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

Improvement of ultra-small-angle XPCS with the Extremely Brilliant Source

Recent technical developments and the performance of the X-ray photon correlation spectroscopy (XPCS) method over the ultra-small-angle range with the Extremely Brilliant Source (EBS) at the ESRF are described. With higher monochromatic coherent photon flux (∼1012 photons s-1) provided by the EBS and the availability of a fast pixel array detector (EIGER 500K detector operating at 23000 frames s-1), XPCS has become more competitive for probing faster dynamics in relatively dilute suspensions. One of the goals of the present development is to increase the user-friendliness of the method. This is achieved by means of a Python-based graphical user interface that enables online visualization and analysis of the processed data. The improved performance of XPCS on the Time-Resolved Ultra-Small-Angle X-ray Scattering instrument (ID02 beamline) is demonstrated using dilute model colloidal suspensions in several different applications.

Lipid vesicle pools studied by passive X-ray microrheology

Vesicle pools can form by attractive interaction in a solution, mediated by proteins or divalent ions such as calcium. The pools, which are alternatively also denoted as vesicle clusters, form by liquid-liquid phase separation (LLPS) from an initially homogeneous solution. Due to the short range liquid-like order of vesicles in the pool or cluster, the vesicle-rich phase can also be regarded as a condensate, and one would like to better understand not only the structure of these systems, but also their dynamics. The diffusion of vesicles, in particular, is expected to change when vesicles are arrested in a pool. Here we investigate whether passive microrheology based on X-ray photon correlation spectroscopy (XPCS) is a suitable tool to study model systems of artificial lipid vesicles exhibiting LLPS, and more generally also other heterogeneous biomolecular fluids. We show that by adding highly scattering tracer particles to the solution, valuable information on the single vesicle as well as collective dynamics can be inferred. While the correlation functions reveal freely diffusing tracer particles in solutions at low CaCl[Formula: see text] concentrations, the relaxation rate [Formula: see text] shows a nonlinear dependence on [Formula: see text] at a higher concentration of around 8 mM CaCl[Formula: see text], characterised by two linear regimes with a broad cross-over. We explain this finding based on arrested diffusion in percolating vesicle clusters.

Intermittent Defect Fluctuations in Oxide Heterostructures

The heterogeneous nature, local presence, and dynamic evolution of defects typically govern the ionic and electronic properties of a wide variety of functional materials. While the last 50 years have seen considerable efforts into development of new methods to identify the nature of defects in complex materials, such as the perovskite oxides, very little is known about defect dynamics and their influence on the functionality of a material. Here, the discovery of the intermittent behavior of point defects (oxygen vacancies) in oxide heterostructures employing X-ray photon correlation spectroscopy is reported. Local fluctuations between two ordered phases in strained SrCoOx with different degrees of stability of the oxygen vacancies are observed. Ab-initio-informed phase-field modeling reveals that fluctuations between the competing ordered phases are modulated by the oxygen ion/vacancy interaction energy and epitaxial strain. The results demonstrate how defect dynamics, evidenced by measurement and modeling of their temporal fluctuations, give rise to stochastic properties that now can be fully characterized using coherent X-rays, coupled for the first time to multiscale modeling in functional complex oxide heterostructures. The study and its findings open new avenues for engineering the dynamical response of functional materials used in neuromorphic and electrochemical applications.

Robotic pendant drop: containerless liquid for μs-resolved, AI-executable XPCS

The dynamics and structure of mixed phases in a complex fluid can significantly impact its material properties, such as viscoelasticity. Small-angle X-ray Photon Correlation Spectroscopy (SA-XPCS) can probe the spontaneous spatial fluctuations of the mixed phases under various in situ environments over wide spatiotemporal ranges (10-6-103 s /10-10-10-6 m). Tailored material design, however, requires searching through a massive number of sample compositions and experimental parameters, which is beyond the bandwidth of the current coherent X-ray beamline. Using 3.7-μs-resolved XPCS synchronized with the clock frequency at the Advanced Photon Source, we demonstrated the consistency between the Brownian dynamics of ~100 nm diameter colloidal silica nanoparticles measured from an enclosed pendant drop and a sealed capillary. The electronic pipette can also be mounted on a robotic arm to access different stock solutions and create complex fluids with highly-repeatable and precisely controlled composition profiles. This closed-loop, AI-executable protocol is applicable to light scattering techniques regardless of the light wavelength and optical coherence, and is a first step towards high-throughput, autonomous material discovery.

Single and multi-pulse based X-ray photon correlation spectroscopy

The ability of pulsed nature of synchrotron radiation opens up the possibility of studying microsecond dynamics in complex materials via speckle-based techniques. Here, we present the study of measuring the dynamics of a colloidal system by combining single and multiple X-ray pulses of a storage ring. In addition, we apply speckle correlation techniques at various pulse patterns to collect correlation functions from nanoseconds to milliseconds. The obtained sample dynamics from all correlation techniques at different pulse patterns are in very good agreement with the expected dynamics of Brownian motions of silica nanoparticles in water. Our study will pave the way for future pulsed X-ray investigations at various synchrotron X-ray sources using individual X-ray pulse patterns.

Speckle contrast of interfering fluorescence X-rays

With the development of X-ray free-electron lasers (XFELs), producing pulses of femtosecond durations comparable with the coherence times of X-ray fluorescence, it has become possible to observe intensity-intensity correlations due to the interference of emission from independent atoms. This has been used to compare durations of X-ray pulses and to measure the size of a focusedX-ray beam, for example. Here it is shown that it is also possible to observe the interference of fluorescence photons through the measurement of the speckle contrast of angle-resolved fluorescence patterns. Speckle contrast is often used as a measure of the degree of coherence of the incident beam or the fluctuations of the illuminated sample as determined from X-ray diffraction patterns formed by elastic scattering, rather than from fluorescence patterns as addressed here. Commonly used approaches to estimate speckle contrast were found to suffer when applied to XFEL-generated fluorescence patterns due to low photon counts and a significant variation of the excitation pulse energy from shot to shot. A new method to reliably estimate speckle contrast under such conditions, using a weighting scheme, is introduced. The method is demonstrated by comparing the speckle contrast of fluorescence observed with pulses of 3 fs to 15 fs duration.

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.

Methods of Coherent X-Ray Diffraction Imaging

Abstract

Methods of coherent X-ray diffraction imaging of the spatial structure of noncrystalline objects and nanocrystals (nanostructures) are considered. Particular attention is paid to the methods of scanning-based coherent diffraction imaging (ptychography), visualization based on coherent surface scattering with application of correlation spectroscopy approaches, and specific features of visualization using X-ray free-electron laser radiation. The corresponding data in the literature are analyzed to demonstrate the state of the art of the methods of coherent diffraction imaging and fields of their application.

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.

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.

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.

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.