X-ray Photon Correlation Spectroscopy Research Articles

Small-angle X-ray scattering in the era of fourth-generation light sources.

Recently, fourth-generation synchrotron sources with several orders of magnitude higher brightness and higher degree of coherence compared with third-generation sources have come into operation. These new X-ray sources offer exciting opportunities for the investigation of soft matter and biological specimens by small-angle X-ray scattering (SAXS) and related scattering methods. The improved beam properties together with the advanced pixel array detectors readily enhance the angular resolution of SAXS and ultra-small-angle X-ray scattering in the pinhole collimation. The high degree of coherence is a major boost for the X-ray photon correlation spectroscopy (XPCS) technique, enabling the equilibrium dynamics to be probed over broader time and length scales. This article presents some representative examples illustrating the performance of SAXS and XPCS with the Extremely Brilliant Source at the European Synchrotron Radiation Facility. The rapid onset of radiation damage is a significant challenge with the vast majority of samples, and appropriate protocols need to be adopted for circumventing this problem.

Nanoparticle Diffusion in Miscible Polymer Nanocomposite Melts

X-ray photon correlation spectroscopy measurements were used to quantify the dynamics of bare and bimodal grafted silica nanoparticles mixed with PEO melts of different molecular weights. In dilute polymer nanocomposite (PNC) samples, we find diffusive NP behavior as described by the Stokes–Einstein relationship so long as the adsorbed PEO polymer layer is taken into account in determining both the effective NP size and its role on composite viscosity. The size of this bound layer was found to be approximately 2Rg, where Rg is the chain radius of gyration. We also expanded our system to investigate how the dynamics of grafted NPs differ from bare NPs with an adsorbed layer. We showed that the dynamics again can be determined by an effective NP radius at a scale smaller than the effective interparticle spacing; however, at larger length scales, the morphology and grafting parameters play a major role in the system dynamics. These results allow us to quantify NP ordering driven by polymer crystallization. It has previously been speculated that behavior is controlled by the relative ratio of time scale of crystal growth and the diffusive time scale of the NPs, a Peclet number. When the former time scale is longer, then the NPs are expected to be segregated into the interlamellar amorphous zones, while the NPs are too slow to be reorganized in the opposite case. We show here that this conjecture is quantitatively correct and the demarcation in behavior occurs for Pe = 1. Thus, we provide a way to estimate a critical spherulite growth rate for any semicrystalline PNC, at which a given NP can be ordered. Together, the results of this study permit us to tunably design PNCs through directed dispersion of NPs in a polymer matrix.

Pressure-induced nonmonotonic cross-over of steady relaxation dynamics in a metallic glass

Relaxation dynamics, as a key to understand glass formation and glassy properties, remains an elusive and challenging issue in condensed matter physics. In this work, insitu high-pressure synchrotron high-energy X-ray photon correlation spectroscopy has been developed to probe the atomic-scale relaxation dynamics of a cerium-based metallic glass during compression. Although the sample density continuously increases, the collective atomic motion initially slows down as generally expected and then counterintuitively accelerates with further compression (density increase), showing an unusual nonmonotonic pressure-induced steady relaxation dynamics cross-over at ~3 GPa. Furthermore, by combining insitu high-pressure synchrotron X-ray diffraction, the relaxation dynamics anomaly is evidenced to closely correlate with the dramatic changes in local atomic structures during compression, rather than monotonically scaling with either sample density or overall stress level. These findings could provide insight into relaxation dynamics and their relationship with local atomic structures of glasses.

Effects of the Grazing Incidence Geometry on X-ray Photon Correlation Spectroscopy Measurements.

