ENERGETICS OF SMALL CLUSTERS OF ALKALI METALS (Li, Na, AND K) ADSORBED

ON GRAPHENE

GAGANDEEP KAUR1,2, SHUCHI GUPTA1,3 & KEYA DHARAMVIR1

1Department of Physics and Centre of Advanced Studies in Physics, Panjab University, Chandigarh, India 2Chandigarh Engineering College, Landran, Mohali, Punjab, India

3University Institute of Engineering and Technology, Panjab University, Chandigarh, India

ABSTRACT

Graphene has unique properties arising from its honeycomb-lattice structure that could maximize the interaction

of adsorbate on the layer. Many experimental methods have been devised to form stable metallic clusters of different sizes.

Metal clusters, especially those of alkali-metal atoms Li, Na, and K, have played an important role in the development of

cluster physics as a branch of modern physics and chemistry. Moreover metal-graphene contacts would play a crucial role

in graphene based electronics.

In this paper, we use a method involving interatomic model potentials to investigate the structure and binding

energies of clusters of alkali metal Mn (M=Li, Na, K; n=1, 3), adsorbed on graphene. For M-M interaction, we use Gupta

potential while Lennard-Jones potential was used for M-C interactions (C = carbon). We find that for each alkali cluster in

the minimum energy configuration, adsorbation at the hollow site on grapheme is favored. Stability of the Mn - graphene

system increases with the increase in size of the cluster. All trimers adopted a geometry close to an equilateral triangle with

significant changes in bond lengths.

KEYWORDS: Graphene, Metal Clusters, Interatomic Potentials

INTRODUCTION

In recent years, graphene, the two-dimensional building block of graphite, has been the focus of attention as a

substrate for new nano structure devices using its two-dimensional property. Fabrication of nanoclusters on graphene is of

great interest in studies of applications in electronics, sensors, biodevices, catalysis, energy storage, etc [1, 2]. Metals

adsorbed on graphene can form different types of structures and change graphene’s electronic behavior, giving rise to

interesting physical properties. It is therefore essential to have a good understanding of metal–carbon (M-C) bond strength

as well as cohesive energies of the system as these play significant roles in the cluster formation process. Small clusters

composed of alkali-metal atoms have been the subject of numerous theoretical studies in recent years due to their structural

and spectroscopic properties [3]. The enhancement of electrical conductivity in alkali atoms doped single-wall carbon

nanotubes has been studied both experimentally and theoretically [4-6]. Spin-valve device structures operated by side gates

were proposed utilizing the site dependence of alkali metal absorption on graphene nano ribbons [7]. It has been proposed

that alkali-metal-plated graphite could have practical applications as a substrate in studying normal and superfluid He films

[8, 9]. Adsorbed alkali atoms have been shown to act as chemical dopants on the CNTs and have been used to fabricate

field effect transistors [10]. Potassium has also been used to chemically dope graphene, allowing graphene quasiparticle

dynamics [11] and minimum conductivity [12] to be studied. Furthermore, the electronic structure of graphene bilayers

[13] can be tuned by K atoms.

International Journal of Physics and Research (IJPR) ISSN 2250-0030 Vol. 3, Issue 2, Jun 2013, 1-6 © TJPRC Pvt. Ltd.

2 Gagandeep Kaur, Shuchi Gupta & Keya Dharamvir

Motivated by the interesting results of adsorption of small metal clusters on graphene, we carry out a systematic

analysis of small sized alkali metal clusters Mn (M= Li, Na, K; n=1,3) adsorbed on graphene using interatomic potentials.

In this work the focus will be entirely on the adsorption site, the structure of small metal clusters adsorbed on grapheme,

and relative stabilities of these various configurations.

THEORETICAL METHODS

Graphene consists of C atoms arranged in a two-dimensional honeycomb lattice with a hexagonal primitive unit

cell containing two atoms. The Mn - graphene system is modeled using Mn adatoms in a 20* 30 hexagonal graphene

supercell. We take up clusters one by one. This setup corresponds to a coverage of Mn (n=1-3) adatoms per 2480 C atoms.

