Application of an ePix100 detector for coherent scattering using a hard X-ray free-electron laser

Femtosecond x-ray photon correlation spectroscopy enables direct observations of atomic-scale relaxations of glass forming liquids

Glass-forming liquids exhibit structural relaxation behaviors, reflecting underlying atomic rearrangements on a wide range of timescales and playing a crucial role in determining material properties. However, the relaxation processes on the atomic scale are not well-understood due to the experimental difficulties in directly characterizing the evolving correlations of atomic-scale order in disordered systems. Here, we harness the coherence and ultrashort pulse characteristics of an x-ray free electron laser to directly probe atomic-scale ultrafast relaxation dynamics in the model system Ge15Te85. We demonstrate an analysis strategy for determining the intermediate scattering function by extracting the contrast decay of summed scattering patterns from two rapidly successive, nearly identical femtosecond x-ray pulses generated by a split-delay system. The result indicates a full decorrelation of atomic-scale order on the sub-picosecond timescale, supporting the argument for a high-fluidity fragile state of liquid Ge15Te85 above its dynamic crossover temperature. The demonstrated strategy opens an avenue for experimental studies of relaxation dynamics in liquids, glasses, and other highly disordered systems.

Direct observation of ultrafast cluster dynamics in supercritical carbon dioxide using X-ray Photon Correlation Spectroscopy

Supercritical fluids exhibit distinct thermodynamic and transport properties, making them of particular interest for a wide range of scientific and engineering applications. These anomalous properties emerge from structural heterogeneities due to the formation of molecular clusters at conditions above the critical point. While the static behavior of these clusters and their effects on the thermodynamic response functions have been recognized, the relation between the ultrafast cluster dynamics and transport properties remains elusive. By measuring the intermediate scattering function in carbon dioxide at conditions near the critical point with X-ray photon correlation spectroscopy, we directly capture the cross-over dynamics between 4 and 13 picoseconds, revealing the transition between ballistic and diffusive motion. Complementary analysis using large-scale molecular dynamics simulations reveals that this behavior arises from collisions between unbound molecules and clusters. This study provides direct evidence of the ultrafast momentum exchange between clusters, which has significant impact on transport properties, solvation processes, and reaction kinetics in supercritical fluids.

A versatile pressure-cell design for studying ultrafast molecular-dynamics in supercritical fluids using coherent multi-pulse x-ray scattering

Supercritical fluids (SCFs) can be found in a variety of environmental and industrial processes. They exhibit an anomalous thermodynamic behavior, which originates from their fluctuating heterogeneous micro-structure. Characterizing the dynamics of these fluids at high temperature and high pressure with nanometer spatial and picosecond temporal resolution has been very challenging. The advent of hard x-ray free electron lasers has enabled the development of novel multi-pulse ultrafast x-ray scattering techniques, such as x-ray photon correlation spectroscopy (XPCS) and x-ray pump x-ray probe (XPXP). These techniques offer new opportunities for resolving the ultrafast microscopic behavior in SCFs at unprecedented spatiotemporal resolution, unraveling the dynamics of their micro-structure. However, harnessing these capabilities requires a bespoke high-pressure and high-temperature sample system that is optimized to maximize signal intensity and address instrument-specific challenges, such as drift in beamline components, x-ray scattering background, and multi-x-ray-beam overlap. We present a pressure cell compatible with a wide range of SCFs with built-in optical access for XPCS and XPXP and discuss critical aspects of the pressure cell design, with a particular focus on the design optimization for XPCS.

A machine learning photon detection algorithm for coherent x-ray ultrafast fluctuation analysis

X-ray free electron laser experiments have brought unique capabilities and opened new directions in research, such as creating new states of matter or directly measuring atomic motion. One such area is the ability to use finely spaced sets of coherent x-ray pulses to be compared after scattering from a dynamic system at different times. This enables the study of fluctuations in many-body quantum systems at the level of the ultrafast pulse durations, but this method has been limited to a select number of examples and required complex and advanced analytical tools. By applying a new methodology to this problem, we have made qualitative advances in three separate areas that will likely also find application to new fields. As compared to the "droplet-type" models, which typically are used to estimate the photon distributions on pixelated detectors to obtain the coherent x-ray speckle patterns, our algorithm achieves an order of magnitude speedup on CPU hardware and two orders of magnitude improvement on GPU hardware. We also find that it retains accuracy in low-contrast conditions, which is the typical regime for many experiments in structural dynamics. Finally, it can predict photon distributions in high average-intensity applications, a regime which up until now has not been accessible. Our artificial intelligence-assisted algorithm will enable a wider adoption of x-ray coherence spectroscopies, by both automating previously challenging analyses and enabling new experiments that were not otherwise feasible without the developments described in this work.

