Emergent rotational symmetries in disordered magnetic domain patterns

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.

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.

Operational properties of fluctuation X-ray scattering data

X-ray scattering images collected on timescales shorter than rotation diffusion times using a (partially) coherent beam result in a significant increase in information content in the scattered data. These measurements, named fluctuation X-ray scattering (FXS), are typically performed on an X-ray free-electron laser (XFEL) and can provide fundamental insights into the structure of biological molecules, engineered nanoparticles or energy-related mesoscopic materials beyond what can be obtained with standard X-ray scattering techniques. In order to understand, use and validate experimental FXS data, the availability of basic data characteristics and operational properties is essential, but has been absent up to this point. In this communication, an intuitive view of the nature of FXS data and their properties is provided, the effect of FXS data on the derived structural models is highlighted, and generalizations of the Guinier and Porod laws that can ultimately be used to plan experiments and assess the quality of experimental data are presented.

The importance of averaging to interpret electron correlographs of disordered materials

The development of effective new tools for structural characterization of disordered materials and systems is becoming increasingly important as such tools provide the key to understanding, and ultimately controlling, their properties. The relatively novel technique of correlograph analysis (i.e., the approach of calculating angular autocorrelations within diffraction patterns) promises unique advantages for probing the local symmetries of disordered structures. Because correlograph analysis examines a component of the high-order four-body correlation function, it is more sensitive to medium-range ordering than conventional diffraction methods. As a follow-up of our previous publication, where we studied thin samples of sputtered amorphous silicon, we describe here the practical experimental method and common systematic errors of electron correlograph analysis. Using both experimental data and numerical simulations, we demonstrate that reliable structural information about the sample can only be extracted from the mean correlograph averaged over a sufficient number of individual results.

Homometry in the light of coherent beams

Two systems are homometric if they are indistinguishable by diffraction. A distinction is first made between Bragg and diffuse scattering homometry, and it is shown that in the last case coherent diffraction can allow the diffraction diagrams to be differentiated. The study of the Rudin–Shapiro sequence, homometric to random sequences, allows one to manipulate independently two-point and four-point correlation functions, and to show their effect on the statistics of speckle patterns. This study provides evidence that long-range order in high-order correlation functions has a measurable effect on the speckle statistics.