This report is the final documentation for the one-year LDRD project 226360: Simulated X-ray Diffraction and Machine Learning for Optimizing Dynamic Experiment Analysis. As Sandia has successfully developed in-house X-ray diffraction tools for study of atomic structure in experiments, it has become increasingly important to develop computational analysis methods to support these experiments. When dynamically compressed lattices and orientations are not known a priori, the identification requires a cumbersome and sometimes intractable search of possible final states. These final states can include phase transition, deformation and mixed/evolving states. Our work consists of three parts: (1) development of an XRD simulation tool and use of traditional data science methods to match XRD patterns to experiments; (2) development of ML-based models capable of decomposing and identifying the lattice and orientation components of multicomponent experimental diffraction patterns; and (3) conducting experiments which showcase these new analysis tools in the study of phase transition mechanisms. Our target material has been cadmium sulfide, which exhibits complex orientation-dependent phase transformation mechanisms. In our current one-year LDRD, we have begun the analysis of high-quality c-axis CdS diffraction data from DCS and Thor experiments, which had until recently eluded orientation identification.
Abstract: Here, we report the high pressure phase and morphology behavior of ordered anatase titanium dioxide (TiO2) nanocrystal arrays. One-dimensional TiO2 nanorods and nanorices were synthesized and self-assembled into ordered mesostructures. Their phase and morphological transitions at both atomic scale and mesoscale under pressure were studied using in situ synchrotron wide- and small-angle x-ray scattering (WAXS and SAXS) techniques. At the atomic scale, synchrotron WAXS reveals a pressure-induced irreversible amorphization up to 35 GPa in both samples but with different onset pressures. On the mesoscale, no clear phase transformations were observed up to 20 GPa by synchrotron SAXS. Intriguingly, sintering of TiO2 nanorods at mesoscale into nano-squares or nano-rectangles, as well as nanorices into nanowires, were observed for the first time by transmission electron microscopy. Such pressure-induced nanoparticle phase-amorphization and morphological changes provide valuable insights for design and engineering structurally stable nanomaterials. Impact statement: The high pressure behavior of nanocrystals (NCs) continues to be of interest, as previous studies have demonstrated that an externally applied pressure can serve as an efficient tool to induce structural phase transitions of NC assemblies at both the atomic scale and mesoscale without altering any chemistry by manipulating NC interatomic and interparticle distances. In addition, the high pressure generated deviatoric stress has been proven to be able to force adjacent NCs to connect and fuse into new crystalline nanostructures. Although the atomic structural evolution of TiO2 NCs under pressure has been widely investigated in the past decades, open questions remain regarding the mesoscale phase transition and morphology of TiO2 NC assemblies as a function of pressure. Therefore, in this work, systemic high pressure experiments on ordered arrays of TiO2 nanorods and nanorices were conducted by employing wide/small angle x-ray scattering techniques. The sintering of TiO2 assemblies at mesoscale into various nanostructures under pressure were revealed by transmission electron microscopy. Overall, this high pressure work fills the current gap in research on the mesoscale phase behavior of TiO2 assemblies. The observed morphology tunability attained by applying pressure opens new pathways for engineering nanomaterials and optimizing their collective properties through mechanical compression stresses. Graphical abstract: [Figure not available: see fulltext.].
Pulsed-power generators using the magnetic loading technique are able to produce well-controlled continuous ramp compression of condensed matter for high-pressure equation-of-state studies. X-ray diffraction (XRD) data from dynamically compressed samples provide direct measurements of the elastic compression of the crystal lattice, onset of plastic flow, strength-strain rate dependence, structural phase transitions, and density of crystal defects such as dislocations. Here, we present a cost effective, compact X-ray source for XRD measurements on pulsed-power-driven ramp-loaded samples. This combination of magnetically-driven ramp compression of materials with single, short-pulse XRD diagnostic will be a powerful capability for the dynamic materials community. The success in fielding this new XRD diagnostic dramatically improves our predictive capability and understanding of rate-dependent behavior at or near phase transition. As Sandia plans the next-generation pulse-power driver platform, a key element needed to deliver new state-of-the-art experiments will be having the necessary diagnostic tools to probe new regimes and phenomena. These diagnostics need to be as versatile, compact, and portable as they are powerful. The development of a platform-independent XRD diagnostic gives Sandia researchers a new window to study the microstructure and phase dynamics of materials under load. This project has paved the way for phase transition research in a variety of materials with mission interest.
