Examination of a Polycrystalline Thin-Film Model to Explore the Relation between Probe Size and Structural Correlation Length in Fluctuation Electron Microscopy

We examine simulated electron microdiffraction patterns from models of thin polycrystalline silicon. The models are made by a Voronoi tessellation of random points in a box. The Voronoi domains are randomly selected to contain either a randomly-oriented cubic crystalline grain or a region of continuous random network material. The microdiffraction simulations from coherent probes of different widths are computed at the ideal kinematical limit, ignoring inelastic and multiple scattering. By examining the normalized intensity variance that is obtained in fluctuation electron microscopy experiments, we confirm that intensity fluctuations increase monotonically with the percentage of crystalline grains in the material. However, anomalously high variance is observed for models that have 100% crystalline grains with no imperfections. We confirm that the reduced normalized variance, V(k, R) 1, that is associated with four-body correlations at scattering vector k, varies inversely with specimen thickness. Further, for probe sizes R larger than the mean grain size, we confirm that the reduced normalized variance obeys the predicted form given by Gibson et al. [Ultramicroscopy, 83, 169-178 (2000)] for the kinematical coherent scattering limit.