University of Huddersfield Repository
Gong, Lei, Young, Robert J., Kinloch, Ian A., Haigh, Sarah J., Warner, Jamie H., Hinks, Jonathan
A., Xu, Ziwei, Li, Li, Ding, Feng, Riaz, Ibtsam, Jalil, Rashid and Novoselov, Kostya S.
Reversible Loss of Bernal Stacking during the Deformation of Few-Layer Graphene in
Original Citation
Gong, Lei, Young, Robert J., Kinloch, Ian A., Haigh, Sarah J., Warner, Jamie H., Hinks, Jonathan
A., Xu, Ziwei, Li, Li, Ding, Feng, Riaz, Ibtsam, Jalil, Rashid and Novoselov, Kostya S. (2013)
Reversible Loss of Bernal Stacking during the Deformation of Few-Layer Graphene in
Nanocomposites. ACS Nano, 7 (8). pp. 7287-7294. ISSN 1936-0851
This version is available at http://eprints.hud.ac.uk/18033/
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Reversible Loss of Bernal Stacking
during the Deformation of Few-Layer
Graphene in Nanocomposites
Lei Gong,† Robert J. Young,†,* Ian A. Kinloch,† Sarah J. Haigh,† Jamie H. Warner,§ Jonathan A. Hinks,^
Ziwei Xu, Li Li, Feng Ding, Ibtsam Riaz,‡ Rashid Jalil,‡ and Kostya S. Novoselov‡
Terms of Use CC-BY
Materials Science Centre, School of Materials and ‡School of Physics and Astronomy, University of Manchester, Oxford Road, Manchester M13 9PL, United Kingdom,
Department of Materials, University of Oxford, 16 Parks Road, Oxford OX1 3PH, United Kingdom, ^Department of Engineering and Technology, University of
Huddersfield, Queensgate, Huddersfield HD1 3DH, United Kingdom, and Institute of Textiles and Clothing, Hong Kong Polytechnic University, Hung Hom,
Hong Kong
ABSTRACT The deformation of nanocomposites containing graphene flakes
with different numbers of layers has been investigated with the use of Raman
spectroscopy. It has been found that there is a shift of the 2D band to lower
wavenumber and that the rate of band shift per unit strain tends to decrease as
the number of graphene layers increases. It has been demonstrated that band
broadening takes place during tensile deformation for mono- and bilayer
graphene but that band narrowing occurs when the number of graphene layers is more than two. It is also found that the characteristic asymmetric
shape of the 2D Raman band for the graphene with three or more layers changes to a symmetrical shape above about 0.4% strain and that it reverts to an
asymmetric shape on unloading. This change in Raman band shape and width has been interpreted as being due to a reversible loss of Bernal stacking in
the few-layer graphene during deformation. It has been shown that the elastic strain energy released from the unloading of the inner graphene layers in
the few-layer material (∼0.2 meV/atom) is similar to the accepted value of the stacking fault energies of graphite and few layer graphene. It is further
shown that this loss of Bernal stacking can be accommodated by the formation of arrays of partial dislocations and stacking faults on the basal plane. The
effect of the reversible loss of Bernal stacking upon the electronic structure of few-layer graphene and the possibility of using it to modify the electronic
structure of few-layer graphene are discussed.
KEYWORDS: graphene . Bernal stacking . nanocomposites . Raman spectroscopy . deformation
raphene is currently inspiring a whole
range of research activities in a number of scientific areas such as physics
and materials science because of its interesting and unusual electronic and mechanical
properties.1,2 Excitement was generated originally because monolayer graphene was the
world's first 2D atomic crystal and the thinnest material every produced.3 It was found
to be extremely electrically conductive,
with its charge carriers being massless Dirac
fermions,4 and to have unprecedented levels
of stiffness and strength,5 consistent with
theoretical predictions.6 Bilayer graphene in
which the two layers of carbon atoms are
in so-called AB Bernal stacking7 has strikingly
different electronic properties and has a
pair of high-energy electronic sub-bands.8
It is also unusual in that it has a band
gap that can be controlled directly by
the size of a current applied across the
layers.1 Similar behavior is found with trilayer
graphene making these few-layer, Bernal
stacked graphene materials strong candidates for optoelectronic and nanoelectronic
applications.9 Although the majority of graphene prepared by mechanical exfoliation
has a high proportion of Bernal stacked material, the situation is not the same for multilayer material produced by CVD or epitaxial
growth where a number of different stacking
configurations may be encountered.9 In such
cases, differences in the stacking sequences
and relative twist between the different layers
gives rise to materials with different optical
and electronic properties.1012 It is important
therefore to have accurate and reliable methods of determining the nature and quality of
the stacking of the graphene layers in multilayer material.
