crystals
Article
A Scheme for the Growth of Graphene Sheets
Embedded with Nanocones
Yu-Peng Liu 1,2 , Jing-Tian Li 1,2 , Quan Song 1,2 , Jun Zhuang 3 and Xi-Jing Ning 1,2, *
1
2
3
*
Institute of Modern Physics, Fudan University, Shanghai 200433, China; [email protected] (Y.-P.L.);
[email protected] (J.-T.L.); [email protected] (Q.S.)
Applied Ion Beam Physics Laboratory, Fudan University, Shanghai 200433, China
Department of Optical Science and Engineering, Fudan University, Shanghai 200433, China;
[email protected]
Correspondence: [email protected]; Tel.: +86-21-65643119; Fax: +86-21-65642787
Academic Editor: Hiroki Nada
Received: 16 November 2016; Accepted: 18 January 2017; Published: 15 February 2017
Abstract: Based on the monolayer growth mode of graphene sheets (2D crystal) by chemical vapor
deposition (CVD) on a Cu surface, it should be possible to grow the 2D crystal embedded with single
wall carbon nanocones (SWCNC) if nano-conical pits are pre-fabricated on the surface. However,
a previous experiment showed that the growing graphene sheet can cross grain boundaries without
bending, which seems to invalidate this route for growing SWCNCs. The criterion of Gibbs free
energy was applied in the present work to address this issue, showing that the sheet can grow into
the valley of a boundary if the boundary has a slope instead of a quarter-turn shape, and SWCNCs
can be obtained by this route as long as the lower diameter of the pre-fabricated pit is larger than
1.6 nm and the deposition temperature is higher than 750 K.
Keywords: graphene; carbon nanocones; molecular dynamics simulation
1. Introduction
As a 2D crystal, graphene has vast applications. It would be highly interesting if single wall carbon
nanocones (SWCNCs) can be growth in graphene sheets since SWCNCs also have many extraordinary
properties. Theoretical studies show that SWCNCs have good mechanical properties [1], a strong
ability for electronic emission [2,3], heat flux rectification [4], and an electrical rectification effect [5].
Molecular dynamics (MD) simulations indicated that SWCNCs are stable even at 1500 K [6], and
our previous work employing a statistical model showed that the cones can survive for 107 years at
room temperature [7], which makes them potential candidates for future nanoscale devices. However,
it remains a challenge to prepare SWCNCs without elaborately tailoring graphene sheets [7]. In the
present work, we explored approaches to grow graphene sheets with desired structures, such as
SWCNCs, carbon nanotubes, or cubic boxes, embedded in the sheets.
Recently, the chemical vapor deposition (CVD) method has been proven to be the most powerful
approach to grow large-scale high-quality monolayer graphene [8], and the sheets are usually grown
on a Cu substrate. Because of the low catalytic reactivity for dehydrogenation on top of graphene and
the negligible carbon solubility in Cu, a graphene sheet with monolayer thickness grows larger and
larger on the surface of a Cu substrate. Thus, if we pre-fabricated some nano-scale pits with conical or
cylindrical shapes on the surface of a Cu substrate by physical or chemical methods (such as highly
focused electron beam bombardment), then the growing sheet might occupy the pits and finally form
some 3D structures embedded in the sheet. However, this seems impossible because of an experimental
observation that the graphene sheet can grow continuously over grain boundaries without bending [9].
Crystals 2017, 7, 35; doi:10.3390/cryst7020035
www.mdpi.com/journal/crystals
Crystals 2017, 7, 35
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In
performed MD
MDsimulations
simulationsofofthe
thegrowth
growthofofa amonolayer
monolayer
graphene
sheet
Inthis
this work,
work, we
we first
first performed
graphene
sheet
on
on
the
grain
boundaries
of
a
Cu
substrate,
showing
that
on
the
quarter-turn
boundary
of
a
Cu
crystal
the grain boundaries of a Cu substrate, showing that on the quarter-turn boundary of a Cu crystal grain,
grain,
the graphene
sheet always
a flat structure,
which
whycan
thegrow
sheet
can grow
the graphene
sheet always
maintainmaintain
a flat structure,
which is why
the is
sheet
continuously
continuously
across
the
grain
boundaries
[9].