We describe recent efforts to improve our predictive modeling of rate-dependent behavior at, or near, a phase transition using molecular dynamics simulations. Cadmium sulfide (CdS) is a well-studied material that undergoes a solid-solid phase transition from wurtzite to rock salt structures between 3 and 9 GPa. Atomistic simulations are used to investigate the dominant transition mechanisms as a function of orientation, size and rate. We found that the final rock salt orientations were determined relative to the initial wurtzite orientation, and that these orientations were different for the two orientations and two pressure regimes studied. The CdS solid-solid phase transition is studied, for both a bulk single crystal and for polymer-encapsulated spherical nanoparticles of various sizes.
Recent dynamic compression experiments [M. D. Knudson, Science 348, 1455 (2015)10.1126/science.aaa7471; P. M. Celliers, Science 361, 677 (2018)10.1126/science.aat0970] 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.
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.
Measurement of the Hugoniot and sound velocity provides information on the bulk modulus and Grüneisen parameter of a material at extreme conditions. The capability to launch multilayered (copper/aluminum) flyer plates at velocities in excess of 20 km/s with the Sandia Z accelerator has enabled high-precision sound-velocity measurements at previously inaccessible pressures. For these experiments, the sound velocity of the copper flyer must be accurately known in the multi-Mbar regime. Here we describe the development of copper as an absolutely calibrated sound-velocity standard for high-precision measurements at pressures in excess of 400 GPa. Using multilayered flyer plates, we performed absolute measurements of the Hugoniot and sound velocity of copper for pressures from 500 to 1200 GPa. These measurements enabled the determination of the Grüneisen parameter for dense liquid copper, clearly showing a density dependence above the melt transition. Combined with earlier data at lower pressures, these results constrain the sound velocity as a function of pressure, enabling the use of copper as a Hugoniot and sound-velocity standard for pressures up to 1200 GPa.
Measurement of the window interface velocity is a common technique for investigating the dynamic response materials at high strain rates. However, these measurements are limited in pressure to the range where the window remains transparent. The most common window material for this application is lithium fluoride, which under single shock compression becomes opaque at ∼200 GPa. To date, no other window material has been identified for use at higher pressures. Here, we present a Lagrangian technique to calculate the interface velocity from a continuously measured shock velocity, with application to quartz. The quartz shock front becomes reflective upon melt, at ∼100 GPa, enabling the use of velocity interferometry to continuously measure the shock velocity. This technique overlaps with the range of pressures accessible with LiF windows and extends the region where wave profile measurements are possible to pressures in excess of 2000 GPa. We show through simulated data that the technique accurately reproduces the interface velocity within 20% of the initial state, and that the Lagrangian technique represents a significant improvement over a simple linear approximation.
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.
Sandia's Z Machine has been used to magnetically drive shockless compression of materials in a planar configuration to multi-megabar pressure levels, allowing accurate measurements of quasi-isentropic mechanical response at relatively low temperatures in the solid phase. This paper details recent improvements to design and analysis of such experiments, including the use of new data on the mechanical and optical response of lithium fluoride windows. Comparison of windowed and free-surface data on copper to 350 GPa lends confidence to the window correction method. Preliminary results are presented on gold to 500 GPa and platinum to 450 GPa; both appear stiffer than existing models.
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.
Single crystal lithium fluoride (LiF), oriented [100], was shock loaded and subsequently shocklessly compressed in two experiments at the Z Machine. Velocimetry measurements were employed to obtain an impactor velocity, shock transit times, and in-situ particle velocities for LiF samples up to ∼1.8 mm thick. A dual thickness Lagrangian analysis was performed on the in-situ velocimetry data to obtain the mechanical response along the loading path of these experiments. An elastic response was observed on one experiment during initial shockless compression from 100 GPa before yielding. The relatively large thickness differences utilized for the dual sample analyses (up to ∼1.8 mm) combined with a relative timing accuracy of ∼0.2 ns resulted in an uncertainty of less than 1% on density and stress at ∼200 GPa peak loading on one experiment and <4% on peak loading at ∼330 GPa for another. The stress-density analyses from these experiments compare favorably with recent equation of state models for LiF.
