Session GO03: HED: Matter in Extreme Conditions and EOS Measurements

Kinematics of plasticity-induced rotation during shock or ramp compression to extreme pressures

When a metallic specimen is rapidly compressed via laser-plasma ablation, its underlying crystal structure must often rotate as it plastically deforms. There is growing interest in the dynamic compression community in exploiting x-ray diffraction measurements of lattice rotation to infer which combinations of plasticity mechanisms are operative in uniaxially shocked crystals, and thus inform materials science at extreme pressures and strain rates [see for example Wehrenberg et. al., Nature 550, 496-499 (2017)]. However, it is not widely appreciated that many existing models linking rotation to slip activity are fundamentally inapplicable to a planar shock-loading scenario. We have conducted molecular dynamics simulations of single crystals suffering true uniaxial strain, and have found that the Schmid and Taylor analyses frequently used in traditional materials science fail to predict the ensuing texture evolution. We propose a simple alternative framework that successfully recovers the observed rotation, and can further be used to correctly identify the active slip systems in the idealised cases of single and conjugate slip [Heighway and Wark, J. Appl. Phys. 129, 085109 (2021)].   

Stability of the compression axis in bcc tantalum and fcc copper under shock-loading conditions

When dynamically compressed via laser-plasma ablation, a metallic specimen will generally undergo changes to its crystallographic texture due to plasticity-induced rotation. The axis and the extent of the local rotation can provide hints about the combination of plasticity mechanisms activated by the rapid uniaxial compression, thus providing valuable information about the underlying dislocation kinetics that are operative under extreme loading conditions. We present molecular dynamics simulations of shock-induced lattice rotation in three model crystals whose behaviour has previously been characterised in dynamic-compression experiments:  tantalum shocked along its [101] direction, and copper shocked along either [001] or [111]. Our simulations indicate that while tantalum loaded along [101] and copper loaded along [001] both show pronounced rotation due to asymmetric multiple slip, the orientation of copper shocked along [111] is stabilised by opposing rotations arising from competing, symmetrically equivalent slip systems. In all three cases, the sense of the reorientation predicted by the simulations is consistent with that measured experimentally using in situ x-ray diffraction.   

Mach wave driver for ultra-high pressure plasma equation of state measurements

Equation of state models are generally unconstrained by experimental data at the tens of terapascal pressure regime, because of the difficulty of generating these conditions in the laboratory.  We will present progress toward developing such a drive platform, using large-scale NIF and Omega laser facilities and taking advantage of the pressure amplification in a Mach stem that forms upon convergence of shock waves in a cone.  We will present equation of state data from shock speed measurements and impedance matching in Au samples compressed to nearly 50 TPa.   

Uncertainty Quantification of High Energy Density Material Models using Bayesian Analysis

The development of accurate material models in the high energy density regime is of considerable interest in a variety of fields, including the study of astrophysical impacts and inertial confinement fusion.  While plasma driven ramp compression, such as is now readily performed at the National Ignition Facility (NIF) and OMEGA Laser Facility, provides a powerful tool for probing this regime, the highly integrated nature of these experiments, together with the limitations on data quantity inherent in using such shared facilities, make it difficult to extract reliable model constraints valid across the entire range of relevant pressures (≤10 Mbar), temperatures (≤10⁴ K), and strain rates (≤10⁸ s^-1).  By performing large ensembles of hydrodynamic simulations, we leverage existing data on tantalum strength up to 8 Mbar, to systematically constrain the parameters of a variety of analytical strength models.  Through Bayesian techniques, we obtain quantitative estimates of these parameters and their uncertainties and propagate these values to estimates and uncertainties in the material strength itself.  Moreover, by explicitly constraining the model parameter space, this method allows us to clearly identify those relatively unconstrained dimensions, thereby pointing the way to future experiments with the greatest potential for producing further improvements in our material models.   

Sound Speed in Shock-Compressed Iron up to 3.7 TPa

The formation of terrestrial planets involves high-velocity impacts of iron-rich planetesimals in the later stages of accretion. The distribution of iron and other highly siderophile elements within the resulting planets depends on the thermodynamic evolution of the heated material after pressure release from the shock states produced by the impact. Sound speed is a critical thermodynamic property that provides information about how a material evolves after isentropic release from the shock state and is directly connected to other thermodynamic derivatives such as the bulk modulus, Grüneisen parameter, and specific heat. We report sound speed measurements in iron shocked to various pressures from slightly above melt near 250 GPa up to 3700 GPa. Steady shocks were produced simultaneously in the iron sample and a sound speed-reference (alpha-quartz) using a pedestal laser pulse shape. Pressure perturbations were then launched simultaneously through the sample and reference by specially-tailored laser power modulations. Sound speed was deduced using the arrival time of the perturbation sequence at the shock front after emerging into a transparent window using high-precision velocimetry. Our results show the sound speed in shocked iron is less than 10% higher than recent isentropic measurements of the sound speed at 20 g/cc.   

