非简谐振动对石墨烯杨氏模量与声子频率的影响

在哈里森键联轨道法框架下, 考虑到原子的短程相互作用和原子的非简谐振动, 应用固体物理理论和方法, 得到了石墨烯的力常数、杨氏模量、扭曲模量、泊松系数以及声子频率随温度的变化关系, 探讨了非简谐振动对它们的影响. 结果表明: 1)杨氏模量与声子频率等随温度变化并遵从一定的规律, 其中力常数、杨氏模量、扭曲模量随温度升高而增大, 但变化较小; 声子频率随温度升高而增大但变化较快; 泊松系数随温度升高而较快地减小; 2)石墨烯原子具有沿键长方向的纵振动和垂直键长方向的横振动, 但以纵振动为主, 纵振动的非简谐效应远大于横振动, 横振动的简谐系数ε₀' 和第二非谐系数ε₂' 均小于纵振动的相应值ε₀,ε₂; 比值为ε₀/ε₀' ≈ 8.477,ε₂/ε₂' ≈ 156; 3)若不考虑非简谐振动项, 则石墨烯的力常数、杨氏模量和扭曲模量、泊松系数、声子频率均为常量, 与实验不符合; 同时考虑到原子的第一、二非简谐振动项后, 它们均随温度升高而变化, 而且温度愈高, 原子振动的非简谐效应愈显著. 本文的结果与文献的实验结果符合较好.

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

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 Poisson’s 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 Poisson’s 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 ε₀/ε₀’ ≈ 8.477 and ε₂/ε₂’ ≈ 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.