关键词: 石墨烯/
低温热膨胀系数/
格林艾森参量/
弛豫时间
English Abstract
Variation of thermal expansion at low temperature and phonon relaxation time in graphene with temperature
Ren Xiao-Xia1,Shen Feng-Juan1,
Lin Xin-You2,
Zheng Rui-Lun1
1.College of Electronic and Electrical Engineering, Electronic Engineering Research Center of New Energy Storage Devices and Applications, Chongqing University of Arts and Sciences, Chongqing 402160, China;
2.School of Mechanical Engineering and Automation, Fuzhou University, Fuzhou 350000, China
Fund Project:Project supported by the National Natural Science Foundation of China (Grant No. 51505086), The Scientific and Technological Research Program of Chongqing Municipal Education Commission, China (Grant Nos. KJ1601118, KJ1601111), and the Natural Science Foundation Project of Chongqing (CSTC), China (Grant No. Cstc2015jcyjA40054).Received Date:20 April 2017
Accepted Date:20 August 2017
Published Online:05 November 2017
Abstract:Considering the anharmonic vibrations and the interactions between electron and phonon of atoms, in this article we study the temperature dependence of Grneisen 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 Grneisen parameter is zero in the harmonic approximation. If the anharmonic vibration is considered, the Grneisen 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 Grneisen 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.
Keywords: graphene/
thermal expansion coefficient at low temperature/
Grüneisen parameter/
relaxation time
