X-ray photon correlation spectroscopy

High-pressure X-ray photon correlation spectroscopy at fourth-generation synchrotron sources

A new experimental setup combining X-ray photon correlation spectroscopy (XPCS) in the hard X-ray regime and a high-pressure sample environment has been developed to monitor the pressure dependence of the internal motion of complex systems down to the atomic scale in the multi-gigapascal range, from room temperature to 600 K. The high flux of coherent high-energy X-rays at fourth-generation synchrotron sources solves the problems caused by the absorption of diamond anvil cells used to generate high pressure, enabling the measurement of the intermediate scattering function over six orders of magnitude in time, from 10-3 s to 103 s. The constraints posed by the high-pressure generation such as the preservation of X-ray coherence, as well as the sample, pressure and temperature stability, are discussed, and the feasibility of high-pressure XPCS is demonstrated through results obtained on metallic glasses.

Bridging length scales in organic mixed ionic-electronic conductors through internal strain and mesoscale dynamics

Understanding the structural and dynamic properties of disordered systems at the mesoscale is crucial. This is particularly important in organic mixed ionic-electronic conductors (OMIECs), which undergo significant and complex structural changes when operated in an electrolyte. In this study, we investigate the mesoscale strain, reversibility and dynamics of a model OMIEC material under external electrochemical potential using operando X-ray photon correlation spectroscopy. Our results reveal that strain and structural hysteresis depend on the sample's cycling history, establishing a comprehensive kinetic sequence bridging the macroscopic and microscopic behaviours of OMIECs. Furthermore, we uncover the equilibrium and non-equilibrium dynamics of charge carriers and material-doping states, highlighting the unexpected coupling between charge carrier dynamics and mesoscale order. These findings advance our understanding of the structure-dynamics-function relationships in OMIECs, opening pathways for designing and engineering materials with improved performance and functionality in non-equilibrium states during device operation.

X-ray-induced piezoresponse during X-ray photon correlation spectroscopy of PbMg1/3Nb2/3O3

X-ray photon correlation spectroscopy (XPCS) holds strong promise for observing atomic-scale dynamics in materials, both at equilibrium and during non-equilibrium transitions. Here an in situ XPCS study of the relaxor ferroelectric PbMg1/3Nb2/3O3 (PMN) is reported. A weak applied AC electric field generates strong response in the speckle of the diffuse scattering from the polar nanodomains, which is captured using the two-time correlation function. Correlated motions of the Bragg peak are also observed, which indicate dynamic tilting of the illuminated volume. This tilting quantitatively accounts for the observed two-time speckle correlations. The magnitude of the tilting would not be expected solely from the modest applied field, since PMN is an electrostrictive material with no linear strain response to the field. A model is developed based on non-uniform static charging of the illuminated surface spot by the incident micrometre-scale X-ray beam and the electrostrictive material response to the combination of static and dynamic fields. The model qualitatively explains the direction and magnitude of the observed tilting, and predicts that X-ray-induced piezoresponse could be an important factor in correctly interpreting results from XPCS and nanodiffraction studies of other insulating materials under applied AC field or varying X-ray illumination.

An active piezoelectric plane X-ray focusing mirror with a linearly changing thickness

X-ray mirrors for synchrotron radiation are often bent into a curved figure and work under grazing-incidence conditions due to the strong penetrating nature of X-rays to most materials. Mirrors of different cross sections have been recommended to reduce the mirror's slope inaccuracy and clamping difficulty in order to overcome mechanical tolerances. With the development of hard X-ray focusing, it is difficult to meet the needs of focusing mirrors with small slope error with the existing mirror processing technology. Deformable mirrors are adaptive optics that can produce a flexible surface figure. A method of using a deformable mirror as a phase compensator is described to enhance the focusing performance of an X-ray mirror. This paper presents an active piezoelectric plane X-ray focusing mirror with a linearly changing thickness that has the ability of phase compensation while focusing X-rays. Benefiting from its special structural design, the mirror can realize flexible focusing at different focusing geometries using a single input driving voltage. A prototype was used to measure its performance under one-dimension and two-dimension conditions. The results prove that, even at a bending magnet beamline, the mirror can easily achieve a single-micrometre focusing without a complicated bending mechanism or high-precision surface processing. It is hoped that this kind of deformable mirror will have a wide and flexible application in the synchrotron radiation field.

Momentum transfer resolved electron correlation microscopy

Electron correlation microscopy (ECM) characterizes local structural relaxation dynamics in fluctuating systems like supercooled liquids with nanometer spatial resolution. We have developed a new type of ECM technique that provides moderate resolution in momentum transfer or k space using five-dimensional scanning transmission electron microscopy. k-resolved ECM on a Pt57.5Cu14.7Ni5.3P22.5 metallic supercooled liquids measures rich spatial and momentum structure in the relaxation time data τ(r,k). Relaxation time maps τ(r) at each azimuthal k are independent samples of the material's underlying relaxation time distribution, and τ of radial k shows more complex behavior than the de Gennes narrowing observed in analogous X-ray experiments. We have determined the requirements for electron counts per k-pixel, number of k-pixels per speckle, and time sampling to obtain reliable k-resolved ECM data.

Two-dimensional spatial coherence measurement of X-ray sources using aperture array mask

Fourth-generation synchrotron radiation delivers x-ray sources with unprecedented coherence and brilliance, which enables the development of many advanced coherent techniques taking advantage of the inherent high coherence of the x-ray beams. Simple and accurate measurement of two-dimensional (2D) coherence is of utmost importance for the applications of these coherent experimental techniques. Here, we propose a novel approach based on diffraction of aperture array mask (AAM) to obtain accurate 2D spatial coherence with a single-shot measurement. We utilize a coherent mode decomposition algorithm to simulate the diffraction of AAM illuminated by Gaussian-Schell model beam and demonstrate that spatial coherence function of the incident light beam can be accurately and robustly retrieved. We expect that this new approach will be applied into transverse coherence measurements for the new-generation synchrotron radiation source and relevant coherent experimental techniques.