Temperature measurements of Magnesium Oxide shock-compressed to 1.1 TPa and 33000 K

Equations of state of rock-forming minerals are fundamental for modeling planetary interiors and mantle convection, whereas measurements are very limited in the warm dense matter regime. In this work, we shock compressed MgO to extreme pressures and temperatures found in exoplanets' interiors. We report the first measurements of pressure, temperature, and crystal structure of MgO in the warm dense matter regime. Crystal orientation-dependent formation was investigated with in-situ x-ray diffraction by shock compressing single-crystal MgO along different orientations.

Decaying shock experiments and PXRDIP experiments were conducted at the Omega-EP at Laboratory for Laser Energetics, University of Rochester. Lasers drive up to 2 KJ over several nanoseconds were used to shock-compress MgO. Velocimetry (VISAR) and Pyrometry (SOP) were employed to monitor velocity history and thermal emissions, respectively. In previous studies, optical depth was assumed to be skin depth, in which case the emission behavior could be described as blackbody emission. Here we present the first direct measurements of optical depth in shock-compressed MgO, showing that MgO is optically semi-transparent below 500 GPa (~12µm at 400 GPa), affecting temperature measurements in decaying shock experiments. Our data suggest that optical properties can potentially be crystal orientation-dependent. Details will be discussed in the presentation.   

Designs for spherically-converging shock experiments to measure wider ranges of states

Radiographic experiments with spherically-converging shocks can access a wider range of pressures and off-Hugoniot states by altering the target design and drive pulse, while still providing absolute equation of state (EOS) measurements. Shaping the laser pulse to drive the sample with a controlled ramp behind the initial shock, it thus strengthens more in the outer region of the sample before convergence effects dominate, exploring a wider range of shock pressures with a single shot. We have also started analyzing the outgoing shock, which in principle provides information on a family of double-shocked states though with larger uncertainty. By inserting a central ball of higher-impedance material, an earlier, reflected outgoing shock is produced which is easier to analyze, providing off-Hugoniot data needed to interpret relative EOS measurements from our Mach wave platform. The shock transmitted into the ball, reflecting from the center, provides an integrated measurement of the EOS at even higher pressures. Finally, a gap or low density region between the ball and shell provides the potential to compress the ball to much higher densities along paths between the Hugoniot and isentrope.   

Principal Hugoniot measurements of CH using Refraction Enhanced Radiography on the Gbar platform at the National Ignition Facility

We have implemented Refractive Enhanced Radiography (RER) [1] for the Gbar platform [2] at the National Ignition Facility (NIF), which allows to obtain the principal Hugoniot over a range of pressures by measuring shock compression of spherically converging shock waves in indirect drive implosion experiments. Here, we present the results of a proof of principle experiment, which repeated a previous experiment using a solid plastic sphere [1] at 30 – 50 Mbar with 4x better spatial and temporal resolution. The trajectory of the shock wave was recorded using x-ray backlighting at 8.4 keV generated by a Cu tube passing a 5 µm wide slit, which defines the spatial resolution and is sufficiently small to generate refraction fringes at the shock front.  Fringe amplitude and integral provide an independent measurement of shock compression in addition to the nominal absorption contrast at the shock front, which is independent of ionization and hence opacity in the sample.

[1] Dewald et al. HEDP 36, 100795 (2020)

[2] Doeppner et al. Phys. Rev. Lett. 121, 025001 (2018)   

X-Ray Diffraction of Ramp-Compressed Silicon to 390 GPa

Silicon exhibits a rich collection of phase transitions under compression at ambient temperature. We report in-situ measurements of the crystal structure of silicon between 41 and 390 GPa achieved through quasi-isentropic compression. Through angle dispersive x ray, we observe hexagonal close-packed structure between 33 and 99 GPa, and face-centered cubic structure above that to 390 GPa, the highest stress at which the crystal structure of silicon has ever been measured. Previously predicted double-hexagonal-close-packed phase between 22 and 55 GPa was not observed. A statistical model is developed to infer sample temperature from optical pyrometry data, previously thought not possible for temperatures below 5000 K, revealing temperature higher than anticipated from hydrodynamic simulations. This material is based upon work supported by the Department of Energy National Nuclear Security Administration under Award Number DE-NA0003856 and NSF Physics Frontier Center award PHY-2020249.   

