Skip to main content

Thank you for visiting You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Letter
  • Published:

Grains and grain boundaries in single-layer graphene atomic patchwork quilts


The properties of polycrystalline materials are often dominated by the size of their grains and by the atomic structure of their grain boundaries. These effects should be especially pronounced in two-dimensional materials, where even a line defect can divide and disrupt a crystal. These issues take on practical significance in graphene, which is a hexagonal, two-dimensional crystal of carbon atoms. Single-atom-thick graphene sheets can now be produced by chemical vapour deposition1,2,3 on scales of up to metres4, making their polycrystallinity almost unavoidable. Theoretically, graphene grain boundaries are predicted to have distinct electronic5,6,7,8, magnetic9, chemical10 and mechanical11,12,13 properties that strongly depend on their atomic arrangement. Yet because of the five-order-of-magnitude size difference between grains and the atoms at grain boundaries, few experiments have fully explored the graphene grain structure. Here we use a combination of old and new transmission electron microscopy techniques to bridge these length scales. Using atomic-resolution imaging, we determine the location and identity of every atom at a grain boundary and find that different grains stitch together predominantly through pentagon–heptagon pairs. Rather than individually imaging the several billion atoms in each grain, we use diffraction-filtered imaging14 to rapidly map the location, orientation and shape of several hundred grains and boundaries, where only a handful have been previously reported15,16,17,18,19. The resulting images reveal an unexpectedly small and intricate patchwork of grains connected by tilt boundaries. By correlating grain imaging with scanning probe and transport measurements, we show that these grain boundaries severely weaken the mechanical strength of graphene membranes but do not as drastically alter their electrical properties. These techniques open a new window for studies on the structure, properties and control of grains and grain boundaries in graphene and other two-dimensional materials.

This is a preview of subscription content, access via your institution

Access options

Buy this article

Prices may be subject to local taxes which are calculated during checkout

Figure 1: Atomic-resolution ADF-STEM images of graphene crystals.
Figure 2: Large-scale grain imaging using DF-TEM.
Figure 3: Statistical analysis of grain size and orientation.
Figure 4: Grain structure and mobilities for three growth conditions.
Figure 5: AFM indentation and AC-EFM studies of graphene grain boundaries.

Similar content being viewed by others


  1. Li, X. et al. Large-area synthesis of high-quality and uniform graphene films on copper foils. Science 324, 1312–1314 (2009)

    Article  ADS  CAS  Google Scholar 

  2. Reina, A. et al. Large area, few-layer graphene films on arbitrary substrates by chemical vapor deposition. Nano Lett. 9, 30–35 (2009)

    Article  ADS  CAS  Google Scholar 

  3. Li, X. et al. Graphene films with large domain size by a two-step chemical vapor deposition process. Nano Lett. 10, 4328–4334 (2010)

    Article  ADS  CAS  Google Scholar 

  4. Bae, S. et al. Roll-to-roll production of 30-inch graphene films for transparent electrodes. Nature Nanotechnol. 5, 574–578 (2010)

    Article  ADS  CAS  Google Scholar 

  5. Cervenka, J. & Flipse, C. F. J. Structural and electronic properties of grain boundaries in graphite: planes of periodically distributed point defects. Phys. Rev. B 79, 195429 (2009)

    Article  ADS  Google Scholar 

  6. Peres, N. M. R., Guinea, F. & Castro-Neto, A. H. Electronic properties of disordered two-dimensional carbon. Phys. Rev. B 73, 125411 (2006)

    Article  ADS  Google Scholar 

  7. Yazyev, O. V. & Louie, S. G. Electronic transport in polycrystalline graphene. Nature Mater. 6, 806–809 (2010)

    Article  ADS  Google Scholar 

  8. Mesaros, A., Papanikolaou, S., Flipse, C. F. J., Sadri, D. & Zaanen, J. Electronic states of graphene grain boundaries. Phys. Rev. B 82, 205119 (2010)

    Article  ADS  Google Scholar 

  9. Cervenka, J., Katsnelson, M. I. & Flipse, C. F. J. Room-temperature ferromagnetism in graphite driven by two-dimensional networks of point defects. Nature Phys. 5, 840–844 (2009)

    Article  ADS  CAS  Google Scholar 

  10. Malola, S., Hakkinen, H. & Koskinen, P. Structural, chemical, and dynamical trends in graphene grain boundaries. Phys. Rev. B 81, 165447 (2010)

    Article  ADS  Google Scholar 

  11. Liu, Y. & Yakobson, B. I. Cones, pringles, and grain boundary landscapes in graphene topology. Nano Lett. 10, 2178–2183 (2010)

    Article  ADS  CAS  Google Scholar 

  12. Grantab, R., Shenoy, V. B. & Ruoff, R. S. Anomalous strength characteristics of tilt grain boundaries in graphene. Science 330, 946–948 (2010)

    Article  ADS  CAS  Google Scholar 

  13. Yazyev, O. V. & Louie, S. G. Topological defects in graphene: dislocations and grain boundaries. Phys. Rev. B 81, 195420 (2010)

    Article  ADS  Google Scholar 

  14. Hirsch, P., Howie, A., Nicholson, R., Pashley, D. W. & Whelan, M. J. Electron Microscopy of Thin Crystals (Krieger, 1965)

    Google Scholar 

  15. Zhao, L. et al. The atomic-scale growth of large-area monolayer graphene on single-crystal copper substrates. Preprint at 〈〉 (2010)

  16. Gao, L., Guest, J. R. & Guisinger, N. P. Epitaxial graphene on Cu(111). Nano Lett. 10, 3512–3516 (2010)

    Article  ADS  CAS  Google Scholar 

  17. Cockayne, E. et al. Rotational grain boundaries in graphene. Preprint at 〈〉 (2010)

  18. Wofford, J. M., Nie, S., McCarty, K. F., Bartlet, N. C. & Dubon, O. D. Graphene islands on Cu foils: the interplay between shape, orientation, and defects. Nano Lett. 10, 4890–4896 (2010)