Diffracted X-ray Tracking for Observing the Internal Motions of Individual Protein Molecules and Its Extended Methodologies

In 1998, the diffracted X-ray tracking (DXT) method pioneered the attainment of molecular dynamics measurements within individual molecules. This breakthrough revolutionized the field by enabling unprecedented insights into the complex workings of molecular systems. Similar to the single-molecule fluorescence labeling technique used in the visible range, DXT uses a labeling method and a pink beam to closely track the diffraction pattern emitted from the labeled gold nanocrystals. Moreover, by utilizing X-rays with extremely short wavelengths, DXT has achieved unparalleled accuracy and sensitivity, exceeding initial expectations. As a result, this remarkable advance has facilitated the search for internal dynamics within many protein molecules. DXT has recently achieved remarkable success in elucidating the internal dynamics of membrane proteins in living cell membranes. This breakthrough has not only expanded our knowledge of these important biomolecules but also has immense potential to advance our understanding of cellular processes in their native environment.

Challenges of Electron Correlation Microscopy on Amorphous Silicon and Amorphous Germanium

Electron correlation microscopy experiments were conducted on amorphous germanium (a-Ge) and amorphous silicon (a-Si) with the goal to study self-diffusion. For this purpose, a series of tilted dark-field images were acquired during in situ heating of the samples in a transmission electron microscope. These experiments show that the measurements are greatly affected by artefacts. Contamination, crystallization, electron beam-induced sputtering, and macroscopic bending of the samples pose major obstacles to the measurements. Other, more subtle experimental artefacts could occur in addition to these which makes interpretations regarding the structural dynamics nearly impossible. The data were nonetheless evaluated to see if some useful information could be extracted. One such result is that the distribution of the characteristic times τKWW, which were obtained from stretched exponential fits to the intensity autocorrelation data, is spatially heterogeneous. This spatial heterogeneity is assumed to be caused by a potential nonergodicity of the materials, the artefacts or an inhomogeneous amorphous structure. Further data processing shows that the characteristic times τKWW are moreover temperature independent, especially for the a-Ge data. It is concluded that the structural rearrangements over time are primarily electron beam-driven and that diffusive dynamics are too slow to be measured at the chosen, experimentally accessible annealing temperatures.

Exploring non-equilibrium processes and spatio-temporal scaling laws in heated egg yolk using coherent X-rays

The soft-grainy microstructure of cooked egg yolk is the result of a series of out-of-equilibrium processes of its protein-lipid contents; however, it is unclear how egg yolk constituents contribute to these processes to create the desired microstructure. By employing X-ray photon correlation spectroscopy, we investigate the functional contribution of egg yolk constituents: proteins, low-density lipoproteins (LDLs), and yolk-granules to the development of grainy-gel microstructure and microscopic dynamics during cooking. We find that the viscosity of the heated egg yolk is solely determined by the degree of protein gelation, whereas the grainy-gel microstructure is controlled by the extent of LDL aggregation. Overall, protein denaturation-aggregation-gelation and LDL-aggregation follows Arrhenius-type time-temperature superposition (TTS), indicating an identical mechanism with a temperature-dependent reaction rate. However, above 75 °C TTS breaks down and temperature-independent gelation dynamics is observed, demonstrating that the temperature can no longer accelerate certain non-equilibrium processes above a threshold value.

Gain dynamics of inner-shell vacancy states pumped by high-intensity XFEL in Mg, Al and Si

High-intensity X-ray free-electron laser (XFEL) beams create transient and non-equilibrium dense states of matter in solid-density targets. These states can be used to develop atomic X-ray lasers with narrow bandwidth and excellent longitudinal coherence, which is not possible with current XFEL pulses. An atomic kinetics model is used to simulate the population dynamics of atomic inner-shell vacancy states in Mg, Al, and Si, revealing the feasibility of population inversion between K-shell and L-shell vacancy states. We also discuss the gain characteristics of these states implying the possibility of atomic X-ray lasers based on inner-shell vacancy states in the 1.5 keV region. The development of atomic X-ray lasers could have applications in high-resolution spectroscopy and nonlinear optics in the X-ray region.

Resolving Salt-Induced Agglomeration of Laponite Suspensions Using X-ray Photon Correlation Spectroscopy and Molecular Dynamics Simulations

Linking the physics of the relaxation behavior of viscoelastic fluids as they form arrested gel states to the underlying chemical changes is essential for developing predictive controls on the properties of the suspensions. In this study, 3 wt.% laponite suspensions are studied as model systems to probe the influence of salt-induced relaxation behavior arising from the assembly of laponite nanodisks. X-ray Photon Correlation Spectroscopy (XPCS) measurements show that laponite suspensions prepared in the presence of 5 mM concentrations of CaCl₂, MgCl₂ and CsCl salts accelerate the formation of arrested gel states, with CaCl₂ having a significant impact followed by CsCl and MgCl₂ salts. The competing effects of ion size and charge on relaxation behavior are noted. For example, the relaxation times of laponite suspensions in the presence of Mg²⁺ ions are slower compared to Cs+ ions despite the higher charge, suggesting that cation size dominates in this scenario. The faster relaxation behavior of laponite suspensions in the presence of Ca²⁺ ions compared to Cs⁺ ions shows that a higher charge dominates the size of the ion. The trends in relaxation behavior are consistent with the cluster formation behavior of laponite suspensions and the electrostatic interactions predicted from MD simulations. Charge balance is achieved by the intercalation of the cations at the negatively charged surfaces of laponite suspensions. These studies show that the arrested gel state of laponite suspensions is accelerated in the presence of salts, with ion sizes and charges having a competing effect on relaxation behavior.

Thermal effects of beam profiles on X-ray photon correlation spectroscopy at megahertz X-ray free-electron lasers

X-ray free-electron lasers (XFELs) with megahertz repetition rates enable X-ray photon correlation spectroscopy (XPCS) studies of fast dynamics on microsecond and sub-microsecond time scales. Beam-induced sample heating is one of the central concerns in these studies, as the interval time is often insufficient for heat dissipation. Despite the great efforts devoted to this issue, few have evaluated the thermal effects of X-ray beam profiles. This work compares the effective dynamics of three common beam profiles using numerical methods. Results show that under the same fluence, the effective temperatures increase with the nonuniformity of the beam, such that the Gaussian beam profile yields a higher effective temperature than the donut-like and uniform profiles. Moreover, decreasing the beam sizes is found to reduce beam-induced thermal effects, in particular the effects of beam profiles.

