Understanding the limits of pair-distribution functions for nanoscale correlation function measurement

We explore the ability of the pair-distribution function (pdf) to accurately measure medium-range correlation lengths in nanoscale crystalline materials. Through simple computer simulations of disordered fcc metals, we find that the presence of quadratic displacement fields is sufficient to mask topological order (mro) at the medium-range (1-3 nm). This reconciles previous measurements and modeling on amorphous silicon-which showed that paracrystalline structures give pair correlation functions which are almost indistinguishable from random networks-with the wide use of pdfs to measure correlation lengths in nanoscale crystalline materials. Through simple analytical considerations, we identify conditions when the pdf method can be trusted for mro measurements in nanocrystalline materials. We show that while the reliability of the technique is dependent on the nature of materials studied, in general the technique fails for sufficiently small grain size in compact materials. When the pdf method does not work, we have previously shown that fluctuation microscopy is a powerful tool to give information on mro.