X-ray photon correlation spectroscopy (XPCS) is a versatile tool to measure dynamics on the nanometer to micrometer scale in bulk samples. XPCS has also been applied in grazing incidence (GI) geometry to examine the dynamics of surface layers. However, considering GI scattering experiments more universally, the GI geometry leads to a superposition of signals due to reflection and refraction effects, also known from the distorted-wave Born approximation (DWBA). In this paper, the impact of these reflection and refraction effects on the correlation analysis is determined experimentally by measuring grazing incidence transmission XPCS (GT-XPCS) and grazing incidence XPCS (GI-XPCS) simultaneously for a thin film sample, showing non-equilibrium dynamics. The results of the GI and GT geometry comparisons are combined within the framework of the standardly applied, simplified DWBA. These calculations allow identifying the main contributions of the detected signal from the leading scattering terms along the out-of-plane direction qz, which dominate the measured intensity pattern on the detector. In combination with the calculation of the non-linear effect of refraction in GTSAXS and GISAXS, it is possible to identify experimental conditions that can be chosen to run experiments and data analysis as close as possible to transmission XPCS and to explain which limitations for data interpretations are observed. Consequently, the beam exposure can be significantly reduced by using GI geometry only. Calculations of experimental settings prior to experiments are detailed to determine suitable qz regions for a variety of material systems measured in bulk-sensitive GI-XPCS experiments, allowing us to determine the scaling behavior of typical decay times as a function of q that is comparable to the scaling behavior obtained in distortion-free GT-XPCS or transmission XPCS experiments.

Selected advances in small-angle scattering and applications they serve in manufacturing, energy and climate change.

Innovations in small-angle X-ray and neutron scattering (SAXS and SANS) at major X-ray and neutron facilities offer new characterization tools for researching materials phenomena relevant to advanced applications. For SAXS, the new generation of diffraction-limited storage rings, incorporating multi-bend achromat concepts, dramatically decrease electron beam emittance and significantly increase X-ray brilliance over previous third-generation sources. This results in intense X-ray incident beams that are more compact in the horizontal plane, allowing significantly improved spatial resolution, better time resolution, and a new era for coherent-beam SAXS methods such as X-ray photon correlation spectroscopy. Elsewhere, X-ray free-electron laser sources provide extremely bright, fully coherent, X-ray pulses of <100 fs and can support SAXS studies of material processes where entire SAXS data sets are collected in a single pulse train. Meanwhile, SANS at both steady-state reactor and pulsed spallation neutron sources has significantly evolved. Developments in neutron optics and multiple detector carriages now enable data collection in a few minutes for materials characterization over nanometre-to-micrometre scale ranges, opening up real-time studies of multi-scale materials phenomena. SANS at pulsed neutron sources is becoming more integrated with neutron diffraction methods for simultaneous structure characterization of complex materials. In this paper, selected developments are highlighted and some recent state-of-the-art studies discussed, relevant to hard matter applications in advanced manufacturing, energy and climate change.

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.

Dynamics and Time Scales of Higher-Order Correlations in Supercooled Colloidal Systems.

The dynamics and time scales of higher-order correlations are studied in supercooled colloidal systems. A combination of X-ray photon correlation spectroscopy (XPCS) and X-ray cross-correlation analysis (XCCA) shows the typical slowing of the dynamics of a hard sphere system when approaching the glass transition. The time scales of higher-order correlations are probed using a novel time correlation function gC, tracking the time evolution of cross-correlation function C. With an increasing volume fraction, the ratio of relaxation times of gC to the standard individual particle relaxation time obtained by XPCS increases from ∼0.4 to ∼0.9. While a value of ∼0.5 is expected for free diffusion, the increasing values suggest that the local orders within the sample are becoming more long-lived for larger volume fractions. Furthermore, the dynamics of local order is more heterogeneous than the individual particle dynamics. These results indicate that not only the presence but also the lifetime of locally favored structures increases close to the glass transition.

Rheological signatures of a glass-glass transition in an aging colloidal clay

The occurrence of non-equilibrium transitions between arrested states has recently emerged as an intriguing issue in the field of soft glassy materials. The existence of one such transition has been suggested for aging colloidal clays (Laponite® suspensions) at a weight concentration of 3.0%, although further experimental evidences are necessary to validate this scenario. Here, we test the occurrence of this transition for spontaneously aged (non-rejuvenated) samples by exploiting the rheological tools of dynamical mechanical analysis. On imposing consecutive compression cycles to differently aged clay suspensions, we find that quite an abrupt change of rheological parameters occurs for ages around three days. For Young’s and elastic moduli, the change with the waiting time is essentially independent from the deformation rate, whereas other “fluid-like” properties, such as the loss modulus, do clearly display some rate dependence. We also show that the crossover identified by rheology coincides with deviations of the relaxation time (obtained through x-ray photon correlation spectroscopy) from its expected monotonic increase with aging. Thus, our results robustly support the existence of a glass-glass transition in aging colloidal clays, highlighting characteristic features of their viscoelastic behavior.

