摘要:
考虑到原子非简谐振动和电子-声子相互作用,用固体物理理论和方法研究了石墨烯格林艾森参量和低温热膨胀系数以及声子弛豫时间随温度的变化规律,探讨了原子非简谐振动项对它们的影响.结果表明:1)在低于室温的温度范围内,石墨烯的热膨胀系数为负值,随着温度的升高,其热膨胀系数的绝对值单调增加,室温热膨胀系数为-3.64×10-6 K-1;2)简谐近似下的格林艾森参量为零.考虑到非简谐项后,格林艾森参量在1.40-1.42之间并随温度升高而缓慢增大,几乎成线性关系,第二非简谐项对格林艾森参量的影响小于第一非简谐项;3)石墨烯声子弛豫时间随着温度的升高而减小,其中,温度很低(T＜ 10 K)时变化很快,此后变化很慢,当温度不太低(T＞ 300K)时,声子弛豫时间与温度几乎成反比关系.
Abstract:
Considering the anharmonic vibrations and the interactions between electron and phonon of atoms,in this article we study the temperature dependence of Grüneisen parameter,thermal expansion coefficient at low temperature and phonon relaxation time by using the theory and method of solid state physics.The influences of the anharmonic vibration of the atom on the above parameters are further discussed.The obtained results are as follows.1) The thermal expansion coefficient of graphene is a negative value when the temperature drops below room temperature.The absolute value of the thermal expansion coefficient of graphene increases monotonically with the increase of temperature.The thermal expansion coefficient of graphene is-3.64 × 10-6 K-1 at room temperature.2) The value of Griineisen parameter is zero in the harmonic approximation.If the anharmonic vibration is considered,the Griineisen parameter will increase slowly with the increase of temperature.Its value is between 1.40 and1.42 and the change is almost linear.And we find that the influence of the second anharmonic term is less than that of the first anharmonic term on Grüneisen parameter.3) The phonon relaxation time decreases with the increase of temperature.The rate changes rapidly at low temperature (T ＜ 10 K),then it changes very slowly.The phonon relaxation time is almost inversely proportional to temperature when the temperature is higher than 300 K.
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