论文标题
石墨烯结构特性中的同位素作用
Isotopic effects in structural properties of graphene
论文作者
论文摘要
同位素效应与了解固体的几种特性有关，并且在这些年中已经进行了彻底的分析。这些影响可能取决于所考虑的固体的维度。在这里，我们评估了它们的大小，用于石墨烯的结构特性，这是一种范式的二维材料。我们使用路径综合分子动力学模拟，这是一种非常适合的技术，可以量化核量子效应对平衡变量的影响，尤其是在不谐波效应很重要的情况下。重点放在原子间距离和均方位移以及石墨烯层的平面区域。在低温下，对于$^{13} $ c和$^{14} $ c的C-C距离相对差，就$^{12} $ c而言，被发现分别为$ -2.5 $和$ -4.6 \ times 10^{ - 4} $，比三维碳基材料（例如钻石）大于三维碳基材料。对于平面区域，相对更改为$ -3.9 $和$ -6.9 \ times 10^{ - 4} $。通过比较内部能量和原子振动振幅与谐波近似衍生的振动的振动，可以估算晶格振动中非谐度的大小。
Isotopic effects are relevant to understand several properties of solids, and have been thoroughly analyzed along the years. These effects may depend on the dimensionality of the considered solid. Here we assess their magnitude for structural properties of graphene, a paradigmatic two-dimensional material. We use path-integral molecular dynamics simulations, a well-suited technique to quantify the influence of nuclear quantum effects on equilibrium variables, especially in cases where anharmonic effects are important. Emphasis is put on interatomic distances and mean-square displacements, as well as on the in-plane area of the graphene layer. At low temperature, the relative difference in C--C distance for $^{13}$C and $^{14}$C, with respect to $^{12}$C, is found to be $-2.5$ and $-4.6 \times 10^{-4}$, respectively, larger than in three-dimensional carbon-based materials such as diamond. For the in-plane area, the relative changes amount to $-3.9$ and $-6.9 \times 10^{-4}$. The magnitude of anharmonicity in the lattice vibrations is estimated by comparing the internal energy and atomic vibrational amplitudes with those derived from a harmonic approximation.
