  We provide a theoretical framework for the prediction and interpretation of
momentum dependent phonon spectra due to coherent inelastic scattering of
electrons. We complete the approach with first principles lattice dynamics
using periodic density functional theory and compare to recent electron energy
loss measurements on cubic and hexagonal boron nitride performed within a
scanning transmission electron microscope (STEM). The combination of theory and
experiment provides the ability to interpret momentum dependent phonon spectra
obtained at nanometer spatial resolution in the electron microscope.
