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

摘要

We have systematically studied the optimal real-space sampling of atomic pairdistribution data by comparing refinement results from oversampled andresampled data. Based on nickel and a complex perovskite system, we demonstratethat the optimal sampling is bounded by the Nyquist interval described by theNyquist-Shannon sampling theorem. Near this sampling interval, the data pointsin the PDF are minimally correlated, which results in more reliable uncertaintyprediction. Furthermore, refinements using sparsely sampled data may run manytimes faster than using oversampled data. This investigation establishes atheoretically sound limit on the amount of information contained in the PDF,which has ramifications towards how PDF data are modeled.