Precession electron diffraction 1: multislice simulation

Precession electron diffraction (PED) is a method that considerably reduces dynamical effects in electron diffraction data, potentially enabling more straightforward solution of structures using the transmission electron microscope. This study focuses upon the characterization of PED data in an effort to improve the understanding of how experimental parameters affect it in order to predict favorable conditions. A method for generating simulated PED data by the multislice method is presented and tested. Data simulated for a wide range of experimental parameters are analyzed and compared to experimental data for the (Ga,In)₂SnO₄ (GITO) and ZSM-5 zeolite (MFI) systems. Intensity deviations between normalized simulated and kinematical data sets, which are bipolar for dynamical diffraction data, become unipolar for PED data. Three-dimensional difference plots between PED and kinematical data sets show that PED data are most kinematical for small thicknesses, and as thickness increases deviations are minimized by increasing the precession cone semi-angle ϕ. Lorentz geometry and multibeam dynamical effects explain why the largest deviations cluster about the transmitted beam, and one-dimensional diffraction is pointed out as a strong mechanism for deviation along systematic rows. R factors for the experimental data sets are calculated, demonstrating that PED data are less sensitive to thickness variation. This error metric was also used to determine the experimental specimen thickness. R₁ (unrefined) was found to be about 12 and 15% for GITO and MFI, respectively.