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

High energy density (HED) physics is a rapidly growing field and spans a wide range of areas, including astrophysics, materials science, nuclear physics, and plasma physics. High energy density conditions are found throughout the universe and defined in a number of ways. The National Academy of Science (NAS) in early 2000⁹ defined the HED regime as any condition where the energy density is very high, specifically when the internal energy/volume is greater than 10¹² erg/cm³. In solid-state materials, this translates to conditions where the shock strength is sufficiently large that the materials become compressible which usually occurs at pressures greater than 100 GPa (1 Mbar). This energy density is similar to the dissociation energy density of a hydrogen molecule. The HED regime can also be reached by laser irradiation at intensities $I L > 10 15$ W/cm², or by blackbody irradiation at radiation temperatures greater than ∼75 eV. The HED regime can be reached by objects of very low density but at high temperatures, such as active galactic nuclei or supernova remnants. Other examples of HED conditions are the high temperature and high density conditions of igniting inertial confinement implosions and the interior of the Sun. Still other objects that are at high density but lower temperatures, such as in the cores of the Earth and Jupiter, also exist in the HED regime, namely, $P > 10 12$ erg/cm³ = 1 Mbar. Thus, high pressure material studies are of key interest to many fields. To understand the relative pressures involved, note that at sea level the atmospheric pressure is 1 atm, i.e., 1 bar. The pressure of a meteor impact is ∼200 kbar; the Earth's core is at pressure of ∼3.5 Mbar; Jupiter's core is at ∼70 Mbar; and an inertial confinement fusion implosion hot spot can reach ∼100 Gbar or higher. These conditions can be found throughout the universe. How materials behave under these high pressure conditions is an important scientific question.

We now have many excellent facilities to study materials under extreme conditions of pressure, temperature, and density. Examples are the National Ignition Facility (NIF)¹⁰ in California, Z¹¹ in New Mexico, Linac Coherent Light Source (LCLS)¹² in California, Omega Laser Facility¹³ in New York, the European x-ray Free Electron Laser (X-FEL)¹⁴ in Germany, Shenguang¹⁵ in China, and SPring-8 Angstrom Compact free electron LAser (SACLA)¹⁶ in Japan. In addition to these medium to large scale facilities, many university-level facilities are conducting important HED experiments.

To reach ultrahigh pressures without melting the sample, the compression must be ramped up along a quasi-isentropic path. The easiest way of compressing a sample is to apply a strong shock. However, this method quickly reaches its limit as the sample follows the Hugoniot curve and melts if the shock strength is too high. Melting can be avoided by either staging the shocks or ramping the compression following a quasi-isentropic path. In this way, as the sample is gradually compressed to higher pressures, compression is achieved with minimal entropy generation; thus, the sample stays in a solid-state while reaching high pressure. Another interesting line of study is to shock melt the sample first and then apply a ramp compression. Interesting material properties are revealed when a material is melted and then rapidly resolidified. There are several ways of creating a ramped compression: In gas gun experiments, one uses a graded-density impactor to shape the impact pressure profile; in laser experiments, one uses the laser pulse shape to control the pressure profile; or one can use a reservoir-gap configuration where a strong shock in a reservoir material releases a plasma across the gap and then stagnates on the sample, creating a ramp compression profile on the sample.

There are many material properties that change dramatically under high pressure. Here, we will cover five parameters, in particular density, that is the equation of state, electrical conductivity, the arrangement of the atomic structure (phase), and the temperature and strength under high pressure. We will go through the methods and diagnostics used to study these properties and present a selection of examples below.

The equation of state (EOS) of a material is the thermo-dynamic relation connecting pressure, volume (density), and temperature. The EOS describes how much a sample compresses in response to an applied stress. The compression is initially a uniaxial elastic compression but then relaxes by plastic deformation to a more 3D hydrostatic state by the generation and transport of lattice defects, such as dislocations. Phase transformations can also occur as the applied pressure is increased. This relationship between pressure and density can be experimentally determined under a number of conditions, including ramp and shock Hugoniot compressions.