However,
if
the
quarter-turn
boundary
is
replaced
with
across the grain boundaries [9]. However, if the quarter-turn boundary is replaced with a slope,
the
asimulations
slope, the simulations
show
that
the
structure
is
a
bent
sheet
which
is
stuck
to
the
surface.
Because
show that the structure is a bent sheet which is stuck to the surface. Because MD simulation
MD
only
cover
very short
timethe
period
(<1 of
μs),
the criterion
of Gibbs
energy
can simulation
only cover acan
very
short
timea period
(<1 µs),
criterion
Gibbs
free energy
(GFE) free
was applied
(GFE)
was
applied
to
address
this
issue,
showing
that
the
bent
graphene
sheets
are
of
lower
GFE
to address this issue, showing that the bent graphene sheets are of lower GFE on a slope than on on
the
aflat
slope
than
on
the
flat
surfaces,
indicating
that
the
bent
graphene
sheet
can
be
obtained
on
the
sloped
surfaces, indicating that the bent graphene sheet can be obtained on the sloped boundary. On this
boundary.
On criterion
this basis,
GFE to
criterion
applied tofor
explore
thegraphene
conditions
forembedded
growing
basis, the GFE
wasthe
applied
explorewas
the conditions
growing
sheets
graphene
sheets
embedded
with
nano-conical
structures
by
pre-fabricating
conical
pits
on
the
surface
with nano-conical structures by pre-fabricating conical pits on the surface of Cu substrates, showing
of
CuSWCNCs
substrates,
showing
that SWCNCs
with
angles
larger
canlower
be achieved
as
that
with
cone angles
larger than
90◦ cone
can be
achieved
as than
long 90°
as the
diameterasoflong
the pit
the
lower
diameter
of
the
pit
is
larger
than
1.6
nm
and
the
growth
temperature
is
higher
than
750
K.
is larger than 1.6 nm and the growth temperature is higher than 750 K.
2.2.Growth
Growthon
onthe
theCu
CuGrain
GrainBoundaries
Boundaries
Regarding
surfaces
should
be be
of of
a
Regarding atomistic
atomisticsizes,
sizes,most
mostcrystal
crystalgrain
grainboundaries
boundariesononmetal
metal
surfaces
should
quarter-turn
shape,
asas
shown
inin
Figure
a quarter-turn
shape,
shown
Figure1.1.Therefore,
Therefore,we
weperformed
performedMD
MDsimulations
simulationson
onthe
therelaxation
relaxation
of
a
piece
of
graphene
sheet
initially
stuck
to
a
quarter-turn
boundary.
Specifically,
a
Cu
substrate
of a piece of graphene sheet initially stuck to a quarter-turn boundary. Specifically, a Cu substrateof
of
nine
nineatomic
atomiclayers
layerswith
with(111)
(111)surfaces
surfaceswas
wasconstructed
constructedaccording
accordingto
tothe
thelattice
latticeconstant
constant3.615
3.615Å,
Å,and
and
the
graphenesheet
sheetcontaining
containing290
290carbon
carbon
atoms
placed
quarter-turn
boundary
the motion
motion of
of aa graphene
atoms
placed
on on
thethe
quarter-turn
boundary
was
was
simulated
by
MD.
In
the
simulation,
the
carbon
atoms
of
the
left-most
two
rows
as
well
as
all
simulated by MD. In the simulation, the carbon atoms of the left-most two rows as well as all thethe
Cu
Cu
atoms
were
fixed,
periodic
conditions
applied
the Y-direction.
Throughout
this
atoms
were
fixed,
andand
the the
periodic
conditions
werewere
applied
in theinY-direction.
Throughout
this work,
work,
the standard
algorithm
was to
used
to integrate
the Newton
equation
timeof
step
the standard
VerletVerlet
algorithm
was used
integrate
the Newton
equation
with awith
timea step
0.2of
fs,
0.2
fs,
and
the
interactions
between
C-C
and
Cu-Cu
were
described
by
the
Brenner
function
[10]
and
and the interactions between C-C and Cu-Cu were described by the Brenner function [10] and the
the
tight-binding
potential
respectively,
the interaction
C atoms
and Cu
atoms
was
tight-binding
potential
[11], [11],
respectively,
while while
the interaction
betweenbetween
C and Cu
was
described
described
by the Lennard-Jones
(L-J) [12].
potential [12].
by the Lennard-Jones
(L-J) potential
Figure
Figure1.1. Schematic
Schematicofofaagrain
grainboundary
boundarywith
withaaquarter-turn
quarter-turnshape
shapecovered
coveredby
byaapiece
pieceof
ofgraphene
graphene
sheet
sheetcontaining
containing290
290CCatoms.
atoms.
