Sampling statistics of diffraction from nanoparticle powder aggregates

In 1948, Alexander, Klug and Kummer published a formalism which, for polycrystalline powder specimens, could be used to compute the number of irradiated grains required to obtain diffraction peak intensities within a specified uncertainty range. The current study shows that part of this analysis is not applicable for all particle sizes and could yield erroneous results for grains with diameters below 10 nm.