This article investigates how accurately lattice parameters, i.e., the lengths and angles defining the shape of the crystal's unit cell, can be determined using three-dimensional electron diffraction (3D ED) data collected in a transmission electron microscope. We show that the main obstacle to achieving high accuracy is the presence of optical distortions in the microscope, which can significantly deform the diffraction patterns. These distortions include well-known types such as barrel-pincushion, spiral, and elliptical, as well as a newly identified "parabolic" distortion. Parabolic distortion, in particular, can cause shifts and splitting of diffraction spots in precession electron diffraction experiments, complicating the analysis.
The work shows that all distortions except the elliptical type can be determined and corrected from a single 3D ED dataset. However, elliptical distortion parameters are strongly correlated with the lattice parameters, making them difficult to separate without additional information. The additional information can be the crystal's symmetry (the Laue class) or a combination of data from multiple crystals. By refining the distortion parameters alongside the lattice parameters, 3D ED data can yield lattice parameter ratios with an accuracy of about 0.1% and unit cell angles accurate to better than 0.03 degrees, a major improvement over the previous standards. The improved precision allows for more reliable identification and characterization of crystalline materials and linking of the crystallographic parameters with material properties.
The work was conceived and executed entirely by the researchers from FzU.