In our notation, we let the y direction be perpendicular to the graphene plane, x and z axes lying in the plane. We consider

the binding of the alkali atom on three sites: the hollow H site at the center of a hexagon, the bridge B site at the midpoint

of a carbon-carbon bond, and the top T site directly above a carbon atom (Figure 1).

Figure 1: Three Adsorption Sites on the Graphene Sheet

We use the atom-atom interaction approach, with Lennard – Jones (LJ) potential [14] for M-C interactions and

Gupta Potential (GP) [15] for M-M interactions, keeping the graphene sheet rigid. The LJ parameters which have been

used in our calculations are taken from reference [14]. The parameters for Gupta potential are taken from [15, 16].

We first find the minimum energy configuration for an Mn cluster. By placing the minimized M1-3 cluster a certain

distance above the graphene sheet at various positions and in various orientations, the total energy of the cluster - graphene

system is obtained by summing over M – C pairs interacting via LJ potential.

RESULTS AND DISCUSSIONS

Binding Energy of a Single Atom on Graphene

For the single adatom - graphene system, the adatom is moved along the y direction for each adsorption site (T, B,

H). By placing the M atom above any of these three sites and then varying the distance between M atom and the sheet, total

energy is obtained by summing over the potential energy (PE) of interaction between all the atoms on the graphene sheet

and M, using LJ potential. Of the three adsorption sites considered above, the site with the minimum binding energy is

referred to as the favored site. Binding energies for the three sites considered are summarized in Table 1. Alkali metal

adatoms prefer to bind more strongly to the H site.

For the isolated atom-graphene system, our conclusions for Li and Na are in agreement with Chan et al. [17]

while for K adatom, he predicted B- site as favored site. For single atom adsorption, the hollow sites were found to be more

favorable than carbon bridge or top of carbon atoms for all alkali metals as predicted by Caragiu et al. [18]. The adsorption

energies and adsorption sites on graphene sheet for alkali metals calculated by K. Nakada et al. [19] using the DFT

formulation also shows the H-site as the most preferred site for adsorption, though values of binding energies were

Energetics of Small Clusters of Alkali Metals (Li, Na, and K) Adsorbed on Graphene 3

somewhat different from our calculations. So our results corroborate their findings on the whole.

Table1: Interaction between Metal Adatom and Graphene Sheet. EB is Binding Energy and d is the Perpendicular Distance between the Metal Atom and the Graphene Sheet. In Each Case, LJ Potential Has Been Used

ATOM STABLE SITE SITES E(eV) d(A0)

Li H-site T -0.315 3.14 B -0.336 3.04 H -0.337 3.04

Na H-site T -0.317 3.44 B -0.318 3.43 H -0.328 3.38

K H-site T -0.362 3.84 B -0.363 3.83 H -0.369 3.81

Binding Energy of Isolated Clusters

Using Gupta potential, we find binding energy and bond lengths for optimized structures of isolated Mn clusters

which are summarized in Table 2. Our results are in good agreement with those available in literature. Our results for Li

dimer matches well with experimentally derived equilibrium bond length of 2.673 Å for the lithium dimer [20]. For the Li

trimer, the initial configurations considered are equilateral, isosceles as well as scalene triangles. However, after

minimization, an isosceles triangle as predicted in ref. [21] is found to be the stable configuration. For the Na dimer, the

calculated bond length is 3.31Å which is comparable to the quoted value of 3.21 Å [22]. However the optimized geometry

obtained by us for this trimer is an isosceles triangle with bond lengths slightly different from the above value. Bond length

of K dimer predicted by our calculations 4.23 Å matches with 4.21 Å and 4.22 Å as obtained by [23] and [24]. For

potassium trimer, results for binding energy per atom -0.331 eV are same (-.3306 eV) as calculated by [25].