    Article  ADS  CAS  Google Scholar 

  19. Park, H. J., Meyer, J., Roth, S. & Skakalova, V. Growth and properties of few-layer graphene prepared by chemical vapor deposition. Carbon 48, 1088–1094 (2010)

    Article  CAS  Google Scholar 

  20. Regan, W. et al. A direct transfer of layer-area graphene. Appl. Phys. Lett. 96, 113102 (2010)

    Article  ADS  Google Scholar 

  21. Krivanek, O. L. et al. Atom-by-atom structural and chemical analysis by annular dark-field electron microscopy. Nature 464, 571–574 (2010)

    Article  ADS  CAS  Google Scholar 

  22. Hashimoto, A., Suenaga, K., Gloter, A., Urita, K. & Iijima, S. Direct evidence for atomic defects in graphene layers. Nature 430, 870–873 (2004)

    Article  ADS  CAS  Google Scholar 

  23. Meyer, J. C. et al. Direct imaging of lattice atoms and topological defects in graphene membranes. Nano Lett. 8, 3582–3586 (2008)

    Article  ADS  CAS  Google Scholar 

  24. de Villeneuve, V. W. A. et al. Hard sphere crystal nucleation and growth near large spherical impurities. J. Phys. Condens. Matter 17, S3371–S3378 (2005)

    Article  CAS  Google Scholar 

  25. Park, S., Floresca, H. C., Suh, Y. & Kim, M. J. Electron microscopy analyses of natural and highly oriented pyrolytic graphites and the mechanically exfoliated graphenes produced from them. Carbon 48, 797–804 (2010)

    Article  CAS  Google Scholar 

  26. 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)

    Article  ADS  CAS  Google Scholar 

  27. Geim, A. K. & Novoselov, K. S. The rise of graphene. Nature Mater. 6, 183–191 (2007)

    Article  ADS  CAS  Google Scholar 

  28. Bachtold, A. et al. Scanned probe microscopy of electronic transport in carbon nanotubes. Phys. Rev. Lett. 84, 6082–6085 (2000)

    Article  ADS  CAS  Google Scholar 

  29. Van Der Zande, A. M. et al. Large-scale arrays of single-layer graphene resonators. Nano Lett. 10, 4869–4873 (2010)

    Article  ADS  CAS  Google Scholar 

  30. Thiel, S. et al. Electron scattering at dislocations in LaAlO3/SrTiO3 interfaces. Phys. Rev. Lett. 102, 046809 (2009)

    Article  ADS  CAS  Google Scholar 

  31. Meyer, J. C., Chuvilin, A. & Kaiser, U. in MC2009, Vol. 3: Materials Science (eds Grogger, W., Hofer, F. & Polt, P. ) 347–348 (Graz Univ. Technology, 2009)

    Google Scholar 

  32. Suenaga, K. et al. Imaging active topological defects in carbon nanotubes. Nature Nanotechnol. 2, 358–360 (2007)

    Article  ADS  CAS  Google Scholar 

  33. Jiao, L. et al. Creation of nanostructures with poly(methyl methacrylate)-mediated nanotransfer printing. J. Am. Chem. Soc. 130, 12612–12613 (2008)

    Article  CAS  Google Scholar 

Download references


The authors acknowledge discussions with M. Blees, J. Cha, S. Gerbode, J. Grazul, E. Kirkland, L. Fitting-Kourkoutis, O. Krivanek, S. Shi, S. Wang and H. Zhuang. This work was supported in part by the National Science Foundation through the Cornell Center for Materials Research and the Nanoscale Science and Engineering Initiative of the National Science Foundation under NSF Award EEC-0117770, 064654. Additional support was provided by the Army Research Office, CONACYT-Mexico, the Air Force Office of Scientific Research, DARPA-MTO and the MARCO Focused Research Center on Materials, Structures, and Devices. Sample fabrication was performed at the Cornell node of the National Nanofabrication Infrastructure Network, funded by the NSF. Additional facilities support was provided by the Cornell Center for Materials Research (NSF DMR-0520404 and IMR-0417392) and NYSTAR.

Author information

Authors and Affiliations



P.Y.H., C.S.R.-V. and A.M.v.d.Z. contributed equally to this work. Electron microscopy and data analysis were carried out by P.Y.H. and D.A.M., with Y.Z. contributing to initial DF-TEM. Graphene growth and sample fabrication were done by A.M.v.d.Z. and C.S.R.-V. under the supervision of P.L.M. and J.P., aided by M.P.L., S.G., W.S.W., J.W.K., J.S.A. and C.J.H. AC-EFM, mobility measurements and analysis were done by A.M.v.d.Z. and P.L.M., aided by C.S.R.-V. and J.W.K. AFM mechanical testing and analysis were done by C.S.R.-V. and J.P., aided by S.G. All authors discussed the results and implications at all stages. P.Y.H, A.M.v.d.Z., C.S.R.-V., P.L.M., J.P. and D.A.M. wrote the paper.

Corresponding author

Correspondence to David A. Muller.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Supplementary information

Supplementary Information

The file contains Supplementary Figures 1-12 with legends, Supplementary Methods and an additional reference. (PDF 4681 kb)

PowerPoint slides

Rights and permissions

Reprints and permissions

About this article

Cite this article

Huang, P., Ruiz-Vargas, C., van der Zande, A. et al. Grains and grain boundaries in single-layer graphene atomic patchwork quilts. Nature 469, 389–392 (2011).

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI:

This article is cited by


By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.


Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing