Applied Surface Science 255 (2008) 893–896
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Applied Surface Science
journal homepage: www.elsevier.com/locate/apsusc
Friction model to describe cluster bombardment
Kathleen E. Ryan a,*, Michael F. Russo Jr.a, Edward J. Smiley a,
Zbigniew Postawa b, Barbara J. Garrison a
a
b
Pennsylvania State University, 104 Chemistry Building, Department of Chemistry, University Park, PA [2_TD$IF]16802, United States
Jagiellonian University, Smoluchowski Institute of Physics, Krakow, Poland
A R T I C L E I N F O
A B S T R A C T
Article history:
Short time molecular dynamics simulations were performed to model C60 and Au3 bombardment of an
amorphous water sample in the projectile energy range of 5–120 keV. A previously proposed friction
model has been applied to describe the fundamental motion of a projectile during cluster bombardment
of a solid. This simple analytical model uses a definition of friction on a single particle to describe the
cluster movement through a medium. Although the mathematics of the friction model vary among
systems, the projectile motion and energy deposition of a single particle into the sample as well as the
reactive environment created is close to that of C60 bombardment.
ß 2008 Elsevier B.V. All rights reserved.
Available online 13 May 2008
Keywords:
Molecular dynamics
Clusters
C60
Au3
SIMS
Friction model
1. Introduction
Cluster bombardment of solids has been shown both experimentally and computationally to possess many different characteristics from atomic bombardment. In particular, energetic
cluster bombardment has become a useful tool for biological and
organic secondary ion mass spectrometry (SIMS) experiments
because cluster bombardment creates less damage accumulation
in the sample and enhances the ejection yield compared to atomic
projectiles [1]. However, in the computational realm, cluster
bombardment creates many challenges due to the increase in
system size needed to contain all the events associated with cluster
projectile impact as well as the use of lower mass/bond strength
solids which may contain chemistry not present in previously used
atomic metal samples. The challenge arises, then, as to how to
understand the motion induced by the cluster bombardment event
without running full simulations that require large samples and
complicated potentials which may take several months to
calculate. If a simple conceptual model exists, then a fundamental
level of understanding can be obtained without extensive
simulations.
We propose a simple analytical model based on friction applied
to a single particle moving through a material. The development of
this model has been discussed previously [2]. In short, the frictional
* Corresponding author.
E-mail address: [email protected] (K.E. Ryan).
0169-4332/$ – see front matter ß 2008 Elsevier B.V. All rights reserved.
doi:10.1016/j.apsusc.2008.05.113
force can be expressed as a power series in the velocity with a
linear term and quadratic term as,
m
dv
1
¼ 6pahv rAC D v2
dt
2
(1)
where m is the mass of the projectile, v is the velocity, t is the time,
a is the initial radius of the projectile plus some interaction
distance between the projectile and the sample atoms, h is a
friction parameter, r is the density of the sample, A is a reference
area of the cluster equal to pa2, and CD is a drag coefficient [3]. In
previous simulations of fullerene bombardment of a molecular
solid, benzene, at short times, it was found that the quadratic term
alone is a sufficient approximation and for short times Eq. (1)
reduces to,
In
v
v0
¼
1 rv0 AC D t
2
m
(2)
where v0 is the velocity at t = 0. That is, the fraction of velocity that
the projectile has relative to its initial velocity follows an
exponential decay where the exponent depends on the initial
velocity of the projectile. The linear term in Eq. (1) shows no such
dependence, and instead decays linearly with a dependence on
size, time, and inverse mass of the projectile.
Here, we explore this model further by comparing results from
simulations of C60 and Au3 bombardment of amorphous water
with previously reported simulations of fullerene bombardment of
benzene. We also discuss the dynamics of cluster motion with
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K.E. Ryan et al. / Applied Surface Science 255 (2008) 893–896
Fig. 1. (a) Results from 10-keV bead bombardment. (b) Results from 10-keV C60 bombardment. (c) Results from 60 separate C bombardments with 166.67 eV/projectile atom.