In situ observation of the structure and dynamics of a polymer solution through nonsolvent-induced phase separation by x-ray photon correlation spectroscopy

Nonsolvent-induced phase separation (NIPS) is a complex but important phenomenon involved in the manufacture of fibers and other polymeric industrial products. We performed in situ x-ray photon correlation spectroscopy (XPCS) measurements on a cuprammonium cellulose solution immersed in aqueous acetone solution to reveal the structure and dynamics involved in the NIPS process on the microscopic scale. A combination of the structural information from the small angle x-ray scattering profiles and the dynamic information from the XPCS analysis revealed that NIPS occurs via two steps: dilution of the polymer solution by the solvent and desorption of the solvent from the polymer solution. This study will provide an opportunity for the fundamental understanding of NIPS, which is important from both the scientific and industrial viewpoints.

Microscopic Origins of the Nonlinear Behavior of Particle-Filled Rubber Probed with Dynamic Strain XPCS.

The underlying microscopic response of filler networks in reinforced rubber to dynamic strain is not well understood due to the experimental difficulty of directly measuring filler network behavior in samples undergoing dynamic strain. This difficulty can be overcome with in situ X-ray photon correlation spectroscopy (XPCS) measurements. The contrast between the silica filler and the rubber matrix for X-ray scattering allows us to isolate the filler network behavior from the overall response of the rubber. This in situ XPCS technique probes the microscopic breakdown and reforming of the filler network structure, which are responsible for the nonlinear dependence of modulus on strain, known in the rubber science community as the Payne effect. These microscopic changes in the filler network structure have consequences for the macroscopic material performance, especially for the fuel efficiency of tire tread compounds. Here, we elucidate the behavior with in situ dynamic strain XPCS experiments on industrially relevant, vulcanized rubbers filled (13 vol %) with novel air-milled silica of ultrahigh-surface area (UHSA) (250 m2/g). The addition of a silane coupling agent to rubber containing this silica causes an unexpected and counterintuitive increase in the Payne effect and decrease in energy dissipation. For this rubber, we observe a nearly two-fold enhancement of the storage modulus and virtually equivalent loss tangent compared to a rubber containing a coupling agent and conventional silica. Interpretation of our in situ XPCS results simultaneously with interpretation of traditional dynamic mechanical analysis (DMA) strain sweep experiments reveals that the debonding or yielding of bridged bound rubber layers is key to understanding the behavior of rubber formulations containing the silane coupling agent and high-surface area silica. These results demonstrate that the combination of XPCS and DMA is a powerful method for unraveling the microscale filler response to strain which dictates the dynamic mechanical properties of reinforced soft matter composites. With this combination of techniques, we have elucidated the great promise of UHSA silica when used in concert with a silane coupling agent in filled rubber. Such composites simultaneously exhibit large moduli and low hysteresis under dynamic strain.

Investigation of the yielding transition in concentrated colloidal systems via rheo-XPCS

We probe the microstructural yielding dynamics of a concentrated colloidal system by performing creep/recovery tests with simultaneous collection of coherent scattering data via X-ray Photon Correlation Spectroscopy (XPCS). This combination of rheology and scattering allows for time-resolved observations of the microstructural dynamics as yielding occurs, which can be linked back to the applied rheological deformation to form structure-property relations. Under sufficiently small applied creep stresses, examination of the correlation in the flow direction reveals that the scattering response recorrelates with its predeformed state, indicating nearly complete microstructural recovery, and the dynamics of the system under these conditions slows considerably. Conversely, larger creep stresses increase the speed of the dynamics under both applied creep and recovery. The data show a strong connection between the microstructural dynamics and the acquisition of unrecoverable strain. By comparing this relationship to that predicted from homogeneous, affine shearing, we find that the yielding transition in concentrated colloidal systems is highly heterogeneous on the microstructural level.

