NATURE NANOTECHNOLOGY | VOL 9 | OCTOBER 2014 | www.nature.com/naturenanotechnology 755
T
he eld of research in two-dimensional (2D) materials has
been enjoying extraordinary growth during the past dec-
ade. is activity was triggered by pioneering works on gra-
phene
1–3
, a 2D semimetallic allotrope of carbon that turned out to
be an exceptionally fertile ground for advancing frontiers of con-
densed matter physics
4–7
. e centre of interest then rapidly shied
from fundamental science to potential technological applications
of this 2D material
8–10
. Furthermore, other atomically thin mon-
olayer systems, which possess some valuable properties for many
applications, soon joined the eld, thus extending the palette of
available 2D materials. Examples include insulating monolayer hex-
agonal boron nitride (h-BN)
11
and semiconducting transition metal
dichalcogenides (TMDCs) MX
2
(M=Mo, W; X=S, Se) character-
ized by electronic bandgaps between 1.1eV and 1.9eV (refs12,13).
e diversity of 2D materials further opens the possibility for such
atomically thin crystals to be combined in complex heterostructures
by stacking them on top of each other, thus giving rise to a whole
new paradigm of nanoscale engineering
7,14–16
.
Technological applications require scalable techniques that
would produce large-area sheets beyond the micrometre-size sam-
ples of graphene used in earlier research, such as single-crystalline
graphene akes readily obtained by mechanical exfoliation of graph-
ite
1
. Statistical physics arguments, however, suggest that crystalline
order in 2D is highly susceptible to various types of uctuation and
disorder
17
, which would hinder production of high-quality single-
crystalline graphene sheets of arbitrarily large size. Practically, typi-
cal lms of graphene of wafer scale or larger size as produced by,
for example, chemical vapour deposition (CVD), are polycrystal-
line
18–20
: that is, composed of single-crystalline domains of vary-
ing lattice orientation. In polycrystalline materials, such rotational
disorder necessarily leads to the presence of grain boundaries —
interfaces between single-crystalline domains
21,22
. Grain bounda-
ries (GBs) represent a class of topological defects — imperfections
described by a structural topological invariant that does not change
upon local modications of the lattice
23
. Of course, such topologi-
cal defects, intrinsic to polycrystalline materials, inevitably aect all
properties of the material under study.
is Review discusses recent experimental advances in the
emerging eld of polycrystalline 2D materials, complemented
Polycrystalline graphene and other
two-dimensional materials
Oleg V. Yazyev
1
and Yong P. Chen
2
Graphene, a single atomic layer of graphitic carbon, has attracted intense attention because of its extraordinary properties
that make it a suitable material for a wide range of technological applications. Large-area graphene films, which are necessary
for industrial applications, are typically polycrystalline — that is, composed of single-crystalline grains of varying orientation
joined by grain boundaries. Here, we present a review of the large body of research reported in the past few years on poly-
crystalline graphene. We discuss its growth and formation, the microscopic structure of grain boundaries and their relations to
other types of topological defect such as dislocations. The Review further covers electronic transport, optical and mechanical
properties pertaining to the characterizations of grain boundaries, and applications of polycrystalline graphene. We also dis-
cuss research, still in its infancy, performed on other two-dimensional materials such as transition metal dichalcogenides, and
oer perspectives for future directions of research.
with necessary theoretical concepts. We rst cover recent progress
in observing the micrometre-scale morphology in polycrystalline
graphene as well as the atomic structure of GBs. e structure of
the latter is explained in terms of hierarchical classication of topo-
logical defects in crystalline lattices. Special attention is devoted to
peculiar behaviour of topological defects in graphene as opposed to
those in bulk crystals. Next we cover important aspects of graphene
growth by CVD for the formation of polycrystalline graphene. We
then consider electronic transport, optical, mechanical and thermal
properties, and related characterization techniques of polycrystal-
line graphene. e nal section reviews several polycrystalline 2D
materials other than graphene: monolayer h-BN, TMDCs and 2D
silica. e Review is concluded with an outlook of future directions
of research in this eld.
Structure of polycrystalline graphene
e details of the structure of polycrystalline graphene at dierent
length scales determine its properties. ese various aspects of the
structure down to atomic length scales have been investigated using
several experimental techniques.