Direct measurement of Stokes-Einstein diffusion of Cowpea mosaic virus with 19 µs-resolved XPCS

Brownian motion of Cowpea mosaic virus (CPMV) in water was measured using small-angle X-ray photon correlation spectroscopy (SA-XPCS) at 19.2 µs time resolution. It was found that the decorrelation time τ(Q) = 1/DQ² up to Q = 0.091 nm^-1. The hydrodynamic radius R_H determined from XPCS using Stokes-Einstein diffusion D = kT/(6πηR_H) is 43% larger than the geometric radius R₀ determined from SAXS in the 0.007 M K₃PO₄ buffer solution, whereas it is 80% larger for CPMV in 0.5 M NaCl and 104% larger in 0.5 M (NH₄)₂SO₄, a possible effect of aggregation as well as slight variation of the structures of the capsid resulting from the salt-protein interactions.

Linking scientific instruments and computation: Patterns, technologies, and experiences

Powerful detectors at modern experimental facilities routinely collect data at multiple GB/s. Online analysis methods are needed to enable the collection of only interesting subsets of such massive data streams, such as by explicitly discarding some data elements or by directing instruments to relevant areas of experimental space. Thus, methods are required for configuring and running distributed computing pipelines—what we call flows—that link instruments, computers (e.g., for analysis, simulation, artificial intelligence [AI] model training), edge computing (e.g., for analysis), data stores, metadata catalogs, and high-speed networks. We review common patterns associated with such flows and describe methods for instantiating these patterns. We present experiences with the application of these methods to the processing of data from five different scientific instruments, each of which engages powerful computers for data inversion,model training, or other purposes. We also discuss implications of such methods for operators and users of scientific facilities.

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Patterns for linking instruments and computers for online analysis are reviewed

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Methods are presented for capturing such “flows” in reusable forms

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The use of Globus automation services to run flows is described

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Implications of these methods for scientists and facilities are discussed

The industrial revolution transformed society via large-scale automation of manufacturing. Today, AI- and robotics-driven automation of scientific research seems set to usher in a new era of accelerated discovery. But just as the industrial revolution depended on new replicable and scalable manufacturing processes and methods for delivering the copious mechanical power required by those processes, so the automated discovery revolution demands new methods for implementing research automation processes and for connecting those processes to computing and data power. We present here new methods that address these essential needs by allowing scientists to capture common automation patterns in reusable flows and to embed such flows in a global trust, data, and computing fabric that enables instant access to powerful AI, simulation, and other computational capabilities. We use examples from synchrotron light sources to show how these methods can be realized in software and applied at scale.

pyXPCSviewer: an open-source interactive tool for X-ray photon correlation spectroscopy visualization and analysis

pyXPCSviewer, a Python-based graphical user interface that is deployed at beamline 8-ID-I of the Advanced Photon Source for interactive visualization of XPCS results, is introduced. pyXPCSviewer parses rich X-ray photon correlation spectroscopy (XPCS) results into independent PyQt widgets that are both interactive and easy to maintain. pyXPCSviewer is open-source and is open to customization by the XPCS community for ingestion of diversified data structures and inclusion of novel XPCS techniques, both of which are growing demands particularly with the dawn of near-diffraction-limited synchrotron sources and their dedicated XPCS beamlines.

Observation of Collective Molecular Dynamics in a Chalcogenide Glass: Results from X-ray Photon Correlation Spectroscopy

The structural relaxation processes in a Ge₃As₅₂S₄₅ molecular chalcogenide glass sample were directly studied by X-ray photon correlation spectroscopy (XPCS). XPCS was conducted at the first sharp diffraction peak at q = 1.16 Å^-1 at temperatures ranging from 123 K to above the glass transition at 328 K, and the results showed two different dynamical regimes. At a low temperature, the observed glass dynamics are slow and dominated by X-ray-photon-induced effects, which are temperature independent. At a higher temperature, we observed a dramatic decrease in the fluctuation timescales, indicating that the dynamics were mainly due to the intermolecular correlation of the As₄S₃ molecule in the glass. The timescales in this high-temperature range agree well with those determined from measurements of the Newtonian viscosity. Our XPCS studies suggest an extended length scale of the relaxation process in glassy Ge₃As₅₂S₄₅ from the single molecule to the intermolecular range across the glass transition, providing a unique direct probe of the dynamics beyond the length scales of the individual molecule.

Ion complexation waves emerge at the curved interfaces of layered minerals

Visualizing hydrated interfaces is of widespread interest across the physical sciences and is a particularly acute need for layered minerals, whose properties are governed by the structure of the electric double layer (EDL) where mineral and solution meet. Here, we show that cryo electron microscopy and tomography enable direct imaging of the EDL at montmorillonite interfaces in monovalent electrolytes with ångstrom resolution over micron length scales. A learning-based multiple-scattering reconstruction method for cryo electron tomography reveals ions bound asymmetrically on opposite sides of curved, exfoliated layers. We observe conserved ion-density asymmetry across stacks of interacting layers in cryo electron microscopy that is associated with configurations of inner- and outer-sphere ion-water-mineral complexes that we term complexation waves. Coherent X-ray scattering confirms that complexation waves propagate at room-temperature via a competition between ion dehydration and charge interactions that are coupled across opposing sides of a layer, driving dynamic transitions between stacked and aggregated states via layer exfoliation.

The structure of hydrated interfaces is essential for understanding of geochemical processes and behavior of layered minerals. The authors show that waves of hydrated ions emerge at curved aqueous interfaces and couple mineral deformation to the chemistry of the solution.

