in this paper, we have used density functional perturbation theory (dfpt) and pseudo-potential method to calculate the phonon spectrum, phonon density of states (dos), specific heat capacity and mechanical properties of (5,5) armchair and (9,0) zigzag single wall carbon nanotubes (swcnts). our calculations show that young’s modulusfor (5,5) and (9,0) nanotubesare higher than 1tpa. we have also ...