Publications

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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.

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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.

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.

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.

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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.

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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.

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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.

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