As an example of using this method to obtain information on the material equation of state, the pressure–density relation of an iron sample was determined from measurements of stepped targets at pressures up to 1.4 TPa (14 Mbar) on NIF² as shown in Fig. 3(a). In this experiment, a hohlraum was illuminated by 176 laser beams with a in particular, designed pulse shape that provided an initial shock of 60 GPa to jump through the α to ε phase transition of iron and then ramped to 1.4 TPa. This pulse shape creates a ramped radiation temperature, Tr, that ablatively exerts a ramped pressure profile on the target sample mounted over a diagnostic window on the side of the hohlraum. The hohlraum provides a planar pressure drive across the target sample that consists of 4 different thicknesses of iron at 83, 96, 106, and 115 μm. The raw VISAR data are shown in Fig. 3(b) from this experiment and the free surface velocity from these data is shown in Fig. 3(c). A Lagrangian analysis, using equations of (8)–(11), is used to transform the measured free surface velocity, $u f s ( t )$⁠, into a continuous pressure–density (⁠ $P − ρ$⁠) curve. The Lagrangian sound speed $C L ( u f s )$ is also determined, where u_fs is the free surface velocity. The final C_L vs free surface velocity, u_fs, is shown in the inset of Fig. 3(c), and the pressure–density relation is shown in Fig. 3(d). The measured iron pressure–density is compared to various theories and models. The uncertainty in C_L was obtained from the thickness measurement errors and VISAR uncertainties. High-pressure iron data are particularly valuable for studying the properties of terrestrial (rocky) exoplanet interiors.

Shock velocity and particle velocity measurements along the Hugoniot have been used to help constrain material pressure–density relation for over fifty years. For this work, the most commonly used window material is α-quartz. Precision calibration of the α-quartz shock velocity to its shock Hugoniot pressure needed to be established as a standard. This calibration experiment was performed on the Sandia Z Machine using plate-impact shock wave method where aluminum or copper impactors created the shocks, and their velocity was measured by the VISAR. This precise α-quartz Hugoniot relation^21,22 is applied to study the molecular-to-atomic transition of liquid deuterium along the principal Hugoniot. The schematic of the experimental setup is shown in the inset of Fig. 4(a) where cryogenic D₂ is placed in between two α-quartz windows. The flyer plate velocity up to impact and the shock velocities in α-quartz and deuterium were measured, as shown in Fig. 4(a). Using Eqs. (5) and (6), the pressure–density relation is derived as shown in Fig. 4(b). The high precision measurements were able to distinguish subtle differences between first-principles theoretical predictions for D₂.³ 

In the Jovian planets, magnetic fields are likely generated by a dynamo process in dense metallic hydrogen fluid in the planetary interior.²³ It is proposed that the pressure and temperture induced metallization of hydrogen could induce hydrogen–helium demixing which could play an important role in the internal structure and evolutions of these planets. Understanding the metallization of dense fluid hydrogen is, therefore, critical. It is also important to test quantum simulations methods.²⁴ 

In order to see the hydrogen insulator to metal transition, cryogenic ramp-compression experiments on liquid deuterium (D₂) were conducted at pressures of up to 600 GPa on the NIF. The cryogenic D₂ target was sandwiched between a Cu ablator and a LiF window and driven with 300 kJ in 168 beams of 351 nm wavelength into an Au hohlraum. The target had 2 areas in the field of view of the VISAR, as shown in Fig. 5(a). Half of the area had a LiF window coated with Al so that the VISAR laser reflected off the Al surface. The other half allowed the VISAR beam to be transmitted through the D₂ liquid and initially reflect off of the Cu ablator surface. As the D₂ gets compressed by the Cu pusher, the VISAR responds to changes in the index and transmission of the D₂ liquid. At the insulator to metallic transition in D₂, the D₂ becomes reflective, and the VISAR probe beam reflects off the D₂ metallic surface. The raw VISAR data are shown in Fig. 5(b): the top part of the image is the reflection of the Al surface, whereas the bottom half is the signal through the D₂ medium. With numerical simulations along with iterative fitting using the standard equation of state, the VISAR velocimetry data are analyzed to produce pressure, density, and temperature after compensating for changes in the index of refraction of the LiF window under high pressure. The change in amplitude of the reflected signal in the D₂ medium in the bottom half of the area is very clear. It shows a loss of amplitude (darkening) due to the bandgap closure in D₂; then, the amplitude rises again, signaling the metallic transition.

