Lattice dynamics of single-walled achiral BC3 nanotubes

The phonon dispersion relation and specific heat of single-walled BC3 nanotubes have been investigated using a force constant model. The obtained phonon dispersion relation of BC3 sheet reproduces well the experimental data. The tube-diameter dependent frequencies of both the radial breathing mode and the lowest phonon mode E2g can be well fitted by a power law ω=C Rα with tube radius R, where the scaling exponent α=1 and the proportional constant C=939.6 cm-1 Å in the former and α=1.1 and C=321.5 cm-1 Å1.1 in the latter, at variance with carbon nanotubes and BN nanotubes. The specific heat of BC3 nanotubes are also calculated, less than that of the BC3 sheet, in which several crossings are observed at low temperature due to the first optical phonon mode excited at different temperature. By virtue of the simple zone-folding model, in addition, a universal formula is derived to describe the tube diameter dependence of specific heat for various types of nanotube systems. The results provide an alternative way to characterize the BC3 nanotubes and suggest the underlying quantized phonon structures in one-dimensional nanotube systems.