Abnormal linear elasticity in polycrystalline phosphorene.

Phosphorene, also known as monolayer black phosphorous, has been widely used in electronic devices due to its superior electrical properties. However, its relatively low Young's modulus, low fracture strength and susceptibility to structural failure has limited its application in nano devices. Therefore, in order to design more mechanically reliable devices that utilize phosphorene, it is necessary to explore the mechanical properties of polycrystalline phosphorene. Here molecular dynamics simulations are performed to study the effect of grain size on the mechanical performance of polycrystalline phosphorene sheets. Unlike other two-dimension materials with planar crystalline structure, polycrystalline phosphorene sheets are almost linear elastic, resulting from its high bending stiffness due to its intrinsic buckled crystalline structure. Moreover, the percentage increase of stiffness for polycrystalline phosphorene associated with the increase of grain size from 2 to 12 nm is only 15.9%, much smaller than that for other two-dimension materials with planar crystalline structure. This insensitivity could be attributed to the small difference between the elastic modulus of the crystalline phase and amorphous phase of polycrystalline phosphorene. In addition, the strength deduction obeys well a logarithm relation of grain size, well explained by the dislocation pile-up theory analogous to that of polycrystalline graphene. Overall, our findings provide a better understanding of mechanical properties of polycrystalline phosphorene and establish a guideline for manufacturing and designing novel phosphorene-based nano devices and nano structures.