Considering that the temperature for graphene growth by CVD is about 1200 K, the C atoms,
Considering that the temperature for graphene growth by CVD is about 1200 K, the C atoms,
except for the ones of the left-most two rows (the yellow balls in Figure 1), were initially assigned
except for the ones of the left-most two rows (the yellow balls in Figure 1), were initially assigned
velocities of Maxwell distribution at 1200 K, and were then allowed to relax freely. After about 50 ps,
velocities of Maxwell distribution at 1200 K, and were then allowed to relax freely. After about 50 ps,
the bent graphene sheet became flat with a little vibration. The initial temperature has little effect on
the bent graphene sheet became flat with a little vibration. The initial temperature has little effect
the process. For example, when the mobile C atoms were initially assigned velocities of Maxwell
on the process. For example, when the mobile C atoms were initially assigned velocities of Maxwell
distribution at 300 K, the bent sheet also turned into a flat structure in about 50 ps. However, things
distribution at 300 K, the bent sheet also turned into a flat structure in about 50 ps. However, things
changed when the quarter-turn boundary was replaced with a slope of bent angles of◦15°,◦ 30°, and◦
changed when the quarter-turn boundary was replaced with a slope of bent angles of 15 , 30 , and 45 ,
45°,
as shown in Figure 2. After the mobile C atoms were assigned the velocities of Maxwell
as shown in Figure 2. After the mobile C atoms were assigned the velocities of Maxwell distribution
distribution
at 1200 K, the graphene sheet kept the curved shape until the end of the MD simulation,
at 1200 K, the graphene sheet kept the curved shape until the end of the MD simulation, at 200 ps.
at
200 ps. Nevertheless, we do not know what will happen if the MD simulation can cover a period
of more than 1 s, so we have to apply the criterion of GFE to approach this problem.
Crystals 2017, 7, 35
3 of 6
Nevertheless, we do not know what will happen if the MD simulation can cover a period of more than
3 of 7
1 s, so we have to apply the criterion of GFE to approach this problem.
Crystals 2017, 7, 35
Figure 2. The structure of a piece of graphene sheet consisting of 290 C atoms on different slopes of the
Figure 2. The structure of a piece of graphene sheet consisting of 290 C atoms on different slopes of
grain boundary after 200 ps relaxation at 1200 K.
the grain boundary after 200 ps relaxation at 1200 K.
For zero
zero pressure,
pressure, the
the GFE
GFE is
is
For
G = U − TS,
(1)
G = U − TS,
(1)
where U is the internal energy, and the entropy S is calculated by
where U is the internal energy, and the entropy S is calculated by
Z T
Cp
S=
dT,
(2)
S=
S0 + +
dT,
(2)
T0 T
was
where S is the entropy for T =0.01 K, and was neglected in this work. The heat capacity
where S0 is the entropy for T0 = 0.01 K, and was neglected in this work. The heat capacity CP was
calculated
by
= dE/dT, where the internal energy E as the function of temperature T was obtained
calculated by C p = dE/dT, where the internal energy E as the function of temperature T was obtained
by MD simulations. Specifically, the mobile C atoms of the graphene sheet of 290 atoms were first
by MD simulations. Specifically, the mobile C atoms of the graphene sheet of 290 atoms were first
cooled below 0.01 K, and were then assigned velocities of the Maxwell velocity distribution at the
cooled below 0.01 K, and were then assigned velocities of the Maxwell velocity distribution at the
temperature T every 0.1 ps until the system reached the prescribed temperature T. Then the system
temperature T every 0.1 ps until the system reached the prescribed temperature T. Then the system was
was allowed to relax freely for about 2 ps, during which the internal energy and temperature was
allowed to relax freely for about 2 ps, during which the internal energy and temperature was recorded
