Orientation-dependent binding energy of graphene on palladiumBranden 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 View Table of Contents: http://apl.aip.org/resource/1/APPLAB/v102/i5 Published by the AIP Publishing LLC. Additional information on Appl. Phys. Lett.Journal Homepage: http://apl.aip.org/ Journal Information: http://apl.aip.org/about/about_the_journal Top downloads: http://apl.aip.org/features/most_downloaded Information for Authors: http://apl.aip.org/authors

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Orientation-dependent binding energy of graphene on palladium

Branden B. Kappes,1,a) Abbas Ebnonnasir,1 Suneel Kodambaka,2

and Cristian V. Ciobanu1,a)

1Department of Mechanical Engineering and Materials Science Program, Colorado School of Mines, Golden,Colorado 80401, USA2Department 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

orientation. VC 2013 American Institute of Physics. [http://dx.doi.org/10.1063/1.4790610]

Since its isolation in 2004,1 graphene has attracted a

great deal of attention because of its unique physical, chemi-

cal, and electronic properties.2–5 A remaining technological

hurdle that prevents the introduction of graphene into spe-

cific applications is a basic, predictable understanding of the

interaction of graphene with supporting substrates.6 The sen-

sitivity of graphene to the substrate material and surface ori-

entation 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 Care-

ful bookkeeping of the local structures (and the associated

interactions) present within a single spatial period of a

(moir�e) 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 atomic-

level carbon–palladium registry affects the binding to the

substrate through changes to molecular orbitals at the gra-

phene–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 bind-

ing energy, we start by constructing perfectly periodic moir�epatterns of graphene on Pd(111). All moir�e 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

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 cho-

sen four different orientations, h¼ 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 car-

bon 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 pseu-

dopotentials in the local density approximation (LDA),15

with a 286 eV plane-wave energy cutoff, and a 12 A

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

than 100 points=A�1

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).

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 VC 2013 American Institute of Physics102, 051606-1

APPLIED PHYSICS LETTERS 102, 051606 (2013)

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kept fixed during relaxation), with the exception of the 5.7�

system, which was modeled with three Pd layers due to com-

putational 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 � EGrPdÞ=A; (1)

where EGrVPd is the total energy of a system in which the gra-

phene 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. We express the area A in carbon atoms rather

than A2 (1 C ¼ffiffiffi

3p

a2=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 me-

chanical stability but also the electrochemical properties.

While calculations of binding energy have become common-

place, our goal here is to correlate it with simple geometric

features that are present in the moir�e superstructures charac-

teristic to various orientations. Seeking such correlation

involves, in order: (a) identifying the possible locations

(coincident sites or simply sites) that a carbon atom in gra-

phene 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 gra-

phene sheet, and (c) finding which of these tracked popula-

tions 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; there-

fore, 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 moir�e patterns corresponding

to the orientations h studied here (Figure 3) suggests that

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 neigh-

bors of a given (central) site, along with that site, in order to

create an inventory of clusters that can occur on the sub-

strate. 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 moir�e patterns shown in

Fig. 3, and we have determined the areal density as a func-

tion 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. 2. The areal density of the individual types of sites occupied by the C

atoms of the graphene sheet as a function of orientation.

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 moir�e 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 car-

bons (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).

051606-2 Kappes et al. Appl. Phys. Lett. 102, 051606 (2013)

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energy, increasing to 60 meV/C at h¼ 30� where the density

of TB3 clusters reaches its maximum of 9:65� 10�2 A�2

.

Since we are dealing with weakly bonded systems using

LDA (systems at 5.7� and 10.9�), it is possible that our con-

clusions regarding these systems are affected because LDA

does not account for dispersion bonding. While there is noth-

ing 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 descrip-

tions 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 cal-

culations, 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 suffi-

cient 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 sys-

tems with a graphene-metal spacing of greater than 3 A are

physisorbed, and those with a spacing smaller than 2.5 A 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 signa-

ture 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 ori-

gin 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. 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.

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.

051606-3 Kappes et al. Appl. Phys. Lett. 102, 051606 (2013)

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charge, Q, in a certain volume,21 are also different with

the highest corresponding to the TB3 case: QTB3¼ 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

h¼ 30 � than their 19.1� counterparts but are present on 2/3

of the surface Pd atoms which accounts for the higher bind-

ing 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 pres-

ence of moir�e structures with different spatial periodicities L.

Recently, Merino et al.26 have catalogued structures of gra-

phene on Pt(111) into minimum-strain “phases,” character-

ized 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�, L¼ 17.12 A (same as in Ref. 26, fphase); 10.9�, L¼ 11.20 A (10.75 A in Ref. 26, j phase);

19.1�, L¼ 7.33 A (7.25 A in Ref. 26, b phase); and 30�,L¼ 4.89 A (5.00 A in Ref. 26, a phase). The most stable

phases (orientations) are those with stronger binding, i.e., aand 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) empha-

sizes 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.