Experimental evidence. Historically, research on polycrystalline
graphene was preceded by investigations of topological defects in
bulk graphite. e rst transmission electron microscopy (TEM)
studies of dislocations in graphite were reported in the early
1960s
24,25
. In 1966, Roscoe and omas proposed an atomistic
model of tilt GBs in graphite, which suggested that the cores of edge
dislocations are composed of pentagon–heptagon pairs
26
. is is
consistent with the structure of topological defects in polycrystal-
line monolayer graphene discussed below. Later, the interest in GB
defects in graphene was renewed with the advent of scanning tun-
nelling microscopy (STM) for investigating surfaces
27–30
. Scanning
tunnelling spectroscopy (STS) allowed the local electronic proper-
ties of these defects in graphite to be investigated in detail
31
. e
scanning probe techniques have also been used recently to explore
the possible role of GBs in the intrinsic ferromagnetism of graphite
32
.
In bulk solids, the structure of dislocations and GBs is gener-
ally dicult to access and image using current microscopy tech-
niques, as these defects are mostly buried deep inside. In contrast,
1
Institute of Theoretical Physics, Ecole Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland.
2
Department of Physics and School of
Electrical and Computer Engineering and Birck Nanotechnology Center, Purdue University, West Lafayette, Indiana 47907, USA.
e-mail: oleg.yazyev@epfl.ch; yongchen@purdue.edu
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2D materials such as graphene provide an exceptional experimen-
tal system where such structural irregularities are exposed and can
be studied in greater detail by microscopy, with resolution down
to atomic levels, and even including temporal evolution. For poly-
crystalline graphene, TEM has become one of the most powerful
and widely used tools to map out both the polycrystalline morphol-
ogy on a large scale (above the size of single-crystalline grains),
and the structural details of individual topological defects down
to atomic scale
33
. Although early TEM observation of a dislocation
in graphene was reported by Hashimoto etal.
34
in 2004, the rst
systematic investigations of GBs in polycrystalline graphene were
published only in 2011
18–20
. ese experiments were performed on
graphene grown by CVD on copper substrate
35
. Huang etal. used
diraction-ltered dark-eld (DF) TEM for large-area mapping of
the location, size, orientation and shape of several hundred grains
and grain boundaries
18
. In their study, individual crystalline orien-
tations were isolated using an aperture to select the appropriate dif-
fraction spot. e resulting images revealed an intricate patchwork
of grains connected by tilt GBs (Fig.1a–c). e grains in graphene
samples produced by Huangetal.
18
are predominantly of submicro-
metre size (Fig.1d), and GB misorientation angles show a complex
multimodal distribution (Fig. 1e). e distribution of grain sizes
and misorientation angles, however, depends strongly on the syn-
thetic protocol used for producing graphene. For instance, An etal.
reported a dierent distribution of misorientation angle, mostly
conned between 10and 30 degrees
20
.
27°27°
d
Grain size (nm)
Counts
0
0
10
10 20
30
20
30
40
Relative rotation (°)
Counts
0
20
40
60
80
Cumulative
probability (%)
0
50
100
Area (µm
2
)
10
−2
10
−1
10
0
ac
e
0.5 nm
fg
1 nm
0.5 nm
0
400 800
1,200
500 nm
b
Figure 1 | Experimental studies of polycrystalline graphene and extended defects. a, Electron diraction pattern from a sample of polycrystalline
graphene showing numerous sets of six-fold-symmetric diraction spots rotated with respect to each other. b, False-coloured dark-field TEM image
revealing individual single-crystalline graphene grains of varying shape, size and orientation. This image was constructed by aperturing the diraction
spots in a such that only the scattered electrons corresponding to one set of diraction spots (colour-coded circles in a) are used to construct the real-
space image. c, Aberration-corrected annular dark-field scanning TEM (ADF-STEM) image of a grain boundary stitching two graphene grains with lattice
orientations rotated by ~27° with respect each other. The dashed lines outline the lattice orientations of the two domains. The structural model of the
interface highlighting heptagons (red), hexagons (green) and pentagons (blue) is overlaid on the image. d,e, Distributions of grain sizes (d) and their
relative orientations (e) in samples of polycrystalline graphene investigated in ref.18. The inset shows the cumulative probability of having more than one
grain given the area. f, STM image of a regular line defect in graphene grown on Ni(111) substrate
45
. The inset shows the structural model. g, STM image
of the flower-shaped point defect in epitaxial graphene grown on SiC(0001)
48
. Inset shows the structural model. Figure reprinted with permission from:
a−e, ref.18, Nature Publishing Group; f, ref.45, Nature Publishing Group; g, ref.48, © American Physical Society.