Real-space observation of fluctuating antiferromagnetic domains

Magnetic domains play a fundamental role in physics of magnetism and its technological applications. Dynamics of antiferromagnetic domains is poorly understood, although antiferromagnets are expected to be extensively used in future electronic devices wherein it determines the stability and operational speed. Dynamics of antiferromagnets also features prominently in the studies of topological quantum matter. Real-space imaging of fluctuating antiferromagnetic domains is therefore highly desired but has never been demonstrated. We use coherent x-ray diffraction to obtain videos of fluctuating micrometer-scale antiferromagnetic domains in Ni₂MnTeO₆ on time scales from 10^-1 to 10³ s. In the collinear phase, thermally activated domain wall motion is observed in the vicinity of the Néel temperature. Unexpectedly, the fluctuations persist through the full range of the higher-temperature helical phase. These observations illustrate the high potential significance of the dynamic domain imaging in phase transition studies and in magnetic device research.

Advancing Chemical Separations: Unraveling the Structure and Dynamics of Phase Splitting in Liquid-Liquid Extraction

Liquid-liquid extraction (LLE), the go-to process for a variety of chemical separations, is limited by spontaneous organic phase splitting upon sufficient solute loading, called third phase formation. In this study we explore the applicability of critical phenomena theory to gain insight into this deleterious phase behavior with the goal of improving separations efficiency and minimizing waste. A series of samples representative of rare earth purification were constructed to include each of one light and one heavy lanthanide (cerium and lutetium) paired with one of two common malonamide extractants (DMDOHEMA and DMDBTDMA). The resulting postextraction organic phases are chemically complex and often form rich hierarchical structures whose statics and dynamics near the critical point were probed herein with small-angle X-ray scattering and high-speed X-ray photon correlation spectroscopy. Despite their different extraction behaviors, all samples show remarkably similar critical behavior with exponents well described by classical critical point theory consistent with the 3D Ising model, where the critical behavior is characterized by fluctuations with a single diverging length scale. This unexpected result indicates a significant reduction in relevant chemical parameters at the critical point, indicating that the underlying behavior of phase transitions in LLE rely on far fewer variables than are generally assumed. The obtained scalar order parameter is attributed to the extractant fraction of the extractant/diluent mixture, revealing that other solution components and their respective concentrations simply shift the critical temperature but do not affect the nature of the critical fluctuations. These findings point to an opportunity to drastically simplify studies of liquid-liquid phase separation and phase diagram development in general while providing insights into LLE process improvement.

Local symmetry predictors of mechanical stability in glasses

The mechanical properties of crystals are controlled by the translational symmetry of their structures. But for glasses with a disordered structure, the link between the symmetry of local particle arrangements and stability is not well established. In this contribution, we provide experimental verification that the centrosymmetry of nearest-neighbor polyhedra in a glass strongly correlates with the local mechanical stability. We examine the distribution of local stability and local centrosymmetry in a glass during aging and deformation using microbeam x-ray scattering. These measurements reveal the underlying relationship between particle-level structure and larger-scale behavior and demonstrate that spatially connected, coordinated local transformations to lower symmetry structures are fundamental to these phenomena. While glassy structures lack obvious global symmetry breaking, local structural symmetry is a critical factor in predicting stability.

Using small-angle scattering to guide functional magnetic nanoparticle design

Magnetic nanoparticles offer unique potential for various technological, biomedical, or environmental applications thanks to the size-, shape- and material-dependent tunability of their magnetic properties. To optimize particles for a specific application, it is crucial to interrelate their performance with their structural and magnetic properties. This review presents the advantages of small-angle X-ray and neutron scattering techniques for achieving a detailed multiscale characterization of magnetic nanoparticles and their ensembles in a mesoscopic size range from 1 to a few hundred nanometers with nanometer resolution. Both X-rays and neutrons allow the ensemble-averaged determination of structural properties, such as particle morphology or particle arrangement in multilayers and 3D assemblies. Additionally, the magnetic scattering contributions enable retrieving the internal magnetization profile of the nanoparticles as well as the inter-particle moment correlations caused by interactions within dense assemblies. Most measurements are used to determine the time-averaged ensemble properties, in addition advanced small-angle scattering techniques exist that allow accessing particle and spin dynamics on various timescales. In this review, we focus on conventional small-angle X-ray and neutron scattering (SAXS and SANS), X-ray and neutron reflectometry, gracing-incidence SAXS and SANS, X-ray resonant magnetic scattering, and neutron spin-echo spectroscopy techniques. For each technique, we provide a general overview, present the latest scientific results, and discuss its strengths as well as sample requirements. Finally, we give our perspectives on how future small-angle scattering experiments, especially in combination with micromagnetic simulations, could help to optimize the performance of magnetic nanoparticles for specific applications.

Diamond channel-cut crystals for high-heat-load beam-multiplexing narrow-band X-ray monochromators

Next-generation high-brilliance X-ray photon sources call for new X-ray optics. Here we demonstrate the possibility of using monolithic diamond channel-cut crystals as high-heat-load beam-multiplexing narrow-band mechanically stable X-ray monochromators with high-power X-ray beams at cutting-edge high-repetition-rate X-ray free-electron laser (XFEL) facilities. The diamond channel-cut crystals fabricated and characterized in these studies are designed as two-bounce Bragg reflection monochromators directing 14.4 or 12.4 keV X-rays within a 15 meV bandwidth to ⁵⁷Fe or ⁴⁵Sc nuclear resonant scattering experiments, respectively. The crystal design allows out-of-band X-rays transmitted with minimal losses to alternative simultaneous experiments. Only ≲2% of the incident ∼100 W X-ray beam is absorbed in the 50 µm-thick first diamond crystal reflector, ensuring that the monochromator crystal is highly stable. Other X-ray optics applications of diamond channel-cut crystals are anticipated.

