This work addresses a fundamental question: To what extent is graphene graphite? In particular does 2D graphene have many of the same 3D mechanical properties as graphite, such as the bulk modulus and elastic constant $c_{33}$? We have obtained, for the first time, unambiguous Raman spectra from unsupported monolayer graphene under pressure. We have used these data to quantify the out-of-plane stiffness of monolayer graphene, which is hard to define due to its 2D nature. Our data indicate a first physically meaningful out-of-plane stiffness of monolayer graphene, and find it to be consistent with that of graphite. We also report a shift rate of the in-plane phonon frequency of unsupported monolayer graphene to be $5.4{\mathrm{cm}}^{-1}{\mathrm{GPa}}^{-1}$, very close to that of graphite ($4.7{\mathrm{cm}}^{-1}{\mathrm{GPa}}^{-1}$), contrary to the previous value for supported graphene. Our results imply that monolayer graphene has similar in-plane and out-of-plane stiffnesses, and anharmonicities to graphite.

中文翻译：

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2D材料中的3D应变：单层石墨烯石墨的应用范围有多大？

这项工作解决了一个基本问题：石墨烯石墨的程度如何？特别是2D石墨烯具有许多与石墨相同的3D机械性能，例如体积模量和弹性常数$C_{33}$？我们首次在压力下从无支撑的单层石墨烯获得了明确的拉曼光谱。我们已经使用这些数据来量化单层石墨烯的平面外刚度，由于其2D性质，很难对其进行定义。我们的数据表明了单层石墨烯的第一个物理意义上的面外刚度，并且发现它与石墨的刚度是一致的。我们还报告了不支持的单层石墨烯的面内声子频率的位移速率为$5.4{\mathrm{厘米}}^{-\mathrm{1个}}{\mathrm{GPa}}^{-\mathrm{1个}}$，非常接近石墨（$4.7{\mathrm{厘米}}^{-\mathrm{1个}}{\mathrm{GPa}}^{-\mathrm{1个}}$），与之前所支持的石墨烯的值相反。我们的结果表明，单层石墨烯具有相似的面内和面外刚度，以及与石墨的非谐性。