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Density-driven ionization potential depression and its effects on material properties

Changes in ionization potential at high density drive changes in material transport properties and often in crystal structure and equation of state. Current models used to describe and predict these effects have not been tested in regimes much beyond ~200 GPa, because of limitations in experimental techniques. Now, however, high-energy laser facilities with flexible pulse-shaping capabilities have made it possible to reach pressures in the 1000 GPa range, while maintaining temperatures below 1 eV. We have used these new methods to ramp-compress cobalt and magnesium and have measured shifts in the k-shell emission lines to infer changes in ionization stage, and x-ray diffraction to measure changes in crystal structure. In the case of cobalt, commonly-used detailed models for effective ionization based on isolated-atom electronic structure are shown to give the wrong answer, while self-consistent density-functional-theory-based models reproduce the data well. In the case of magnesium, zero-kelvin density functional theory predictions of density-driven electron localization in lattice interstitials (so-called electride phases) at high pressure are found to be too simple to describe material evolution along a laser ramp-compression pathway. Instead, by a combination of experiment, first-principles theory and evolutionary structure-searching algorithms, we have discovered several unexpected lower-symmetry metastable structures. First principles results find that the density of localized interstitial charge in the high-pressure magnesium phases is too low to be measurable with x-ray diffraction, and the body of theory work which has predicted high pressure electride phases for many systems, based on analysis of electron localization function, needs to be re-examined.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Extracting strength from high pressure ramp-release experiments

Unloading from a plastically deformed state has long been recognized as a sensitive measure of a material's deviatoric response. In the case of a ramp compression and unload, time resolved particle velocity measurements of a sample/window interface may be used to gain insight into the sample material's strength. Unfortunately, measurements of this type are often highly perturbed by wave interactions associated with impedance mismatches. Additionally, wave attenuation, the finite pressure range over which the material elastically unloads, and rate effects further complicate the analysis. Here, we present a methodology that overcomes these shortcomings to accurately calculate a mean shear stress near peak compression for experiments of this type. A new interpretation of the self-consistent strength analysis is presented and then validated through the analysis of synthetic data sets on tantalum to 250 GPa. The synthetic analyses suggest that the calculated shear stresses are within 3% of the simulated values obtained using both rate-dependent and rate-independent constitutive models. Window effects are addressed by a new technique referred to as the transfer function approach, where numerical simulations are used to define a mapping to transform the experimental measurements to in situ velocities. The transfer function represents a robust methodology to account for complex wave interactions and a dramatic improvement over the incremental impedance matching methods traditionally used. The technique is validated using experiments performed on both lithium fluoride and tantalum ramp compressed to peak stresses of 10 and 15 GPa, respectively. In each case, various windows of different shock impedance are used to ensure consistency within the transfer function analysis. The data are found to be independent of the window used and in good agreement with previous results.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Phase transitions in high-purity zirconium under dynamic compression

In this work, we present results from ramp compression experiments on high-purity Zr that show the α → ω, ω → β, as well as reverse β → ω phase transitions. Simulations with a multi-phase equation of state and phenomenological kinetic model match the experimental wave profiles well. While the dynamic α ! ! transition occurs ~ 9 GPa above the equilibrium phase boundary, the ω → β transition occurs within 0.9 GPa of equilibrium. We estimate that the dynamic compression path intersects the equilibrium ω – β line at P = 29:2 GPa, and T = 490 K. The thermodynamic path in the interior of the sample lies ~ 100 K above the isentrope at the point of the ω → β transition. Approximately half of this dissipative temperature rise is due to plastic work, and half is due to the non-equilibrium α → ω transition. The inferred rate of the α → ω transition is several orders of magnitude higher than that measured in dynamic diamond anvil cell (DDAC) experiments in an overlapping pressure range. We discuss a model for the influence of shear stress on the nucleation rate. We find that the shear stress s ji has the same effect on the nucleation rate as a pressure increase δP = cϵ ij s ji /(ΔV/V); where c is a geometric constant ~ 1 and, ϵ ij are the transformation shear strains. The small fractional volume change ΔV/V ≈ 0:1 at the α → ω transition amplifies the effect of shear stress, and we estimate that for this case δP is in the range of several GPa. Correcting our transition rate to a hydrostatic rate brings it approximately into line with the DDAC results, suggesting that shear stress plays a significant role in the transformation rate.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Measurement of the strengths of Be and Pb4Sb by quasi-isentropic compress and release at near 100 GPa

The Ramp-compression experiments have been performed on the “Z” pulsed-power facility to investigate the strengths of Be and lead-antimony alloy. Yield strength and shear stress near peak pressure were obtained from measurements of the sound speed on release and using the Asay self-consistent method. Two S-65 grade Be samples, from batches which showed a significant difference in yield strength at ambient conditions, were found to have near identical yield strengths, which were also in agreement with similar earlier measurements on S-200 grade Be. Yield strength of Pb4Sb alloy at ~120 GPa was 1.35 GPa, while a National Ignition Facility (NIF) experiment by A. Krygier et al. (Phys. Rev. Lett. 123, 205701 (2020)) found 3.8 GPa at ~400 GPa pressure. Our result is intermediate between the ambient value and the Krygier one, but the significantly increased strength is probably not associated with the transition to the high-pressure bcc phase of lead.

