Mechanical Properties and Failure Behavior of Phosphorene with Grain   Boundaries
  Using 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 large angle tilt boundaries with a higher density of (5|7) defect pairs (oriented along the AC direction) are stronger than the low-angle tilt boundaries with a lower defect density, and similarly the large angle boundaries with a higher density of (4|8) defect pairs (oriented along the ZZ 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 large-angle grain boundaries are better off in accommodating the pre-strained bonds in heptagons and octagons defects, leading to a higher failure stress and strain. The results cannot be described by Griffith-type fracture mechanics criterion since it 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 born-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. 
V. Sorkin and Y.W. Zhang
cond-mat.mtrl-sci