X-Ray Cross-Correlation Analysis of Disordered Ensembles of Particles: Potentials and Limitations

Angular X-ray cross-correlation analysis (XCCA) is an approach to study the structure of disordered systems using the results of X-ray scattering experiments. In this paper we summarize recent theoretical developments related to the Fourier analysis of the cross-correlation functions. Results of our simulations demonstrate the application of XCCA to two- and three-dimensional (2D and 3D) disordered ensembles of particles. We show that the structure of a single particle can be recovered using X-ray data collected from a 2D disordered system of identical particles. We also demonstrate that valuable structural information about the local structure of 3D systems, inaccessible from a standard small-angle X-ray scattering experiment, can be resolved using XCCA.