ISSN 1063?7834, Physics of the Solid State, 2011, Vol. 53, No. 9, pp. 1952–1956. © Pleiades Publishing, Ltd., 2011.
Original Russian Text © A.V. Fedorov, A.Yu. Varykhalov, A.M. Dobrotvorskii, A.G. Chikina, V.K. Adamchuk, D.Yu. Usachov, 2011, published in Fizika Tverdogo Tela, 2011,
Vol. 53, No. 9, pp. 1850–1854.
Graphene, as the two?dimensional carbon mono?
layer, has attracted wide?range interest due to its
promising application in nanoelectronic devices .
The transport characteristics of graphene defining the
possibility of building such devices depend on the
electron bandstructure of graphene and the quality of
its crystal lattice. The electronic structure is strongly
correlated with the crystal structure, therefore knowl?
edge of topographic characteristics is an aspect with?
out which one can hardly hope to understand the pro?
cesses underlying formation of the energy bands.
Indeed, the lattice mismatch between graphene and
the Ir(111) substrate leads to gap formation in the
Dirac cone in the vicinity of the graphene Fermi level
. The crystal structure of such graphene exhibits
superperiodicity, which can be demonstrated by scan?
ning tunneling microscopy (STM) [2, 3]. As a result of
lattice mismatch, the local atomic environment of
carbon atoms varies periodically to produce the so?
called Moire pattern observed by STM on substrates of
Ir(111) [2–5], Pt(111) [6, 7], 6H?SiC(0001) ,
Ru(111) [9–12], Ni(110) [13–15], graphite  etc,
as well as on intercalated graphene [17, 18]. A partic?
ular case is the Ni(111) substrate whose lattice param?
eters approach most closely those of graphene, with
the results that one can grow a (1 × 1) structure in the
graphene/Ni(111) system, with no Moire structure
present, as a rule. For the other nickel surfaces, the lat?
tice mismatch leads to graphene corrugation which is
accompanied by the appearance of Moire patterns in
STM images . The present work reports on an
experimental and theoretical study of the structure of
graphene on the Ni(110) surface and analysis of
graphene Moire patterns in STM images of this sys?
tem. A theoretical calculation performed for graphene
clusters of different sizes on the nickel surface has per?
mitted certain inferences on the mechanisms involved
in graphene layer formation, which affect the orienta?
tion angle of graphene relative to nickel crystal struc?
The evolvement of the Moire structure in STM
images should be assigned to the high sensitivity of this
method to variation of the local density of graphene
electronic states caused by variation of the position of
a carbon atom relative to substrate atoms along the
surface . One should not overlook also the possi?
bility of a lateral variation of the graphene work func?
tion . A theoretical description of this electronic
effect requires calculation of the electronic structure
of the system, with subsequent simulation of STM
measurements. An analysis of STM images for incom?
mensurate systems is complex problem due to theoret?
ical calculation in this case is hard?realizing in prac?
tice. This is why to achieve the simplest possible
description of the Moire pattern one resorts quite fre?
quently to superposition of the crystal structures of the
adsorbate and the substrate, by visualizing the lattice
with spheres or sections of straight line [6, 17]. In the
case of graphene grown on (111) surfaces of fcc crys?
tals, this construction provides a graphic idea of for?
mation of the Moire structure observed in the form of
a lateral variation of the local concentration of atoms.
In the case of a substrate with a rectangular lattice,
which can be exemplified by Ni(110), the efficiency of
this approach turns out fairly low and not suitable for
Structure of Graphene on the Ni(110) Surface
A. V. Fedorova, *, A. Yu. Varykhalovb, A. M. Dobrotvorskiia,
A. G. Chikinaa, V. K. Adamchuka, and D. Yu. Usachova
a St. Petersburg State University, Universitetskaya nab. 7–9, St. Petersburg, 199034 Russia
* e?mail: email@example.com
b Helmholtz?Zentrum Berlin fur Materialien und Energie, Elektronenspeicherring BESSY II,
Glienicker Str. 100, Berlin, 14109 Germany
Received February 16, 2011
Abstract—The structure of graphene on Ni(110) was studied using scanning tunneling microscopy (STM)
and low?energy electron diffraction spectroscopy. STM images show a Moire structure, depending on the ori?
entation of the domains making up the graphene layer. A simple model has been proposed which permits pre?
diction of the Moire structure and interpretation of STM images based on calculation of the distances
between the nearest neighbor carbon and nickel atoms. Our theoretical calculation suggests that the final ori?
entation of graphene domains forming in the course of synthesis is defined by the angle of rotation of small
clusters in the initial stages of growth.
PHYSICS OF THE SOLID STATE
Vol. 53 No. 9 2011
STRUCTURE OF GRAPHENE ON THE Ni(110) SURFACE 1953
identification of the specific features of STM images.
