We study the high-pressure melting behavior of titanium using laser-driven shock compression with in situ femtosecond x-ray diffraction and molecular-dynamics simulations based on a machine-learned interatomic potential. The MD simulations predict the solid-liquid coexistence on the Hugoniot in the '111-124 GPa range. Experimentally, we observe the first evidence of liquid at 86 GPa. We also observe pronounced microstructural changes with pressure, with strong grain refinement associated with the emergence of liquid, within the solid-liquid coexistence ('110-126 GPa). Above 126 GPa, we observe the persistence of residual levels of highly textured crystalline Ti to '180 GPa, well above the expected melt completion pressure. We discuss the accuracy that current laser-shock experimental platforms have at determining the melt onset and completion pressures.

Powder x-ray diffraction (PXRD) under laser-driven dynamic compression is a powerful tool to investigate material response to extreme pressure, temperature and strain rates. Robust PXRD platforms have been developed at kJ and MJ laser facilities worldwide including the Powder X-Ray Diffraction Image Plate (PXRDIP) at the Omega Laser Facility at the Laboratory for Laser Energetics (LLE) and the TARget Diffraction In Situ (TARDIS) at the National Ignition Facility (NIF). Here we present further developments of data analysis methods focused towards improving the fidelity of the PXRD intensity determination for these platforms. We illustrate these methods by discussing how they can be implemented in a data analysis package and applied to shock compression data on diamond near 1 TPa. We discuss using the XRD signal from the collimating pinhole or a layer of un-compressed material in the sample package as in-situ references for XRD intensity. We detail how to compare data collected with different x-ray sources and how to account for thermal damping of XRD signal when comparing XRD from a shock-compressed, hot material with the reference material at ambient.

Understanding the formation timescale and structure of carbonaceous reaction products is critical for modeling the high-pressure equation-of-state of organic materials. We use the National Ignition Facility to shock-compress polycrystalline TATB (C6H6N6O6) samples to ~70–130 GPa and ~4000–5500 K, employing in situ nanosecond X-ray diffraction to probe reaction products and velocimetry to measure transmitted compression wave profiles. Our diffraction data is consistent with the formation of diamond over timescales less than ~60 ns. This represents carbon condensation from a molecular explosive on timescales three times faster than previously reported and the earliest observation of diamond produced from reacting TATB. Reactive flow simulations with explicit chemistry reproduce the observed temporal structure within wave profiles to inform the distribution of P-T states. These findings provide direct evidence of ultrafast diamond formation in a reactive system at extreme conditions and provide new constraints for models of shock and detonation chemistry. Understanding the formation timescale and structure of carbonaceous reaction products is crucial for modeling the high-pressure equation-of-state of organic materials. Here, the authors use the National Ignition Facility to shock-compress TATB, revealing ultrafast diamond formation in under 60 ns, offering new insights for shock and detonation chemistry models.

Carbon’s abundance, strong covalent bonding and relevance to inertial confinement fusion and planetary science have motivated extensive investigation of its phase diagram at terapascal pressures. However, the melting curve and the existence of phases beyond diamond remain uncertain. Here we resolve the discrepancy between experiments and theoretical simulations of the melting temperature of diamond and show that the diamond structure persists up to 1 TPa. This contradicts a previous report of a transition to the BC8 phase, which density functional theory predicts to be the thermodynamically stable phase of carbon above pressures around 1 TPa. We combine optical velocimetry, pyrometry and X-ray diffraction to probe microcrystalline diamond under nanosecond shock compression. Shock temperature and reflectivity measurements reveal changes in thermodynamic and optical properties, along with a decrease in X-ray diffraction intensity. These results provide evidence for shock-induced melting with a slight decrease in melting temperature with increasing pressure near 7,300 K. Our work delivers atomic-scale benchmarks for quantum simulations of condensed matter at extreme conditions, with implications for planetary interiors. Our improved understanding of diamond melting might also be relevant for achieving higher energy gain in laser-driven nuclear fusion. The location of the melting curve of diamond is unclear. Now, this is illuminated with shock compression experiments that provide strong evidence for shock-induced melting.

