English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We compare the Frequency-Resolved Frozen Phonon Multislice (FRFPMS) method,introduced in Phys. Rev. Lett. 124, 025501 (2020), with other theoreticalapproaches used to account for the inelastic scattering of high energyelectrons, namely the first-order Born approximation and the quantum excitationof phonons model. We show, that these theories lead to similar expressions forthe single inelastically scattered intensity as a function of momentum transferfor an anisotropic quantum harmonic oscillator in a weak phase objectapproximation of the scattered waves, except for a too small smearing of thescattering potential by the effective Debye-Waller factor (DWF) in the FRFPMSmethod. We propose that this issue can be fixed by including an explicit DWFsmearing into the potential and demonstrate numerically, that in any realisticsituation, a FRFPMS approach revised in this way, correctly accounts for thesingle inelastically scattered intensity and the correct elastic scatteringintensity. Furthermore our simulations illustrate that the only requirement forsuch a revised FRFPMS method is the smallness of mean squared displacements forall atomic species in all frequency bins. The analytical considerations for theFRFPMS method also explain the $1/\omega^2$-scaling of FRFPMS spectra observedin Phys. Rev. B 104, 104301 (2021) by the use of classical statistics in themolecular dynamics simulation. Moreover, we find that the FRFPMS methodinherently adds the contributions of phonon loss and gain within each frequencybin. Both of these issues related to the frequency-scaling can be fixed by asystem-independent post-processing step.

Lessons from the harmonic oscillator -- a reconciliation of the Frequency-Resolved Frozen Phonon Multislice Method with other theoretical approaches