Solid iron compressed up to 560 GPa

Measurements of K-edge and L-edge extended x-ray absorption fine structure at the national ignition facility (invited)

High-energy-density laser facilities and advances in dynamic compression techniques have expanded access to material states in the Terapascal regime relevant to inertial confinement fusion, planetary science, and geophysics. However, experimentally determining the material temperature in these extreme conditions has remained a difficult challenge. Extended X-ray Absorption Fine Structure (EXAFS), referring to the modulations in x-ray absorption above an absorption edge from photoelectrons' interactions with neighboring atoms, has proven to be a versatile and robust technique for probing material temperature and density for mid-to-high Z elements under dynamic compression. The current platform at the National Ignition Facility has developed six configurations for EXAFS measurements between 7 and 18 keV for different absorption edges (Fe K, Co K, Cu K, Ta L3, Pb L3, and Zr K) using a curved-crystal spectrometer and a bright, continuum foil x-ray source. In this work, we describe the platform geometry, x-ray source performance, spectrometer resolution and throughput, design considerations, and data in ambient and dynamic-compression conditions.

Extended X-ray absorption fine structure of dynamically-compressed copper up to 1 terapascal

Large laser facilities have recently enabled material characterization at the pressures of Earth and Super-Earth cores. However, the temperature of the compressed materials has been largely unknown, or solely relied on models and simulations, due to lack of diagnostics under these challenging conditions. Here, we report on temperature, density, pressure, and local structure of copper determined from extended x-ray absorption fine structure and velocimetry up to 1 Terapascal. These results nearly double the highest pressure at which extended x-ray absorption fine structure has been reported in any material. In this work, the copper temperature is unexpectedly found to be much higher than predicted when adjacent to diamond layer(s), demonstrating the important influence of the sample environment on the thermal state of materials; this effect may introduce additional temperature uncertainties in some previous experiments using diamond and provides new guidance for future experimental design.

Single-shot X-ray absorption spectroscopy at X-ray free electron lasers

X-ray Absorption Spectroscopy (XAS) is a widely used X-ray diagnostic method for studying electronic and structural properties of matter. At first glance, the relatively narrow bandwidth and the highly fluctuating spectral structure of X-ray Free Electron Lasers (XFEL) sources seem to require accumulation over many shots to achieve high data quality. To date the best approach to implementing XAS at XFEL facilities has been using monochromators to scan the photon energy across the desired spectral range. While this is possible for easily reproducible samples such as liquids, it is incompatible with many important systems. Here, we demonstrate collection of single-shot XAS spectra over 10s of eV using an XFEL source, with error bars of only a few percent. We additionally show how to extend this technique over wider spectral ranges towards Extended X-ray Absorption Fine Structure measurements, by concatenating a few tens of single-shot measurements. Our results pave the way for future XAS studies at XFELs, in particular those in the femtosecond regime. This advance is envisioned to be especially important for many transient processes that can only be initiated at lower repetition rates, for difficult to reproduce excitation conditions, or for rare samples, such as those encountered in high-energy density physics.

Ideal plasticity and shape memory of nanolamellar high-entropy alloys

Understanding the relationship among elemental compositions, nanolamellar microstructures, and mechanical properties enables the rational design of high-entropy alloys (HEAs). Here, we construct nanolamellar AlxCoCuFeNi HEAs with alternating high- and low-Al concentration layers and explore their mechanical properties using a combination of molecular dynamic simulation and density functional theory calculation. Our results show that the HEAs with nanolamellar structures exhibit ideal plastic behavior during uniaxial tensile loading, a feature not observed in homogeneous HEAs. This remarkable ideal plasticity is attributed to the unique deformation mechanisms of phase transformation coupled with dislocation nucleation and propagation in the high-Al concentration layers and the confinement and slip-blocking effect of the low-Al concentration layers. Unexpectedly, this ideal plasticity is fully reversible upon unloading, leading to a remarkable shape memory effect. Our work highlights the importance of nanolamellar structures in controlling the mechanical and functional properties of HEAs and presents a fascinating route for the design of HEAs for both functional and structural applications.

Double-Shock Compression Pathways from Diamond to BC8 Carbon

Carbon is one of the most important elements for both industrial applications and fundamental research, including life, physics, chemistry, materials, and even planetary science. Although theoretical predictions on the transition from diamond to the BC8 (Ia3[over ¯]) carbon were made more than thirty years ago, after tremendous experimental efforts, direct evidence for the existence of BC8 carbon is still lacking. In this study, a machine learning potential was developed for high-pressure carbon fitted from first-principles calculations, which exhibited great capabilities in modeling the melting and Hugoniot line. Using the molecular dynamics based on this machine learning potential, we designed a thermodynamic pathway that is achievable for the double shock compression experiment to obtain the elusive BC8 carbon. Diamond was compressed up to 584 GPa after the first shock at 20.5  km/s. Subsequently, in the second shock compression at 24.8 or 25.0  km/s, diamond was compressed to a supercooled liquid and then solidified to BC8 in around 1 ns. Furthermore, the critical nucleus size and nucleation rate of BC8 were calculated, which are crucial for nano-second x-ray diffraction measurements to observe BC8 carbon during shock compressions. The key to obtaining BC8 carbon lies in the formation of liquid at a sufficient supercooling. Our work provides a feasible pathway by which the long-sought BC8 phase of carbon can be reached in experiments.

