Orientation-dependent binding energy of graphene on palladium
Branden B. Kappes, Abbas Ebnonnasir, Suneel Kodambaka, and Cristian V. Ciobanu
Citation: Appl. Phys. Lett. 102, 051606 (2013); doi: 10.1063/1.4790610
View online: http://dx.doi.org/10.1063/1.4790610
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APPLIED PHYSICS LETTERS 102, 051606 (2013)
Orientation-dependent binding energy of graphene on palladium
Branden B. Kappes,1,a) Abbas Ebnonnasir,1 Suneel Kodambaka,2
and Cristian V. Ciobanu1,a)
1
Department of Mechanical Engineering and Materials Science Program, Colorado School of Mines, Golden,
Colorado 80401, USA
2
Department of Materials Science and Engineering, University of California, Los Angeles, Los Angeles,
California 90095, USA
(Received 6 August 2012; accepted 23 January 2013; published online 5 February 2013)
Using density functional theory calculations, we show that the binding strength of a graphene
monolayer on Pd(111) can vary between physisorption and chemisorption depending on its
orientation. By studying the interfacial charge transfer, we have identified a specific four-atom
carbon cluster that is responsible for the local bonding of graphene to Pd(111). The areal density of
such clusters varies with the in-plane orientation of graphene, causing the binding energy to change
accordingly. Similar investigations can also apply to other metal substrates and suggests that
physical, chemical, and mechanical properties of graphene may be controlled by changing its
C 2013 American Institute of Physics. [http://dx.doi.org/10.1063/1.4790610]
orientation. V
Since its isolation in 2004,1 graphene has attracted a
great deal of attention because of its unique physical, chemical, and electronic properties.2–5 A remaining technological
hurdle that prevents the introduction of graphene into specific applications is a basic, predictable understanding of the
interaction of graphene with supporting substrates.6 The sensitivity of graphene to the substrate material and surface orientation is well established, but even relative azimuthal
orientation of graphene on these substrates can affect its
properties.7–10 These recent works address manifestations of
the interactions between graphene and its host substrate,
showing that these interactions actually vary with the local
environment, that is, the chemical or electronic environment
in the immediate vicinity of certain carbon atom(s).11 Careful bookkeeping of the local structures (and the associated
interactions) present within a single spatial period of a
(moire) superstructure can be compared to variations in the
global properties, such as binding energy, to deduce the
impact of the orientation of the graphene layer.
In this letter, we study monolayer graphene on Pd(111)
for a range of in-plane orientations and show that the atomiclevel carbon–palladium registry affects the binding to the
substrate through changes to molecular orbitals at the graphene–metal interface. Furthermore, we uncover a link
between the interfacial binding strength and the areal density
of certain four-atom clusters centered atop Pd atoms in the
first substrate layer. This link provides fundamental insight
into the physical origin of the orientation dependence of the
binding energy and can be exploited for understanding the
interaction of graphene with other substrates as well.
In order to study the orientation dependence of the binding energy, we start by constructing perfectly periodic moire
patterns of graphene on Pd(111). All moire patterns are
incommensurate when using the equilibrium lattice constants
of graphene and Pd, so we have ensured commensurability at
each orientation h (defined as in Fig. 1) by applying small
a)
Authors to whom correspondence should be addressed. Electronic
addresses: bkappes@mines.edu and cciobanu@mines.edu.
0003-6951/2013/102(5)/051606/5/$30.00
strains to the graphene lattice. We have performed density
functional theory (DFT) calculations of graphene domains
having orientations between 0 and 30 with respect to the
substrate; other angular domains reduce to 0 h < 30 through rotational symmetry. For convenience, we have chosen four different orientations, h ¼ 5.7, 10.9, 19.1, and 30.0 ,
the first three of which have been experimentally identified
in Ref. 12; the 30 orientation helps compare our results with
those of Giovannetti et al.6 To understand the impact of
atomic registry on the graphene-Pd(111) binding, each carbon atom is designated as a top (T), bridge (B), gap (G), or
hollow (H) site, as shown in Figure 1, based on its position
relative to the substrate.
Total energy calculations were performed using the
Vienna Ab-initio Simulation Package13,14 with ultrasoft pseudopotentials in the local density approximation (LDA),15
with a 286 eV plane-wave energy cutoff, and a 12 Å
vacuum thickness. The Brillouin zone was sampled using a
Monkhorst-Pack grid—7 7 1 (5.7 ), 9 9 1 (10.9 ),
17 17 1 (19.1 ), and 35 35 1 (30.0 )—with more
1
than 100 points=Å along each reciprocal lattice vector. The
substrate was modeled with four Pd(111) layers (lowest two
FIG. 1. Possible occupancy sites for carbon atoms on Pd(111): T (top, C
atom atop a Pd atom), B (bridge, C atom directly above the midpoint of a
surface Pd-Pd bond), H (hollow, C atom above the hollow site), and G (gap,
C atom at the center of the smallest TBB triangles).
