非简谐振动对石墨烯杨氏模量与声子频率的影响

发布时间：2019-05-29 13:23

【摘要】：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ε′0和第二非谐系数ε′2均小于纵振动的相应值ε_0,ε_2;比值为ε_0/ε′_0≈8.477,ε_2/ε′_2≈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.
[Abstract]:In the framework of Harrison bond orbital method, considering the short-range interaction of atoms and the anharmonic vibration of atoms, the force constant, Young's modulus and distortion modulus of graphene are obtained by using the theory and method of solid state physics. The relationship between Poisson coefficient and phonon frequency with temperature is discussed, and the influence of anharmonic vibration on them is discussed. The results show that: 1) Young's modulus and phonon frequency vary with temperature and follow a certain law, in which force constant, Young's modulus and distortion modulus increase with the increase of temperature, but the change is small; The phonon frequency increases but changes rapidly with the increase of temperature, and the Poisson coefficient decreases rapidly with the increase of temperature. 2) graphene atoms have longitudinal vibration along the bond length direction and transverse vibration in the vertical bond length direction, but the longitudinal vibration is the main one, and the anharmonic effect of the longitudinal vibration is much greater than that of the transverse vibration. The simple harmonic coefficient and the second anharmonic coefficient of transverse vibration are smaller than the corresponding values of longitudinal vibration. The ratio of 蔚 _ 0 / 蔚'_ 0 is 8.477, and that of 蔚 _ 2 / 蔚'_ 2 is 156. the ratio of 蔚 _ 0 / 蔚'_ 0 is 8.477. 3) if the anharmonic vibration term is not taken into account, the force constant, Young's modulus and distortion modulus, Poisson coefficient and phonon frequency of graphene are constant, which are not in good agreement with the experiment. At the same time, after considering the first and second anharmonic vibration terms of atoms, they all change with the increase of temperature, and the higher the temperature is, the more obvious the anharmonic effect of atomic vibration is. The results of this paper are in good agreement with the experimental results in the literature.
【作者单位】：重庆文理学院电子电气工程学院;
【基金】：国家自然科学基金(批准号:11574253) 重庆市基础与前沿研究项目(批准号:cstc2015jcyj A40054)资助的课题~~
【分类号】：O613.71

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