Scaling Law for the Onset of Solidification at Extreme Undercooling

Quasi-isentropic compression enables one to study the solidification of metastable liquid states that are inaccessible through other experimental means. The onset of this nonequilibrium solidification is known to depend on the compression rate and material-specific factors, but this complex interdependence has not been well characterized. In this study, we use a combination of experiments, theory, and computational simulations to derive a general scaling law that quantifies this dependence. One of its applications is a novel means to elucidate melt temperatures at high pressures.

Toward better understanding of the high-pressure structural transformation in beryllium by the statistical moment method

Beryllium is a vital alkaline-earth metal for plasma physics, space science, and nuclear technology. Unfortunately, its accurate phase diagram is clouded by many controversial results, even though solid beryllium can only exist with hcp or bcc crystalline structures. Herein, we offer a simple quantum-statistical solution to the above problem. Our core idea is to develop the moment expansion technique to determine the Helmholtz free energy under extreme conditions. This strategy helps elucidate the underlying correlation among symmetric characteristics, vibrational excitations, and physical stabilities. In particular, our analyses reveal that the appearance of anharmonic effects forcefully straightens up the hcp-bcc boundary. This phenomenon explains why it has been difficult to detect bcc signatures via diamond-anvil-cell measurements. Besides, we modify the work-heat equivalence principle to quickly obtain the high-pressure melting profile from the room-temperature equation of state. The hcp-bcc-liquid triple point of beryllium is found at 165 GPa and 4559 K. Our theoretical findings agree excellently with cutting-edge ab initio simulations adopting the phonon quasiparticle method and the thermodynamic integration. Finally, we consider the principal Hugoniot curve and its secondary branches to explore the behaviors of beryllium under shock compression. Our predictions would be advantageous for designing inertial-confinement-fusion experiments.

Cooperative diffusion in body-centered cubic iron in Earth and super-Earths' inner core conditions

The physical chemistry of iron at the inner-core conditions is key to understanding the evolution and habitability of Earth and super-Earth planets. Based on full first-principles simulations, we report cooperative diffusion along the longitudinally fast⟨111⟩directions of body-centered cubic (bcc) iron in temperature ranges of up to 2000-4000 K below melting and pressures of ∼300-4000 GPa. The diffusion is due to the low energy barrier in the corresponding direction and is accompanied by mechanical and dynamical stability, as well as strong elastic anisotropy of bcc iron. These findings provide a possible explanation for seismological signatures of the Earth's inner core, particularly the positive correlation between P wave velocity and attenuation. The diffusion can also change the detailed mechanism of core convection by increasing the diffusivity and electrical conductivity and lowering the viscosity. The results need to be considered in future geophysical and planetary models and should motivate future studies of materials under extreme conditions.

Imaging velocity interferometer system for any reflector (VISAR) diagnostics for high energy density sciences

Two variants of optical imaging velocimetry, specifically the one-dimensional streaked line-imaging and the two-dimensional time-resolved area-imaging versions of the Velocity Interferometer System for Any Reflector (VISAR), have become important diagnostics in high energy density sciences, including inertial confinement fusion and dynamic compression of condensed matter. Here, we give a brief review of the historical development of these techniques, then describe the current implementations at major high energy density (HED) facilities worldwide, including the OMEGA Laser Facility and the National Ignition Facility. We illustrate the versatility and power of these techniques by reviewing diverse applications of imaging VISARs for gas-gun and laser-driven dynamic compression experiments for materials science, shock physics, condensed matter physics, chemical physics, plasma physics, planetary science and astronomy, as well as a broad range of HED experiments and laser-driven inertial confinement fusion research.

High-resolution x-ray spectrometer for x-ray absorption fine structure spectroscopy

Two extended x-ray absorption fine structure flat crystal x-ray spectrometers (EFX's) were designed and built for high-resolution x-ray spectroscopy over a large energy range with flexible, on-shot energy dispersion calibration capabilities. The EFX uses a flat silicon [111] crystal in the reflection geometry as the energy dispersive optic covering the energy range of 6.3-11.4 keV and achieving a spectral resolution of 4.5 eV with a source size of 50 μm at 7.2 keV. A shot-to-shot configurable calibration filter pack and Bayesian inference routine were used to constrain the energy dispersion relation to within ±3 eV. The EFX was primarily designed for x-ray absorption fine structure (XAFS) spectroscopy and provides significant improvement to the Laboratory for Laser Energetics' OMEGA-60 XAFS experimental platform. The EFX is capable of performing extended XAFS measurements of multiple absorption edges simultaneously on metal alloys and x-ray absorption near-edge spectroscopy to measure the electron structure of compressed 3d transition metals.