The analyzed reflectivity of ramp compresses D₂ is shown in Fig. 6(a) as a function of analyzed pressure. The conductivity analysis was divided into 2 pressure regimes: P < 150 GPa and P > 150 GPa. For P < 150 GPa, the optical conductivity is derived from the absorption coefficient and the real part of the index of refraction by fitting to the apparent velocity of the piston and comparing with the Lorentz model.¹ For P > 150 GPa, the optical conductivity is inferred from the reflectivity model using the Smith–Drude model.¹ The resulting conductivity is shown in the bottom of Fig. 6(a). By defining the metallic transition in D₂ to occur when the reflectivity is >30%, the transition pressure is ∼200 GPa and below 2000 K. Figure 6(b) shows the metallic transition in pressure–temperature space along with additional data from other experiments. These measurements show discrepancies in transition pressure from insulator to metal between static and dynamic experiments in dense fluid hydrogen isotopes. Thus, further high-pressure high-energy-density experiments on electrical conductivity will be needed to better constrain our understanding of the Jovian planetary systems.

Time-resolved x-ray diffraction can probe the crystal structure of materials under compression. Crystal structure dramatically affects material properties as seen in graphite vs diamond. While they both are composed of pure carbon, their appearance, strength, and behavior are dramatically different due to their crystal arrangement. The atomic lattice spacing can be measured by x-ray diffraction. Dynamic diffraction experiments can observe phase changes under compression and time-resolved measurements probe the kinetics of the transitions. Figure 7 shows a notional schematic of a dynamic diffraction measurement. The material is compressed along one direction by the uniaxial pressure drive forming a region of uniaxial compression, followed by a 3D relaxed state, resulting from defect generation and transport. The atomic crystal lattice spacing is measured by observing the diffraction pattern created from the constructive interference of monoenergetic x rays reflecting off of the atomic layers according to Bragg's law: 2dsin $θ = n λ$⁠, where d is the crystal lattice spacing, θ is the x-ray beam angle, λ is the incident x-ray wavelength, and n is the order of the reflection.

Polycrystalline x-ray diffraction experiments require bright monoenergetic x-ray sources. Free-Electron Lasers (FEL) create monoenergetic x rays by passing electrons from an accelerator through an array of alternating magnets (called undulators) causing them to emit monoenergetic coherent x rays by a self-amplified spontaneous emission mechanism. The resulting x-ray source can be very bright and quasi-coherent, providing an ideal probe for x-ray diffraction experiments. Using seeding techniques, FELs can demonstrate higher coherence both spatially and temporally.²⁵ Examples of such facilities are the LCLS (US),¹² the European XFEL (Germany),¹⁴ SACLA (Japan),¹⁶ and FERMI (Italy).²⁶ These facilities typically have separate laser drives to compress samples of interest to a moderately high-pressure state.

Laser-generated x-ray sources are commonly used in diffraction experiments at laser facilities. A subset of the lasers is used to heat a backlighter foil to generate helium-like, quasi-monoenergetic x rays.^5,27 These laser-generated x-ray sources convert ∼1% of the laser energy into x rays and usually include different emission lines and continuum bremsstrahlung components. The most dominant source is the He_α line emission with the spectral resolution of: $Δ E$_x/E_x $≲$ 0.6%, where E_x is the backlighter x-ray energy. The large laser facilities that use laser generated x-ray sources have the advantage of also providing much higher energy drives that can create ultrahigh pressures, P $≫$ 1 Mbar in the sample.

Three dynamic diffraction experiments will be presented here as examples: one done at the LCLS using the x-ray FEL probe, another performed on the NIF laser facility, and the third performed on the Omega laser facility.

