Lattice resolution of vibrational modes in the electron microscope

The combination of aberration correction and ultra high energy resolution with monochromators has made it possible to record images showing lattice resolution in phonon modes, both with a displaced collection aperture and more recently with an on -axis collection aperture. In practice the objective aperture has to include Bragg reflections that correspond to the observed lattice image spacings, and the specimen has to be sufficiently thick for adequate phonon scattered intensity. There has been controversy as to whether the images with the on axis detector are really a consequence of lattice resolution in a phonon mode or just a transfer of information from an image that was formed by elastically scattered electrons. We present results of calculations based on a theory that includes the possibility of dynamical electron diffraction for both incident and scattered electrons and the full phonon dispersion relation. We show that Umklapp scattering from the second Brillouin Zone back to the first Brillouin Zone is necessary for lattice resolution with the on axis detector and that it is therefore reasonable to attribute the lattice resolution to the phonon scattering.