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. 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 .
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. 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.
Magnetic loading was used to shocklessly compress four different metals to extreme pressures. Velocimetry monitored the behavior of the material as it was loaded to a desired peak state and then decompressed back down to lower pressures. Two distinct analysis methods, including a wave profile analysis and a novel Bayesian calibration approach, were employed to estimate quantitative strength metrics associated with the loading reversal. Specifically, we report for the first time on strength estimates for tantalum, gold, platinum, and iridium under shockless compression at strain rates of ∼ 5 × 10 5/s in the pressure range of ∼ 100–400 GPa. The magnitude of the shear stresses supported by the different metals under these extreme conditions are surprisingly similar, representing a dramatic departure from ambient conditions.
The outer core of the Earth is composed primarily of liquid iron, and the inner core boundary is governed by the intersection of the melt line and the geotherm. While there are many studies on the thermodynamic equation of state for solid iron, the equation of state of liquid iron is relatively unexplored. In this work, we use dynamic compression to diagnose the high-pressure liquid equation of state of iron by utilizing the shock-ramp capability at Sandia National Laboratories’ Z-Machine. This technique enables measurements of material states off the Hugoniot by initially shocking samples and subsequently driving a further, shockless compression. Planetary studies benefit greatly from isentropic, off-Hugoniot experiments since they can cover pressure-temperature (P-T) conditions that are close to adiabatic profiles found in planetary interiors. We used this method to drive iron to P-T conditions similar to those of the Earth’s outer-inner core boundary, along an elevated-temperature isentrope in the liquid from 275 GPa to 400 GPa. We derive the equation of state using a hybrid backward integration – forward Lagrangian technique on particle velocity traces to determine the pressure-density history of the sample. Our results are in excellent agreement with SESAME 92141, a previously published equation of state table. With our data and previous experimental data on liquid iron we provide new information on the iron melting line and derive new parameters for a Vinet-based equation of state. The table and our parameterized equation of state are applied to provide an updated means of modeling the pressure, mass, and density of liquid iron cores in exoplanetary interiors.
Nanosecond in situ x-ray diffraction and simultaneous velocimetry measurements were used to determine the crystal structure and pressure, respectively, of ramp-compressed aluminum at stress states between 111 and 475 GPa. The solid-solid Al phase transformations, fcc-hcp and hcp-bcc, are observed at 216±9 and 321±12 GPa, respectively, with the bcc phase persisting to 475 GPa. The high-pressure crystallographic texture of the hcp and bcc phases suggests close-packed or nearly close-packed lattice planes remain parallel through both transformations.
The CHEDS researchers are engaged in a collaborative research project to study the properties of iron and iron alloys under Earth’s core conditions. The Earth’s core, inner and outer, is composed primarily of iron, thus studying iron and iron alloys at high pressure and temperature conditions will give the best estimate of its properties. Also, comparing studies of iron alloys with known properties of the core can constrain the potential light element compositions found within the core, such as fitting sound speeds and densities of iron alloys to established inner- Earth models. One of the lesser established properties of the core is the thermal conductivity, where current estimates vary by a factor of three. Therefore, one of the primary goals of this collaboration is to make relevant measurements to elucidate this conductivity.
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 work 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.
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.
An understanding of the mechanical and optical properties of lithium fluoride (LiF) is essential to its use as a transparent tamper and window for dynamic materials experiments. In order to improve models for this material, we applied iterative Lagrangian analysis to ten independent sets of data from magnetically driven planar shockless compression experiments on single crystal [100] LiF to pressures as high as 350 GPa. We found that the compression response disagreed with a prevalent tabular equation of state for LiF that is commonly used to interpret shockless compression experiments. We also present complementary data from ab initio calculations performed using the diffusion quantum Monte Carlo method. The agreement between these two data sets lends confidence to our interpretation. In order to aid in future experimental analysis, we have modified the tabular equation of state to match the new data. We have also extended knowledge of the optical properties of LiF via shock-compression and shockless compression experiments, refining the transmissibility limit, measuring the refractive index to ∼300 GPa, and confirming the nonlinear dependence of the refractive index on density. We present a new model for the refractive index of LiF that includes temperature dependence and describe a procedure for correcting apparent velocity to true velocity for dynamic compression experiments.
