Efficient fitting of single-crystal diffuse scattering in interaction space: a mean-field approach

Abstract

The diffraction patterns of crystalline materials with strongly-correlated disorder are characterised by the presence of structured diffuse scattering. Conventional analysis approaches generally seek to interpret this scattering either atomistically or in terms of pairwise (Warren-Cowley) correlation parameters. Here we demonstrate how a mean-field methodology allows efficient fitting of diffuse scattering directly in terms of a microscopic interaction model. In this way the approach gives as its output the underlying physics responsible for correlated disorder. Moreover, the use of a very small number of parameters during fitting renders the approach surprisingly robust to data incompleteness, a particular advantage when seeking to interpret single-crystal diffuse scattering measured in complex sample environments. We use as the basis of our proof-of-concept study a toy model based on strongly-correlated disorder in diammine mercury(II) halides.

Crystal structures

“…Several global optimization algorithms, such as differential evolution, genetic algorithms or particle swarm optimization, have been compared (Michels-Clark et al, 2013, 2016. In the presence of highly structured diffuse scattering, direct optimization of the interaction parameters in a mean-field type of approach is a possible alternative (Schmidt et al, 2021). Whatever method is used, the required computational resources are still orders of magnitude larger than those for even the most detailed analysis of Bragg diffraction.…”