The fluctuation-dissipation measurement instrument at the Linac Coherent Light Source

The development of new modes at x-ray free electron lasers has inspired novel methods for studying fluctuations at different energies and timescales. For closely spaced x-ray pulses that can be varied on ultrafast time scales, we have constructed a pair of advanced instruments to conduct studies targeting quantum materials. We first describe a prototype instrument built to test the proof-of-principle of resonant magnetic scattering using ultrafast pulse pairs. This is followed by a description of a new endstation, the so-called fluctuation-dissipation measurement instrument, which was used to carry out studies with a fast area detector. In addition, we describe various types of diagnostics for single-shot contrast measurements, which can be used to normalize data on a pulse-by-pulse basis and calibrate pulse amplitude ratios, both of which are important for the study of fluctuations in materials. Furthermore, we present some new results using the instrument that demonstrates access to higher momentum resolution.

Nonuniform Flow Dynamics Probed by Nanosecond X-Ray Speckle Visibility Spectroscopy

We report observations of nanosecond nonuniform colloidal dynamics in a free flowing liquid jet using ultrafast x-ray speckle visibility spectroscopy. Utilizing a nanosecond double-bunch mode, the Linac Coherent Light Source free electron laser produced pairs of femtosecond coherent hard x-ray pulses. By exploring anisotropy in the visibility of summed speckle patterns which relates to the correlation functions, we evaluate not only the average particle flow rate in a colloidal nanoparticle jet, but also the nonuniform flow field within. The methodology presented here establishes the foundation for the study of nano- and atomic-scale inhomogeneous fluctuations in complex matter using x-ray free electron laser sources.

From Femtoseconds to Hours—Measuring Dynamics over 18 Orders of Magnitude with Coherent X-rays

X-ray photon correlation spectroscopy (XPCS) enables the study of sample dynamics between micrometer and atomic length scales. As a coherent scattering technique, it benefits from the increased brilliance of the next-generation synchrotron radiation and Free-Electron Laser (FEL) sources. In this article, we will introduce the XPCS concepts and review the latest developments of XPCS with special attention on the extension of accessible time scales to sub-μs and the application of XPCS at FELs. Furthermore, we will discuss future opportunities of XPCS and the related technique X-ray speckle visibility spectroscopy (XSVS) at new X-ray sources. Due to its particular signal-to-noise ratio, the time scales accessible by XPCS scale with the square of the coherent flux, allowing to dramatically extend its applications. This will soon enable studies over more than 18 orders of magnitude in time by XPCS and XSVS.

Beyond integration: modeling every pixel to obtain better structure factors from stills

Most crystallographic data processing methods use pixel integration. In serial femtosecond crystallography (SFX), the intricate interaction between the reciprocal lattice point and the Ewald sphere is integrated out by averaging symmetrically equivalent observations recorded across a large number (104-106) of exposures. Although sufficient for generating biological insights, this approach converges slowly, and using it to accurately measure anomalous differences has proved difficult. This report presents a novel approach for increasing the accuracy of structure factors obtained from SFX data. A physical model describing all observed pixels is defined to a degree of complexity such that it can decouple the various contributions to the pixel intensities. Model dependencies include lattice orientation, unit-cell dimensions, mosaic structure, incident photon spectra and structure factor amplitudes. Maximum likelihood estimation is used to optimize all model parameters. The application of prior knowledge that structure factor amplitudes are positive quantities is included in the form of a reparameterization. The method is tested using a synthesized SFX dataset of ytterbium(III) lysozyme, where each X-ray laser pulse energy is centered at 9034 eV. This energy is 100 eV above the Yb3+ L-III absorption edge, so the anomalous difference signal is stable at 10 electrons despite the inherent energy jitter of each femtosecond X-ray laser pulse. This work demonstrates that this approach allows the determination of anomalous structure factors with very high accuracy while requiring an order-of-magnitude fewer shots than conventional integration-based methods would require to achieve similar results.

Accurate contrast determination for X-ray speckle visibility spectroscopy

X-ray speckle visibility spectroscopy using X-ray free-electron lasers has long been proposed as a probe of fast dynamics in noncrystalline materials. In this paper, numerical modeling is presented to show how the data interpretation of visibility spectroscopy can be impacted by the nonidealities of real-life X-ray detectors. Using simulated detector data, this work provides a detailed analysis of the systematic errors of several contrast extraction algorithms in the context of low-count-rate X-ray speckle visibility spectroscopy and their origins are discussed. Here, it was found that the finite detector charge cloud and pixel size lead to an unavoidable `degeneracy' in photon position determination, and that the contrasts extracted using different algorithms can all be corrected by a simple linear model. The results suggest that experimental calibration of the correction coefficient at the count rate of interest is possible and essential. This allows computationally lightweight algorithms to be implemented for on-the-fly analysis.