In dynamic-compression experiments, the line-imaging Velocity Interferometer System for Any Reflector (VISAR) is a well-established diagnostic used to probe the velocity history, including wave profiles derived from dynamically compressed interfaces and wavefronts, depending on material optical properties. Knowledge of the velocity history allows for the determination of the pressure achieved during compression. Such a VISAR analysis is often based on Fourier transform techniques and assumes that the recorded interferograms are free from image distortions. In this paper, we describe the VISAR diagnostic installed at the HED-HIBEF instrument located at the European XFEL along with its calibration and characterization. It comprises a two-color (532, 1064 nm), three-arm (with three velocity sensitivities) line imaging system. We provide a procedure to correct VISAR images for geometric distortions and evaluate the performance of the system using Fourier analysis. We finally discuss the spatial and temporal calibrations of the diagnostic. As an example, we compare the pressure extracted from the VISAR analysis of shock-compressed polyimide and silicon.

We present 50-fs, single-shot measurements of the x-ray thermal diffuse scattering (TDS) from copper foils that have been shocked via nanosecond laser ablation up to pressures above ∼135 GPa. We hence deduce the x-ray Debye–Waller factor, providing a temperature measurement. The targets were laser-shocked with the DiPOLE 100-X laser at the High Energy Density endstation of the European X-ray Free-Electron Laser. Single x-ray pulses, with a photon energy of 18 keV, were scattered from the samples and recorded on Varex detectors. Despite the targets being highly textured (as evinced by large variations in the elastic scattering) and with such texture changing upon compression, the absolute intensity of the azimuthally averaged inelastic TDS between the Bragg peaks is largely insensitive to these changes, and allowing for both Compton scattering and the low-level scattering from a sacrificial ablator layer provides a reliable measurement of T/ΘD2, where ΘD is the Debye temperature. We compare our results with the predictions of the SESAME 3336 and LEOS 290 equations of state for copper and find good agreement within experimental errors. We, thus, demonstrate that single-shot temperature measurements of dynamically compressed materials can be made via thermal diffuse scattering of XFEL radiation.

X-ray free electron laser (XFEL) sources coupled to high-power laser systems offer an avenue to study the structural dynamics of materials at extreme pressures and temperatures. The recent commissioning of the DiPOLE 100-X laser on the high energy density (HED) instrument at the European XFEL represents the state-of-the-art in combining x-ray diffraction with laser compression, allowing for compressed materials to be probed in unprecedented detail. Here, we report quantitative structural measurements of molten Sn compressed to 85(5) GPa and ∼3500 K. The capabilities of the HED instrument enable liquid density measurements with an uncertainty of ∼1% at conditions which are extremely challenging to reach via static compression methods. We discuss best practices for conducting liquid diffraction dynamic compression experiments and the necessary intensity corrections which allow for accurate quantitative analysis. We also provide a polyimide ablation pressure vs input laser energy for the DiPOLE 100-X drive laser which will serve future users of the HED instrument.

As part of a program to measure phase transition timescales in materials under dynamic compression, we have designed new x-ray imaging diagnostics to record multiple x-ray diffraction measurements during a single laser-driven experiment. Our design places several ns-gated hybrid CMOS (hCMOS) sensors within a few cm of a laser-driven target. The sensors must be protected from an extremely harsh environment, including debris, electromagnetic pulses, and unconverted laser light. Another key challenge is reducing the x-ray background relative to the faint diffraction signal. Building on the success of our predecessor (Target Diffraction In Situ), we implemented a staged approach to platform development. First, we built a demonstration diagnostic (Gated Diffraction Development Diagnostic) with two hCMOS sensors to confirm we could adequately protect them from the harsh environment and also acquire acceptable diffraction data. This allowed the team to quickly assess the risks and address the most significant challenges. We also collected scientifically useful data during development. Leveraging what we learned, we recently developed a much more ambitious instrument (Flexible Imaging Diffraction Diagnostic for Laser Experiments) that can field up to eight hCMOS sensors in a flexible geometry and participate in back-to-back shots at the National Ignition Facility (NIF). The design also allows for future iterations, such as faster hCMOS sensors and an embedded x-ray streak camera. The enhanced capabilities of the new instrument required a much more complex design, and the unexpected issues encountered on the first few shots at NIF remind us that complexity has consequences. Our progress in addressing these challenges is described herein, as is our current focus on improving data quality by reducing x-ray background and quantifying the uncertainties of our diffraction measurements.

