Strategies and Considerations for Least-Squares Analysis of Total Scattering Data

Abstract

The process of least-squares analysis has been applied for decades in the field of crystallography. Here, we discuss the application of this process to total scattering data, primarily in the combination of least-squares Rietveld refinements and fitting of the atomic pair distribution function (PDF). While these two approaches use the same framework, the interpretation of results from least-squares fitting of PDF data should be done with caution through carefully constructed analysis approaches. We provide strategies and considerations for applying least-squares analysis to total scattering data, combining both crystallographic Rietveld and fitting of PDF data, given in context with recent examples from the literature. This perspective is aimed to be an accessible document for those new to the total scattering approach, as well as a reflective framework for the total scattering expert.

Molecular Structure, Dynamics, and Vibrational Spectroscopy of the Acetylene:Ammonia (1:1) Plastic Co-Crystal at Titan Conditions

“…Ammonia molecules within the co-crystal are orientationally disordered and undergo rotational motion on a picosecond time scale. The rotational correlation functions C 1 ( t ) and C 2 ( t ) should be accessible experimentally through IR and Raman spectroscopies, respectively, and τ 2 through NMR spectroscopy. ,, Radial distribution functions, g ( r ), can also provide some insight into the orientational disorder and can be obtained through scattering experiments. , At 30 K, the acetylene:ammonia (1:1) co-crystal is in a crystalline phase (translationally and orientationally ordered), such that a co-crystal–to–plastic co-crystal phase transition occurs between 30 and 90 K. These conclusions agree well with the early experimental hints at the orientational disorder of ammonia molecules within the co-crystalline phase . The rotational dynamics of the ammonia molecules are dictated by the breakage and reformation of N–H···π hydrogen bonds within the co-crystal, which we predict to have a lifetime on the order of a picosecond.…”

Polar Metals Taxonomy for Materials Classification and Discovery

“…Nonetheless, for sufficient carrier densities local polar displacements can persist. Therefore, beyond how one simulates dop- ing in these materials, as discussed in Appendix A, it is also imperative to recognize that how we understand the manner in which the atomic structure responds to doping relies intimately on whether the experimental probe interrogates local or average structure [58,59]. In any case, changes in the Fermi level of doped proper FEs will almost always eventually affect the ground state crystallocal and average -structure whereas similar changes in the Fermi level of polar metals are more likely to leave the crystal structure unaltered independent of the experimental probe volume.…”

POMFinder: identifying polyoxometallate cluster structures from pair distribution function data using explainable machine learning

“…For many X-ray-and neutron-based scattering techniques such as small-angle scattering, powder diffraction and total scattering with pair distribution function (PDF) analysis, data analysis is often done through least-squares optimization (Pedersen, 1997;Rietveld, 1969;Chepkemboi et al, 2022). Here, structure models found in e.g.…”