Ultrafast X-Ray Diffraction Studies of the Phase Transitions and Equation of State of Scandium Shock Compressed to 82 GPa

Cylindrical compression of thin wires by irradiation with a Joule-class short-pulse laser

Equation of state measurements at Jovian or stellar conditions are currently conducted by dynamic shock compression driven by multi-kilojoule multi-beam nanosecond-duration lasers. These experiments require precise design of the target and specific tailoring of the spatial and temporal laser profiles to reach the highest pressures. At the same time, the studies are limited by the low repetition rate of the lasers. Here, we show that by the irradiation of a thin wire with single-beam Joule-class short-pulse laser, a converging cylindrical shock is generated compressing the wire material to conditions relevant to the above applications. The shockwave was observed using Phase Contrast Imaging employing a hard X-ray Free Electron Laser with unprecedented temporal and spatial sensitivity. The data collected for Cu wires is in agreement with hydrodynamic simulations of an ablative shock launched by highly impulsive and transient resistive heating of the wire surface. The subsequent cylindrical shockwave travels toward the wire axis and is predicted to reach a compression factor of 9 and pressures above 800 Mbar. Simulations for astrophysical relevant materials underline the potential of this compression technique as a new tool for high energy density studies at high repetition rates.

A comparative review of time-resolved x-ray and electron scattering to probe structural dynamics

The structure of molecules, particularly the dynamic changes in structure, plays an essential role in understanding physical and chemical phenomena. Time-resolved (TR) scattering techniques serve as crucial experimental tools for studying structural dynamics, offering direct sensitivity to molecular structures through scattering signals. Over the past decade, the advent of x-ray free-electron lasers (XFELs) and mega-electron-volt ultrafast electron diffraction (MeV-UED) facilities has ushered TR scattering experiments into a new era, garnering significant attention. In this review, we delve into the basic principles of TR scattering experiments, especially focusing on those that employ x-rays and electrons. We highlight the variations in experimental conditions when employing x-rays vs electrons and discuss their complementarity. Additionally, cutting-edge XFELs and MeV-UED facilities for TR x-ray and electron scattering experiments and the experiments performed at those facilities are reviewed. As new facilities are constructed and existing ones undergo upgrades, the landscape for TR x-ray and electron scattering experiments is poised for further expansion. Through this review, we aim to facilitate the effective utilization of these emerging opportunities, assisting researchers in delving deeper into the intricate dynamics of molecular structures.

Structure and Ultrafast X-ray Diffraction of the Hydrated Metaphosphate

We study the pathway of metaphosphate hydration when a metaphosphate anion is dissolved in liquid water with an explicit water model. For this purpose, we propose a sequential Monte Carlo algorithm incorporated with the ab initio quantum mechanics/molecular mechanics (QM/MM) method, which can reduce the amount of ab initio QM/MM sampling while retaining the accuracy of the simulation. We demonstrate the numerical calculation of the standard enthalpy change for the successive addition reaction PO3-·2H2O + H2O ⇌ PO3-·3H2O in the liquid phase, which helps to clarify the hydration pathway of the metaphosphate. With the obtained hydrated structure of the metaphosphate anion, we perform ab initio calculations for its relaxation dynamics upon vibrational excitation and characterize the energy transfer process in solution with simulated ultrafast X-ray diffraction signals, which can be experimentally implemented with X-ray free-electron lasers.

Real-time (nanoseconds) determination of liquid phase growth during shock-induced melting

Melting of solids is a fundamental natural phenomenon whose pressure dependence has been of interest for nearly a century. However, the temporal evolution of the molten phase under pressure has eluded measurements because of experimental challenges. By using the shock front as a fiducial, we investigated the time-dependent growth of the molten phase in shock-compressed germanium. In situ x-ray diffraction measurements at different times (1 to 6 nanoseconds) behind the shock front quantified the real-time growth of the liquid phase at several peak stresses. These results show that the characteristic time for melting in shock-compressed germanium decreases from ~7.2 nanoseconds at 35 gigapascals to less than 1 nanosecond at 42 gigapascals. Our melting kinetics results suggest the need to consider heterogeneous nucleation as a mechanism for shock-induced melting and provide an approach to measuring melting kinetics in shock-compressed solids.

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.