X-ray diffraction is a powerful measurement technique for determining material properties, and it is now possible to perform these experiments at pressures exceeding 1 TPa [Rygg et al., Rev. Sci. Instrum. 91, 043902 (2020)] at the National Ignition Facility (NIF). The x-ray source for these experiments is the quasi-monochromatic Heα emission from metal foils heated to multi-keV temperatures. A critical aspect for understanding the sample's thermodynamic state is the amount of heating caused by absorption of the probe x-rays. In this work, we characterize the performance of the Ge foil x-ray source over more than 60 NIF x-ray diffraction experiments. We use this information to constrain the level of diffraction sample heating from the x-ray source and discuss the impact on the thermodynamic state.

The principal Hugoniot of carbon, initially diamond, was measured from 3 to 80 TPa (30 to 800 million atmospheres), the highest pressure ever achieved, using radiography of spherically-converging shocks. The shocks were generated by ablation of a plastic coating by soft x-rays in a laser-heated hohlraum at the National Ignition Facility (NIF). Experiments were performed with low and high drive powers, spanning different but overlapping pressure ranges. The radius-time history of the shock, and the profile of mass density behind, were determined by profile-matching from a time-resolved x-ray radiograph across the diameter of the sphere. Above 50 TPa, the heating induced by the shock was great enough to ionize a significant fraction of K-shell electrons, reducing the opacity to the 10.2 keV probe x-rays. The opacity and mass density were deduced simultaneously using the constraint that the total mass of the sample was constant. The Hugoniot and opacity were consistent with density functional theory calculations of the electronic states and equation of state (EOS), and varied significantly from theoretical Hugoniots based on Thomas-Fermi theory. Theoretical models used to predict the compressibility of diamond ablator experiments at the NIF, producing the highest neutron yields so far from inertial confinement fusion experiments, are qualitatively consistent with our EOS measurements but appear to overpredict the compressibility slightly. These measurements help to evaluate theoretical techniques and constrain wide-range EOS models applicable to white dwarf stars, which are the ultimate evolutionary form of at least 97

This study investigates methods to optimize quasi-monochromatic, ∼10 ns long x-ray sources (XRS) for time-resolved x-ray diffraction measurements of phase transitions during dynamic laser compression measurements at the National Ignition Facility (NIF). To support this, we produce continuous and pulsed XRS by irradiating a Ge foil with NIF lasers to achieve an intensity of 2 × 1015 W/cm2, optimizing the laser-to-x-ray conversion efficiency. Our x-ray source is dominated by Ge He-α line emission. We discuss methods to optimize the source to maintain a uniform XRS for ∼10 ns, mitigating cold plasma and higher energy x-ray emission lines.

The properties of all materials at one atmosphere of pressure are controlled by the configurations of their valence electrons. At extreme pressures, neighboring atoms approach so close that core-electron orbitals overlap, and theory predicts the emergence of unusual quantum behavior. We ramp-compress monovalent elemental sodium, a prototypical metal at ambient conditions, to nearly 500 GPa (5 million atmospheres). The 7-fold increase of density brings the interatomic distance to 1.74 Å well within the initial 2.03 Å of the Na+ ionic diameter, and squeezes the valence electrons into the interstitial voids suggesting the formation of an electride phase. The laser-driven compression results in pressure-driven melting and recrystallization in a billionth of a second. In situ x-ray diffraction reveals a series of unexpected phase transitions upon recrystallization, and optical reflectivity measurements show a precipitous decrease throughout the liquid and solid phases, where the liquid is predicted to have electronic localization. These data reveal the presence of a rich, temperature-driven polymorphism where core electron overlap is thought to stabilize the formation of peculiar electride states.

