Identification of the kinematical forbidden reflections from precession electron diffraction
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Identification of the kinematical forbidden reflections from precession electron diffraction Jean-Paul Morniroli* and Gang Ji Laboratoire de Métallurgie Physique et Génie des Matériaux, UMR CNRS 8517, USTL & ENSCL, Cité Scientifique, 59655 Villeneuve d’Ascq, France *Corresponding author: Jean-Paul Morniroli Tel: 33 3 20 43 69 37 Fax: 33 3 20 43 40 40 E-mail: [email protected] ABSTRACT The visibility of the kinematical forbidden reflections due to glide planes, screw axes and Wyckoff positions is considered both on experimental and theoretical electron precession patterns as a function of the precession angle. The forbidden reflections due to glide planes and screw axes become very weak and disappear at large precession angle so that they can be distinguished from the allowed reflections and used to deduce the space groups. Contrarily, those due to Wyckoff positions remain visible and strong provided they are located on a major systematic row. This difference of behavior between the forbidden reflections is confirmed by observation of the corresponding dark-field LACBED patterns and is interpreted using the Ewald sphere and the Laue circles from the availability of double diffraction routes. This study also proves that dynamical interactions remain strong along the main systematic rows present on precession patterns. Keywords: Electron diffraction, Electron Precession, Crystallography INTRODUCTION The identification of the kinematical forbidden reflections due to glide planes and screw axes is very useful for the determination of the space group of a crystal. This identification is usually easy to carry out from x-ray and neutron diffraction patterns. These patterns exhibit a kinematical behavior so that the kinematical forbidden reflections present on them are actually invisible and can be surely identified. With electron diffraction, the interactions between the incident beam and the crystal produce strong diffracted beams which may intera ct dynamically with the transmitted beam and with the other diffracted beams to produce double diffraction. Thus, on a Zone-Axis Pattern (ZAP), many double diffraction routes are available and some of them may produce intensity at the locations of the kinematical forbidden reflections. As a result, these forbidden reflections become visible and cannot be distinguished from the allowed reflections. Several methods have been proposed to overcome this difficulty. The diffraction patterns can be observed on extremely thin crystal areas where a kinematical behavior prevails but this method suffers very strong limitations. Other possibilities involve the cancelation of the double diffraction routes to the forbidden reflections. On a ZAP, this situation is observed when the
zone axis is perpendicular to a glide plane. In this case, all the kinematical forbidden reflections due to the glide planes are located in the Zero-Order Laue Zone (ZOLZ) and they cannot appear by double diffraction. A typical periodicity difference is then observed between the allow
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