A study on the elongation of embedded Au nanoclusters

in SiO2 by swift heavy ion irradiation using MD

simulations

Aleksi A. Leinoa, Olli H. Pakarinena, Flyura Djurabekovaa, Kai Nordlunda

aHelsinki Institute of Physics and Department of Physics, P.O. Box 43, FI-00014,

University of Helsinki, Finland

Abstract

We have studied the elongation of Au nanoclusters embedded in amorphous

SiO2 using MD simulations. The effect of swift heavy ions (SHI) was im-

plemented using instantaneous energy deposition with a radial profile that

was obtained from the inelastic thermal spike model. During the first impact

on the cluster, the clusters (d=9..11nm) gained about 20% in length due to

melting and thermal expansion of the cluster to the ion track in silica. Our

simulations also show that high temperatures at the track core may flatten

the cluster due to vapor pressure.

Keywords: MD simulation; SHI; Elongation; Nanoclusters; Nanoparticles

1. Introduction

It is experimentally known that swift heavy ion (SHI) irradiation (Ekin

> 1 MeV/amu) can be used to transform spherical metal nanoclusters that

are embedded in amorphous silicon dioxide into elongated shapes such as

nanorods or prolate spheroids, so that their major axis is parallel to the ion

Email address: aleksi.leino@helsinki.fi (Aleksi A. Leino)

Preprint submitted to Nuclear Instruments and Methods in Physics Research BJune 13, 2011

beam direction. The mechanism of elongation is somewhat unclear and it

has been studied by several groups since the first report of the phenomenon,

D’Orleans et al. in 2003 [1].

Metal nanoclusters in an insulating matrix give rise to additional con-

duction electrons that are bound to the clusters. Shaping the clusters by ion

beam strongly modifies their response to external electromagnetic radiation

and therefore has potential applications in a variety of optical devices such

as optical memories or filters. The elongated clusters also exhibit non-linear

optical properties [2].

Common for SHIs is that when they interact with target materials, they

lose their energy mainly in inelastic interactions with the electrons of the

target, instead of elastic collisions with the nuclei that is typical for lower

energies [3]. This results in a highly excited electronic subsystem in the nano-

metric vicinity of the ion track. To explain how and why these excitations

are turned into observable changes in the configuration of the atomic system

(e.g. latent tracks [4]), several models have been proposed [5]. A popular

model that has been successfully used to explain the structure of latent ion

tracks in amorphisable materials is the inelastic thermal spike model (i-TS)

[6, 7], which is a phenomenological description of the energy transfer between

the excited electronic subsystem and the atomic lattice. The model utilizes

coupled heat equations, which can be solved to give out the temperature

evolution of the atomic lattice, from which e.g. track radii can be deduced

by examining the size of the area that the ion melts. However, solving them

does not as such describe the transport of the atoms which ought to be cru-

cial in understanding the elongation. To include that, we have used classical

2

molecular dynamics (MD) to study the elongation. Classical MD gives a

direct view on the evolution of atomic system from given initial condition

[8], but does not carry any explicit information about the electronic system.

2. Method

The initial configuration of atoms was obtained by cutting a sphere out

of FCC bulk gold, typically 9 nm in diameter, compressing it by 2 %, and

inserting this sphere into a slightly larger void that was created into the

middle of a cubic a-SiO2 cell, 23 nm in width. This system was then heated

and kept at 300 K for 20 ps under pressure relaxation using the Berendsen

method [9].

The amorphous silica cell was constructed by replicating a smaller cell

four times in order to obtain a cell of sufficient size. For the initial cell,

we used the WWW-method for ideal bonding environment [10], which was

subsequently relaxed with the Watanabe-Samela potential [11, 12].

To mimic the effect of a SHI, instantaneous deposition of energy to atoms

was applied at the beginning of the simulation. This simple energy deposition

model is motivated by the inelastic thermal spike model (i-TS). Extensive cal-

culations using the i-TS model for the Au-silica system was performed in an

independent work by Awazu et al. [13]. Their calculations show that major-

ity of the energy is imparted to the lattice in SiO2 at femtosecond timescales,

less than needed for substantial movement of the atoms. On the other hand,

high electronic temperatures equilibrate quickly with the surrounding heat

bath, which motivates the use of standard empirical potentials. For gold, the

energy transfer from the excited electrons to the lattice is slower and the in-

3

stantaneous energy deposition approximation is therefore not as valid within

the i-TS model. This should be accounted for in future work. However, in the

calculations of Awazu et al., a 10 nm cluster in diameter is already molten at

1 ps, and in our simulations, the interesting dynamics due to heating of the

cluster occur later, typically during the first 30 ps. For SiO2, the deposition

profile was obtained from calculations for bulk sample. Strictly, due to the

spherical cluster, the radial symmetry of the i-TS equations that were used

for the profile is not conserved, which is not accounted for in our current

approach. For gold, a constant energy per atom deposition profile was used,

motivated by the low electron phonon-coupling of Au [14] and the electronic

barrier at metal-SiO2 interface [15] that should trap electronic heat.