Evaluating the transferability of machine-learned force fields for material property modeling

Machine-learned force fields have generated significant interest in recent years as a tool for molecular dynamics (MD) simulations, with the aim of developing accurate and efficient models that can replace classical interatomic potentials. However, before these models can be confidently applied to materials simulations, they must be thoroughly tested and validated. The existing tests on the radial distribution function and mean-squared displacements are insufficient in assessing the transferability of these models. Here we present a more comprehensive set of benchmarking tests for evaluating the transferability of machine-learned force fields. We use a graph neural network (GNN)-based force field coupled with the OpenMM package to carry out MD simulations for Argon as a test case. Our tests include computational X-ray photon correlation spectroscopy (XPCS) signals, which capture the density fluctuation at various length scales in the liquid phase, as well as phonon density-of-states in the solid phase and the liquid-solid phase transition behavior. Our results show that the model can accurately capture the behavior of the solid phase only when the configurations from the solid phase are included in the training dataset. This underscores the importance of appropriately selecting the training data set when developing machine-learned force fields. The tests presented in this work provide a necessary foundation for the development and application of machine-learned force fields for materials simulations.

In situ high-pressure wide-angle hard x-ray photon correlation spectroscopy: A versatile tool probing atomic dynamics of extreme condition matter

With the advent of new synchrotron radiation x-ray sources that provide a significantly enhanced coherent flux, high-energy x-ray photon correlation spectroscopy measurements can be performed on materials in a diamond anvil cell. Essential information on atomic dynamics that was previously inaccessible can be obtained for various novel phenomena emerging under extreme conditions. This article discusses the importance, feasibility, and experimental details of this technique, as well as the opportunities that it offers to address critical scientific challenges.

Effects of temperature and ionic strength on the microscopic structure and dynamics of egg white gels.

We investigate the thermal gelation of egg white proteins at different temperatures with varying salt concentrations using x-ray photon correlation spectroscopy in the geometry of ultra-small angle x-ray scattering. Temperature-dependent structural investigation suggests a faster network formation with increasing temperature, and the gel adopts a more compact network, which is inconsistent with the conventional understanding of thermal aggregation. The resulting gel network shows a fractal dimension δ, ranging from 1.5 to 2.2. The values of δ display a non-monotonic behavior with increasing amount of salt. The corresponding dynamics in the q range of 0.002-0.1 nm-1 is observable after major change of the gel structure. The extracted relaxation time exhibits a two-step power law growth in dynamics as a function of waiting time. In the first regime, the dynamics is associated with structural growth, whereas the second regime is associated with the aging of the gel, which is directly linked with its compactness, as quantified by the fractal dimension. The gel dynamics is characterized by a compressed exponential relaxation with a ballistic-type of motion. The addition of salt gradually makes the early stage dynamics faster. Both gelation kinetics and microscopic dynamics show that the activation energy barrier in the system systematically decreases with increasing salt concentration.

Spatial-Temporal Dynamics at the Interface of 3D-Printed Photocurable Thermoset Resin Layers

Additive manufacturing (AM) is used to fabricate polymeric materials into complex three-dimensional (3D) structures. As the 3D structure is built by sequential layer-by-layer deposition of filaments dispensed from a translating nozzle (in the case of extrusion-based printing), defects often form at the filament-filament interface. The out-of-equilibrium structural development that occurs during the printing process is difficult to directly measure by quantitative means, limiting our understanding of the physical mechanisms at play. Here, we utilize in operando X-ray photon correlation spectroscopy (XPCS) measurements with microbeam capability to probe the real-time structural evolution at the filament-filament interface during extrusion 3D printing. We investigate the solidification of a dual-cure (UV/thermal) acrylate/epoxy resin during multilayer 3D printing as a rational model by tracking the nanoscale motion of filler particles embedded in the resin. The spatially and temporally resolved dynamics (on length scales from several nm to a few hundreds of nm and time scales of 10–3 < t < 103 seconds) are measured during the deposition of a single filament as well as during the deposition of a second layer on top of the cured underlayer. The addition of a second layer introduces structural perturbations at the interface and results in accelerated interfacial dynamics compared to those of the cured underlayer. However, as time proceeds, the local dynamical heterogeneity disappears, and the evolution of the dynamics progresses uniformly within the entire interfacial region. The homogeneity across the interface results from the formation of an interpenetrated epoxy network that spans across the first and second filaments. This homogeneous interface is responsible for the isotropic tensile properties of a 3D-printed sample that are independent of print direction and nearly the same as the bulk (non-3D-printed) sample. The XPCS microrheology approach provides insight into the dynamics-process-property relationship at the printed filament interfaces.

