局域键合二维晶体中的熔化和波纹现象
Melting and Rippling Phenomenan in Two Dimensional Crystals with localized bonding
摘要：
我们计算均方根（RMS）偏离平衡的原子在一个二维晶体与本地（例如共价键）之间的近邻键合。大规模的Monte Carlo计算结果与谐波近似下的分析结果吻合得很好。当运动被限制在平面上时，我们发现随着晶体越来越大，原子围绕其平衡位置的波动缓慢（对数）增加。我们考虑到垂直于晶格平面的波动，表现为起伏的波纹，通过检查双层系统与层之间的耦合，以赋予局部刚性（即在石墨烯片中，由于其有限的厚度而变硬）。令人惊讶的是，我们发现一个快速的发散与系统的大小增加的垂直均方差，独立的面间耦合的强度。我们认为一个有吸引力的耦合到一个平面基板，发现即使是一个弱的吸引力显着限制的振幅和平均波长的波纹。我们验证我们的结果是通用的，通过检查各种不同的几何形状，在每种情况下获得相同的现象。
英文摘要：
We calculate Root Mean Square (RMS) deviations from equilibrium for atoms in a two dimensional crystal with local (e.g. covalent) bonding between close neighbors. Large scale Monte Carlo calculations are in good agreement with analytical results obtained in the harmonic approximation. When motion is restricted to the plane, we find a slow (logarithmic) increase in fluctuations of the atoms about their equilibrium positions as the crystals are made larger and larger. We take into account fluctuations perpendicular to the lattice plane, manifest as undulating ripples, by examining dual layer systems with coupling between the layers to impart local rigidly (i.e. as in sheets of graphene made stiff by their finite thickness). Surprisingly, we find a rapid divergence with increasing system size in the vertical mean square deviations, independent of the strength of the interplanar coupling. We consider an attractive coupling to a flat substrate, finding that even a weak attraction significantly limits the amplitude and average wavelength of the ripples. We verify our results are generic by examining a variety of distinct geometries, obtaining the same phenomena in each case.
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