Material shock release generally happens in the targets of high-energy-density (HED) and inertial confinement fusion (ICF) experiments but has been challenging to study experimentally, theoretically, or computationally. Here, we report extensive studies of polystyrene (CH) shock release by employing large-scale nonequilibrium molecular dynamics and laser-drive experiments at various shock strengths. Our experimental design prevents radiation preheating of the sample and employs a witness foil to investigate the release of shocked CH across a vacuum gap. We observe earlier acceleration of the foil by the release of CH under stronger shocks as well as reflectivity changes in the interferometry data before the foil moves, which is strong evidence of hydrogen streaming ahead of carbon at the release front, consistent with findings from our simulations. Furthermore, our calculations show that lighter species or hydrogen isotopes can carry more mass by one to two orders of magnitude to farther distances during the release and that only less than 0.1 times thermal expansion as predicted by hydrodynamics is needed to explain the high velocities and large scale lengths of low-density plasmas observed in radiation-preheated CH release experiments. These results highlight the significant role of species separation in the shock release of compounds. This process shall be considered, and its potential effects shall be clarified, in the design, interpretation, and analysis of future HED and ICF experiments.

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.

Combining an x-ray free electron laser with a high-power laser driver enables the study of equations-of-state, high strain-rate deformation processes, structural phase transitions, and transformation pathways as a function of pressure to hundreds of GPa along different thermodynamic compression paths. Future high repetition-rate laser operation will enable data to be accumulated at >1 Hz, which poses a number of experimental challenges, including the need to rapidly replenish the target. Here, we present a combined shock compression and an x-ray diffraction study on epoxy (50% vol.)-crystalline grains (50% vol.) slurry targets, which can be fashioned into extruded ribbons for high repetition-rate operation. For shock-loaded NaCl-slurry samples, we observe pressure, density, and temperature states within the embedded NaCl grains consistent with observations from shock-compressed single-crystal NaCl.

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.

The discovery of more than 4500 extrasolar planets has created a need for modeling their interior structure and dynamics. Given the prominence of iron in planetary interiors, we require accurate and precise physical properties at extreme pressure and temperature. A first-order property of iron is its melting point, which is still debated for the conditions of Earth's interior. We used high-energy lasers at the National Ignition Facility and in situ x-ray diffraction to determine the melting point of iron up to 1000 gigapascals, three times the pressure of Earth's inner core. We used this melting curve to determine the length of dynamo action during core solidification to the hexagonal close-packed (hcp) structure. We find that terrestrial exoplanets with four to six times Earth's mass have the longest dynamos, which provide important shielding against cosmic radiation.

Diamond is used extensively as a component in high-energy-density experiments, but existing equation of state (EOS) models do not capture its observed response to dynamic loading. In particular, in contrast with first-principles theoretical models of equilibrium multiphase EOS, no solid-solid phase changes have been detected, and no general-purpose EOS models match the measured ambient isotherm. We have performed density functional theory (DFT) calculations of the diamond phase to -10 TPa, well beyond its predicted range of thermodynamic stability, and used these results as the basis of a Mie-Gruneisen EOS. We also performed DFT calculations of the elastic moduli, and calibrated an algebraic elasticity model for use in simulations. We then estimated the flow stress of diamond by comparison with the stress-density relation measured experimentally in ramp-loading experiments. The resulting constitutive model allows us to place a constraint on the Taylor-Quinney factor (the fraction of plastic work converted to heat) from the observation that diamond does not melt on ramp compression.