Coherent X-ray Scattering Research Articles

Data-driven discovery of dynamics from time-resolved coherent scattering

Coherent X-ray scattering (CXS) techniques are capable of interrogating dynamics of nano- to mesoscale materials systems at time scales spanning several orders of magnitude. However, obtaining accurate theoretical descriptions of complex dynamics is often limited by one or more factors—the ability to visualize dynamics in real space, computational cost of high-fidelity simulations, and effectiveness of approximate or phenomenological models. In this work, we develop a data-driven framework to uncover mechanistic models of dynamics directly from time-resolved CXS measurements without solving the phase reconstruction problem for the entire time series of diffraction patterns. Our approach uses neural differential equations to parameterize unknown real-space dynamics and implements a computational scattering forward model to relate real-space predictions to reciprocal-space observations. This method is shown to recover the dynamics of several computational model systems under various simulated conditions of measurement resolution and noise. Moreover, the trained model enables estimation of long-term dynamics well beyond the maximum observation time, which can be used to inform and refine experimental parameters in practice. Finally, we demonstrate an experimental proof-of-concept by applying our framework to recover the probe trajectory from a ptychographic scan. Our proposed framework bridges the wide existing gap between approximate models and complex data.

Coherent X-ray Scattering Reveals Nanoscale Fluctuations in Hydrated Proteins.

Hydrated proteins undergo a transition in the deeply supercooled regime, which is attributed to rapid changes in hydration water and protein structural dynamics. Here, we investigate the nanoscale stress-relaxation in hydrated lysozyme proteins stimulated and probed by X-ray Photon Correlation Spectroscopy (XPCS). This approach allows us to access the nanoscale dynamics in the deeply supercooled regime (T = 180 K), which is typically not accessible through equilibrium methods. The observed stimulated dynamic response is attributed to collective stress-relaxation as the system transitions from a jammed granular state to an elastically driven regime. The relaxation time constants exhibit Arrhenius temperature dependence upon cooling with a minimum in the Kohlrausch-Williams-Watts exponent at T = 227 K. The observed minimum is attributed to an increase in dynamical heterogeneity, which coincides with enhanced fluctuations observed in the two-time correlation functions and a maximum in the dynamic susceptibility quantified by the normalized variance χT. The amplification of fluctuations is consistent with previous studies of hydrated proteins, which indicate the key role of density and enthalpy fluctuations in hydration water. Our study provides new insights into X-ray stimulated stress-relaxation and the underlying mechanisms behind spatiotemporal fluctuations in biological granular materials.

Developments in SRW Code and Sirepo Framework Supporting Simulation of Time-Dependent Coherent X-ray Scattering Experiments

Physical optics simulations for beamlines and experiments are essential for the effective use of synchrotron light source facilities such as NSLS-II at BNL. The SRW software package supports such source-to-detector simulations for coherent X-ray scattering and imaging experiments through its Python interface and Sirepo browser-based graphical user interface. This allows one to define custom sample models, assess the feasibility of an experiment, and estimate most appropriate beamline settings before using valuable beamtime. We discuss the recent use of general-purpose GPU resources and coherent mode decomposition algorithms in SRW to accelerate physical optics simulations with partially coherent X-rays. To illustrate these new capabilities, we describe simulations of typical time series of partially coherent scattering images used in X-ray Photon Correlation Spectroscopy (XPCS) experiments; aiming to characterize the nanoscale dynamics of a disordered sample, representing a solution of nanoparticles undergoing Brownian diffusion.

Phasing Magnet for CSX-2 Beamline at NSLS-II

A phasing magnet has been developed at National Synchrotron Light Source II (NSLS-II) for the Coherent Soft X-ray Scattering (CSX) beamline. The phasing magnet will be located at the center of the straight section in between two identical and independent variably polarized APPLE-II devices. Based on Permanent Magnet technology, the phasing magnet has been designed to achieve the required electron beam delay to properly adjust the phase matching of these two consecutive EPUs (Elliptically Polarizing Undulators) and ensure a positive interference between the photon beam emitted in each device. This paper will describe the mechanical and magnetic design together with the final field measurements and magnetic tuning results. Also, the spectral performance of the two EPUs and the method used to properly set the field strength of the phasing magnet for any given radiation wavelength and polarization mode will be presented as well.

Single-Shot Coherent X-ray Imaging Instrument at PAL-XFEL

We developed a single-shot coherent X-ray imaging instrument at the hard X-ray beamline of the Pohang Accelerator Laboratory X-ray Free Electron Laser (PAL-XFEL). This experimental platform was established to conduct a variety of XFEL experiments, including coherent diffraction imaging (CDI), X-ray photon correlation spectroscopy (XPCS), and coherent X-ray scattering (CXS). Based on the forward-scattering geometry, this instrument utilizes a fixed-target method for sample delivery. It is well optimized for single-shot-based experiments in which one expects to observe the ultrafast phenomena of nanoparticles at picosecond temporal and nanometer spatial resolutions. In this paper, we introduce a single-shot coherent X-ray imaging instrument and report pump–probe coherent diffraction imaging (PPCDI) of Ag nanoparticles as an example of its applications.