Amorphous-amorphous transformation induced in glasses by intense x-ray beams

The atomic displacements induced by an x-ray beam of relatively low energy, $\ensuremath{\epsilon}\ensuremath{\sim}8$ KeV, are investigated in pure boron oxide and in a set of sodium silicate glasses by means of x-ray photon correlation spectroscopy. We observe the complete x-ray induced transformation of the initial glass into a new amorphous state which remains stable under irradiation. The new phase continues to rearrange under the beam with a stretched exponential relaxation similar to the one observed with macroscopic measurements in the corresponding high-temperature supercooled liquid, suggesting that the new configuration lies in a higher energy minimum of the potential energy landscape. We investigate the temperature dependence of the observed dynamics for a specific sodium concentration and we observe a temperature dependence of the beam induced motion, which suggests that the defect creation rate is thermally activated. The radiation dose needed for the initial structural variation is sample dependent and correlates well with the number of constraints per vertex, within the framework of rigidity theory. This observation provides a quantitative tool to evaluate the efficiency of the radiolytic process in different network topologies.

Discerning element and site-specific fluctuations of the charge-orbital order in Fe3O4 below the Verwey transition

Despite countless experimental probes into magnetite's electronic structure across the Verwey transition ${\mathrm{Fe}}_{3}{\mathrm{O}}_{4}$, the exact origin of this archetypical metal-insulator transition remains a puzzle. Advanced x-ray diffraction techniques have mostly resolved the monoclinic structure of the insulating phase, including interatomic bond lengths, but the complexity of the charge-orbitally ordered state is difficult to disentangle. We combined resonant elastic x-ray scattering and x-ray photon correlation spectroscopy to probe charge-orbital fluctuations in the insulating state of magnetite. By accessing the Bragg forbidden ${(00\frac{1}{2})}_{\mathrm{c}}$ peak at the oxygen $K$-edge, we complement our previous study on the iron ${L}_{\mathit{3}}\ensuremath{-}\mathrm{edge}$ to reveal the dynamics of the iron $3d$ and oxygen $2p$ orbital domains. Our new results reveal a decoupling of the orbital correlation lengths between the oxygen $2p$ states and site-specific iron $3d$ states, and we further show charge-orbital domain fluctuations at the iron ${t}_{2g}$ orbital sites of trimeron chains. These results also demonstrate an experimental method capable of distinguishing electronic dynamics between the oxygen ligands and the transition metal that underpins emergent behaviors in complex oxides.

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.

Memory in aging colloidal gels with time-varying attraction.

We report a combined rheology, x-ray photon correlation spectroscopy, and modeling study of gel formation and aging in suspensions of nanocolloidal spheres with volume fractions of 0.20 and 0.43 and with a short-range attraction whose strength is tuned by changing temperature. Following a quench from high temperature, where the colloids are essentially hard spheres, to a temperature below the gel point, the suspensions form gels that undergo aging characterized by a steadily increasing elastic shear modulus and slowing, increasingly constrained microscopic dynamics. The aging proceeds at a faster rate for stronger attraction strength. When the attraction strength is suddenly lowered during aging, the gel properties evolve non-monotonically in a manner resembling the Kovacs effect in glasses, in which the modulus decreases and the microscopic dynamics become less constrained for a period before more conventional aging resumes. Eventually, the properties of the gel following the decrease in attraction strength converge to those of a gel that has undergone aging at the lower attraction strength throughout. The time scale of this convergence increases as a power law with the age at which the attraction strength is decreased and decreases exponentially with the magnitude of the change in attraction. A model for gel aging in which particles attach and detach from the gel at rates that depend on their contact number reproduces these trends and reveals that the non-monotonic behavior results from the dispersion in the rates that the populations of particles with different contact number adjust to the new attraction strength.

Stochastic atomic acceleration during the X-ray-induced fluidization of a silica glass

The X-ray-induced, nonthermal fluidization of the prototypical SiO2 glass is investigated by X-ray photon correlation spectroscopy in the small-angle scattering range. This process is initiated by the absorption of X-rays and leads to overall atomic displacements which reach at least few nanometers at temperatures well below the glass transition. At absorbed doses of ∼5 GGy typical of many modern X-ray-based experiments, the atomic displacements display a hyperdiffusive behavior and are distributed according to a heavy-tailed, Lévy stable distribution. This is attributed to the stochastic generation of X-ray-induced point defects which give rise to a dynamically fluctuating potential landscape, thus providing a microscopic picture of the fluidization process.