X-ray Cross-correlation Analysis Research Articles

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 4.9nm. X-ray scattering measurements of the system were performed at temperatures between 290 and 150K. 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 3.8nm, stronger correlation peaks are present in more hydrophilically functionalized pores and seem to be connected to stronger shifts in the lattice parameters.

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.

Going beyond ensemble average angular cross-correlation analysis.

Commentary is given on a paper [Lapkin et al. (2022). IUCrJ, 9, 425-438] reporting the application of angular X-ray cross-correlation analysis to the scattered intensity distribution measured in 3D reciprocal space from a single-crystalline sample.

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.

Shear-induced ordering in liquid microjets seen by x-ray cross correlation analysis.

We applied shear to a silica nanoparticle dispersion in a microfluidic jet device and observed direction-dependent structure along and across the flow direction. The asymmetries of the diffraction patterns were evaluated by x-ray cross correlation analysis. For different Rayleigh nozzle sizes and shapes, we measured the decay of the shear-induced ordering after the cessation of the shear. At large tube sizes and small shear rates, the characteristic times of the decay become longer, but Péclet-weighted times do not scale linearly with Péclet numbers. By modeling particle distributions with the corresponding diffraction patterns and comparing measured shape asymmetry to simulations, we determined the variation of volume fraction over the azimuthal angle for the maximum ordered state in the jet.

Structure–Transport Correlation Reveals Anisotropic Charge Transport in Coupled PbS Nanocrystal Superlattices

The assembly of colloidal semiconductive nanocrystals into highly ordered superlattices predicts novel structure-related properties by design. However, those structure-property relationships, such as charge transport depending on the structure or even directions of the superlattice, have remained unrevealed so far. Here, electric transport measurements and X-ray nanodiffraction are performed on self-assembled lead sulfide nanocrystal superlattices to investigate direction-dependent charge carrier transport in microscopic domains of these materials. By angular X-ray cross-correlation analysis, the structure and orientation of individual superlattices is determined, which are directly correlated with the electronic properties of the same microdomains. By that, strong evidence for the effect of superlattice crystallinity on the electric conductivity is found. Further, anisotropic charge transport in highly ordered monocrystalline domains is revealed, which is attributed to the dominant effect of shortest interparticle distance. This implies that transport anisotropy should be a general feature of weakly coupled nanocrystal superlattices.

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.

Monitoring Nanocrystal Self-Assembly in Real Time Using In Situ Small-Angle X-Ray Scattering.

Self-assembled nanocrystal superlattices have attracted large scientific attention due to their potential technological applications. However, the nucleation and growth mechanisms of superlattice assemblies remain largely unresolved due to experimental difficulties to monitor intermediate states. Here, the self-assembly of colloidal PbS nanocrystals is studied in real time by a combination of controlled solvent evaporation from the bulk solution and in situ small-angle X-ray scattering (SAXS) in transmission geometry. For the first time for the investigated system a hexagonal closed-packed (hcp) superlattice formed in a solvent vapor saturated atmosphere is observed during slow solvent evaporation from a colloidal suspension. The highly ordered hcp superlattice is followed by a transition into the final body-centered cubic superlattice upon complete drying. Additionally, X-ray cross-correlation analysis of Bragg reflections is applied to access information on precursor structures in the assembly process, which is not evident from conventional SAXS analysis. The detailed evolution of the crystal structure with time provides key results for understanding the assembly mechanism and the role of ligand-solvent interactions, which is important both for fundamental research and for fabrication of superlattices with desired properties.

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.

Heterogeneous local order in self-assembled nanoparticle films revealed by X-ray cross-correlations.

We report on the self-assembly of gold nanoparticles coated with a soft poly(ethylene glycol) shell studied by X-ray cross-correlation analysis. Depending on the initial concentration of gold nanoparticles used, structurally heterogeneous films were formed. The films feature hot spots of dominating four- and sixfold local order with patch sizes of a few micrometres, containing 104-105 particles. The amplitude of the order parameters suggested that a minimum sample amount was necessary to form well ordered local structures. Furthermore, the increasing variation in order parameters with sample thickness demonstrated a high degree of structural heterogeneity. This wealth of information cannot be obtained by the conventional microscopy techniques that are commonly used to study nanocrystal superstructures, as illustrated by complementary scanning electron microscopy measurements.

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.

Structural studies of the bond-orientational order and hexatic–smectic transition in liquid crystals of various compositions

We report on the X-ray studies of freely suspended hexatic films of three different liquid crystal compounds. By applying angular X-ray cross-correlation analysis (XCCA) to the measured diffraction patterns the parameters of the bond-orientational (BO) order in the hexatic phase were directly determined. The temperature evolution of the BO order parameters was analyzed on the basis of the multicritical scaling theory (MCST). Our results confirmed the validity of the MCST in the whole temperature range of the existence of the hexatic phase for all three compounds. The temperature dependence of the BO order parameters in the vicinity of the hexatic-smectic transition was fitted by a conventional power law with a critical exponent β ≈ 0.1 of extremely small value. We found that the temperature dependence of higher order harmonics of the BO order scales as the powers of the first harmonic, with an exponent equal to the harmonic number. This indicates a nonlinear coupling of the BO order parameters of different order. We demonstrate that compounds of various compositions, possessing different phase sequences at low temperatures, display the same thermodynamic behavior in the hexatic phase and in the vicinity of the smectic-hexatic phase transition.