Theoretical calculation of this crystal structure 
likewise cannot offer a reasonable interpretation of the
observed Moire patterns. We are going to present here
a simple model making it possible to predict the Moire
structure by calculating the variation of the distance
separating a carbon atom from the nearest nickel
atom. Application of this model has provided interpre?
tation of the STM images of the graphene/Ni(110)
2. EXPERIMENTAL CONDITIONS
The pure nickel surface was prepared by alternately
ion beam etching with flash annealing at a tempera?
ture of 700°C in ultrahigh vacuum. The graphene was
prepared by cracking of propylene C3H6 at 500°C, a
gas pressure of 10–6 mbar and exposure time of 10 min.
The system was studied by STM and low electron?
energy diffraction (LEED). STM images were
obtained with the use of Omicron VT SPM scanning
tunneling microscope in the tunneling current mea?
surement mode. The recorded parameters specify the
bias voltage (Vt) and the tunneling current (Isp).
3. EXPERIMENTAL RESULTS
Figure 1 displays
graphene/Ni(110) system. It has clearly pronounced
reflections of nickel and graphene. The nickel reflec?
tions make up the rectangular reciprocal lattice corre?
sponding to the Ni(110) surface, which is traced in the
figure with a dashed line. This suggests strongly that
synthesis of graphene does not induce any structural
changes on the surface of the substrate. We can readily
see also two series of reflections rotated with respect to
one another and associated with the hexagonal lattice
of graphene, which implies domain structure of the
graphene and correlates well with our preceding stud?
ies . We will assume the angle between the [
directions in nickel and [
bond direction) is an orientation angle of graphene.
Then for the most probable domain orientation we
obtain ±12°. The shape of the graphene reflections
extended along the circle suggests that domain orien?
tation relative to the substrate is not very strict. And
this implies that graphene structure is incommensu?
rate with that of the substrate.
The STM images of the graphene/Ni(110) shows a
complex Moire pattern which depends strongly on
graphene orientation relative to the substrate. Figures 2a,
2b, 3a, and 4a present images corresponding to differ?
ent orientation angles of graphene. Figure 2a illus?
trates Moire patterns of two types. Some bands are
diagonally aligned and spaced with a period of 13 Å.
The period of the vertical bands is 3.5 Å, which is cor?
responding to the substrate lattice constant in the
a LEED pattern of
] in graphite (the C–C
 direction. This suggests convincingly that bands
of the second type are initiated by the effect of nickel
atoms on the crystal and electronic structure of
graphene. This suggests the main parameter determin?
ing the degree of interaction between graphene and
substrate is the distance bettwen carbon and neckel
atoms. It appears probable that the smaller inter?
atomic distance corresponds to the stronger wavefunc?
tion overlap, leading to increasing contribution of
metallic electrons in the density of state on carbon
atom. In this case, the STM signal intensity will fall off
monotonically with distance between the carbon atom
and the nearest atom of nickel. This assumption can
form a basis for construction of a simple model per?
mitting one to obtain a qualitative description of the
STM patterns obtained.
Assuming the STM signal from a carbon atom to
fall off in inverse proportion to increasing distance to
the nearest nickel atom, we succeeded in obtaining
models of STM images of the graphene/Ni(110) sys?
tem for different angles of tilt of graphene based on the
Here, I(r) is the STM signal intensity at point r, G(r, w)
is a Gaussian distribution of width w (this parameter
defines the image resolution), ri is the vector of the
coordinates of a carbon atom labeled by i, and di is the
distance from the carbon atom to the nearest atom of
nickel. In this model, graphene was assumed to be
plane with a lattice constant of 2.46 Å. The distance
between the graphene layer and the substrate was cho?
sen to be 2.1 Å. This model permitted reconstruction
of the Moire structure in the STM image of Fig. 2 and
I r ( )
?? ?G rri
Fig. 1. LEED pattern of the graphene/Ni(110) system.
The dashed line shows the reciprocal lattice of nickel, and
the dotted line connects the reflections produced by
domains with two most probable orientations (1 and 2).
PHYSICS OF THE SOLID STATE Vol. 53 No. 9 2011
FEDOROV et al.
determination of the mutual arrangement of graphene
and nickel (Fig, 2d).
Presented in Fig. 3a is an STM image of the Moire
structure correspond to 9.5°?rotated graphene
domain. The corresponding model (Fig. 3b) repro?
duces adequately all the features of this structure. The
scaled?up pattern (Fig. 3c) specifies the relative
arrangement of the nickel and carbon atoms. It is clear
visible that the bright regions of the image correspond
to the case where a group of carbon atoms is above a
nickel atom (inset 2), and dark ones, when the group
falls into the region between the neighboring nickel
atoms (inset 1).
One more example of an STM image is shown in
Fig. 4a. The model permits reconstruction of the STM
image obtained at an orientation angle 17.5° and
parameter w = 1.05 Å.
