The statistics of the thermal motion of the atoms during imaging process in transmission electron microscopy and related techniques

The concern of this work is the influence of the thermal motion of the atoms on electron scattering simulations, used for quantitative interpretation of results in high-resolution electron microscopy. We distinguish between the influence of inelastic phonon excitation and the effect of a moving lattice on images generated by elastically scattered electrons. It is shown that, analog to aberrations, the impact of a moving lattice differs substantially with respect to different imaging conditions and cannot be described by the Debye–Waller damping applicable in XRD. We derive a new formalism, based on the frozen lattice and multislice approach, to incorporate the statistics of the thermal motion into elastic TEM imaging simulations, taking into account different imaging conditions. The averaging over different atom positions is generally performed within a density matrix framework, which can be linearized in the special case of off-axis electron holography. All findings are supported by explicit numerical simulations: molecular dynamics simulations are performed to get a realistic thermal motion and the electron scattering simulations are performed within the new multislice algorithm.