Reflection profile and angular resolution with Precession Electron Diffraction

Abstract

Template matching has proved to be an efficient numerical approach to identify orientation and/or phase signatures in electron diffraction patterns [1]. With this technic, all patterns for all orientations and all phases considered are pre-calculated and compared to the experimental data by cross-correlation. The capacity of the approach to recognize the diffracting signal is substantially improved with precession electron diffraction (PED). This is because dynamic effects are partly swept out of the experimental signal. Of interest is the fact that, up to now, templates were always computed without including precession. In particular the specific reflection profile resulting from the beam rotation was never considered properly. The present work is an attempt to enhance the degree of matching by adapting the templates to precession in particular for large precession angles. First, the Bragg spot profile is determined for Si single crystal by tilting progressively the sample. The pattern collection procedure is similar to the fast diffraction tomography setup of Gemmi et al [2]. The precession angle was monitored with the Nanomegas Digistar P1000 attachment to a JEOL 2100F TEM and set up to 0.3, 0.6 and 1.2°. The crystal orientation evolution is followed with the ASTAR system through template matching and compared to the quasi linear trend expected from the constant angular speed of 1°/min imposed by the TEM goniometer. The change in reflection profile with increasing precession angle is illustrated in figure 1. The profile exhibits two maximums separated by twice the precession angle. This shape, systematically recorded, is modeled and introduced in the template generation routine. The improvement in angular resolution is characterized by comparing the misorientation measurements with respect to the expected linear trend (Fig 2). The templates computed with the recorded PED profile, differ significantly from the standard ones (Fig 3). The resulting set of templates being closer to the diffraction patterns acquired with precession, the crystal orientation is determined with an increased accuracy (Fig. 2.b), at least at large precession angles. The standard deviation obtained without and with precession adaptation is nearly identical and equal to 0.17° for precession angles lower or equal to 0.6°. By contrast, this value degrades down to 0.5° at the largest precession angle if no precession correction are included (Fig. 2) but remains equal to 0.17° with adapted templates. Besides, the orientation resolution may be further refined by using the interpolating algorithm presented elsewhere [3]. With adapted templates and interpolation the standard deviation decreases down to 0.13°, for the largest precession angle. A non-intuitive conclusion of the present work is that the angular resolution of the orientation determination is not bounded by the precession angle.