Mechanical properties and failure behavior of phosphorene with grain boundaries

Using the density-functional tight-binding method, we studied the effect of grain boundaries on the mechanical properties and failure behavior of phosphorene. We found that the high-angle tilt boundaries with a higher density of (5∣7) defect pairs (oriented along the armchair direction) are stronger than the low-angle tilt boundaries with a lower defect density, and similarly the high-angle boundaries with a higher density of (4∣8) defect pairs (oriented along the zigzag direction) are stronger than the low-angle boundaries with a lower defect density. The failure is due to the rupture of the most pre-strained bonds in the heptagons of the (5∣7) defect pair or octagons of the (4∣8) pairs. The high-angle grain boundaries are better at accommodating the pre-strained bonds in heptagon and octagon defects, leading to a higher failure stress and strain. The results cannot be described by a Griffith-type fracture mechanics criterion, since this does not take into account the bond pre-stretching. Interestingly, these anomalous mechanical and failure characteristics of tilt grain boundaries in phosphorene are also shared by graphene and hexagonal boron nitride, signifying that they may be universal for 2D materials. The findings revealed here may be useful in tuning the mechanical properties of phosphorene via defect engineering for specific applications.