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Direct Imaging of Lattice Atoms and
Topological Defects in Graphene Membranes
Jannik C. Meyer, C. Kisielowski, R. Erni, Marta D. Rossell, M. F. Crommie, and A. Zettl
Nano Lett., 2008, 8 (11), 3582-3586 • DOI: 10.1021/nl801386m • Publication Date (Web): 19 June 2008
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Direct Imaging of Lattice Atoms and
Topological Defects in Graphene
Jannik C. Meyer,†C. Kisielowski,‡R. Erni,‡Marta D. Rossell,‡M. F. Crommie,†
and A. Zettl*,†
Materials Sciences DiVision, Lawrence Berkeley National Laboratory and Department
of Physics, UniVersity of California at Berkeley, and National Center for Electron
Microscopy, Lawrence Berkeley National Laboratory, Berkeley, California 94720
Received May 14, 2008
We present a transmission electron microscopy investigation of graphene membranes, crystalline foils with a thickness of only 1 atom. By
usingaberration-correctionincombinationwithamonochromator, 1-Åresolutionisachievedatanaccelerationvoltageofonly80kV. Thelow
voltageiscrucial for thestabilityof thesemembranes. Asaresult, everyindividual carbonatominthefieldof viewisdetectedandresolved.
Weobserveahighlycrystallinelatticealongwithoccasional point defects. Theformationandannealingof Stone-Walesdefectsisobserved
in situ. Multiple five- and seven-membered rings appear exclusively in combinations that avoid dislocations and disclinations, in contrast to
previous observations on highly curved (tube- or fullerene-like) graphene surfaces.
Graphene is a single atomic layer of graphite that has only
recently become experimentally accessible in an isolated
form.1,2Because the electronic, thermal, and mechanical
properties of graphene are exceptionally sensitive to lattice
imperfections,3–6a study of defects in this material is
critically important. Although highly curved graphene de-
rivatives such as carbon nanotubes and fullerenes have been
studied extensively,9–11defects and their dynamics in a planar
graphene remain experimentally unexplored.
The optimal experimental configuration for defect study
in planar graphene would be free-standing membranes, that
is, crystalline foils with a thickness of only 1 carbon atom,
probed by a microscopy with true single-atom resolution and
with a sufficient data acquisition rate to record real-time
defect formation and dynamics. Although it would seem that
transmission electron microscopes (TEMs) are ideally suited
to this task, traditional TEMs lack the necessary resolution
at the required low operating voltages. Here we show the
first results obtained with a new microscope design, the
aberration-corrected, monochromated TEAM 0.5 transmis-
sion electron microscope, operated at 80 kV.7,8This unique
microscope achieves subangstrom resolution even at 80 kV,
thus providing the capability to resolve every single carbon
atom in the graphene lattice even for suspended single-layer
graphene. Indeed, experimentally we find that, even for
single-shot data aquisition, each atom in the field of view is
detected with a signal well above the noise. We are able to
directly image theoretically predicted configurations such as
Stone-Wales defects and explore their real-time dynamics.
We find that the dynamics are significantly different from
those for closed-shell graphenes such as nanotubes or
Graphene membranes were prepared as described in ref
12. In brief, graphene was isolated on a silicon wafer with
a 300-nm oxide layer by mechanical cleavage and located
by optical microscopy. A commercially available TEM grid
(c-flat, Protochips inc.) with 1-µm holes was placed onto
the flake and the grid with its perforated amorphous carbon
film was pulled into contact with the substrate by evaporating
a drop of solvent. Then, the grid along with the graphene
sheet was floated off using a second drop of solvent. The
as-prepared membranes were irradiated briefly in a conven-
tional TEM or scanning electron microscope along the edges
of the thin regions, thereby pinning them down by hydro-
carbon deposits12(without this step, we found that the sheets
may detach from the support and collapse into a crumpled
configuration upon heating). Then, they were heated on a
hot plate in air at 200 °C for 10 min, in order to reduce the
amount of adsorbates, just prior to insertion into the high-
* To whom correspondence should be addressed. E-mail: azettl@
†Materials Sciences Division, Lawrence Berkeley National Laboratory
and Department of Physics, University of California at Berkeley.
‡National Center for Electron Microscopy, Lawrence Berkeley National
Vol. 8, No. 11
Published on Web 06/19/2008
2008 American Chemical Society
The high-resolution TEAM 0.5 microscope was operated
at 80 kV with the third-order spherical aberration tuned to
Cs )-17 µm. For a Schottky field-emission microscope,
the resolution and the information limit at this operating
voltage are limited by chromatic aberration. In order to
achieve subangstrom resolution and information transfer, it
is necessary to decrease the energy spread of the incoming
electron beam. We therefore employed the gun electron
monochromator in order to have an energy spread of 0.22
eV on the sample. Using a negative value of the third-order
spherical aberration in combination with a positive fifth-order
spherical aberration constant (5 mm), a small positive defocus
yields white-atom contrast.13–15The images shown here were
obtained for an overfocus of about 8 nm. At these settings,
images can be interpreted directly in terms of the structure
because the sample is small enough to be completely within
the optimum focus window of about 1 nm.
