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Direct measurement of local phonon dispersion in individual nanostructurescan greatly advance our understanding of their electrical, thermal, andmechanical properties. However, such experimental measurements requireextremely high detection sensitivity and combined spatial, energy and momentumresolutions, thus has been elusive. Here, we develop a four-dimensionalelectron energy loss spectroscopy (4D-EELS) technique based a monochromatedscanning transmission electron microscope (STEM), and present theposition-dependent phonon dispersion measurement in individual boron nitridenanotubes (BNNTs). Our measurement shows that the unfolded phonon dispersion ofmulti-walled BNNTs is close to hexagonal-boron nitride (h-BN) crystals,suggesting that interlayer coupling and curved geometry have no substantialimpacts on phonon dispersion. We also find that the acoustic phonons areextremely sensitive to momentum-dependent defect scattering, while opticalphonons are much less susceptible. This work not only provides useful insightsinto vibrational properties of BNNTs, but also demonstrates huge prospects ofthe developed 4D-EELS technique in nanoscale phonon dispersion measurements.

Four-dimensional Vibrational Spectroscopy for Nanoscale Mapping of Phonon Dispersion in BN Nanotubes