(Top) Time-lapsed views (blue to red) of the projectile motion until 90% of the projectile energy has been deposited to the sample. (Bottom) The energy deposition profile
overlaid on a snapshot of the reaction environment of the [1_TD$IF]sample. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of
the article.)
respect to a single bead projectile and a collective of 60 separate
single carbon atomic projectiles.
2. Simulation method
The friction model is tested for a water ice system for which
previous molecular dynamics simulations have been performed for
C60 and Au3 projectiles given incident energies of 5, 10, 15, 20, 40,
80, and 120 keV and were aimed normal to the surface [4]. The
simulations were run only for short times until 90% of the
projectile kinetic energy was deposited in the sample. This interval
has been shown to be a critical time for cluster bombardment
when examining the energy deposition and its connection to the
ejection yield as estimated using the mesoscale energy deposition
footprint (MEDF) model [4,5]. In order to test the reaction
dynamics of the sample during bombardment, simulations were
also performed to model 10-keV C60 bombardment of water using
an interaction potential that allows for dissociation of water into
ions [6]. This process has a large activation energy for occurrence
and therefore acts as an indicator for a wide range of reactions and
electronic events that are energetically accessible during cluster
bombardment.
For comparison, a simulation of a 10-keV single bead projectile
with the mass and size of an intact C60 molecule was implemented.
The bead was assigned a potential that allows interaction between
the edge of the bead and the sample atoms. The potentials used are
identical to the C[3_TD$IF]–O and C–H potentials used for the atomistic C60
bombardment simulation.
Lastly, 60 separate individual carbon trajectories each with
an initial kinetic energy of 166.67 eV, the same energy per atom
as the C60 projectile at 10 keV, were calculated on the same
water sample. The initial positions of the C atoms corresponded
to the 2D projection of the C atom positions in the C60 cluster.
The motivation for this calculation arises from the concept that
the energy deposition rate of a cluster of n atoms can be
described by n times the energy deposition rate by one atom at
the same velocity [7,8].
3. Results and [4_TD$IF]discussion
In order to test the assumption that cluster bombardment may
be described by friction acting on a single particle moving through
a solid, we have compared a simulation of 10-keV C60 bombardment of a reactive water sample with that of a single bead
projectile. Fig. 1 b shows the results from C60 bombardment of
amorphous water. The top snapshot is a time-lapsed view of the
projectile motion where dark blue represents t = 0 and red
represents the time at which 90% of the projectile energy has
been deposited to the substrate. The C60 projectile is able to
penetrate into the substrate in a nearly straight trajectory and
begins to break up as it approaches the 90% time. The projectile
deposits its energy within a depth of 35 Å and a width of 20 Å
from the impact point as shown by the bottom of Fig. 1b. The
energy deposition profile is represented by changes in Ẽ ¼ Eexc =U 0 ,
where Eexc is the excitation energy and U0 is the binding energy of
the substrate. Therefore, according to the legend, grey represents
molecules in their initial state respectively, and yellow to blue
represent energized molecules from slightly energized to highly
energized. This contour plot is overlaid on the original positions of
the water molecules (colored beads) that have reacted. The
reaction zone created following C60 bombardment is very dense
and located near the point of impact indicating that multiple or
adjacent molecules react simultaneously [6].
The results from the bead simulation (Fig. 1a) closely mirror
those of C60 bombardment. The bead projectile is also able to
penetrate into the sample in a nearly straight line and deposits its
energy in approximately the same region as the C60 projectile
resulting in similar yields according to the MEDF model [4,5].
Likewise, the reaction profile also shows a dense near surface
region where multiple molecules may react concurrently.
