Direct Observation of Melting in Shock-Compressed Bismuth With Femtosecond X-ray Diffraction

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.

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.

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.

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.

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.

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.

Novel experimental setup for megahertz X-ray diffraction in a diamond anvil cell at the High Energy Density (HED) instrument of the European X-ray Free-Electron Laser (EuXFEL)

The high-precision X-ray diffraction setup for work with diamond anvil cells (DACs) in interaction chamber 2 (IC2) of the High Energy Density instrument of the European X-ray Free-Electron Laser is described. This includes beamline optics, sample positioning and detector systems located in the multipurpose vacuum chamber. Concepts for pump-probe X-ray diffraction experiments in the DAC are described and their implementation demonstrated during the First User Community Assisted Commissioning experiment. X-ray heating and diffraction of Bi under pressure, obtained using 20 fs X-ray pulses at 17.8 keV and 2.2 MHz repetition, is illustrated through splitting of diffraction peaks, and interpreted employing finite element modeling of the sample chamber in the DAC.

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).

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.

Cinema:Bandit: a visualization application for beamline science demonstrated on XFEL shock physics experiments

A new visualization tool, Cinema:Bandit, and its demonstration with a continuous workflow for analyzing shock physics experiments and visually exploring the data in real time at X-ray light sources is presented. Cinema:Bandit is an open-source, web-based visualization application in which the experimenter may explore an aggregated dataset to inform real-time beamline decisions and enable post hoc data analysis. The tool integrates with experimental workflows that process raw detector data into a simple database format, and it allows visualization of disparate data types, including experimental parameters, line graphs, and images. Use of parallel coordinates accommodates the irregular sampling of experimental parameters and allows for display and filtering of both experimental inputs and measurements. The tool is demonstrated on a dataset of shock-compressed titanium collected at the Matter in Extreme Conditions hutch at the Linac Coherent Light Source.

Nonisentropic Release of a Shocked Solid

We present molecular dynamics simulations of shock and release in micron-scale tantalum crystals that exhibit postbreakout temperatures far exceeding those expected under the standard assumption of isentropic release. We show via an energy-budget analysis that this is due to plastic-work heating from material strength that largely counters thermoelastic cooling. The simulations are corroborated by experiments where the release temperatures of laser-shocked tantalum foils are deduced from their thermal strains via in situ x-ray diffraction and are found to be close to those behind the shock.

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.

Recent Advances in Ultrafast Structural Techniques

A review that summarizes the most recent technological developments in the field of ultrafast structural dynamics with focus on the use of ultrashort X-ray and electron pulses follows. Atomistic views of chemical processes and phase transformations have long been the exclusive domain of computer simulators. The advent of femtosecond (fs) hard X-ray and fs-electron diffraction techniques made it possible to bring such a level of scrutiny to the experimental area. The following review article provides a summary of the main ultrafast techniques that enabled the generation of atomically resolved movies utilizing ultrashort X-ray and electron pulses. Recent advances are discussed with emphasis on synchrotron-based methods, tabletop fs-X-ray plasma sources, ultrabright fs-electron diffractometers, and timing techniques developed to further improve the temporal resolution and fully exploit the use of intense and ultrashort X-ray free electron laser (XFEL) pulses.

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.

Liquid Structure of Shock-Compressed Hydrocarbons at Megabar Pressures

We present results for the ionic structure in hydrocarbons (polystyrene, polyethylene) that were shock compressed to pressures of up to 190 GPa, inducing rapid melting of the samples. The structure of the resulting liquid is then probed using in situ diffraction by an x-ray free electron laser beam, demonstrating the capability to obtain reliable diffraction data in a single shot, even for low-Z samples without long range order. The data agree well with ab initio simulations, validating the ability of such approaches to model mixed samples in states where complex interparticle bonds remain, and showing that simpler models are not necessarily valid. While the results clearly exclude the possibility of complete carbon-hydrogen demixing at the conditions probed, they also, in contrast to previous predictions, indicate that diffraction is not always a sufficient diagnostic for this phenomenon.

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.

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.

Shock drive capabilities of a 30-Joule laser at the matter in extreme conditions hutch of the Linac Coherent Light Source

We measure the shock drive capabilities of a 30 J, nanosecond, 527 nm laser system at the matter in extreme conditions hutch of the Linac Coherent Light Source. Using a velocity interferometer system for any reflector, we ascertain the maximum instantaneous ablation pressure and characterize its dependence on a drive laser spot size, spatial profile, and temporal profile. We also examine the effects of these parameters on shock spatial and temporal uniformity. Our analysis shows the drive laser capable of generating instantaneous ablation pressures exceeding 160 GPa while maintaining a 1D shock profile. We find that slope pulses provide higher instantaneous ablation pressures than plateau pulses. Our results show instantaneous ablation pressures comparable to those measured at the Omega Laser Facility in Rochester, NY under similar optical drive parameters. Finally, we analyze how optical laser ablation pressures are compare with known scaling relations, accounting for variable laser wavelengths.

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.

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

Using x-ray diffraction at the Linac Coherent Light Source x-ray free-electron laser, we have determined simultaneously and self-consistently the phase transitions and equation of state (EOS) of the lightest transition metal, scandium, under shock compression. On compression scandium undergoes a structural phase transition between 32 and 35 GPa to the same bcc structure seen at high temperatures at ambient pressures, and then a further transition at 46 GPa to the incommensurate host-guest polymorph found above 21 GPa in static compression at room temperature. Shock melting of the host-guest phase is observed between 53 and 72 GPa with the disappearance of Bragg scattering and the growth of a broad asymmetric diffraction peak from the high-density liquid.

Measurement of Electron-Ion Relaxation in Warm Dense Copper

Experimental investigation of electron-ion coupling and electron heat capacity of copper in warm and dense states are presented. From time-resolved x-ray absorption spectroscopy, the temporal evolution of electron temperature is obtained for non-equilibrium warm dense copper heated by an intense femtosecond laser pulse. Electron heat capacity and electron-ion coupling are inferred from the initial electron temperature and its decrease over 10 ps. Data are compared with various theoretical models.