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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Li, X. et al. Large-area synthesis of high-quality and uniform graphene films on copper foils. Science 324, 1312–1314 (2009).
Kim, K. S. et al. Large-scale pattern growth of graphene films for stretchable transparent electrodes. Nature 457, 706–710 (2009).
Reina, A. et al. Large area, few-layer graphene films on arbitrary substrates by chemical vapor deposition. Nano Lett. 9, 30–35 (2009).
Park, S. & Ruoff, R. S. Chemical methods for the production of graphenes. Nature Nanotech. 4, 217–224 (2009).
Zhao, L. et al. Influence of copper crystal surface on the CVD growth of large area monolayer graphene. Solid State Commun. 151, 509–513 (2011).
Yu, Q. K. et al. Control and characterization of individual grains and grain boundaries in graphene grown by chemical vapour deposition. Nature Mater. 10, 443–449 (2011).
Yazyev, O. V. & Louie, S. G. Electronic transport in polycrystalline graphene. Nature Mater. 9, 806–809 (2010).
Yazyev, O. V. & Louie, S. G. Topological defects in graphene: Dislocations and grain boundaries. Phys. Rev. B 81, 195420 (2010).
Huang, P. Y. et al. Grains and grain boundaries in single-layer graphene atomic patchwork quilts. Nature 469, 389–392 (2011).
Grantab, R., Shenoy, V. B. & Ruoff, R. S. Anomalous strength characteristics of tilt grain boundaries in graphene. Science 330, 946–948 (2010).
Malola, S., Häkkinen, H. & Koskinen, P. Structural, chemical, and dynamical trends in graphene grain boundaries. Phys. Rev. B 81, 165447 (2010).
Cockayne, E. et al. Grain boundary loops in graphene. Phys. Rev. B 83, 195425 (2011).
Kim, P. Graphene: Across the border. Nature Mater. 9, 792–793 (2010).
Rogers, J. A., Lagally, M. G. & Nuzzo, R. G. Synthesis, assembly and applications of semiconductor nanomembranes. Nature 477, 45–53 (2011).
Novoselov, K. S. et al. Electric field effect in atomically thin carbon films. Science 306, 666–669 (2004).
Geim, A. K. & Novoselov, K. S. The rise of graphene. Nature Mater. 6, 183–191 (2007).
Geim, A. K. Graphene: Status and prospects. Science 324, 1530–1534 (2009).
Lin, Y. M. et al. 100-GHz transistors from wafer-scale epitaxial graphene. Science 327, 662 (2010).
Lee, C., Wei, X., Kysar, J. W. & Hone, J. Measurement of the elastic properties and intrinsic strength of monolayer graphene. Science 321, 385–388 (2008).
Koenig, S. P., Boddeti, N. G., Dunn, M. L. & Bunch, J. S. Ultrastrong adhesion of graphene membranes. Nature Nanotech. 6, 543–546 (2011).
Li, J. C. M. Disclination model of high angle grain boundaries. Surf. Sci. 31, 12–26 (1972).
Liu, Y. & Yakobson, B. I. Cones, pringles, and grain boundary landscapes in graphene topology. Nano Lett. 10, 2178–2183 (2010).
Yakobson, B. I. & Ding, F. Observational geology of graphene, at the nanoscale. ACS Nano 5, 1569–1574 (2011).
Romanov, A. E. & Kolesnikova, A. L. Application of disclination concept to solid structures. Prog. Mater. Sci. 54, 740–769 (2009).
Kleman, M. & Friedel, J. Disclinations, dislocations, and continuous defects: A reappraisal. Rev. Mod. Phys. 80, 61–115 (2008).
Shih, K. K. & Li, J. C. M. Energy of grain boundaries between cusp misorientations. Surf. Sci. 50, 109–124 (1975).
Eshelby, J. D. A simple derivation of the elastic field of an edge dislocation. Br. J. Appl. Phys. 17, 1131–1135 (1966).
Jia, X., Campos-Delgado, J., Terrones, M., Meunier, V. & Dresselhaus, M. S. Graphene edges: A review of their fabrication and characterization. Nanoscale 3, 86–95 (2011).
Stuart, S. J., Tutei, A. B. & Harrison, J. A. A reactive potential for hydrocarbons with intermolecular interactions. J. Chem. Phys. 112, 6472–6486 (2000).
Plimpton, S. J. Fast parallel algorithms for short-range molecular dynamics. J. Comput. Phys. 117, 1–19 (1995).
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.
The authors declare no competing financial interests.
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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). https://doi.org/10.1038/nmat3370
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