Quantitative analysis of diffraction by liquids using a pink-spectrum X-ray source

A new approach for performing quantitative structure-factor analysis and density measurements of liquids using X-ray diffraction with a pink-spectrum X-ray source is described. The methodology corrects for the pink beam effect by performing a Taylor series expansion of the diffraction signal. The mean density, background scale factor, peak X-ray energy about which the expansion is performed, and the cutoff radius for density measurement are estimated using the derivative-free optimization scheme. The formalism is demonstrated for a simulated radial distribution function for tin. Finally, the proposed methodology is applied to experimental data on shock compressed tin recorded at the Dynamic Compression Sector at the Advanced Photon Source, with derived densities comparing favorably with other experimental results and the equations of state of tin.

Pressure tuned incommensurability and guest structure transition in compressed scandium from machine learning atomic simulation

Scandium (Sc) is the lightest non-main-group element and transforms to a host-guest (H-G) incommensurate structure under gigapascal (GPa) pressures. While the host structure is stable over a wide pressure range, the guest structure may exist in multiple forms, featuring different incommensurate ratios, and mixing up to generate long-range "disordered" guest structures. Here, we employed the recently developed global neural network (g-NN) potential and the stochastic surface walking (SSW) global optimization algorithm to explore the global potential energy surface of Sc under various pressures. We probe the global minima structure in a system made of hundreds of atoms and revealed that the solid-phase transition between Sc-I and H-G Sc-II phases is fully reconstructive in nature. Above 62.5 GPa, the pressure will further destabilize the face-centered tetragonal (fct, Sc-IIa) guest structure to a body-centered tetragonal phase (bct, Sc-IIb), while sustaining the host structure. The structural transition mechanism of this work will shed light on the nature of the complex H-G structural modifications in compressed metals.

Probing extreme states of matter using ultra-intense x-ray radiation

Extreme states of matter, that is, matter at extremes of density (pressure) and temperature, can be created in the laboratory either statically or dynamically. In the former, the pressure-temperature state can be maintained for relatively long periods of time, but the sample volume is necessarily extremely small. When the extreme states are generated dynamically, the sample volumes can be larger, but the pressure-temperature conditions are maintained for only short periods of time (ps toμs). In either case, structural information can be obtained from the extreme states by the use of x-ray scattering techniques, but the x-ray beam must be extremely intense in order to obtain sufficient signal from the extremely-small or short-lived sample. In this article I describe the use of x-ray diffraction at synchrotrons and XFELs to investigate how crystal structures evolve as a function of density and temperature. After a brief historical introduction, I describe the developments made at the Synchrotron Radiation Source in the 1990s which enabled the almost routine determination of crystal structure at high pressures, while also revealing that the structural behaviour of materials was much more complex than previously believed. I will then describe how these techniques are used at the current generation of synchrotron and XFEL sources, and then discuss how they might develop further in the future at the next generation of x-ray lightsources.

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).

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.

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.

Intense Reactivity in Sulfur-Hydrogen Mixtures at High Pressure under X-ray Irradiation

Superconductivity near room temperature in the sulfur-hydrogen system arises from a sequence of reactions at high pressures, with X-ray diffraction experiments playing a central role in understanding these chemical-structural transformations and the corresponding S:H stoichiometry. Here we document X-ray irradiation acting as both a probe and as a driver of chemical reaction in this dense hydride system. We observe a reaction between molecular hydrogen (H₂) and elemental sulfur (S₈) under high pressure, induced directly by X-ray illumination, at photon energies of 12 keV using a free electron laser. The rapid synthesis of hydrogen sulfide (H₂S) at 0.3 GPa was confirmed by optical observations, spectroscopic measurements, and microstructural changes detected by X-ray diffraction. These results document X-ray induced chemical synthesis of superconductor-forming dense hydrides, revealing an alternative production strategy and confirming the disruptive nature of X-ray exposure in studies on high-pressure hydrogen chalcogenides, from water to high-temperature superconductors.

Development of shock-dynamics study with synchrotron-based time-resolved X-ray diffraction using an Nd:glass laser system

The combination of high-power laser and synchrotron X-ray pulses allows us to observe material responses under shock compression and release states at the crystal structure on a nanosecond time scale. A higher-power Nd:glass laser system for laser shock experiments was installed as a shock driving source at the NW14A beamline of PF-AR, KEK, Japan. It had a maximum pulse energy of 16 J, a pulse duration of 12 ns and a flat-top intensity profile on the target position. The shock-induced deformation dynamics of polycrystalline aluminium was investigated using synchrotron-based time-resolved X-ray diffraction (XRD) under laser-induced shock. The shock pressure reached up to about 17 GPa with a strain rate of at least 4.6 × 10⁷ s^-1 and remained there for nanoseconds. The plastic deformation caused by the shock-wave loading led to crystallite fragmentation. The preferred orientation of the polycrystalline aluminium remained essentially unchanged during the shock compression and release processes in this strain rate. The newly established time-resolved XRD experimental system can provide useful information for understanding the complex dynamic compression and release behaviors.