The Thor pulsed power generator is being developed at Sandia National Laboratories. The design consists of up to 288 decoupled and transit time isolated capacitor-switch units, called “bricks”, that can be individually triggered to achieve a high degree of pulse tailoring for magnetically-driven isentropic compression experiments (ICE). The connecting transmission lines are impedance matched to the bricks, allowing the capacitor energy to be efficiently delivered to an ICE strip-line load with peak pressures of over 100 GPa. Thor will drive experiments to explore equation of state, material strength, and phase transition properties of a wide variety of materials. We present an optimization process for producing tailored current pulses, a requirement for many material studies, on the Thor generator. This technique, which is unique to the novel “current-adder” architecture used by Thor, entirely avoids the iterative use of complex circuit models to converge to the desired electrical pulse. We describe the optimization procedure for the Thor design and show results for various materials of interest. Also, we discuss the extension of these concepts to the megajoule-class Neptune machine design. Given this design, we are able to design shockless ramp-driven experiments in the 1 TPa range of material pressure.
In this study, we have developed a conceptual design of a next-generation pulsed-power accelerator that is optmized for driving megajoule-class dynamic-material-physics experiments at pressures as high as 1 TPa. The design is based on an accelerator architecture that is founded on three concepts: single-stage electrical-pulse compression, impedance matching, and transit-time-isolated drive circuits. Since much of the accelerator is water insulated, we refer to this machine as Neptune. The prime power source of Neptune consists of 600 independent impedance-matched Marx generators. As much as 0.8 MJ and 20 MA can be delivered in a 300-ns pulse to a 16-mΩ physics load; hence Neptune is a megajoule-class 20-MA arbitrary waveform generator. Neptune will allow the international scientific community to conduct dynamic equation-of-state, phase-transition, mechanical-property, and other material-physics experiments with a wide variety of well-defined drive-pressure time histories. Because Neptune can deliver on the order of a megajoule to a load, such experiments can be conducted on centimeter-scale samples at terapascal pressures with time histories as long as 1 μs.
An absolute stress-density path for shocklessly compressed copper is obtained to over 450 GPa. A magnetic pressure drive is temporally tailored to generate shockless compression waves through over 2.5-mm-thick copper samples. The free-surface velocity data is analyzed for Lagrangian sound velocity using the iterative Lagrangian analysis (ILA) technique, which relies upon the method of characteristics. We correct for the effects of strength and plastic work heating to determine an isentropic compression path. By assuming a Debye model for the heat capacity, we can further correct the isentrope to an isotherm. Our determination of the isentrope and isotherm of copper represents a highly accurate pressure standard for copper to over 450 GPa.
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.
We report on experiments where cylindrical beryllium liners filled with liquid deuterium were compressed to extreme pressure and density with current pulse shaping. In one set of experiments the pressure at stagnation is inferred to be & 100 Mbar using penetrating radiography. A peak liner convergence ratio (initial radius over final radius) of 7.6 was measured resulting in an average deuterium density of 10 g=cm3 and areal density of 0.45 g=cm2. The stagnation shock propagating radially outward through the liner wall was directly measured with a strength of ≈ 120 Mbar. In a second set of experiments the liner was imploded to a peak convergence of 19 resulting in a density of 55 g=cm3 and areal density of 0.5 g=cm2. The pressure at stagnation in this experiment is estimated to be 2 Gbar. This platform enables the study of high-pressure, high-density, implosion deceleration and stagnation dynamics at spatial scales that are readily diagnosable (R ~ 0.1 -- 0.4 mm). Thus, these experiments are directly relevant to both Inertial Con nement Fusion and the study of material properties under extreme conditions.
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.
The intense magnetic field generated by the Z accelerator at Sandia National Laboratories is used as a pressure source for material science studies. A current of ∼20 MA can be delivered to the loads used in experiments on a time scale of ∼100-600 ns. Magnetic fields (pressures) exceeding 1200 T (600 GPa) have been produced in planar configurations. In one application we have developed, the magnetic pressure launches a flyer plate to ultra-high velocity in a plate impact experiment; equation of state data is obtained on the Hugoniot of a material that is shock compressed to multi-megabar pressure. This capability has been enhanced by the recent development of a planar stripline configuration that increases the magnetic pressure for a given current. Furthermore, the cross sectional area of a stripline flyer plate is larger than in previous coaxial loads; this improves the planarity of the flyer thereby reducing measurement uncertainty. Results of experiments and multi-dimensional magneto hydrodynamic (MHD) simulation are presented for ultra-high velocity aluminum and copper flyer plates. Aluminum flyer plates with dimensions ∼25 mm by ∼13 mm by ∼1 mm have been launched to velocities up to ∼45 km/s; for copper the peak velocity is ∼22 km/s. The significance of these results is that part of the flyer material remains solid at impact with the target; an accomplishment that is made possible by shaping the dynamic pressure (current) ramp so that the flyer compresses quasi-isentropically (i.e., shocklessly) during acceleration.