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By using high-resolution TEM (HR-TEM), the details of atomic-
scale structure of GB defects were determined
18,19
. Many GBs
exhibited atomically sharp interface regions formed by chains of
alternating pentagons and heptagons embedded in the hexagonal
lattice of graphene (Fig.1c), in full agreement with previous theo-
retical predictions
36,37
. is structure can be understood in light of
the Read–Shockley model
38
, which views tilt GBs as arrays of edge
dislocations. Dislocations in graphene are represented by pairs of
pentagons and heptagons (disclinations), the elementary structural
topological defects in graphene. Hierarchical relations between the
above-mentioned classes of structural topological defects
23,36,37,39,40
and the denitions of their topological invariants are explained
in Box1. Importantly, this construction based on pentagonal and
heptagonal units conserves the coordination environment of all car-
bon atoms, thus automatically resulting in energetically favourable
structures. In contrast, the HR-TEM images by An etal. show the
presence of undercoordinated atoms (‘twinlike’ structures) in the
GB regions
20
, likely to be stabilized by adsorbates found in almost all
of the boundary areas. Models of GBs containing undercoordinated
carbon atoms, either with dangling bonds or forming complexes
with extrinsic adsorbates, have been investigated theoretically
41,42
.
Besides GBs involving interatomic bonds across the interface region,
Polycrystalline materials are composed of single-crystalline domains
with dierent lattice orientations. e changes of the lattice orienta-
tion are accommodated by the presence of topological defects. e
structure of such defects is described by some topological invari-
ant, a non-locally dened quantity conserved upon local structural
transformations. ere are three types of topological defect relevant
to 2D materials — disclinations, dislocations and GBs — related to
each other by hierarchical relations
23,36,39
. Importantly, in graphene
these defects can be constructed without perturbing the native
three-fold coordination sphere of sp
2
carbon atoms
36
.
Disclinations (a) are the elementary topological defects obtained
by adding a semi-innite wedge of material to, or removing it
from, an ideal 2D crystalline lattice. For 60° wedges, the result-
ing cores of positive (s=60°) and negative (s=−60°) disclinations
are pentagons (red) and heptagons (blue), respectively, embedded
into the honeycomb lattice of graphene. Wedge angle s is the top-
ological invariant of a disclination. e presence of isolated dis-
clinations in graphene is unlikely as it inevitably results in highly
non-planar structures.
Dislocations (b) are the topological defects equivalent to pairs of
complementary disclinations. e topological invariant of a dislo-
cation is the Burgers vector b, which is a proper translation vector
of the crystalline lattice. A dislocation eectively embeds a semi-
innite strip of material of width b into a 2D lattice
36
. An edge-
sharing heptagon–pentagon is a dislocation in graphene with
the smallest possible Burgers vector equal to one lattice constant
(b=(1,0)). Larger distances between disclinations result in longer
Burgers vectors, as illustrated by the b=(1,1) dislocation.
Grain boundaries (c) in 2D materials are equivalent to 1D chains
of aligned dislocations
38
. ese topological defects are the ultimate
interfaces between single-crystalline grains in polycrystalline
materials. e topological invariant of a GB in 2D is the misorien-
tation angle θ=θ
L
+θ
R
(0°<θ<60°), which is related to the density
of dislocations and their Burgers vectors b via the so-called Frank’s
equations
21
. Large dislocation density (or, equivalently, small dis-
tance between the neighbouring dislocations) corresponds to
large misorientation angles. Two examples of particularly stable
large-angle GBs (θ=21.8° and θ=32.3°) in graphene are shown.
Box 1 | Relations between dierent types of topological defect in graphene.
Disclinations Dislocations Grain boundaries
s
b
θ
L
θ
R
abc
θ = 21.8°
θ = 32.3°
b = (1,0)
b = (1,1)
s = 60°
s = −60°
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several studies have also reported weakly connected GBs formed by
‘overlapping’ individual grains: that is, with one domain grown over
the top of a neighbouring domain
43,44
.
