X-ray cross-correlation analysis applied to disordered two-dimensional systems

Angular x-ray cross-correlation analysis (XCCA) is an approach to study the structure of disordered systems using the results of coherent x-ray scattering experiments. Here, we present the results of simulations that validate our theoretical findings for XCCA obtained in a previous paper [Altarelli et al., Phys. Rev. B 82, 104207 (2010)]. We consider as a model two-dimensional (2D) disordered systems composed of noninteracting colloidal clusters with fivefold symmetry and with orientational and positional disorder. We simulate a coherent x-ray scattering in the far field from such disordered systems and perform the angular cross-correlation analysis of calculated diffraction data. The results of our simulations show the relation between the Fourier series representation of the cross-correlation functions (CCFs) and different types of correlations in disordered systems. The dependence of structural information extracted by XCCA on the density of disordered systems and the degree of orientational disorder of clusters is investigated. The statistical nature of the fluctuations of the CCFs in the model single-shot experiments is demonstrated and the potential of extracting structural information from the analysis of CCFs averaged over a large number of diffraction patterns is discussed. We also demonstrate the effect of partial coherence of the incident x-ray beams on the results of XCCA.