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

B1-B2 transition in shock-compressed MgO

Magnesium oxide (MgO) is a major component of the Earth's mantle and is expected to play a similar role in the mantles of large rocky exoplanets. At extreme pressures, MgO transitions from the NaCl B1 crystal structure to a CsCl B2 structure, which may have implications for exoplanetary deep mantle dynamics. In this study, we constrain the phase diagram of MgO with laser-compression along the shock Hugoniot, with simultaneous measurements of crystal structure, density, pressure, and temperature. We identify the B1 to B2 phase transition between 397 and 425 gigapascal (around 9700 kelvin), in agreement with recent theory that accounts for phonon anharmonicity. From 425 to 493 gigapascal, we observe a mixed-phase region of B1 and B2 coexistence. The transformation follows the Watanabe-Tokonami-Morimoto mechanism. Our data are consistent with B2-liquid coexistence above 500 gigapascal and complete melting at 634 gigapascal. This study bridges the gap between previous theoretical and experimental studies, providing insights into the timescale of this phase transition.

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.

Collective motion in hcp-Fe at Earth's inner core conditions

Earth's inner core is predominantly composed of solid iron (Fe) and displays intriguing properties such as strong shear softening and an ultrahigh Poisson's ratio. Insofar, physical mechanisms to explain these features coherently remain highly debated. Here, we have studied longitudinal and shear wave velocities of hcp-Fe (hexagonal close-packed iron) at relevant pressure-temperature conditions of the inner core using in situ shock experiments and machine learning molecular dynamics (MLMD) simulations. Our results demonstrate that the shear wave velocity of hcp-Fe along the Hugoniot in the premelting condition, defined as T/Tm (Tm: melting temperature of iron) above 0.96, is significantly reduced by ~30%, while Poisson's ratio jumps to approximately 0.44. MLMD simulations at 230 to 330 GPa indicate that collective motion with fast diffusive atomic migration occurs in premelting hcp-Fe primarily along [100] or [010] crystallographic direction, contributing to its elastic softening and enhanced Poisson's ratio. Our study reveals that hcp-Fe atoms can diffusively migrate to neighboring positions, forming open-loop and close-loop clusters in the inner core conditions. Hcp-Fe with collective motion at the inner core conditions is thus not an ideal solid previously believed. The premelting hcp-Fe with collective motion behaves like an extremely soft solid with an ultralow shear modulus and an ultrahigh Poisson's ratio that are consistent with seismic observations of the region. Our findings indicate that premelting hcp-Fe with fast diffusive motion represents the underlying physical mechanism to help explain the unique seismic and geodynamic features of the inner core.

A MHz X-ray diffraction set-up for dynamic compression experiments in the diamond anvil cell

An experimental platform for dynamic diamond anvil cell (dDAC) research has been developed at the High Energy Density (HED) Instrument at the European X-ray Free Electron Laser (European XFEL). Advantage was taken of the high repetition rate of the European XFEL (up to 4.5 MHz) to collect pulse-resolved MHz X-ray diffraction data from samples as they are dynamically compressed at intermediate strain rates (≤103 s-1), where up to 352 diffraction images can be collected from a single pulse train. The set-up employs piezo-driven dDACs capable of compressing samples in ≥340 µs, compatible with the maximum length of the pulse train (550 µs). Results from rapid compression experiments on a wide range of sample systems with different X-ray scattering powers are presented. A maximum compression rate of 87 TPa s-1 was observed during the fast compression of Au, while a strain rate of ∼1100 s-1 was achieved during the rapid compression of N2 at 23 TPa s-1.

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

Silicon (Si) exhibits a rich collection of phase transitions under ambient-temperature isothermal and shock compression. This report describes in situ diffraction measurements of ramp-compressed Si between 40 and 389 GPa. Angle-dispersive x-ray scattering reveals that Si assumes an hexagonal close-packed (hcp) structure between 40 and 93 GPa and, at higher pressure, a face-centered cubic structure that persists to at least 389 GPa, the highest pressure for which the crystal structure of Si has been investigated. The range of hcp stability extends to higher pressures and temperatures than predicted by theory.