Table 2: Binding Energy and Bond Length of Isolated Optimized Mn Clusters

M n Binding

Energy/Atom (eV)

Bond Length (Å)

Li 2 -0.321 2.67

3 -0.437 2.59, 2.47, 2.59

Na 2 -0.288 3.31

3 -0.383 3.44, 3.74, 3.44

K 2 -0.245 4.23

3 -0.331 4.36, 4.32, 4.36

Binding Energies of Minimized Dimers and Trimers on Graphene Sheet

Calculations were performed for a variety of initial orientations (parallel and perpendicular) for the M2 dimers

placed above the graphene sheet. All calculational details were the same as in the case of the single atom. For each dimer,

initial configuration is not necessarily the same as that obtained after the system has relaxed. The preferred orientation of

each dimer was found to be parallel to graphene sheet with the two atoms of the dimer occupying adjacent H-sites on the

graphene as shown in figure 2. Our results for bond lengths of dimers of all three alkali metals compare well with ref. [26]

where the values obtained were 2.95Å (2.68), 3.07Å (3.05), 4.65Å (4.04) respectively for Li2, Na2, K2 adsorbed on

graphene. The value in parentheses denotes the gas phase (or free dimer) value.

4 Gagandeep Kaur, Shuchi Gupta & Keya Dharamvir

Figure 2: Parallel Orientations of Dimer on Graphene Sheet after Minimization (Top View)

For all trimers, we take the minimized isosceles triangle structures obtained by using Gupta potential as the initial

structure. After minimization on the graphene sheet, however, M3 adopts a geometry close to an equilateral triangle with

significant changes in bond lengths. For the Na3 trimer, optimized geometry on graphene is an equilateral triangle with

bond length 3.47 Å which is comparable to the DFT work of Rytkönen et al. [27] who find a value of 3.35 Å.

Figure 3: Parallel Orientations of Trimer on Graphene Sheet after Minimization (Top View)

Figure 4 shows the binding energies (BE) of clusters M1-3 on graphene. The minimized energy configurations of

Mn have been tabulated in Table 3.

Figure 4: Binding Energy of M1-3 on a Graphene Sheet

Energetics of Small Clusters of Alkali Metals (Li, Na, and K) Adsorbed on Graphene 5

Table 3: Minimized Energy Structures for Mn – Grapheme System

Metal (M) n

EB (eV/atom)

dC-M ( Å )

Initial Bond Lengths

d M-M ( Å)

Initial Structure

Final Bond Length

d M-M ( Å )

Final Structure

Li 1 -0.337 3.04 - - - - 2 -0.6576 3.04 2.67 - 2.56 - 3 -0.7738 3.04 2.59,2.47,2.59 Isosceles 2.69 Equilateral

Na 1 -0.328 3.38 - - - - 2 -0.613 3.4 3.31 - 3.28 - 3 -0.7113 3.4 3.44,3.74,3.44 Isosceles 3.47 Equilateral

K 1 -0.369 3.81 - - - - 2 -0.6134 3.81 4.23 - 4.16 - 3 -0.6995 3.81 4.36,4.32,4.36 Isosceles 4.32 Equilateral

CONCLUSIONS

The structure and binding energies of small clusters of alkali metals on graphene has been studied using

interatomic potential model. Of the three possible symmetric sites of adsorption, the H-site was found to be energetically

favourable. For dimers and trimers, parallel orientations were preferred over perpendicular, on the graphene sheet. In order

of stability of a single metal atom and their dimers on the grapheme sheet, we find Li > K > Na, indicating weak binding

of Na and Na2 with graphene sheet. However, Na trimer was found to be more stable than K trimer on graphene sheet. Our

results are in good agreement with available literature. Since for large clusters (of hundreds or thousands of atoms) ab

initio electronic structure calculations are still, at present, computationally expensive, there has been much interest in

developing atomic potentials for the simulation of such clusters.

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