recorded every 20 fs to produce the average value. Setting the temperature T from 10 K–40 K with an
every 20 fs to produce the average value. Setting the temperature T from 10 K–40 K with an interval of
interval of 10 K, we obtained the relationship between the internal energy and temperature. The
10 K, we obtained the relationship between the internal energy and temperature. The obtained GFE
obtained GFE of the graphene sheets stuck on the slopes of different angles are shown in Figure 3a,
of the graphene sheets stuck on the slopes of different angles are shown in Figure 3a, where the GFE
where the GFE of a flat sheet on a quarter-turn boundary is also presented, indicating that the GFE
of a flat sheet on a quarter-turn boundary is also presented, indicating that the GFE of the curved
of the curved graphene on the slopes is significantly smaller than the flat graphene on the
graphene on the slopes is significantly smaller than the flat graphene on the quarter-turn boundary,
quarter-turn boundary, and the smaller the slope angle, the smaller the GFE. For a given slope, the
and the smaller the slope angle, the smaller the GFE. For a given slope, the GFE of the flat sheet (G f )
GFE of the flat sheet ( ) is significantly larger than for the bent sheet ( ) if the slope angle
is smaller
is significantly larger than for the bent sheet (Gb ) if the slope angle is smaller than 60◦ (Figure 3b),
than 60° (Figure 3b), indicating that in the process of graphene growth on the Cu surface by CVD, the
indicating that in the process of graphene growth on the Cu surface by CVD, the sheet would stick to
sheet would stick to the surface of the slopes to form a bent structure as long as the angle
is smaller
the surface of the slopes to form a bent structure as long as the angle is smaller than 60◦ , and an angle
than ◦60°, and an angle of 30° should be favorable for growth of the bent sheet.
of 30 should be favorable for growth of the bent sheet.
Crystals 2017, 7, 35
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Figure 3. (a) The GFE of a piece of graphene sheet on boundaries of different slopes as a function of
Figure 3.the
(a)temperature,
The GFE ofand
a piece
of graphene sheet on boundaries
of different slopes as a function of the
(b) the difference defined as -
for a given slope.
temperature, and (b) the difference defined as G f − Gb for a given slope.
3. SWCNC Growth by CVD Methods
3. SWCNC Growth
by
CVD
Methods
Figure on
3. (a)
GFE of
a in
piece
graphenesection,
sheet onitboundaries
of different
slopes
as a function
of
Based
theThe
discussion
theofprevious
is not impossible
to grow
SWCNCs
embedded
the temperature, and (b) the difference defined as
-
for a given slope.
in graphene sheets by pre-fabricating conical pits on the surface of Cu substrates, and it is necessary
Based
on the discussion in the previous section, it is not impossible to grow SWCNCs embedded
to explore the specific conditions for growth. MD simulation seems to be an ideal method to display
in graphene
sheetsprocess
by pre-fabricating
conical
pitsunder
on the
surface
of Cu
substrates,
and on
it is
3. SWCNC
Growth
by CVD
Methods
the
growth
and
therefore
can
determine
what
conditions
SWCNCs
may grow
Cunecessary
to explore
theBased
specific
growth.
MD
simulation
seems
togrow
be an
method
to display
substrates.
However,
the realistic
rate
of graphene
CVD
is too
slow
forideal
MD to
simulate,
on theconditions
discussion
infor
thegrowth
previous
section,
it is not by
impossible
to
SWCNCs
embedded
and
we havesheets
to resort
to the GFE
that
forsurface
an isobaric
such
as itCVD
growth,
the growth
process
and
therefore
cancriterion
determine
under
what
conditions
SWCNCs
grow on Cu
in graphene
by pre-fabricating
conical
pitsstates
on the
of Cuprocess,
substrates,
and
is may
necessary
the
system
tends
to a realistic
structure
of
lower
GFE.
we calculated
GFE
ofslow
amethod
piecefor
ofto
graphene
to explore
the
specific
conditions
for growth.
MD
simulation
seems
to the
be is
an
ideal
display
substrates.
