STRUCTURAL ANALYSIS BY X-RAY INTENSITY ANGULAR CROSS CORRELATIONS

The structure of ice under confinement in periodic mesoporous organosilicas (PMOs)

We investigated the structure of ice under nanoporous confinement in periodic mesoporous organosilicas (PMOs) with different organic functionalities and pore diameters between 3.4 and 4.9 nm. X-ray scattering measurements of the system were performed at temperatures between 290 and 150 K. We report the emergence of ice I with both hexagonal and cubic characteristics in different porous materials, as well as an alteration of the lattice parameters when compared to bulk ice. This effect is dependent on the pore diameter and the surface chemistry of the respective PMO. Investigations regarding the orientation of hexagonal ice crystals relative to the pore wall using x-ray cross correlation analysis reveal one or more discrete preferred orientation in most of the samples. For a pore diameter of around 3.8 nm, stronger correlation peaks are present in more hydrophilically functionalized pores and seem to be connected to stronger shifts in the lattice parameters.

The pypadf package: computing the pair angle distribution function from fluctuation scattering data

The pair angle distribution function (PADF) is a three- and four-atom correlation function that characterizes the local angular structure of disordered materials, particles or nanocrystalline materials. The PADF can be measured using X-ray or electron fluctuation diffraction data, which can be collected by scanning or flowing a structurally disordered sample through a focused beam. It is a natural generalization of established pair distribution methods, which do not provide angular information. The software package pypadf provides tools to calculate the PADF from fluctuation diffraction data. The package includes tools for calculating the intensity correlation function, which is a necessary step in the PADF calculation and also the basis for other fluctuation scattering analysis techniques.

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 g_C, tracking the time evolution of cross-correlation function C. With an increasing volume fraction, the ratio of relaxation times of g_C 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.

Angular X-ray cross-correlation analysis applied to the scattering data in 3D reciprocal space from a single crystal

An application of angular X-ray cross-correlation analysis (AXCCA) to the scattered intensity distribution measured in 3D reciprocal space from a single-crystalline sample is proposed in this work. Contrary to the conventional application of AXCCA, when averaging over many 2D diffraction patterns collected from different randomly oriented samples is required, the proposed approach provides an insight into the structure of a single specimen. This is particularly useful in studies of defect-rich samples that are unlikely to have the same structure. The application of the method is shown on an example of a qualitative structure determination of a colloidal crystal from simulated as well as experimentally measured 3D scattered intensity distributions.

Preferred orientation and its effects on intensity-correlation measurements

Intensity-correlation measurements allow access to nanostructural information on a range of ordered and disordered materials beyond traditional pair-correlation methods. In real space, this information can be expressed in terms of a pair-angle distribution function (PADF) which encodes three- and four-body distances and angles. To date, correlation-based techniques have not been applied to the analysis of microstructural effects, such as preferred orientation, which are typically investigated by texture analysis. Preferred orientation is regarded as a potential source of error in intensity-correlation experiments and complicates interpretation of the results. Here, the theory of preferred orientation in intensity-correlation techniques is developed, connecting it to the established theory of texture analysis. The preferred-orientation effect is found to scale with the number of crystalline domains in the beam, surpassing the nanostructural signal when the number of domains becomes large. Experimental demonstrations are presented of the orientation-dominant and nanostructure-dominant cases using PADF analysis. The results show that even minor deviations from uniform orientation produce the strongest angular correlation signals when the number of crystalline domains in the beam is large.

The Sensitivity of the Pair-Angle Distribution Function to Protein Structure

The continued development of X-ray free-electron lasers and serial crystallography techniques has opened up new experimental frontiers. Nanoscale dynamical processes such as crystal growth can now be probed at unprecedented time and spatial resolutions. Pair-angle distribution function (PADF) analysis is a correlation-based technique that has the potential to extend the limits of current serial crystallography experiments, by relaxing the requirements for crystal order, size and number density per exposure. However, unlike traditional crystallographic methods, the PADF technique does not recover the electron density directly. Instead it encodes substantial information about local three-dimensional structure in the form of three- and four-body correlations. It is not yet known how protein structure maps into the many-body PADF correlations. In this paper, we explore the relationship between the PADF and protein conformation. We calculate correlations in reciprocal and real space for model systems exhibiting increasing degrees of order and secondary structural complexity, from disordered polypeptides, single alpha helices, helix bundles and finally a folded 100 kilodalton protein. These models systems inform us about the distinctive angular correlations generated by bonding, polypeptide chains, secondary structure and tertiary structure. They further indicate the potential to use angular correlations as a sensitive measure of conformation change that is complementary to existing structural analysis techniques.

