On the inclusion of upper Laue layers in computational methods in high resolution transmission electron microscopy

Abstract

Three different methods for computing scattering amplitudes in High Resolution Transmission Electron Microscopy (HRTEM) have been investigated as to their ability to include upper Laue layer (ULL) interaction. The conventional first-order multislice method using fast Fourier transform (FFT) and the second-order multislice method (SOM method) are shown to yield calculated intensities of first-order Laue reflections with the use of slice thicknesses smaller than the crystal periodicity along the incident electron beam direction. It is argued that the calculated intensities of ULL reflections approach the correct values in the limiting case of vanishing slice thickness and electron wavelength. The third method, the improved phasegrating method (IPG), does also in principle include ULL effects, but is severely limited as to choice of slice thickness and sampling interval. A practical way to use slice thicknesses less than the crystal periodicity along the incident beam direction is shown for both the conventional FFT method and the second-order multislice method and tested on a spinel structure. It is also shown that the IPG method does not easily allow for aslice thickness different from the crystal periodicity in the beam direction.