A number of different experimental techniques can be used to characterize the
stacking sequences in few-layer graphene
and the most direct method is transmission
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* Address correspondence to
[email protected]
Received for review June 5, 2013
and accepted July 30, 2013.
Published online July 30, 2013
C 2013 American Chemical Society
evidence of failure of the graphenepolymer interface24,25 coupled with matrix cracking.25 There is a
recent report of graphene cracking39 at higher strain
levels and the loss of Bernal stacking in bilayer graphene near a boundary with monolayer material. In
the case of model nanocomposites reinforced with
few-layer graphene, the behavior has been found to be
more complex with evidence of inferior levels of stress
transfer even at low strains. This has been modeled
in terms of poorer stress transfer between the inner
graphene layers than between the polymer matrix and
the outer graphene layers.26
The present study is concerned with understanding
the mechanism behind this poor internal stress transfer within few-layer graphene. There is accumulated
evidence in the literature going back over 40 years that
basal plane slip can take place easily in graphite.4042
Early TEM studies of thin graphite “foils” showed that
extensive faulting could take place on the basal plane
of graphite giving rise to arrays of dislocation ribbons
and stacking faults.40,41 It was shown that it is favorable
energetically for full dislocations on the basal plane to
dissociate into two partial dislocations with a stacking
fault between them40 and that the separation of the
partials is typically 100 nm.41 This process takes place
without breaking the in-plane CC bonds and the
strain is accommodated by distortion of the graphene
hexagons in the vicinity of the dislocation core.
A typical stacking fault would contain a region of
rhombohedral ABC rather than hexagonal ABA stacking and the stacking fault energy on the basal plane
of graphite has been shown to be very low,42 in the
order of only 1 mJ m2. This behavior is related to the
relatively low value of c44, the elastic constant for basal
plane shear, which is thought to be only of the order of
5 GPa.42 Another parameter that gives further insight
into the ease of movement of the dislocations and their
diffuse nature is the vanishingly small value of Peierls
stress of 1017 Pa that has been calculated for a partial
basal edge dislocation in graphite.42 In a very recent
study it was shown that Raman spectroscopy could
also be used to monitor the interlayer shear mode
of few-layer graphenes.43 The position of the lowfrequency Raman band that appears at around
42 cm1 in graphite is found to be sensitive to the
number of layers in few-layer graphene and falls to
31 cm1 in bilayer material. This E2g mode Raman
band, which is not accessible using conventional
spectrometer geometries, has been termed “C”.43 Its
dependence upon the number of layer has been
explained using a linear chain model and this has
enabled the value of the elastic constant for basal
plane shear to be determined as c44 = 4.3 GPa.
electron microscopy (TEM).9,1316 Twisting and rotation of the graphene layers leads to the loss of Bernal
stacking7 and the degree of misalignment can be
evaluated from electron diffraction or Moiré patterns.
