Structure Determination Feasibility of Three-Dimensional Electron Diffraction in Case of Limited Data

Abstract

During the last two decades, three-dimensional electron diffraction (3D ED) has undergone a renaissance, starting with the introduction of precession (Precession Electron Diffraction Tomography, PEDT) that led to variations on the idea of collecting as much of the diffraction space as possible in order to solve crystal structures from sub-micron sized crystals. The most popular of these acquisition methods is based on the continuous tilting/rotation of the crystal (so-called Microcrystal Electron Diffraction, MicroED) akin to the oscillating crystal method in X-ray crystallography, which was enabled by the increase of sensitivity and acquisition speed in electron detectors. While 3D ED data is more complex than the equivalent X-ray data due to the higher proportion of dynamical scattering, the same basic principles of what is required in terms of data quality and quantity in order to solve a crystal structure apply; high completeness, high data resolution and good signal-to-noise statistics on measured reflection intensities. However, it may not always be possible to collect data in these optimum conditions, the most common limitations being the tilt range of the goniometer stage, often due to a small pole piece gap or the use of a non-tomography holder, or the position of the sample on the TEM grid, which may be too close to a grid bar and then the specimen of interest becomes occluded during tilting. Other factors that can limit the quality of the acquired data include the limited dynamic range of the detector, which can result on truncated intensities, or the sensitivity of the crystal to the electron beam, whereby the crystallinity of the particle is changing under the illumination of the beam. This limits the quality and quantity of the measured intensities and makes structure analysis of such data challenging. Under these circumstances, traditional approaches may fail to elucidate crystal structures, and global optimization methods may be used here as an alternative powerful tool. In this context, this work presents a systematic study on the application of a global optimization method to crystal structure determination from 3D ED data. The results are compared with known structure models and crystal phases obtained from traditional ab initio structure solution methods demonstrating how this strategy can be reliably applied to the analysis of partially complete 3D ED data.