Structure beyond pair correlations: X-ray cross-correlation from colloidal crystals.

The results of an X-ray cross-correlation analysis (XCCA) study on hard-sphere colloidal crystals and glasses are presented. The article shows that cross-correlation functions can be used to extract structural information beyond the static structure factor in such systems. In particular, the powder average can be overcome by accessing the crystals' unit-cell structure. In this case, the results suggest that the crystal is of face-centered cubic type. It is demonstrated that XCCA is a valuable tool for X-ray crystallography, in particular for studies on colloidal systems. These are typically characterized by a rather poor crystalline quality due to size polydispersity and limitations in experimental resolution because of the small q values probed. Furthermore, nontrivial correlations are observed that allow a more detailed insight into crystal structures beyond conventional crystallography, especially to extend knowledge in structure formation processes and phase transitions.

Multiple-wavelength resonant fluctuation x-ray scattering

A multiple-wavelength resonant fluctuation x-ray scattering approach is proposed for element-specific imaging of nanoscale objects in random ensembles with short positional and rotational relaxation times. It is shown, that by applying x-ray cross-correlation analysis in combination with iterative phase retrieval to the scattering data measured at multiple x-ray energies near an absorption edge of a substance, it is possible to image the nanoscale structure of an individual object with chemical sensitivity. The elemental distribution in distinct two-component model nanostructures was reconstructed using the simulated scattering data from two-dimensional random ensembles of particles. The approach might be especially advantageous for structural studies at x-ray free electron lasers.

Colloidal crystallite suspensions studied by high pressure small angle x-ray scattering.

We report on high pressure small angle x-ray scattering on suspensions of colloidal crystallites in water. The crystallites made out of charge-stabilized poly-acrylate particles exhibit a complex pressure dependence which is based on the specific pressure properties of the suspending medium water. The dominant effect is a compression of the crystallites caused by the compression of the water. In addition, we find indications that also the electrostatic properties of the system, i.e. the particle charge and the dissociation of ions, might play a role for the pressure dependence of the samples. The data further suggest that crystallites in a metastable state induced by shear-induced melting can relax to a similar structural state upon the application of pressure and dilution with water. X-ray cross correlation analysis of the two-dimensional scattering patterns indicates a pressure-dependent increase of the orientational order of the crystallites correlated with growth of these in the suspension. This study underlines the potential of pressure as a very relevant parameter to understand colloidal crystallite systems in aqueous suspension.

Spatially resolved x-ray studies of liquid crystals with strongly developed bond-orientational order.

We present an x-ray study of freely suspended hexatic films of the liquid crystal 3(10)OBC. Our results reveal spatial inhomogeneities of the bond-orientational (BO) order in the vicinity of the hexatic-smectic phase transition and the formation of large-scale hexatic domains at lower temperatures. Deep in the hexatic phase up to 25 successive sixfold BO order parameters have been directly determined by means of angular x-ray cross-correlation analysis (XCCA). Such strongly developed hexatic order allowed us to determine higher order correction terms in the scaling relation predicted by the multicritical scaling theory over a full temperature range of the hexatic phase existence.

Detecting orientational order in model systems by X-ray cross-correlation methods

The results of a computational X-ray cross-correlation analysis (XCCA) study on two-dimensional polygonal model structures are presented. This article shows how to detect and identify the orientational order of such systems, demonstrates how to eliminate the influence of the `computational box' on the XCCA results and develops new correlation functions that reflect the sample's orientational order only. For this purpose, the dependence of the correlation functions on the number of polygonal clusters and scattering vector magnitude q is studied for various types of polygons, including mixtures of polygons and randomly placed particles. An order parameter that describes the orientational order within the sample is defined. Finally, the influence of detector noise and nonplanar wavefronts on the XCCA data is determined, both of which appear to affect the results significantly and have thus to be considered in real experiments.

X-ray cross-correlation analysis of the low-mass X-ray binary 4U 1636-53

AbstractWe analyze the cross-correlation function of the soft and hard X-rays of the atoll source 4U 1636-53 with RXTE data. The results show that the cross-correlations evolve along the different branches of the color-color diagram. At the lower left banana states, we have both positive and ambiguous correlations, and positive correlations are dominant for the lower banana and the upper banana states. The anti-correlation is detected at the top of the upper banana states. The cross-correlations of two atoll sources 4U 1735-44 and 4U 1608-52 have been studied in previous work, and the anti-correlations are detected at the lower left banana or the top of the upper banana states. Our results show that, in the 4U 1636-53, the distribution of the cross-correlations in the color-color diagram is similar to those of 4U 1735-44 and 4U 1608-52, and confirm further that the distribution of cross-correlations in color-color diagram could be correlated with the luminosity of the source.

Structural properties of π-π conjugated network in polymer thin films studied by x-ray cross-correlation analysis

We present results of an x-ray study of structural properties of π-π conjugated networks in semicrystalline polymer thin films using nanofocused x-ray beam. We applied the x-ray cross-correlation analysis to x-ray scattering data from blends of poly(3-hexylthiophene) (P3HT) with gold nanoparticles. The Fourier spectra of the intensity cross-correlation functions for different films contain non-zero components of orders n = 2,4 and 6 revealing structural order in the system. The results suggest inhomogeneous structure of both samples, with preferential edge-on orientation of domains in one sample and mixed orientation in another sample.