astudyontheelongationofembeddedaunanoclusters insio
Post on 28-Oct-2021
1 Views
Preview:
TRANSCRIPT
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
115
120
125
130
135
140
145
150
155
160
0 10 20 30 40 50 60 70 80 90 100 0
1000
2000
3000
4000
5000
6000
7000
8000
9000
Clu
ster
dim
ensi
on [Å
]
Tem
pera
ture
[K]
Time [ps]
T within r = 2 nmcluster major axiscluster minor axis
cluster temperature
a) 1st ion
115
120
125
130
135
140
145
150
155
160
0 10 20 30 40 50 60 70 80 90 100 0
1000
2000
3000
4000
5000
6000
7000
8000
9000
Clu
ster
dim
ensi
on [Å
]
Tem
pera
ture
[K]
Time [ps]
b) 2nd ion
115
120
125
130
135
140
145
150
155
160
0 10 20 30 40 50 60 70 80 90 100 0
1000
2000
3000
4000
5000
6000
7000
8000
9000
Clu
ster
dim
ensi
on [Å
]
Tem
pera
ture
[K]
Time [ps]
c) 4th ion
modified depositions
d) truncated profile e) broadened profile f) narrowed profile
115
120
125
130
135
140
145
150
155
160
0 10 20 30 40 50 60 70 80 90 100 0
1000
2000
3000
4000
5000
6000
7000
8000
9000
Clu
ster
dim
ensi
on [Å
]
Tem
pera
ture
[K]
Time [ps]
115
120
125
130
135
140
145
150
155
160
0 10 20 30 40 50 60 70 80 90 100 0
1000
2000
3000
4000
5000
6000
7000
8000
9000
Clu
ster
dim
ensi
on [Å
]
Tem
pera
ture
[K]
Time [ps]
115
120
125
130
135
140
145
150
155
160
0 10 20 30 40 50 60 70 80 90 100 0
1000
2000
3000
4000
5000
6000
7000
8000
9000
Clu
ster
dim
ensi
on [Å
]
Tem
pera
ture
[K]
Time [ps]
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.
References
[1] C. D’Orleans, J. P. Stoquert, C. Estourns, C. Cerruti, J. J. Grob,
J. L. Guille, F. Haas, D. Muller, M. Richard-Plouet, Anisotropy of
co nanoparticles induced by swift heavy ions, Phys. Rev. B 67 (2003)
220101.
[2] J. A. Reyes-Esqueda, V. Rodrguez-Iglesias, H.-G. Silva-Pereyra,
C. Torres-Torres, A.-L. Santiago-Ramırez, J. C. Cheang-Wong,
A. Crespo-Sosa, L. Rodrıguez-Fernandez, A. Lopez-Surez, A. Oliver,
12
Anisotropic linear and nonlinear optical properties from anisotropy-
controlled metallic nanocomposites, Optics Express 17 (5) (2009) 12849–
12868.
[3] J. F. Ziegler, J. P. Biersack, M. D. Ziegler, SRIM - The Stopping and
Range of Ions in Matter, SRIM Co., Chester, Maryland, USA, 2008.
[4] P. Kluth, C. S. Schnohr, O. H. Pakarinen, F. Djurabekova, D. J.
Sprouster, R. Giulian, M. C. Ridgway, A. P. Byrne, C. Trautmann,
D. J. Cookson, K. Nordlund, M. Toulemonde, Fine structure in swift
heavy ion tracks in amorphous sio2, Phys. Rev. Lett. 101 (2008) 175503.
[5] N. Itoh, D. M. Duffy, S. Khakshouri, A. M. Stoneham, Making tracks:
electronic excitation roles in forming swift heavy ion tracks, Journal of
Physics: Condensed Matter 21 (2009) 474205.
[6] A. Meftah, F. Brisard, J. M. Costantini, E. Dooryhee, M. Hage-Ali,
M. Hervieu, J. P. Stoquert, F. Studer, M. Toulemonde, Track formation
in sio2 quartz and the thermal-spike mechanism, Phys. Rev. B 49 (1994)
12457 – 12463.
[7] M. Toulemonde, C. Dufour, A. Meftah, E. Paunier, Transient thermal
processes in heavy ion irradiation of crystalline inorganic insulators,
Nucl. Instr. Meth. Phys. Res. B 166-167 (2000) 903–912.
[8] M. P. Allen, D. J. Tildesley, Computer Simulation of Liquids, Oxford
University Press, Oxford, England, 1989.
13
[9] H. J. C. Berendsen, J. P. M. Postma, W. F. van Gunsteren, A. Di-
Nola, J. R. Haak, Molecular dynamics with coupling to external bath,
J. Chem. Phys. 81 (8) (1984) 3684.
[10] S. von Alfthan, A. Kuronen, K. Kaski, Realistic models of amorphous
silica: A comparative study of different potentials, Phys. Rev. B 68
(2003) 073203.
[11] T. Watanabe, D. Yamasaki, K. Tatsumura, I. Ohdomari, X, Appl. Surf.
Sci. 234 (2004) 207.
[12] J. Samela, K. Nordlund, V. N. Popok, E. E. B. Campbell, Origin of
complex impact craters on native oxide coated silicon surfaces, Phys.
Rev. B 77 (2008) 075309.