The Z machine is a fast pulsed-power machine at Sandia National Laboratories designed to deliver a 100-ns rise-time, 26-MA pulse of electrical current to Z-pinch experiments for research in radiation effects and inertial confinement fusion. Since 1999, Z has also been used as a current source for magnetically driven, high-pressure, high-strain-rate experiments in condensed matter. In this mode, Z produces simultaneous planar ramp-wave loading, with rise times in the range of 300-800 ns and peak longitudinal stress in the range of 4-400 GPa, of multiple macroscopic material samples. Control of the current-pulse shape enables shockless propagation of these ramp waves through samples 1-2 mm thick to measure quasi-isentropic compression response, as well as shockless acceleration of copper flyer plates to at least 28 km/s for impact experiments to measure ultra-high-pressure (-3000 GPa) shock compression response. This presentation will give background on the relevant physics, describe the experimental technique, and show recent results from both types of experiments.
CHARICE (CHARacteristics-based inverse analysis of Isentropic Compression Experiments) is a computer application, previously documented in SAND2007-4948, that analyzes velocity waveform data from ramp-wave experiments to determine a material's quasi-isentropic loading response in stress and density using an iterative characteristics-based approach. This short report documents only the changes in CHARICE release version 1.1 relative to release version 1.0, and is not intended to stand alone. CHARICE version 1.1 corrects an error in the algorithm of the method, fixes several bugs, improves robustness and performance, provides more useful error descriptions, and adds a number of minor features.
CHARICE is a multi-platform computer application that analyzes velocity waveform data from ramp-wave experiments to determine a material's quasi-isentropic loading response in stress and density using an iterative characteristics-based approach. The application was built using ITT Visual Information Solutions Interactive Data Language (IDL{reg_sign}), and features graphical interfaces for all user interaction. This report describes the calculation method and available analysis options, and gives instructions for using the application.
Using a magnetic pressure drive, an absolute measurement of stress and density along the principal compression isentrope is obtained for solid aluminum to 240 GPa. Reduction of the free-surface velocity data relies on a backward integration technique, with approximate accounting for unknown systematic errors in experimental timing. Maximum experimental uncertainties are +/-4.7% in stress and +/-1.4% in density, small enough to distinguish between different equation-of-state (EOS) models. The result agrees well with a tabular EOS that uses an empirical universal zero-temperature isotherm.
The intense magnetic field generated in the 20 MA Z-machine is used to accelerate metallic flyer plates to high velocity for the purpose of generating strong shocks in equation of state experiments. We present results pertaining to experiments in which a 0.085 cm thick Al flyer plate is magnetically accelerated across a vacuum gap into a quartz target. Peak magnetic drive pressures up to 4.9 Mbar were produced, which yielded a record 34 km/s flyer velocity without destroying it by shock formation or Joule heating. Two-dimensional MHD simulation was used to optimize the magnetic drive pressure on the flyer surface, shape the current pulse to accelerate the flyer without shock formation (i.e., quasi-isentropically), and predict the flyer velocity. Shock pressures up to 11.5 Mbar were produced in quartz. Accurate measurements of the shock velocity indicate that a fraction of the flyer is at solid density when it arrives at the target. Comparison of measurements and simulation results yields a consistent picture of the flyer state at impact with the quartz target.
INVICE (INVerse analysis of Isentropic Compression Experiments) is a FORTRAN computer code that implements the inverse finite-difference method to analyze velocity data from isentropic compression experiments. This report gives a brief description of the methods used and the options available in the first beta version of the code, as well as instructions for using the code.
Using a magnetic pressure drive, an absolute measurement of stress and density along the principal compression isentrope is obtained for solid aluminum to 240 GPa. Reduction of the free-surface velocity data relies on a backward integration technique, with approximate accounting for unknown systematic errors in experimental timing. Maximum experimental uncertainties are {+-}4.7% in stress and {+-}1.4% in density, small enough to distinguish between different equation-of-state (EOS) models. The result agrees well with a tabular EOS that uses an empirical universal zero-temperature isotherm.
