Abstract
The investigation of the static and dynamic structural properties of colloidal systems relies on techniques capable of atomic resolution in real space and femtosecond resolution in time. Recently, the cross-correlation function (CCF) analysis of both X-rays and electron diffraction patterns from dilute and dense aggregates has demonstrated the ability to retrieve information on the sample’s local order and symmetry. Open questions remain regarding the role of the beam coherence in the formation of the diffraction pattern and the properties of the CCF, especially in dense systems. Here, we simulate the diffraction patterns of dense two-dimensional monodisperse systems of different symmetries, varying the transverse coherence of the probing wave, and analyze their CCF. We study samples with different symmetries at different size scale, as for example, pentamers arranged into a four-fold lattice where each pentamer is surrounded by triangular lattices, both ordered and disordered. In such systems, different symmetry modulations are arising in the CCF at specific scattering vectors. We demonstrate that the amplitude of the CCF is a fingerprint of the degree of the ordering in the sample and that at partial transverse coherence, the CCF of a dense sample corresponds to that of an individual scattering object.
Highlights
Pattern with partially coherent X-ray radiation of 0.154 nm wavelength
We studied the diffraction patterns and their CCFs in dense samples under different coherence lengths of the probing wave
For dense samples we developed a particle-by-particle algorithm for the simulation of the diffraction patterns, which allows obtaining more accurate results than those obtained by conventional approach by convolution with the mutual coherence function
Summary
Pattern with partially coherent X-ray radiation of 0.154 nm wavelength. The diffraction pattern exhibited rings typical of a disordered system. It has been shown that the diffraction pattern of an individual particle can be extracted from the average over many diffraction patterns of a diluted ensemble of randomly oriented particles This method uses the assumption that the interference between the waves scattered from different particles is negligible. The effect of infinite and partial coherence on the XCCA and single particle retrieval methods for two-dimensional dilute samples have been studied by Kurta et al.. The effect of infinite and partial coherence on the XCCA and single particle retrieval methods for two-dimensional dilute samples have been studied by Kurta et al.3 They have shown that the diffraction pattern of a sample consisting of 121 randomly distributed and randomly rotated pentagons (300 nm in size) exhibits no distinct peaks but only rings when it is acquired at infinite coherence. We provide a detailed numerical study of the diffraction patterns and of the related CCFs for dense two-dimensional systems at different coherence of the probing wave, from infinite coherence to the coherence length comparable to the size of single particle
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