Angular X-Ray Cross-Correlation Analysis (AXCCA): Basic Concepts and Recent Applications to Soft Matter and Nanomaterials

Angular X-ray cross-correlation analysis (AXCCA) is a technique which allows quantitative measurement of the angular anisotropy of X-ray diffraction patterns and provides insights into the orientational order in the system under investigation. This method is based on the evaluation of the angular cross-correlation function of the scattered intensity distribution on a two-dimensional (2D) detector and further averaging over many diffraction patterns for enhancement of the anisotropic signal. Over the last decade, AXCCA was successfully used to study the anisotropy in various soft matter systems, such as solutions of anisotropic particles, liquid crystals, colloidal crystals, superlattices composed by nanoparticles, etc. This review provides an introduction to the technique and gives a survey of the recent experimental work in which AXCCA in combination with micro- or nanofocused X-ray microscopy was used to study the orientational order in various soft matter systems.

Coexistence of hcp and bct Phases during In Situ Superlattice Assembly from Faceted Colloidal Nanocrystals

We study the in situ self-assembly of faceted PbS nanocrystals from colloidal suspensions upon controlled solvent evaporation using time-resolved small-angle X-ray scattering and X-ray cross-correlation analysis. In our bulk-sensitive experiment in transmission geometry, the superlattice crystallization is observed in real time, revealing a hexagonal closed-packed (hcp) structure followed by formation of a body-centered cubic (bcc) superlattice. The bcc superlattice undergoes continuous tetragonal distortion in the solvated state shortly after its formation, resulting in the body-centered tetragonal (bct) structure. Upon solvent evaporation, the bct superstructure becomes more pronounced with the still coexisting hcp phase. These findings corroborate the existing simulations of assembling cuboctahedral-shaped particles and illustrate that we observed the predicted equilibrium states. This work is essential for a deeper understanding of the fundamental forces that direct nanocrystal assembly including nanocrystal shape and ligand coverage.

Ultrafast structural dynamics of photo-reactions observed by time-resolved x-ray cross-correlation analysis

We applied angular X-ray Cross-Correlation analysis (XCCA) to scattering images from a femtosecond resolution X-ray free-electron laser pump-probe experiment with solvated PtPOP {[Pt₂(P₂O₅H₂)₄]^4-} metal complex molecules. The molecules were pumped with linear polarized laser pulses creating an excited state population with a preferred orientational (alignment) direction. Two time scales of 1.9 ± 1.5 ps and 46 ± 10 ps were revealed by angular XCCA associated with structural changes and rotational dephasing of the solvent molecules, respectively. These results illustrate the potential of XCCA to reveal hidden structural information in the analysis of time-resolved x-ray scattering data from molecules in solution.

Quantifying Angular Correlations between the Atomic Lattice and the Superlattice of Nanocrystals Assembled with Directional Linking

We show that the combination of X-ray scattering with a nanofocused beam and X-ray cross correlation analysis is an efficient way for the full structural characterization of mesocrystalline nanoparticle assemblies with a single experiment. We analyze several hundred diffraction patterns at individual sample locations, that is, individual grains, to obtain a meaningful statistical distribution of the superlattice and atomic lattice ordering. Simultaneous small- and wide-angle X-ray scattering of the same sample location allows us to determine the structure and orientation of the superlattice as well as the angular correlation of the first two Bragg peaks of the atomic lattices, their orientation with respect to the superlattice, and the average orientational misfit due to local structural disorder. This experiment is particularly advantageous for synthetic mesocrystals made by the simultaneous self-assembly of nanocrystals and surface-functionalization with conductive ligands. While the structural characterization of such materials has been challenging so far, the present method now allows correlating the mesocrystalline structure with optoelectronic properties.