42 ENGINEERING↗

Crystal structure and equation of state of Fe-Si alloys at super-Earth core conditions

The high-pressure behavior of Fe alloys governs the interior structure and dynamics of super-Earths, rocky extrasolar planets that could be as much as ten times more massive than Earth. In experiments reaching up to 1300 GPa, we combine laser-driven dynamic ramp compression with in situ X-ray diffraction to study the effect of composition on the crystal structure and density of Fe-Si alloys, a potential constituent of super-Earth cores. We find that Fe-7wt.%Si adopts the hexagonal close packed (hcp) structure over the measured pressure range, whereas Fe-15wt.%Si is observed in a body-centered cubic (bcc) structure. This study represents the first experimental determination of the density and crystal structure of Fe-Si alloys at pressures corresponding to the center of a ~3 Earth-mass terrestrial planet. Our results allow for direct determination of the effects of light elements on core radius, density, and pressures for such planets.

36 MATERIALS SCIENCE↗

Techniques for studying materials under extreme states of high energy density compression

The properties of materials under extreme conditions of pressure and density are of key interest to a number of fields, including planetary geophysics, materials science, and inertial confinement fusion. In geophysics, the equations of state of planetary materials, such as hydrogen and iron, under ultrahigh pressure and density provide a better understanding of their formation and interior structure [Celliers et al., “Insulator-metal transition in dense fluid deuterium,” Science 361, 677–682 (2018) and Smith et al., “Equation of state of iron under core conditions of large rocky exoplanets,” Nat. Astron. 2, 591–682 (2018)]. The processes of interest in these fields occur under conditions of high pressure (100 GPa–100 TPa), high temperature (>3000 K), and sometimes at high strain rates (>103 s−1) depending on the process. With the advent of high energy density (HED) facilities, such as the National Ignition Facility (NIF), Linear Coherent Light Source, Omega Laser Facility, and Z, these conditions are reachable and numerous experimental platforms have been developed. To measure compression under ultrahigh pressure, stepped targets are ramp-compressed and the sound velocity, measured by the velocity interferometer system for any reflector diagnostic technique, from which the stress-density of relevant materials is deduced at pulsed power [M. D. Knudson and M. P. Desjarlais, “High-precision shock wave measurements of deuterium: Evaluation of exchange-correlation functionals at the molecular-to-atomic transition,” Phys. Rev. Lett. 118, 035501 (2017)] and laser [Smith et al., “Equation of state of iron under core conditions of large rocky exoplanets,” Nat. Astron. 2, 591–682 (2018)] facilities. To measure strength under high pressure and strain rates, experimenters measure the growth of Rayleigh–Taylor instabilities using face-on radiography [Park et al., “Grain-size-independent plastic flow at ultrahigh pressures and strain rates,” Phys. Rev. Lett. 114, 065502 (2015)]. The crystal structure of materials under high compression is measured by dynamic x-ray diffraction [Rygg et al., “X-ray diffraction at the national ignition facility,” Rev. Sci. Instrum. 91, 043902 (2020) and McBride et al., “Phase transition lowering in dynamically compressed silicon,” Nat. Phys. 15, 89–94 (2019)]. Medium range material temperatures (a few thousand degrees) can be measured by extended x-ray absorption fine structure techniques, Yaakobi et al., “Extended x-ray absorption fine structure measurements of laser-shocked V and Ti and crystal phase transformation in Ti,” Phys. Rev. Lett. 92, 095504 (2004) and Ping et al., “Solid iron compressed up to 560 GPa,” Phys. Rev. Lett. 111, 065501 (2013), whereas more extreme temperatures are measured using x-ray Thomson scattering or pyrometry. This manuscript will review the scientific motivations, experimental techniques, and the regimes that can be probed for the study of materials under extreme HED conditions.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Design of a double-sided laser heating compatible piezoelectrically driven dynamic diamond anvil cell