The LCLS x-ray probe has been used as an x-ray backlighter to obtain high quality diffraction data including the one-dimensional (1D) elastic to 3D plastically relaxed states in Cu within a few tens of picoseconds using Debye–Scherrer geometry.²⁸ Here, we show an example where the laser driven dynamic phase transition occurs at different pressures than in the static compression case. Figure 8(a) shows a schematic of the experimental setup at the LCLS facility.⁶ The 20 ns optical drive laser illuminates a polyimide ablator, shock compressing the silicon sample to different pressures up to ∼30 Gpa, while the x-ray FEL probe beam creates diffraction patterns of the compressed samples that are recorded on the CSPADs CCD detectors. This experiment uses both collinear (the drive beam and x-ray probe beam coming from the same side) and transverse (the drive beam and x-ray probe being orthogonal) configurations. The transverse configuration is to collect diffraction signal from a greater volume of material. A selection of the resulting diffraction images of shocked silicon at different phase and pressure states is shown in Fig. 8(b). The spacings of the ring patterns are indications of different phases and compressions. When the sample is shock compressed to above the melt line, the solid crystal structure disappears, and the constructive diffraction pattern becomes very broad and spread out, as shown in Fig. 8(b). The azimuthal diffraction pattern can be integrated and parameterized in terms of the reciprocal lattice parameter, $Q = 4 π$ sin  $θ / λ$⁠, where λ is the probe x-ray wavelength and θ is half the scattering angle. The resulting analysis is shown in Fig. 8(c) demonstrating clear distinctions between the different silicon phases from the ambient diamond cubic phase to the β-tin, imma, then the mixed state of a simple hexagonal with liquid, and finally into the liquid state as the shock strength increases to higher pressures and temperatures. From these high-quality diffraction data, it was discovered that the melt line (solid-liquid transition) occurs at the same pressures as observed in the hydrostatic measurements, whereas the diamond cubic to beta β-tin and the β-tin to the imma solid-solid phase transitions occur at lower pressures than in hydrostatic experiments.

While the x-ray FEL facilities produce high-quality diffraction data, they are limited to medium pressure experiments due to limitations of the available drive lasers. High-pressure diffraction experiments are performed at the large laser facilities. Figure 9(a) shows the diffraction experimental configuration at the NIF using a detector called TARget Diffraction In Situ (TARDIS).⁵ The target is typically composed of an ablator, an x-ray shield, the diffraction sample, and a tamper window. It is typically driven by 16 NIF beams that deliver up to 50 kJ of laser energies to reach pressures of up to 2 TPa (20 Mbar). Another 24 beams are used for the probe x-ray source to generate quasi-monoenergetic He_α x-ray radiation. The diffraction patterns are recorded on image plates mounted on the surfaces of the wedge-shaped detector. The backside of the detector has a window for the VISAR laser to measure the driven target velocity providing a simultaneous pressure measurement. In this experiment, diamond was compressed to 2.01 TPa. Early density functional theory (DFT) studies predict that a new body-centered (BC8) phase of carbon will replace the diamond (FC8) phase as the minimum enthalpy structure between ∼1–2 TPa, as shown in the phase diagram in Fig. 9(b). NIF experiments were carried out to ramp-compress carbon in the form of diamond beyond 2.0 TPa. The diffraction data [examples at 1.74 TPa and 2.01 TPa are shown in Fig. 9(c)] reveal a persistent FC8 structure with no indication of BC8 or any other of the several phases of carbon which have been predicted to form at even higher pressures.²⁹ The result is consistent with a predicted high enthalpy barrier associated with the large number of strong electronic bonds that must be broken to transform from the FC8 into the BC8 phase. The observation that ramp-compressed carbon is solid at 2 TPa has the potential to place some new bounds on the strength and the melting temperature of carbon in a new regime, as well as the percentage of plastic work converted to heat during compression, since DFT-based models and our understanding of typical material response would have suggested that it ought to have melted at these conditions.³⁰ The high pressure HED experimental platforms discussed here should enable new understanding leading to new models and theories under extreme conditions, particularly if they could be accompanied by temperature measurements.

