Influence of the anharmonic vibration on the Young modulus and the phonon frequency of the graphene

Abstract

In the frame of the Harrison bonded-orbital method, the variations of the force constant, the Young modulus, the torsional modulus and the phonon frequency with temperature are given through the relevant theory or method of the solid state physics with considering the non-harmonic effect and the short-range interaction of atoms. Results show that the force constant, the Young modulus, the torsional modulus, the phonon frequency and the Poissons coefficient all vary with temperature. The results show that the first three quantities increase with temperature but not very much; the phonon frequency increases with temperature rapidly; the Poissons coefficient decreases fast with the increase of temperature. There are transverse vibrations along the direction perpendicular to the bond-length direction and the longitudinal vibrations along the bond-length direction, in which the longitudinal vibrations are dominant. The nonharmonic effect of the longitudinal vibration is much larger than that of the transverse vibration. The first and the second non-harmonic coefficient of the transverse vibration are both much less than those of the longitudinal vibration, where 0/0 8.477 and 2/2 156. The above five physical quantities are constant at different temperatures if the first and second nonhamonic effects are omitted, which does not conform to the experimental results. After the first and second nonhamonic effects are considered, they all increase with temperature and results are in good agreement with experimental data. The anharmonic effect increases with temperature.