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

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 Schrodinger 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.