论文标题
石墨烯双层的热力学特性
Thermodynamic properties of graphene bilayers
论文作者
论文摘要
石墨烯双层的热力学特性通过路径综合分子动力学（PIMD）模拟研究，考虑了振动模式和非谐作用的量化。使用LCBOPII的有效潜力，已经在12至1500 k的温度下研究了双层石墨烯。我们集中于热膨胀，面内和平面外的可压缩性以及特定的热量。从与单层石墨烯和石墨的PIMD模拟获得的数据相比，获得了对我们对双层石墨烯结果含义的更多见解。鉴于石墨的实验数据，它们还进行了分析。研究了对双层石墨烯的面内和“真实”面积的零点和热效应。平面面积的热膨胀系数$α_{xy} $在低温下为负，$ t \ gtrsim $ 800〜k为阳性。最低$α_{xy} $是$ -6.6 \ times 10^{ - 6} $ k $^{ - 1} $ at $ t \ of 220 $ 〜k。在平面内（$χ_{xy} $）和平面外（$χ_z$）的石墨烯双层可压缩性都在温度上升时会增加，并且结果均高于与单层石墨烯相对应的，并且低于Graphite的升高。在300 K时，我们找到了双层$χ_{xy} = 9.5 \ times 10^{ - 2} $Å$^2 $/eV和$χ_z= 2.97 \ times 10^{ - 2} $ gpa $^$^$^{ - 1} $。比较了从模拟获得的特定热量的结果，与振动模式的谐波近似所给出的结果进行了比较。在低于200〜k的温度下，这种方法明显准确。
Thermodynamic properties of graphene bilayers are studied by path-integral molecular dynamics (PIMD) simulations, considering quantization of vibrational modes and anharmonic effects. Bilayer graphene has been studied at temperatures between 12 and 1500~K for zero external stress, using the LCBOPII effective potential. We concentrate on the thermal expansion, in-plane and out-of-plane compressibility, and specific heat. Additional insight into the meaning of our results for bilayer graphene is obtained from a comparison with data obtained from PIMD simulations for monolayer graphene and graphite. They are also analyzed in view of experimental data for graphite. Zero-point and thermal effects on the in-plane and "real" area of bilayer graphene are studied. The thermal expansion coefficient $α_{xy}$ of the in-plane area is negative at low temperatures and positive for $T \gtrsim$ 800~K. The minimum $α_{xy}$ is $-6.6 \times 10^{-6}$ K$^{-1}$ at $T \approx 220$~K. Both in-plane ($χ_{xy}$) and out-of-plane ($χ_z$) compressibilities of graphene bilayers are found to increase for rising temperature, and turn out to be lower than that corresponding to monolayer graphene and higher than those found for graphite. At 300 K, we find for the bilayer $χ_{xy} = 9.5 \times 10^{-2}$ Å$^2$/eV and $χ_z = 2.97 \times 10^{-2}$ GPa$^{-1}$. Results for the specific heat obtained from the simulations are compared with those given by a harmonic approximation for the vibrational modes. This approach is noticeably accurate at temperatures lower than 200~K.
