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

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

2011-04-05

arxiv.org/abs/1104.0874v1

Physics

Condensed Matter

Materials Science

10 pages, 4 figures

Scientific paper

10.1103/PhysRevB.84.134105

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.

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