Microsecond hydrodynamic interactions in dense colloidal dispersions probed at the European XFEL

Many soft-matter systems are composed of macromolecules or nanoparticles suspended in water. The characteristic times at intrinsic length scales of a few nanometres fall therefore in the microsecond and sub-microsecond time regimes. With the development of free-electron lasers (FELs) and fourth-generation synchrotron light-sources, time-resolved experiments in such time and length ranges will become routinely accessible in the near future. In the present work we report our findings on prototypical soft-matter systems, composed of charge-stabilized silica nanoparticles dispersed in water, with radii between 12 and 15 nm and volume fractions between 0.005 and 0.2. The sample dynamics were probed by means of X-ray photon correlation spectroscopy, employing the megahertz pulse repetition rate of the European XFEL and the Adaptive Gain Integrating Pixel Detector. We show that it is possible to correctly identify the dynamical properties that determine the diffusion constant, both for stationary samples and for systems driven by XFEL pulses. Remarkably, despite the high photon density the only observable induced effect is the heating of the scattering volume, meaning that all other X-ray induced effects do not influence the structure and the dynamics on the probed timescales. This work also illustrates the potential to control such induced heating and it can be predicted with thermodynamic models.

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.

Noise reduction in X-ray photon correlation spectroscopy with convolutional neural networks encoder-decoder models

Like other experimental techniques, X-ray photon correlation spectroscopy is subject to various kinds of noise. Random and correlated fluctuations and heterogeneities can be present in a two-time correlation function and obscure the information about the intrinsic dynamics of a sample. Simultaneously addressing the disparate origins of noise in the experimental data is challenging. We propose a computational approach for improving the signal-to-noise ratio in two-time correlation functions that is based on convolutional neural network encoder–decoder (CNN-ED) models. Such models extract features from an image via convolutional layers, project them to a low dimensional space and then reconstruct a clean image from this reduced representation via transposed convolutional layers. Not only are ED models a general tool for random noise removal, but their application to low signal-to-noise data can enhance the data’s quantitative usage since they are able to learn the functional form of the signal. We demonstrate that the CNN-ED models trained on real-world experimental data help to effectively extract equilibrium dynamics’ parameters from two-time correlation functions, containing statistical noise and dynamic heterogeneities. Strategies for optimizing the models’ performance and their applicability limits are discussed.

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.

Photon-counting MCP/Timepix detectors for soft X-ray imaging and spectroscopic applications

Detectors with microchannel plates (MCPs) provide unique capabilities to detect single photons with high spatial (<10 µm) and timing (<25 ps) resolution. Although this detection technology was originally developed for applications with low event rates, recent progress in readout electronics has enabled their operation at substantially higher rates by simultaneous detection of multiple particles. In this study, the potential use of MCP detectors with Timepix readout for soft X-ray imaging and spectroscopic applications where the position and time of each photon needs to be recorded is investigated. The proof-of-principle experiments conducted at the Advanced Light Source demonstrate the capabilities of MCP/Timepix detectors to operate at relatively high input counting rates, paving the way for the application of these detectors in resonance inelastic X-ray scattering and X-ray photon correlation spectroscopy (XPCS) applications. Local count rate saturation was investigated for the MCP/Timepix detector, which requires optimization of acquisition parameters for a specific scattering pattern. A single photon cluster analysis algorithm was developed to eliminate the charge spreading effects in the detector and increase the spatial resolution to subpixel values. Results of these experiments will guide the ongoing development of future MCP devices optimized for soft X-ray photon-counting applications, which should enable XPCS dynamics measurements down to sub-microsecond timescales.

Real-time interfacial electron dynamics revealed through temporal correlations in x-ray photoelectron spectroscopy

We present a novel technique to monitor dynamics in interfacial systems through temporal correlations in x-ray photoelectron spectroscopy (XPS) signals. To date, the vast majority of time-resolved x-ray spectroscopy techniques rely on pump-probe schemes, in which the sample is excited out of equilibrium by a pump pulse, and the subsequent dynamics are monitored by probe pulses arriving at a series of well-defined delays relative to the excitation. By definition, this approach is restricted to processes that can either directly or indirectly be initiated by light. It cannot access spontaneous dynamics or the microscopic fluctuations of ensembles in chemical or thermal equilibrium. Enabling this capability requires measurements to be performed in real (laboratory) time with high temporal resolution and, ultimately, without the need for a well-defined trigger event. The time-correlation XPS technique presented here is a first step toward this goal. The correlation-based technique is implemented by extending an existing optical-laser pump/multiple x-ray probe setup by the capability to record the kinetic energy and absolute time of arrival of every detected photoelectron. The method is benchmarked by monitoring energy-dependent, periodic signal modulations in a prototypical time-resolved XPS experiment on photoinduced surface-photovoltage dynamics in silicon, using both conventional pump-probe data acquisition, and the new technique based on laboratory time. The two measurements lead to the same result. The findings provide a critical milestone toward the overarching goal of studying equilibrium dynamics at surfaces and interfaces through time correlation-based XPS measurements.

Demonstration of single-frame coherent X-ray diffraction imaging using triangular aperture: Towards dynamic nanoimaging of extended objects

Coherent diffraction imaging (CDI) is a powerful method for visualizing the structure of an object with a high spatial resolution that exceeds the performance limits of the lens. Single-frame CDI in the X-ray region has potential use for probing dynamic phenomena with a high spatiotemporal resolution. Here, we experimentally demonstrate a general method for single-frame X-ray CDI using a triangular aperture and a Fresnel zone plate. Using 5 keV synchrotron radiation X-rays, we reconstructed the object image of the locally illuminated area with a spatial resolution of higher than 50 nm and an exposure time of more than 0.1 s without prior information about the sample. After a 10 s exposure, a resolution of 17 nm was achieved. The present method opens new frontiers in the study of dynamics at the nanoscale by using next-generation synchrotron radiation X-rays/free-electron lasers as light sources.

Charge Condensation and Lattice Coupling Drives Stripe Formation in Nickelates

Revealing the predominant driving force behind symmetry breaking in correlated materials is sometimes a formidable task due to the intertwined nature of different degrees of freedom. This is the case for La_{2-x}Sr_{x}NiO_{4+δ}, in which coupled incommensurate charge and spin stripes form at low temperatures. Here, we use resonant x-ray photon correlation spectroscopy to study the temporal stability and domain memory of the charge and spin stripes in La_{2-x}Sr_{x}NiO_{4+δ}. Although spin stripes are more spatially correlated, charge stripes maintain a better temporal stability against temperature change. More intriguingly, charge order shows robust domain memory with thermal cycling up to 250 K, far above the ordering temperature. These results demonstrate the pinning of charge stripes to the lattice and that charge condensation is the predominant factor in the formation of stripe orders in nickelates.

