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

Abstract

Keywords: grain boundary plane, non-negative matrix factorization, electron diffraction, computer program, polycrystalline thin films Microscopy and Microanalysis, a Cambridge University Press journal AbstractGrain 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 grain boundaries that can be used to determine the latter one. The novelty is that an additional parameter of GB-s 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 (NBD) mode in a transmission electron microscope (TEM) 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 the a commercially available ASTAR system (ASTAR). Our method is based on non-negative matrix factorization (NMF) 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 grain boundary plane, as given in Microsc. Microanal. 21, 422-435Kiss et al., 2015.

Grain Boundary Specific Segregation in Nanocrystalline Fe(Cr)

“…The inclination angle was determined by either measuring the PED projected boundary by the method in ref. 25 and/or assuming that the boundary itself was perpendicular to the plane normal when the PED scan was inconclusive. This latter assumption was confirmed by the TEM cross sectional view, Fig.…”

“…The estimated inclination angle of the grain boundary using the PED was done following the procedure by Kiss et al . 25 with details specific to this work given in the supplementary material section. For these experiments, the beam was precessed at 0.1° at a scanning step size of 2 nm.…”

“…The inclination angle “REF” refers to reference inclination angle as described in the supplementary section and the inclination angle “PED” refers to measured values from the method found in the paper of Kiss et al . 25 also detailed in the supplementary section . Finally the interfacial excess, IE, for each to the measured special character boundaries is given.…”

“…Though similar restrictions can also exist in PED scans, recent work by Kiss et al . 25 26 27 has shown how the inclination angle can be estimated by a weight average from the overlapping transmission diffraction patterns across the boundary. Moreover, one could also conceive using the APT data set volume itself to reveal the grain boundary topology 13 .…”

Linking Experimental Solute Segregation Specificity in Nanocrystalline Alloys to Computational Predictions

“…Three parameters can be obtained by the boundary misorientation whereas the other two are determined by the grain boundary inclination [5]. Using a recent technique reported by Kiss and Lábár [6], the inclination angle of the boundaries was quantified by PED of an atom probe tip prior to its field evaporation, Fig. 1(a)-(b).…”