102, 051606-1
C 2013 American Institute of Physics
V
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Kappes et al.
Appl. Phys. Lett. 102, 051606 (2013)
kept fixed during relaxation), with the exception of the 5.7
system, which was modeled with three Pd layers due to computational limitations; we have tested that binding energy
trends obtained with three or four substrate layers are indeed
consistent with one another. We have computed the binding
energy per unit area Eb via
Eb ¼ ðEGrVPd EGrPd Þ=A;
(1)
where EGrVPd is the total energy of a system in which the graphene sheet is far from the Pd surface, and EGrPd is the total
energy of a system where the graphene layer is relaxed on
the substrate. Wepexpress
the area A in carbon atoms rather
ffiffiffi
than Å2 (1 C ¼ 3a2 =4, where a is the lattice constant of
graphene).
Binding energy is a fundamental property of epitaxial
graphene systems, affecting not only its structural and mechanical stability but also the electrochemical properties.
While calculations of binding energy have become commonplace, our goal here is to correlate it with simple geometric
features that are present in the moire superstructures characteristic to various orientations. Seeking such correlation
involves, in order: (a) identifying the possible locations
(coincident sites or simply sites) that a carbon atom in graphene can occupy with respect to the substrate, (b) tracking
the populations of these sites (i.e., their areal densities) or
groups of them, as functions of the orientation of the graphene sheet, and (c) finding which of these tracked populations depend on the orientation angle in a manner similar to
the binding energy. Following this plan, we start by selecting
four distinct types of sites to describe the positions of a
carbon atom relative to the Pd surface—top (T), bridge (B),
hollow (H), and gap (G), as described in Figure 1. To avoid
counting ambiguities when tracking site populations, we
have chosen to identify the regions for which coincident sites
are populated by site-centered circles that touch without
overlapping, as shown in Fig. 1. This convention ensures
that 90.7% of the substrate surface is accounted for in terms
of possible sites to be occupied by carbon atoms; atoms that
may fall within the remaining 9.3% of the surface (colored
dark blue in Fig. 1) are disregarded.
Tracking changes in coincident site population requires
a fixed reference, and we have selected this reference to be
the expected fraction of carbon atoms that would lie at a
certain site under the assumption of random distribution of
carbon atoms. Placed at random, 1/12 of carbon atoms lie on
top sites and 1/4, 1/6, and 1/2 at bridge, hole, and gap sites,
respectively. Figure 2 shows the variation in the population
of each coincident site as a function of angle. Although a
given population of single-type coincident site may vary by
as much as 45% with respect to its reference, no clear trends
emerge for the variation of any coincident site population
with the orientation h (Fig. 2). On the other hand, as we
show below, the binding energy of a graphene monolayer on
Pd varies monotonically with the orientation angle; therefore, no correlation exists with between binding energy and
populations of any of the single coincident sites, T, B, H, or
G (Fig. 2).
A simple inspection of the moire patterns corresponding
to the orientations h studied here (Figure 3) suggests that
FIG. 2. The areal density of the individual types of sites occupied by the C
atoms of the graphene sheet as a function of orientation.
coincident sites are occupied in a coordinated manner, which
is expected since the carbon atoms that occupy them are part
of the same graphene lattice (refer to the examples given in
the caption to Fig. 3). Therefore, we consider nearest neighbors of a given (central) site, along with that site, in order to
create an inventory of clusters that can occur on the substrate. We have identified these clusters by a two-letter
abbreviation; for example, HG3 is a hollow-site (H) carbon
surrounded by three gap-site (G3) nearest neighbors. Eight
such clusters are represented in the moire patterns shown in
Fig. 3, and we have determined the areal density as a function of angle h for all of them [Fig. 4(a)]. As seen in Fig.