Kinetics of Network Formation and Heterogeneous Dynamics of an Egg White Gel Revealed by Coherent X-Ray Scattering

The kinetics of heat-induced gelation and the microscopic dynamics of a hen egg white gel are probed using x-ray photon correlation spectroscopy along with ultrasmall-angle x-ray scattering. The kinetics of structural growth reveals a reaction-limited aggregation process with a gel fractal dimension of ≈2 and an average network mesh size of ca. 400nm. The dynamics probed at these length scales reveals an exponential growth of the characteristic relaxation times followed by an intriguing steady state in combination with a compressed exponential correlation function and a temporal heterogeneity. The degree of heterogeneity increases with decreasing length scale. We discuss our results in the broader context of experiments and models describing attractive colloidal gels.

Gelation Mechanism and Structural Dynamics of Chitosan Self-Healing Hydrogels by In Situ SAXS and Coherent X-ray Scattering.

Self-healing hydrogels with intrinsic self-healing ability, injectability, and biocompatibility have good potential in biomedical applications. The relevance between the self-healing ability and inner structure of hydrogels, however, has rarely been examined. The design criteria of self-healing hydrogels remain to be established. In this study, we utilized in situ small-angle X-ray scattering (in situ SAXS) and coherent X-ray scattering (CXS) to analyze the dynamics and gelation mechanism of three types of chitosan-based self-healing hydrogels with different dynamic interactions. In situ SAXS revealed the nucleation and growth mechanism for the gelling process, which has not been reported in a system of self-healing hydrogels. The critical nucleation radius (CNR) with different interactions could further influence the gelation rate and self-healing ability. Moreover, the continuous time-resolved CXS profile unveiled the dynamic behavior of different self-healing hydrogels in mesoscale, supported by rheological experiments. Information linking the rheological properties and structural changes could be useful in designing self-healing hydrogels for biomedical applications.

Probing Organic Thin Films by Coherent X-ray Imaging and X-ray Scattering

An important and integral effort toward understanding the formation and reorganization of mesoscale structures in functional organic thin films, being of fundamental importance to the development o...

Coherent X-ray Scattering for Microanalysis at Taiwan Photon Source

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Classification of fracture and non-fracture groups by analysis of coherent X-ray scatter.

Osteoporotic fractures present a significant social and economic burden, which is set to rise commensurately with the aging population. Greater understanding of the physicochemical differences between osteoporotic and normal conditions will facilitate the development of diagnostic technologies with increased performance and treatments with increased efficacy. Using coherent X-ray scattering we have evaluated a population of 108 ex vivo human bone samples comprised of non-fracture and fracture groups. Principal component fed linear discriminant analysis was used to develop a classification model to discern each condition resulting in a sensitivity and specificity of 93% and 91%, respectively. Evaluating the coherent X-ray scatter differences from each condition supports the hypothesis that a causal physicochemical change has occurred in the fracture group. This work is a critical step along the path towards developing an in vivo diagnostic tool for fracture risk prediction.

Heterophase fluctuations nearTcin the relaxor ferroelectrics(1−x)Pb(Zn1/3Nb2/3)O3−xPbTiO3(x=0.09) studied by x-ray diffuse scattering and coherent x-ray scattering

Using a unique combination of two powerful experimental techniques, x-ray diffuse scattering (XDS) and coherent x-ray scattering (CXS), a heterophase fluctuation has been observed for the first time near the paraelectric to ferroelectric first-order phase transition in the relaxor ferroelectric (1-$x$)Pb(Zn${}_{1/3}$Nb${}_{2/3}$)O${}_{3}$-$x$PbTiO${}_{3}$. This heterophase fluctuation, during which two phases coexist as if they are in a thermodynamic equilibrium state, acts as a precursor phenomenon for the phase transition. The CXS technique used here is still under development but shows promise for future study of heterogeneous solids.

The Coherent X-ray Scattering Beamline at Taiwan Photon Source

The coherent X-ray scattering beamline is one of the phase I beamlines designed for the Taiwan Photon Source, a new 3 GeV ring under construction at the National Synchrotron Radiation Research Center in Taiwan. By using a pair of 2m-long in-vacuum undulators, this beamline will provide a highly coherent beam for X-ray photon correlation spectroscopy principally; moreover, it will share a part of beamtime for small-angle X-ray scattering (SAXS) experiments with similar setup of the beamline. The operating photon energy is designed within the range of 5-20 keV. In vertical direction, the beam spot size at sample position is 1 μm with focusing mirror and by using 1D compound refractive lenses (CRLs) the beam spot size is 10 μm. The horizontal beam spot size is in the range of 1 to 10 μm with a two-stage focusing design. The vertical and horizontal transverse coherence lengths of the 10 μm2 beam spot size at the photon energy of 5 KeV are 212 and 6 μm at sample position respectively. Beside XPCS the beamline configuration can cope with the requirements of most SAXS experiments, including anomalous measurements and micro-beam mapping. In addition, the increasing biological SAXS demand is also considered and the on-line fast performance liquid chromatography (FPLC) will be enclosed for biological users.