Several examples of topologically trivial defects (that is, character-
ized by zero values of the relevant structural topological invariants)
derived from GBs in graphene deserve special attention. Lahiri etal.
reported an observation of highly regular line defects in graphene
grown on Ni(111) substrate
45
. Such a one-dimensional defect formed
by alternating octagons and pentagon pairs aligned along the zigzag
direction (Fig.1f) can be viewed as a degenerate GB as it has zero
misorientation angle. Because of its topologically trivial structure,
this defect can be engineered in a controlled way, as demonstrated
by Chen etal.
46
. Another work observed a dierent line defect in gra-
phene oriented along the armchair direction
47
. GB loops are formally
equivalent to point defects in crystal lattices. A striking example is
the highly symmetric ower-shaped defect found in graphene pro-
duced using dierent methods (Fig. 1g)
48,49
. Less-symmetric small
GB loops have also been observed in TEM studies
50–52
.
Finally, a dierent type of topological defect is possible in multi-
layer systems such as bilayer graphene. Several groups have reported
observations of boundaries between domains with structurally
equivalent AB and AC stacking orders in bilayer graphene
53–57
. ese
stacking domain boundaries observed by means of DF-TEM appear
as regions of continuous registry shi that are a few-nanometres
wide, and oen form dense networks in bilayer graphene.
Grain boundary energies and out-of-plane deformations.
Formation energies play a crucial role in determining the atomic
structure of GBs at conditions close to thermodynamic equilibrium.
is has been investigated theoretically using density functional the-
ory
36
and empirical force elds
37,58,59
. Figure2a shows the computed
GB energies γ for a number of symmetric periodic congurations
characterized by dierent values of misorientation angle θ (ref. 36).
Two scenarios can be considered here. First, GBs are constrained to
assume at morphology when strong adhesion of graphene to a sub-
strate takes place. In this case, the energetics of these defects (lled
symbols in Fig.2a) can be described by the Read–Shockley equa-
tion as for bulk materials (solid line in Fig.2a)
21,38
.e denition
of misorientation angle θ given in Box1 results in two small-angle
regimes for which the distance d between neighbouring disloca-
tions forming the GB is larger than the length of their Burgers vec-
torsb. ese regimes imply that γ decreases as d increases for θ→0°
and θ→60°, respectively. For intermediate values of θ the distance
between neighbouring dislocations is comparable to their Burgers
vectors (large-angle GBs). Importantly, this regime is characterized
by a minimum in γ(θ) (Fig.2a). e low formation energies of large-
angle GBs are explained by ecient mutual cancellation of in-plane
elastic strain elds induced by closely packed dislocations. In par-
ticular, the two regular GB congurations shown in Box1 have espe-
cially low formation energies of 0.34 and 0.28eVÅ
–1
, respectively,
according to the results of rst-principles calculations
36
.
0
0.2
0.4
0.6
0.8
1
010 20 30 40 50 60
γ (eV Å
−1
)
θ (°)
(1,0)
(1,0) + (0,1)
θ = 21.8°
θ = 32.3°
Flat
Buckled
1.2 nm
1.7 nm
b
acd
f
g
h
i
j
Climb
Glide
Complex glide
e
Buckled Flat Buckled
Figure 2 | Out-of-plane deformations and transformations of topological defects. a, Grain-boundary energies γ plotted as a function of misorientation
angle θ for symmetric defect configurations
36
. The colour of symbols reflects the Burgers vectors of constituent dislocations (red, b=(1,0) dislocations;
blue, b=(1,0)+(0,1) dislocation pairs). The low-formation-energy, large-angle grain bounadries shown in the Box1 figure, panel c are indicated by
the corresponding values of the misorientation angle (θ=21.8° and θ=32.3°). Solid and open symbols correspond to flat and buckled configurations,
respectively. Shaded areas indicate the ranges of misorientation angle in which the buckled configurations are energetically preferred over the flat ones.
