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SCATTERING OF IONS BEYOND THE SINGLE SCATTERING
CRITICAL ANGLE IN HIERDA
P.N. Johnston, I.F. Bubb and R. Franich
Department of Applied Physics, Royal Melbourne Institute of Technology, GPO Box 2476V, Melbourne 3001, Australia.
D.D. Cohen and N. Dytlewski
Australian Nuclear Science and Technology Organisation, PMB 1, Menai 2234, Australia.
K. Arstila and T. Sajavaara
Accelerator Laboratory, University of Helsinki, P.O. Box 43, FIN-00014, Finland
In Heavy Ion Elastic Recoil Detection Analysis (HIERDA), Rutherford scattering determines the number of scattered
and recoiled ions that reach the detector. Because plural scattering is a major contributor to the spectrum and can mask
important features and otherwise distort the spectrum it needs to be described correctly. Scattering more than once is a
frequent occurrence so many ions scatter beyond the maximum scattering angle possible by a single scattering event. In this
work we have chosen projectile/target combinations which enable the exploitation of the scattering critical angle to obtain
spectra which are from ions which have all been scattered more than once. Monte Carlo simulation of the ion transport is
used to study the plural scattering using a fast FORTRAN version of TRIM. The results of the simulations are compared
with experimental measurements on samples of Si, V and Co performed with 20-100 MeV beams of Br, I and Au ions using
ToF-E HIERDA facilities at Lucas Heights and Helsinki.
in terms of the number of large angle scattering events and
the histories of individual ions that reach the detection
system. There is also specific interest in the capability
limits of existing analytical tools.
INTRODUCTION
Heavy ion scattering is an increasingly important tool
for materials analysis. Heavy ions undergo a great deal of
plural scattering in these analysis techniques and the effects
of large angle plural scattering in heavy ion elastic recoil
detection analysis (HIERDA) have been previously
demonstrated [1, 2].
In many cases, there is overlap of the signal due to
plural scattering and the signal due to single scattering. In
the case of Rutherford scattering, there is a critical angle
which we can exploit experimentally to obtain scattered
spectra where single scattering is not present. When the
scattering angle, θ, satisfies the relation
In this work, (large angle) plural scattering is
differentiated from small angle multiple scattering which is
well described by Sigmund and co-workers [7, 8]. This
differentiation is not because these phenomena are
fundamentally different but because they are handled
differently in analysis of heavy ion scattering data. Small
angle multiple scattering is usually handled as a continuum
process and is often incorporated into “slab” analyses, but
large angle plural scattering is handled as a discrete process
and cannot be incorporated into “slab” analysis.
 M2 


 M1 
θ > sin −1 
where M1 is the mass of the incident ion and M2 is the mass
of the target atom, then the detected scattered ion has
undergone more than one scattering event.
For this reason, more sophisticated methods are used to
simulate HIERDA spectra than the "slab" analysis method
which has traditionally been used for light ion analysis
techniques.
These techniques include Monte Carlo
techniques, e.g. [3, 4], and simulation tools that include
double scattering, e.g. SIMNRA [5]. In this work, we make
use of the Monte Carlo techniques described by Franich et
al. [6] to examine the effect of plural scattering in HIERDA
Scattering beyond the critical angle is examined by
reference to experimental measurements, but includes
examination of the number and size of angles in scattering
events which lead to an ion reaching the detection system.
EXPERIMENT
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Experimental work to obtain scattering spectra beyond
the critical angle was conducted at Lucas Heights,
Australia and the University of Helsinki, Finland. The
experimental apparatus at each of these facilities uses a
time of flight and energy (ToF-E) telescope design based
on the telescope at Uppsala which has been described [9].
As described in [1], the Si detector and therefore the entire
ToF-E detector telescope subtends 0.02 msr. In order to
allow efficient modelling, if we define the scattering and
azimuthal angles to be θ and φ respectively, then the
simulated spectra were chosen on the criteria that (i) 44° < θ
< 46° and (ii) φ was restricted so that the excess path length
in the exiting ion's path is less than 10% in total.
At Lucas Heights, the experimental data were obtained
using 60 MeV 81Br8+ and 60 MeV 127I9+ ions from the
ANTARES 8 MV FN Tandem accelerator of the Australian
Nuclear Science and Technology Organisation. The ToF-E
detector telescope has a flight path of 495 mm and has
carbon foils of 25.3 µg/cm2 as described elsewhere [10].
