X-ray cross-correlation analysis and local symmetries of disordered systems. I. General theory

TL;DR

This paper develops a general theoretical framework for analyzing x-ray scattering intensity correlations in disordered systems, revealing how angular correlations encode local bond orientations and structural properties.

Contribution

It provides a comprehensive analytical derivation linking x-ray intensity correlations to local symmetries and bond arrangements in disordered materials.

Findings

Angular intensity correlations follow cos(n φ) dependence revealing local symmetries.

The theory clarifies the relationship between intensity correlations and bond-orientation order.

The approach applies to a wide range of structural properties in disordered systems.

Abstract

In a recent article (P.Wochner et al., PNAS (2009)) x-ray scattering intensity correlations around a ring, in the speckle diffraction pattern of a colloidal glass, were shown to display a remarkable ~ cos(n $\phi$) dependence on the angular coordinate $\phi$ around the ring, with integer index n depending on the magnitude of the scattering wavevector. With an analytical derivation that preserves full generality in the Fraunhofer diffraction limit, we clarify the relationship of this result to previous x-ray studies of bond-orientation order, and provide a sound basis to the statement that the angular intensity correlations deliver information on local bond arrangements in a disordered (or partially ordered) system. We present a detailed analysis of the angular cross-correlation function and show its applicability for studies of wide range of structural properties of disordered systems, from local structure to spatial correlations between distant structural elements.