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Using density functional tight-binding method, we studied the effect of grainboundaries on the mechanical properties and failure behavior of phosphorene. Wefound 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-angletilt boundaries with a lower defect density, and similarly the large angleboundaries with a higher density of (4|8) defect pairs (oriented along the ZZdirection) are stronger than the low-angle boundaries with a lower defectdensity. The failure is due to the rupture of the most pre-strained bonds inthe heptagons of the (5|7) defect pair or octagons of the (4|8) pairs. Thelarge-angle grain boundaries are better off in accommodating the pre-strainedbonds in heptagons and octagons defects, leading to a higher failure stress andstrain. The results cannot be described by Griffith-type fracture mechanicscriterion since it does not take into account the bond pre-stretching.Interestingly, these anomalous mechanical and failure characteristics of tiltgrain boundaries in phosphorene are also shared by graphene and hexagonalborn-nitride, signifying that they may be universal for 2D materials. Thefindings revealed here may be useful in tuning the mechanical properties ofphosphorene via defect engineering for specific applications.

Mechanical Properties and Failure Behavior of Phosphorene with Grain Boundaries