  We explore the inelastic electron scattering in SrTiO3, PbTiO3, and SiC in
their phonon energy range, challenging the assumption that phonon polaritons
are excluded at large angles in high-resolution transmission electron
energy-loss spectroscopy. We demonstrate that through multiple scattering, the
electron beam can excite both phonons and phonon polaritons, and the relative
proportion of each varies depending on the structure factor and scattering
angle. Integrating dielectric theory, density functional theory, and
multi-slice simulations, we provide a comprehensive framework for understanding
these interactions in materials with polar optical phonons.
