标题： 各向异性杨氏模量对于单层黑磷：除了扶手椅方向和锯齿形方向的第三主方向 显示英文标题

标题： Anisotropic Young's Modulus for Single-Layer Black Phosphorus: The Third Principle Direction Besides Armchair and Zigzag

摘要： 我们使用价键场模型推导出单层黑磷的杨氏模量的解析公式。 通过分析杨氏模量的方向依赖性，我们探索了第三主方向，其方向角 φ_tp = 0.268π，除了锯齿和扶手椅方向。 最大杨氏模量值出现在第三主方向。 更具体地说，杨氏模量在锯齿方向、扶手椅方向和第三主方向分别为 52.2 N/m、85.4 N/m 和 111.4 N/m。 这一新的主方向对于未来讨论单层黑磷中的其他各向异性属性具有重要意义。 显示英文摘要

摘要： We derive an analytic formula for the Young's modulus in single-layer black phosphorus using the valence force field model. By analyzing the directional dependence for the Young's modulus, we explore the third principle direction with direction angle phi_tp = 0.268pi besides armchair and zigzag directions. The maximum Young's modulus value is in the third principle direction. More specifically, the Young's modulus is 52.2 N/m, 85.4 N/m, and 111.4 N/m in the armchair direction, zigzag direction, and the third principle direction, respectively. This new principle direction is of significance for future discussions of other anisotropic properties in the single-layer black phosphorus.