Probing atomic physics at ultrahigh pressure using laser-driven implosions

Spectroscopic measurements of dense plasmas at billions of atmospheres provide tests to our fundamental understanding of how matter behaves at extreme conditions. Developing reliable atomic physics models at these conditions, benchmarked by experimental data, is crucial to an improved understanding of radiation transport in both stars and inertial fusion targets. However, detailed spectroscopic measurements at these conditions are rare, and traditional collisional-radiative equilibrium models, based on isolated-atom calculations and ad hoc continuum lowering models, have proved questionable at and beyond solid density. Here we report time-integrated and time-resolved x-ray spectroscopy measurements at several billion atmospheres using laser-driven implosions of Cu-doped targets. We use the imploding shell and its hot core at stagnation to probe the spectral changes of Cu-doped witness layer. These measurements indicate the necessity and viability of modeling dense plasmas with self-consistent methods like density-functional theory, which impact the accuracy of radiation transport simulations used to describe stellar evolution and the design of inertial fusion targets.

Atoms and molecules under extreme temperature and pressure can be investigated using dense plasmas achieved by laser-driven implosion. Here the authors report spectral change of copper in billions atmosphere pressure that can only be explained by a self-consistent approach.

Dynamic Strength of Iron at High Pressures and Strain Rates

Accurate modeling of meteorite impacts, and deformation of planetary cores require characterization of the flow strength and in-elasticity of iron in its different phases. In this Letter, we investigate the flow strength of both the ambient α phase and high-pressure ε phase of iron at strain rates of 1×10^{5}  s^{-1} and pressures up to 42 GPa using high-pressure-pressure shear plate impact experiments. We report the strength of the ε iron to be significantly higher than α phase but consequently one order smaller than the previously reported dynamic strength at high pressures. The complete stress-strain response of the ε phase is reported for the first time.

Towards a dynamic compression facility at the ESRF

Results of the 2018 commissioning and experimental campaigns of the new High Power Laser Facility on the Energy-dispersive X-ray Absorption Spectroscopy (ED-XAS) beamline ID24 at the ESRF are presented. The front-end of the future laser, delivering 15 J in 10 ns, was interfaced to the beamline. Laser-driven dynamic compression experiments were performed on iron oxides, iron alloys and bismuth probed by online time-resolved XAS.

Femtosecond Visualization of hcp-Iron Strength and Plasticity under Shock Compression

Iron is a key constituent of planets and an important technological material. Here, we combine in situ ultrafast x-ray diffraction with laser-induced shock compression experiments on Fe up to 187(10) GPa and 4070(285) K at 10^{8}  s^{-1} in strain rate to study the plasticity of hexagonal-close-packed (hcp)-Fe under extreme loading states. {101[over ¯]2} deformation twinning controls the polycrystalline Fe microstructures and occurs within 1 ns, highlighting the fundamental role of twinning in hcp polycrystals deformation at high strain rates. The measured deviatoric stress initially increases to a significant elastic overshoot before the onset of flow, attributed to a slower defect nucleation and mobility. The initial yield strength of materials deformed at high strain rates is thus several times larger than their longer-term flow strength. These observations illustrate how time-resolved ultrafast studies can reveal distinctive plastic behavior in materials under extreme environments.

Simultaneously enhancing the ultimate strength and ductility of high-entropy alloys via short-range ordering

Simultaneously enhancing strength and ductility of metals and alloys has been a tremendous challenge. Here, we investigate a CoCuFeNiPd high-entropy alloy (HEA), using a combination of Monte Carlo method, molecular dynamic simulation, and density-functional theory calculation. Our results show that this HEA is energetically favorable to undergo short-range ordering (SRO), and the SRO leads to a pseudo-composite microstructure, which surprisingly enhances both the ultimate strength and ductility. The SRO-induced composite microstructure consists of three categories of clusters: face-center-cubic-preferred (FCCP) clusters, indifferent clusters, and body-center-cubic-preferred (BCCP) clusters, with the indifferent clusters playing the role of the matrix, the FCCP clusters serving as hard fillers to enhance the strength, while the BCCP clusters acting as soft fillers to increase the ductility. Our work highlights the importance of SRO in influencing the mechanical properties of HEAs and presents a fascinating route for designing HEAs to achieve superior mechanical properties.

New frontiers in extreme conditions science at synchrotrons and free electron lasers

Synchrotrons and free electron lasers are unique facilities to probe the atomic structure and electronic properties of matter at extreme thermodynamical conditions. In this context, 'matter at extreme pressures and temperatures' was one of the science drivers for the construction of low emittance 4th generation synchrotron sources such as the Extremely Brilliant Source of the European Synchrotron Radiation Facility and hard x-ray free electron lasers, such as the European x-ray free electron laser. These new user facilities combine static high pressure and dynamic shock compression experiments to outstanding high brilliance and submicron beams. This combination not only increases the data-quality but also enlarges tremendously the accessible pressure, temperature and density space. At the same time, the large spectrum of available complementary x-ray diagnostics for static and shock compression studies opens unprecedented insights into the state of matter at extremes. The article aims at highlighting a new horizon of scientific opportunities based on the synergy between extremely brilliant synchrotrons and hard x-ray free electron lasers.