The targets were pure silicon, vanadium, and cobalt
samples. The samples were irradiated at 67.5º to the surface
normal.
The ion energies were then corrected for energy loss in the
first timing foil and expressed as flight time over the known
flight length. These flight times were then converted to a
time histogram (simulated spectrum).
RESULTS AND DISCUSSION
Figure 1 shows a comparison of a simulation
experimental data for Br scattering off V as discussed
above. Although the shape of the experimental and
simulated spectra are similar the match is not perfect. The
differences are likely to arise from both experimental and
theoretical sources. These sources of difference are most
likely due to the approximations used in TRIM, in
particular the ‘magic formula’ which simplifies the
scattering calculation. Nevertheless the shapes are
sufficiently similar to indicate that useful information can
be gained from further examination of the simulated
spectrum.
In Helsinki, the ToF-E HIERDA measurements were
performed using ions from the 5 MV EGP-10-II tandem
accelerator. The Helsinki system has a variable scattering
geometry in 10º increments (we used 30º and 40º) and a
684 mm flight length [11-13]. Experiments were performed
on the same samples using 20, 28 and 37 MeV 81Br, 22, 32
and 42 MeV 127I as well as 21 and 42 MeV 197Au ions on
the same samples used at Lucas Heights.
Time spectra were extracted from the raw data as these
have better resolution for heavy elements than the energy
spectra exhibit [14] as well as being subject to a far simpler
and more direct calibration process. Time calibration is
established from the ToF of recoiled and scattered ions
from the surfaces of different samples which span a wide
range of atomic masses as described by Stannard et al [10].
Normalised Counts
MONTE-CARLO SIMULATION
Franich [6] has described the Monte Carlo simulation
FasTRIM as modified at RMIT to analyse HIERDA data to
study the effects of plural scattering. FasTRIM is based on
the original TRIM code of Ziegler et al. [15]). Unlike the
approach of Arstila [4], this software allows the simulation
of the scattered as well as recoiled spectra and is
necessarily more time consuming for that reason.
As Franich [6] has described, in addition to the energy
and species of the ion reaching the detector, the ten largest
scatter angles are stored. This allows us to gain
considerable insight into the plural scattering phenomenon.
1000
100
Model
Expt.
10
1
50
70
90
110
130
Flight Time (ns)
The FasTRIM software has been used to model several
systems. In this paper we examine the simulation of 60
MeV Br ions on a solid V target at 45˚ in the Lucas Heights
experimental arrangement. The critical angle for scattering
of Br from V is 40.2˚, so this scattered spectrum should not
contain singly scattered ions. Simulations were conducted
with 6x109 ion histories for this example.
FIGURE 1. Comparison of the experiment and simulation for
scattering of 60 MeV Br ions from a V surface at 45˚.
In Figure 2, the simulated data is partitioned by the
number of scatter events of more than 3˚ that the ion
undergoes before reaching the detector. We have arbitrarily
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assigned 3º per scattering event as the limit of small angle
multiple scattering. Firstly we see that there is a
contribution due to ‘singly’ scattered ions. More correctly,
these are ions that have undergone small angle multiple
scattering – but only one scatter has been of greater than 3˚.
This emphasises the arbitrary nature of any division
between small angle multiple scattering and large angle
plural scattering. These ions are not at the highest energies
in the spectrum which indicates that they arise from a
considerable depth in the sample where small angle
multiple scattering has had the opportunity to cause
significant beam divergence both for the incident and
exiting ions. This angular deviation combined with the
single scattering event is sufficient for the ion to reach the
detector.
The 2nd and 3rd largest scattering angles are mostly less
than 10˚ but the distributions have long tails to angles
above 30˚ and 20˚ respectively. The 8th to 10th largest
scatters are normally of approximately 1-2˚ but there
remains a significant tail to the distribution extending
beyond 5˚.
CONCLUSION
The Monte Carlo simulation software for HIERDA has
been used to examine the number and angle of scattering
events undergone by heavy ions that are detected beyond
the critical scattering angle.
The largest contributions to the spectrum come from
double and triple scattering, but there are contributions
from ions scattered by more than 3º up to the maximum of
10 times recorded in the simulation. The largest number of
events comes from double scattering, but the number of
events declines slowly reducing by a factor of 2 after 6
plural scattering events. The contributions from ions
undergoing successive numbers of plural scattering events
shows a similar shape, but each contribution is moved to a
lower energy (or longer flight time).
