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Drive-pressure optimization in ramp-wave compression experiments through differential evolution
Ramp-wave dynamic-compression experiments are used to examine quasi-isentropic loading paths in materials. The gradual and continuous increase in pressure created by ramp waves make these types of experiments ideal for studying nonequilibrium material behavior, such as solidification kinetics. In ramp-wave compression experiments, the input drive pressure to the experimental setup may be exerted through one of a number of different mechanisms (e.g., magnetic fields, gas-gun-driven impactors, or high-energy lasers) and is generally required for simulating such experiments. Yet, regardless of the specific mechanism, this drive pressure cannot be measured directly (measurements are generally taken at a location near the back of the experimental setup through a transparent window), leading to an inverse problem where one must determine the drive pressure at the front of the experimental setup (i.e., the input) that corresponds to the particle velocity (the output) measured near the back of the experimental setup. Furthermore, we solve this inverse problem using a heuristic optimization algorithm, known as differential evolution, coupled with a multiphysics, hydrodynamics code that simulates the compression of the experimental setup. By running many rounds of forward simulations of the experimental setup, our optimization process iteratively searches for a drive pressure that is optimized to closely reproduce the experimentally measured particle velocity near the back of the experimental setup. While our optimization methodology requires a significant number of hydrodynamics simulations to be conducted, many of these can be performed in parallel, which greatly reduces the time cost of our methodology. One novel aspect of our method for determining the drive pressure is that it does not require physical modeling of the drive mechanism and can thus be broadly applied to many types of ramp-compression experiments, regardless of the drive mechanism.
Ta compressibility to 20+ Mbar
Developing techniques for experimentally constraining equation of state (EOS) models for important programmatic materials under extreme conditions is vital for advancing our modeling and predictive capabilities. Tantalum is a frequently used standard material for both calibration and testing, and this report describes our work to both measure Ta compressibility to very high pressures and densities using the Ramp Compression Equation of State platform on the National Ignition Facility (NIF). Using a series of seven shots, increasing in peak pressure with each shot, we have made absolute measurements of the compressibility of Ta along the ramp compression path up to 2.3 TPa. Previous experimental measurements constrained the cold compressibility up to ~400 GPa, and there is a spread in the EOS models above that pressure. To improve communication and collaboration between the experimental team and the EOS development group, these new data, along with other experimental and theoretical constraints, were used to develop a Ta equation of state table, M73000. This report first describes the experimental measurements made at the NIF, and then discusses the construction of the EOS model. The ramp compression data can be found in tabular form in Appendix A. Appendix B contains some additional experimental details. In Appendix C we include some additional details on the EOS modeling. At the end of this document, we have attached a detailed report on the NIF ramp compression platform itself and in the main text referenced specific sections for additional details.
Superfast assembly and synthesis of gold nanostructures using nanosecond low-temperature compression via magnetic pulsed power
Gold nanostructured materials exhibit important size- and shape-dependent properties that enable a wide variety of applications in photocatalysis, nanoelectronics and phototherapy. Here we show the use of superfast dynamic compression to synthesize extended gold nanostructures, such as nanorods, nanowires and nanosheets, with nanosecond coalescence times. Using a pulsed power generator, we ramp compress spherical gold nanoparticle arrays to pressures of tens of GPa, demonstrating pressure-driven assembly beyond the quasi-static regime of the diamond anvil cell. Our dynamic magnetic ramp compression approach produces smooth, shockless (that is, isentropic) one-dimensional loading with low-temperature states suitable for nanostructure synthesis. Transmission electron microscopy clearly establishes that various gold architectures are formed through compressive mesoscale coalescences of spherical gold nanoparticles, which is further confirmed by in-situ synchrotron X-ray studies and large-scale simulation. As a result, this nanofabrication approach applies magnetically driven uniaxial ramp compression to mimic established embossing and imprinting processes, but at ultra-short (nanosecond) timescales.
Atomic structure and melting of Ni and Fe 36 Ni up to 400 GPa
Iron, nickel and its alloys are critically important materials for industrial and technological applications due to their unique magnetic properties, strength, and thermal expansion. In this study, lasers were used to compress and heat Fe 36 Ni alloy (36 wt% Ni) and pure nickel up to the melting temperature using a combination of shock and ramp compression. The structure was measured using nanosecond in-situ x-ray diffraction, and simultaneous velocimetry was used to measure the pressure up to 454 GPa. A mixed face-centered-cubic (fcc) solid–liquid phase in Fe 36 Ni at 311 GPa provides experimental evidence that, compared to pure iron, the incorporation of nickel expands the stability field of the fcc phase to the melting curve. At lower temperatures, a mixed fcc and hexagonal-close-packed (hcp) phase is observed in ramp-compressed Fe 36 Ni at 278 GPa. At the higher compressions, a structure inconsistent with fcc, hcp, and body-centered cubic (bcc) is observed. In the case of pure Ni, the fcc phase is stable under ramp compression up to 402 GPa.