[13] K. Awazu, X. Wang, M. Fujimaki, J. Tominaga, H. Aiba, Y. Ohki,
T. Komatsubara, Elongation of gold nanoparticles in silica glass by ir-
radiation with swift heavy ions, Phys. Rev. B 78 (2008) 054102.
[14] Z. G. Wang, C. Dufour, E. Paumier, M. Toulemonde, The se sensitivity
of metal under swift-heavy-ion irradiation: a transient thermal process,
J. Phys.: Condens. Matter 6 (1994) 6733–6750.
[15] J. Robertson, Band offsets of wide-band-gap oxides and implications for
future electronic devices, J. Vac. Sci. Technol. B. 18 (2000) 1785.
[16] M. Toulemonde, W. Assman, C. Trautmann, F. Gruner, H. D. Mieskes,
H. Kucal, Z. G. Wang, Electronic sputtering of metals and insulators by
swift heavy ions, Nucl. Instr. Meth. Phys. Res. B 212 (2003) 346–357,
nice overview.
14
[17] C.-L. Kuo, P. Clancy, Development of atomistic meam potentials for the
silicon-oxygen-gold ternary system, Modelling and Simulation in Mate-
rials Science and Engineering 13 (8) (2005) 1309.
[18] S. Ryu, W. Cai, A gold-silicon potential fitted to the binary phase dia-
gram, Journal of Physics: Condensed Matter 22 (5) (2010) 055401.
[19] O. H. Pakarinen, F. Djurabekova, K. Nordlund, P. Kluth, M. Ridg-
way, Molecular dynamics simulations of the structure of latent tracks in
quartz and amorphous sio2, Nucl. Instr. Meth. Phys. Res. B 267 (2009)
1456–1459.
[20] S. M. Foiles, M. I. Baskes, M. S. Daw, Embedded-atom-method func-
tions for the fcc metals cu, ag, au, ni, pd, pt, and their alloys, Phys.
Rev. B 33 (12) (1986) 7983, Erratum: ibid, Phys. Rev. B 37, 10378
(1988).
[21] K. Nordlund, parcas computer code. The main principles of the molec-
ular dynamics algorithms are presented in [33, 34]. The adaptive time
step and electronic stopping algorithms are the same as in [35] (2006).
[22] P. M. Morse, Diatomic molecules according to the wave mechanics. ii.
vibrational levels, Phys. Rev. 34 (1930) 57.
[23] J. J. Scherer, J. B. Paul, C. P. Collier, A. O’Keefe, R. J. Saykally,
Cavity ringdown laser-absorption spectroscopy and time-of-flight mass-
spectroscopy of jet-cooled gold silicides, J. Chem. Phys. 103 (1995) 9187–
9192.
15
[24] P. Turski, On the ground states of copper, silver and gold silicides,
Chemical Physics Letters 315 (1-2) (1999) 115 – 118. doi:DOI:
10.1016/S0009-2614(99)01205-1.
[25] A. Citra, L. Andrews, Reactions of laser-ablated silver and gold atoms
with dioxygen and density functional theory calculations of product
molecules, J. Mol. Struct.: THEOCHEM 489 (2-3) (1999) 95 – 108.
[26] W. M. Haynes, CRC Handbook of Chemistry and Physics, 91st Edition
(Internet Version 2011), CRC Press/Taylor and Francis, Boca Raton,
FL, USA.
[27] J. F. Ziegler, J. P. Biersack, U. Littmark, The Stopping and Range of
Ions in Matter, Pergamon, New York, 1985.
[28] K. Awazu, X. Wang, M. Fujimaki, T. Komatsubara, J. Watanabe,
Y. Matsumoto, S. Warisawa, S. Ishihara, The fabrication of aligned
pairs of gold nanorods in sio2 films by ion irradiation, Nanotechnology
20 (2009) 325303.
[29] W. Humphrey, A. Dalke, K. Schulten, VMD – Visual Molecular Dynam-
ics, Journal of Molecular Graphics 14 (1996) 33–38.
[30] S. Klaumunzer, Modification of nanostructures by high-energy ion
beams, Nucl. Instr. Meth. Phys. Res. B 244 (1) (2006) 1–7.
[31] S. Roorda, T. vanDillen, A. Polman, C. Graf, A. vanBlaaderen, B. J.
Kooi, Aligned gold nanorods in silica made by ion irradiation of coreshell
colloidal particles, Advanced Materials 16 (3) (2004) 235–237.
16
[32] M. C. Ridgway, P. Kluth, R. Giulian, D. J. Sprouster, L. L. Araujo,
C. S. Schnohr, D. J. Llewellyn, A. P. Byrne, G. J. Foran, D. J. Cookson,
Changes in metal nanoparticle shape and size induced by swift heavy-ion
irradiation, Nucl. Instr. Meth. Phys. Res. B 267 (2009) 931.
[33] K. Nordlund, M. Ghaly, R. S. Averback, M. Caturla, T. Diaz de la
Rubia, J. Tarus, Defect production in collision cascades in elemental
semiconductors and fcc metals, Phys. Rev. B 57 (13) (1998) 7556–7570.
[34] M. Ghaly, K. Nordlund, R. S. Averback, Molecular dynamics investi-
gations of surface damage produced by kev self-bombardment of solids,
Phil. Mag. A 79 (4) (1999) 795.
[35] K. Nordlund, Molecular dynamics simulation of ion ranges in the 1 –
100 kev energy range, Comput. Mater. Sci. 3 (1995) 448.
17
top related