Lattice dynamics of single-walled boron nitride nanotubes

The phonon dispersion of single-walled boron nitride nanotubes is calculated within a valence shell model of the lattice dynamics. The model parameters are derived from fittings to the measured phonon dispersion of hexagonal boron nitride and available optical data. The calculated phonon dispersion curves for the tubes $\mathrm{}(10,10),$ $\mathrm{}(17,0),$ and $\mathrm{}(15,4)\mathrm{}$ are presented. An analysis of the vibrational patterns of the zone-center phonons is given. The results for the phonon dispersion, zone-center phonons, and nonresonant Raman intensity can be used for the needs of characterization of boron nitride nanotube samples by Raman scattering and infrared spectroscopies.