Experimental characterization and constitutive modeling of the mechanical behavior of molybdenum under electromagnetically applied compression-shear ramp loading
Magnetically applied pressure-shear (MAPS) is a new experimental technique that provides a platform for direct measurement of material strength at extreme pressures. The technique employs an imposed quasi-static magnetic field and a pulsed power generator that produces an intense current on a planar driver panel, which in turn generates high amplitude magnetically induced longitudinal compression and transverse shear waves into a planar sample mounted on the drive panel. In order to apply sufficiently high shear traction to the test sample, a high strength material must be used for the drive panel. Molybdenum is a potential driver material for the MAPS experiment because of its high yield strength and sufficient electrical conductivity. To properly interpret the results and gain useful information from the experiments, it is critical to have a good understanding and a predictive capability of the mechanical response of the driver. In this work, the inelastic behavior of molybdenum under uniaxial compression and biaxial compression-shear ramp loading conditions is experimentally characterized. It is observed that an imposed uniaxial magnetic field ramped to approximately 10 T through a period of approximately 2500 μs and held near the peak for about 250 μs before being tested appears to anneal the molybdenum panel. In order to provide a physical basis for model development, a general theoretical framework that incorporates electromagnetic loading and the coupling between the imposed field and the inelasticity of molybdenum was developed. Based on this framework, a multi-axial continuum model for molybdenum under electromagnetic loading is presented. The model reasonably captures all of the material characteristics displayed by the experimental data obtained from various experimental configurations. Additionally, data generated from shear loading provide invaluable information not only for validating but also for guiding the development of the material model for multiaxial loadings.
Time-dependence of the alpha to epsilon phase transformation in iron
Here, iron was ramp-compressed over timescales of 3 ≤ t(ns) ≤ 300 to study the time-dependence of the α→ε (bcc→hcp) phase transformation. Onset stresses (σ α→ε ) for the transformation ~14.8-38.4 GPa were determined through laser and magnetic ramp-compression techniques where the transition strain-rate was varied between 10 6 ≤ $\dot{μ}$ α→ε (s ₋1 ) ≤ 5×10 8 . We find σ α→ε = 10.8 + 0.55 ln($\dot{μ}$ α→ε ) for $\dot{μ}$ α→ε < 10 6 /s and σ α→ε = 1.15($\dot{μ}$ α→ε ) 0.18 for $\dot{μ}$ α→ε > 10 6 /s. This $\dot{μ}$ response is quite similar to recent results on incipient plasticity in Fe suggesting that under high rate ramp compression the α→ε phase transition and plastic deformation occur through similar mechanisms, e.g., the rate limiting step for $\dot{μ}$ > 10 6 /s is due to phonon scattering from defects moving to relieve strain. We show that over-pressurization of equilibrium phase boundaries is a common feature exhibited under high strain-rate compression of many materials encompassing many orders of magnitude of strain-rate.
Shock-ramp analysis test problem
Quasi-isentropic (ramp) compression is now a well-established experimental method and so are the analysis techniques to give Lagrangian sound speed, pressure, and density along the sample material's isentrope. A shock followed by ramp compression is a natural extension to investigate, for example, shock melt and refreeze on compression, or isentropes of states off the Hugoniot or principal isentrope. In practice, graded-density impactors produce initial shocks, compression by shaped laser pulses may be unable to produce a smooth pressure increase from zero, and incidental perturbations on the drive pulse may also give rise to shocks, so robust shock-ramp analysis methods will be needed. Appropriate analysis methods are needed for shock-ramp experiments, based on those for quasi-isentropic compression, and these require validation. This paper describes three different analyses of a shock-ramp test problem, including an assessment of their estimated errors. The methods tested were based on hydrodynamic characteristics or integration backward in space. All methods gave the known Lagrangian sound speed to within ~1%, and pressure and volume to within less than 2% and 1%, demonstrating that the analysis methods of isentropic compression experiments can be confidently extended to the analysis of shock and ramp compression.
Transformation of shock-compressed copper to the body-centered-cubic structure at 180 GPa
Abstract not provided
A compact x-ray diffraction system for dynamic compression experiments on pulsed-power generators
Pulsed-power generators can produce well-controlled continuous ramp compression of condensed matter for high-pressure equation-of-state studies using the magnetic loading technique. 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, pulsed x-ray source for XRD measurements on pulsed-power-driven ramp-loaded samples. This combination of magnetically driven ramp compression of materials with a single, short-pulse XRD diagnostic will be a powerful capability for the dynamic materials’ community to investigate in situ dynamic phase transitions critical to equation of states. Finally, we present results using this new diagnostic to evaluate lattice compression in Zr and Al and to capture signatures of phase transitions in CdS.