It is even possible to image the misaligned structures
using atomic resolution bright field and high angle
annular dark field TEM where good correlation is found
between the experimental and simulated images.15
Raman spectroscopy is also a very useful technique
to evaluate the stacking of the graphene layers in
few-layer material.1620 There are major differences
between the form of the 2D (or G0 ) band between
samples of graphene that are either Bernal stacked or
have twisted layers; it is relatively broad and asymmetric in Bernal stacked material and significantly
narrower and more symmetric in twisted or turbostratic stacked graphene layers. It is also possible to
distinguish between ABA Bernal-stacked or ABC rhombohedral stacked trilayer material from the form of
the 2D Raman band.18,19 Synchrotron-based infrared
absorption spectroscopy has been employed to show
that the electronic structure of mechanically exfoliated
few-layer graphene in which there is either ABA or
ABC stacking depends strongly upon the stacking
sequence.21 Scanning tunneling microscopy (STM)22
and spectroscopy are particularly useful techniques to
understand the effect of stacking upon the electronic
structure of few-layer graphene as they can simultaneously measure the local twist angle, the Fermi
velocity and the degree of interlayer coupling.23 It
has been found for CVD-grown material that the low
energy carriers start to exhibit Landau level spectra
characteristic of massless Dirac fermions for twist
angles of over about 3 and that above 20 the layers
effectively decouple with their electronic properties
becoming similar to those of single-layer graphene.23
It is well established that Raman spectroscopy is one
of the most versatile methods of both characterizing
graphene and following its deformation in nanocomposites.2426 Strong, well-defined resonance
Raman spectra are obtained even from single atomic
graphene layers and the technique can be used relatively easily to differentiate between monolayer,
bilayer, trilayer and few-layer material, from the shape
and position of the 2D (or G0 ) Raman band.2729 It is
also found that the positions of the Raman bands in
graphene shift with stress3039 and that such stressinduced Raman band shifts can be used to determine
the stress in the material and so determine its effective Young's modulus.38 These stress-induced band
shifts have been used to monitor the transfer of
stress between a polymer matrix and the graphene
reinforcement in model nanocomposites consisting
of monolayer24,25 or few-layer26 graphene flakes sandwiched between thin polymer films. The behavior of
model monolayer nanocomposites has been shown to
follow classical shear-lag behavior at low strains with
In this present study we have followed the effect of
deformation upon the 2D band in the Raman spectra of
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Figure 1. Shifts of the 2D Raman band with strain for graphene flakes in a model nanocomposite. Overall band shift for (a) the
monolayer and (b) the bilayer materials.
a number of model nanocomposites consisting of
exfoliated monolayer, bilayer, trilayer and few-layer
graphene flakes embedded in a polymer matrix on a
poly(methyl methacrylate) (PMMA) beam.26 We have
monitored the changes with strain in position and
fwhm (full width at half-maximum height) of the bands
fitted to a single peak.
The shift of the 2D band with strain for monolayer
and bilayer graphene is shown in Figure 1. It can be
seen that both bands shift to lower wavenumber and
broaden as the tensile strain is increased, with some
evidence of the band splitting for the monolayer
graphene at the higher strain levels that has been
discussed at length in the literature.35,36 Details of
the behavior are shown in Figures S1 and S2 of the
Supporting Information. The 2D band shift per unit
strain is similar for both the monolayer material,26,39
and the bilayer band, which actually consists of 4 subbands,2729 appears to undergo broadening even
when fitted to a single Lorentzian peak (Figure S2).
The fwhm (full width at half-maximum) of the 2D band
increases from 28 to 44 cm1 for the monolayer and
from 48 to 59 cm1 for the bilayer (fitted to a single
peak) up to 0.4% strain.
