Simulations of Kikuchi patterns due to thermal diffuse scattering on MgO crystals

Abstract

Inelastic scattering of fast transmission electrons from a perfect crystal is investigated using the Bloch wave theory. A comprehensive expression for the scattering of electrons is given, which includes both elastic and inelastic multiple scatterings. This expression is an extended form of Fujimoto's expression for elastic scattering (J. Phys. Soc. Japan 14:1558 (1959)). For the approximation of single inelastic scattering, the expression becomes equivalent to the formula of Rez et al. (Phil. Mag. 35: 81 (1977)). When thermal diffuse scattering (TDS) is considered using the Einstein model or the scattering factor for TDS given by Hall and Hirsch (Proc. R. Soc. A 286: 158 (1965)), Rossouw and Bursill's expression (Acta Cryst. A 41: 320 (1985)) is derived. This expression has been used in computer simulations of TDS intensity distribution (Kikuchi pattern). It is shown that the simulations for magnesium oxide (MgO) using 357 beams agree quite well with the experimental ones.

Thermal diffuse scattering in sub-angstrom quantitative electron microscopy—phenomenon, effects and approaches

“…TDS is also mainly responsible to the Kikuchi patterns observed in electron diffraction. A recent dynamic calculation by Omoto et al (2002) gives excellent agreement with the experimental data.…”

Position averaged convergent beam electron diffraction: Theory and applications

“…This background is partially structured: thermal scattering is responsible for the familiar Kikuchi patterns seen in diffraction imaging. Various approaches, such as the frozen phonon model [18] and multiple scattering matrix methods [30], exist to simulate this contribution, but they increase the computational burden of the calculation. As will be shown below, features used in comparisons of experiments and simulations for thickness, tilt and polarity determination are dominated by the elastic scattering rather than the thermal scattering, and the simpler absorptive model suffices.…”

Differential quantitative analysis of background structure in energy-filtered convergent-beam electron diffraction patterns

“…TDS. It would then be necessary to perform a series of calculations using both multislice and Bloch-wave methods (Dwyer, 2003;Dwyer & Etheridge, 2003;Dwyer, 2005;Omoto et al, 2002) to formalize a theoretical description of this background. Whilst this remains for future work, the present results are reassuring because they suggest that energy-filtered CBED patterns from specimens that have been prepared by standard approaches could still be sufficient for high-accuracy QCBED via a differential approach.…”

“…Arguments against applying calculations incorporating a full treatment of TDS because of their nearly prohibitive cost in computing power and time (compared with purely elastic scattering calculations) will eventually fade with the advent of new supercomputing technologies such as graphics processing units. A growing number of CBED calculations incorporate TDS (Rossouw et al, 1990;Loane et al, 1991;Wang, 1992;Muller et al, 2001;Omoto et al, 2002;Dwyer, 2003Dwyer, , 2005Dwyer & Etheridge, 2003), with Omoto et al (2002) illustrating how TDS calculations can be included (non-iteratively) in QCBED. However, there is very little information in the literature about the structure of the background associated with each disc in a CBED pattern.…”

“…Most calculations deal only with the total signal in the pattern, without separating the TDS and elastic components. Omoto et al (2002) examined the background due to TDS experimentally and theoretically in the absence of the CBED pattern, but without comment as to how the TDS component relates in structure to the elastic component within CBED discs.…”