Marcus D. Knudson

Shockless compression and release behavior of beryllium to 110 GPa

A magnetohydrodynamic loading technique was used to shocklessly compress beryllium to peak longitudinal stresses of 19–110 GPa and, subsequently, unload in order to determine both the compressive response and also the shear stress supported upon release. Loading strain rates were on the order of 106 s−1, while the unloading rates were nearly constant at 3 × 105 s−1. Velocimetry was used to monitor the ramp and release behavior of a beryllium/lithium fluoride window interface. After applying window corrections to infer in situ beryllium velocities, a Lagrangian analysis was employed to determine the material response. The Lagrangian wavespeed-particle velocity response is integrated to generate the stress-strain path, average change in shear stress over the elastic unloading, and estimates of the shear modulus at peak compression. These data are used to infer the pressure dependence of the flow strength at the unloading rate. Comparisons to several strength models reveal good agreement to 45 GPa, but the d...

Probing off-Hugoniot states in Ta, Cu, and Al to 1000 GPa compression with magnetically driven liner implosions

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.

Transformation kinetics for the shock wave induced phase transition in cadmium sulfide crystals

Initial stage kinetics of the cadmium sulfide (CdS) phase transition was investigated using picosecond time-resolved electronic spectroscopy in plate-impact shock wave experiments. Real-time changes in the electronic spectra were observed, with 100 ps time resolution, in CdS single crystals shocked along a and c axes to stresses ranging between 35 and 90 kbar, which is above the phase-transition threshold stress of approximately 30 kbar. Significant difference in the transformation kinetics was observed for the two crystal orientations. At sufficiently high instantaneous stress, above approximately 60 to 70 kbar for a axis and 50 kbar for c axis, transformation to a metastable state appears to reach a constant state within the 100 ps time resolution. At lower instantaneous stresses, an incubation period on the order of several nanoseconds is observed prior to the onset of electronic changes that mark the onset of the structural change. The subsequent increase in absorbance was quite rapid, with a constant...

Mechanical and optical response of [100] lithium fluoride to multi-megabar dynamic pressures

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.

Feasibility of stimulated emission to measure R-line shifts in shock compressed ruby

In previous studies, ruby R-line shifts under shock compression and tension have been measured using the spontaneous luminescence from optically pumped samples. The signal intensities obtained are limited by the short time duration of the experiments in comparison to the long lifetime of the luminescence. We have investigated the use of stimulated emission for measuring R-line shifts in shocked ruby crystals. Experiments were performed both at ambient conditions and under shock compression to 6 GPa using an experimental configuration similar to that used for time resolved ruby luminescence measurements in previous shock wave studies. Signal gain due to stimulated emission was observed, with gains ranging from 1.1 to 3.4, in agreement with calculations performed for the particular experimental configuration used. The present results make a good case for incorporating this technique into the measurement of shock induced R-line shifts in ruby.

Extension of the Hugoniot and analytical release model of α-quartz to 0.2–3 TPa

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.

Aluminum equation of state validation and verification for the ALEGRA HEDP simulation code.

Determining whether an equation of state (EOS) table is vali d for a given regime requires several steps that include confirming that it obeys the thermodynami c consistency relations and that the table matches available existing experimental data. Once the EOS is analyzed, then we must ensure the simulation code can reproduce analytical results. In this report, we show analytical results of Hugoniot calcu lations and compare them with values calculated from experimental Us−UP data. Next we check that the tables are thermodynamically consistent. Then, we show analytical results of impedance m atching using one of the aluminum EOS models and compare those analytical results to data. Fin ally, ALEGRA-HEDP is used to run a pseudo 1-D shock simulation, which is compared to the an alytical model with an error of approximately 0.1%. This implies that ALEGRA-HEDP can simu late the shock Hugoniot to within the error of the EOS table when compared to the experimental d a for an ideal simulation.

Mechanical response of lithium fluoride under off-principal dynamic shock-ramp loading

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.

Equation of state and optical properties of warm dense helium

We used molecular dynamics simulations based on density functional theory to study the thermophysical properties of warm dense helium. The influence of different exchange-correlation (XC) functionals was analyzed. We calculated the equation of state at high pressures up to several Mbar and temperatures up to 100 000 K in order to reconstruct recent static, single shock, and quasi-isentropic compression experiments. Furthermore, we calculated the dynamic electrical conductivity and determined the reflectivity and DC conductivity. We compared our results with experimental data and found good agreement between our calculations and the high-pressure experiments. The different XC functionals give similar results in the equation of state calculations, but have a strong impact on the reflectivity and the DC conductivity.

Shock compression response of poly(4-methyl-1-pentene) plastic to 985 GPa

Poly(4-methyl-1-pentene) plastic (PMP) is a hydrocarbon polymer with potential applications to inertial confinement fusion experiments and as a Hugoniot impedance matching standard for equation of state experiments. Using Sandias Z-machine, we performed a series of flyer plate experiments to measure the principal Hugoniot and reshock states of PMP up to 985 GPa. The principal Hugoniot measurements validate density functional theory (DFT) calculations along the Hugoniot. The DFT calculations are further analyzed using a bond tracking method to understand the dissociation pathway under shock compression. Complete dissociation occurs at a compression factor similar to other sp3-hybridized, C-C bonded systems, which suggests a limiting compression for C-C bonds. The combined experimental and DFT results provide a solid basis for constructing an equation of state model for PMP.