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

TL;DR

This paper explores the optimal real-space sampling of atomic pair distribution data, demonstrating that the Nyquist-Shannon theorem bounds sampling efficiency and impacts data reliability and computational speed.

Contribution

It establishes the Nyquist-Shannon sampling theorem as a fundamental limit for atomic pair distribution function data analysis, guiding optimal sampling and modeling.

Findings

Optimal sampling is bounded by the Nyquist interval.

Near this interval, data points are minimally correlated.

Sparse sampling can significantly increase refinement speed.

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.