The Nyquist-Shannon sampling theorem and the atomic pair distribution function

Abstract

We have systematically studied the optimal real-space sampling of atomic pair distribution data by comparing refinement results from oversampled and resampled data. Based on nickel and a complex perovskite system, we demonstrate that the optimal sampling is bounded by the Nyquist interval described by the Nyquist-Shannon sampling theorem. Near this sampling interval, the data points in the PDF are minimally correlated, which results in more reliable uncertainty prediction. Furthermore, refinements using sparsely sampled data may run many times faster than using oversampled data. This investigation establishes a theoretically sound limit on the amount of information contained in the PDF, which has ramifications towards how PDF data are modeled.

10 pages, 4 figures

References in corpus (5)

• Direct observation of the formation of polar nanoregions in Pb(Mg${}_{1/3}$Nb${}_{2/3}$)O${}_3$ using neutron pair distribution function analysis
• Quantitative size-dependent structure and strain determination of CdSe nanoparticles using atomic pair distribution function analysis
• Relationship between the atomic pair distribution function and small angle scattering: implications for modeling of nanoparticles
• Orbital correlations in the pseudo-cubic \emph{O} and rhombohedral $R$-phases of LaMnO${}_3$
• Topological Defects Coupling Smectic Modulations to Intra-unit-cell Nematicity in Cuprate

Cited by in corpus (8)

• Verification of Anderson superexchange in MnO via magnetic pair distribution function analysis and \textit{ab initio} theory
• Structure-mining: screening structure models by automated fitting to the atomic pair distribution function over large numbers of models
• Mapping Structural Heterogeneity at the Nanoscale with Scanning Nano-structure Electron Microscopy (SNEM)
• Influence of interstitial Mn on local structure and magnetism in Mn${}_{1+\delta }$Sb
• Interpretable Multimodal Machine Learning Analysis of X-ray Absorption Near-Edge Spectra and Pair Distribution Functions
• Algorithm for distance list extraction from pair distribution functions
• Cross-Tokamak Deployment Study of Plasma Disruption Predictors Based on Convolutional Autoencoder
• Deep insights into the local structure of amorphous Ta2O5 thin films by X-ray pair distribution function analysis