Of the above examples, only the 9.5°?rotated
graphene approaches the most probable orientation of
±12° observed in the LEED pattern. The two other
Fig. 2. STM images of the system obtained (a) at Vt = 1100 mV, Isp = 8 nA and (b) at Vt = 2.4 mV, Isp = 0.8 nA. (c) Model of
Moire structure calculated for w = 1.3 Å and (d) model on an enlarged scale with superposed structures of nickel (large spheres)
and graphene (small spheres) rotated 0.7° with respect to one another.
Fig. 3. (a) STM image of the system obtained experimentally with Vt = 2.7 mV, Isp = 30 nA. (b) Model of the Moire structure with
w = 1.3 Å and (c) model on an enlarged scale with superposed structures of nickel (large spheres) and graphene (small spheres)
rotated 9.5° with respect to one another.
PHYSICS OF THE SOLID STATE
Vol. 53 No. 9 2011
STRUCTURE OF GRAPHENE ON THE Ni(110) SURFACE 1955
angles (0.7° and 17.5°) do not fit the preferential
directions of graphene orientation; at the same time,
they are not in direct contradiction with it, because the
STM images were obtained from specific regions and,
on the whole, should not necessarily coincide with the
data statistically averaged over the whole surface.
Thus, modeling performed in the frame of a fairly sim?
ple approximation offers a satisfactory qualitative
description of the graphene Moire pattern in a good
agreement with the STM images obtained.
4. THEORETICAL ANALYSIS
To study the mechanisms involved in formation of
graphene domains with the two preferential orienta?
tions which are observed in LEED patterns, a theoret?
ical calculation was carried out. A many?center poten?
tial was used to model the structure of the nickel?
graphene system . The surface of nickel was simu?
lated in terms of the model of a built?in cluster which
consists of five layers of atoms arranged in the (110)
plane. The built?in cluster of cylindrical shape
included 539 Ni atoms, and the enclosing one,1 941.
The C–C bond length accepted in the calculations
was 1.42 Å. The total energy of the system was calcu?
lated as a function of the angle of tilt of graphene clus?
ters containing 13, 37, 67, and 103 atoms.
The angular dependences of the binding energy of
a many?atom graphene fragment with the nickel sur?
face in the arrangement with the central carbon atom
above the nickel atom are displayed in Fig. 5. As the
number of atoms in graphene increases, one witnesses
a gradual falloff of the amplitude of energy variation
with the angle, as well as a decrease in the number of
extrema, which should be attributed to an increasing
number of possible positions of carbon atoms relative
to nickel atoms.
For clusters of 13 and 37 atoms, the absolute mini?
mum of the binding energy lies close to 10°, with the
second?in?depth local minimum located near 20°.
For clusters containing 67 and 103 atoms, the mini?
mum near 20° becomes the deepest. This means that
as the number of atoms in a cluster increases, the
1This model takes into account interactions among all atoms of
the built?in and enclosing clusters, thus permitting correct
inclusion of the boundary conditions for the metallic substrate.
Fig. 4. (a) STM image of the system obtained experimen?
tally at Vt = 3.4 mV, Isp = 35 nA and (b) model of the Moire
structure. The inset shows the atomic structure of the lat?
tices of nickel (large spheres) and graphene (small spheres)
rotated 17.5° with respect to one another.
Rotation angle, deg
Relative binding energy, eV
Fig. 5. Binding energy of clusters of different sizes as a
function of the rotation angle. The energy for each curve is
referenced with respect to the zero angle.
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PHYSICS OF THE SOLID STATE Vol. 53 No. 9 2011
FEDOROV et al.
energy of the second minimum decreases, as does the
magnitude of the potential barrier separating them.
Indeed, for 67 atoms the position with the angle of 20°
becomes preferable. The original positions of the clus?
ters, however, were at 10°, and in order to transfer to a
more favorable position, the domain has to tilt through
an angle of 10°, which required hopping over a fairly
high energy barrier. A comparison of the data obtained
with the diffraction pattern suggests that most of
domains cannot change orientation when in the initial
growth stage, and, thus, remains in the first minimum
with an angle of tilt of about 10°. Further increase
results in a growth of the potential barrier separating
these states, and, although for a 103?atom cluster the
state with the angle of 20° is energetically preferable, a
cluster with a smaller angle of tilt requires a larger acti?
vation energy for a change of its orientation. Thus, the
final orientation is defined by the orientation of clus?
ters less than 15 Å in size.
Images of graphene on the Ni(110) surface have
been obtained by scanning tunneling microscopy,
which reveal a Moire pattern depending on the orien?
tation of graphene domains. A simple model is pro?
posed, which offers description of the Moire structure
of an acceptable quality under the assumption that the
effect of nickel on the local graphene density of states
depends monotonically on the distance between each
carbon atom and the nearest atom of nickel.
A theoretical analysis has revealed that the final
orientation of graphene domains observed in a LEED
pattern is determined by the orientation angle of small
size clusters at the initial stages of growth.
This study was supported by the Russian Science
Support Foundation and the St. Petersburg State Uni?
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Translated by G. Skrebtsov