Unraveling the intrinsic atomic physics behind x-ray absorption line shifts in warm dense silicon plasmas

We present a free-energy density functional theory (DFT)-based methodology for optical property calculations of warm dense matter to cover a wide range of thermodynamic conditions and photon energies including the entire x-ray range. It uses Mermin-Kohn-Sham density functional theory with exchange-correlation (XC) thermal effects taken into account via a fully temperature dependent generalized gradient approximation XC functional. The methodology incorporates a combination of the ab initio molecular dynamics (AIMD) snapshotted Kubo-Greenwood optic data with a single atom in simulation cell calculations to close the photon energy gap between the L and K edges and extend the K-edge tail toward many-keV photon energies. This gap arises in the standard scheme due to a prohibitively large number of bands required for the Kubo-Greenwood calculations with AIMD snapshots. Kubo-Greenwood data on snapshots provide an accurate description of optic properties at low photon frequencies slightly beyond the L edge and x-ray absorption near edges structure (XANES) spectra, while data from periodic calculations with single atoms cover the tail regions beyond the edges. To demonstrate its applicability to mid-Z materials where the standard DFT-based approach is not computationally feasible, we have applied it to opacity calculations of warm dense silicon plasmas. These first-principles calculations revealed a very interesting phenomenon of redshift-to-blueshift in K-L (1s→2p) and K-edge absorptions along both isotherm and isochore, which are absent in most continuum-lowering models of traditional plasma physics. This new physics phenomenon can be attributed to the underlying competition between the screening of deeply bound core electrons and the screening of outer-shell electrons caused by warm-dense-plasma conditions. We further demonstrate that the ratio of 1s→2p to the K-edge x-ray absorptions can be used to characterize warm-dense-plasma conditions. Eventually, based on our absorption calculations, we have established a first-principles opacity table (FPOT) for silicon in a wide range of material densities and temperatures.

Ni Doping: A Viable Route to Make Body-Centered-Cubic Fe Stable at Earth’s Inner Core

With the goal of answering the highly debated question of whether the presence of Ni at the Earth’s inner core can make body-centered cubic (bcc) Fe stable, we performed a computational study based on first-principles calculations on bcc, hexagonal closed packed (hcp), and face-centered cubic (fcc) structures of the Fe1−xNix alloys (x = 0, 0.0312, 0.042, 0.0625, 0.084, 0.125, 0.14, 0.175) at 200–364 GPa and investigated their relative stability. Our thorough study reveals that the stability of Ni-doped bcc Fe is crucially dependent on the nature of the distribution of Ni in the Fe matrix. We confirm this observation by considering several possible configurations for a given concentration of Ni doping. Our theoretical evidence suggests that Ni-doped bcc Fe could be a stable phase at the Earth’s inner core condition as compared to its hcp and fcc counterparts.

Metastability of diamond ramp-compressed to 2 terapascals

Carbon is the fourth-most prevalent element in the Universe and essential for all known life. In the elemental form it is found in multiple allotropes, including graphite, diamond and fullerenes, and it has long been predicted that even more structures can exist at pressures greater than those at Earth's core^1-3. Several phases have been predicted to exist in the multi-terapascal regime, which is important for accurate modelling of the interiors of carbon-rich exoplanets^4,5. By compressing solid carbon to 2 terapascals (20 million atmospheres; more than five times the pressure at Earth's core) using ramp-shaped laser pulses and simultaneously measuring nanosecond-duration time-resolved X-ray diffraction, we found that solid carbon retains the diamond structure far beyond its regime of predicted stability. The results confirm predictions that the strength of the tetrahedral molecular orbital bonds in diamond persists under enormous pressure, resulting in large energy barriers that hinder conversion to more-stable high-pressure allotropes^1,2, just as graphite formation from metastable diamond is kinetically hindered at atmospheric pressure. This work nearly doubles the highest pressure at which X-ray diffraction has been recorded on any material.

Crystal Structure and Melting of Fe Shock Compressed to 273 GPa: In Situ X-Ray Diffraction

Despite extensive shock wave and static compression experiments and corresponding theoretical work, consensus on the crystal structure and the melt boundary of Fe at Earth's core conditions is lacking. We present in situ x-ray diffraction measurements in laser-shock compressed Fe that establish the stability of the hexagonal-close-packed (hcp) structure along the Hugoniot through shock melting, which occurs between ∼242 to ∼247  GPa. Using previously reported hcp Fe Hugoniot temperatures, the melt temperature is estimated to be 5560(360) K at 242 GPa, consistent with several reported Fe melt curves. Extrapolation of this value suggests ∼6400  K melt temperature at Earth's inner core boundary pressure.

