摘要:
This paper calculated, in Harrison bonded orbital method framework, the harmonic coefficients and non-harmonic coefficients of atomic vibrations by establishing the graphene elastic model with considering the anharmonic vibration of atoms and short-range interaction of atoms. Then the variation relationships among gra-phene force constants, temperature and deformation potential parametric, were obtained, and the variation rela-tionships among graphene elastic wave velocity, temperature and deformation potential parametric, were also ob-tained. Moreover, we discussed how the atomic anharmonic vibration impacts on graphene force constants and e-lastic wave velocity. The results were threefold. First, the three graphene force constants C11, C12、C44 the elastic wave velocity, unanimously, decrease nonlinearly with the temperature increasing, which the change order from largest to smallest of the constants is C12 , C11 , C44 , and the longitudinal wave velocity variation with temperature changes bigger than the shear wave. Second, the C11, C12、C44 with the change of deformation potential parame-ters have different characteristics:C11 enlargesw ith the increasing of η or γ, and C12 reduces with the increase ofη and increases with the increase ofγ, C44 increases with biggerηand nearly not change withγ. Third, the gra-phene force constants Cij and the elastic wave velocity vi are verified to be constants if we ignored the anharmonic term of atomic vibrations. Considering the anharmonic terms, all of these parameters Cij,vi, and |Cij-Cij0|、|vi-vi0|, the operator 'o' represents the approximate computing, decrease with increasing temperature, which means that the non-harmonic phenomenon is more obvious with higher temperature.%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,建立石墨烯弹性模型并求出原子振动的简谐系数和非简谐系数.在此基础上,确定了石墨烯的力常数随温度和形变势参量的变化关系式,以及弹性波波速随温度和形变势参量的变化关系式,并探讨了原子非简谐振动对它们的影响.结果表明:(1)石墨烯的力常数和弹性波波速均随温度升高而非线性减小,但有不同的变化特征:在C11、C12、C44这三个力常数中,以C12随温度的变化最大,以C44的变化最小;纵波波速随温度的变化要大于横波;(2)石墨烯的三个力常数随形变势参量的变化有不同的特征:C11随η和γ的增大而增大、而C12则随η的增大而减小,随γ的增大而增大;C44随η的增大而增大,而几乎不随γ而变;(3)若不考虑原子振动的非简谐项,则石墨烯的力常数和弹性波波速均为常数.考虑到非简谐项后,不仅它们均随温度的升高而减小,而且,非简谐情况的力常数Cij和弹性波波速vi与简谐近似的值Cij0、vi0的差|Cij-Cij0|、|vi-vi0|均随温度的升高而增大,即温度愈高,非简谐效应愈显著.