Structure and thermal properties of supported catalyst

clusters for single-walled carbon nanotube growth

Feng Ding a,*, Kim Bolton a,b, Arne Rosen a

a Department of Physics, Goteborg University, SE-412 96, Goteborg, Swedenb School of Engineering, University College of Boras, SE-501 90, Boras, Sweden

Available online 10 January 2006

Abstract

Structure and thermal properties of supported iron clusters were studied using molecular dynamics simulations. When supported clusters are in

the liquid state, their surfaces have spherical curvature, whereas solid clusters form a layered crystalline structure. The cluster freezing (melting)

point increases dramatically with increasing cluster–substrate interaction strength, and rapid diffusion of cluster surface atoms is observed below

the freezing point.

# 2005 Elsevier B.V. All rights reserved.

PACS: 61.48.+c; 61.46.+w; 81.10.Aj

Keywords: Supported cluster; MD simulation; Surface diffusion

www.elsevier.com/locate/apsusc

Applied Surface Science 252 (2006) 5254–5258

1. Introduction

The three most common methods for carbon nanotube

(CNT) production are arc discharge, [1,2] laser ablation [3] and

catalytic chemical vapor deposition (CCVD). [4] Of these

methods, CCVD presently attracts the most interest because of

the advantages for large scale production, diameter controlled

growth, growing ultra long CNTs, well aligned CNT structures/

patterns, in situ growth for electronics, etc. [5] The transition

metal catalyst (e.g., Fe, Co, Ni and their alloys) plays a crucial

role in CNT growth. For the arc discharge and laser ablation

methods, the catalyst particle is believed to be ‘floating’ in the

gas feedstock and buffer gas during CNT (often single-walled

CNT – SWNT) growth. In contrast, during CCVD growth the

catalyst particle may be floating or may initially be on the

substrate. It is difficult to produce CNTs in large quantities or

CNTs that are ultra long when one has floating catalyst particles

because the growth time is not sufficiently long. In addition, the

position of the CNTs and the growth direction cannot be

controlled when one uses a floating catalyst. Hence, CCVD

methods that involve supported catalyst particles (i.e.,

* Corresponding author. Tel.: +46 31 7723296; fax: +46 31 7723496.

E-mail address: fengding@fy.chalmers.se (F. Ding).

0169-4332/$ – see front matter # 2005 Elsevier B.V. All rights reserved.

doi:10.1016/j.apsusc.2005.12.022

particles supported on a substrate) are most suitable for

controlled CNT production and hence may become more

important in CNT applications. This is substantiated by the fact

that most recent progress towards controlling CNT growth,

such as growing ultra-long SWNTs [6] and chirality controlled

production [7], are based on the supported catalyst CCVD

method.

There are several ways to deposit catalyst particles on the

substrate, such as depositing a thin metal layer and then

annealing the metal layer to metal particles [8], wet catalyst

methods [9] and depositing metal atoms into the pores of the

substrate [10]. The substrate plays many important roles during

CNT growth, such as affecting the structure of the catalyst (e.g.,

iron silicide is formed from iron on silicon surfaces [11]) and

determining the growth mode (tip growth mode or root growth

mode) [12]. It is generally believed that tip growth – where the

catalyst particle is at the CNT end that is not joined to the

substrate – occurs if the interaction between the catalyst particle

and the substrate is weak, and that root growth – where the

catalyst particle is on the substrate during CNT growth – occurs

when the particle–substrate interaction is strong [12].

In spite of the importance of the substrate effects on catalyst

particles, and the fact that many experimental studies use

supported catalysts, theoretical studies are scarce. In this paper,

we present some preliminary molecular dynamics (MD)

F. Ding et al. / Applied Surface Science 252 (2006) 5254–5258 5255

simulations of the thermal properties and structure of supported

catalyst particles on a flat substrate. In addition to the interest in

these systems, this study also sheds light on the properties of

these catalyst particles during CNT root growth mechanisms,

which may well affect the properties of the CNT that is

produced.

2. Potential energy surface and simulation details

The many-body interaction potential, which is based on the

second moment approximation of the tight binding model

[13,14] is suitable for studying the thermal properties of the

pure and alloy transition metal systems. The interaction energy

between iron atoms can be written as:

E ¼Xi 6¼ j

A exp

�� p

�ri j

r0

� 1

��

�X

i

�Xj 6¼ i

j2 exp

�� 2q

�ri j

r0

� 1

���1=2

(1)

where rij is the distance between the ith and jth iron atoms. The

parameters A = 0.13315 eV, j = 1.6179 eV, p = 10.50, q = 2.60

and r0 = 2.553 A are taken from [15].

The metal–substrate interaction is crucial for understanding

the substrate effect on the catalyst particle. Although ab initio

and density functional theory (DFT) can be used to study

supported transition clusters, only extremely small systems can

be investigated [16]. Although these first principle studies are

needed for studies of specific substrate–cluster systems, here

we perform preliminary calculations that are generic in nature.