An approach for the measurement of the bulk temperature of single crystal diamond using an X-ray free electron laser

We present a method to determine the bulk temperature of a single crystal diamond sample at an X-Ray free electron laser using inelastic X-ray scattering. The experiment was performed at the high energy density instrument at the European XFEL GmbH, Germany. The technique, based on inelastic X-ray scattering and the principle of detailed balance, was demonstrated to give accurate temperature measurements, within [Formula: see text] for both room temperature diamond and heated diamond to 500 K. Here, the temperature was increased in a controlled way using a resistive heater to test theoretical predictions of the scaling of the signal with temperature. The method was tested by validating the energy of the phonon modes with previous measurements made at room temperature using inelastic X-ray scattering and neutron scattering techniques. This technique could be used to determine the bulk temperature in transient systems with a temporal resolution of 50 fs and for which accurate measurements of thermodynamic properties are vital to build accurate equation of state and transport models.

Pressure effects on the EXAFS Debye-Waller factor of iron

The pressure effects on atomic mean-square relative displacement characterizing the extended X-ray absorption fine structure (EXAFS) Debye-Waller factor of iron metal have been investigated based on the Debye model. The analytical expressions of the Debye frequency and EXAFS Debye-Waller factor have been derived as functions of crystal volume compressibility. Based on the well established equation-of-state including the contributions of the anharmonic and electronic thermal pressures, numerical calculations have been performed for iron up to a pressure of 220 GPa and compared with experimental data when possible. These results show that the Debye frequency increases rapidly with compression, and beyond 150 GPa it behaves as a linear function of pressure. Meanwhile the mean-square relative displacement curve drops robustly with pressure, especially at pressures smaller than 100 GPa. This phenomenon causes the enhancement of EXAFS signals at high pressure. Reversely, the increasing of temperature will reduce the amplitude of EXAFS spectra.

Single-pulse (100 ps) extended x-ray absorption fine structure capability at the Dynamic Compression Sector

Determining real-time changes in the local atomistic order is important for a mechanistic understanding of shock wave induced structural and chemical changes. However, the single event and short duration (nanosecond times) nature of shock experiments pose challenges in obtaining Extended X-ray Absorption Fine Structure (EXAFS) measurements-typically used for monitoring local order changes. Here, we report on a new single pulse (∼100 ps duration) transmission geometry EXAFS capability for use in laser shock-compression experiments at the Dynamic Compression Sector (DCS), Advanced Photon Source. We used a flat plate of highly oriented pyrolytic graphite (HOPG) as the spectrometer element to energy disperse x rays transmitted through the sample. It provided high efficiency with ∼15% of the x rays incident on the HOPG reaching an x-ray area detector with high quantum efficiency. This combination resulted in a good signal-to-noise ratio (∼10³), an energy resolution of ∼10 eV at 10 keV, EXAFS spectra covering 100 s of eV, and a good pulse to pulse reproducibility of our single pulse measurements. Ambient EXAFS spectra for Cu and Au are compared to the reference spectra, validating our measurement system. Comparison of single pulse EXAFS results for ambient and laser shocked Ge(100) shows large changes in the local structure of the short lived state of shocked Ge. The current DCS EXAFS capability can be used to perform single pulse measurements in laser shocked materials from ∼9 keV to 13 keV. These EXAFS developments will be available to all users of the DCS.

Foil backlighter development at the OMEGA laser facility for extended x-ray absorption fine structure experiments

Extended x-ray absorption fine structure (EXAFS) measurements require a bright and continuous x-ray source and a detection system with high spectral resolution to capture the modulations of the absorption coefficient above the material absorption edge. When performing EXAFS measurements under laser-driven dynamic compression, it is hence critical to optimize the backlighter x-ray emission. A series of experiments has been conducted at the OMEGA laser facility to characterize titanium (Z = 22), iron (Z = 26), germanium (Z = 32), molybdenum (Z = 42), silver (Z = 47), and gold (Z = 79) foil backlighters irradiated with 3 kJ-12 kJ of laser energy. The spectra have been recorded using a dual crystal spectrometer (DCS), a two-channel transmission spectrometer covering 11 keV-45 keV and 19 keV-90 keV energy bands. The DCS has been calibrated so that the spectral intensities can be compared between different campaigns.

Theoretical development and experimental validation on the measurement of temperature by extended X-ray absorption fine structure

A systematic investigation on the theoretical framework of the ultra-fast measurement of temperature by extended X-ray absorption fine structure (EXAFS) applied in laser-driven-compression experiments has been carried out and a new temperature measurement scheme based on the EXAFS cumulant expansion analysis and anharmonic correlated Debye model has been advanced. By considering the anharmonic effect of thermal vibration and avoiding the employment of the empirical model as well as parameters which have large inherent uncertainties in the temperature determination, this new scheme is theoretically more accurate than traditional ones. Then the performance of the new measurement scheme and traditional methods were validated on a synchrotron radiation platform by temperature-dependent EXAFS (TDEXAFS) experiments on Au, Fe, V and Ti; the results showed that the new scheme could provide the most accurate measured temperatures with much lower uncertainties. This accurate scheme gives a firmer physical ground to the EXAFS temperature measurement technique and can expect to be applied in laser-driven compression experiments and promote the development of matter state research at extreme conditions.

