Recently, Prof. Yujie Wei and his research team at the State Key Laboratory of Nonlinear Mechanics, Institute of Mechanics, Chinese Academy of Sciences published their work online in Nature Materials (July 2012, DOI: 10.1038/NMAT3370). Their present work provides fundamental guidance to understand how defects interact in two-dimensional crystals, which is important for utilizing high strength and stretchable graphene for biological and electronic applications.
The two-dimensional crystalline structures in graphene challenge the applicability of existing theories that have been used for characterizing its three-dimensional counterparts. It is crucial to establish reliable structure-property relationships in the presently important two-dimensional crystals for fully utilizing their remarkable properties. With the success in synthesizing large-area polycrystalline graphene, understanding how grain boundaries (GBs) in graphene alter its physical properties is of both scientific and technological importance. Combined with molecular dynamics, continuum modeling, and density functional theory calculations, we reveal here that GB strength can either increase or decrease with the tilt. It is not just the density of defects that affects the mechanical properties, but the detailed arrangements of defects are also important. There exists interactions between pentagon-heptagon defects, and the stress fields of a pentagon-heptagon defect can be well characterized by a disclination dipole (Fig. 1). The strengths of tilt GBs increase as a square of tilt angles if pentagon-heptagon defects are evenly spaced, and the trend breaks down in other cases. We find that mechanical failure always starts from the bond shared by hexagon-heptagon rings (Fig. 2).
Figure 1: A pentagon-heptagon pair in graphene induces stress fields which resemble the stress by a disclination dipole. Continuum mechanics prediction versus molecular dynamics simulations. a, b, and c, the stress contours of σxx, σyy, and txy predicted by the disclination dipole model; and e, f, and g, the corresponding contours for σxx, σyy, and txy from molecular dynamics simulations.
Figure 2: The electron density contour at the middle plane (z=0, the graphene lays in the x-y plane) to show the lowest electron density in the critical bonds shared by hexagon-heptagon rings, where bond breakage initiates. (a) Atomic view of the pentagon-heptagon defect in a symmetrical tilt grain boundary in graphene. (b) Electron density contour for the atoms shown in (a). The weakest bonds (with lowest electron density) are shared by hexagon and heptagon rings, and are pointed by arrows. The high peak of electron density is in red and zero electron density is in blue.