Experimental studies of material strength of metals with artificially implanted helium bubbles in the high energy density regime

Plasma-driven ramp compression is a powerful means of studying materials at high-pressure conditions without melting. Understanding plastic deformation dynamics of materials under extreme conditions is of high interest to a number of fields, including meteor impact dynamics and advanced inertial confinement fusion. We infer the strength of samples at pressures up to 8 Mbar, strain rates of ~10⁷ s^-1, and high strains > 30% by measuring the growth of Rayleigh-Taylor instabilities (RTI) under ramped compression. We are now studying the dynamic response of materials that are aged by the radioactive alpha decay process. We fabricated lead samples that were artificially implanted with helium bubbles to mimic the effects of alpha decay. We conducted side-by-side comparisons of pure versus helium-doped lead samples using the NIF laser facility. Initial results from these experiments will be presented.   

X-Ray Diffraction of Shocked Platinum

Platinum is often used as a pressure calibrant in diamond-anvil cell experiments, where it is routinely compressed to high pressure–temperature states. Previous experiments have observed the face-centered cubic (fcc) phase of platinum up to 383 GPa.[1]  Laser-driven experiments at the University of Rochester’s Laboratory for Laser Energetics used the powder x-ray diffraction platform [2] on OMEGA EP to extend these measurements for shock and shock-ramped platinum up to 500 GPa. The fcc phase remained stable upon compression until liquid diffraction was observed. This material is based upon work supported by the Department of Energy National Nuclear Security Administration under Award Number DE-NA0003856.

Thermal Emission and Reflectivity of Shocked SiO2 Aerogel

The thermodynamic behavior of shock-compressed SiO₂ was studied over a broad density and temperature range using low-density foams. Temperature and reflectance measurements were performed on single-shocked SiO₂ at initial densities of 2.65 (a‑quartz), 2.2 (fused silica), 0.3 (silica aerogel), 0.2, and 0.11 g/cm³. Thermodynamic derivatives are calculated across P–T phase space using the SiO₂ Hugoniot measurements combined with other experimental data sets. This work extends the capability of SiO₂ as a thermodynamic calibrant for high-energy-density physics experiments.   

D2 Double Shock Equation of State and Transport Data

We present recent findings of double-shock experiments in D₂, where due to a transparent first shock, a second shock state is observed directly in addition to the resulting coalesced shock. We deduce mechanical, thermal, and transport, properties of the double-shocked material to pressures of several Mbar with reflectivity, shock velocity, and temperature data obtained from the VISAR (velocity interferometer system for any reflector) and the SOP (streaked optical pyrometer) diagnostics. From these data we explore the off-Hugoniot behavior of D₂ and conclude with a comparison of our findings to previous experiments, models, and off-Hugoniot techniques.    

Equation of State Determination of Lead to 800 GPa at the National Ignition Facility

By compressing materials over 10s to 100s of nanoseconds, ramp compression equation of state (EOS) experiments provide access to the highest stress and density conditions in solids. In highly compressible materials, the rapidly increasing sound speeds with compression make ramp EOS measurements difficult to obtain due to shock formation and the associated sample heating. Furthermore, the presence of multiple solid phases may complicate the analysis and interpretation of these experiments. In this work, we ramp compressed lead, a model highly compressible post-transition metal with multiple accessible solid phases, to test the pulse shaping and design capabilities/limitations of the National Ignition Facility for EOS development. Using a 168-beam indirect hohlraum drive to deliver precisely shaped input stress pulses, we successfully ramp-compressed and obtained EOS data on lead up to ~800 GPa peak longitudinal stress — twice the previously achieved maximum stress under ramp compression. Although highly incompressible materials, such as diamond, have been successfully ramp compressed to ~5 terapascals using the National Ignition Facility, this work demonstrates the feasibility of studying highly compressible solids up to near terapascal conditions. Since no features of potential phase transformations were observed in the data, this work also demonstrates the potential limited effect of small-volume phase transformations on EOS measurements. (LLNL-ABS-824485)   

Inferred electron beam radius via a thermodynamic model of target expansion

Flash x-ray radiography with Intense relativistic electron beams (IREBs) is used in several application areas.

In typical usage, an intense electron beam ($>1$kA, typical) rapidly impinges a high-Z converter target and

produces \emph{bremsstrahlung} radiation for imaging.

This process rapidly deposits significant energy into the target material which heats and expands due to internal pressure.

Previous estimates attempt to use ideal gas relationships to describe the state of the expanding target.

For high-Z materials, however, significant complications arise because of changing ionization fraction.

This work constructs a thermodynamic description of the target material using ionization balance and excited states

determined by the collisional-radiative code FLYCHK[1].

A simple fluid expansion is then modeled using isochoric heating and adiabatic expansion steps.

Velocity is determined by momentum balance an an entropy limit.

Experiments varying beam time by a factor of two show a change in terminal velocity from 2.5--6 km/s of an expanding

Mo foil.

Inferred beam spot-sizes radii range from 350-650$\mu$m.

[1] H.-K. Chung, \emph{et al.}, \emph{High Energy Density Phys.} \textbf{1} (2005) 3--12.