On the estimation of average crystallite size of zeolites from the Scherrer equation: A critical evaluation of its application to zeolites with one-dimensional pore systems

This article presents an overview of the application of the Scherrer equation and Williamson–Hall analysis for the approximation of crystallite sizes of zeolites. Special emphasis is placed on the proper selection of hkl reflections for estimating a particular dimension of a specimen with anisotropic crystals. Crystal sizes of zeolites with one-dimensional pores (such as ZSM-12, ZSM-48, ferrierite, or Theta-1) are especially prone to misreporting or error from a direct application of the Scherrer equation. We have collected synchrotron powder diffraction data on a group of MTT-type zeolites of varying morphologies. For typical values of strain we have determined for these zeolites, we find that large crystal lengths can be underestimated by orders of magnitude when the effects of stress are not (or cannot be) included in the analysis.