Diffraction from inhomogeneous material systems

TL;DR

This paper derives a comprehensive expression for diffraction intensity in inhomogeneous materials, accounting for structural disturbances and interactions, with implications for analyzing small angle scattering in complex systems.

Contribution

It introduces a detailed theoretical framework for diffraction from inhomogeneous systems, including effects of inhomogeneity coupling and interactions, extending previous models.

Findings

Diffraction intensity can be expressed as a modification of the homogeneous system.

Inhomogeneity effects include coupling with the system and self-coupling among inhomogeneities.

Small angle scattering may deviate from Guinier law in certain inhomogeneous cases.

Abstract

The static diffraction intensity distribution from large material system conceived as perfectly homogeneous system made inhomogeneous, though substitution of groups of atoms, small particles, by other groups of atoms, is explicitly expressed in terms of all possible partial contributions subsequent to the particle exchange operation. This gives the diffracted intensity as that from the homogeneous system modified by additional part and, thus, yields result that may prove to be quite useful in comparative studies of materials with the same sort of atomic network. The additional part embodies the effects of the presence of the structural disturbances and consists in two main components. One of these represents the inhomogeneity coupling with the system in its homogeneous state and, the other, represents the inhomogeneity self-coupling, the coupling of the inhomogeneities with one another. Two particular cases of deviation from homogeneity are considered in more details: the case of non-interacting inhomogeneities and that of interacting inhomogeneities. The effects on the small angle scattering (SAS) due to possible structural differences (chemical nature, atomic distribution and dimensions) between the deficient and substitute particles are given. The SAS distribution does not obey the very attractive Guinier law in some cases of non-interacting inhomogeneities.