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amu 1H+ and 4He+ ions in polyvinyl formal
Nuclear Instruments and Methods in Physics Research B 268 (2010) 1759–1762
Contents lists available at ScienceDirect
Nuclear Instruments and Methods in Physics Research B journal homepage: www.elsevier.com/locate/nimb
Stopping of 0.2–3.4 MeV/amu 1H+ and 4He+ ions in polyvinyl formal S. Damache a, D. Moussa b, S. Ouichaoui b,* a b
Division de Physique, CRNA, 02 Bd. Frantz Fanon, B.P. 399 Alger-gare, Algiers, Algeria USTHB, Faculté de Physique, B.P. 32, 16111 Bab-Ezzouar, Algiers, Algeria
a r t i c l e
i n f o
Article history: Available online 26 February 2010 Keywords: Stopping power Bragg’s additivity rule Polymer compound
a b s t r a c t The stopping powers of polyvinyl formal resin for protons and alpha particles have been measured over the energy range (0.2–3.4) MeV/amu with an overall relative uncertainty of less than 2.5% using the ion beam transmission method. The obtained results are discussed in comparison to scarce experimental data from the literature and to values calculated by the SRIM-2008 computer code assuming Bragg-Kleeman’s additivity rule of stopping powers. Departures from additivity attaining 5.5% and 3.0% for the proton and alpha particle data, respectively, are observed at moderate projectile velocities, increasingly as one evolves towards the stopping power maximum dominated by charge exchange effects. They are presumed to be mainly due to valence structure effects involving the C–H bonds of the studied polymer compound. The less pronounced deviation for alpha particles is probably due to the projectile screening effect that occurs in distant collisions tending to reduce the contribution of valence electrons in the low projectile velocity regime. Ó 2010 Elsevier B.V. All rights reserved.
1. Introduction The stopping of light charged particles in matter (either elemental or composite) is of considerable interest both from the fundamental and practical points of view. Besides providing valuable information on energy-loss mechanisms, it is widely exploited in many applications involving ion-beam bombardment such as, e.g., radiation therapy [1,2], materials analysis [3,4] and ion implantation technology [5]. Most of ion beam applications use compound materials for which the accurate knowledge of stopping powers for protons and alpha particles is essential for investigating, e.g., materials aggregation effects that may induce significant departures from the Bragg-Kleeman linear additivity rule [6] assuming that the interaction between the projectile and a target atom is independent of its environment within the compound. However, in the case of polymer compounds like polyvinyl formal resin (or formvar), stopping power experimental data for protons and alpha particles are very scarce. To our knowledge, the only available ones are those reported by the Belgian-Finnish group in Ref. [7] taken, in case of protons, over the energy range 0:55 MeV 6 E 6 1:75 MeV, far above the energy region corresponding to the stopping power maximum expected to occur around 100 keV. Besides, thin films of formvar are potentially used in nuclear physics experiments where stopping power data both for H+ and 4He+ are needed. Thus, formvar is used as ultra thin * Corresponding author. Fax: +213 21 24 73 44. E-mail addresses: [email protected] (S. Damache), [email protected] (S. Ouichaoui). 0168-583X/$ - see front matter Ó 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.nimb.2010.02.068
film targets in Coulomb-explosion experiments [8] as well as in heavy ion energy measurements using the proton recoil technique [9]. Among polymer materials, formvar is known for its high resistance to heat and radiation effects, and as plastic conductive foils, it is very suitable for position sensitive micro-channel plate detector systems [10]. The present paper reports on our measurements of formvar stopping powers for E (0.2–3.4) MeV/amu 1H+ and 4He+ projectiles using the transmission method where an overall relative uncertainty of less than 2.5% was achieved. The obtained S(E) data are thus reported and discussed in comparison to scarce previous ones [7] from the literature and to values generated by the SRIM2008 semi-empirical computer code [11] assuming the validity of Bragg-Kleeman’s additivity rule for stopping powers. 2. Experimental þ Incident H+ and 4He+ ion beams as well as molecular Hþ 2 and H3 ones were generated by the CRN Algiers 3.75 MV Van de Graaff accelerator with optimum energy resolution DE/E 0.1% and current intensity I 30 nA. The experimental set up and procedure used for energy loss measurements were described in details elsewhere [12,13]. In brief, primary beams collimated by 1.5 mm diameter slits were first directed onto a very thin Au layer evaporated onto a Si substrate. Then, secondary back-scattered beams of considerably reduced intensity were used in the energy loss measurements by means of a 500 lm-thick ULTRA ion implanted Si detector (Ortec U-011-025-500) placed at a laboratory angle of 165° relative to the incident primary beam direction. The detector,
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S. Damache et al. / Nuclear Instruments and Methods in Physics Research B 268 (2010) 1759–1762