However,
the
growth
rateTherefore,
of graphene
by CVD
too
MD
to simulate,
sheet
crossing
over aand
pit therefore
on the surface
(Figure 4a),
or bending
into the pit
(Figure may
4b), to
see on
which
the
growth
process
can
determine
under
what
conditions
SWCNCs
grow
and we have to resort to the GFE criterion that states for an isobaric process, such as CVD Cu
growth, the
geometry
of smallerthe
GFE.
substrates.isHowever,
realistic growth rate of graphene by CVD is too slow for MD to simulate,
system tends to a structure of lower GFE. Therefore, we calculated the GFE of a piece of graphene
and we have to resort to the GFE criterion that states for an isobaric process, such as CVD growth,
sheet crossing
over
a pit
the surface
(Figure
4a), or we
bending
into
to see which
the system
tends
to aon
structure
of lower
GFE. Therefore,
calculated
thethe
GFEpit
of a(Figure
piece of 4b),
graphene
geometrysheet
is ofcrossing
smaller
GFE.
over
a pit on the surface (Figure 4a), or bending into the pit (Figure 4b), to see which
geometry is of smaller GFE.
Figure 4. (a) Schematic of a piece of flat graphene sheet covering half of a conical pit with an angle of
90°; or (b) the sheet bending into the pit.
A technique of time-going-backwards [13,14] in the MD simulation was employed to obtain the
probable
structure
of a piece
graphene
sheet bent
into
the pithalf
(Figure
4b). Specifically,
a graphene
Figure
4. (a) Schematic
of aof
piece
of flat graphene
sheet
covering
of a conical
pit with an angle
of
Figure
4. (a)
Schematic
ofCa piece
ofwas
flat initially
graphene
sheetover
covering
half of
a with
conical
pit with
anslope
angle of
sheet
containing
176
atoms
placed
a
conical
pit
a
45°
angle
90°; or (b) the sheet bending into the pit.
90◦ ; (Figure
or (b) the
bending into
pit. angle of 90°, and then the C atoms of the leftmost two rows
4a),sheet
corresponding
to a the
conical
and all
the Cu atoms
were kept fixed while
the Newton’s
forwas
theemployed
other mobile
C atoms
A technique
of time-going-backwards
[13,14]
in the MDequations
simulation
to obtain
the
were
integrated
byofa anegative
step
of −0.2
fs, during
which
every
mobile
C atom was aassigned
a
probable
structure
piece
of
graphene
sheet
bent
into
the
pit
(Figure
4b).
Specifically,
graphene
A technique of time-going-backwards [13,14] in the MD simulation was employed to obtain
the
velocity
every 0.16176
ps by
sheet containing
C atoms was initially placed over a conical pit with a 45° angle slope
probable structure of a piece of graphene sheet bent into the pit (Figure 4b). Specifically, a graphene
(Figure 4a), corresponding to a conical
then
) /(1
− the
) / C ,atoms of the ◦leftmost two rows
= angle
− of/90°,(and
(3)
sheet containing
176
atoms
was
initially
placed
a conical
pit for
with
45 angle
(Figure 4a),
and all the
CuCatoms
were
kept
fixed while
the over
Newton’s
equations
theaother
mobileslope
C atoms
◦
(
)
are
the
present
velocity
of
atom
i
and
the
velocity
randomly
chosen
from
the
and
where
corresponding
to a conical
of step
90 ,ofand
the Cwhich
atomsevery
of the
leftmost
two
and aall the Cu
were integrated
by a angle
negative
−0.2then
fs, during
mobile
C atom
wasrows
assigned
Maxwell
distribution
respectively,
while
isfor
a random
number
(1 C atoms
1). In this
process,
velocity
psat
by300
atoms were
keptevery
fixed0.16
while
theK,Newton’s
equations
the other
mobile
were
integrated by
the temperature increased step by step, and when
the temperature/ increased to 4000 K, the Newton’s
/
(
)
a negative
step
of
−
0.2
fs,
during
which
every
mobile
C
atom
was
assigned
a
velocity
every
/(1 − )
=
−
,
(3)0.16 ps by
equations were integrated by a positive step of 0.2 fs and the mobile C atoms were assigned a velocity
every
ps by ( ) are the presenth velocity of atom iiand the velocity randomly chosen from the
where0.16 and
0
1/2 T
(1 − θnumber
)1/2 , (1
(3)
Maxwell distribution at 300 K,vrespectively,
random
1). In this process,
i = vi − θwhilev ( ξis)a /
the temperature increased step by step, and when the temperature increased to 4000 K, the Newton’s
integrated by a positive step of 0.2 fs and the mobile C atoms were assigned a velocity
where v0i equations
and v T (were
ξ ) are
the present velocity of atom i and the velocity randomly chosen from the
every 0.16 ps by
Maxwell distribution at 300 K, respectively, while θ is a random number (1 < θ < 1). In this process,
the temperature increased step by step, and when the temperature increased to 4000 K, the Newton’s
equations were integrated by a positive step of 0.2 fs and the mobile C atoms were assigned a velocity
every 0.16 ps by
vi = (1 − θ )1/2 v0i + θ 1/2 v T (ξ )
(4)
Crystals 2017, 7, 35
5 of 7
Crystals 2017, 7, 35
= (1 − )
/
+
/
( )
5 of 6
(4)
When
about
300300
K, we
cooled
the system
downdown
to 0.01toK0.01
by aKdamping
When the
thesystem
systemarrived
arrivedatat
about
K, we
cooled
the system
by a damping
method
[13],
and
recorded
the
geometrical
structure
as
well
as
the
potential
energy.