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 pressure phase transition and strength estimate in polycrystalline alumina during laser-driven shock compression

Alumina (Al₂O₃) is an important ceramic material notable for its compressive strength and hardness. It represents one of the major oxide components of the Earth's mantle. Static compression experiments have reported evidence for phase transformations from the trigonalα-corundum phase to the orthorhombic Rh₂O₃(II)-type structure at ∼90 GPa, and then to the post-perovskite structure at ∼130 GPa, but these phases have yet to be directly observed under shock compression. In this work, we describe laser-driven shock compression experiments on polycrystalline alumina conducted at the Matter in Extreme Conditions endstation of the Linac Coherent Light Source. Ultrafast x-ray pulses (50 fs, 10¹²photons/pulse) were used to probe the atomic-level response at different times during shock propagation and subsequent pressure release. At 107 ± 8 GPa on the Hugoniot, we observe diffraction peaks that match the orthorhombic Rh₂O₃(II) phase with a density of 5.16 ± 0.03 g cm^-3. Upon unloading, the material transforms back to theα-corundum structure. Upon release to ambient pressure, densities are lower than predicted assuming isentropic release, indicating additional lattice expansion due to plastic work heating. Using temperature values calculated from density measurements, we provide an estimate of alumina's strength on release from shock compression.

Structure and density of silicon carbide to 1.5 TPa and implications for extrasolar planets

There has been considerable recent interest in the high-pressure behavior of silicon carbide, a potential major constituent of carbon-rich exoplanets. In this work, the atomic-level structure of SiC was determined through in situ X-ray diffraction under laser-driven ramp compression up to 1.5 TPa; stresses more than seven times greater than previous static and shock data. Here we show that the B1-type structure persists over this stress range and we have constrained its equation of state (EOS). Using this data we have determined the first experimentally based mass-radius curves for a hypothetical pure SiC planet. Interior structure models are constructed for planets consisting of a SiC-rich mantle and iron-rich core. Carbide planets are found to be ~10% less dense than corresponding terrestrial planets.

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.

Iterative diffraction pattern retrieval from a single focal construct geometry image

Understanding the crystal structure of materials under extreme conditions of pressure and temperature has been revolutionized by major advances in laser-driven dynamic compression and in situ X-ray diffraction (XRD) technology. Instead of the well known Debye–Scherrer configuration, the focal construct geometry (FCG) was introduced to produce high-intensity diffraction data from laser-based in situ XRD experiments without increasing the amount of laser energy, but the resulting reflections suffered from profoundly asymmetrical broadening, leading to inaccuracy in determination of the crystal structure. Inspired by fast-neutron energy spectrum measurements, proposed here is an iterative retrieval method for recovering diffraction data from a single FCG image. This iterative algorithm restores both the peak shape and relative intensity with rapid convergence and requires no prior knowledge about the expected diffraction pattern, allowing the FCG to increase the in situ XRD intensity while simultaneously preserving the angular resolution. The feasibility and validity of the method are shown by successful recovery of the diffraction pattern from both a single simulated FCG image and a single laser-based nanosecond XRD measurement.

X-ray powder diffraction in reflection geometry on multi-beam kJ-type laser facilities

An ultrafast x-ray powder diffraction setup for laser-driven dynamic compression has been developed at the LULI2000 laser facility. X-ray diffraction is performed in reflection geometry from a quasi-monochromatic laser-generated plasma x-ray source. In comparison to a transmission geometry setup, this configuration allows us to probe only a small portion of the compressed sample, as well as to shield the detectors against the x-rays generated by the laser-plasma interaction on the front side of the target. Thus, this new platform facilitates probing of spatially and temporarily uniform thermodynamic conditions and enables us to study samples of a large range of atomic numbers, thicknesses, and compression dynamics. As a proof-of-concept, we report direct structural measurements of the bcc-hcp transition both in shock and ramp-compressed polycrystalline iron with diffraction signals recorded between 2θ ∼ 30° and ∼150°. In parallel, the pressure and temperature history of probed samples is measured by rear-side visible diagnostics (velocimetry and pyrometry).

Investigating off-Hugoniot states using multi-layer ring-up targets

Laser compression has long been used as a method to study solids at high pressure. This is commonly achieved by sandwiching a sample between two diamond anvils and using a ramped laser pulse to slowly compress the sample, while keeping it cool enough to stay below the melt curve. We demonstrate a different approach, using a multilayer ‘ring-up’ target whereby laser-ablation pressure compresses Pb up to 150 GPa while keeping it solid, over two times as high in pressure than where it would shock melt on the Hugoniot. We find that the efficiency of this approach compares favourably with the commonly used diamond sandwich technique and could be important for new facilities located at XFELs and synchrotrons which often have higher repetition rate, lower energy lasers which limits the achievable pressures that can be reached.

