Several aspects of phonon scattering in the transmission electron microscope are investigated with focus on the physically distinct effects of the thermal average over initial states as well as the excitation or annihilation of phonons. Coupled-channel calculations for the model system of a single atom in a harmonic potential are presented and interpreted in terms of inelastic scattering and thermal fluctuations. Furthermore, common approximations for inelastic scattering calculations are compared to this model. Additionally, the description of phonon scattering by means of an $S$-matrix approach is investigated. The $S$-matrix approach allows differentiation between scattering events and propagation of scattered waves within the specimen. Within this approach, it is rigorously proven that by suitable integration over calculations with static atomic coordinates inelastic phonon scattering can be approximated for any initial object state. The limits of this approximation are discussed.

• Received 22 May 2019
• Revised 16 September 2019

DOI:https://doi.org/10.1103/PhysRevB.100.144305