The magnetic-pressure drive technique allows single-shot measurements of compression isentropes. We have used this method to measure the isentropes in the pressure-volume space of bulk and single-crystal lead, and lead-antimony alloy to {approx}400 kbar. The isentrope pressure-volume curves were found from integration of the experimentally deduced Lagrangian sound speed as a function of particle velocity. A characteristics calculation method was used to convert time-resolved free-surface velocity measurements to corresponding in situ particle-velocity histories, from which the Lagrangian sound speed was determined from the times for samples of different thicknesses to reach the same particle velocity. Use of multiple velocity interferometry probes decreased the uncertainty due to random errors by allowing multiple measurements. Our results have errors of from 4% to 6% in pressure, {approx}1% to 1.5% in volume, depending on the number of measurements, and are consistent with existing isotherm and Hugoniot data and models for lead.
The intense magnetic field generated in the 20 MA Z-machine is used to accelerate metallic flyer plates to high velocity (peak velocity {approx}20-30 km/s) for the purpose of generating strong shocks (peak pressure {approx}5-10 Mb) in equation of state experiments. We have used the Sandia developed, 2D magneto-hydrodynamic (MHD) simulation code ALEGRA to investigate the physics of accelerating flyer plates using multi-megabar magnetic drive pressures. Through detailed analysis of experimental data using ALEGRA, we developed a 2D, predictive MHD model for simulating material science experiments on Z. The ALEGRA MHD model accurately produces measured time dependent flyer velocities. Details of the ALEGRA model are presented. Simulation and experimental results are compared and contrasted for shots using standard and shaped current pulses whose peak drive pressure is {approx}2 Mb. Isentropic compression of Al to 1.7 Mb is achieved by shaping the current pulse.
Isentropic compression experiments were performed on molten tin (initial temperature 500-600 K), using the Sandia Z Accelerator to generate magnetically driven, planar ramp waves compressing the tin across the equilibrium liquid-solid phase boundary. Velocity interferometry measured time-resolved wave profiles at the tin/window interface. The experiments exhibit a departure from expected liquid response, time-dependent behavior above 8 GPa, and, at higher pressure, reduced wave speed relative to calculations using a nonequilibrium phase-mixture model. These phenomena may be due to a nonequilibrium solidification process, but verification of this conjecture will require further work.
Recently an innovative technique known as the Isentropic Compression Experiment (ICE) was developed that allows the dynamic compressibility curve of a material to be measured in a single experiment. Hence, ICE significantly reduces the cost and time required for generating and validating theoretical models of dynamic material response. ICE has been successfully demonstrated on several materials using the 20 MA Z accelerator, resulting in a large demand for its use. The present project has demonstrated its use on another accelerator, Saturn. In the course of this study, Saturn was tailored to produce a satisfactory drive time structure, and instrumented to produce velocity data. Pressure limits are observed to be approximately 10-15 GPa (''LP'' configuration) or 40-50 GPa (''HP'' configuration), depending on sample material. Drive reproducibility (panel to panel within a shot and between shots) is adequate for useful experimentation, but alignment fixturing problems make it difficult to achieve the same precision as is possible at Z. Other highlights included the useful comparison of slightly different PZT and ALOX compositions (neutron generator materials), temperature measurement using optical pyrometry, and the development of a new technique for preheating samples. 28 ICE tests have been conducted at Saturn to date, including the experiments described herein.
In order to provide real-time data for validation of three dimensional numerical simulations of heterogeneous materials subjected to impact loading, an optically recording velocity interferometer system (ORVIS) has been adapted to a line-imaging instrument capable of generating precise mesoscopic scale measurements of spatially resolved velocity variations during dynamic deformation. Combining independently variable target magnification and interferometer fringe spacing, this instrument can probe a velocity field along line segments up to 15 mm in length. In high magnification operation, spatial resolution better than 10 {micro}m can be achieved. For events appropriate to short recording times, streak camera recording can provide temporal resolution better than 0.2 ns. A robust method for extracting spatially resolved velocity-time profiles from streak camera image data has been developed and incorporated into a computer program that utilizes a standard VISAR analysis platform. The use of line-imaging ORVIS to obtain measurements of the mesoscopic scale dynamic response of shocked samples has been demonstrated on several different classes of heterogeneous materials. Studies have focused on pressed, granular sugar as a simulant material for the widely used explosive HMX. For low-density (65% theoretical maximum density) pressings of sugar, material response has been investigated as a function of both impact velocity and changes in particle size distribution. The experimental results provide a consistent picture of the dispersive nature of the wave transmitted through these samples and reveal both transverse and longitudinal wave structures on mesoscopic scales. This observed behavior is consistent with the highly structured mesoscopic response predicted by 3-D simulations. Preliminary line-imaging ORVIS measurements on HMX as well as other heterogeneous materials such as foam and glass-reinforced polyester are also discussed.