Electron diffraction and lattice image simulations with the inclusion of HOLZ reflections

Abstract

The formulae that can be used to calculate wave functions for transmission high-energy electron diffraction including reflections from higher-order Laue zones (HOLZs) are summarized by using the Bloch wave formulation and the multislice formulation for the dynamical electron diffraction theory, respectively. In the multislice formulation, three different algorithms of calculating phase grating functions, fraction projection algorithm (FPA), section projection algorithm (SPA) and conditional projection algorithm (CPA) are examined. Electron diffraction patterns and lattice images for the YBa 2Cu 3O 7 crystals are simulated and compared with Bloch wave calculations. In summary, the FPA calculations do not include HOLZ reflections; the SPA and CPA give much stronger HOLZ reflection intensities than the Bloch wave algorithm. Experimental diffraction patterns support the Bloch wave results. However, there is no detectable difference found in the simulated lattice images by using the above-mentioned computing schemes, which suggests that the HOLZ reflections only play a minor role in forming lattice images.