A single slice approach for simulating two-beam electron diffraction of nanocrystals

A simple computational method that can be used to simulate TEM image contrast of an electron beam diffracted by a crystal under two-beam dynamical scattering conditions is presented. The approach based on slicing the shape factor is valid for a general crystal morphology, with and without crystalline defects, avoids the column approximation, and provides the complex exit wave at the focal and the image planes also under weak-beam conditions. The approach is particularly efficient for large crystals and the 3D model required for the calculations can be measured experimentally using electron tomography. The method is applied to show that the shape of a diffracted spot can be affected by shifts, broadening and secondary maxima of appreciable intensity, even for a perfect crystal. The methodology is extended for the case of electron precession diffraction, and to show how can be used to improve nanometrology from diffraction patterns. The method is used also to perform simulations of simple models of crystalline defects. The accuracy of the method is demonstrated through examples of experimental and simulated dark-field images of MgO and ZrO₂ nanocrystals and thin layers of CeO₂.