To mimic bulk behavior and heat conduction further in to the material, we

apply periodic boundaries at each side of the simulation cell with boundary

cooling using the Berendsen thermostat [9]. Schematic picture of the simula-

tion cell is given in figure 1. This setup also dampens the pressure wave that

travels through the periodic boundary, created in the rapid introduction of

energy at the center of the cell.

2.1. Interatomic potentials

There exists no unified potential model for the Au-Si-O ternary system

that has been parameterized for amorphous SiO2. However, for quartz and

other crystalline forms, there exists a MEAM potential by Kuo and Clancy

[17]. The implementation of this potential appeared to be troublesome in a

similar manner as reported by other groups [18]. Therefore, we generated and

tested various pair potentials for silica-gold interactions, which shall be dis-

cussed in the results section. For silica interactions, we used the Watanabe-

4

Figure 1: Schematics of the simulation cell. The ion is not explicitly included in the

simulation, but the atoms are given random kinetic energies according to a radial profile

that was obtained from inelastic thermal spike model [16]. The sides of the simulation cell

are 23 nm in length, and the widths of the boundary cooling volumes, ∆X and ∆Y , are

about ten percent of the total cell width.

Samela many-body potential [11, 12]. This potential has been successfully

used previously to describe tracks due to inelastic effects in amorphous SiO2

[4, 19]. For gold, we use the EAM potential [20].

3. Results

We started to test the simulation setup with a deposition profile that

was obtained from inelastic thermal spike calculations for a 164 MeV Au

ion in SiO2 and had previously given a track diameter in agreement with

experiments [4, 19]. All simulations were run with the classical molecular

dynamics code PARCAS [21]. The energy deposition to Au was 0.5 eV per

atom, which heated the cluster instantaneously to about 2000 K from the

initial 300 K. Size of the Au cluster for these initial runs was 9 nm in diameter.

The pair potentials were obtained from a fit of Morse potential [22] expression

5

into dimer potential parameters for Au-Si [23, 24] and Au-O [25, 26]. We then

weakened the attractive part of the Morse potential expression with different

scaling factors to qualitatively account for bonding environment. With the

attractive potentials, the clusters (d=9 nm) dissolute into silica during the

simulation of SHI impact. Next, we tested the system with a purely repulsive

potential of the Ziegler-Biersack-Littmark (ZBL) form [27] for Au-Si and Au-

O dimers. While it’s not intended to be used as a interface potential, unlike

the attractive pair potentials, this potential enables the clustering of Au

atoms in silica under heating, which is a key factor in ion beam synthesis of

metal nanocrystal-silica composites. On the other hand, the ZBL potential

might overestimate the potential energy barrier at Au-SiO2 interface that

prevents the ejection of Au atoms into silica. For the ZBL potential, the

cluster gained about 20 % length during the first 20 picoseconds after impact

without losing width noticeably. Giving a promising result, the ZBL potential

were chosen for the rest of the simulation runs.

We then tested how subsequent impacts to the cluster continue to deform

it. In these runs, the ion is intersecting the cluster from the center at all times.

Judging from the experimental flux densities that was reported by Awazu et

al. (6× 1010 ions / cm2 s) [28], the time between consecutive impacts to the

cluster should be more than a second (from 22 s / ion for d=9 nm). It is

not possible to simulate this timescale in a MD simulation. Therefore, as a

first approximation, the system was quenched to 300 K after 95 ps and ran

30 ps at 300 K before next ion impact to ensure that the elongated shape

remains for both over and under melting point of Au. It was found out

that the cluster will not elongate as much after subsequent hits (figure 2).

6

0 1 2 3 48.5

9

9.5

10

10.5

11

11.5

12

Number of ions

Clu

ster

dia

met

er [

nm ]

major axisminor axis

Figure 2: Evolution of the major and minor axis of d = 9 nm cluster as a function of

number of ion impacts. The values are calculated from the maximal distance differences

of Au atoms. The ion is intersecting the cluster from center at all times. Images [29] from

the left show the shape of the initial cluster, shape after second and third hit, respectively.

During the 30 ps relaxation, the cluster will not re-crystallize, but remains in

an amorphous state. It is clear that in experiment, during the considerably

larger relaxation time, the cluster has more time to re-crystallize. Also,

the effect of ions that are hitting elsewhere to the matrix is not included.

However, we did study the effect of ions that are bypassing the cluster from

it’s side without intersecting it: with no or little energy deposition to Au, the

cluster maintains its aspect ratio, but by increasing the energy deposition, the

cluster flattens. In addition, we studied the effect changing the intersection

position within the cluster. The positions were chosen intentionally to avoid

overlapping of consecutive tracks. As an approximation, the deposition to

Au remains the same with respect to the ion position. The final cluster

length still seems to saturate to the same value as in simulations using a

single position (figure 3).

