Indexation of diffraction patterns for overlapping crystals in
TEM
thin foils ‐ Application to orientation mappings
Authors: Valery Alexia , Lorut Frederic , Clément Laurent , Rauch Edgar 
Published: December 2016

The indexing of Precession Electron Diffraction (PED) patterns in TEMs for crystals orientation and phase determination as operated by the ACOM‐TEM technique [1] tends to become a standard procedure. However, analyzing transmitted signals requires to deal with significant effects related to the lamella thickness. Indexing limitations emerge as soon as grain size is smaller than the sample thickness. In contrast with TKD patterns [2], information in PED patterns comes from all of the overlapping grains crossed by the electron beam. Analyzing such a mixture of Bragg reflections prevents the safe recognition of the orientations and phases and leads to two specific outcomes. First, the grains appearing in the resulting maps are not necessarily located on a same exact layer of the sample thickness. Second, the probability of mis‐indexing is increased as reflections from every crystal may be taken for template matching. While it remains unclear which of the overlapping crystals is selected by template matching, it is necessary to understand if and in what means the Bragg spots number and related intensity of each crystal can differ from each other in the acquired patterns. In the present work, the influence of volume fraction and arrangement of grains with respect to the illumination direction are examined.

A sample composed of two overlaid copper plates was considered for the present purpose. ACOM‐TEM characterizations were realized on a planar section of the stacked plates for different lamella orientations: at zero tilt, zero tilt after a 180° flip of the grid in the sample holder, and a 15° tilt. Seven cross sections were then cut to determine the respective microstructures and thicknesses of the superimposed plates. Using TEM images of the cross views, the overall thickness of the stacked plates was found to evolve from 330 nm to 470 nm from one side to the other, with one plate being 1.4 to 2 times thicker than the other. The crystallographic orientations were determined using the NanoMEGAS ASTAR
TM
system implemented on a FEI Tecnai G2 F20 S‐Twin FEG (S)TEM operating at 200 keV. A precession angle of 0.5° was systematically applied to a quasi‐parallel probe of 4 nm at HMFW and 0.4 mrad semi‐angle of convergence. TEM lamellae were prepared using a FEI HELIOS FIB.

No significant differences are observed when the orientation maps related to the non‐tilted sample and its 180° flip are compared (Fig. 1c‐d). In other terms, the intensity distribution of Bragg reflections in diffraction patterns is not governed by the illumination direction. The comparison between the planar orientation maps and the cross cuts (Fig. 2) shows that the detected grains are mostly related to the thickest plate. At the light of this, it seems reasonable to expect the Bragg reflections related to the thickest plate to be the most intense and, consequently, the ones mainly detected in the acquired diffraction patterns. Nevertheless, a few grains related to the thinnest plate are indexed in the planar cuts. This means that the pattern selection is not solely sensitive to the volume fraction of the diffracting crystals. The last finding is confirmed with the sample tilted at 15°. With such tilt, the number of Bragg spots and their related intensities vary as different crystal planes are excited by the electron beam. It can be seen in Fig. 1b that some variations are detected in the grains orientation. The main conclusion of this study is that, although volume fraction of each plate is here the dominant factor that determines the template matching orientation selection, the correlation index appears to be also dependent on crystals orientation and potentially related dynamical effects. More details on the effects of volume fraction with respect to crystal favorable orientations will be discussed.