Inversion of dynamical scattering from large‐angle rocking‐beam electron diffraction patterns

Abstract

A method for ab‐initio structure factor retrieval from large‐angle rocking‐beam electron diffraction (LARBED)[1] data of thin crystals is described and tested. This method determines crystal structure factors and specimen thickness from the intensities of the diffraction spots alone, solving a nonlinear least‐squares problem. No additional information, such as atomicity or information about chemical composition, have been made use of. In addition to a demonstration of the method on 120 keV experimental data of SrTiO 3 , where 456 structure factors have been retrieved, we analyze the dependence of the success of the reconstruction on specimen thickness and tilt range by applying this algorithm to simulated data. Our numerical experiments show that the dynamical inversion by gradient optimization works best if the beam tilt range is large and the specimen not too thick. At specimen thicknesses which allow for moderate multiple scattering, the large tilt amplitude effectively removes local minima in this global optimization problem, making ab‐initio structure factor retrieval possible. In addition, a dynamic parallelism framework based on the Compute Unified Device Architecture (CUDA) is introduced, reducing the runtime of the optimization routine by two orders of magnitude when compared to running on a CPU. The authors acknowledge funding by the Carl Zeiss Foundation as well as the German Research Foundation (Grant no. KO 2911/7‐1 and SFB 951).