The sum of results from 60 separate single carbon trajectories
paints a very different picture (Fig. 1c). All the figures for the [5_TD$IF]60 C
atoms correspond to a sum of 60 individual calculations. The
individual C atoms begin to randomize immediately upon impact
with the surface as shown by the time-lapsed snapshot and do not
penetrate as deeply as either the bead or C60 projectiles. The energy
K.E. Ryan et al. / Applied Surface Science 255 (2008) 893–896
895
Fig. 2. (a) lnðv=v0 Þ vs. 6pt/m for C60 bombardment. (b) lnðv=v0 Þ vs. 6pt/m for Au3 bombardment. (c) lnðv=v0 Þ vs. ð1=2Þrv0 t=m for C60 bombardment. (d) lnðv=v0 Þ vs.
ð1=2Þrv0 t=m for Au3 bombardment.
deposition profile is confined to a volume of 27 Å deep and 13 Å
wide. The most energized region, the dark blue area, is located
towards the center and top of the impact point whereas for the
bead and C60 projectile, the most energized molecules are toward
the bottom of the energized region. The largest difference,
however, is found when the reaction dynamics are examined.
The 60 single carbon trajectories create, when summed, significantly fewer reacted molecules than the bead or C60 projectiles.
The relative velocity decay, lnðv=v0 Þ, from the simulations up to
90% energy loss, or lnðv=v0 Þ ¼ 1:15; is shown in Fig. 2 where a and
b represent the lnðv=v0 Þ for C60 and Au3 plotted against 6pt/m, the
critical parameter for first order friction (the linear term in Eq. (1)),
and c and d represent the simulation data plotted against 12rv0 t=m;
the critical parameter for second order friction (Eq. (2)). The data
look alluringly simple and linear in both representations. The C60
and Au3 simulation data appear to fit the linear friction term quite
well. In contrast, simulations of fullerene bombardment of a
coarse-grained benzene target could be approximated well by
using only the second order friction model [2]. Therefore, it is not
clear which friction term can best be used to describe all systems or
why the linear term better describes some systems while the
quadratic term describes others. Both terms depend on the initial
size of the projectile including an interaction radius. Previously, we
found the interaction radius between C60 and benzene to equal
1.95 Å [2]. If we use this interaction radius to describe the
interaction between C60 and water, as well as using the slope of the
overlapping curves in Fig. 2a, we can define a value of h. In this case,
h = 1.52 cP, which is the same order of magnitude as the viscosity
of water, approximately 1 cP [9], although there is no justification
that the physics of h is that of viscosity. It may not be appropriate to
apply the same analysis technique to Au3 simulations because the
Au3 projectile breaks apart almost immediately upon bombarding
the surface and may act more like three separate Au atomic
projectiles than a collective cluster. However, it is clear that the
dynamics of cluster bombardment can be described by friction on a
single particle moving through a solid.
4. Conclusions
We have presented a friction model to describe the fundamental motion of cluster bombardment. The model contains a
linear term and a quadratic term in velocity. It is not clear which
term may best describe the fundamental motion of all systems;
however, each term was able to describe well the motion of the
projectile in simulations of C60 and Au3 bombardment of
amorphous water and fullerene bombardment of benzene. It is
clear that the dynamics of cluster bombardment are more closely
related to that of a single large particle moving through a solid
rather than to the sum of several smaller individual trajectories as
the projectile motion, energy deposition, and reaction dynamics of
the sample are strikingly similar for the bead and C60 projectiles.
Acknowledgments
Financial support is gratefully acknowledged from the Chemistry Division of the National Science Foundation Grant [6_TD$IF]no.
0456514 as well as the Polish Ministry of Science and High
Education programs no. N204 4097 33, PB2030/H03/2006/31.
Computation support was provided by the Academic Services and
Emerging Technologies (ASET) group at Pennsylvania State
University. The authors would also like to acknowledge a number
of collaborators who have contributed many insights to this work
including Arnaud Delcorte, Kristin Krantzman, John Vickerman,
Roger Webb, Nick Winograd, and Andreas Wucher.
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K.E. Ryan et al. / Applied Surface Science 255 (2008) 893–896
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