Molecular Characterization of Polymer Networks

Polymer networks are complex systems consisting of molecular components. Whereas the properties of the individual components are typically well understood by most chemists, translating that chemical insight into polymer networks themselves is limited by the statistical and poorly defined nature of network structures. As a result, it is challenging, if not currently impossible, to extrapolate from the molecular behavior of components to the full range of performance and properties of the entire polymer network. Polymer networks therefore present an unrealized, important, and interdisciplinary opportunity to exert molecular-level, chemical control on material macroscopic properties. A barrier to sophisticated molecular approaches to polymer networks is that the techniques for characterizing the molecular structure of networks are often unfamiliar to many scientists. Here, we present a critical overview of the current characterization techniques available to understand the relation between the molecular properties and the resulting performance and behavior of polymer networks, in the absence of added fillers. We highlight the methods available to characterize the chemistry and molecular-level properties of individual polymer strands and junctions, the gelation process by which strands form networks, the structure of the resulting network, and the dynamics and mechanics of the final material. The purpose is not to serve as a detailed manual for conducting these measurements but rather to unify the underlying principles, point out remaining challenges, and provide a concise overview by which chemists can plan characterization strategies that suit their research objectives. Because polymer networks cannot often be sufficiently characterized with a single method, strategic combinations of multiple techniques are typically required for their molecular characterization.

Simultaneous ambient pressure x-ray photoelectron spectroscopy and grazing incidence x-ray scattering in gas environments

We have developed an experimental system to simultaneously measure surface structure, morphology, composition, chemical state, and chemical activity for samples in gas phase environments. This is accomplished by simultaneously measuring x-ray photoelectron spectroscopy (XPS) and grazing incidence x-ray scattering in gas pressures as high as the multi-Torr regime while also recording mass spectrometry. Scattering patterns reflect near-surface sample structures from the nano-scale to the meso-scale, and the grazing incidence geometry provides tunable depth sensitivity of structural measurements. Scattered x rays are detected across a broad range of angles using a newly designed pivoting-UHV-manipulator for detector positioning. At the same time, XPS and mass spectrometry can be measured, all from the same sample spot and under ambient conditions. To demonstrate the capabilities of this system, we measured the chemical state, composition, and structure of Ag-behenate on a Si(001) wafer in vacuum and in O₂ atmosphere at various temperatures. These simultaneous structural, chemical, and gas phase product probes enable detailed insights into the interplay between the structure and chemical state for samples in gas phase environments. The compact size of our pivoting-UHV-manipulator makes it possible to retrofit this technique into existing spectroscopic instruments installed at synchrotron beamlines. Because many synchrotron facilities are planning or undergoing upgrades to diffraction limited storage rings with transversely coherent beams, a newly emerging set of coherent x-ray scattering experiments can greatly benefit from the concepts we present here.

X-ray-Based Techniques to Study the Nano-Bio Interface

X-ray-based analytics are routinely applied in many fields, including physics, chemistry, materials science, and engineering. The full potential of such techniques in the life sciences and medicine, however, has not yet been fully exploited. We highlight current and upcoming advances in this direction. We describe different X-ray-based methodologies (including those performed at synchrotron light sources and X-ray free-electron lasers) and their potentials for application to investigate the nano-bio interface. The discussion is predominantly guided by asking how such methods could better help to understand and to improve nanoparticle-based drug delivery, though the concepts also apply to nano-bio interactions in general. We discuss current limitations and how they might be overcome, particularly for future use in vivo.

Outlook for artificial intelligence and machine learning at the NSLS-II

We describe the current and future plans for using artificial intelligence and machine learning (AI/ML) methods at the National Synchrotron Light Source II (NSLS-II), a scientific user facility at the Brookhaven National Laboratory. We discuss the opportunity for using the AI/ML tools and techniques developed in the data and computational science areas to greatly improve the scientific output of large scale experimental user facilities. We describe our current and future plans in areas including from detecting and recovering from faults, optimizing the source and instrument configurations, streamlining the pipeline from measurement to insight, through data acquisition, processing, analysis. The overall strategy and direction of the NSLS-II facility in relation to AI/ML is presented.

Towards molecular movies with X-ray photon correlation spectroscopy

In this perspective article we highlight research opportunities and challenges in probing structural dynamics of molecular systems using X-ray Photon Correlation Spectroscopy (XPCS). The development of new X-ray sources, such as 4th generation storage rings and X-ray free-electron lasers (XFELs), provides promising new insights into molecular motion. Employing XPCS at these sources allows to capture a very broad range of timescales and lengthscales, spanning from femtoseconds to minutes and atomic scales to the mesoscale. Here, we discuss the scientific questions that can be addressed with these novel tools for two prominent examples: the dynamics of proteins in biomolecular condensates and the dynamics of supercooled water. Finally, we provide practical tips for designing and estimating feasibility of XPCS experiments as well as on detecting and mitigating radiation damage.

Binary Amplitude Reflection Gratings for X-ray Shearing and Hartmann Wavefront Sensors

New, high-coherent-flux X-ray beamlines at synchrotron and free-electron laser light sources rely on wavefront sensors to achieve and maintain optimal alignment under dynamic operating conditions. This includes feedback to adaptive X-ray optics. We describe the design and modeling of a new class of binary-amplitude reflective gratings for shearing interferometry and Hartmann wavefront sensing. Compact arrays of deeply etched gratings illuminated at glancing incidence can withstand higher power densities than transmission membranes and can be designed to operate across a broad range of photon energies with a fixed grating-to-detector distance. Coherent wave-propagation is used to study the energy bandwidth of individual elements in an array and to set the design parameters. We observe that shearing operates well over a ±10% bandwidth, while Hartmann can be extended to ±30% or more, in our configuration. We apply this methodology to the design of a wavefront sensor for a soft X-ray beamline operating from 230 eV to 1400 eV and model shearing and Hartmann tests in the presence of varying wavefront aberration types and magnitudes.