Solid and dashed lines correspond to the fits assuming the Read–Shockley equation and the finite formation energy (7.5eV) of dislocations. b, Transition to
an out-of-plane corrugated state of graphene sheet produced by the presence of a b=(1,0) dislocation. c, HR-TEM image of a pair of b=(1,0) dislocations
in graphene separated by 1.2-nm glide distance and 1.7-nm climb distance. d, Filtered image revealing the apparent in-plane compression (dark) and
extension (bright). e,f, Simulated filtered images corresponding to flat (e) and buckled configurations (f). g, Lowest-energy configuration of the corrugation
produced by a pair of dislocations in relative arrangement similar to the one shown in c. Out-of-plane displacements of carbon atoms are colour-coded.
h,i, Maximum filtered HR-TEM images reveal the dislocation climb (h) and glide (i) processes. j, An observation of a complex glide process that starts
with a bond rotation event next to the dislocation core and involves an intermediate aggregate of three dislocations. The positions of dislocation cores are
indicated by red symbols. Blue boxes serve as a fixed reference. Scale bars in panels g, h, j: 1 nm. Panels c−j reprinted from ref.63, Nature Publishing Group.
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e situation of freely suspended graphene is remarkably dif-
ferent. Unlike bulk materials, the atoms of 2D graphene sheets are
allowed to displace in the third, out-of-plane dimension. e pos-
sibility of out-of-plane displacement has profound eects on the
energetics of topological defects in suspended graphene or gra-
phene weakly bound to substrates. In particular, the out-of-plane
corrugations eectively ‘screen’ the in-plane elastic elds produced
by topological defects, thus greatly reducing their formation ener-
gies
23,39
. Whereas large-angle GBs in suspended graphene are at,
the stable congurations of small-angle defects are strongly cor-
rugated (open symbols in Fig. 2a). Moreover, the out-of-plane
displacements lead to nite magnitudes of otherwise diverging
formation energies of isolated dislocations. First-principles and
empirical force-eld calculations predict formation energies of
7.5eV (ref.36) and 6.2eV (ref.60), respectively, for an isolated
b=(1,0) dislocation. Remarkably, these values are comparable to
formation energies of simple point defects in graphene, for exam-
ple the Stone–Wales defect (4.8 eV) and single-atom vacancy
(7.6eV)
61
.e corrugation prole produced by a b=(1,0) disloca-
tion appears as a prolate hillock (Fig.2b), in agreement with the
results of an STM study of dislocations in epitaxial graphene on
Ir(111) substrate
62
.
Out-of-plane deformations induced by the presence of topologi-
cal defects in graphene have been investigated using electron micros-
copy techniques
63,64
. In TEM, the corrugation elds are observed
indirectly as apparent in-plane compressive strain due to the tilting
eect of the graphene sheet. An example from ref.63 considers the
case of a pair of dislocations separated by about 2nm (Fig.2c). e
ltered image reveals the presence of an extended region of com-
pressive strain connecting the two dislocations (Fig.2d). Atomistic
simulations assuming a perfectly at graphene layer show only the
presence of two localized in-plane stress dipoles (Fig.2e), whereas
allowing for out-of-plane relaxation reproduces the experimentally
observed region of apparent compression (Fig.2f). A 3D view of the
out-of-plane deformation prole produced by a pair of dislocations
is shown in Fig.2g.
Out-of-plane corrugation can also act as an ecient mechanism
for relieving the mist strain at asymmetric GBs in graphene. In this
case, compressive strain was predicted to result in periodic ripples
along the GB defects
40,65
. Such periodic ripples have recently been
observed in a STM study of GBs on the surface of graphite
66
.
Transformations of topological defects. Understanding the trans-
formation pathways of topological defects is important for describ-
ing its plastic deformation. e motion of individual dislocations in
graphene has been observed using HR-TEM
63,67
. In accord with early
theory predictions, the two basic steps of dislocation motion — glide
and climb — are realized by means of a single C–C bond rotation
(the Stone–Wales transformation)
68,69
and removal of two carbon
atoms
69,70
, respectively. e energy barriers associated with these
processes are high enough to render them unlikely under equilib-
rium conditions. For instance, the energy barrier of a bond rotation
step was predicted to lie in the 5–10 eV range
61
. Even higher energy
barriers are expected for the sputtering of carbon atoms
71,72
. Under
TEM conditions, however, irradiation by high-energy electrons at
accelerating voltages close to the displacement threshold (80kV in
refs 63,67) promotes the above-mentioned elementary processes of
dislocation motion. In particular, both dislocation climb (Fig.2h)
and glide (Fig. 2i) have been observed. A complex glide process
with an intermediate conguration involving an aggregate of three
dislocations has also been evidenced (Fig.2j).
