# The interpretation of broad diffuse maxima using superspace crystallography

## TL;DR

This paper introduces a novel superspace-based method to interpret diffuse maxima in single crystal diffuse scattering, enabling flexible modeling of diffuse features while respecting superspace symmetry.

## Contribution

It presents a disordered superspace approach that generates diffuse maxima with arbitrary width and position, extending traditional correlation-based interpretations.

## Key findings

- Diffuse maxima can be modeled at any position and width.
- Superspace symmetry rules are satisfied by the diffuse maxima.
- The method is demonstrated on a 2D binary disordered system.

## Abstract

Single crystal diffuse scattering is generally interpreted using correlation parameters that describe probabilities for certain configurations on a local scale. In this paper we present a novel interpretation of diffuse maxima using a disordered superspace approach. In (D+d)-dimensional superspace two modulation functions are disordered along the superspace axis $\vec{a}_{s,i}$ for i = 1,..,D, while the periodicity along the internal dimensions is maintained. This simple approach allows the generation of diffuse maxima of any width at any position in reciprocal space. The extinction rules that are introduced by superspace symmetry are also fulfilled by the diffuse maxima from structures generated using the disordered superspace approach. In this manuscript we demonstrate the disordered superspace approach using a simple a simple two-dimensional binary disordered system. The extension of the approach to (3+D)-dimensional superspace is trivial. The treatment of displacement and magnetic disorder in a similar approach is straight forward.