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The nature of strength enhancement and weakening by pentagon–heptagon defects in graphene


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 important two-dimensional crystals to fully use their remarkable properties. With the success in synthesizing large-area polycrystalline graphene1,2,3,4,5, understanding how grain boundaries (GBs) in graphene2,3,4 alter its physical properties5,6,7,8,9,10,11,12,13 is of both scientific and technological importance. A recent work showed that more GB defects could counter intuitively give rise to higher strength in tilt GBs (ref. 10). We show here that GB strength can either increase or decrease with the tilt, and the behaviour can be explained well by continuum mechanics. It is not just the density of defects that affects the mechanical properties, but the detailed arrangements of defects are also important. The strengths of tilt GBs increase as the square of the 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. Our present work provides fundamental guidance towards understanding how defects interact in two-dimensional crystals, which is important for using high-strength and stretchable graphene14 for biological and electronic applications.

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Figure 1: Stress–strain behaviour and GB energy in both armchair and zigzag tilt GBs.
Figure 2: Typical defects and their stress fields in tilt GBs in graphene from MD simulations.
Figure 3: Normal stress contour (from the disclination dipole model) for tilt GBs at different tilt angles.
Figure 4: Dependence of initial maximum GB tensile stress and GB strength on tilt angles.


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The authors acknowledge support from Chinese Academy of Sciences (CAS) and Natural Science Foundation of China (NSFC)#11021262 (Y.W.), NSFC#11023001 (X.S.), Air Force of Scientific Research#FA9550-11-1-0109 (R.Y.) and US Department of Energy#DE-SC0001299/DE-FG02-09ER46577 (M.D.). The simulations are conducted at the Supercomputing Center of CAS.

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Y.W., R.Y. and M.D. conceived the project. Y.W. developed the theory. Y.W., J.W., H.Y. and X.S. performed the calculations. Y.W., R.Y. and M.D. analysed the characteristics of defect interactions in graphene and wrote the paper. All authors were involved in data analysis and revision of the paper.

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Correspondence to Yujie Wei or Ronggui Yang.

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Wei, Y., Wu, J., Yin, H. et al. The nature of strength enhancement and weakening by pentagon–heptagon defects in graphene. Nature Mater 11, 759–763 (2012).

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