Time resolved X-ray diffraction using the FIDDLE diagnostic at NIF: Preliminary assessment of diffraction precision
The Flexible Imaging Diffraction Diagnostic for Laser Experiments (FIDDLE) is a new diagnostic at the National Ignition Facility (NIF) designed to observe in situ solid-solid phase changes at high pressures using time resolved X-ray diffraction. FIDDLE currently incorporates five Icarus Ultrafast X-ray Imager sensors that take 2 ns snapshots and can be tuned to collect X-rays for tens of ns. The platform utilizes the laser power at NIF for both the laser drive and the generation of 10 keV X-rays for ~10 ns using a Ge backlighter foil. We aim to use FIDDLE to observe diffraction at different times during compression to probe the kinetics of phase changes. Pb undergoes two solid-solid phase transitions during ramp compression: from FCC to HCP and HCP to BCC. Results will be reported on some of the first shots using the FIDDLE diagnostic at NIF on ramp compressed Pb to a peak pressure of ~110 GPa and a single undriven CeO2 calibration shot. A discussion of the uncertainties in the observed diffraction is included.
Quantifying uncertainty in analysis of shockless dynamic compression experiments on platinum. I. Inverse Lagrangian analysis
Absolute measurements of solid-material compressibility by magnetically driven shockless dynamic compression experiments to multi-megabar pressures have the potential to greatly improve the accuracy and precision of pressure calibration standards for use in diamond anvil cell experiments. Here, to this end, we apply characteristics-based inverse Lagrangian analysis (ILA) to 11 sets of ramp-compression data on pure platinum (Pt) metal and then reduce the resulting weighted-mean stress–strain curve to the principal isentrope and room-temperature isotherm using simple models for yield stress and Grüneisen parameter. We introduce several improvements to methods for ILA and quasi-isentrope reduction, the latter including calculation of corrections in wave speed instead of stress and pressure to render results largely independent of initial yield stress while enforcing thermodynamic consistency near zero pressure. More importantly, we quantify in detail the propagation of experimental uncertainty through ILA and model uncertainty through quasi-isentrope reduction, considering all potential sources of error except the electrode and window material models used in ILA. Compared to previous approaches, we find larger uncertainty in longitudinal stress. Monte Carlo analysis demonstrates that uncertainty in the yield-stress model constitutes by far the largest contribution to uncertainty in quasi-isentrope reduction corrections. We present a new room-temperature isotherm for Pt up to 444 GPa, with 1-sigma uncertainty at that pressure of just under ±1.2%; the latter is about a factor of three smaller than uncertainty previously reported for multi-megabar ramp-compression experiments on Pt. The result is well represented by a Vinet-form compression curve with (isothermal) bulk modulus K 0 = 270.3 ± 3.8 GPa, pressure derivative K$^{'}_{0}$= 5.66 ± 0.10, and correlation coefficient $R_{K_{0},K^{'}_{0}}$= –0.843.
A Platform-Independent X-ray Diffraction Diagnostic for Phase Transition Kinetics in Traditional and Synthetic Microstructure Materials (LDRD Project 213088 Final Report)
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.
200-fold increase in dynamic strength of platinum at 430 GPa without a phase transformation
Here, the high-pressure strength of solid platinum is studied at the National Ignition Facility via Rayleigh-Taylor ripple growth under ramp compression. Laser-driven experiments reached pressures up to 430 GPa, collecting velocimetry and radiography data. Despite no phase transformation, the observed ripple growth aligns with hydrodynamic simulations using an amplified Steinberg-Guinan model, resulting in a 200-fold increase in strength. Molecular dynamics simulations of platinum ramp compression yield similar von Mises stress at comparable high pressure and high strain rate conditions. These findings represent the highest-pressure strength measurements ever achieved for platinum and offer critical insight into its significant strengthening behavior under high pressure and strain rate conditions.
Body-Centered-Cubic Phase Transformation in Gold at TPa Pressures
In situ x-ray diffraction at both the National Ignition Facility and Omega-EP Laser Facility has been utilized to determine the crystallographic state of ramp and shock-ramp compressed gold up to 1.2 TPa (1 TPa=10 Mbar = 10 × 10 6 atmospheres). In this Letter, we describe a series of experiments that explore a variety of pressure-temperature states in Au, accessed using tailored laser pulses. Here, we find that the ambient pressure face-centered-cubic phase is stable under ramp compression to pressures of at least 1 TPa where the body-centered-cubic phase is observed simultaneously.
Analysis of shockless dynamic compression data on solids to multi-megabar pressures: Application to tantalum
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 330 GPa 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.
The direct measurement of ablation pressure driven by 351-nm laser radiation
The instantaneous scaling of ablation pressure to laser intensity is directly inferred for ramp compression of diamond targets irradiated by 351-nm light. Continuously increasing pressure profiles from 100 to 970 GPa are produced by direct-drive laser ablation at intensities up to 7 × 1013 W/cm2. The free-surface velocity on the rear of the target is used to directly infer the instantaneous ablation-pressure profile at the front of the target. The laser intensity on target is determined by laser power measurements and fully characterized laser spots. The ablation pressure is found to depend on the laser intensity as P(GPa)=42(±3)[I(TW/cm2)]0.71(±0.01).