Figure 1a shows an optical micrograph of a large graphene
sample on the support grid (the 1-µm grid perforation holes
are barely visible), whereas Figure 1b shows a low-
magnification TEM image with the essentially invisible (at
this magnification) single-layer graphene membrane spanning
several holes. Figure 1c shows high-resolution TEM data
obtained by zooming in on one of the suspended membrane
regions. This image represents a single, unfiltered CCD
exposure, and the intensity profile (carbon atoms are here
white) is a direct and striking representation of the carbon
atomic structure in graphene. The additional structure near
the upper-left, upper-right, and bottom-center regions of the
figure are adsorbates. Importantly, significant areas shown
in Figure 1c appear clean and structurally perfect.
The exceptional resolution afforded by such microscopy
allows detailed examination of the atomic structure of
graphene, in particular contrast profile, single versus mul-
tilayers, and defect configurations. We first briefly summarize
the image processing parameters and determine the signal-
to-noise for detection of individual carbon atoms in the
graphene lattice. Images (Figures 2 and 3) were high-pass
filtered with a smooth cut off near 20 Å in order to
compensate the slightly uneven illumination intensity. The
exposure time was 1 s with a pixel size of 0.24 Å. After
Fourier-filtering (i.e., essentially subtracting the ideal lattice;
not shown), the images of the clean areas could not be
distinguished from an image of empty space. We then
estimated the noise after smoothing these empty images to
the actual resolution of 1 Å (by either a low-pass filter or
Gaussian blur). The resulting noise level (standard deviation)
is about 0.8% (ca. 2% before smoothing). Thus, an individual
carbon atom with a contrast of about 6% is detected against
the noise even in single exposures (Figures 1c and 3a-d).
Even better signal-to-noise ratios could be obtained by
averaging drift-compensated images if features clearly did
not change between subsequent exposures (Figures 2 and
A direct image of a single-layer graphene sheet (average
of 7 exposures) is shown in Figure 2a along with the contrast
profile (Figure 2b). Image simulations for the contrast profile,
where the atoms are well-approximated as weak phase
objects, are straightforward and were carried out using
MacTempas, the computer code in ref 16 and our own
computer code (based on scattering factors in refs and 18)
for comparison, with very similar simulation results. Interest-
ingly, although the form of the pattern matches very well,
the simulated contrast is a factor of 2 greater than the contrast
observed experimentally. Figure 2c shows a comparison of
data to the simulation with the simulated contrast precisely
halved; the match is remarkably good. This kind of correction
may be related to the well-known so-called “Stobbs fac-
tor”19,20for imaging of three-dimensional samples. Therefore,
we establish a correction factor of 2 in contrast of lattice
images from a crystalline single layer of carbon recorded at
80 kV on the CCD camera.
Because single-layer graphene is only half a unit cell in
the c axis of graphite, it has a unique signature in the direct
image (as well as in a diffraction pattern). Figure 2d and e
shows the difference at the step from a single to a bilayer
region. The AB stacked bilayer region (bottom half of the
figures) shows a qualitatively different pattern than the single-
layer area. However, care must be taken in using such images
for identification because the single-layer region indeed
appears like a bilayer (and vice versa) at a different defocus.
Here, electron-diffraction analysis was used to verify the
presence of a single layer or bilayer.21–23Figure 2f shows
the Fourier transform of a larger image of the bilayer region.
The outermost set of peaks corresponds to an information
transfer of 1.06 Å. The bilayer image is chosen here to
demonstrate this extraordinary transfer because the third ring
of spots is almost zero in the single-layer structure. This is
the highest reflection that is visible in these ultrathin, low-
contrast samples and may not represent the ultimate limit of
the microscope. The two innermost sets of hexagons cor-
respond to 2.13 and 1.23 Å. It must be noted that although
resolving the 2.13 Å reflection provides lattice images of
graphene already in moderate resolution microscopes, the
individual carbon atoms in graphene are resolved only if the
second reflection at 1.23 Å is transferred.
The real-time atomic-scale observation of the formation
and dynamics of defects in graphene at this resolution has
heretofore been experimentally inaccessible. The TEAM
instrument makes these studies possible. The formation and
dynamics of defects in single-layer graphene was observed
by recording a sequence of images at or near the optimum
Figure 1. (a) Optical micrograph, and (b) low-magnification TEM
image of graphene sheets on the perforated carbon film. A single-
layer region is outlined by a red dashed line. (c) Unfiltered CCD
exposure (1 s) of a single-layer graphene membrane. The structures
near the edge of the image are adsorbates, and a hole (formed after
prolonged irradiation) is seen near the lower-edge left. Scale bars
are 10 µm (a), 1 µm (b), and 1 nm (c).
