Microsc. Microanal. Microstruct. 7, 27-47 (1996)
DOI: 10.1051/mmm:1996105

Can the Multislice Method Be Used To Calculate HOLZ Reflections in High-Energy Electron Diffraction and Imaging?

Jiang Hua Chen, Marc Op de Beeck et Dirk Van Dyck

EMAT, University of Antwerp (RUCA), Groenenborgerlaan 171, 2020 Antwerpen, Belgium

Abstract
The validity of the use of the conventional multislice (MS) method for the calculation of higher-order Laue zone (HOLZ) reflections is tested by detailed calculations as well as a theoretical analysis. It is shown that if sufficiently thin slices are employed and the Debye-Waller (DW) factors for atoms are included the MS method can calculate HOLZ effects correctly up to the exact solution of the modified Schrödinger equation for high-energy electron diffraction. It is pointed out that the MS method is accurate up to second order in the slice thickness for zero-order Laue zone (ZOLZ) reflections but only up to first order for HOLZ reflections. As a consequence, the accurate calculation of HOLZ reflections requires a much smaller slice thickness. Using MS procedures in the standard way can then lead to accurate ZOLZ intensities but inaccurate HOLZ intensities. Without the introduction of DW factors for atoms, the atomic cores act as points of singularity for the MS formula and may cause severe errors for both the calculated HOLZ and ZOLZ reflections. It is also pointed out that if no so-called lower order HOLZ reflections are involved, one can simply use the projection approximation in HRTEM image simulations.

PACS
6114D - Theories of electron diffraction and scattering.
6116D - Electron microscopy determinations of structures.
6370 - Statistical mechanics of lattice vibrations.

Key words
Debye Waller factors -- electron diffraction -- Schrodinger equation -- transmission electron microscopy -- higher order Laue zone reflections -- Debye Waller factors -- zero order Laue zone -- multislice method -- Schrodinger equation -- high energy electron diffraction -- slice thickness -- ZOLZ intensities -- projection approximation -- HRTEM image simulations


© EDP Sciences 1996