Can Kinematic Diffraction Distinguish Order from Disorder?

TL;DR

This paper investigates whether diffraction patterns can reliably distinguish ordered from disordered structures, revealing that different systems can produce identical diffraction spectra despite varying degrees of order.

Contribution

It demonstrates through model systems that diffraction patterns alone may be insufficient to determine the degree of order or disorder in a material.

Findings

Different systems with varying entropy can have identical diffraction spectra.

Purely diffuse diffraction does not necessarily indicate disorder.

Some ordered and disordered systems are indistinguishable by diffraction.

Abstract

Diffraction methods are at the heart of structure determination of solids. While Bragg-like scattering (pure point diffraction) is a characteristic feature of crystals and quasicrystals, it is not straightforward to interpret continuous diffraction intensities, which are generally linked to the presence of disorder. However, based on simple model systems, we demonstrate that it may be impossible to draw conclusions on the degree of order in the system from its diffraction image. In particular, we construct a family of one-dimensional binary systems which cover the entire entropy range but still share the same purely diffuse diffraction spectrum.