In contrast to the monolayer and bilayer materials,
the stress-induced 2D band shift behavior of the
trilayer and few-layer graphene in the nanocomposites
is quite different as can be seen in Figure 2. The fewlayer graphene was probably a tetralayer flake, but it is
difficult to be sure of the exact number of layers in thin
graphene flakes with more than 3 layers. In both cases
the 2D band, fitted arbitrarily to 6 peaks,28 shifts to
lower wavenumber with tensile strain and changes
shape. It can be seen from Figure 2 that the shape of
the Raman bands change markedly during deformation, becoming narrower and more symmetric at 0.4%
strain. It can also be fitted to single Lorentzian peaks,
similar to, but broader than, that of the monolayer
material in Figure 1. Moreover, when the stress is
removed, the Raman bands shift back to higher wavenumber and the shape and width of the bands revert to
those of the materials before deformation. Deformation was limited to 0.4% strain to avoid complications
from failure of the graphene/polymer interfaces seen
in our earlier studies.24,25 Details of the behavior for the
trilayer and few-layer materials are shown in Figures S3
and S4 of the Supporting Information. The 2D band
shift rate per unit strain for the specimens containing
material with more than two layers is found to be
significantly lower than that for monolayer graphene,
as has been found before,26 and the band shows considerable narrowing with tensile strain (see Supporting
Information). The fwhm for the 2D band decreases
from 71 to 67 cm1 for the trilayer and from 88 to
78 cm1 for the few-layer material (all fitted to single
Lorenztian peaks) up to 0.4% strain.
It is well established that for few-layer graphene,
Raman spectroscopy can be used to distinguish between materials in which the layers are either stacked
randomly or in regular Bernal AB stacking.1620 For
random stacking, the appearance of the 2D band
is symmetric and similar to that of the monolayer
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Figure 2. Shifts of the 2D Raman band with strain for graphene flakes in a model nanocomposite. Overall band shift for (a) the
trilayer and (b) the few-layer materials.
graphene but broadened, whereas in the case of Bernal
stacking, the bands are broad and asymmetric.17 The
clear conclusion of the behavior shown in Figure 2 is
that for both the trilayer and few-layer graphene Bernal
AB stacking is lost in the material by around 0.4%
strain but is restored on unloading the nanocomposite
specimen. Mapping of the 2D band after unloading
(Figure S7, Supporting Information) has shown a larger
scatter in the bandwidth than before deformation
implying that the Bernal stacking is not completely
regained throughout the flake.
The multilayer graphene produced by the mechanical exfoliation procedure,2 used in this present study,
generally shows Bernal stacking unless it is folded. It is
possible to visualize the differences between Bernal
and non-Bernal stacked material using transmission
electron microscopy by comparing exfoliated few-layer
graphene samples with graphene grown by chemical
vapor deposition (CVD), where non-Bernal stacking is
more commonly found, as shown in Figure 3. In the case
of the Bernal stacking shown in Figure 3a, the FFT (fast
Fourier transform) of the high resolution image shows a
single orientation of the graphene with similar atomic
arrangements being resolved in all layers. In Figure 3b,
the FFT shows that one layer is rotated relative to the
other and a characteristic Moiré pattern is found in the
region of bilayer material.1315
At this stage it is important to consider the process
that must take place on the atomic level leading to the
loss of Bernal stacking in the tri- and few-layer materials. The process is shown schematically in Figure 4 for a
Bernal stacked trilayer graphene nanocomposite. When
the polymer matrix is deformed, stress is transferred by
interfacial stress transfer to the two outer graphene
layers (both will be A-type layers) as has been found
before for monolayer and bilayer specimens. They will
become elongated in the tensile direction and narrower
in the transverse direction due to Poisson contraction.31
Stress transfer to the inner B-type layer can only take
place by shear from the two outer A-type layers. If this
does not take place efficiently, then the two A-type
outer layers will become deformed and the inner layer
will remain relatively undeformed, as shown in
Figure 4b. The consequence of this is that the Bernal
stacking will be lost. On unloading the outer layers will
revert to their original form and Bernal stacking will be
regained. It is envisaged that a similar process will also
occur for few-layer material investigated in this study.
It should be noted that the Bernal stacking is not lost in
the case of bilayer specimens as both graphene layers
have interfaces with the polymer matrix that remain
intact up to 0.4% strain.
This stress transfer in composites takes place through
shear at the interfaces between the different components24 as shown schematically for the nanocomposite in Figure 4c. Stress transfer will take place from the
polymer matrix to the outer graphene layer and this is
then transferred to the inner layers by shear between
the outer graphene layer and the next layer as indicated. It has been found in a previous study26 that
transfer between the inner graphene layers is no more
than 70% efficient, leading to a reduction in effective
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Young's modulus as the number of graphene layers is
increased above two. In addition, the shear yield stresses for stress transfer at the different graphene interfaces are known from the literature as indicated in Table 1.