Another HED material study using the diffraction technique led to the remarkable discovery of a superionic water ice phase at conditions expected within the interiors of Uranus and Neptune.^31,32 Based on astronomical observations, planetary scientists determined that the interior structure of these planets should consist of a rocky core surrounded by a mantle consisting of ice mixtures (mostly water, ammonia, and methane), surrounded by a H/He envelop. However, because of the scarcity of data, it is unknown whether such layers are mixed or separated³³ as shown in Figs. 10(a)–10(d). Superionic ice, or ice XVIII, is a phase of water that exists at extremely high P and ρ (density) conditions where the oxygen ions crystalize into bcc or fcc structure, depending on pressure, whereas the hydrogen ions remain liquid. The mobile liquid hydrogen ions enhance the electrical conductivity by factors of 3–5 times that of fluid ionic water. The magnetic field of the ice giants can be partially explained by thin shell convection in a model where the deep ice mantle consists of superionic ice and the outer layers of fluid water which are at the origin of the planetary dynamo. In order to observe the superionic phase of water, experiments were conducted using the Omega laser facilities.^31,32 Multiple beams created a multi-shock compression on the initially liquid water layer that was compressed to pressures of 100–400 GPa and reached temperatures of 2000–3000 K. Additional beams were used to create an x-ray probe near 6–7 keV which enable a collection of in situ diffraction patterns of water ices compressed in a nano-second timescale. These experiments were able to observe a phase transition in water from the bcc state known as ice phase X [blue squares in Fig. 10(e)] to the new superionic ice state, ice XVIII [red squares in Fig. 10(e)]. These diffraction experiments were the first direct observation of the new superionic structure.³² 

The temperature of material under high pressure is a key parameter for the EOS and strength measurements. For material studies, the temperatures of interest are typically 300 ∼ 10 000 K, i.e., less than 1 eV (1 eV = 11 606 K). At this relatively low temperature, commonly known temperature diagnostics, such as optical Thomson scattering, x-ray Thompson scattering, embedded micro-dot spectroscopy, and pyrometry techniques, do not work since their threshold is typically ∼ tens of eV. One can use Extended x-ray Absorption Fine Structure (EXAFS) techniques to measure temperatures <1 eV.³⁴ Here, one measures the oscillations in the x-ray absorption spectrum due to the constructive and destructive interference of photoelectrons scattering off nearby atoms. As the temperature increases, the disorder in the crystal lattice spacing also increases, reducing scattering coherence, and damping the EXAFS oscillations.

One of the key components of the EXAFS measurement is a broadband white-light x-ray backlighter source. One way of creating such a source is to use the laser to an implode a capsule either filled with gas or empty.^35,36 The brightness of such sources has been measured with various spectrometers comparing capsules filled with H₂, D₂, or Kr vs empty capsules. Also, their absolute brightness has been compared with long-pulse (∼ns long) vs short-pulse (10–100 ps long) foil backlighters. It was observed that the capsule backlighter does produce a bright source but is limited to low x-ray energies.³⁷ Recently, it was demonstrated that foil backlighters with hundreds of kJ of laser energy can produce enough bright x rays at higher energies^38,39 to adequately perform EXAFS experiments on high-Z samples.

Another important component of EXAFS experiments is a high-resolution x-ray spectrometer. Spectral resolution is a key for measuring the absorption oscillations for small variations in temperature. One example is the HiRAXS⁴⁰ detector developed for Cu EXAFS experiments on NIF that is built on a Rowland circle geometry⁴¹ and tuned to see 8.9–9.5 keV x rays with better than ∼3eV spectral resolution. Its geometry is shown in Fig. 11(a). And the undriven (i.e., at ambient room temperature) Cu EXAFS spectrum is shown in Fig. 11(b). The analysis shows that the spectral resolution is E/ΔE ∼ 3000, which is sufficient for EXAFS.⁴² 

The absorption measurements are characterized by the structure function: $χ ( k ) = μ ( k ) / μ 0 ( k ) − 1$⁠, where μ is absorption coefficient and k is the wavenumber. The structure function $χ ( k )$ is a function of the nearest-neighbor distance, R, the number of neighboring atoms, N, and the vibration amplitude, $σ 2$⁠.

