Sapphire (Al2O3) is a major constituent of the Earth's mantle and has significant contributions to the field of high-pressure physics. Constraining its Hugoniot over a wide pressure range and identifying the location of shock-driven phase transitions allows for development of a multiphase equation of state and enables its use as an impedance-matching standard in shock physics experiments. In this paper we present measurements of the principal Hugoniot and sound velocity from direct impact experiments using magnetically launched flyers on the Z machine at Sandia National Laboratories. The Hugoniot was constrained for pressures from 0.2–2.1 TPa and a four-segment piecewise linear shock-velocity–particle-velocity fit was determined. First-principles molecular dynamics simulations were conducted and agree well with the experimental Hugoniot. Sound-speed measurements identified the onset of melt between 450 and 530 GPa, and the Hugoniot fit refined the onset to 525 ± 13 GPa. A phase diagram which incorporates literature diamond-anvil cell data and melting measurements is presented.
Fully characterizing high energy density (HED) phenomena using pulsed power facilities (Z machine) and coherent light sources is possible only with complementary numerical modeling for design, diagnostic development, and data interpretation. The exercise of creating numerical tests, that match experimental conditions, builds critical insight that is crucial for the development of a strong fundamental understanding of the physics behind HED phenomena and for the design of next generation pulsed power facilities. The persistence of electron correlation in HED materials arising from Coulomb interactions and the Pauli exclusion principle is one of the greatest challenges for accurate numerical modeling and has hitherto impeded our ability to model HED phenomena across multiple length and time scales at sufficient accuracy. An exemplar is a ferromagnetic material like iron, while familiar and widely used, we lack a simulation capability to characterize the interplay of structure and magnetic effects that govern material strength, kinetics of phase transitions and other transport properties. Herein we construct and demonstrate the Molecular-Spin Dynamics (MSD) simulation capability for iron from ambient to earth core conditions, all software advances are open source and presently available for broad usage. These methods are multi-scale in nature, direct comparisons between high fidelity density functional theory (DFT) and linear-scaling MSD simulations is done throughout this work, with advancements made to MSD allowing for electronic structure changes being reflected in classical dynamics. Main takeaways for the project include insight into the role of magnetic spins on mechanical properties and thermal conductivity, development of accurate interatomic potentials paired with spin Hamiltonians, and characterization of the high pressure melt boundary that is of critical importance to planetary modeling efforts.
Two-dimensional electromagnetic (EM) particle-in-cell (PIC) simulations of a radial magnetically-insulated-transmission-line are presented and compared to the model of E. M. Waisman, M. P. Desjarlais, and M. E. Cuneo [Phys. Rev. Accel. Beams 22, 030402 (2019) in the “high-enhancement” (WDC-HE) limit. The simulations use quasi-equilibrium current and voltage values based on the Sandia National Laboratories Z accelerator, with prescribed injection of an electron sheath that gives electron density profiles qualitatively similar to those used in the WDC-HE model. We find that the WDC-HE model accurately predicts the quasiequilibrium ion current losses in the EM PIC simulations for a wide range of current and voltage values. For the case of two ion species where one is magnetically insulated by the ambient magnetic field and the other is not, the charge of the lighter insulated species in the anode-cathode gap can modify the electric field profile, reducing the ion current density enhancement for the heavier ion species. On the other hand, for multiple ion species, when the lighter ions are not magnetically insulated and are a significant fraction of the anode plasma, they dominate the current loss, producing loss currents which are a significant fraction of the lighter ion WDC values. The observation of this effect in the present work is new to the field and may significantly impact the analysis of ion current losses in the Z machine inner MITL and convolute.
Compression-induced solidification has been observed in cerium on nanosecond timescales. A series of experiments was conducted in Sandia National Laboratories' Z Facility in which cerium was shock melted and subsequently shocklessly, or ramp, loaded across the melt line inducing solidification. The signature of solidification manifested in the recovery of material strength and the propagation of waves at the local elastic sound velocity. Density functional theory simulations of cerium along the experimental phase-space path exhibit spontaneous freezing to a tetragonal phase at the same pressure and closely predict the observed physical properties of solid and liquid cerium near melt.