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The detection of ions that have only undergone one
scattering event of more than 3º demonstrates that there is
no clear boundary between small angle multiple scattering
and large angle plural scattering.
There are many ions reaching the detector in such
experiments that have undergone many large angle plural
scattering events. Situations where 10 large angle
scattering events have occurred have been observed.
1
1 scatter
2 scatters
3 scatters
5 scatters
8 scatters
Total spectrum
Largest
Cumulative Distribution Pr(θ >θ s )
2nd largest
Counts
100
10
3rd largest
0.8
5th largest
8th largest
0.6
0.4
0.2
1
60
90
120
150
180
210
0
Time of Flight (ns)
0
10
20
30
40
50
Scattering Angle θ s (º)
FIGURE 2. Components of the total spectrum associated with
1, 2, 3, 5 and 8 scattering events of more than 3˚.
FIGURE 3. The cumulative probability distributions for the
largest, 2nd, 3rd, 5th and 8th largest scattering angles for ions
reaching the detector. The critical scattering angle is 40.2º while
the detector spans angles from 44º to 46º.
In Figure 3 the distribution of scattering angles is shown
for the largest as well as 2nd, 3rd, 5th and 8th largest
scattering angles for ions that reached the detector. The
largest scattering angle approaches the critical scattering
angle of 40.2˚ as the largest available angle for a single
scatter. There is a very long tail to the distribution with
some ions only undergoing scatters of less than 20˚.
Simulation software incorporating double scattering is
likely to reproduce the highest energy features of the
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spectrum, but will undoubtedly fail to predict many aspects
of the spectra, including intensity and spectral shape.
ACKNOWLEDGEMENTS
This work is supported by the The Australian Institute of
Nuclear Science and Engineering.
REFERENCES
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
P.N. Johnston, I.F. Bubb, M. El Bouanani, D.D. Cohen
and N. Dytlewski, American Institute of Physics
Conference Proceedings 475, AIP Press, New York
(1999), Editors J.L. Duggan and I.L. Morgan, p.517.
P. N. Johnston, R. D. Franich, I. F. Bubb, M. El
Bouanani, D. D. Cohen, N. Dytlewski and R. Siegele,
Nucl. Instr. and Meth. B 161-163, 314-317 (2000).
R. D. Franich, P. N. Johnston, I. F. Bubb, N. Dytlewski
and D. D. Cohen, Nucl. Instr. and Meth. B 190, 252255 (2002).
K. Arstila, T. Sajavaara and J. Keinonen, Nucl. Instr.
and Meth. B 174, 163-172 (2001).
M. Mayer, American Institute of Physics Conference
Proceedings 475, AIP Press, New York (1999), Editors
J.L. Duggan and I.L. Morgan, p.541; M. Mayer,
SIMNRA User’s Guide, Report IPP 9/113, MaxPlanck-Institut für Plasmaphysik, Garching, Germany,
1997.
R.D. Franich, P.N. Johnston and I.F. Bubb, (this
Proceedings)
P. Sigmund and K.B. Winterbon, Nucl. Instr. and
Meth. 119, 541 (1974).
A.D. Marwick and P. Sigmund, Nucl. Instr. and Meth.
126, 317 (1975).
H.J. Whitlow, G. Possnert and C.S. Petersen, Nucl.
Instr. and Meth. B 27, 448 (1987).
W. B. Stannard, P. N. Johnston, S. R. Walker, I. F.
Bubb, J. F. Scott, D. D. Cohen, N. Dytlewski and J. W.
Martin, Nucl. Instr. and Meth. B 99, 447-449 (1995).
J. Jokinen, J. Keinonen, P. Tikkanen, A. Kuronen, T.
Ahlgren and K. Nordlund. Nucl. Instr. and Meth. B
119, 533 (1996).
J. Jokinen, P. Haussalo, J. Keinonen, M. Ritala, D.
Riihelä and M. Leskelä. Thin Solid Films 289, 159
(1996).
J. Jokinen, Acta Polytechn. Scand., Appl. Phys. Ser.
212 (1997).
P.N. Johnston, M. El Bouanani, W.B. Stannard, I.F.
Bubb, D.D. Cohen, N. Dytlewski and R. Siegele, Nucl.
Instr. and Meth. B 136-138, 669-673 (1998).
J.F. Ziegler, J.P. Biersack, TRIM-95 Computer Code,
version 95.9.
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