Measurement of Body-Centered Cubic Gold and Melting under Shock Compression

We combined laser shock compression with in situ x-ray diffraction to probe the crystallographic state of gold (Au) on its principal shock Hugoniot. Au has long been recognized as an important calibration standard in diamond anvil cell experiments due to the stability of its face-centered cubic (fcc) structure to extremely high pressures (P >600  GPa at 300 K). This is in contrast to density functional theory and first principles calculations of the high-pressure phases of Au that predict a variety of fcc-like structures with different stacking arrangements at intermediate pressures. In this Letter, we probe high-pressure and high-temperature conditions on the shock Hugoniot and observe fcc Au at 169 GPa and the first evidence of body-centered cubic (bcc) Au at 223 GPa. Upon further compression, the bcc phase is observed in coexistence with liquid scattering as the Hugoniot crosses the Au melt curve before 322 GPa. The results suggest a triple point on the Au phase diagram that lies very close to the principal shock Hugoniot near ∼220  GPa.

Identification of Phase Transitions and Metastability in Dynamically Compressed Antimony Using Ultrafast X-Ray Diffraction

Ultrafast x-ray diffraction at the LCLS x-ray free electron laser has been used to resolve the structural behavior of antimony under shock compression to 59 GPa. Antimony is seen to transform to the incommensurate, host-guest phase Sb-II at ∼11  GPa, which forms on nanosecond timescales with ordered guest-atom chains. The high-pressure bcc phase Sb-III is observed above ∼15  GPa, some 8 GPa lower than in static compression studies, and mixed Sb-III/liquid diffraction are obtained between 38 and 59 GPa. An additional phase which does not exist under static compression, Sb-I^{'}, is also observed between 8 and 12 GPa, beyond the normal stability field of Sb-I, and resembles Sb-I with a resolved Peierls distortion. The incommensurate Sb-II high-pressure phase can be recovered metastably on release to ambient pressure, where it is stable for more than 10 ns.

On the chain-melted phase of matter

Various single elements form incommensurate crystal structures under pressure, where a zeolite-type "host" sublattice surrounds a "guest" sublattice comprising 1D chains of atoms. On "chain melting," diffraction peaks from the guest sublattice vanish, while those from the host remain. Diffusion of the guest atoms is expected to be confined to the channels in the host sublattice, which suggests 1D melting. Here, we present atomistic simulations of potassium to investigate this phenomenon and demonstrate that the chain-melted phase has no long-ranged order either along or between the chains. This 3D disorder provides the extensive entropy necessary to make the chain melt a true thermodynamic phase of matter, yet with the unique property that diffusion remains confined to 1D only. Calculations necessitated the development of an interatomic forcefield using machine learning, which we show fully reproduces potassium's phase diagram, including the chain-melted state and 14 known phase transitions.

Direct imaging of ultrafast lattice dynamics

Under rapid high-temperature, high-pressure loading, lattices exhibit complex elastic-inelastic responses. The dynamics of these responses are challenging to measure experimentally because of high sample density and extremely small relevant spatial and temporal scales. Here, we use an x-ray free-electron laser providing simultaneous in situ direct imaging and x-ray diffraction to spatially resolve lattice dynamics of silicon under high-strain rate conditions. We present the first imaging of a new intermediate elastic feature modulating compression along the axis of applied stress, and we identify the structure, compression, and density behind each observed wave. The ultrafast probe x-rays enabled time-resolved characterization of the intermediate elastic feature, which is leveraged to constrain kinetic inhibition of the phase transformation between 2 and 4 ns. These results not only address long-standing questions about the response of silicon under extreme environments but also demonstrate the potential for ultrafast direct measurements to illuminate new lattice dynamics.