Piezoelectrically driven dynamic diamond anvil cells are generally limited to use at room temperature due to spatial conflicts with the optical components necessary for double-sided laser heating. Here, this work describes the design of a double-sided laser-heating-compatible, piezoelectrically driven dynamic diamond anvil cell (LH-dDAC) that expands the range of experimentally accessible compression rate/temperature space. By developing a spatially in-parallel design, in which the diamond anvils and the piezo actuators lie alongside each other, the total length of the apparatus is reduced to 66.5 mm. The new LH-dDAC is capable of probing both overpressure and compression-rate effects on the kinetics of phase transitions. We illustrate the capability of the new LH-dDAC using the following cases: (1) a simultaneous pressure and temperature jump from 19.5 GPa and room temperature to 40 GPa and ≈1550 K and (2) a controlled compression ramp at ≈1850 K and ≈100 GPa/s. By pairing rapid compression with laser heating, the new LH-dDAC opens the door to studies of diffusionally controlled transformations at high pressures and temperatures.

Copley, J. A. [Princeton Univ., NJ (United States)↗

Influence of defects on the thermal conductivity of compressed LiF

We report defect formation in LiF, which is used as an observation window in ramp and shock experiments, has significant effects on its transmission properties. Given the extreme conditions of the experiments it is hard to measure the change in transmission directly. Using molecular dynamics, we estimate the change in conductivity as a function of the concentration of likely point and extended defects using a Green-Kubo technique with careful treatment of size effects. With this data, we form a model of the mean behavior and its estimated error; then, we use this model to predict the conductivity of a large sample of defective LiF resulting from a direct simulation of ramp compression as a demonstration of the accuracy of its predictions. Given estimates of defect densities in a LiF window used in an experiment, the model can be used to correct the observations of thermal energy through the window. Also, the methodology we develop is extensible to modeling, with quantified uncertainty, the effects of a variety of defects on the thermal conductivity of solid materials.

36 MATERIALS SCIENCE↗

X-ray diffraction at the National Ignition Facility

We report details of an experimental platform implemented at the National Ignition Facility to obtain in situ powder diffraction data from solids dynamically compressed to extreme pressures. Thin samples are sandwiched between tamper layers and ramp compressed using a gradual increase in the drive-laser irradiance. Pressure history in the sample is determined using high-precision velocimetry measurements. Up to two independently timed pulses of x rays are produced at or near the time of peak pressure by laser illumination of thin metal foils. The quasi-monochromatic x-ray pulses have a mean wavelength selectable between 0.6 Å and 1.9 Å depending on the foil material. The diffracted signal is recorded on image plates with a typical 2 θ x-ray scattering angle uncertainty of about 0.2° and resolution of about 1°. Analytic expressions are reported for systematic corrections to 2 θ due to finite pinhole size and sample offset. A new variant of a nonlinear background subtraction algorithm is described, which has been used to observe diffraction lines at signal-to-background ratios as low as a few percent. Variations in system response over the detector area are compensated in order to obtain accurate line intensities; this system response calculation includes a new analytic approximation for image-plate sensitivity as a function of photon energy and incident angle. This experimental platform has been used up to 2 TPa (20 Mbar) to determine the crystal structure, measure the density, and evaluate the strain-induced texturing of a variety of compressed samples spanning periods 2–7 on the periodic table.

47 OTHER INSTRUMENTATION↗

Three-dimensional full-field velocity measurements in shock compression experiments using stereo digital image correlation

Shock compression plate impact experiments conventionally rely on point-wise velocimetry measurements based on laser-based interferometric techniques. This study presents an experimental methodology to measure the free surface full-field particle velocity in shock compression experiments using high-speed imaging and three-dimensional (3D) digital image correlation (DIC). The experimental setup has a temporal resolution of 100 ns with a spatial resolution varying from 90 to 200 μm/pixel. Experiments were conducted under three different plate impact configurations to measure spatially resolved free surface velocity and validate the experimental technique. First, a normal impact experiment was conducted on polycarbonate to measure the macroscopic full-field normal free surface velocity. Second, an isentropic compression experiment on Y-cut quartz–tungsten carbide assembly is performed to measure the particle velocity for experiments involving ramp compression waves. To explore the capability of the technique in multiaxial loading conditions, a pressure shear plate impact experiment was conducted to measure both the normal and transverse free surface velocities under combined normal and shear loading. The velocities measured in the experiments using digital image correlation are validated against previous data obtained from laser interferometry. Numerical simulations were also performed using established material models to compare and validate the experimental velocity profiles for these different impact configurations. The novel ability of the employed experimental setup to measure full-field free surface velocities with high spatial resolutions in shock compression experiments is demonstrated for the first time in this work.