method [13], and recorded the geometrical structure as well as the potential energy.
The
aboveheating
heatingand
and
cooling
cycle
100 times
forofeach
of the pits
conical
with
lower
The above
cooling
cycle
ran ran
100 times
for each
the conical
withpits
lower
diameters
diameters
of
1.2,
1.6
or
2.0
nm,
producing
100
geometrical
structures
for
each
pit.
As
listed
in
of 1.2, 1.6 or 2.0 nm, producing 100 geometrical structures for each pit. As listed in Table 1, among
Table
1, configurations
among the 100there
configurations
there5 are
41, 25 and
5 structures
extending
the pitsof
with
the 100
are 41, 25 and
structures
extending
into the
pits withinto
diameters
2.0,
diameters
of
2.0,
1.6,
and
1.2
nm,
respectively,
indicating
that
the
larger
pits
are
more
favorable
to
the
1.6, and 1.2 nm, respectively, indicating that the larger pits are more favorable to the growth of the
growth
of the bent
structures.
potential
energy ofstructures
the resultant
structures
the range
of
bent structures.
The
potential The
energy
of the resultant
changes
in thechanges
range ofin30–40
eV, and
30–40
eV,the
and
some
of the bent
have lower
potential
butimplying
others do
not,
implying
the
some of
bent
structures
havestructures
lower potential
but others
do not,
that
the
potentialthat
energy
potential
energy
is
insufficient
to
judge
the
dynamic
probability
for
growth
of
the
bent
structure.
is insufficient to judge the dynamic probability for growth of the bent structure.
Table
Table 1.
1. Number
Number of
of bent
bent structures
structures appearing
appearing in
in 100
100 rounds
rounds of
of heating
heating and
and cooling
cooling cycles.
cycles.
Substrate
Substrate
2
2
44
2626
Diameter of Pit Bottom (nm)
Diameter of Pit Bottom (nm)
2.0
2.0
1.6
1.6
1.2
1.2
Number of Bent Structures
Number of Bent Structures
41
41
25 25
5 5
We calculated the GFE of the above bent structures (G ) and of the flat structure (G ) with the
calculated
the GFE
the above bent
structures
(Gb )that
andthe
of the
flatthe
structure
(Gof
the
sameWe
number
of C atoms.
Theofcalculations
showed,
generally,
lower
potential
the bent
f ) with
same number
of C atoms.
The So
calculations
showed,
generally,
that the with
lowerlower
the potential
ofenergies
the bent
structure,
the lower
the GFE.
only the GFE
of the
bent structures
potential
structure,
lower the
GFE.
GFE of
the bentofstructures
with bent
lowerstructures
potential of
energies
need
to bethe
inspected.
For
the So
pit only
withthe
a lower
diameter
2.0 nm, three
lower
need to be
inspected.
For
withS3
a are
lower
diameter
2.0in
nm,
three5a,bent
structures
of lower
potential
energy
denoted
bythe
S1,pit
S2 and
shown
in the of
inset
Figure
where
the temperature
potential energy
denoted
by S1, S2 ΔG
and=S3G are
in the inset
Figure
5a,structures.
where the Below
temperature
dependence
of the
GFE difference,
− shown
G , is presented
forineach
of the
room
dependence ofthe
the GFE
GFE difference,
=G
− Gb , is presented
forthan
each the
of the
structures.