Deducing density and strength of nanocrystalline Ta and diamond under extreme conditions from X-ray diffraction

In situ X-ray diffraction with advanced X-ray sources offers unique opportunities for investigating materials properties under extreme conditions such as shock-wave loading. Here, Singh's theory for deducing high-pressure density and strength from two-dimensional (2D) diffraction patterns is rigorously examined with large-scale molecular dynamics simulations of isothermal compression and shock-wave compression. Two representative solids are explored: nanocrystalline Ta and diamond. Analysis of simulated 2D X-ray diffraction patterns is compared against direct molecular dynamics simulation results. Singh's method is highly accurate for density measurement (within 1%) and reasonable for strength measurement (within 10%), and can be used for such measurements on nanocrystalline and polycrystalline solids under extreme conditions (e.g. in the megabar regime).

Observation of the shock-induced β-Sn to b.c.t.-Sn transition using time-resolved X-ray diffraction

Time-resolved X-ray diffraction measurements have been carried out on dynamically compressed Sn up to a maximum pressure of ∼13 GPa at the European Synchrotron Radiation Facility. The phase transition from β-Sn to body-centered tetragonal (b.c.t.) Sn has been observed using synchrotron X-ray diffraction for the first time undergoing shock compression and release. Following maximum compression, the sample releases to lower pressures for several nanoseconds until the reverse transition occurs. The data are in good agreement with previous shock boundaries that indicate that the β-Sn phase is stable ∼2 GPa higher than the static boundary upon compression and the b.c.t.-Sn phase is stable ∼1 GPa lower upon release. The transition to the high-pressure phase reveals a loss of texture in the X-ray diffraction data from the `quasi' single-crystal β-Sn structure to a more powder-like Debye-Scherrer ring.

Femtosecond diffraction studies of solid and liquid phase changes in shock-compressed bismuth

Bismuth has long been a prototypical system for investigating phase transformations and melting at high pressure. Despite decades of experimental study, however, the lattice-level response of Bi to rapid (shock) compression and the relationship between structures occurring dynamically and those observed during slow (static) compression, are still not clearly understood. We have determined the structural response of shock-compressed Bi to 68 GPa using femtosecond X-ray diffraction, thereby revealing the phase transition sequence and equation-of-state in unprecedented detail for the first time. We show that shocked-Bi exhibits a marked departure from equilibrium behavior - the incommensurate Bi-III phase is not observed, but rather a new metastable phase, and the Bi-V phase is formed at significantly lower pressures compared to static compression studies. We also directly measure structural changes in a shocked liquid for the first time. These observations reveal new behaviour in the solid and liquid phases of a shocked material and give important insights into the validity of comparing static and dynamic datasets.

Nanosecond Melting and Recrystallization in Shock-Compressed Silicon

In situ, time-resolved, x-ray diffraction and simultaneous continuum measurements were used to examine structural changes in Si shock compressed to 54 GPa. Shock melting was unambiguously established above ∼31-33  GPa, through the vanishing of all sharp crystalline diffraction peaks and the emergence of a single broad diffraction ring. Reshock from the melt boundary results in rapid (nanosecond) recrystallization to the hexagonal-close-packed Si phase and further supports melting. Our results also provide new constraints on the high-temperature, high-pressure Si phase diagram.

Femtosecond X-Ray Diffraction Studies of the Reversal of the Microstructural Effects of Plastic Deformation during Shock Release of Tantalum

We have used femtosecond x-ray diffraction to study laser-shocked fiber-textured polycrystalline tantalum targets as the 37-253 GPa shock waves break out from the free surface. We extract the time and depth-dependent strain profiles within the Ta target as the rarefaction wave travels back into the bulk of the sample. In agreement with molecular dynamics simulations, the lattice rotation and the twins that are formed under shock compression are observed to be almost fully eliminated by the rarefaction process.

Pulse intensity characterization of the LCLS nanosecond double-bunch mode of operation

The recent demonstration of the `nanosecond double-bunch' operation mode, i.e. two X-ray pulses separated in time between 0.35 and hundreds of nanoseconds and by increments of 0.35 ns, offers new opportunities to investigate ultrafast dynamics in diverse systems of interest. However, in order to reach its full potential, this mode of operation requires the precise characterization of the intensity of each X-ray pulse within each pulse pair for any time separation. Here, a transmissive single-shot diagnostic that achieves this goal for time separations larger than 0.7 ns with a precision better than 5% is presented. It also provides real-time monitoring feedback to help tune the accelerator parameters to deliver double pulse intensity distributions optimized for specific experimental goals.

