Theory and hierarchical calculations of the structure and energetics of [0001] tilt grain boundaries in graphene
Theory and hierarchical calculations of the structure and energetics of [0001] tilt grain boundaries in graphene
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DOI：
10.1103/physrevb.84.165423
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发表时间：
2011-10-11
影响因子：
3.7
通讯作者：
Fasolino, Annalisa
中科院分区：
文献类型：
--
作者：
Carlsson, Johan M.;Ghiringhelli, Luca M.;Fasolino, Annalisa
一些实验揭示了石墨烯中晶界的存在，这可能会改变其电子和弹性特性。在这里，我们基于重合位点晶格（CSL）理论提出了石墨烯中[0001]倾斜晶界结构的一般理论。我们证明，CSL 理论使用两个晶界指数（m，n）根据取向差角 theta 和周期性 d 对晶界进行独特的分类，类似于纳米管指数。由 CSL 理论生成的 0 度 < θ < 60 度（最多 15 608 个原子）的大量晶界的结构和形成能通过分层方法进行了优化，并通过密度泛函计算进行了验证。我们发现石墨烯中的低能晶界可以被识别为位错阵列。位错形成小丘，就像通过扫描隧道显微镜在 Ir(111) 上生长的石墨烯中观察到的小丘一样，小 θ 在较大的取向差角处变平。我们发现，与三维材料相比，晶界产生的应变可以通过面外畸变释放，从而导致位错核之间产生有效的吸引相互作用。因此，形成能对 θ 的依赖性与面外畸变的依赖性相似，在 θ = 32.2 度处具有次要最小值，其中晶界由仅由 5 个和 7 个环构成的平坦锯齿形阵列组成。对于 θ > 32.2 度，其他非六边形环也是可能的。我们讨论这些发现对于解释最近实验结果的重要性。
Several experiments have revealed the presence of grain boundaries in graphene that may change its electronic and elastic properties. Here, we present a general theory for the structure of [0001] tilt grain boundaries in graphene based on the coincidence site lattice (CSL) theory. We show that the CSL theory uniquely classifies the grain boundaries in terms of the misorientation angle theta and periodicity d using two grain-boundary indices (m, n), similar to the nanotube indices. The structure and formation energy of a large set of grain boundaries generated by the CSL theory for 0 degrees < theta < 60 degrees (up to 15 608 atoms) were optimized by a hierarchical methodology and validated by density functional calculations. We find that low-energy grain boundaries in graphene can be identified as dislocation arrays. The dislocations form hillocks like those observed by scanning tunneling microscopy in graphene grown on Ir(111) for small theta that flatten out at larger misorientation angles. We find that, in contrast to three-dimensional materials, the strain created by the grain boundary can be released via out-of-plane distortions that lead to an effective attractive interaction between dislocation cores. Therefore, the dependence on theta of the formation energy parallels that of the out-of-plane distortions, with a secondary minimum at theta = 32.2 degrees where the grain boundary is made of a flat zigzag array of only 5 and 7 rings. For theta > 32.2 degrees, other nonhexagonal rings are also possible. We discuss the importance of these findings for the interpretation of recent experimental results.