We report on a new technique for obtaining off-Hugoniot pressure vs. density data for solid metals compressed to extreme pressure by a magnetically driven liner implosion on the Z-machine (Z) at Sandia National Laboratories. In our experiments, the liner comprises inner and outer metal tubes. The inner tube is composed of a sample material (e.g., Ta and Cu) whose compressed state is to be inferred. The outer tube is composed of Al and serves as the current carrying cathode. Another aluminum liner at much larger radius serves as the anode. A shaped current pulse quasi-isentropically compresses the sample as it implodes. The iterative method used to infer pressure vs. density requires two velocity measurements. Photonic Doppler velocimetry probes measure the implosion velocity of the free (inner) surface of the sample material and the explosion velocity of the anode free (outer) surface. These two velocities are used in conjunction with magnetohydrodynamic simulation and mathematical optimization to obtain the current driving the liner implosion, and to infer pressure and density in the sample through maximum compression. This new equation of state calibration technique is illustrated using a simulated experiment with a Cu sample. Monte Carlo uncertainty quantification of synthetic data establishes convergence criteria for experiments. Results are presented from experiments with Al/Ta, Al/Cu, and Al liners. Symmetric liner implosion with quasi-isentropic compression to peak pressure ∼1000 GPa is achieved in all cases. These experiments exhibit unexpectedly softer behavior above 200 GPa, which we conjecture is related to differences in the actual and modeled properties of aluminum.
We have developed the design of Thor: a pulsed power accelerator that delivers a precisely shaped current pulse with a peak value as high as 7 MA to a strip-line load. The peak magnetic pressure achieved within a 1-cm-wide load is as high as 100 GPa. Thor is powered by as many as 288 decoupled and transit-time isolated bricks. Each brick consists of a single switch and two capacitors connected electrically in series. The bricks can be individually triggered to achieve a high degree of current pulse tailoring. Because the accelerator is impedance matched throughout, capacitor energy is delivered to the strip-line load with an efficiency as high as 50%. We used an iterative finite element method (FEM), circuit, and magnetohydrodynamic simulations to develop an optimized accelerator design. When powered by 96 bricks, Thor delivers as much as 4.1 MA to a load, and achieves peak magnetic pressures as high as 65 GPa. When powered by 288 bricks, Thor delivers as much as 6.9 MA to a load, and achieves magnetic pressures as high as 170 GPa. We have developed an algebraic calculational procedure that uses the single brick basis function to determine the brick-triggering sequence necessary to generate a highly tailored current pulse time history for shockless loading of samples. Thor will drive a wide variety of magnetically driven shockless ramp compression, shockless flyer plate, shock-ramp, equation of state, material strength, phase transition, and other advanced material physics experiments.
Eighty years ago, it was proposed that solid hydrogen would become metallic at sufficiently high density. Despite numerous investigations, this transition has not yet been experimentally observed. More recently, there has been much interest in the analog of this predicted metallic transition in the dense liquid, due to its relevance to planetary science. Here, we show direct observation of an abrupt insulator-to-metal transition in dense liquid deuterium. Experimental determination of the location of this transition provides a much-needed benchmark for theory and may constrain the region of hydrogen-helium immiscibility and the boundary-layer pressure in standard models of the internal structure of gas-giant planets.
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.
Magnetically-driven, planar shockless-compression experiments to multi-megabar pressures were performed on tantalum samples using a stripline target geometry. Free-surface velocity waveforms were measured in 15 cases; nine of these in a dual-sample configuration with two samples of different thicknesses on opposing electrodes, and six in a single-sample configuration with a bare electrode opposite the sample. Details are given on the application of inverse Lagrangian analysis (ILA) to these data, including potential sources of error. The most significant source of systematic error, particularly for single-sample experiments, was found to arise from the pulse-shape dependent free-surface reflected wave interactions with the deviatoric-stress response of tantalum. This could cause local, possibly temporary, unloading of material from a ramp compressed state, and thus multi-value response in wave speed that invalidates the free-surface to in-material velocity mapping step of ILA. By averaging all 15 data sets, a final result for the principal quasi-isentrope of tantalum in stress-strain was obtained to a peak longitudinal stress of 330GPa with conservative uncertainty bounds of ±4.5% in stress. The result agrees well with a tabular equation of state developed at Los Alamos National Laboratory.
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.