47 OTHER INSTRUMENTATION↗

Powder diffraction from solids in the terapascal regime

A method of obtaining powder diffraction data on dynamically compressed solids has been implemented at the Jupiter and OMEGA laser facilities. Thin powdered samples are sandwiched between diamond plates and ramp compressed in the solid phase using a gradual increase in the drive-laser intensity. The pressure history in the sample is determined by back-propagation of the measured diamond free-surface velocity. A pulse of x rays is produced at the time of peak pressure by laser illumination of a thin Cu or Fe foil and collimated at the sample plane by a pinhole cut in a Ta substrate. The diffracted signal is recorded on x-ray sensitive material, with a typical d-spacing uncertainty of {approx}0.01 A. This diagnostic has been used up to 0.9 TPa (9 Mbar) to verify the solidity, measure the density, constrain the crystal structure, and evaluate the strain-induced texturing of a variety of compressed samples spanning atomic numbers from 6 (carbon) to 82 (lead). Further refinement of the technique will soon enable diffraction measurements in solid samples at pressures exceeding 1 TPa.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

In situ x-ray diffraction study of dynamically compressed α -cristobalite using a dynamic diamond anvil cell

Here we present results of the dynamic compression of α -cristobalite up to a pressure of 106 GPa with the use of the dynamic diamond anvil cell. X-ray diffraction images were recorded at different ramp compression and decompression rates to investigate in situ the high-pressure phase transitions of α -cristobalite. Our results suggest that the pressure onset of the phase transformation of α -cristobalite to cristobalite II, cristobalite X-I, and ultimately to seifertite ( α – PbO 2 type SiO 2 ) is dependent on the applied compression rates and stress conditions of the experiment. Increasing compression rates in general shift the studied phase transitions to higher pressures. Furthermore, our results indicate for single crystals under hydrostatic conditions a suppression of a phase transition from cristobalite X-I to seifertite at pressures of up to 82 GPa.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Ultra-High Pressure Dynamic Compression of Geological Materials

Dynamic-compression experiments on geological materials are important for understanding the composition and physical state of the deep interior of the Earth and other planets. These experiments also provide insights into impact processes relevant to planetary formation and evolution. Recently, new techniques for dynamic compression using high-powered lasers and pulsed-power systems have been developed. These methods allow for compression on timescales ranging from nanoseconds to microseconds and can often achieve substantially higher pressure than earlier gas-gun-based loading techniques. The capability to produce shockless (i.e., ramp) compression provides access to new regimes of pressure–temperature space and new diagnostics allow for a more detailed understanding of the structure and physical properties of materials under dynamic loading. This review summarizes these recent advances, focusing on results for geological materials at ultra-high pressures above 200 GPa. Implications for the structure and dynamics of planetary interiors are discussed.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Simultaneous x-ray diffraction measurements of nine pressure calibrants to 140 GPa

Accurate pressure calibration is fundamental to quantitative high-pressure science, yet inconsistencies among widely used secondary pressure scales persist. In this work, we report simultaneous synchrotron x-ray diffraction meatogether in diamond anvil cells to 140 GPa. This simultaneous-measurement strategy minimizes transitive errors and run-to-run inconsistencies inherent to paired-measurement approaches, yielding direct experimental volume-volume (V-V) relations among the calibrants. These V-V relations link the compression state of each phase to that of every other phase measured in the same experiment. By anchoring these V-V relations to the reduced 300 K equation of state (EOS) of copper derived from ramp-compression measurements, we derive an internally consistent set of Cu-referenced pressure scales via Vinet EOS fits. Because the primary experimental result is the V-V dataset, it provides an EOS-independent constraint that can be rereferenced if primary standards are revised. The dataset further enables a direct experimental cross-check of consistency between the adopted reduced 300 K Cu EOS and the corresponding reduced 300 K ramp-derived EOSs for Pt, Au, Ta, and hcp-Fe under a fixed V-V constraint. The residuals quantify small, material-dependent mismatches between each phase EOS and the Cu reference EOS.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Refractive index of lithium fluoride at high dynamic stresses

Alkali halides are prototypical ionic solids whose refractive index is a fundamental property related to their lattice structure and ionic polarizability. In particular, lithium fluoride (LiF) has the largest band gap of any known transparent material and maintains transparency at high pressures, making it well suited for use as an optical window in dynamic compression experiments. While empirical fits to the measured density dependence of the refractive index have been provided, a model that is valid over the entire pressure range of experiments and based on a polarization-based theoretical description is lacking. We present a refractive index model for dynamically compressed LiF based on the Lorentz-Lorenz equation, where the molecular polarizability is determined using a single oscillator model with a strain polarizability parameter Λ=0.73. Here, we show that our modeling approach provides an excellent match to the LiF refractive index data for both shock and ramp compression experiments to 900 GPa (density compression greater than threefold). Additionally, updated fits are provided to determine the refractive index correction for LiF windows used in dynamic compression experiments.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