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 CP680, Application of Accelerators in Research and Industry: 17th Int'l. Conference, edited by J. L. Duggan and I. L. Morgan © 2003 American Institute of Physics 0-7354-0149-7/03/$20.00 460 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 461 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). 1000 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 462 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. 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