  Phonon scattering at grain boundaries (GBs) is significant in controlling
nanoscale device thermal conductivity. However, GBs could also act as
waveguides for selected modes. To measure localized GB phonon modes, meV energy
resolution is needed with sub-nm spatial resolution. Using monochromated
electron energy loss spectroscopy (EELS) in the scanning transmission electron
microscope (STEM) we have mapped the 60 meV optic mode across GBs in silicon at
atomic resolution and compared it to calculated phonon densities of states
(DOS). The intensity is strongly reduced at GBs characterised by the presence
of five- and seven-fold rings where bond angles differ from the bulk. The
excellent agreement between theory and experiment strongly supports the
existence of localized phonon modes and thus of GBs acting as waveguides.