Recent dynamic compression experiments [M. D. Knudson et al., Science 348, 1455 (2015); P. M. Celliers et al., Science 361, 677 (2018)] have observed the insulator-metal transition in dense liquid deuterium, but with an approximately 95-GPa difference in the quoted pressures for the transition at comparable estimated temperatures. It was claimed in the latter of these two papers that a very large latent heat effect on the temperature was overlooked in the first, requiring correction of those temperatures downward by a factor of 2, thereby putting both experiments on the same theoretical phase boundary and reconciling the pressure discrepancy. We have performed extensive path-integral molecular dynamics calculations with density functional theory to directly calculate the isentropic temperature drop due to latent heat in the insulator-metal transition for dense liquid deuterium and show that this large temperature drop is not consistent with the underlying thermodynamics.
Bailly-Grandvaux, M.; Kim, J.; Krauland, C.M.; Zhang, S.; Dozieres, M.; Wei, M.S.; Theobald, W.; Grabowski, P.E.; Santos, J.J.; Nicolai, Ph; Mckenna, P.; Desjarlais, Michael P.; Beg, F.N.
We report experimental results on relativistic electron beam (REB) transport in a set of cold and shock-heated carbon samples using the high-intensity kilojoule-class OMEGA EP laser. The REB energy distribution and transport were diagnosed using an electron spectrometer and X-ray fluorescence measurements from a Cu tracer buried at the rear side of the samples. The measured rear REB density shows brighter and narrower signals when the targets were shock-heated. Hybrid PIC simulations using advanced resistivity models in the target warm-dense-matter (WDM) conditions confirm this observation. We show that the resistivity response of the media, which governs the self-generated resistive fields, is of paramount importance to understand and correctly predict the REB transport.
Magnetically launched flyer plates were used to investigate the shock response of beryllium between 90 and 300 GPa. Solid aluminum flyer plates drove steady shocks into polycrystalline beryllium to constrain the Hugoniot from 90 to 190 GPa. Multilayered copper/aluminum flyer plates generated a shock followed by an overtaking rarefaction which was used to determine the sound velocity in both solid and liquid beryllium between 130 and 300 GPa. Disappearance of the longitudinal wave was used to identify the onset of melt along the Hugoniot and measurements were compared to density functional theory calculations to explore the proposed hcp-bcc transition at high pressure. The onset of melt along the Hugoniot was identified at ∼205GPa, which is in good agreement with theoretical predictions. These results show no clear indication of an hcp-bcc transition prior to melt along the beryllium Hugoniot. Rather, the shear stress, determined from the release wave profiles, was found to gradually decrease with stress and eventually vanish at the onset of melt.
Outstanding problems in the high-pressure phase diagram of hydrogen have demonstrated the need for more accurate ab initio methods for thermodynamic sampling. One promising method that has been deployed extensively above 100 GPa is coupled electron-ion Monte Carlo (CEIMC), which treats the electronic structure with quantum Monte Carlo (QMC). However, CEIMC predictions of the deuterium principal Hugoniot disagree significantly with experiment, overshooting the experimentally determined peak compression density by 7% and lower temperature gas-gun data by well over 20%. By deriving an equation relating the predicted Hugoniot density to underlying equation of state errors, we show that QMC and many-body methods can easily spoil the error cancellation properties inherent in the Rankine-Hugoniot relation, and very likely suffer from error addition. By cross validating QMC based on systematically improvable trial functions against post-Hartree-Fock many-body methods, we find that these methods introduce errors of the right sign and magnitude to account for much of the observed discrepancy between CEIMC and experiment. We stress that this is not just a CEIMC problem, but that thermodynamic sampling based on other many-body methods is likely to experience similar difficulties.
Celliers et al. (Reports, 17 August 2018, p. 677), in an attempt to reconcile differences in inferred metallization pressures, provide an alternative temperature analysis of the Knudson et al. experiments (Reports, 26 June 2015, p. 1455). We show here that this reanalysis implies an anomalously low specific heat for the metallic fluid that is clearly inconsistent with first-principles calculations.