Measurements of pressure-induced Kβ line shifts in ramp compressed cobalt up to 8 Mbar

We report measurements of K-shell fluorescence lines induced by fast electrons in ramp-compressed Co targets. The fluorescence emission was stimulated by fast electrons generated through short-pulse laser-solid interaction with an Al target layer. Compression up to 2.1× solid density was achieved while maintaining temperatures well below the Fermi energy, effectively removing the thermal effects from consideration. We observed small but unambiguous redshifts in the Kβ fluorescence line relative to unshifted Cu Kα. Redshifts up to 2.6 eV were found to increase with compression and to be consistent with predictions from self-consistent models based on density-functional theory.

Single-Shot Multi-keV X-Ray Absorption Spectroscopy Using an Ultrashort Laser-Wakefield Accelerator Source

Single-shot absorption measurements have been performed using the multi-keV x rays generated by a laser-wakefield accelerator. A 200 TW laser was used to drive a laser-wakefield accelerator in a mode which produced broadband electron beams with a maximum energy above 1 GeV and a broad divergence of ≈15  mrad FWHM. Betatron oscillations of these electrons generated 1.2±0.2×10^{6}  photons/eV in the 5 keV region, with a signal-to-noise ratio of approximately 300∶1. This was sufficient to allow high-resolution x-ray absorption near-edge structure measurements at the K edge of a titanium sample in a single shot. We demonstrate that this source is capable of single-shot, simultaneous measurements of both the electron and ion distributions in matter heated to eV temperatures by comparison with density functional theory simulations. The unique combination of a high-flux, large bandwidth, few femtosecond duration x-ray pulse synchronized to a high-power laser will enable key advances in the study of ultrafast energetic processes such as electron-ion equilibration.

Heat-release equation of state and thermal conductivity of warm dense carbon by proton differential heating

Warm dense carbon is generated at 0.3-2.0 g/cc and 1-7 eV by proton heating. The release equation of state (EOS) after heating and thermal conductivity of warm dense carbon are studied experimentally in this regime using a Au/C dual-layer target to initiate a temperature gradient and two picosecond time-resolved diagnostics to probe the surface expansion and heat flow. Comparison between the data and simulations using various EOSs and thermal conductivity models is quantified with a statistical χ^{2} analysis. Out of seven EOS tables and five thermal conductivity models, only L9061 with the Lee-More model provides a probability above 50% to match all data.

Extreme Hardening of Pb at High Pressure and Strain Rate

We study the high-pressure strength of Pb and Pb-4wt%Sb at the National Ignition Facility. We measure Rayleigh-Taylor growth of preformed ripples ramp compressed to ∼400  GPa peak pressure, among the highest-pressure strength measurements ever reported on any platform. We find agreement with 2D simulations using the Improved Steinberg-Guinan strength model for body-centered-cubic Pb; the Pb-4wt%Sb alloy behaves similarly within the error bars. The combination of high-rate, pressure-induced hardening and polymorphism yield an average inferred flow stress of ∼3.8  GPa at high pressure, a ∼250-fold increase, changing Pb from soft to extremely strong.

Electronic correlations in dense iron: from moderate pressure to Earth's core conditions

We discuss the role of dynamical many-electron effects in the physics of iron and iron-rich solid alloys under applied pressure on the basis of recent ab initio studies employing the dynamical mean-field theory (DMFT). We review in detail two particularly interesting regimes: first, a moderate pressure range up to 60 GPa and, second, the ultra-high pressure of about 360 GPa expected inside the solid inner core of Earth. Electronic correlations in iron under the moderate pressure of several tens GPa are discussed in the first section. DMFT-based methods predict an enhancement of electronic correlations at the pressure-induced body-centered cubic α to hexagonal close-packed [Formula: see text] phase transition. In particular, the electronic effective mass, scattering rate and electron-electron contribution to the electrical resistivity undergo a step-wise increase at the transition point. One also finds a significant many-body correction to the [Formula: see text]-Fe equation of state, thus clarifying the origin of discrepancies between previous DFT studies and experiment. An electronic topological transition is predicted to be induced in [Formula: see text]-Fe by many-electron effects; its experimental signatures are analyzed. The next section focuses on the geophysically relevant pressure-temperature regime of the Earth's inner core (EIC) corresponding to the extreme pressure of 360 GPa combined with temperatures up to 6000 K. The three iron allotropes ([Formula: see text], [Formula: see text] and face-centered-cubic [Formula: see text]) previously proposed as possible stable phases at such conditions are found to exhibit qualitatively different many-electron effects as evidenced by a strongly non-Fermi-liquid metallic state of [Formula: see text]-Fe and an almost perfect Fermi liquid in the case of [Formula: see text]-Fe. A recent active discussion on the electronic state and transport properties of [Formula: see text]-Fe at the EIC conditions is reviewed in details. Estimations for the dynamical many-electron contribution to the relative phase stability are presented. We also discuss the impact of a Ni admixture, which is expected to be present in the core matter. We conclude by outlining some limitation of the present DMFT-based framework relevant for studies of iron-base systems as well as perspective directions for further development.

