Family behaviour of Raman-active phonon frequencies of single-wall nanotubes of C, BN and BC3

Using a symmetry-based force-constant model of the lattice dynamics, the Raman-active phonon frequencies are calculated for almost 200 single-wall nanotubes of C, BN and BC3. The n + m = constant family behaviour is found in most branches and these three kinds of nanotubes display different diameter and chirality dependence in different branches. In these branches, vibration modes that C, BN and BC3 nanotubes have in common are presented in detail. For a particular family, the phonon frequency at Γ point changes regularly with the chiral angle. Therefore, we may distinguish among single-wall nanotubes with similar diameter and different chiral angle.