We introduce a 1D planar static model to elucidate the underlying mechanism of large ion current losses in the vacuum convolute and the inner magnetically insulated transmission line (MITL) of the Z machine. We consider E×B electron flow, parallel to the electrodes, and ion motion across the vacuum gap, for given voltage V, gap distance d, anode magnetic field Ba, and vacuum electron current ΔI. This model has been introduced and solved before by Desjarlais [Phys. Rev. Lett. 59, 2295 (1987)PRLTAO0031-900710.1103/PhysRevLett.59.2295] for the applied magnetic field ion diode. Here we apply it to convolute and inner MITL ion losses of Z, relaxing the fix magnetic flux condition of that reference. In the absence of ions we show that the electron vacuum flow must be close to the anode if its current exceeds the value given by the local flow impedance, implying high electric fields there. We then introduce space charge limited ion emission from the anode, neglecting the magnetic force on ions. We obtain the solution of the steady state equations for two special cases: (a) when both the electric potential and the electric field are zero inside the gap, and there is a layer of electrons not carrying current that neutralizes the ion charge between the virtual and the electrode cathode, making that region electric field free, and (b) when the electric field is zero inside the gap, but the potential is not, and zero electron charge between that point and the physical cathode. For case (a) we obtain an ion current density which we conjecture is the maximum attainable for any electron charge distribution in the electron current carrying layer, given V,d,Ba,ΔI an ion species. We obtain the enhancement factor for both cases with respect to the ion-only Child-Langmuir ion current density, and show that it can be significantly larger than that of the electron saturated flow case. Furthermore, imposing electron current conservation as the flow enters the inner MITL from the four outer MITLs, we recover the well-known dependence jion∼V3/2/d2, where voltage and gap are taken near the joining point of those outer MITLs. The implications and limitations of the proposed model are discussed.
Ab intio molecular dynamics simulations show that the electrical conductivity of liquid SiO2 is semimetallic at the conditions of the deep molten mantle of early Earth and super-Earths, raising the possibility of silicate dynamos in these bodies. Whereas the electrical conductivity increases uniformly with increasing temperature, it depends nonmonotonically on compression. At very high pressure, the electrical conductivity decreases on compression, opposite to the behavior of many materials. We show that this behavior is caused by a novel compression mechanism: the development of broken charge ordering, and its influence on the electronic band gap.
In recent years, α-quartz has been used prolifically as an impedance matching standard in shock wave experiments in the multi-Mbar regime (1 Mbar = 100 GPa = 0.1 TPa). This is due to the fact that above ∼90-100 GPa along the principal Hugoniot α-quartz becomes reflective, and thus, shock velocities can be measured to high precision using velocity interferometry. The Hugoniot and release of α-quartz have been studied extensively, enabling the development of an analytical release model for use in impedance matching. However, this analytical release model has only been validated over a range of 300-1200 GPa (0.3-1.2 TPa). Here, we extend this analytical model to 200-3000 GPa (0.2-3 TPa) through additional α-quartz Hugoniot and release measurements, as well as first-principles molecular dynamics calculations.
Materials in nuclear and conventional weapons can reach multi-megabar pressures and 1000s of degree temperatures on timescales ranging from microseconds to nanoseconds. Understanding the response of complex materials under these conditions is important for designing and assessing changes to nuclear weapons. In the next few decades, a major concern will be evaluating the behavior of aging materials and remanufactured components. The science to enable the program to underwrite decisions quickly and confidently on use, remanufacturing, and replacement of these materials will be critical to NNSA’s new Stockpile Responsiveness Program. Material response is also important for assessing the risks posed by adversaries or proliferants. Dynamic materials research, which refers to the use of high-speed experiments to produce extreme conditions in matter, is an important part of NNSA’s Stockpile Stewardship Program.