4(b), only one of these four-atom clusters, TB3, has a density
that varies with the orientation angle in the same way in
which the binding energy does. At small orientations, the
graphene sheet physisorbs to the Pd(111) substrate with a
binding energy of only 41 meV/C. As the sheet is rotated and
the number of TB3 clusters increases, so does the binding
FIG. 3. Graphene on Pd(111) oriented at h ¼ 5:7 , 10.9 , 19.1 , and 30.0 ,
with the carbon atoms colored according to the site they occupy (defined in
Fig. 1). The moire surface unit cells are outlined in white. Despite the nearly
random distribution of top, bridge, hole, and gap sites, we note the periodic
repetition of distinctive clusters of sites such as TB3 [three bridge site carbons (yellow) surrounding a top site (red)], TH3 (three green, central red),
BG3 (three cyan, central yellow), HT3 (three red, central green), HH3 (three
green, central green), HG3 (three cyan, central green), GB3 (three yellow,
central cyan), and GG3 (three cyan, central cyan).
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Appl. Phys. Lett. 102, 051606 (2013)
FIG. 4. (a) Density of different types of 4-site clusters for the orientations of h ¼ 5:7 , 10.9 , 19.1 , and 30.0 . (b) The binding energy Eb of graphene on
Pd(111) increases as a function of orientation h. The only cluster whose areal density increases monotonously with h is TB3, which we show to be responsible
for the bonding of graphene to the substrate. (c) The mean distance between the C atoms and the top Pd layer; the vertical bars around each point show the
range of distances spanned between C atoms and the top Pd layer at each orientation.
energy, increasing to 60 meV/C at h ¼ 30 where the density
2
of TB3 clusters reaches its maximum of 9:65 102 Å .
Since we are dealing with weakly bonded systems using
LDA (systems at 5.7 and 10.9 ), it is possible that our conclusions regarding these systems are affected because LDA
does not account for dispersion bonding. While there is nothing in LDA to purposely account for dispersion, the exchange
part of the LDA exchange-correlation functional compensates
for the lack of dispersion treatment and leads to good descriptions of dispersion-bonded systems. For example, recent
work by Brako et al.16 has shown that LDA gives a good
agreement for binding energy and interlayer distance in a
classic dispersion-bonded system such as graphite and also
describes reasonably well (though only semi-quantitatively)
the very weak binding between a graphene layer and the
Ir(111) surface. In order to ensure that our conclusions based
on LDA hold, we have also performed DFT calculations with
a van der Waals functional (vdW-DF calculations using the
optB86b functional, see Ref. 17). Upon performing these calculations, we have found out that the binding energy of the
two physisorbed increased. However, the binding energy of
the two chemisorbed ones (systems at 19.1 and 30 ) also
increased, because even the chemisorbed systems have sufficient electrons that are not committed into chemical bonds,
and so end up generating van der Waals contributions. The
binding energy range spanned by our graphene-Pd structures
(Fig. 3) changes to 63 meV=atom Eb 78 meV=atom at
the vdW-DF level. We are still able to tell apart physisorbed
systems from chemisorbed ones from these binding energies,
from the distances between the C atoms in graphene and the
top layer of Pd atoms, and from charge transfer calculations
(see below). The distances between C atoms and the top Pd
layer are shown in Fig. 4(c), and they change little from the
LDA case. A cursory look at the literature suggests that systems with a graphene-metal spacing of greater than 3 Å are
physisorbed, and those with a spacing smaller than 2.5 Å are
chemisorbed.6,16
To substantiate the link between areal density of TB3
clusters and binding energy beyond the comparison offered
by Fig. 4(b), we have analyzed the site-projected density of
states (PDOS) corresponding to the atoms of the TB3 cluster,
as well as the electronic transfer occurring upon the creation
of the graphene–Pd interface. PDOS plots require very dense
k-point grids in order for the noise in the data to be reduced
to acceptable levels; at these dense grids, we encounter
memory limitations when using VASP. Given the need for
very fine Brillouin-zone sampling, we performed the PDOS
calculations on the relaxed structures using the SIESTA20 code
with a 70 70 1 Monkhorst-Pack grid. SIESTA is known
to produce correct PDOS analysis on structures relaxed using
plane-wave approaches.18,19 Figure 5 shows the pz states of
the carbon atoms in a TB3 cluster and the d states of the Pd
atom beneath this cluster. The presence of common peaks
for these projected densities of states (marked by vertical
gray lines in Fig. 5) below the Fermi level and close to it
indicates the formation of hybridized, bonding orbitals
between the pz states of the carbon atoms of the cluster and
the d-states of the Pd atom underneath.