Belowasroom
temperatures,
of the flat ∆G
sheet
isf significantly
smaller
bent
sheets, while
the
temperatures,
the GFEabove
of the
flat
is significantly
smaller S1
than
the
bent sheets,
while
as the
temperature
increases
470
K,sheet
the GFE
of the bent structure
gets
smaller
than the
flat sheets.
temperature
increases
above 470
the GFE
bent structure
S1 gets
than the
flat sheets.
Among
the three
structures,
theK,GFE
of S1ofisthe
significantly
lower
thansmaller
the others
in the
entire
Among the three
structures,
theso
GFE
of S1 is1200
significantly
lower
than the
others in the
entire
temperature
temperature
range
(0–1200 K),
at about
K, the CVD
growth
of graphene
on Cu
surface
should
range (0–1200
K), so atFor
about
K, theaCVD
growth
of graphene
on Cu
should probably
be
probably
be formed.
the1200
pit with
lower
diameter
of 1.6 nm,
twosurface
bent structures
of lower
formed.
For
the
pit
with
a
lower
diameter
of
1.6
nm,
two
bent
structures
of
lower
potential
energy,
potential energy, denoted by C1 and C2 in Figure 5b, have GFEs smaller than the flat structures when
denoted
by C1 and
C2 in Figure
5b, have
GFEsofsmaller
than the flatsmaller
structures
when
the temperature
temperature
the
temperature
is above
950 K, and
the GFE
C1 is significantly
in the
entire
is
above
950
K,
and
the
GFE
of
C1
is
significantly
smaller
in
the
entire
temperature
range.
Therefore,
range. Therefore, the bent structure C1 would be more probable in the CVD growth. However,
for
the pit
bent
structure
C1diameter
would be
probable
in the
CVD
However,
the pit
withthan
a lower
the
with
a lower
ofmore
1.2 nm,
the GFEs
of all
the growth.
bent structures
arefor
always
larger
the
diameter
of 1.2innm,
GFEs of allrange
the bent
structures
are
always larger
than
thestructures
flat structures
in the
flat
structures
thethe
temperature
from
0–1200 K,
implying
that the
bent
can not
be
temperature
range
from
0–1200
K,
implying
that
the
bent
structures
can
not
be
formed
in
this
pit.
formed in this pit.
Figure
∆G =
Figure 5.
5. (a)
(a) Temperature
Temperature dependence
dependence of
of the
the GFE
GFE difference
difference ∆G
= G f−− Gb for
for structures
structures S1,
S1, S2
S2 and
and
S3
bent
into
the
pit
with
a
lower
diameter
of
2.0
nm,
and
(b)
for
structure
C1
and
C2
bent
into
S3 bent into the pit with a lower diameter of 2.0 nm, and (b) for structure C1 and C2 bent into the
the pit
pit
with
with aa lower
lower diameter
diameter of
of 1.6
1.6 nm.
nm.
Crystals 2017, 7, 35
6 of 6
4. Conclusions
Based on the GFE criterion, it is shown that single wall carbon nanocones embedded in single
layer graphene sheets can be obtained by CVD on a Cu surface with pre-existing conical pits. For a 90◦
conical angle, the growth requires that the lower diameter of the pit must be larger than 1.6 nm and
the temperature of the substrate should be higher than 750 K, which is below the temperature required
for the CVD growth of graphene. Certainly, it is necessary to understand the dynamics of how the
carbon atoms move into the pit to form the nanocone, but the process is too slow to be simulated by
MD, so the specific pathway or mechanism for the nanocone growth and the exact structures of the
bent sheet still escape prediction.
Acknowledgments: This work was supported by Specialized Research Fund for the Doctoral Program of Higher
Education under Grant No. 20130071110018 and the National Natural Science Foundation of China under
Grant No. 11274073.
Author Contributions: Yu-Peng Liu performed the simulation and prepared the manuscript. Jing-Tian Li and
Quan Song edited the manuscript. All authors contributed to the discussions. Xi-Jing Ning designed and
supervised this project.
Conflicts of Interest: The authors declare no conflict of interest.
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