The Selection of Beams for Multi-Beam Dynamical Theory Calculations Used for Weak-Beam Dark Field Image Interpretation

Abstract

The use of computers as aid for TEM image interpretation has increased considerably during the recent years. In particular, the interpretation of weak-beam dark field (WBDF) equal thickness fringes for the determination of the habit of nanometer-size crystallites has been emphasized to be dependent on the concomitant ability of image intensity calculations using the many- beam dynamical theory (DT). On the other hand, some researchers have been using simple 2-beam kinemathical theory (KT) calculations for similar image interpretations. No attempt has been reported to quantify the necessity and the limitations of either approach. We are now reporting first results of comparative DT and KT calculations, emphasizing the definition of the number and selection criterion of the beams that should be included in DT calculations which are intended to be superior in accuracy to KT calculations.We modified a program developed by Yacamán, following the n-beam dynamical theory principles, to accept up to 100 beams at various selection criteria, and studied the influence of the number and selection criterion of the beams included in the calculation on the extinction distance and its dependence on the crystal thickness.