In particular, the substrate–cluster interaction is described by a

LJ (9-3) potential, where the LJ parameters are systematically

varied to simulate a broad range of substrate–cluster adhesion

strengths. Hence, we are not studying detailed properties of a

specific cluster–substrate system, but are focusing on general

trends in structural and thermal properties of supported catalyst

particles (such as the interaction strength dependence of the

particle shape and melting point). In addition, we model the

substrate as an atomically smooth surface that interacts with the

particle in the perpendicular (z) direction only, so that the LJ (9-

3) potential is:

VðzÞ ¼ e3ffiffiffi3p

2

��s

z

�9

��

s

z

�3�(2)

Fig. 1. Structure of liquid (a–g) and solid (h–n) metal clusters at 1400 and 800 K, r

panels a to g for liquid particles and h to n for solid particles. The insert shows th

where e is the potential well depth. Using well-depths, e, from 0.1

to 0.7 eV provides a spectrum from weak to strong cluster–

substrate adhesions (s = 0.3 nm is kept constant). Also, although

the MD simulations are for substrates with varying adhesion

strengths, which dominates changes in the cluster shape and

melting points, they are for smooth and flat surfaces. Explicit

modeling of substrate atoms, as well as the effect of changing the

substrate shape and including defects, is in progress.

The constant temperature molecular dynamics (CTMD)

technique, using the Berendsen scaling method [17] and the

integration time step of 3 fs, was used to study the structural and

thermal properties of a supported Fe147 cluster. For each

trajectory a cluster was placed on the substrate before

thermalizing at 1600 K. The thermalized cluster, which was

liquid for all substrate–cluster interaction strengths, was cooled

to 1400 K (where it was still liquid) before further cooling to

200 K in steps of 20 K. 106 MD steps were propagated at each

temperature, and the Lindemann index [18] of each atom and

for the entire cluster were calculated at each temperature as:

di ¼1

N � 1

Xjð 6¼ iÞ

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffihr2

i jiT � hr2i ji

2T

qhri jiT

; d ¼ 1

N

Xi

di (3)

where di and d are the Lindemann indices of ith atom and the

cluster, respectively, h. . .iT denotes the thermal average at

temperature T, rij is the distance between the ith and jth atoms

and N = 147 is the number of atoms in the system.

3. Results and discussion

3.1. Structural variation of the supported Fe147 cluster

The minimum energy structure of Fe147 in vacuum has perfect

icosahedral symmetry, which leads to an increase in the melting

point of this cluster compared to other clusters of similar size but

that do not have perfect symmetry [19]. When this cluster is

placed ona substrate, the symmetry isbroken even for theweakest

metal–substrate interaction studied here (i.e., 0.1 eV per atom as

shown in Fig. 1h). This leads to a lowering in the melting point

compared to the isolated cluster (meltingpointof940 K) forweak

substrate–cluster interactions. It may be noted that the bulk

melting point extrapolated from simulations of clusters with

increasing size is1617 K [19]. This is lower than theexperimental

value of 1812 K, and may be due to the high fraction of surface

atoms in the simulations [20].

espectively. The substrate–cluster interaction strengths (e in eV) increases from

e ground state icosahedral structure of the isolated Fe147 cluster.

F. Ding et al. / Applied Surface Science 252 (2006) 5254–52585256

Fig. 2. Temperature dependence of supported cluster shapes for different cluster–substrate interaction: Panels a–d for e = 0.1 eV and Panels e–h for e = 0.3 eV.

Fig. 3. Energy and the lindemann index variation during the cooling process of

free and supported Fe147 clusters for various substrate–cluster interaction

strengths.

Fig. 1 shows the structure of the cluster for different metal–

substrate interactions at 1400 K (where all clusters are liquid)

and 800 K (all clusters are solid). Panels a–g show the

structures of the liquid clusters, and it is clear that the upper

surfaces of these clusters have a spherical curvature (i.e., the

cluster can be visualized as being part of a sphere with

increasing radius as the substrate-cluster interaction strength

increases). For a weak interaction of e = 0.1 eV the cluster is

essentially a sphere (non-wetting). At intermediate interaction

strength of e = 0.3 eV the cluster is nearly hemispherical. When

the interaction becomes even stronger, e > 0.3 eV, the cluster

can be visualized as being part of a larger sphere. Wetting of the

substrate begins at e = 0.7 eV.

In contrast to liquid clusters, it can be seen from Fig. 1h–n

that solid particles have a layered crystal structure and that their

upper surfaces are flat (i.e., they do not have a spherical

curvature that was seen for liquid clusters). The change from

spherical to layered structures between liquid and solid

particles is due to the fact that a liquid drop is isotropic in

all directions whereas a crystal is anisotropic.

