Estimating crystallite size in polydispersed samples using EXAFS

It has long been understood that EXAFS is sensitive to crystallite size, since the average coordination number for a given scattering path is suppressed by a factor that depends upon the distance between the absorbing and scattering atoms. Careful analyses by other researchers have demonstrated the feasibility of determining crystallite size and even morphology in this way, but have in general been limited to well-characterized monodispersed samples. Here, we compare various techniques for estimating mean particle size in a polydispersed sample, using both EXAFS and conventional techniques. It is found that for polydispersed samples with an unknown size distribution, an analysis utilizing a simple spherical model performs nearly as well as more sophisticated models using realistic morphologies. Using simulations as well as experimental data, we demonstrate that EXAFS selects a "mean" size considerably smaller than that found by Scherrer analysis of XRD data; the two in combination can thus be used to give a crude estimate of polydispersion even in samples in which the form of the size distribution is unknown. Finally, we show that the sensitivity of EXAFS to the smallest crystallites present in the sample make it a useful adjunct to TEM in some cases.