Nano Lett., Vol. 8, No. 11, 20083583
white-atom defocus parameter. Although the sample holder
was maintained at room temperature, the observed region
might have been heated by the electron beam. Figure 3 shows
examples starting with the unperturbed lattice, the defect
structure, and then again the ideal lattice after the defect has
disappeared. An isolated Stone-Wales (SW) defect was
found during one exposure (1 s) of the sequence and relaxed
to the unperturbed lattice in the next exposure (4 s later)
(Figure 3a-d). Defects consisting of multiple five- and
seven-membered rings of carbon atoms spontaneously ap-
peared and remained stable for up to 20 s. Remarkably, all
defect configurations relax to the unperturbed graphene lattice
and contain the same number of pentagons and heptagons
in an arrangement that does not involve a dislocation or
disclination. In addition, Figure 3e and f shows a recon-
structed vacancy configuration involving a pentagon, which
also returned to the unperturbed lattice after a few seconds.
In this case, the missing carbon atom must have been
replaced, from a mobile adsorbate, via surface diffusion on
the graphene sheet.
Pentagon-heptagon (5-7) defects, in particular the
Stone-Wales defect,24are proposed to play a key role in
the formation and transformation of sp-2 bonded carbon
nanostructures.25It is customarily assumed that, after forma-
tion of SW defects, pentagon-heptagon pairs separate,
thereby inducing dislocations and curvature. These defects
are involved in the coalescence of fullerenes and nano-
tubes,25,26and their mobility is relevant for the plastic
response of carbon nanotubes under strain.27In our case of
the (almost22) planar graphene membrane, however, the
separation of pentagon-heptagon pairs is clearly not the
favored pathway: In all cases we have observed, the multiple
5-7 defects relax to the original unperturbed lattice. This
contrasts findings from highly curved graphene structures
where the introduction of dislocations in the electron beam9
and the motion of pentagons and heptagons10has been
Figure 2. (a) Direct image of a single-layer graphene membrane (atoms appear white). (b) Contrast profile along the dotted line in panel
a (solid) along with a simulated profile (dashed). The experimental contrast is a factor of 2 smaller: Panel c shows the same experimental
profile with the simulated contrast scaled down by a factor of 2. (d and e) Step from a monolayer (upper part) to a bilayer (lower part of
the image), showing the unique appearance of the monolayer. Panel e shows the same image with an overlay of the graphene lattice (red)
and the second layer (blue), offset in the Bernal (AB) stacking of graphite. In the bilayer region, white dots appear where two carbon atoms
align in the projection. (f) Numerical diffractogram, calculated from an image of the bilayer region. The outermost peaks, one of them
indicated by the arrow, correspond to a resolution of 1.06 Å. The scale bars are 2 Å.
Nano Lett., Vol. 8, No. 11, 2008
observed. Evidently, the rearrangements after formation of
a defect can transform a curved, closed-shell graphene
derivative into a slightly different shape by local deforma-
tions (such as shrinking of single-walled carbon nanotubes
in an electron beam28). However, in the planar geometry with
a fixed boundary, this is not the case. This result also implies
that the membranes are not under a significant strain that
would favor the formation of dislocations. In a comparison
experiment, we indeed found that graphene membranes are
much more stable than single-walled carbon nanotubes under
the same dose and voltage of the electron beam. The
maximum energy that can be transferred from an 80 keV
electron to a carbon atom is 15.6 eV, which is below the
threshold for knock-on damage29but sufficient to form
multiple SW defects.24,27,26,25
In conclusion, we have demonstrated direct imaging that
resolves all individual carbon atoms in suspended single-
layer graphene membranes. We find that the dynamics of
defects in extended, two-dimensional graphene membranes
are different than in closed-shell graphenes such as nanotubes
or fullerenes. The study of defects, vacancies, and edges in
graphene, as well as absorbates, is important for basic
understanding of this novel material as well as for potential
electronic, mechanical, and thermal applications. Low-
voltage imaging in combination with aberration correction
enables atomic resolution imaging of samples that are too
fragile at higher electron energies, and the detection of
individual carbon atoms is relevant for organic materials.
Graphene membranes are highly promising as support
structure for TEM imaging of other materials as well because
the graphene provides a highly transparent, crystalline
background, and the precisely known structure is an ideal
tuning and calibration tool for electron microscopy develop-
Acknowledgment. NCEM is supported by the Department
of Energy under contract no. DE-AC02-05CH11231. The
TEAM project is supported by the Department of Energy,
Office of Science, Office of Basic Energy Sciences. J.C.M.,
M.F., and A.Z. were supported by the Director, Office of
Energy Research, Office of Basic Energy Sciences, Materials
Sciences and Engineering Division, of the U.S. Department
of Energy under contract no. DE-AC02-05CH11231, via the
sp2-bonded nanostructures program.
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