Mechanical properties of monocrystalline and polycrystalline monolayer black phosphorus

The mechanical properties of monocrystalline and polycrystalline monolayer black phosphorus (MBP) are systematically investigated using classic molecular dynamic simulations. For monocrystalline MBP, it is found that the shear strain rate, sample dimensions, temperature, atomic vacancies and applied statistical ensemble affect the shear behaviour. The wrinkled morphology is closely connected with the direction of the in-plane shear, dimensions of the samples, and applied ensembles. Particularly, small samples subjected to loading/unloading of the shear deformation along the armchair direction demonstrate a clear mechanical hysteresis loop. For polycrystalline MBP, the maximum shear stress as a function of the average grain size follows an inverse pseudo Hall-Petch type relationship under an isothermal-isobaric (NPT) ensemble, whereas under a canonical (NVT) ensemble, the maximum shear stress of polycrystalline MBP exhibits a 'flipped' behaviour. Furthermore, polycrystalline MBP subjected to uniaxial tension also exhibits a strongly grain size-dependent mechanical response, and it can fail by brittle intergranular and transgranular fractures because of its weaker grain boundary structures and the direction-dependent edge energy, respectively. These findings provide useful insight into the mechanical design of BP for nanoelectronic devices.