GAPD: a GPU-accelerated atom-based polychromatic diffraction simulation code

GAPD, a graphics-processing-unit (GPU)-accelerated atom-based polychromatic diffraction simulation code for direct, kinematics-based, simulations of X-ray/electron diffraction of large-scale atomic systems with mono-/polychromatic beams and arbitrary plane detector geometries, is presented. This code implements GPU parallel computation via both real- and reciprocal-space decompositions. With GAPD, direct simulations are performed of the reciprocal lattice node of ultralarge systems (∼5 billion atoms) and diffraction patterns of single-crystal and polycrystalline configurations with mono- and polychromatic X-ray beams (including synchrotron undulator sources), and validation, benchmark and application cases are presented.

Texture of nanocrystalline solids: atomic scale characterization and applications

A methodology is presented to characterize the crystallographic texture of atomic configurations on the basis of Euler angles. Texture information characterized by orientation map, orientation distribution function, texture index, pole figure and inverse pole figure is obtained. The paper reports the construction and characterization of the texture of nanocrystalline configurations with different grain numbers, grain sizes and percentages of preferred orientation. The minimum grain number for texture-free configurations is ∼2500. The effect of texture on deducing grain size from simulated X-ray diffraction curves is also explored as an application case of texture analysis. In addition, molecular dynamics simulations are performed on initially texture-free nanocrystalline Ta under shock-wave loading, which shows a 〈001〉 + 〈111〉 double fiber texture after shock-wave compression.

Short-wavelength free-electron laser sources and science: a review

This review is focused on free-electron lasers (FELs) in the hard to soft x-ray regime. The aim is to provide newcomers to the area with insights into: the basic physics of FELs, the qualities of the radiation they produce, the challenges of transmitting that radiation to end users and the diversity of current scientific applications. Initial consideration is given to FEL theory in order to provide the foundation for discussion of FEL output properties and the technical challenges of short-wavelength FELs. This is followed by an overview of existing x-ray FEL facilities, future facilities and FEL frontiers. To provide a context for information in the above sections, a detailed comparison of the photon pulse characteristics of FEL sources with those of other sources of high brightness x-rays is made. A brief summary of FEL beamline design and photon diagnostics then precedes an overview of FEL scientific applications. Recent highlights are covered in sections on structural biology, atomic and molecular physics, photochemistry, non-linear spectroscopy, shock physics, solid density plasmas. A short industrial perspective is also included to emphasise potential in this area.

The Linac Coherent Light Source: Recent Developments and Future Plans

The development of X-ray free-electron lasers (XFELs) has launched a new era in X-ray science by providing ultrafast coherent X-ray pulses with a peak brightness that is approximately one billion times higher than previous X-ray sources. The Linac Coherent Light Source (LCLS) facility at the SLAC National Accelerator Laboratory, the world’s first hard X-ray FEL, has already demonstrated a tremendous scientific impact across broad areas of science. Here, a few of the more recent representative highlights from LCLS are presented in the areas of atomic, molecular, and optical science; chemistry; condensed matter physics; matter in extreme conditions; and biology. This paper also outlines the near term upgrade (LCLS-II) and motivating science opportunities for ultrafast X-rays in the 0.25–5 keV range at repetition rates up to 1 MHz. Future plans to extend the X-ray energy reach to beyond 13 keV (<1 Å) at high repetition rate (LCLS-II-HE) are envisioned, motivated by compelling new science of structural dynamics at the atomic scale.

Melting dynamics of ice in the mesoscopic regime

How does a crystal melt? How long does it take for melt nuclei to grow? The melting mechanisms have been addressed by several theoretical and experimental works, covering a subnanosecond time window with sample sizes of tens of nanometers and thus suitable to determine the onset of the process but unable to unveil the following dynamics. On the other hand, macroscopic observations of phase transitions, with millisecond or longer time resolution, account for processes occurring at surfaces and time limited by thermal contact with the environment. Here, we fill the gap between these two extremes, investigating the melting of ice in the entire mesoscopic regime. A bulk ice I _h or ice VI sample is homogeneously heated by a picosecond infrared pulse, which delivers all of the energy necessary for complete melting. The evolution of melt/ice interfaces thereafter is monitored by Mie scattering with nanosecond resolution, for all of the time needed for the sample to reequilibrate. The growth of the liquid domains, over distances of micrometers, takes hundreds of nanoseconds, a time orders of magnitude larger than expected from simple H-bond dynamics.