The role of the coherence in the cross-correlation analysis of diffraction patterns from two-dimensional dense mono-disperse systems

TL;DR

This paper investigates how beam coherence affects the cross-correlation analysis of diffraction patterns from dense 2D colloidal systems, revealing that partial coherence simplifies the CCF to resemble that of individual particles.

Contribution

It demonstrates through simulations that beam coherence significantly influences the CCF in dense systems and clarifies the role of coherence in interpreting local order and symmetry.

Findings

CFF amplitude indicates the degree of order in the sample.

Partial coherence causes the CCF to reflect individual scattering objects.

Symmetry modulations appear at specific scattering vectors.

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.