The first EXAFS experiments in a laser facility were conducted at Omega on a Ti sample,⁷ and its setup is shown in Fig. 12(a). In this experiment, an imploding capsule backlighter was used to generate a bright x-ray continuum source. Three beams were used to drive the sample to pressures of up to 40 GPa. The initial fit produced an unexpectedly high temperature of 2100 K (blue-line). A correction was required due to a Ti phase transition from the α to the ω phase to produce the correct temperature of ∼900 K. In a recent experiment at the NIF, Cu EXAFS measurement, using the HiRAXS detector, is shown in Fig. 1(b). The experimental uncertainty in the temperature inferred from the Cu K-edge EXAFS is estimated to be $∼ ±$15% at ∼3000–4000 K.⁴³ It is known that the EXAFS measurements are sensitive to the dynamic material temperature relative to the Debye temperature, which varies with compression. For some materials, such as iron, the Debye temperature was measured at certain range of pressures.⁴⁴ For materials without Debye temperature measurements, we employ state-of-the-art quantum molecular dynamics (QMD) to calculate the Debye temperature. In addition, at extreme pressure and temperatures, the anharmonic effect becomes non-negligible. We either use an anharmonic model⁸ or compare data directly with calculated EXAFS spectra using atomic positions from QMD or molecular dynamics (MD) simulations since both of them intrinsically include the non-linear lattice dynamics. The measured data are compared with EXAFS spectra predicted from these simulations over a range of temperatures until there is agreement between simulations and experimental data, thus allowing temperature to be inferred without calculating a Debye temperature.

Streaked Optical Pyrometry (SOP) is another diagnostic method that can infer the temperature of the sample by assuming the heated sample is a gray-body emitter. The threshold temperature for SOP is ∼0.3 eV (∼3500 K), and it is used for higher-temperature measurements.⁴⁵ SOP is particularly suitable to measure the shock temperature of initially transparent samples, such as hydrogen and helium,⁴⁶ and detect phase transformations, such as melting.^47,48

Strength is the resistance to plastic deformation. When shear stress, σ_shear, is applied to a sample, the material deforms and the amount of deformation is characterized by the shear strain, $ε shear ∼ Δ x / L$⁠, where $Δ x$ is the amount of plastic shear deformation and L is the characteristic length. In a strong material, a large shear stress, σ_shear, is needed to deform a material irreversibly with the formation of defects in the crystal lattice. The strength at high pressure is important for understanding high velocity impacts, such as meteor impacts, the implosion processes, and planetary core formation dynamics. Strength is a function of temperature, pressure, strain, strain rate, compression, phase, and grain size. Many constitutive strength models have been verified at low pressures, but there is little data at high pressures and high strain rates to test strength models at extreme HED conditions.

One way of studying material strength is to utilize the Rayleigh–Taylor (RT) instability at an interface between materials of different density.⁴ When acceleration, or pressure, is applied from the low-density side of the interface, perturbations at the interface will grow via the RT instability. If the material has strength, this RT growth will be suppressed. Using face-on x-ray radiography, the growth of a prescribed sinusoidal ripple under acceleration can be measured; then, the material strength can be inferred by comparing the ripple growth with different strength models, as depicted in Fig. 14(a).

The x-ray radiographic diagnostic is a key to carrying out strength experiments. X-ray radiography is generally performed in two configurations: point source projection as shown in Fig. 13(a) and area backlighting, as shown in Fig. 13(b). The former relies on a point source of x rays to obtain the required spatial resolution. The imaging magnification is: $M prj = ( d 1 + d 2 ) / d 1$⁠, where M_prj is the magnification, d₁ is the distance between the x-ray source to the object, and d₂ is the distance between the object and the detector. The point projection configuration generally provides a more uniform illumination and is easier to have a larger field of view simply by changing the distances for a given backlighter source. The area backlighter relies on an x-ray source that is as large as the object and the imaging resolution is determined by the pinhole size (for pinhole imagers). The magnification for a pinhole imager with an area backlighter is $M area = d 3 / d 1$⁠, where d₁ is the distance from the object to the pinhole and d₃ is the distance from the pinhole array to the detector. The choice of backlighter configurations depends on the radiographic requirements of each experiment.

