Abstract: In contrast to perfectly periodic crystals, materials with short-range order produce diffraction patterns that contain both Bragg reflections and diffuse scattering. To understand the influence of short-range order on material properties, current research focuses increasingly on the analysis of diffuse scattering. This article verifies the possibility to refine the short-range order parameters in submicrometre-sized crystals from diffuse scattering in single-crystal electron diffraction data. The approach was demonstrated on Li_1.2Ni_0.13Mn_0.54Co_0.13O₂, which is a state-of-the-art cathode material for lithium-ion batteries. The intensity distribution of the 1D diffuse scattering in the electron diffraction patterns of Li_1.2Ni_0.13Mn_0.54Co_0.13O₂depends on the number of stacking faults and twins in the crystal. A model of the disorder in Li_1.2Ni_0.13Mn_0.54Co_0.13O₂was developed and both the stacking fault probability and the percentage of the different twins in the crystal were refined using an evolutionary algorithm in<italic>DISCUS</italic>. The approach was applied on reciprocal space sections reconstructed from 3D electron diffraction data since they exhibit less dynamical effects compared with in-zone electron diffraction patterns. A good agreement was achieved between the calculated and the experimental intensity distribution of the diffuse scattering. The short-range order parameters in submicrometre-sized crystals can thus successfully be refined from the diffuse scattering in single-crystal electron diffraction data using an evolutionary algorithm in<italic>DISCUS</italic>.

Abstract: The increasing need for precise determination of the atomic arrangement of non-periodic structures in materials design and the control of nanostructures explains the growing interest in quantitative transmission electron microscopy. The aim is to extract precise and accurate numbers for unknown structure parameters including atomic positions, chemical concentrations and atomic numbers. For this purpose, statistical parameter estimation theory has been shown to provide reliable results. In this theory, observations are considered purely as data planes, from which structure parameters have to be determined using a parametric model describing the images. As such, the positions of atom columns can be measured with a precision of the order of a few picometres, even though the resolution of the electron microscope is still one or two orders of magnitude larger. Moreover, small differences in average atomic number, which cannot be distinguished visually, can be quantified using high-angle annular dark-field scanning transmission electron microscopy images. In addition, this theory allows one to measure compositional changes at interfaces, to count atoms with single-atom sensitivity, and to reconstruct atomic structures in three dimensions. This feature article brings the reader up to date, summarizing the underlying theory and highlighting some of the recent applications of quantitative model-based transmisson electron microscopy.