Desjarlais, Michael P.; Scullard, Christian R.; Benedict, Lorin X.; Whitley, Heather D.; Redmer, Ronald
We compute electrical and thermal conductivities of hydrogen plasmas in the nondegenerate regime using Kohn-Sham density functional theory (DFT) and an application of the Kubo-Greenwood response formula, and demonstrate that for thermal conductivity, the mean-field treatment of the electron-electron (e-e) interaction therein is insufficient to reproduce the weak-coupling limit obtained by plasma kinetic theories. An explicit e-e scattering correction to the DFT is posited by appealing to Matthiessen's Rule and the results of our computations of conductivities with the quantum Lenard-Balescu (QLB) equation. Further motivation of our correction is provided by an argument arising from the Zubarev quantum kinetic theory approach. Significant emphasis is placed on our efforts to produce properly converged results for plasma transport using Kohn-Sham DFT, so that an accurate assessment of the importance and efficacy of our e-e scattering corrections to the thermal conductivity can be made.
Shock compression experiments in the few hundred GPa (multi-Mbar) regime were performed on Lithium Deuteride single crystals. This study utilized the high velocity flyer plate capability of the Sandia Z Machine to perform impact experiments at flyer plate velocities in the range of 17-32 km/s. Measurements included pressure, density, and temperature between ∼190 and 570 GPa along the Principal Hugoniot - the locus of end states achievable through compression by large amplitude shock waves - as well as pressure and density of reshock states up to ∼920 GPa. The experimental measurements are compared with density functional theory calculations, tabular equation of state models, and legacy nuclear driven results that have been reanalyzed using modern equations of state for the shock wave standards used in the experiments.
1- and 2-D simulations of 1-cm radius, gas-puff liners of Ne, Ar, Kr, and Xe imploding onto a deuterium target are conducted using the discharge parameters for the Zebra (1 MA, 130 ns) driver using the resistive MHD code MACH2. This is an implementation of the Staged Z-pinch concept, in which the target is driven to high-energy-density first by shock compression launched by a diffused azimuthal magnetic field ( J×B force), and then by the adiabatic compression as the liner converges on axis. During the run-in phase, the initial shock heating preheats the deuterium plasma, with a subsequent stable, adiabatic compression heating the target to high energy density. Shock compression of the target coincides with the development of a J×B force at the target/liner interface. Stronger B-field transport and earlier shock compression increases with higher-Z liners, which results in an earlier shock arrival on axis. Delayed shock formation in lower-Z liners yields a relative increase in shock heating, however, the 2-D simulations show an increased target isolation from magneto-Rayleigh-Taylor instability penetration, suggesting that an optimal balance between these two effects is reached in an Ar or Kr liner, rather than with Xe.
Accurate theoretical calculations of the nonlinear elastic response of strong solids (e.g., diamond) constitute a fundamental and important scientific need for understanding the response of such materials and for exploring the potential synthesis and design of novel solids. However, without corresponding experimental data, it is difficult to select between predictions from different theoretical methods. Recently the complete set of third-order elastic constants (TOECs) for diamond was determined experimentally, and the validity of various theoretical approaches to calculate the same may now be assessed. We report on the use of density functional theory (DFT) methods to calculate the six third-order elastic constants of diamond. Two different approaches based on homogeneous deformations were used: (1) an energy-strain fitting approach using a prescribed set of deformations, and (2) a longitudinal stress-strain fitting approach using uniaxial compressive strains along the [100], [110], and [111] directions, together with calculated pressure derivatives of the second-order elastic constants. The latter approach provides a direct comparison to the experimental results. The TOECs calculated using the energy-strain approach differ significantly from the measured TOECs. In contrast, calculations using the longitudinal stress-uniaxial strain approach show good agreement with the measured TOECs and match the experimental values significantly better than the TOECs reported in previous theoretical studies. Our results on diamond have demonstrated that, with proper analysis procedures, first-principles calculations can indeed be used to accurately calculate the TOECs of strong solids.