Monte Carlo simulation of novel breast imaging modalities based on coherent x-ray scattering

We present upgraded versions of MC-GPU and penEasy_Imaging, two open-source Monte Carlo codes for the simulation of radiographic projections and CT, that have been extended and validated to account for the effect of molecular interference in the coherent x-ray scatter. The codes were first validation by comparison between simulated and measured energy dispersive x-ray diffraction (EDXRD) spectra. A second validation was by evaluation of the rejection factor of a focused anti-scatter grid. To exemplify the capabilities of the new codes, the modified MC-GPU code was used to examine the possibility of characterizing breast tissue composition and microcalcifications in a volume of interest inside a whole breast phantom using EDXRD and to simulate a coherent scatter computed tomography (CSCT) system based on first generation CT acquisition geometry. It was confirmed that EDXRD and CSCT have the potential to characterize tissue composition inside a whole breast. The GPU-accelerated code was able to simulate, in just a few hours, a complete CSCT acquisition composed of 9758 independent pencil-beam projections. In summary, it has been shown that the presented software can be used for fast and accurate simulation of novel breast imaging modalities relying on scattering measurements and therefore can assist in the characterization and optimization of promising modalities currently under development.

In Situ Coherent X-ray Scattering and Scanning Tunneling Microscopy Studies of Hexagonally Reconstructed Au(001) in Electrolytes

We studied dynamics of Au(001) surface in situ in 0.1 M HClO4 electrolyte solution using both coherent x-ray scattering and scanning tunneling microscopy (STM). The surface of Au(001) is known to reconstruct at cathodic potentials; the reconstruction lifts at anodic potentials. In our in-situ STM experiments, the measurements focus on time-dependent progressions of surface morphology during slow potential sweep. In our in-situ coherent x-ray scattering measurements, we demonstrate that the equilibrium surface dynamics are directly measurable and the measured dynamics are consistent with morphological evolution of the STM images. These experiments represent the first successful application of coherent x-ray scattering to the study of electrochemical interfaces in situ.

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Direct Measurement of Microstructural Avalanches during the Martensitic Transition of Cobalt Using Coherent X-Ray Scattering

Heterogeneous microscale dynamics in the martensitic phase transition of cobalt is investigated with real-time x-ray scattering. During the transformation of the high-temperature face-centered cubic phase to the low-temperature hexagonal close-packed phase, the structure factor evolution suggests that an initial rapid local transformation is followed by a slower period during which strain relaxes. Coherent x-ray scattering measurements performed during the latter part of the transformation show that the kinetics is dominated by discontinuous sudden changes-avalanches. The spatial size of observed avalanches varies widely, from 100 nm to 10 μm, the size of the x-ray beam. An empirical avalanche amplitude quantifies this behavior, exhibiting a power-law distribution. The avalanche rate decreases with inverse time since the onset of the transformation.

In situ Coherent X-ray Scattering and STM Studies of Hexagonally Reconstructed Au(001) in Electrolytes

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Magnetic Domain Fluctuations in an Antiferromagnetic Film Observed with Coherent Resonant Soft X-Ray Scattering

We report the direct observation of slow fluctuations of helical antiferromagnetic domains in an ultrathin holmium film using coherent resonant magnetic x-ray scattering. We observe a gradual increase of the fluctuations in the speckle pattern with increasing temperature, while at the same time a static contribution to the speckle pattern remains. This finding indicates that domain-wall fluctuations occur over a large range of time scales. We ascribe this nonergodic behavior to the strong dependence of the fluctuation rate on the local thickness of the film.

Speckle Structure in Small-Angle Coherent X-ray Scattering

Small-angle coherent X-ray scattering measurements on a polymer gel and on a single crystal of Al–9at.% Li are reported. Speckle structures were recorded using a direct-illumination CCD camera. A speckle intensity fluctuation of ~20% was observed. Time and space statistics for the signal provided estimates of the coherence effects and the measurements demonstrate the wavevector dependence of the coherence effects. Preliminary intensity-fluctuation spectroscopy was performed for Al–Li.

Slits as Adjustable Pinholes for Coherent X-ray Scattering Experiments

The combination of accurate translation stages with carefully polished slit blades leads to slits that have many advantages as pinholes for coherent X-ray scattering experiments. The size is adjustable and can be made as small as 0.5 mum. Setting up is easy, while the blade thickness (1 mm tungsten) also makes the slits useful for hard X-rays. A relation between the slit-sample distance and the minimum beam size, together with the corresponding slit size, is derived. This shows that a micrometer-sized beam can be achieved with this type of slits.