X-ray Photon Correlation Spectroscopy Data Research Articles

AI-NERD: Elucidation of relaxation dynamics beyond equilibrium through AI-informed X-ray photon correlation spectroscopy

Understanding and interpreting dynamics of functional materials in situ is a grand challenge in physics and materials science due to the difficulty of experimentally probing materials at varied length and time scales. X-ray photon correlation spectroscopy (XPCS) is uniquely well-suited for characterizing materials dynamics over wide-ranging time scales. However, spatial and temporal heterogeneity in material behavior can make interpretation of experimental XPCS data difficult. In this work, we have developed an unsupervised deep learning (DL) framework for automated classification of relaxation dynamics from experimental data without requiring any prior physical knowledge of the system. We demonstrate how this method can be used to accelerate exploration of large datasets to identify samples of interest, and we apply this approach to directly correlate microscopic dynamics with macroscopic properties of a model system. Importantly, this DL framework is material and process agnostic, marking a concrete step towards autonomous materials discovery.

Beam Effects on Atomic Dynamics in Metallic Glasses Studied With Electron Correlation Microscopy.

Electron correlation microscopy (ECM) is used to investigate atomic dynamics in metallic glasses (MG) close to metastable equilibrium. It temporally correlates diffracted intensities of a time series of dark-field images to deduce a metric for structural decays. The measurement parameters, such as time and temperature, must be chosen according to the material of interest. In this work, ECM was extended to measurements at room temperature. To ensure, or select, a time window with quasi-thermodynamic equilibrium/steady-state measurement conditions, two-time correlation functions of diffracted intensities were calculated. The dynamics at room temperature are partly driven by the electron beam, thus affecting the material and the results. A systematic analysis of the influence of the electron beam is presented, revealing an inverse relation between electron dose rate and intensity correlation decay times at 300 kV acceleration voltage. However, the underlying dynamical mechanisms, described by a stretching exponent, are found to be independent of the applied electron dose rate for a Pd40Ni40P20 MG. An extrapolation of the results to infinite long measurement times and zero dose rate agrees with X-ray photon correlation spectroscopy data and justifies the application of beam-driven ECM at room temperature to study the dynamics of disordered systems.

Machine Learning for analysis of speckle dynamics: quantification and outlier detection

X-ray photon correlation spectroscopy (XPCS) provides an understanding of complex dynamics in materials that are tied to their synthesis, properties, and behaviors. Analysis of XPCS data for dynamics that are far from equilibrium is labor intense and often can impede the discovery process, especially in experiments with high collection rates. Moreover, binning and averaging, involved in the analysis for alleviating poor signal-to-noise ratio, leads to a loss of temporal resolution and the accumulation of systematic error for the parameters quantifying the dynamics. Here, we integrate a denoising autoencoder model into workflows for the analysis of nonequilibrium two-time intensity-intensity correlation functions. Noise reduction allows for extracting the parameters that characterize the sample's dynamics with the temporal resolution limited only by frame rates. Not only does it improve the quantitative usage of the data, but it also creates the potential for automating the analytical workflow, which is a key to high-throughput or autonomous XPCS experiments. Various approaches for the uncertainty quantification and extension of the model for anomalies' detection are discussed.

Cross-correlation analysis of X-ray photon correlation spectroscopy to extract rotational diffusion coefficients.

Coefficients for translational and rotational diffusion characterize the Brownian motion of particles. Emerging X-ray photon correlation spectroscopy (XPCS) experiments probe a broad range of length scales and time scales and are well-suited for investigation of Brownian motion. While methods for estimating the translational diffusion coefficients from XPCS are well-developed, there are no algorithms for measuring the rotational diffusion coefficients based on XPCS, even though the required raw data are accessible from such experiments. In this paper, we propose angular-temporal cross-correlation analysis of XPCS data and show that this information can be used to design a numerical algorithm (Multi-Tiered Estimation for Correlation Spectroscopy [MTECS]) for predicting the rotational diffusion coefficient utilizing the cross-correlation: This approach is applicable to other wavelengths beyond this regime. We verify the accuracy of this algorithmic approach across a range of simulated data.

The Effect of Intensity Fluctuations on Sequential X-ray Photon Correlation Spectroscopy at the X-ray Free Electron Laser Facilities

How materials evolve at thermal equilibrium and under external excitations at small length and time scales is crucial to the understanding and control of material properties. X-ray photon correlation spectroscopy (XPCS) at X-ray free electron laser (XFEL) facilities can in principle capture dynamics of materials that are substantially faster than a millisecond. However, the analysis and interpretation of XPCS data is hindered by the strongly fluctuating X-ray intensity from XFELs. Here we examine the impact of pulse-to-pulse intensity fluctuations on sequential XPCS analysis. We show that the conventional XPCS analysis can still faithfully capture the characteristic time scales, but with substantial decrease in the signal-to-noise ratio of the g2 function and increase in the uncertainties of the extracted time constants. We also demonstrate protocols for improving the signal-to-noise ratio and reducing the uncertainties.

Dynamics of soft nanoparticle suspensions at hard X-ray FEL sources below the radiation-damage threshold.