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 pro-

vided by the Golden Energy Computing Organization at

Colorado School of Mines.

1K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V.

Dubonos, I. V. Grigorieva, and A. A. Firsov, Science 306, 666 (2004).2S. J. Altenburg, J. Kr€oger, B. Wang, M.-L. Bocquet, N. Lorente, and R.

Berndt, Phys. Rev. B 105, 236101 (2010).3K. Donner and P. Jakob, J. Chem. Phys. 131, 164701 (2009).4S.-Y. Kwon, C. V. Ciobanu, V. Petrova, V. B. Shenoy, J. Bare~no, V. Gambin,

I. Petrov, and S. Kodambaka, Nano Lett. 9, 3985 (2009).5C. Lee, X. Wei, J. W. Kysar, and J. Hone, Science 321, 385 (2008).6G. Giovannetti, P. A. Khomyakov, G. Brocks, V. M. Karpan, J. van den

Brink, and P. J. Kelly, Phys. Rev. Lett. 101, 26803 (2008).7E. Starodub, A. Bostwick, L. Moreschini, S. Nie, F. Gabaly, K. McCarty,

and E. Rotenberg, Phys. Rev. B 83, 125428 (2011).8A. L. V. de Parga, F. Calleja, B. Borca, M. C. G. Passeggi, Jr., J. J. Hinarejos,

F. Guinea, and R. Miranda, Phys. Rev. Lett. 100, 056807 (2008).9J. Coraux, A. T. N’Diaye, C. Busse, and T. Michely, Nano Lett. 8, 565

(2008).10Y. Murata, S. Nie, A. Ebnonnasir, E. Starodub, B. Kappes, K. McCarty,

C. Ciobanu, and S. Kodambaka, Phys. Rev. B 85, 205443 (2012).11B. Wang, M. Caffio, C. Bromley, H. Fr€uchtl, and R. Schaub, ACS Nano 4,

5773 (2010).12Y. Murata, E. Starodub, B. B. Kappes, C. V. Ciobanu, N. C. Bartelt, K. F.

McCarty, and S. Kodambaka, Appl. Phys. Lett. 97, 143114 (2010).13G. Kresse and J. Furthm€uller, Phys. Rev. B 54, 11169 (1996).14G. Kresse and J. Hafner, J. Phys.: Condens. Matter 6, 8245 (1994).15J. Perdew and A. Zunger, Phys. Rev. B 23, 5048 (1981).16R. Brako, D. �Sokcevic, P. Lazic, and N. Atodiresei, New J. Phys. 12,

113016 (2010).17J. Klime�s, D. R. Bowler, and A. Michaelides, Phys. Rev. B 83, 195131

(2011).18L. Romaner, G. Heimel, J.-L. Br�edas, A. Gerlach, F. Schreiber, R. L. Johnson,

J. Zegenhagen, S. Duhm, N. Koch, and E. Zojer, Phys. Rev. Lett. 99, 256801

(2007).19H. Yang, A. Hallal, D. Terrade, X. Waintail, S. Roche, and M. Chshiev,

Phys. Rev. Lett. 110, 046603 (2013).20J. M. Soler, E. Artacho, J. D. Gale, A. Garc�ıa, J. Junquera, P. Ordej�on, and

D. S�anchez-Portal, J. Phys.: Condens. Matter 14, 2745 (2002).

FIG. 6. Electron density transfer for (a) 19.1� and (b) 30.0� orientations,

showing regions of charge accumulation (red-orange spectrum) and deple-

tion (blue spectrum). Three types of bonds can be identified at these orienta-

tions, 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 differ-

ent types of bonds identified in (a).

051606-4 Kappes et al. Appl. Phys. Lett. 102, 051606 (2013)

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21In the plot of spatial charge distribution, the electronic charge “contained”

within a bond, Q, depends on the choice of the isosurface contour limits,

but the relative strengths of the bonds in a structure can be compared when

the charge contained in each is measured using the same contour limits.

Studies of the spatial inflections of the density of charge transfer lead us to

an isosurface limit level of 1� 10�5 e.22D.-e. Jiang, M.-H. Du, and S. Dai, J. Chem. Phys. 130, 074705 (2009).

23P. Sutter, J. T. Sadowski, and E. Sutter, Phys. Rev. B 80, 245411 (2009).24M. Gao, Y. Pan, L. Huang, H. Hu, L. Z. Zhang, H. M. Guo, S. X. Du, and

H.-J. Gao, Appl. Phys. Lett. 98, 033101 (2011).25E. Loginova, S. Nie, K. Th€urmer, N. C. Bartelt, and K. F. Mccarty, Phys.

Rev. B 80, 085430 (2009).26P. Merino, M. Svec, A. Pinardi, G. Otero, and J. A. Martin-Gago, ACS

Nano 5, 5627 (2011).

051606-5 Kappes et al. Appl. Phys. Lett. 102, 051606 (2013)

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