High-angle scattering of fast electrons from crystals containing heavy elements: Simulation and experiment

The paper reports on quantitative comparisons of experimental and simulated image intensities in high-angle annular dark-field imaging in scanning transmission electron microscopy of a ${\text{PbWO}}_4$ single crystal. The experimental image intensities are normalized to the incident beam. Provided that the effects of spatial incoherence and multiple thermal diffuse scattering events are taken into account in the simulations, excellent agreement within about 5% is achieved between theory and experiments. The comparisons depend critically on accurate knowledge of the Debye-Waller factors, which were determined by x-ray single-crystal structure refinement, and of the experimental thickness values. The Debye-Waller factors are different for different atomic columns, causing column intensities to not be a simple function of their atomic number. Channeling effects associated with the oxygen columns contribute to intensity variations between the Pb and W columns. The results show that even for single crystals, image simulations are required to correctly interpret the contrast.