The application of X-ray photon correlation spectroscopy (XPCS) at free-electron laser (FEL) facilities enables, for the first time, the study of dynamics on a (sub-)nanometre scale in an unreached time range between femtoseconds and seconds. For soft-matter materials, radiation damage is a major limitation when going beyond single-shot applications. Here, an XPCS study is presented at a hard X-ray FEL on radiation-sensitive polymeric poly(N-isopropylacrylamide) (PNIPAM) nanoparticles. The dynamics of aqueous suspensions of densely packed silica-PNIPAM core-shell particles and a PNIPAM nanogel below the radiation-damage threshold are determined. The XPCS data indicate non-diffusive behaviour, suggesting ballistic and stress-dominated heterogeneous particle motions. These results demonstrate the feasibility of XPCS experiments on radiation-sensitive soft-matter materials at FEL sources and pave the way for future applications at MHz repetition rates as well as ultrafast modes using split-pulse devices.

Distributed X-ray photon correlation spectroscopy data reduction using Hadoop MapReduce.

Multi-speckle X-ray photon correlation spectroscopy (XPCS) is a powerful technique for characterizing the dynamic nature of complex materials over a range of time scales. XPCS has been successfully applied to study a wide range of systems. Recent developments in higher-frame-rate detectors, while aiding in the study of faster dynamical processes, creates large amounts of data that require parallel computational techniques to process in near real-time. Here, an implementation of the multi-tau and two-time autocorrelation algorithms using the Hadoop MapReduce framework for distributed computing is presented. The system scales well with regard to the increase in the data size, and has been serving the users of beamline 8-ID-I at the Advanced Photon Source for near real-time autocorrelations for the past five years.

Inverse Transformation: Unleashing Spatially Heterogeneous Dynamics with an Alternative Approach to XPCS Data Analysis.

X-ray photon correlation spectroscopy (XPCS), an extension of dynamic light scattering (DLS) in the X-ray regime, detects temporal intensity fluctuations of coherent speckles and provides scattering vector-dependent sample dynamics at length scales smaller than DLS. The penetrating power of X-rays enables probing dynamics in a broad array of materials with XPCS, including polymers, glasses and metal alloys, where attempts to describe the dynamics with a simple exponential fit usually fails. In these cases, the prevailing XPCS data analysis approach employs stretched or compressed exponential decay functions (Kohlrausch functions), which implicitly assume homogeneous dynamics. In this paper, we propose an alternative analysis scheme based upon inverse Laplace or Gaussian transformation for elucidating heterogeneous distributions of dynamic time scales in XPCS, an approach analogous to the CONTIN algorithm widely accepted in the analysis of DLS from polydisperse and multimodal systems. Using XPCS data measured from colloidal gels, we demonstrate the inverse transform approach reveals hidden multimodal dynamics in materials, unleashing the full potential of XPCS.

CONTIN XPCS: Software for Inverse Transform Analysis of X-Ray Photon Correlation Spectroscopy Dynamics.

X-ray photon correlation spectroscopy (XPCS) and dynamic light scattering (DLS) both reveal dynamics using coherent scattering, but X-rays permit investigating of dynamics in a much more diverse array of materials. Heterogeneous dynamics occur in many such materials, and we showed how classic tools employed in analysis of heterogeneous DLS dynamics extend to XPCS, revealing additional information that conventional Kohlrausch exponential fitting obscures. This work presents the software implementation of inverse transform analysis of XPCS data called CONTIN XPCS, an extension of traditional CONTIN that accommodates dynamics encountered in equilibrium XPCS measurements.

On the use of two-time correlation functions for X-ray photon correlation spectroscopy data analysis.

Multi-time correlation functions are especially well suited to study non-equilibrium processes. In particular, two-time correlation functions are widely used in X-ray photon correlation experiments on systems out of equilibrium. One-time correlations are often extracted from two-time correlation functions at different sample ages. However, this way of analysing two-time correlation functions is not unique. Here, two methods to analyse two-time correlation functions are scrutinized, and three illustrative examples are used to discuss the implications for the evaluation of the correlation times and functional shape of the correlations.

First experimental feasibility study of VIPIC: a custom-made detector for X-ray speckle measurements.

The Vertically Integrated Photon Imaging Chip (VIPIC) was custom-designed for X-ray photon correlation spectroscopy, an application in which occupancy per pixel is low but high time resolution is needed. VIPIC operates in a sparsified streaming mode in which each detected photon is immediately read out as a time- and position-stamped event. This event stream can be fed directly to an autocorrelation engine or accumulated to form a conventional image. The detector only delivers non-zero data (sparsified readout), greatly reducing the communications overhead typical of conventional frame-oriented detectors such as charge-coupled devices or conventional hybrid pixel detectors. This feature allows continuous acquisition of data with timescales from microseconds to hours. In this work VIPIC has been used to measure X-ray photon correlation spectroscopy data on polystyrene latex nano-colliodal suspensions in glycerol and on colloidal suspensions of silica spheres in water. Relaxation times of the nano-colloids have been measured for different temperatures. These results demonstrate that VIPIC can operate continuously in the microsecond time frame, while at the same time probing longer timescales.

