Wave-packet numerical investigation of thermal diffuse scattering: A time-dependent quantum approach to electron diffraction simulations

Abstract

The effects of thermal diffuse scattering on diffraction of highly-accelerated electrons by crystal lattices are investigated with a method that combines the frozen phonon approximation with an exact numerical solution of the time-dependent Schrödinger equation. The phonon configuration for each single-electron diffraction process is determined by means of Einstein's model. It is shown that this procedure provides the possibility of describing and explaining, in a natural way, after averaging over a number of electron realizations, how the typical diffraction features that characterize a fully coherent pattern are gradually suppressed by thermally-induced incoherence. This is achieved by a controlled increase of the lattice atomic vibrations and is in contrast to the use of attenuating Debye-Waller factors and complex potential absorbers. A lattice with reduced dimensionality is first considered as a working model, where the method renders results compatible with those reported in the literature. Subsequently, a full three-dimensional system is simulated and results are compared to experimental imaging displaying the method's reliability.