2011/04/05 by Christopher L. Farrow, Margaret Shaw, Hyunjeong Kim +3
Earth and Planetary Sciences · Engineering · Materials Science · Mathematics · Physics and Astronomy · #Algorithm #Bounded function #Combinatorics #Computer science #Geophysical Methods and Applications #High-pressure geophysics and materials #Interval (graph theory) #Mathematical analysis #Mathematics #Nonuniform sampling #Nyquist–Shannon sampling theorem #Sampling (signal processing) #Telecommunications #X-ray Diffraction in Crystallography #cond-mat.mtrl-sci #physics.data-an
paper · pdf · doi:10.1103/physrevb.84.134105
10 pages, 4 figures
arxiv created 2011/04/05 · openalex publication_date 2011/10/18 · arxiv updated 2015/03/18 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We have systematically studied the optimal real-space sampling of atomic pair distribution (PDF) data by comparing refinement results from oversampled and resampled data. Based on nickel and a complex perovskite system, we show that not only is the optimal sampling bounded by the Nyquist interval described by the Nyquist-Shannon (NS) sampling theorem as expected, but near this sampling interval, the data points in the PDF are minimally correlated, which results in more reliable uncertainty estimates in the modeling. Surprisingly, we find that PDF refinements quickly become unstable for data on coarser grids. Although the Nyquist-Shannon sampling theorem is well known, it has not been applied to PDF refinements, despite the growing popularity of the PDF method and its adoption in a growing number of communities. Here, we give explicit expressions for the application of NS sampling theorem to the PDF case, and establish through modeling that it is working in practice, which lays the groundwork for this to become more widely adopted. This has implications for the speed and complexity of possible refinements that can be carried out many times faster than currently with no loss of information, and it establishes a theoretically sound limit on the amount of information contained in the PDF that will prevent over-parametrization during modeling.