Low viscosity of the Earth's inner core

The Earth's solid inner core is a highly attenuating medium. It consists mainly of iron. The high attenuation of sound wave propagation in the inner core is at odds with the widely accepted paradigm of hexagonal close-packed phase stability under inner core conditions, because sound waves propagate through the hexagonal iron without energy dissipation. Here we show by first-principles molecular dynamics that the body-centered cubic phase of iron, recently demonstrated to be thermodynamically stable under the inner core conditions, is considerably less elastic than the hexagonal phase. Being a crystalline phase, the body-centered cubic phase of iron possesses the viscosity close to that of a liquid iron. The high attenuation of sound in the inner core is due to the unique diffusion characteristic of the body-centered cubic phase. The low viscosity of iron in the inner core enables the convection and resolves a number of controversies.

Two-phase equation of state for lithium fluoride

We present an equation of state for the solid and liquid phases of lithium fluoride that covers a wide range of conditions from ambient pressure and temperature to the high pressures and temperatures exhibited in shock- and ramp-compression studies. The particular solid phase we have focused on in this work is the B1 phase. We have followed an approach where the pressure and heat-capacity functions of both phases are fit to experimental data and our own quantum molecular dynamics simulations and are then integrated in a thermodynamically consistent way to obtain the corresponding free-energy functions. This approach yields a two-phase equation of state that provides better overall agreement with experimental data than other equations of state for lithium fluoride, such as SESAME 7271v3, LEOS 2240, and the model presented by Smirnov. The last of these is a three-phase equation of state that predicts a B1-B2 transition along the shock Hugoniot at a pressure of about 140 GPa. This solid-solid transition has been a topic of speculation and debate in the literature for over 50 years, culminating in the work of Smirnov, who has developed the only potentially viable equation of state that allows for this transition. We explain why the proposed B1-B2 transition at 140 GPa is not consistent with recent velocimetry data.

Developing a high-flux, high-energy continuum backlighter for extended x-ray absorption fine structure measurements at the National Ignition Facility

Extended X-ray absorption fine structure (EXAFS) spectroscopy is a powerful tool for in situ characterization of matter in the high energy density regime. An EXAFS platform is currently being developed on the National Ignition Facility. Development of a suitable X-ray backlighter involves minimizing the temporal duration and source size while maximizing spectral smoothness and brightness. One approach involves imploding a spherical shell, which generates a high-flux X-ray flash at stagnation. We present results from a series of experiments comparing the X-ray source properties produced by imploded empty and Ar-filled capsules.

Neural Network Approach for Characterizing Structural Transformations by X-Ray Absorption Fine Structure Spectroscopy

The knowledge of the coordination environment around various atomic species in many functional materials provides a key for explaining their properties and working mechanisms. Many structural motifs and their transformations are difficult to detect and quantify in the process of work (operando conditions), due to their local nature, small changes, low dimensionality of the material, and/or extreme conditions. Here we use an artificial neural network approach to extract the information on the local structure and its in situ changes directly from the x-ray absorption fine structure spectra. We illustrate this capability by extracting the radial distribution function (RDF) of atoms in ferritic and austenitic phases of bulk iron across the temperature-induced transition. Integration of RDFs allows us to quantify the changes in the iron coordination and material density, and to observe the transition from a body-centered to a face-centered cubic arrangement of iron atoms. This method is attractive for a broad range of materials and experimental conditions.

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 10 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-Si alloy with 7 weight % (wt %) Si adopts the hexagonal close-packed structure over the measured pressure range, whereas Fe-15wt%Si is observed in a body-centered cubic 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 these planets.

X-ray source development for EXAFS measurements on the National Ignition Facility

Extended X-ray absorption Fine Structure (EXAFS) measurements require a bright, spectrally smooth, and broad-band x-ray source. In a laser facility, such an x-ray source can be generated by a laser-driven capsule implosion. In order to optimize the x-ray emission, different capsule types and laser irradiations have been tested at the National Ignition Facility (NIF). A crystal spectrometer is used to disperse the x-rays and high efficiency image plate detectors are used to measure the absorption spectra in transmission geometry. EXAFS measurements at the K-edge of iron at ambient conditions have been obtained for the first time on the NIF laser, and the requirements for optimization have been established.

High resolution spectrometer for extended x-ray absorption fine structure measurements in the 6 keV to 15 keV energy range

A Cauchois transmission-crystal spectrometer has been developed with high crystal resolving power in the 6 keV-15 keV energy range and sufficient sensitivity to record single-shot spectra from the Lawrence Livermore National Laboratory (LLNL) Titan laser and other comparable or more energetic lasers. The spectrometer capabilities were tested by recording the W L transitions from a laboratory source and the extended x-ray absorption fine structure (EXAFS) spectrum through a Cu foil.

Probing local and electronic structure in Warm Dense Matter: single pulse synchrotron x-ray absorption spectroscopy on shocked Fe

Understanding Warm Dense Matter (WDM), the state of planetary interiors, is a new frontier in scientific research. There exists very little experimental data probing WDM states at the atomic level to test current models and those performed up to now are limited in quality. Here, we report a proof-of-principle experiment that makes microscopic investigations of materials under dynamic compression easily accessible to users and with data quality close to that achievable at ambient. Using a single 100 ps synchrotron x-ray pulse, we have measured, by K-edge absorption spectroscopy, ns-lived equilibrium states of WDM Fe. Structural and electronic changes in Fe are clearly observed for the first time at such extreme conditions. The amplitude of the EXAFS oscillations persists up to 500 GPa and 17000 K, suggesting an enduring local order. Moreover, a discrepancy exists with respect to theoretical calculations in the value of the energy shift of the absorption onset and so this comparison should help to refine the approximations used in models.

