powders and high-dimensional composites. By dispersing ceria nanoparticles in a polyethylene matrix, we are able to examine the hydrodynamic behavior of a nonporous, heterogenous solid in thermal equilibrium during weak shock compression. Phase-driven discontinuities in the Hugoniot particle velocity–shock velocity (u−D) relationship of pure polyethylene are replicated in the nanocomposites but are shifted to lower velocity and to higher pressure with higher particle concentration. The results are explained using an isothermal, two-velocity fluid model under the hydrodynamic approximation. The model, which assumes a theoretical equation-of-state for ceria and either a low-order or high-order fit to the measured polyethylene Hugoniot, reasonably predicts the Hugoniot for two different polyethylene/ceria nanocomposites. Using the model, the mixture Hugoniot is shown to be insensitive to the Hugoniot of the stiffer constituent when the moduli are sufficiently disparate, while dependence on particle density and volume fraction is preserved through fluid-like motion.

Moore, Nathan W. [Sandia National Laboratories (SN↗

DOE OSTI2025

Continuum shock mixture models for Ni+Al multilayers: Inert mesoscale simulations

Mesoscale modeling of shock waves in Ni+Al multilayers poses significant challenges that are due, in part, to shock-induced chemical reactions. Current modeling approaches utilize reactive molecular dynamics (MD), but they are limited to resolving domains of only a few hundred nanometers. In contrast, actual multilayer superlattices can be tens of micrometers thick, and they exhibit non-ideal (i.e., wavy) interfaces. The second part of our research builds upon previous work developing physically based, thermodynamically complete equations of state for various Ni and Al intermetallic compositions. Here, we introduce a novel workflow for high-fidelity mesoscale simulations of Ni+Al multilayers using a continuum hydrocode. By increasing the simulation domain size beyond MD limitations (e.g., 2 × 6 μm 2 ) and incorporating explicit interfacial roughness, we investigate the shock response of Ni+Al multilayers at previously unexplored scales. Our experimental design encompasses nine multilayer geometries with varying roughness amplitudes and tilt angles (θ = 15°, 30°, and 45°), alongside 19 flyer impact velocities ranging from 0.3 to 3.0 km/s, resulting in a total of 171 high-fidelity simulations. The bulk shock state from inert 2D mesoscale simulations aligns with the law of mixtures, while temperature and pressure fluctuations strongly correlate with multilayer geometry types. A new metric dubbed the “hot spot probability integral” shows a greater dependence on a tilt angle than interfacial roughness.

Kittell, David E. [Sandia National Laboratories (S↗

DOE OSTI2026

Accessing terapascal pressures on two-stage light-gas guns for high-energy-density research

We present pressure amplifiers that have been developed to enable the study of material behavior at terapascal (TPa) pressures using two-stage light-gas gun (2SLGG) facilities. When impacted by a hyper-velocity projectile, Mach reflections within the pressure amplifier eventually merge to form a Mach stem, generating a planar output shock that greatly exceeds the initial drive. Validation experiments demonstrated that peak pressures of 0.6 and 1.073 TPa were achieved in quartz samples for two different amplifier designs. These pressures represent an approximately fivefold increase over the sample pressures typically attainable at 2SLGG facilities. The temporal and spatial uniformity of the pressure drive is suitable for high-precision equation-of-state measurements of materials relative to a shock standard. This work greatly extends the capabilities of 2SLGG facilities and opens new avenues of study in high-energy-density physics using these drivers.

Gorman, Martin G. [First Light Fusion, Oxford (Uni↗

DOE OSTI2025

Shear strength of a refractory high entropy alloy MoNbTaVW under high pressure

Radial X-ray diffraction (R-XRD) was performed in situ using a Panoramic Diamond Anvil Cell on the refractory high entropy alloy MoNbTaVW. The lattice parameters were determined through a Le Bail fit using a body centered cubic (BCC) lattice of symmetry $Im$$\overline{3}$$m$ (international space group number 229). Upper and lower bounds to the shear strength were determined up to 80 GPa nonhydrostatically using copper as a pressure standard. The equation of state was derived at the magic angle ψ = 54.7° and yielded a bulk modulus of K 0 = 220.8 ± 1.65 GPa. The experimental lattice parameters and bulk modulus match closely with corresponding density functional theory (DFT) calculations. The BCC phase remains stable up to the highest pressure of 80 GPa studied and is shown to be elastically anisotropic. The shear strength was found to saturate around 70 GPa with a value of τ = 1.75 GPa, and the shear moduli are presented in different limits of iso-strain and iso-stress.