Capturing dynamics with Eiger, a fast-framing X-ray detector

Eiger is the next-generation single-photon-counting pixel detector following the widely used Pilatus detector. Its smaller pixel size of 75 µm × 75 µm, higher frame rate of up to 22 kHz, and practically zero dead-time (~4 µs) between exposures will further various measurement methods at synchrotron sources. In this article Eiger's suitability for X-ray photon correlation spectroscopy (XPCS) is demonstrated. By exploiting its high frame rate, complementary small-angle X-ray scattering (SAXS) and XPCS data are collected in parallel to determine both the structure factor and collective diffusion coefficient of a nano-colloid suspension. For the first time, correlation times on the submillisecond time scale are accessible with a large-area pixel detector.

Firmware lower-level discrimination and compression applied to streaming x-ray photon correlation spectroscopy area-detector data

We present a data acquisition system to perform on-the-fly background subtraction and lower-level discrimination compression of streaming x-ray photon correlation spectroscopy data from a fast charge-coupled device (CCD) area detector. The system is built using a commercial frame grabber with an on-board field-programmable gate array. The system is capable of continuously processing at least 60 CCD frames per second each consisting of 1024 × 1024 16-bit pixels with ≲ 15,000 photon hits per frame at a maximum compression factor of ≈95%.

MPICorrelator: A parallel code for performing time correlations

Abstract The MPICorrelator application is a parallel application for processing multi-speckle X-ray photon correlation spectroscopy data via a data-parallelized implementation of the multi-tau algorithm. MPICorrelator spreads the analysis across a number of computing nodes in a cluster. Leveraging a number of computing nodes in this manner has led to a 30 times decrease in the amount of time required to analyze a multi-speckle time series. The system has recently gone operational at the 8 ID I beamline and has demonstrated the ability to keep up with acquisition rates of megapixel frames acquired at 60 Hz. Future improvements will increase the analysis rate to allow for real-time operation and feedback on live acquired data.

The dynamic behavior of magnetic colloids in suspension

The dynamic behavior of magnetic colloidal particles in suspension is investigated. The particles of the core–shell colloid consist of a cobalt ferrite core embedded in a silica shell and are stabilized by surface charges. As the suspension is strongly opaque to visible light, it can not be probed by dynamic light scattering techniques as a result of strong multiple scattering as well as absorption effects. Therefore, the static and dynamic behavior is probed with small-angle X-ray scattering and X-ray photon correlation spectroscopy (XPCS), respectively. Using XPCS, we are able to study the diffusion coefficient of an opaque colloidal system as a function of the scattering vector. In this paper, we report on the behavior of the colloidal system in the absence of an external magnetic field, meaning that the magnetic moments of the particles are oriented randomly. We find no evidence for magnetic interactions in the static data, while the dynamic XPCS data deviate very significantly from the predictions of model calculations.

Detrended fluctuation analysis in x-ray photon correlation spectroscopy for determining coarsening dynamics in alloys

We study the dynamics of precipitate coarsening in phase-separating alloys at late stages of phase separation by x-ray photon correlation spectroscopy (XPCS). For analyzing time series of fluctuating speckle intensities from small-angle scattering of coherent x rays, the method of detrended fluctuation analysis (DFA), which is ideal for determining power-law correlations, is applied. We discuss the application of DFA with respect to XPCS data by means of simulated time series. In particular, the effects of different signal-to-noise ratios are examined. Results from measurements of the two model systems Al-6 at. % Ag at 140 degrees C and Al-9 at. % Zn at 0 degrees C are presented. Since the DFA effectively removes adulterating trends in the data, quantitative agreement with Monte Carlo simulations is obtained. It is verified that two different coarsening mechanisms are predominant in the two systems--coarsening either by diffusion of single atoms or by movement of whole precipitates.

Investigating slow dynamics in alloys using X-ray photon correlation spectroscopy

We show that the emerging method of X-ray photon correlation spectroscopy (XPCS) is a promising tool for investigations of slow dynamics in alloys. Examples for such dynamics are precipitate coarsening in phase-separating alloys at late stages of phase separation and movement of antiphase boundaries. For the sake of brevity we concentrate on latest results for the determination of the coarsening mechanism in the phase-separating system Al–12at.%Li at 150°C and compare it with results for Al–9at.%Zn at 0°C. Thereby, XPCS data is evaluated by the so-called fluctuation analysis technique.

Area detector based photon correlation in the regime of short data batches: Data reduction for dynamic x-ray scattering

A method for reducing time sequences of raw scattering images to intensity time-autocorrelation functions is presented. The procedure is based on the use of a charge coupled device (CCD) area detector, and optimized for operating in the regime of short data batches. Its application to x-ray photon correlation spectroscopy (XPCS) measurements is described in detail. Using a slow-scan CCD, we explain how to achieve data acquisition on a 30 ms or faster time scale, while simultaneously acquiring data from many coherence areas in parallel. The statistical uncertainties of the acquired XPCS data are quantified experimentally, and compared to the theoretically expected noise levels of the correlation functions.