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

R P Kurta,I A Vartanyants,M Altarelli

doi:10.1155/2013/959835

Abstract

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.

Highlights

Correlation methods are widely used in the physics of disordered materials such as amorphous and glassy systems [1, 2]
In this paper we summarize recent theoretical developments related to the Fourier analysis of the cross-correlation functions
We 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 X-ray cross-correlation analysis (XCCA)

Summary

Introduction

Correlation methods are widely used in the physics of disordered materials such as amorphous and glassy systems [1, 2]. XCCA is performed for each diffraction pattern in a sequence, and angular cross-correlation functions (CCFs) are averaged over the whole data set In this way structural information about an individual particle in the system can be obtained. The three-point CCF for a single realization of a system is defined at three resolution rings q1, q2, and q3 as [7] (see Figure 3(d)), In practical applications one would need to consider CCFs ⟨C(q1, q2, Δ)⟩M and ⟨C(q1, q2, q3, Δ 1, Δ 2)⟩M averaged over a sufficiently large number M of diffraction patterns [6],. {qC2qn,11Δ,,qn22),}qm3 }maanrde the Fourier components {C(q1, q2, q3, Δ 1, Δ 2)}m, respectively, defined for the mth realization of the system (see (3a) and (3b))

Scattering from a Disordered System of Identical Particles

Results and Discussion

Conclusions