Transformation of large-angle (θ ≈ 30°) GBs described as nearly
continuous chains of pentagon–heptagon pairs has also been
investigated using TEM
52
. According to a simple thermodynamic
argument, one expects a GB line to evolve only in the presence of
signicant boundary curvature. Indeed, nearly straight GBs showed
uctuating transformations without any time-averaged translation
of the boundary line. In contrast, closed GB loops were shown to
shrink under the electron irradiation, leading to complete elimi-
nation of small graphene grains fully enclosed within another
single-crystalline domain.
CVD growth of polycrystalline graphene
Although there are numerous ways to produce graphene, CVD on
polycrystalline Cu foils
35
has now become the most widely used
method to synthesize high-quality, large-size monolayer graphene
lms because of its simplicity, low cost and scalability. is tech-
nique produces the largest (over a metre so far
73
) graphene sheets
that can be easily transferred to other substrates for diverse appli-
cations. e vast majority of experimental studies on GBs in gra-
phene have been performed on such CVD-grown samples. In such
a CVD growth, thermal decomposition of hydrocarbon gas (most
commonly CH
4
, mixed with Ar and H
2
) at high temperature pro-
vides the source of carbon atoms that will ultimately assemble into
graphene on the surface of Cu substrate. Details of this process are
subject to much research and are believed to involve multiple steps
and intermediates
74,75
. Single-crystalline graphene grains nucleate
around multiple spots (the nucleation centres) on the substrate,
grow in size, and as the growth proceeds, eventually merge to form
a continuous polycrystalline graphene. Its properties will be deter-
mined by the constituent grains (their size, shape, edge orientation
and other properties) and how they are merged or stitched together
(that is, the structure of GBs).
By stopping the growth before all the grains merge into a continu-
ous polycrystalline lm, single crystal grains (as well as isolated GBs
between two grains) can be obtained
35,76,77
, allowing the formation
and properties of these building blocks of polycrystalline graphene
to be studied. e polycrystallinity of the Cu foil is not a limiting
factor for single-crystalline graphene growth, as a graphene grain
can grow across GBs in Cu (Fig.3a,b). is indicates weak inter-
action between graphene and Cu surfaces with no clear epitaxial
relationship
76,77
. On the other hand, such interactions still exist, and
Cu crystal orientation can still have some inuence on the growth of
the graphene overlayer
78–83
. Imperfections (defects, GBs and surface
steps) and impurities in the Cu substrate can provide the nuclea-
tion centres for growth
79,84
. Recently, it was discovered that the pres-
ence of oxygen on the Cu surface can substantially decrease the
graphene nucleation density by passivating Cu surface active sites
(Fig.3c)
77
. Reducing the density of nucleation centres is the key to
growing large single crystals of graphene
77,85–87
. Nucleation can also
be articially started using growth seeds
76,88
.
Changing various growth parameters can control both the size
and shape of graphene grains. For instance, grain size can be tuned
by varying the growth rate
44
. Earlier studies noted that dierent
CVD growth pressures can lead to dierent grain shapes, with the
two most common being ower-shaped grains oen obtained in
low-pressure CVD
35,76
and hexagonal grains in atmospheric-pres-
sure CVD (Fig. 3a,b)
76
. e ower-like (dendritic) shape
35
, with
irregular and multifractal-like edges
35,89,90
, indicates a diusion-
limited growth mechanism. e more regular hexagonal grains
76
,
whose edges are shown to be predominantly oriented along the zig-
zag directions of graphene lattice
76,91
, represent an edge-attachment-
limited growth
77
. Hydrogen plays an important role by serving as an
activator of the surface-bound carbon needed in graphene growth
as well as an etching reagent that controls the size and morphol-
ogy of the graphene grains
92
. e shape and size of the grains can
be continuously tuned by hydrogen partial pressure (Fig.3d,e)
90,92
.
Oxygen also accelerates graphene grain growth and shis the
growth kinetics from edge-attachment-limited (hexagonal-shaped
grains) to diusion-limited (dendritic-shaped grains) by reducing
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