It is clear from the table that the weakest interface is
that between the inner graphene layers which in graphite fail at a shear stress of only τg ∼ 30 kPa.44
Investigations upon model monolayer graphene composites have shown that the shear stress for interfacial
stress transfer between the graphene and the polymer is
of the order of τi ∼ 1 MPa.24 Studies upon the mechanical properties of glassy polymers45 have shown that
such materials have a shear yield stress of the order of τy
∼ 40 MPa so that the polymer matrix would be unlikely
to undergo yielding in this system. Hence, it would be
expected that the first interface to fail during the
deformation of the few-layer graphene nanocomposites
studied would be that between the inner graphene
The loss of Bernal stacking shown in Figure 4b leads
to the formation of a basal-plane stacking fault in the
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Figure 3. High resolution electron micrographs and associated FFTs of the images for (a) chemically exfoliated
graphene showing Bernal stacking and (b) CVD-grown
graphene showing non-Bernal stacking (the numbers indicate the different number of layers present in the different
trilayer graphene. It is shown in the Supporting Information that this occurs at around 0.4% strain. The
elastic strain energy released upon the unloading the
inner graphene layer from this strain can be readily
calculated and is found to be the order of 0.2 meV/
atom (see Supporting Information).
Telling and Heggie42 have reviewed the literature
upon stacking faults on the basal plane of graphite and
pointed out that, although the binding energy from
the van der Waals forces between the graphene layers
is of the order of 35 meV/atom, the basal plane is prone
to stacking faults and readily accommodates basal
dislocations. They showed that the stacking fault energy in graphite varies with the geometry of the fault
between as low as 0.11 meV/atom for ABC rhombohedral stacking to 9.7 meV/atom for AA simple hexagonal
stacking. In a recent study, Shibuta and Elliott46 investigated the interaction between two graphene sheets
with a turbostratic orientational relationship. They
investigated the loss of AB stacking through either
rotation or displacement of the two sheets relative to
each other and the showed that in this case the energy
gap between AB and AA stacking is only the order of
0.36 meV/atom. They also pointed out that, since this
energy is much smaller than the average thermal
energy at room temperature (kBT = 25.7 meV/atom),
the two graphene sheets will have easy rotational
and translational motion at room temperature.46 For
example, Figure 3b shows a relative rotation of two
graphene sheets that readily results from CVD growth.
It is clear therefore that the elastic energy of 0.2 meV/
atom released from the unloading of the inner graphene layer at around 0.4% strain is capable of leading
to the loss of Bernal stacking in the few-layer graphene
observed by Raman spectroscopy.
It is most likely that this loss of Bernal stacking in fewlayer graphene will not occur through affine deformation (as shown in Figure 4) but would be accommodated by the formation of arrays of partial dislocations
and stacking faults as was observed more than 50 years
ago in the case of graphite.40,41 The situation is shown
for trilayer material in Figure 5. The material with
ABA Bernal stacking before deformation is shown in
Figure 5a (the two outer A layers are assumed to
deform equally and are thus identical). Figure 5b shows
the situation during deformation with the middle
B layer unloaded and two partial dislocations in each
outer layer with a stacking fault between them. The
fault will be of the CBC type (and hence still Bernal
stacked) if identical dislocations form in both the top
and bottom layers, or of the rhombohedral CBA type if
only the top layer is deformed. The full development of
the dislocations and stacking faults is shown in Figure
S5 of the Supporting Information.
It is possible to estimate the critical size of the partial
dislocations in the few-layer material as shown in the
Supporting Information. It is found that the width of
Figure 4. Schematic illustration of the loss of Bernal stacking during the deformation of trilayer graphene in a nanocomposite: (a) undeformed structure; (b) deformed structure showing the loss of Bernal stacking through affine deformation; (c) the
shear process that take place at the different interfaces along with their values at yield or failure (the A layers are colored black
and the B layer is colored red).