To study if larger clusters show better elongation, we increased the size

of the cluster to d=11.7 nm without increasing the cell size, but then the

7

0 2 4 68.5

9

9.5

10

10.5

11

11.5

12

Number of ions

Clu

ster

dia

met

er [

nm ]

major axisminor axis

Figure 3: The effect of intersection position in relation to cluster. Images show the shape

of the cluster after 4th, 5th and 6th hit respectively.

risk of unrealistic correlation effects due to periodicity increases. However,

the larger cluster shows qualitatively similar behavior as the smaller one, see

figure 4.

Finally, we studied the effect of energy deposition to both Au and SiO2

with the setup of the large cluster. By scaling the deposition profiles it was

seen that large enough depositions to both Au and SiO2 are needed for any

significant elongation. When the Au deposition was scaled while keeping

the SiO2 deposition at its original shape, the elongation shows a clear trend

(figure 6): the shape of the cluster becomes more prolate with increasing

deposition. Since the cluster does not lose any of its width, this suggests

that the elongation that is obtained in the simulation is due to the thermal

expansion of Au [30], and not a direct consequence of relieving in-plane stress

[31]. The deposition to SiO2 opens a channel for Au to expand [4, 19].

3.1. Effect of deposition profile shape

With the original deposition to both Au and SiO2 (i-TS model), the clus-

ter flattens during the 2nd and later impacts in the beginning, succeeded

8

0 1 2 3 411

12

13

14

15

16

Number of ionsC

lust

er d

iam

eter

[ nm

]

major axisminor axis

Figure 4: Evolution of the major and minor axis of d = 11.7 nm cluster as a function of

number of ion impacts.

by elongation, see figures 5b and 5c. This can be understood by looking at

the temperature evolution in SiO2. At the track core, SiO2 is raised to high

temperatures and vaporized. The vapor should exert more pressure to the

cluster with increasing temperature. In the case where the track is inter-

secting the cluster, the pressure is exerted along the track direction, causing

flattening. In order to test whether the flattening prevents further progress

in elongation, the maximal values of the deposition profile in SiO2 were sat-

urated to a threshold value, while keeping deposition in Au the same (the

truncated profile in figure 7). However, now the cluster elongates roughly

to the same net distance, but without strong flattening at first, as seen in

figure 5d. During the first hit, the cluster will not flatten even with the orig-

inal deposition, so the amorphous and elongated state of the cluster during

the 2nd and later hits makes it more susceptible to flattening. Next, we

tested how the width of the deposition profile affects the gain in length: with

the wide deposition profile, the track cools slower, resulting in longer lasting

expansion (figure 5e). With a narrowed profile, the track core cools down

quickly and elongation is barely noticeable (figure 5f).

9

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cluster temperature

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d) truncated profile e) broadened profile f) narrowed profile

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Figure 5: Shown on the first row is the evolution of cluster dimensions as function of time

from impact (a)-(c). Also shown is the temperature in SiO2 within r = 2 nm cylinder and

the temperature of the Au cluster, calculated from instantaneous average kinetic energies.

The second row (d)-(f) shows the effect of modified deposition profiles, given in figure 7.

The modified depositions are applied to the initial configuration of the 2nd impact (b).

Figure 6: Time evolution of the aspect ratio of the cluster with variable energy deposition

to Au. The energy deposited to SiO2 remains unchanged (i-TS profile).

10

Figure 7: The deposition profiles for SiO2 for figure 5. In the broadened deposition the

total energy deposition to the SiO2 cell is the same as with original i-TS shape.

4. Discussion and conclusions

We have observed elongation in a MD simulation. This elongation mecha-

nism seems to be closely related to the thermal expansion of Au. The energy

deposition to SiO2 provides a channel for Au to expand. However, the lack

of well justified Au-silica potential and treatment of the time between con-

secutive hits to the cluster renders uncertainty to our simulations. In our

simulations, the clusters do not lose width noticeably or gain atoms but still

gain increase in height by increase of volume due to amorphization. In ex-

perimental work, the loss of width is evident [32, 28]). However, we have

only hit few ions to the cluster, whereas experimentally it is expected that

in the order of hundred ions will hit the cluster before significant elongation

(for our cluster sizes, judging from the typical 1014 1 / cm2 fluence [32, 28])).

Also, given more simulation time than in our current approach, the cluster

should lose volume after impacts due to re-crystallization. If this occurs so

that the cluster aspect ratio is conserved and the cluster remains supported,

the cluster would have more potential for thermal expansion in major axis

11

direction while losing length in minor axis direction. Furthermore, we have

not tried to implement the effect of lateral stress that is reported in SiO2

during SHI irradiation [31], originated outside of our simulation cell. Our

study shows that molecular dynamics is a promising way to study the elon-

gation and provides insight to the elongation dynamics. As a future work,

we shall study the cluster size dependence on the elongation and the role

of the density changes [4, 19] in the track core in relation to the observed

elongation.

5. Acknowledgements

We would like to thank Marcel Toulemonde for providing the energy

deposition profile for SiO2 and Patrick Kluth and Mark Ridgway for useful

discussions. Funding by the Academy of Finland is gratefully acknowledged.

We would also like to thank CSC - the IT Center for Science Ltd (Finland)

for generous grants of computation time.

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