Solving local structure around dopants in metal nanoparticles with ab initio modeling of X-ray absorption near edge structure

XANES analysis guided by ab initio modeling is proposed for refinement of local environments around metal impurities in heterogeneous catalysts.

The Time-resolved and Extreme-conditions XAS (TEXAS) facility at the European Synchrotron Radiation Facility: the energy-dispersive X-ray absorption spectroscopy beamline ID24

The European Synchrotron Radiation Facility has recently made available to the user community a facility totally dedicated to Time-resolved and Extreme-conditions X-ray Absorption Spectroscopy--TEXAS. Based on an upgrade of the former energy-dispersive XAS beamline ID24, it provides a unique experimental tool combining unprecedented brilliance (up to 10(14) photons s(-1) on a 4 µm × 4 µm FWHM spot) and detection speed for a full EXAFS spectrum (100 ps per spectrum). The science mission includes studies of processes down to the nanosecond timescale, and investigations of matter at extreme pressure (500 GPa), temperature (10000 K) and magnetic field (30 T). The core activities of the beamline are centered on new experiments dedicated to the investigation of extreme states of matter that can be maintained only for very short periods of time. Here the infrastructure, optical scheme, detection systems and sample environments used to enable the mission-critical performance are described, and examples of first results on the investigation of the electronic and local structure in melts at pressure and temperature conditions relevant to the Earth's interior and in laser-shocked matter are given.

X-Ray Diffraction of Solid Tin to 1.2 TPa

We report direct in situ measurements of the crystal structure of tin between 0.12 and 1.2 TPa, the highest stress at which a crystal structure has ever been observed. Using angle-dispersive powder x-ray diffraction, we find that dynamically compressed Sn transforms to the body-centered-cubic (bcc) structure previously identified by ambient-temperature quasistatic-compression studies and by zero-kelvin density-functional theory predictions between 0.06 and 0.16 TPa. However, we observe no evidence for the hexagonal close-packed (hcp) phase found by those studies to be stable above 0.16 TPa. Instead, our results are consistent with bcc up to 1.2 TPa. We conjecture that at high temperature bcc is stabilized relative to hcp due to differences in vibrational free energy.

Single Hit Energy-resolved Laue Diffraction

In situ white light Laue diffraction has been successfully used to interrogate the structure of single crystal materials undergoing rapid (nanosecond) dynamic compression up to megabar pressures. However, information on strain state accessible via this technique is limited, reducing its applicability for a range of applications. We present an extension to the existing Laue diffraction platform in which we record the photon energy of a subset of diffraction peaks. This allows for a measurement of the longitudinal and transverse strains in situ during compression. Consequently, we demonstrate measurement of volumetric compression of the unit cell, in addition to the limited aspect ratio information accessible in conventional white light Laue. We present preliminary results for silicon, where only an elastic strain is observed. VISAR measurements show the presence of a two wave structure and measurements show that material downstream of the second wave does not contribute to the observed diffraction peaks, supporting the idea that this material may be highly disordered, or has undergone large scale rotation.

Thermal transport in shock wave-compressed solids using pulsed laser heating

A pulsed laser heating method was developed for determining thermal transport properties of solids under shock-wave compression. While the solid is compressed, a laser deposits a known amount of heat onto the sample surface, which is held in the shocked state by a transparent window. The heat from the laser briefly elevates the surface temperature and then diffuses into the interior via one-dimensional heat conduction. The thermal effusivity is determined from the time history of the resulting surface temperature pulse, which is recorded with optical pyrometry. Thermal effusivity is the square root of the product of thermal conductivity and volumetric heat capacity and is the key thermal transport parameter for relating the surface temperature to the interior temperature of the sample in a dynamic compression experiment. Therefore, this method provides information that is needed to determine the thermodynamic state of the interior of a compressed metal sample from a temperature measurement at the surface. The laser heat method was successfully demonstrated on tin that was shock compressed with explosives to a stress and temperature of ~25 GPa and ~1300 K. In this state, tin was observed to have a thermal effusivity of close to twice its ambient value. The implications on determining the interior shock wave temperature of tin are discussed.

A platform for x-ray absorption fine structure study of dynamically compressed materials above 1 Mbar

A platform consisting of a multi-shock drive and an implosion backlighter has been developed for x-ray absorption fine structure (XAFS) measurements on materials compressed to multi-Mbar pressures. The experimental setup, target design, and backlighter characteristics are presented. Extended XAFS (EXAFS) measurements for various materials have been demonstrated. A quintuple-crystal design is described to enhance the efficiency of the x-ray spectrometer, enabling observation of very weak EXAFS signals in a single shot.