Modelling dynamical 3D electron diffraction intensities

3D electron diffraction (3D ED) is a powerful technique for crystallographic characterisation of nanometre-sized crystals that are too small for X-ray diffraction. For accurate crystal structure refinement however it is important that the Bragg diffracted intensities are treated dynamically. Bloch wave simulations are often used in 3D ED, but can be computationally expensive for large unit cell crystals due to the large number of diffracted beams. Here we propose an alternative method, the ‘scattering cluster algorithm’ (SCA), that replaces the eigen-decomposition operation in Bloch waves with a simpler matrix multiplication. The underlying principle of SCA is that the intensity of a given Bragg reflection is largely determined by scattering from a cluster of neighbouring diffracted beams. However, the penalty for using matrix multiplication is that the sample must be divided into a series of thin slices and the diffracted beams calculated iteratively, similar to multislice. Therefore, SCA is more suitable for thin specimens. The accuracy and speed of SCA has been demonstrated on tri-isopropyl silane (TIPS) pentacene and rubrene, two exemplar organic materials with large unit cells. The strong interaction of high energy electrons with a crystal results in both dynamical elastic diffraction as well as inelastic scattering, particularly phonon and plasmon excitation, which have relatively large cross-sections. For accurate crystal structure refinement it is therefore important to uncover the role of inelastic scattering on the Bragg beam intensities. Here a combined Bloch wave-Monte Carlo method is used to simulate phonon and plasmon scattering in crystals. The simulated thermal and plasmon diffuse scattering are consistent with experiment. Furthermore, the simulations also confirm the empirical observation of larger Bragg beam intensities relative to the unscattered beam with increasing energy loss in the low loss regime. It is proposed that the random azimuthal scattering angle during inelastic events gives rise to a precession-type effect, where part of the unscattered beam intensity is transferred to the inner Bragg reflections. The precession effect can be quite large (e.g. 25% change in relative intensities) and could therefore be an important artefact in 3D electron crystallography.