20 µs-resolved high-throughput X-ray photon correlation spectroscopy on a 500k pixel detector enabled by data-management workflow

The performance of the new 52 kHz frame rate Rigaku XSPA-500k detector was characterized on beamline 8-ID-I at the Advanced Photon Source at Argonne for X-ray photon correlation spectroscopy (XPCS) applications. Due to the large data flow produced by this detector (0.2 PB of data per 24 h of continuous operation), a workflow system was deployed that uses the Advanced Photon Source data-management (DM) system and high-performance software to rapidly reduce area-detector data to multi-tau and two-time correlation functions in near real time, providing human-in-the-loop feedback to experimenters. The utility and performance of the workflow system are demonstrated via its application to a variety of small-angle XPCS measurements acquired from different detectors in different XPCS measurement modalities. The XSPA-500k detector, the software and the DM workflow system allow for the efficient acquisition and reduction of up to ∼10⁹ area-detector data frames per day, facilitating the application of XPCS to measuring samples with weak scattering and fast dynamics.

Extracting contrast in an X-ray speckle visibility spectroscopy experiment under imperfect conditions

Pump-probe experiments at synchrotrons and free-electron lasers to study ultrafast dynamics in materials far from equilibrium have been well established, but techniques to investigate equilibrium dynamics on the nano- and pico-second timescales remain underdeveloped and experimentally challenging. A promising approach relies on a double-probe X-ray speckle visibility spectroscopy setup at split-and-delay beamlines of X-ray free-electron lasers. However, the logistics in consistently producing two collinear, perfectly overlapping pulses necessary to conduct a faithful experiment is difficult to achieve. In this paper, a method is introduced to extract contrast in the case where an angular misalignment and imperfect overlap exists between the two pulses. Numerical simulations of a dynamical system show that contrast can still be extracted for significant angular misalignments accompanied by partial overlap between the two pulses.

Nanoscale Critical Phenomena in a Complex Fluid Studied by X-Ray Photon Correlation Spectroscopy

The advent of high-speed x-ray photon correlation spectroscopy now allows the study of critical phenomena in fluids to much smaller length scales and over a wider range of temperatures than is possible with dynamic light scattering. We present an x-ray photon correlation spectroscopy study of critical fluctuation dynamics in a complex fluid typical of those used in liquid-liquid extraction (LLE) of ions, dodecane-DMDBTDMA with extracted aqueous Ce(NO_{3})_{3}. We observe good agreement with both static and dynamic scaling without the need for significant noncritical background corrections. Critical exponents agree with 3D Ising values, and the fluctuation dynamics are described by simple exponential relaxation. The form of the dynamic master curve deviates somewhat from the Kawasaki result, with a more abrupt transition between the critical and noncritical asymptotic behavior. The concepts of critical phenomena thus provide a quantitative framework for understanding the structure and dynamics of LLE systems and a path forward to new LLE processes.

Emergence of anomalous dynamics in soft matter probed at the European XFEL

Dynamics and kinetics in soft matter physics, biology, and nanoscience frequently occur on fast (sub)microsecond but not ultrafast timescales which are difficult to probe experimentally. The European X-ray Free-Electron Laser (European XFEL), a megahertz hard X-ray Free-Electron Laser source, enables such experiments via taking series of diffraction patterns at repetition rates of up to 4.5 MHz. Here, we demonstrate X-ray photon correlation spectroscopy (XPCS) with submicrosecond time resolution of soft matter samples at the European XFEL. We show that the XFEL driven by a superconducting accelerator provides unprecedented beam stability within a pulse train. We performed microsecond sequential XPCS experiments probing equilibrium and nonequilibrium diffusion dynamics in water. We find nonlinear heating on microsecond timescales with dynamics beyond hot Brownian motion and superheated water states persisting up to 100 μs at high fluences. At short times up to 20 μs we observe that the dynamics do not obey the Stokes-Einstein predictions.

X-Ray Photon Correlation Spectroscopy with Coherent Nanobeams: A Numerical Study

X-ray photon correlation spectroscopy accesses a wide variety of dynamic phenomena at the nanoscale by studying the temporal correlations among photons that are scattered by a material in dynamical equilibrium when it is illuminated with a coherent X-ray beam. The information that is obtained is averaged over the illuminated area, which is generally of the order of several square microns. We propose here that more local information can be obtained by using nanobeams with great potential for the study of heterogeneous systems and show the feasibility of this approach with the support of numerical simulations.

Wave-Vector Dependence of the Dynamics in Supercooled Metallic Liquids

We present a detailed investigation of the wave-vector dependence of collective atomic motion in Au_{49}Cu_{26.9}Si_{16.3}Ag_{5.5}Pd_{2.3} and Pd_{42.5}Cu_{27}Ni_{9.5}P_{21} supercooled liquids close to the glass transition temperature. Using x-ray photon correlation spectroscopy in a previously uncovered spatial range of only a few interatomic distances, we show that the microscopic structural relaxation process mimics the structure and presents a marked slowing down at the main average interparticle distance. This behavior is accompanied by dramatic changes in the shape of the intermediate scattering functions, which suggest the presence of large dynamical heterogeneities at length scales corresponding to a few particle diameters. A ballisticlike mechanism of particle motion seems to govern the structural relaxation of the two systems in the highly viscous phase, likely associated with hopping of caged particles in agreement with theoretical studies.

