Ruslan Kurta

X-ray cross-correlation analysis of liquid crystal membranes in the vicinity of the hexatic-smectic phase transition.

We present an x-ray study of liquid crystal membranes in the vicinity of the hexatic-smectic phase transition by means of angular x-ray cross-correlation analysis. By applying two-point angular-intensity cross-correlation functions to the measured series of diffraction patterns the parameters of bond-orientational (BO) order in hexatic phase were directly determined. The temperature dependence of the positional correlation lengths was analyzed as well. The obtained correlation lengths show larger values for the higher-order Fourier components of BO order. These findings indicate a strong coupling between BO and positional order.

Structural Evolution of Colloidal Crystal Films in the Process of Melting Revealed by Bragg Peak Analysis

In situ X-ray diffraction studies of structural evolution of colloidal crystal films formed by polystyrene spherical particles upon incremental heating are reported. The Bragg peak parameters, such as peak position, integrated intensity, and radial and azimuthal widths were analyzed as a function of temperature. A quantitative study of colloidal crystal lattice distortions and mosaic spread as a function of temperature was carried out using Williamson-Hall plots based on mosaic block model. The temperature dependence of the diameter of polystyrene particles was obtained from the analysis of Bragg peaks, and the form factor contribution extracted from the diffraction patterns. Four stages of structural evolution in a colloidal crystal upon heating were identified. Based on this analysis, a model of the heating and melting process in the colloidal crystal film is suggested.

Statistical properties of a free-electron laser revealed by Hanbury Brown–Twiss interferometry

We present a comprehensive experimental analysis of statistical properties of the self-amplified spontaneous emission (SASE) free-electron laser (FEL) FLASH at DESY in Hamburg by means of Hanbury Brown and Twiss (HBT) interferometry. The experiments were performed at the FEL wavelengths of 5.5 nm, 13.4 nm, and 20.8 nm. We determined the 2-nd order intensity correlation function for all wavelengths and different operation conditions of FLASH. In all experiments a high degree of spatial coherence (above 50%) was obtained. Our analysis performed in spatial and spectral domains provided us with the independent measurements of an average pulse duration of the FEL that were below 60 fs. To explain complicated behaviour of the 2-nd order intensity correlation function we developed advanced theoretical model that includes the presence of multiple beams and external positional jitter of the FEL pulses. By this analysis we determined that in most experiments several beams were present in radiating field and in one of the experiments external positional jitter was about 25% of the beam size. We envision that methods developed in our study will be used widely for analysis and diagnostics of the FEL radiation.

Sorting algorithms for single-particle imaging experiments at X-ray free-electron lasers

Modern X-ray free-electron lasers (XFELs) operating at high repetition rates produce a tremendous amount of data. It is a great challenge to classify this information and reduce the initial data set to a manageable size for further analysis. Here an approach for classification of diffraction patterns measured in prototypical diffract-and-destroy single-particle imaging experiments at XFELs is presented. It is proposed that the data are classified on the basis of a set of parameters that take into account the underlying diffraction physics and specific relations between the real-space structure of a particle and its reciprocal-space intensity distribution. The approach is demonstrated by applying principal component analysis and support vector machine algorithms to the simulated and measured X-ray data sets.

Coherent soft X-ray diffraction imaging of coliphage PR772 at the Linac coherent light source

Single-particle diffraction from X-ray Free Electron Lasers offers the potential for molecular structure determination without the need for crystallization. In an effort to further develop the technique, we present a dataset of coherent soft X-ray diffraction images of Coliphage PR772 virus, collected at the Atomic Molecular Optics (AMO) beamline with pnCCD detectors in the LAMP instrument at the Linac Coherent Light Source. The diameter of PR772 ranges from 65–70 nm, which is considerably smaller than the previously reported ~600 nm diameter Mimivirus. This reflects continued progress in XFEL-based single-particle imaging towards the single molecular imaging regime. The data set contains significantly more single particle hits than collected in previous experiments, enabling the development of improved statistical analysis, reconstruction algorithms, and quantitative metrics to determine resolution and self-consistency.

Characterization of spatial coherence of synchrotron radiation with non-redundant arrays of apertures.

A method to characterize the spatial coherence of soft X-ray radiation from a single diffraction pattern is presented. The technique is based on scattering from non-redundant arrays (NRAs) of slits and records the degree of spatial coherence at several relative separations from 1 to 15 µm, simultaneously. Using NRAs the spatial coherence of the X-ray beam at the XUV X-ray beamline P04 of the PETRA III synchrotron storage ring was measured as a function of different beam parameters. To verify the results obtained with the NRAs, additional Youngs double-pinhole experiments were conducted and showed good agreement.

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.

Direct reconstruction of the two-dimensional pair distribution function in partially ordered systems with angular correlations

An x-ray scattering approach to determine the two-dimensional (2D) pair distribution function (PDF) in partially ordered 2D systems is proposed. We derive relations between the structure factor and PDF that enable quantitative studies of positional and bond-orientational (BO) order in real space. We apply this approach in the x-ray study of a liquid crystal (LC) film undergoing the smectic-A-hexatic-B phase transition, to analyze the interplay between the positional and BO order during the temperature evolution of the LC film. We analyze the positional correlation length in different directions in real space.

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.

Double hexagonal close-packed structure revealed in a single colloidal crystal grain by Bragg rod analysis

A coherent X-ray diffraction study of a single colloidal crystal grain composed of silica spheres is reported. The diffraction data contain Bragg peaks and additional features in the form of Bragg rods, which are related to the stacking of the hexagonally close-packed layers. The profile of the Bragg rod shows distinct intensity modulations which, under the specific experimental conditions used here, are directly related to the stacking sequence of the layers. Using a model for the scattered intensity along the Bragg rod for an exact stacking sequence of a finite number of hexagonally close-packed layers, it is found that a double hexagonal close-packed stacking sequence is present in the colloidal crystal grain. This analysis method opens up ways to obtain crucial structural information from finite-sized crystalline samples by employing advanced third-generation X-ray sources.