Snapshots showing typical structures of the cluster at

different temperatures (when cooling from liquid to solid) at

e = 0.1 eV (Panels a–d) and e = 0.3 eV (Panels e–h) are shown

in Fig. 2. It is clear that the spherical shape of the liquid cluster

(Panels a and e) transforms to a layered crystalline solid

structure (Panels b and f). In spite of the fact that the clusters are

solid below 900 K (Panel b) and 1000 K (Panel f) for e = 0.1

and e = 0.3 eV, respectively, atoms on the surface of the cluster

show substantial diffusion. This leads to the change in cluster

shapes as the temperature decreases below the freezing point

(from b to d for e = 0.1 eVand from f to h for e = 0.3 eV). This is

illustrated in Panels c and d where the atoms identified by balls

at 700 K (Panel c) have new positions in Panel d. This motion,

which is on the order of nanoseconds, occurs even though the

temperature is about 300 K below freezing.

3.2. Thermal properties and surface diffusion of supported

clusters

The energies and Lindemann indices of the clusters during

cooling are shown for different particle–substrate interaction

strengths in Fig. 3. The freezing point is defined as the

temperature where the energy abruptly decreases. Fig. 3a shows

that the freeing point increases with increasing metal–substrate

interaction strength. When the interaction increases from 0.1 to

0.7 eV, the freezing point increases by about 400 K (from 880 to

1260 K).

Fig. 3a also shows that the temperature interval over which

freezing (or melting) occurs increases for higher metal–

substrate interaction strengths. This is also seen in Fig. 3b for

the Lindemann index, and is due to the fact that, for larger

metal–substrate interaction strengths, higher temperatures are

required to ‘melt’ regions of the cluster that are close to the

substrate (i.e., atoms strongly bound to the substrate require

large kinetic energy to overcome this attraction). Hence, for

large metal–substrate interaction strengths the regions of the

F. Ding et al. / Applied Surface Science 252 (2006) 5254–5258 5257

Fig. 4. Lindemann indices for atoms in the iron cluster as a function of their perpendicular distance, z, from the substrate. The panels are for different temperatures

and the left and right columns are for cluster-substrate interaction strengths of e = 0.1 and 0.3 eV, respectively.

cluster that are close to the surface melt at far higher

temperatures than those that are far away from the substrate,

which results in the broadened melting interval seen in Fig. 3.

The atomic motion in the clusters can be further clarified by

monitoring their individual Lindemann indices. These are

shown in Fig. 4 as a function of the atoms’ perpendicular

distance from the surface (obtained as an average over the

trajectory). Each panel is for a different temperature and the

panels in the left and right columns are for e = 0.1 and 0.3 eV,

respectively. At the temperatures below the melting point the

Lindemann indices of atoms that are far from the substrate are

larger than those that are close to the substrate (820 and 840 K

for e = 0.1 eV – left panel and 800, 900 and 960 K for

e = 0.3 eV –). Hence, atoms that are further from the substrate

have a higher mobility and diffusion rate than those near or

bonded to the substrate.

Fig. 4 also shows that, at the temperatures below the freezing

point, there is a periodic lowering of the Lindemann indices in

the direction perpendicular to the surface. This shows the

ordering – or layering – of the atoms as discussed above. The

increase in the Lindemann indices of atoms ‘between’ these

layers is due to the ‘hopping’ of atoms between the layers.

Detailed analysis of the trajectories show that atoms can diffuse

between neighboring layers or within the same layer, and the

periodic distribution of the Lindemann indexes shows that

diffusion between layers is faster than diffusion within layers.

The change in the cluster structure, dynamics and melting

points due to increasing interaction strengths with the substrate

is expected to have a large effect on the growth of CNTs. For

example, previous simulations indicate that, following feed-

stock decomposition, carbon atoms penetrate deep into liquid

iron clusters before being incorporated into the growing CNT

structure. In contrast, there is very little penetration when the

cluster is solid, and the rapid diffusion of cluster surface atoms

is required for transport of carbon atoms from the place of

feedstock decomposition to the CNT end (where it is

incorporated into the CNT structure). This rapid surface

diffusion of atoms on solid clusters is found for isolated and

supported clusters discussed above.

4. Conclusion

Structural and thermal properties of supported catalyst

particles have been studied by molecular dynamics. Analysis of

the particle structure revealed that the exposed surfaces of

liquid clusters have spherical curvature whereas solid clusters

have flat surfaces. In addition, solid particles have a layered

crystal structure where the atoms are well ordered in the

F. Ding et al. / Applied Surface Science 252 (2006) 5254–52585258

direction perpendicular to the substrate. Analyses of the

thermal properties show that strong interaction between the

substrate and the catalyst atoms increases the freezing (or

melting) point significantly, and that the temperature window

over which freezing occurs increases with increasing substrate–

cluster bonding strength. In addition, solid clusters can change

shape via the diffusion of the surface atoms, especially those on

the exposed surfaces of the catalyst particle.

Acknowledgements

The authors are grateful for the time allocated on the

Swedish National Supercomputing facilities and for financial

support from the Swedish Research Council, the Swedish

Foundation for Strategic Research (CARAMEL consortium).

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