Metrics of graininess: robust quantification of grain count from the non-uniformity of scattering rings

Abstract

The diffraction rings that arise in X-ray scattering experiments frequently exhibit non-uniformity or `spottiness' as a result of the finite number of grains within the probed volume. This article explores a variety of ways to assess this graininess and shows that scaling relationships can be used to quantitatively relate ring non-uniformity to the number of grains within the scattering volume. The applicability of the method is demonstrated for grain counts from 10 to 107, enabling measurement of the crystalline fraction or of the average grain size from 6 nm to 120 µm. This method enables quantification of grain size even in cases where the intrinsic peak width is much smaller than the instrumental broadening. The method is validated with experimental measurements on a variety of systems.