36 MATERIALS SCIENCE↗

DOE OSTI2026

Enabling accurate chemical modeling of shocked energetic materials using a machine learning interatomic potential

Understanding the complex chemistry of organic materials under dynamic compression is important for many applications, but it is challenging due to the large number of reactions occurring at various time scales. Here, in this study, we develop a machine learning potential based on Chebyshev polynomials to study the insensitive energetic material 1,3,5-triamino-2,4,6-trinitrobenzene (TATB) under detonation. We discuss a strategy for constructing diverse training data needed to capture the complex chemistry of TATB. Our potential demonstrates strong transferability across a wide range of thermodynamic conditions and other explosives, enabling accurate and reliable chemical modeling of organic materials under extreme conditions. The efficiency of our approach allows for simulations over several nanoseconds and for large system sizes, providing detailed insights into the chemistry of shocked TATB. The model accurately reproduces experimental Hugoniot equation of state data, and our simulations reveal the rapid formation of nitrogen-rich carbon clusters following shock. The methods and datasets developed here offer a robust framework for accurate chemical modeling of other shocked organic energetic materials.

Chemistry↗

DOE OSTI2026

Experimental shock Hugoniot and melt boundary temperatures of aluminum

Aluminum is a ubiquitous component in dynamic compression, pulsed power, and other high energy density physics studies. Its high-pressure behavior and phase diagram are extensively studied standards in shockwave physics. While theoretical calculations and multiphase equations of state have been benchmarked to velocity measurements of loading and unloading waves, pressure and density under shock, and other mechanical data, experimental temperature data under these conditions have not been reported. We conducted a series of experiments shocking and releasing aluminum 6061 and 1100 samples into lithium fluoride windows. We measured temperature at the sample–window interface under steady compression and subsequent isentropic release. These results allow us to constrain the temperature of the solid Hugoniot and the boundary between the liquid and face-centered cubic solid phases.

Hartsfield, Thomas Murray [Sandia National Laborat↗

DOE OSTI2026

Investigating shock-induced chemical reactions in Ni+Al multilayers: A continuum-based mesoscale approach with Arrhenius kinetics and artificial thermal conduction

A new continuum-based mesoscale modeling approach for shock-induced chemical reactions (SICRs) in Ni+Al multilayers is demonstrated in Sandia’s shock physics hydrocode, CTH. The approach utilizes Arrhenius-type kinetics and artificial thermal conduction. Our work builds upon previous efforts to parameterize equations of state for Ni x Al y [J. Appl. Phys. 137, 075102 (2025)], as well as simulations of inert shocks in realistic 2D microstructures [J. Appl. Phys. 137, 225301 (2025)]. To calibrate the reaction kinetics, pairs of the reaction coordinate, R′, vs time are extracted from the molecular dynamics (MD) literature. Here, the MD-informed kinetics are used to simulate the dynamic evolution of pressure and temperature in 2D mesoscale simulations. Overall, the MD-informed kinetics obtained for planar interfaces are too slow, as initial reaction is not observed on a nanosecond time scale. Even with quasi-periodic shock focusing leading to the formation of so-called “hot-spots,” the hot spots are unable to grow and coalesce using the fitted Arrhenius rate constants. However, by increasing the rate constants by two orders of magnitude, SICRs are observed at a shock pressure near 30 GPa, which is supported by experiments. Consequently, these mesoscale simulations suggest that unresolved shear-based mechanical mixing might possibly account for the discrepancies in kinetic rates, with shock-generated intense perturbations, interfacial vortical flows, and elevated temperatures serving as favorable reaction conditions. Future work will calibrate a shear-dependent reaction rate from the MD simulations with realistic interfaces that are wavy, diffuse, and disordered.