Electronic transfer calculations also reveal a clear signature of the bonding between graphene and Pd for a certain
range of the orientations. At small angles (h 10:9 ), there
is no significant charge transfer, consistent with the low
binding energy values shown in Fig. 4(b). However, for
h ¼ 19:1 and 30 the electron transfer becomes significant,
as shown in Figs. 6(a) and 6(c): this transfer amounts to the
formation of chemical bonds (occupied bonding orbitals)
between graphene and substrate, which are the physical origin of the binding energy increase computed at large h
[Fig. 4(b)]. In Figure 6(a), we can identify three bonding
orbitals by their shapes: the axially symmetric TB3 bond, the
ovoid bond that lies below the r-bond between two carbon
atoms, and the oblong bond where adjacent carbon sites are
not directly atop a first-layer Pd atom. The “strengths” of the
bonds formed, as estimated by the increased electronic
FIG. 5. Site and angular momentum projected density of states (PDOS) for
the top and the bridge site carbons in a TB3 cluster and for the corresponding
Pd atom at the 30.0 orientation. The presence of common peaks (vertical
gray lines) for the C–pz, Pd–dxz, Pd–dyz, and Pd dz2 r2 projected density of
states is consistent with the formation of hybridized orbitals at the interface.
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Kappes et al.
Appl. Phys. Lett. 102, 051606 (2013)
19.1 , L ¼ 7.33 Å (7.25 Å in Ref. 26, b phase); and 30 ,
L ¼ 4.89 Å (5.00 Å in Ref. 26, a phase). The most stable
phases (orientations) are those with stronger binding, i.e., a
and b, as shown before in Fig. 4(b).
In summary, we have shown that the binding energy of
graphene on Pd(111) depends on its orientation and that this
dependence arises not from the population of any single
coincident site but from coincident site four-atom clusters
made of a top-site C atom surrounded by three bridge-site
carbons. The 50% increase in binding energy at the LDA
level (and somewhat smaller at the vdW-DF level) emphasizes the sensitivity of this property to the carbon–palladium
coincidence. The distinction between the physisorbed and
chemisorbed regimes can be made not only from binding
energies but also from the distance between the carbon atoms
and the top Pd layer and from analyzing the electronic
charge transfer at the interface. The approach presented here
can be applied to other metal substrates also, in order to see
if equally simple clusters (and which ones) are responsible
for controlling the binding strength between physisorption
and chemisorption.
FIG. 6. Electron density transfer for (a) 19.1 and (b) 30.0 orientations,
showing regions of charge accumulation (red-orange spectrum) and depletion (blue spectrum). Three types of bonds can be identified at these orientations, marked in (a) as ovoid, oblong, and TB3. Only the TB3 type exists at
h ¼ 30 (b), and no bonds are formed at orientations of 5.7 or 10.9 . Panel
(c) shows side-views of the charge transfer regions corresponding to different types of bonds identified in (a).
charge, Q, in a certain volume,21 are also different with
the highest corresponding to the TB3 case: QTB3 ¼ 0:055e
>Qovoid ¼ 0:042e > Qoblong ¼ 0:007e. This reinforces, albeit
qualitatively, our earlier observation that the combined effect
of the top and bridge-site neighboring carbons is responsible
for bonding. Unlike the case of the 19.1 system where three
types of bonds are found, in the case of 30 only TB3 is
present [Figure 6(b)]. The TB3 bonds are 24% weaker for
h ¼ 30 than their 19.1 counterparts but are present on 2/3
of the surface Pd atoms which accounts for the higher binding energy.
When bound strongly to a substrate, graphene tends to
adopt one predominant orientation, as seen on Ru(0001)22
and Ni(111).7 On substrates with weaker binding, including
Pd(111),12 Pt(111),23,24 and Ir(111),25 multiple azimuthal
orientations are observed and readily identified by the presence of moire structures with different spatial periodicities L.
Recently, Merino et al.26 have catalogued structures of graphene on Pt(111) into minimum-strain “phases,” characterized by their orientation-dependent spatial periodicities. It is
worth noting that when applied to the graphene on Pd(111)
system, the Merino et al. model describes well the structures
we examined here: 5.7 , L ¼ 17.12 Å (same as in Ref. 26, f
phase); 10.9 , L ¼ 11.20 Å (10.75 Å in Ref. 26, j phase);
B.B.K., A.E., and C.V.C. gratefully acknowledge the
support of National Science Foundation through Grant Nos.
CMMI-0825592, CMMI-0846858, and OCI-1048586. S.K.
gratefully acknowledges funding from the Office of Naval
Research, ONR Award No. N00014-12-1-0518 (Dr. Chagaan
Baatar). Computational resources for this work were provided by the Golden Energy Computing Organization at
Colorado School of Mines.
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