石墨带的晶格动力学研究

Lattice dynamics of graphene ribbon

基于晶格动力学理论,采用力常数模型,计算了石墨带的声子色散关系、振动模式密度和比热.计算结果表明,石墨带的声子谱特征介于一维碳纳米管和二维石墨片之间.扶手椅型和锯齿型石墨带的中、高频声子支分别与锯齿型和扶手椅型碳纳米管的类似.由于声子限域效应,低频声子支随着石墨带带宽的改变出现明显的频移现象.振动模式密度在高频区几乎不敏感于带宽,而低频区的峰位随着带宽的增加而逐渐向低频移动.此外,无论是在低温还是高温,比热都随着带宽的增加而逐渐降低,呈现量子尺寸效应.在300K时,比热可以拟合成CV=CVg+A/n,其中CVg为石墨片的热容,而A/n项反映了石墨带中边缘效应对比热的影响.

Based on lattice dynamics theory and force constant model, we calculated phonon dispersion relation, density of states, and specific heat of graphene ribbons.It is shown that the characteristics of phonon spectra behaves as those of a system between one-dimensional carbon nanotube and two-dimensional graphene. The high and intermediate phonon branches of armchair and zigzag nanoribbons resemble those of zigzag and armchair carbon nanotubes, respectively. With the ribbon width increasing, interestingly, it is found that the low frequency peaks in density of states shifted to lower frequency, indicating a phonon confinement effect.At both low and high temperature,specific heat decreased with the increase of the band width,showing up as a singular quantum size effect.The specific heat at 300 K can be fitted by CV=CVg＋A/n, where CVg is specific heat of graphene and the A/n term represents the effect of edge on specific heat of ribbons.