Determining Projections of Grain Boundaries from Diffraction Data in Transmission Electron Microscope

Abstract Grain boundaries (GB) are characterized by disorientation of the neighboring grains and the direction of the boundary plane between them. A new approach presented here determines the projection of GB that can be used to determine the latter one. The novelty is that an additional parameter of GB is quantified in addition to the ones provided by the orientation maps, namely the width of the projection of the GB is measured from the same set of diffraction patterns that were recorded for the orientation map, without the need to take any additional images. The diffraction patterns are collected in nanobeam diffraction mode in a transmission electron microscope, pixel-by-pixel, from an area containing two neighboring grains and the boundary between them. In our case, the diffraction patterns were recorded using the beam scanning function of a commercially available system (ASTAR). Our method is based on non-negative matrix factorization applied to the mentioned set of diffraction patterns. The method is encoded in a MATLAB environment, making the results easy to interpret and visualize. The measured GB-projection width is used to determine the orientation of the GB-plane, as given in the study by Kiss et al.