Effect of vacancies on the mechanical properties of phosphorene nanotubes

Using density functional tight-binding method, we studied the mechanical properties, deformation and failure of armchair (AC) and zigzag (ZZ) phosphorene nanotubes (PNTs) with monovacancies and divacancies subjected to uniaxial tensile strain. We found that divacancies in AC PNTs and monovacancies in ZZ PNTs possess the lowest vacancy formation energy, which decreases with the tube diameter in AC PNTs and increases in ZZ PNTs. The Young's modulus is reduced, while the radial and thickness Poisson's ratios are increased by hosted vacancies. In defective AC PNTs, deformation involves fracture of the intra-pucker bonds and formation of the new inter-pucker bonds at a critical strain, and the most stretched bonds around the vacancy rupture first, triggering a sequence of the structural transformations terminated by the ultimate failure. The critical strain of AC PNTs is reduced significantly by hosted vacancies, whereas their effect on the critical stress is relatively weaker. Defective ZZ PNTs fail in a brittle-like manner once the most stretched bonds around a vacancy rupture, and vacancies are able to significantly reduce the failure strain but only moderately reduce the failure stress of ZZ PNTs. The understandings revealed here on the mechanical properties and the deformation and failure mechanisms of PNTs provide useful guidelines for their design and fabrication as building blocks in nanodevices.