Ab initio calculation of ideal strength and phonon instability of graphene under tension
Ab initio calculation of ideal strength and phonon instability of graphene under tension
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张力下石墨烯理想强度和声子不稳定性的从头算
DOI：
10.1103/physrevb.76.064120
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发表时间：
2007-08-01
影响因子：
3.7
通讯作者：
Li, Ju
中科院分区：
文献类型：
--
作者：
Liu, Fang;Ming, Pingbing;Li, Ju
2007 年 5 月 14 日收稿； 2007 年 6 月 16 日收到修订稿；发表于 2007 年 8 月 28 日 基于石墨烯的 sp 2 碳纳米结构，如碳纳米管和纳米纤维，由于其尺寸极小，可能无法达到其理想强度。我们通过密度泛函微扰理论计算了石墨烯的声子谱作为单轴张力的函数，以评估应变路径上声子不稳定性的首次出现，该不稳定性控制着 0 K 下无缺陷晶体的强度。单轴拉伸应变应用于 x 最近邻和 y 第二最近邻方向，分别与锯齿形和扶手椅纳米管的拉伸变形相关。我们的小应变结果中的杨氏模量 E = 1050 GPa 和泊松比 = 0.186 与之前的计算结果非常吻合。我们发现，在 x 和 y 单轴张力中，声子不稳定性发生在布里渊区中心附近，分别为 xx= 0.194、xx = 110 GPa、yy= 0.016 和 yy= 0.266、yy= 121 GPa、xx= 0.027。两个软声子都是拉伸方向上的纵向弹性波，表明脆性解理断裂可能是石墨烯和碳纳米管在低温下的固有行为。我们还预测，声子带隙将出现在高度拉伸的石墨烯中，这可能是高应力碳纳米管的有用光谱特征。
Received 14 May 2007; revised manuscript received 16 June 2007; published 28 August 2007 Graphene-based sp 2 -carbon nanostructures such as carbon nanotubes and nanofibers can fail near their ideal strengths due to their exceedingly small dimensions. We have calculated the phonon spectra of graphene as a function of uniaxial tension by density functional perturbation theory to assess the first occurrence of phonon instability on the strain path, which controls the strength of a defect-free crystal at 0 K. Uniaxial tensile strain is applied in the x nearest-neighbor and y second nearest-neighbor directions, related to tensile deformation of zigzag and armchair nanotubes, respectively. The Young’s modulus E = 1050 GPa and Poisson’s ratio = 0.186 from our small-strain results are in good agreement with previous calculations. We find that in both x and y uniaxial tensions, phonon instabilities occur near the center of the Brillouin zone, at xx= 0.194, xx = 110 GPa, yy= 0.016 and yy= 0.266, yy= 121 GPa, xx= 0.027, respectively. Both soft phonons are longitudinal elastic waves in the pulling direction, suggesting that brittle cleavage fracture may be an inherent behavior of graphene and carbon nanotubes at low temperatures. We also predict that a phonon band gap will appear in highly stretched graphene, which could be a useful spectroscopic signature for highly stressed carbon nanotubes.