Department of Materials Science and NanoEngineering, Rice University, Houston, Texas 77005, USA.
Department of Mechanical Engineering, Columbia University, New York, New York 10027, USA.
Phys Rev Lett. 2015 Mar 20;114(11):115502. doi: 10.1103/PhysRevLett.114.115502. Epub 2015 Mar 16.
In graphene growth, island symmetry can become lower than the intrinsic symmetries of both graphene and the substrate. First-principles calculations and Monte Carlo modeling explain the shapes observed in our experiments and earlier studies for various metal surface symmetries. For equilibrium shape, edge energy variations δE manifest in distorted hexagons with different ground-state edge structures. In growth or nucleation, energy variation enters exponentially as ∼e(δE/k(B)T), strongly amplifying the symmetry breaking, up to completely changing the shapes to triangular, ribbonlike, or rhombic.
在石墨烯生长过程中，岛的对称性可能会低于石墨烯和衬底各自的内在对称性。第一性原理计算和蒙特卡罗建模解释了我们的实验和早期研究中观察到的各种金属表面对称性的形状。对于平衡形状，边缘能量变化 δE 表现为具有不同基态边缘结构的扭曲六边形。在生长或成核过程中，能量变化以指数形式进入，如 ∼e(δE/k(B)T)，强烈放大了对称性破缺，直到完全将形状改变为三角形、带状或菱形。