Kittell, David E. [Sandia National Laboratories (S↗

DOE OSTI2026

Energy-conserving contact dynamics of nonspherical rigid-body particles

Understanding the contact dynamics of nonspherical particles is crucial for accurately modeling colloidal and granular systems where shape anisotropy dictates structural organization and transport properties. We here introduce an energy-conserving contact dynamics framework for arbitrary convex rigid-body particles by implementing vertex–boundary interactions in 2D and vertex–surface and edge–edge detection in 3D. The established formulation enables continuous force evaluation and prevents particle overlap while conserving total energy during translational and rotational motion. We demonstrate the framework’s stability and its utility to capture packing behavior, anisotropic diffusion, and equations of state of polygonal and polyhedral particles as examples. The framework establishes a robust and extensible foundation for investigating nonequilibrium dynamics of complex nonspherical particulate systems, enabling enhanced understanding of phenomena across spatiotemporal scales in self- and directed-assembly, granular flows, and hydrodynamics, potentially coupled with interactions that represent underlying physical mechanisms.

Discrete element method↗

DOE OSTI2021

Experimental test of a predicted dynamics–structure–thermodynamics connection in molecularly complex glass-forming liquids

Significance The physical origin of cooperative activated relaxation in glass-forming liquids, which underlies the huge growth of viscosity and suppression of diffusion with cooling, remains elusive. Understanding this problem is of fundamental scientific interest and can assist in the design of new materials. We combine experimental relaxation time and equation-of-state data of molecular liquids to provide strong evidence for the recent theoretical prediction that activated relaxation, though causally driven by dynamically coupled cage-scale hopping and nonlocal collective elasticity quantified by local structural correlations, is well captured based on a thermodynamic description with dimensionless compressibility as the key variable. A mechanistic deduction is the crossover from fragile to strong (e.g., inorganic networks) relaxation behavior arises from the irrelevance of long-range elasticity effects.

36 MATERIALS SCIENCE↗

DOE OSTI2023

Scientific machine learning for modeling and simulating complex fluids

The formulation of rheological constitutive equations—models that relate internal stresses and deformations in complex fluids—is a critical step in the engineering of systems involving soft materials. While data-driven models provide accessible alternatives to expensive first-principles models and less accurate empirical models in many engineering disciplines, the development of similar models for complex fluids has lagged. The diversity of techniques for characterizing non-Newtonian fluid dynamics creates a challenge for classical machine learning approaches, which require uniformly structured training data. Consequently, early machine-learning based constitutive equations have not been portable between different deformation protocols or mechanical observables. Here, we present a data-driven framework that resolves such issues, allowing rheologists to construct learnable models that incorporate essential physical information, while remaining agnostic to details regarding particular experimental protocols or flow kinematics. These scientific machine learning models incorporate a universal approximator within a materially objective tensorial constitutive framework. By construction, these models respect physical constraints, such as frame-invariance and tensor symmetry, required by continuum mechanics. We demonstrate that this framework facilitates the rapid discovery of accurate constitutive equations from limited data and that the learned models may be used to describe more kinematically complex flows. This inherent flexibility admits the application of these “digital fluid twins” to a range of material systems and engineering problems. We illustrate this flexibility by deploying a trained model within a multidimensional computational fluid dynamics simulation—a task that is not achievable using any previously developed data-driven rheological equation of state.

Science & Technology - Other Topics↗

DOE OSTI2022

High pressure structural phase transitions in Dysprosium to 202 GPa

High pressure structural phase transitions in heavy lanthanide metal Dysprosium (Dy) have been studied to 202 GPa (Volume Compression V/V 0 = 0.36) in a diamond anvil cell employing copper as an internal x-ray pressure standard. The previously assigned monoclinic (C2/m) phase above 72 GPa has been reexamined and assigned to an orthorhombic phase with sixteen atoms per cell (oF16) based on structural refinements. The equation of state is presented to 202 GPa and indicates a volume change of 2.3% during the structural phase transition from distorted face-centered cubic (hR24) phase to oF16 phase at 72 GPa. The oF16 phase can be regarded as a pseudo-orthorhombic eight-layered structure with (b/c) ratio decreasing from an ideal value of $\sqrt{3}$ with increasing pressure to 202 GPa. The ultrahigh pressure structural phases of Dy are compared with other members of the lanthanide series.

36 MATERIALS SCIENCE↗