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

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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.

At a glance


  1. Atomic-resolution ADF-STEM images of graphene crystals.
    Figure 1: Atomic-resolution ADF-STEM images of graphene crystals.

    a, Scanning electron microscope image of graphene transferred onto a TEM grid with over 90% coverage using novel, high-yield methods. Scale bar, 5μm. b, ADF-STEM image showing the defect-free hexagonal lattice inside a graphene grain. c, Two grains (bottom left, top right) intersect with a 27° relative rotation. An aperiodic line of defects stitches the two grains together. d, The image from c with the pentagons (blue), heptagons (red) and distorted hexagons (green) of the grain boundary outlined. bd were low-pass-filtered to remove noise; scale bars, 5Å.

  2. Large-scale grain imaging using DF-TEM.
    Figure 2: Large-scale grain imaging using DF-TEM.

    ae, Grain imaging process. a, Samples appear uniform in bright-field TEM images. b, Diffraction pattern taken from a region in a reveals that this area is polycrystalline. Placing an aperture in the diffraction plane filters the scattered electrons forming c, a corresponding dark-field image showing the real-space shape of these grains. d, Using several different aperture locations and colour-coding them produces e, a false-colour, dark-field image overlay depicting the shapes and lattice orientations of several grains. f, g, Images of regions where many grains emanate from a few points. Scale bars, 500nm.

  3. Statistical analysis of grain size and orientation.
    Figure 3: Statistical analysis of grain size and orientation.

    a, Histogram of grain sizes, taken from three representative samples using DF-TEM. The mean grain size is 250±11nm (s.e.m., n = 535). Inset, plot of the cumulative probability of having more than one grain given the area of a device. b, Histogram of relative grain rotation angles measured from 238 grain boundaries. c, d, Large-area diffraction patterns (c) and a low-magnification DF-TEM image (d) show that grains are globally aligned near particular directions. Scale bar, 2μm.

  4. Grain structure and mobilities for three growth conditions.
    Figure 4: Grain structure and mobilities for three growth conditions.

    ac, Composite DF-TEM images of grain structure show variations with growth condition. The mean grain sizes are 250±11nm (s.e.m.; growth method A, 99.8% pure copper), 470±36nm (s.e.m.; growth method B, 99.999% pure (ultrapure) copper) and 1.7±0.15μm (s.e.m.; growth method C (rapid thermal anneal)). The graphene is visible through the 20-nm, perforated amorphous-carbon Quantifoil support film. The graphene is broken over three of the perforations in a. Scale bars, 2μm. d, Vertically stacked histogram of room-temperature mobilities, μ, measured from 39 devices using graphene growth methods A, B, and C. N, number of devices. See Methods for further details.

  5. AFM indentation and AC-EFM studies of graphene grain boundaries.
    Figure 5: AFM indentation and AC-EFM studies of graphene grain boundaries.

    a, b, AFM phase images of a graphene grain before and after an indentation measurement. a, Indentation takes place at the centre of this grain as shown by the arrow. b, The region is torn along grain boundaries after indentation. Scale bars, 200nm. c, Electrostatic potential, averaged over three adjacent line scans along a suspended graphene sheet between two electrodes (schematic at top) and measured using AC-EFM. Although on average each line scan should cross 12 grains, no measureable features are present. Dashed lines indicate the locations of the electrodes.


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Author information

  1. These authors contributed equally to this work.

    • Pinshane Y. Huang,
    • Carlos S. Ruiz-Vargas &
    • Arend M. van der Zande


  1. School of Applied and Engineering Physics, Cornell University, Ithaca, New York 14853, USA

    • Pinshane Y. Huang,
    • Carlos S. Ruiz-Vargas,
    • Jonathan S. Alden,
    • Ye Zhu &
    • David A. Muller
  2. Department of Physics, Cornell University, Ithaca, New York 14853, USA

    • Arend M. van der Zande,
    • William S. Whitney &
    • Paul L. McEuen
  3. Department of Chemistry and Chemical Biology, Cornell University, Ithaca, New York 14853, USA

    • Mark P. Levendorf,
    • Shivank Garg &
    • Jiwoong Park
  4. Department of Physics, Oregon State University, Corvallis, Oregon 97331, USA

    • Joshua W. Kevek
  5. Department of Physics and Astronomy, Brigham Young University, Provo, Utah 84602, USA

    • Caleb J. Hustedt
  6. Kavli Institute at Cornell for Nanoscale Science, Ithaca, New York 14853, USA

    • Jiwoong Park,
    • Paul L. McEuen &
    • David A. Muller


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.

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