Experiments on the Sandia Z pulsed-power accelerator have demonstrated the ability to produce warm dense matter (WDM) states with unprecedented uniformity, duration, and size, which are ideal for investigations of fundamental WDM properties. For the first time, space-resolved x-ray Thomson scattering (XRTS) spectra from shocked carbon foams were recorded on Z. The large (>20 MA) electrical current produced by Z was used to launch Al flyer plates up to 25 km/s. The impact of the flyer plate on a CH2 foam target produced a shocked state with an estimated pressure of 0.75 Mbar, density of 0.52 g/cm3, and temperature of 4.3 eV. Both unshocked and shocked portions of the foam target were probed with 6.2 keV x-rays produced by focusing the Z-Beamlet laser onto a nearby Mn foil. The data are composed of three spatially distinct spectra that were simultaneously captured with a single spectrometer with high spectral (4.8 eV) and spatial (190 μm) resolutions. Detailed spectral information from three target locations is provided simultaneously: the incident x-ray source, the scattered signal from unshocked foam, and the scattered signal from shocked foam.
We construct thermodynamic potentials for two superionic phases of water [with body-centered cubic (bcc) and face-centered cubic (fcc) oxygen lattice] using a combination of density functional theory (DFT) and molecular dynamics simulations (MD). For this purpose, a generic expression for the free energy of warm dense matter is developed and parametrized with equation of state data from the DFT-MD simulations. A second central aspect is the accurate determination of the entropy, which is done using an approximate two-phase method based on the frequency spectra of the nuclear motion. The boundary between the bcc superionic phase and the ices VII and X calculated with thermodynamic potentials from DFT-MD is consistent with that directly derived from the simulations. As a result, differences in the physical properties of the bcc and fcc superionic phases and their impact on interior modeling of water-rich giant planets are discussed.
The moon-forming impact and the subsequent evolution of the proto-Earth is strongly dependent on the properties of materials at the extreme conditions generated by this violent collision. We examine the high pressure behavior of MgO, one of the dominant constituents in Earth's mantle, using high-precision, plate impact shock compression experiments performed on Sandia National Laboratories' Z Machine and extensive quantum calculations using density functional theory (DFT) and quantum Monte Carlo (QMC) methods. The combined data span from ambient conditions to 1.2 TPa and 42 000 K, showing solid-solid and solid-liquid phase boundaries. Furthermore our results indicate that under impact the solid and liquid phases coexist for more than 100 GPa, pushing complete melting to pressures in excess of 600 GPa. The high pressure required for complete shock melting has implications for a broad range of planetary collision events.
Aluminum has been used prolifically as an impedance matching standard in the multimegabar regime (1 Mbar = 100 GPa), particularly in nuclear driven, early laser driven, and early magnetically driven flyer plate experiments. The accuracy of these impedance matching measurements depends upon the knowledge of both the Hugoniot and release or reshock response of aluminum. Here, we present the results of several adiabatic release measurements of aluminum from ∼400-1200 GPa states along the principal Hugoniot using full density polymethylpentene (commonly known as TPX), and both ∼190 and ∼110 mg/cc silica aerogel standards. These data were analyzed within the framework of a simple, analytical model that was motivated by a first-principles molecular dynamics investigation into the release response of aluminum, as well as by a survey of the release response determined from several tabular equations of state for aluminum. Combined, this theoretical and experimental study provides a method to perform impedance matching calculations without the need to appeal to any tabular equation of state for aluminum. As an analytical model, this method allows for propagation of all uncertainty, including the random measurement uncertainties and the systematic uncertainties of the Hugoniot and release response of aluminum. This work establishes aluminum for use as a high-precision standard for impedance matching in the multimegabar regime.
Motivated by the disagreement between recent diffusion Monte Carlo calculations of the phase transition pressure between the ambient and beta-Sn phases of silicon and experiments, we present a study of the HCP to BCC phase transition in beryllium. This lighter element provides an opportunity for directly testing many of the approximations required for calculations on silicon and may suggest a path towards increasing the practical accuracy of diffusion Monte Carlo calculations of solids in general. We demonstrate that the single largest approximation in these calculations is the pseudopotential approximation and after removing this we find excellent agreement with experiment for the ambient HCP phase and results similar to careful calculations using density functional theory for the phase transition pressure.
Whitley, Heather D.; Scullard, Christian R.; Benedict, Lorin X.; Castor, John I.; Randles, Amanda; Glosli, James N.; Richards, David F.; Desjarlais, Michael P.; Graziani, Frank R.
Here we present a discussion of kinetic theory treatments of linear electrical and thermal transport in hydrogen plasmas, for a regime of interest to inertial confinement fusion applications. In order to assess the accuracy of one of the more involved of these approaches, classical Lenard-Balescu theory, we perform classical molecular dynamics simulations of hydrogen plasmas using 2-body quantum statistical potentials and compute both electrical and thermal conductivity from our particle trajectories using the Kubo approach. Our classical Lenard-Balescu results employing the identical statistical potentials agree well with the simulations. Comparison between quantum Lenard-Balescu and classical Lenard-Balescu for conductivities then allows us to both validate and critique the use of various statistical potentials for the prediction of plasma transport properties. Lastly, these findings complement our earlier MD/kinetic theory work on temperature equilibration, and reach similar conclusions as to which forms of statistical potentials best reproduce true quantum behavior.
We present an improved first-principles description of melting under pressure based on thermodynamic integration comparing density functional theory (DFT) and quantum Monte Carlo (QMC) treatments. The method is applied to address the longstanding discrepancy between DFT calculations and diamond anvil cell (DAC) experiments on the melting curve of xenon, a noble gas solid where van der Waals binding is challenging for traditional DFT methods. The calculations show agreement with data below 20 GPa and that the high-pressure melt curve is well described by a Lindemann behavior up to at least 80 GPa, in contrast to DAC data.
S hock compression exper iments in the few hundred GPa (multi - Mabr) regime were performed on Lithium Deuteride (LiD) single crystals . This study utilized the high velocity flyer plate capability of the Sandia Z Machine to perform impact experiments at flyer plate velocities in the range of 17 - 32 km/s. Measurements included pressure, density, and temperature between %7E200 - 600 GPa along the Principal Hugoniot - the locus of end states achievable through compression by large amplitude shock waves - as well as pressure and density of re - shock states up to %7E900 GPa . The experimental measurements are compared with recent density functional theory calculations as well as a new tabular equation of state developed at Los Alamos National Labs.
In recent years, DFT-MD has been shown to be a useful computational tool for exploring the properties of WDM. These calculations achieve excellent agreement with shock compression experiments, which probe the thermodynamic parameters of the Hugoniot state. New X-ray Thomson Scattering diagnostics promise to deliver independent measurements of electronic density and temperature, as well as structural information in shocked systems. However, they require the development of new levels of theory for computing the associated observables within a DFT framework. The experimentally observable x-ray scattering cross section is related to the electronic density-density response function, which is obtainable using TDDFT - a formally exact extension of conventional DFT that describes electron dynamics and excited states. In order to develop a capability for modeling XRTS data and, more generally, to establish a predictive capability for first principles simulations of matter in extreme conditions, real-time TDDFT with Ehrenfest dynamics has been implemented in an existing PAW code for DFT-MD calculations. The purpose of this report is to record implementation details and benchmarks as the project advances from software development to delivering novel scientific results. Results range from tests that establish the accuracy, efficiency, and scalability of our implementation, to calculations that are verified against accepted results in the literature. Aside from the primary XRTS goal, we identify other more general areas where this new capability will be useful, including stopping power calculations and electron-ion equilibration.
Density-functional theory calculations, ab-initio molecular dynamics, and the Kubo-Greenwood formula are applied to predict electrical conductivity in Ta2Ox (0 x 5) as a function of composition, phase, and temperature, where additional focus is given to various oxidation states of the O monovacancy (VOn; n=0,1+,2+). Our calculations of DC conductivity at 300K agree well with experimental measurements taken on Ta2Ox thin films and bulk Ta2O5 powder-sintered pellets, although simulation accuracy can be improved for the most insulating, stoichiometric compositions. Our conductivity calculations and further interrogation of the O-deficient Ta2O5 electronic structure provide further theoretical basis to substantiate VO0 as a donor dopant in Ta2O5 and other metal oxides. Furthermore, this dopant-like behavior appears specific to neutral VO cases in both Ta2O5 and TiO2 and was not observed in other oxidation states. This suggests that reduction and oxidation reactions may effectively act as donor activation and deactivation mechanisms, respectively, for VO0 in transition metal oxides.