Phonon dispersion relation calculations of armchair and zigzag carbon nanotubes

Abstract

When we calculate the phonon dispersion relations by using the force constant parameters for two_dimensional(2D) graphite, it is necessary to consider the problem that a 3D nanotube is formed by a rolled 2D graphene sheet. The present paper reports results on phonon dispersion relations of armchair and zigzag carbon nanotubes calculated with the considerations to the effect of curvature. Based on the results of the calculations and the symmetry analysis of the structures of single wall armchair and zigzag carbon nanotubes, the decomposition of the vibration modes at the Γ point is discussed.