Focal construct geometry for high-intensity x-ray diffraction from laser-shocked polycrystalline

An increasing number of dynamic experiments, especially those involving laser drive, are employing in situ x-ray diffraction as a probe to interrogate structure evolution between states of matter under extreme pressure and temperature. We present an alternative configuration, focal construct geometry, for in situ x-ray diffraction to measure the structure and evolution of dynamically compressed polycrystalline materials on a laser platform. This configuration makes full use of the isotropically emitted He-α x rays by employing an annular (or semi-annular) collimator rather than a regular pinhole collimator and thus increases the flux of incident x rays reaching the sample as well as the intensity of the diffracted x rays, enabling the detection of a diffraction pattern with less laser energy. Its effectiveness and applicability are validated against the conventional Debye-Scherrer geometry through direct molecular dynamics simulations and x-ray diffraction simulations for two representative shock-induced phase transition events, solid-solid and solid-liquid (or melting). This configuration reproduces all the Debye-Scherrer diffraction profiles in good accuracy and demonstrates superior efficiency in utilizing the isotropic x-ray source and harvesting diffracted x rays while preserving the angular resolution.

Subnanosecond phase transition dynamics in laser-shocked iron

Iron is one of the most studied chemical elements due to its sociotechnological and planetary importance; hence, understanding its structural transition dynamics is of vital interest. By combining a short pulse optical laser and an ultrashort free electron laser pulse, we have observed the subnanosecond structural dynamics of iron from high-quality x-ray diffraction data measured at 50-ps intervals up to 2500 ps. We unequivocally identify a three-wave structure during the initial compression and a two-wave structure during the decaying shock, involving all of the known structural types of iron (α-, γ-, and ε-phase). In the final stage, negative lattice pressures are generated by the propagation of rarefaction waves, leading to the formation of expanded phases and the recovery of γ-phase. Our observations demonstrate the unique capability of measuring the atomistic evolution during the entire lattice compression and release processes at unprecedented time and strain rate.

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 2θ x-ray scattering angle uncertainty of about 0.2° and resolution of about 1°. Analytic expressions are reported for systematic corrections to 2θ 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.

Probing the Solid Phase of Noble Metal Copper at Terapascal Conditions

Ramp compression along a low-temperature adiabat offers a unique avenue to explore the physical properties of materials at the highest densities of their solid form, a region inaccessible by single shock compression. Using the National Ignition Facility and OMEGA laser facilities, copper samples were ramp compressed to peak pressures of 2.30 TPa and densities of nearly 30  g/cc, providing fundamental information regarding the compressibility and phase of copper at pressures more than 5 times greater than previously explored. Through x-ray diffraction measurements, we find that the ambient face-centered-cubic structure is preserved up to 1.15 TPa. The ramp compression equation-of-state measurements shows that there are no discontinuities in sound velocities up to 2.30 TPa, suggesting this phase is likely stable up to the peak pressures measured, as predicted by first-principal calculations. The high precision of these quasiabsolute measurements enables us to provide essential benchmarks for advanced computational studies on the behavior of dense monoatomic materials under extreme conditions that constitute a stringent test for solid-state quantum theory. We find that both density-functional theory and the stabilized jellium model, which assumes that the ionic structure can be replaced by an ionic charge distribution by constant positive-charge background, reproduces our data well. Further, our data could serve to establish new international secondary scales of pressure in the terapascal range that is becoming experimentally accessible with advanced static and dynamic compression techniques.

Optimized x-ray sources for x-ray diffraction measurements at the Omega Laser Facility

The use of x-ray diffraction (XRD) measurements in laser-driven dynamic compression experiments at high-power laser facilities is becoming increasingly common. Diffraction allows one to probe in situ the transformations occurring at the atomic level at extreme conditions of pressure, temperature, and time scale. In these measurements, the x-ray source is generated by irradiation of a solid foil. Under certain laser drive conditions, quasimonochromatic He-α radiation is generated. Careful analysis of the x-ray source plasma spectra reveals that this radiation is not a single line emission and that monochromaticity is highly dependent on the laser irradiance. In this work, we analyze how the spectra emitted by laser-irradiated copper, germanium, and iron foils at the Omega Laser vary depending on different laser drive conditions and discuss the implications for XRD experiments.

Astromimetics: The dawn of a new era for (bio)materials science?

Composite, multifunctional fine particles are likely to be at the frontier of materials science in the foreseeable future. Here we present a submicron composite particle that mimics the stratified structure of the Earth by having a zero-valent iron core, a silicate/silicide mantle, and a thin carbonaceous crust resembling the biosphere and its biotic deposits. Particles were formulated in a stable colloidal form and made to interact with various types of healthy and cancer cells in vitro. A selective anticancer activity was observed, promising from the point of view of the intended use of the particles for tumor targeting across the blood–brain barrier. As an extension of the idea underlying the fabrication of a particle mimicking the planet Earth, we propose a new field of mimetics within materials science: astromimetics. The astromimetic approach in the context of materials science consists of the design of particles after the structure of celestial bodies. With Earth being the most chemically diverse and fertile out of all the astral bodies known, it is anticipated that the great majority of astromimetic material models will fall in the domain of geo-inspired ones.