Another requirement is high x-ray energy (>20 keV) which is needed to penetrate high-Z materials when performing face-on radiography. High intensity (>10¹⁷W/cm²) short pulse (<100 ps) lasers can generate high energy x rays efficiently.⁴⁹ The x rays are generated by hot-electrons knocked out of the bound k-shell electrons and the resulting transition produces mainly K_α x rays in the backlighter material. A unique feature of this mechanism is that the x-ray emission is confined to the volume of the target where the hot electrons are interacting. Thus, by using a thin foil (<5 μm) or wire (<10 μm dia), high-resolution radiography can be achieved.⁵⁰ The large area x-ray emitting plasma plumes produced by long pulse lasers do not allow for high resolution imaging without a sophisticated x-ray imaging optic. High intensity (>10¹⁶W/cm²) long-pulse laser illumination with ∼50 kJ laser, small laser spot of ∼150 μm diameter, and ∼3 ns long can create intense bremsstrahlung emission that can be energy filtered to generate effective high energy x-ray sources.⁵¹ The effective source size can be decreased by a thick tapered pinhole aperture or by slits to give high spatial resolution.

An example of a Pb strength experiment is shown in Fig. 14.⁵² The ramp drive is created using the reservoir-gap configuration where 800 kJ 351 nm laser in 4 ns illuminates the inside of the hohlraum. The target package is a layered reservoir with varying densities and a gap that creates a ramped compression from the released plasma. This configuration created up to ∼400 GPa of peak pressure. The pressure–temperature phase diagram of Pb is shown in Fig. 14(c). The initial shock causes the material to quickly pass through the fcc and hcp states and for the majority of the experimental time the material is in its bcc phase. Face-on radiography of the driven Pb ripples is shown in Fig. 14(b). The radiography data has been converted to areal density using in situ steps. The x-ray source size and the modulation transfer function are derived from the x-ray knife edge images. Additional calibration is performed using the undriven large-amplitude reference ripples. The perturbation growth factor (GF) is calculated from: $G F = ( ρ Z ) driven / [ ( ρ Z ) initial · MTF ]$⁠, where $( ρ Z ) driven$ is the areal density of the driven ripples, $( ρ Z ) initial$ is the initial ripple areal density, and MTF is the modulation transfer function representing the spatial resolution of the x-ray source. The resulting GFs as a function of backlighter delay times are shown in Fig. 14(d) and compared with different strength models. The inferred Pb strength from this study is ∼3.8 GPa, which is a ∼250-fold increase compared to the ambient strength.⁵² 

In conclusion, modern high energy density (HED) facilities and novel diagnostics allow theory and simulations to be tested at high pressures and densities relevant to planetary interior conditions and other extreme environments. HED conditions are produced by high-energy lasers, x-ray free-electron lasers, or at magnetic pulsed power facilities using plasma drives. Bright and coherent x-ray sources enable the probing of atomic lattice-level material properties and deformation mechanisms. Dynamic high-pressure experiments have revealed new insights into equations of state, phase, temperature, and strength behavior at extreme HED conditions relevant to hypervelocity impact phenomena, planetary formation dynamics, planetary interiors, and inertial confinement fusion implosion dynamics.

This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract No. DE-AC52-07NA27344. E.E.M. acknowledges that her work was supported by the Department of Energy, Laboratory Directed Research and Development program at SLAC National Accelerator Laboratory, under Contract No. DE-AC02-76SF00515 and as part of the Panofsky Fellowship awarded to E.E.M.

Data are available from the corresponding author with reasonable request.