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

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

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

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

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

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

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

Ab initio calculation of X-ray and related core-level spectroscopies: Green's function approaches

X-Ray and related spectroscopies are powerful probes of atomic, vibrational, and electronic structure. In order to unlock the full potential of such experimental techniques, accurate and efficient theoretical and computational approaches are essential. Here we review the status of a variety of first-principles and nearly first principles techniques for X-ray spectroscopies such as X-ray absorption, X-ray emission, and X-ray photoemission, with a focus on Green's function based methods. In particular, we describe the current state of multiple scattering Green's function techniques available in the FEFF10 code and cumulant Green's function techniques for including the effects of many-body electronic excitations. Illustrative examples are shown for a variety of materials and compared with other theoretical and experimental results.

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.

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.

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).

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

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

Pressure effects on the EXAFS Debye-Waller factor of iron

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

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

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

Melting properties by X-ray absorption spectroscopy: common signatures in binary Fe-C, Fe-O, Fe-S and Fe-Si systems

X-ray absorption spectroscopy (XAS) is a widely used technique to probe the local environment around specific atomic species. Applied to samples under extreme pressure and temperature conditions, XAS is sensitive to phase transitions, including melting, and allows gathering insights on compositional variations and electronic changes occurring during such transitions. These characteristics can be exploited for studies of prime interest in geophysics and fundamental high-pressure physics. Here, we investigated the melting curve and the eutectic composition of four geophysically relevant iron binary systems: Fe-C, Fe-O, Fe-S and Fe-Si. Our results show that all these systems present the same spectroscopic signatures upon melting, common to those observed for other pure late 3d transition metals. The presented melting criterion seems to be general for late 3d metals bearing systems. Additionally, we demonstrate the suitability of XAS to extract melt compositional information in situ, such as the evolution of the concentration of light elements with increasing temperature. Diagnostics presented in this work can be applied to studies over an even larger pressure range exploiting the upgraded synchrotron machines, and directly transferred to time-resolved extreme condition studies using dynamic compression (ns) or fast laser heating (ms).

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.

Control of temporal shape of nanosecond long lasers using feedback loops

We present developments in the control of the temporal pulse shape of nanosecond lasers. An active feedback loop between a regenerative amplified laser's output and input was controlled in order to obtain the desired pulse shape. We used several algorithms to achieve this and the differences caused by the target pulse shape and duration are compared. It is found that the algorithm based on the ratio of the target pulse shape and measured pulse profile provides the most robust solution. The methods proposed here can be used to obtain any pulse shape with minimal knowledge of the laser amplification system.

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.

Soft X-ray backlighter source driven by a short-pulse laser for pump-probe characterization of warm dense matter

Here we propose a pump-probe X-ray absorption spectroscopy temperature measurement technique appropriate for matter having temperature in the range of 10 to a few 100 eV and density up to solid density. Atomic modeling simulations indicate that for various low- to mid-Z materials in this range the energy and optical depth of bound-bound and bound-free absorption features are sensitive to temperature. We discuss sample thickness and tamp layer considerations. A series of experimental investigations was carried out using a range of laser parameters with pulse duration ≤5 ps and various pure and alloyed materials to identify backlighter sources suitable for the technique.

Improving the quality of XAFS data

Following the Q2XAFS Workshop and Satellite to IUCr Congress 2017 on `Data Acquisition, Treatment, Storage - quality assurance in XAFS spectroscopy', a summary is given of the discussion on different aspects of a XAFS experiment that affect data quality. Some pertinent problems ranging from sources and minimization of noise to harmonic contamination and uncompensated monochromator glitches were addressed. Also, an overview is given of the major limitations and pitfalls of a selection of related methods, such as photon-out spectroscopies and energy-dispersive XAFS, and of increasingly common applications, namely studies at high pressure, and time-resolved investigations of catalysts in operando. Advice on how to avoid or deal with these problems and a few good practice recommendations are reported, including how to correctly report results.

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

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

Spatio-temporal analysis of glass volume processing using ultrashort laser pulses

Ultrashort laser pulses allow for the in-volume processing of glass through non-linear absorption, resulting in permanent material changes and the generation of internal stress. Across the manifold potential applications of this technology, process optimization requires a detailed understanding of the laser-matter interaction. Of particular relevance are the deposition of energy inside the material and the subsequent relaxation processes. In this paper, we investigate the spatio-temporal evolution of free carriers, energy transfer, and the resulting permanent modifications in the volume of glass during and after exposure to femtosecond and picosecond pulses. For this purpose, we employ time-resolved microscopy in order to obtain shadowgraphic and interferometric images that allow relating the transient distributions to the refractive index change profile. Whereas the plasma generation time is given by the pulse duration, the thermal dynamics occur over several microseconds. Among the most notable features is the emergence of a pressure wave due to the sudden increase of temperature and pressure within the interaction volume. We show how the structure of the modifications, including material disruptions as well as local defects, can be directly influenced by a judicious choice of pulse duration, pulse energy, and focus geometry.

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

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