Influence of TMAO as co-solvent on the gelation of silica-PNIPAm core-shell nanogels at intermediate volume fractions

We study the structure and dynamics of poly(N-isopropylacrylamide) (PNIPAm) core-shell nanogels dispersed in aqueous trimethylamine N-oxide (TMAO) solutions by means of small-angle X-ray scattering and X-ray photon correlation spectroscopy (XPCS). Upon increasing the temperature above the lower critical solution temperature of PNIPAm at 33 °C, a colloidal gel is formed as identified by an increase of I(q) at small q as well as a slowing down of sample dynamics by various orders of magnitude. With increasing TMAO concentration the gelation transition shifts linearly to lower temperatures. Above a TMAO concentration of approximately 0.40 mol/L corresponding to a 1 : 1 ratio of TMAO and NIPAm groups, collapsed PNIPAm states are found for all temperatures without any gelation transition. This suggests that reduction of PNIPAm-water hydrogen bonds due to the presence of TMAO results in a stabilisation of the collapsed PNIPAm state and suppresses gelation of the nanogel.

Narrow-band hard-x-ray lasing with highly charged ions

A scheme is put forward to generate fully coherent x-ray lasers based on population inversion in highly charged ions, created by fast inner-shell photoionization using broadband x-ray free-electron-laser (XFEL) pulses in a laser-produced plasma. Numerical simulations based on the Maxwell–Bloch theory show that one can obtain high-intensity, femtosecond x-ray pulses of relative bandwidths Δω/ω = 10⁻⁵–10⁻⁷, by orders of magnitude narrower than in x-ray free-electron-laser pulses for discrete wavelengths down to the sub-ångström regime. Such x-ray lasers can be applicable in the study of x-ray quantum optics and metrology, investigating nonlinear interactions between x-rays and matter, or in high-precision spectroscopy studies in laboratory astrophysics.

Direct 2D spatial-coherence determination using the Fourier-analysis method: multi-parameter characterization of the P04 beamline at PETRA III

We present a systematic 2D spatial-coherence analysis of the soft-X-ray beamline P04 at PETRA III for various beamline configurations. The influence of two different beam-defining apertures on the spatial coherence properties of the beam is discussed and optimal conditions for coherence-based experiments are found. A significant degradation of the spatial coherence in the vertical direction has been measured and sources of this degradation are identified and discussed. The Fourier-analysis method, which gives fast and simple access to the 2D spatial coherence function of the X-ray beam, is used for the experiment. Here, we exploit the charge scattering of a disordered nanodot sample allowing the use of arbitrary X-ray photon energies with this method.

The phase diagram of colloidal silica-PNIPAm core-shell nanogels

We study the structure and dynamics of aqueous dispersions of densely packed core-shell nanoparticles composed of a silica core and a poly(N-isoproylacrylamide) (PNIPAm) shell as a function of temperature and concentration. With small angle X-ray scattering (SAXS) and X-ray photon correlation spectroscopy (XPCS) we shed light on the structural and dynamical changes of the thermo-responsive colloidal nanogel during its volume phase transition at a lower critical solution temperature (LCST) of 32 °C. A transition of the dynamics and its distinct dependency on the particle number concentration could be determined by analysing the intensity autocorrelation function while the structural transition remains concentration independent. We found the dynamics of a jammed system beyond a critical concentration. In addition, by variation of the PNIPAm shell size we tuned both the effective volume fraction and the underlying nature of the dynamics in the system. With our results we can present a full phase diagram of a PNIPAm core-shell system that spans from diluted suspensions, where the system behaves like a liquid, to an effective volume fraction of more than ninety percent where after exceeding a critical concentration the system undergoes a temperature-induced transition from a liquid towards a colloidal gel.

Coherence properties of the high-energy fourth-generation X-ray synchrotron sources

An analysis of the coherence properties of the fourth-generation high-energy storage rings with emittance values of 10 pm rad is performed. It is presently expected that a storage ring with these low emittance values will reach diffraction limit at hard X-rays. Simulations of coherence properties were performed with the XRT software and an analytical approach for different photon energies from 500 eV to 50 keV. It was demonstrated that a minimum photon emittance (diffraction limit) reached at such storage rings is λ/2π. Using mode decomposition it is shown that, for the parameters of the storage ring considered in this work, the diffraction limit will be reached for soft X-ray energies of 500 eV. About ten modes will contribute to the radiation field at 12 keV photon energy and even more modes give a contribution at higher photon energies. Energy spread effects of the electron beam in a low-emittance storage ring were analysed in detail. Simulations were performed at different relative energy spread values from zero to 2 × 10^-3. A decrease of the degree of coherence with an increase of the relative energy spread value was observed. This analysis shows that, to reach the diffraction limit for high photon energies, electron beam emittance should go down to 1 pm rad and below.

X-ray photon correlation spectroscopy of protein dynamics at nearly diffraction-limited storage rings

This study explores the possibility of measuring the dynamics of proteins in solution using X-ray photon correlation spectroscopy (XPCS) at nearly diffraction-limited storage rings (DLSRs). We calculate the signal-to-noise ratio (SNR) of XPCS experiments from a concentrated lysozyme solution at the length scale of the hydrodynamic radius of the protein molecule. We take into account limitations given by the critical X-ray dose and find expressions for the SNR as a function of beam size, sample-to-detector distance and photon energy. Specifically, we show that the combined increase in coherent flux and coherence lengths at the DLSR PETRA IV yields an increase in SNR of more than one order of magnitude. The resulting SNR values indicate that XPCS experiments of biological macromolecules on nanometre length scales will become feasible with the advent of a new generation of synchrotron sources. Our findings provide valuable input for the design and construction of future XPCS beamlines at DLSRs.

Implications of disturbed photon-counting statistics of Eiger detectors for X-ray speckle visibility experiments

This paper reports on coherent scattering experiments in the low-count regime with less than one photon per pixel per acquisition on average, conducted with two detectors based on the Eiger single-photon-counting chip. The obtained photon-count distributions show systematic deviations from the expected Poisson-gamma distribution, which result in a strong overestimation of the measured speckle contrast. It is shown that these deviations originate from an artificial increase of double-photon events, which is proportional to the detected intensity and inversely proportional to the exposure time. The observed miscounting effect may have important implications for new coherent scattering experiments emerging with the advent of high-brilliance X-ray sources. Different correction schemes are discussed in order to obtain the correct photon distributions from the data. A successful correction is demonstrated with the measurement of Brownian motion from colloidal particles using X-ray speckle visibility spectroscopy.