Towards the spatial resolution of metalloprotein charge states by detailed modeling of XFEL crystallographic diffraction

Oxidation states of individual metal atoms within a metalloprotein can be assigned by examining X-ray absorption edges, which shift to higher energy for progressively more positive valence numbers. Indeed, X-ray crystallography is well suited for such a measurement, owing to its ability to spatially resolve the scattering contributions of individual metal atoms that have distinct electronic environments contributing to protein function. However, as the magnitude of the shift is quite small, about +2 eV per valence state for iron, it has only been possible to measure the effect when performed with monochromated X-ray sources at synchrotron facilities with energy resolutions in the range 2-3 × 10-4 (ΔE/E). This paper tests whether X-ray free-electron laser (XFEL) pulses, which have a broader bandpass (ΔE/E = 3 × 10-3) when used without a monochromator, might also be useful for such studies. The program nanoBragg is used to simulate serial femtosecond crystallography (SFX) diffraction images with sufficient granularity to model the XFEL spectrum, the crystal mosaicity and the wavelength-dependent anomalous scattering factors contributed by two differently charged iron centers in the 110-amino-acid protein, ferredoxin. Bayesian methods are then used to deduce, from the simulated data, the most likely X-ray absorption curves for each metal atom in the protein, which agree well with the curves chosen for the simulation. The data analysis relies critically on the ability to measure the incident spectrum for each pulse, and also on the nanoBragg simulator to predict the size, shape and intensity profile of Bragg spots based on an underlying physical model that includes the absorption curves, which are then modified to produce the best agreement with the simulated data. This inference methodology potentially enables the use of SFX diffraction for the study of metalloenzyme mechanisms and, in general, offers a more detailed approach to Bragg spot data reduction.

Compact hard x-ray split-delay system based on variable-gap channel-cut crystals

We present the concept and a prototypical implementation of a compact x-ray split-delay system that is capable of performing continuous on-the-fly delay scans over a range of ∼10  ps with sub-100 nanoradian pointing stability. The system consists of four channel-cut silicon crystals, two of which have gradually varying gap sizes from intentional 5 deg asymmetric cuts. The delay adjustment is realized by linear motions of these two monolithic varying-gap channel cuts, where the x-ray beam experiences pairs of anti-parallel reflections, and thus becomes less sensitive in output beam pointing to motion imperfections of the translation stages. The beam splitting is accomplished by polished crystal edges. A high degree of mutual coherence between the two branches at the focus is observed by analyzing small-angle coherent x-ray scattering patterns. We envision a wide range of applications including single-shot x-ray pulse temporal diagnostics, studies of high-intensity x-ray-matter interactions, as well as measurement of dynamics in disordered material systems using split-pulse x-ray photon correlation spectroscopy.

Coherent X-rays reveal the influence of cage effects on ultrafast water dynamics

The dynamics of liquid water feature a variety of time scales, ranging from extremely fast ballistic-like thermal motion, to slower molecular diffusion and hydrogen-bond rearrangements. Here, we utilize coherent X-ray pulses to investigate the sub-100 fs equilibrium dynamics of water from ambient conditions down to supercooled temperatures. This novel approach utilizes the inherent capability of X-ray speckle visibility spectroscopy to measure equilibrium intermolecular dynamics with lengthscale selectivity, by measuring oxygen motion in momentum space. The observed decay of the speckle contrast at the first diffraction peak, which reflects tetrahedral coordination, is attributed to motion on a molecular scale within the first 120 fs. Through comparison with molecular dynamics simulations, we conclude that the slowing down upon cooling from 328 K down to 253 K is not due to simple thermal ballistic-like motion, but that cage effects play an important role even on timescales over 25 fs due to hydrogen-bonding.

Nanosecond X-Ray Photon Correlation Spectroscopy on Magnetic Skyrmions

We report an x-ray photon correlation spectroscopy method that exploits the recent development of the two-pulse mode at the Linac Coherent Light Source. By using coherent resonant x-ray magnetic scattering, we studied spontaneous fluctuations on nanosecond time scales in thin films of multilayered Fe/Gd that exhibit ordered stripe and Skyrmion lattice phases. The correlation time of the fluctuations was found to differ between the Skyrmion phase and near the stripe-Skyrmion boundary. This technique will enable a significant new area of research on the study of equilibrium fluctuations in condensed matter.