TABLE 1. Values of Shear Yield Stress and Interfacial Shear
Stress for Interfacial Failure in PolymerGraphene Nanocomposites
value (MPa)
Figure 6. Transmission electron micrograph showing dislocation arrays (dislocation lines indicated by arrows) in a manylayer graphene flake prepared by mechanical cleavage.
Figure 5. Bernal stacked trilayer graphene lattice structure.
(a) undeformed material; (b) deformed structure showing
an undeformed B layer and the formation of two partial
dislocations and a stacking fault between them (the top and
bottom A layers are shown identically with the same
deformation for clarity). The left-hand side partial dislocation has edge character, and the right-hand side one is
mixed edge and screw. The top and bottom (A stacked at
edges and C stacked in stacking fault) layers are colored
black and the middle layer (B stacked) is colored red.
the partial dislocation is expected to be of the order of
40 nm and their separation is also around 35 nm. For
clarity, the dislocations shown schematically in Figure 5
have been given a width of only around 10 nm, by
imposing a sinusoidal displacement. The calculation in
the Supporting Information shows that in reality the
partial dislocations will be much broader as a result of
the low stacking fault energy and the whole area will
effectively be faulted.
There is extensive literature upon the observation
and analysis of basal plane dislocations and stacking
faults in graphite by transmission electron microscopy.
The best examples are as a result of radiation damage
where extensive arrays of basal plane stacking faults
bounded by partial dislocations are obtained.40,41 Since
in our case the dislocations and stacking faults are only
expected to be present during shear deformation, it is
difficult to observe their formation in the transmission
electron microscope. In addition, the contrast from such
defects in few-layer graphene would be very weak.
Figure 6 shows an array of dislocations and stacking
faults in a relatively thick graphene flake (>20 layers)
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In this present study we have followed the effect of deformation upon the 2D band in the Raman spectra of a number of
model nanocomposites consisting of exfoliated monolayer,
bilayer, trilayer, and few-layer graphene flakes embedded in a
polymer matrix on a poly(methyl methacrylate) (PMMA) beam.
The flakes were sandwiched between thin layers of cured SU-8
(spin-coated to ∼300 nm thick). Full details of the specimen
preparation and test procedures are given in the Supporting
Information and elsewhere.2426
The Raman spectra were excited using a 785 nm (1.59 eV)
laser with a Renishaw 2000 Raman spectrometer and obtained
from the middle of a number of different flakes on the PMMA
beam, with a laser power at the sample of <1 mW. The beam
was deformed in steps of ∼0.05 to 0.4% strain (monitored using
a resistance stain gauge fixed to the beam) and then unloaded.
Spectra were obtained from the central regions of each the
flakes being monitored at each strain level.
The high resolution TEM images in Figure 3 were obtained using
JEOL 2200MCO (S)TEM aberration corrected to third order and
operated at an accelerating voltage of 80 kV. The TEM image in
Figure 6 was obtained using a JEOL200FX TEM operated at 80 kV.
Conflict of Interest: The authors declare no competing
financial interest.
Supporting Information Available: Details of specimen preparation; full details of the dependence of the 2D band position
upon strain for monolayer, bilayer, trilayer, and few-layer
graphene; schematic illustration of straining of the trilayer
graphene lattice leading to the loss of Bernal stacking and
calculations of the energetics of formation of the dislocations
and stacking faults. This material is available free of charge via
the Internet at http://pubs.acs.org.
Acknowledgment. The authors of this work are grateful to
the Engineering and Physical Sciences Research Council for
support in the form of a Science and Innovation Award (EP/
G035954/1). One of the authors (K.S.N.) is also supported by the
Royal Society.
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It has been demonstrated that few-layer graphene
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shear deformation in nanocomposites. This behavior
leads to a reduction in the effective Young's modulus
of the graphene that has been observed as the number
of layers increases. It has been shown that the process
can take place through the formation of arrays of
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