collimated with a 3 mm diameter slit and set 1.5 cm apart from the formvar stopping sample, was associated to standard Ortec data acquisition electronics comprising a charge pre-amplifier (Ortec A142), a pulse height amplifier (Ortec 572) and an advanced multichannel analyzer (Ortec 4096 MCB Card). During all experimental runs, a maximum bias voltage was applied to the detector while the electronic gain of the pulse processing chain was set to fixed, adequately chosen values for all used projectile species in order to minimize pulse high defects (PHDs) that are the main cause of non linearity in the detector energy response ([14] and references cited therein). These conditions corresponded to a minimum level of the dead time, permanently checked during the experiment. A detailed energy-channel calibration curve was accurately determined for each projectile specie with recording data points without the target sample in place that was found to be essentially linear. Notice that the maximum uncertainty (0.31%) in the calibration slope was obtained in the case of alpha particles. It mainly arose from neglected ion energy losses within the detector entrance window (dead layer of 50 nm of equivalent Si [15]) that represents the main contribution to PHDs [14]. Indeed, e.g., the calculated energy loss, DEDL [14], in this inactive region of the detector for the considered alpha particle energies ranged between 10.68 keV and 16.01 keV (corresponding relative energy losses of 1.66% and 7.01%, respectively), and therefore the absolute uncertainty thus introduced in the calibration slope amounted to a value of 0.01 keV/channel. The measured energy resolution of the detection system was found to be of 0.2% (i.e., 11 keV FWHM of the 5.486 MeV alpha particle peak from a 241Am radioactive source). In each experimental run, ion energy spectra obtained with and without the target sample in place were successively recorded without breaking the high vacuum (pressure of 2 106 Torr) inside the scattering chamber by using a special target holder as detailed in Ref. [12]. Fig. 1 reports a typical energy loss spectrum with and without the formvar film installed, recorded only over a portion of 2048 channels of the multichannel analyzer for 1 MeV primary protons. Notice that, the detector PHDs should not induce a significant uncertainty in the deduced energy loss measurements (see section below) over the investigated ion energy ranges since they are practically compensated. Indeed, the dead layer PHDs (DEDL), calculated with and without formvar sample in place, are practically of the same magnitude (the difference amounts to, at most, 1.95 keV) and no noticeable error is thus introduced on the obtained ion energy losses (relative uncer-
tainty < 0.35%). The formvar foil used was supplied by the Chemistry laboratory of the InESS/CRNS Strasbourg (France) with a specified thickness of 2.5 lm. It is a single-bonded polymer compound with chemical formula (C5H8O2)n having 8 C–H bonds, 4 C–C bonds (with 2 12 ones from the bonding to neighboring molecules), and 4 C–O bonds per molecule. Its elemental composition expressed in weight fraction is: C: 59.98%, H: 8.05% and O: 31.97%. The foil thickness and non-uniformity was investigated following the method described in [12,16] using a very thin mixed 241 Am–239Pu–233U radioactive source and standard alpha particle stopping powers from the SRIM-2008 computer code assuming Bragg-Kleeman’s additivity rule. The details of this procedure are reported in Ref. [17] devoted to light particle stopping in Ag. A thickness value x ffi (277.46 ± 6.66) lg/cm2 was derived on the basis of the 2% accuracy of the SRIM-2008 S(E) computed values. 3. Stopping power determination and results The difference in mean peak positions of the recorded particle spectra without and with the polyvinyl formal target in place (see Fig. 1) yields the mean energy loss, DE, of secondary backscattered ions across the latter. The peak positions were obtained from Gaussian fits to the measured energy loss distributions over energy intervals defined by about 4 times the standard deviation, r, around the mean value [12]. First, the experimental distributions have been inspected for their Gaussian shapes by computing their overall dimensionless path-length parameters [18,19] that were found to exceed unity for both used projectiles, i.e., X2 X2 1:32 P T 2t P 323:58 for H+ and 210 P T 2t P 1624:81 for 4He+ (with m m 2 Xt and Tm denoting respectively the total straggling variance and the maximum energy transferred in a single collision). Therefore, neglecting single and free Coulomb collisions, the Gaussian character of the measured energy loss distributions was thus checked. According to Andersen et al. [20], the target sample average stopping power, SðEÞ, at the mean energy E ¼ E D2E (with E denoting the energy of backscattered projectiles off the Au–Si target) can be determined to within 0.05% by the ratio DE=x, provided that the energy loss fraction, DE/E amounts to less than 20%. In cases where this condition is not fulfilled, our calculated SðEÞ values were corrected by adding a quadratic correction term derived from an expansion of the SðEÞ function as in Ref. [20]. Besides, the average path lengths of the H+ and 4He+ ions within the formvar target sample were assumed to be equal to the sample mean thickness value x determined above. Indeed, this polymer material is constituted of light elements and therefore the increase of both proton and alpha particle path lengths within the target due to multiple scattering was neglected. The maximum error introduced by this assumption is of less than 0.1%. The derived SðEÞ results are reported in Table 1 together with corresponding relative uncertainties and ion energy loss fractions, and plotted in Fig. 2(a) for protons and (b) for alpha particles. The overall relative uncertainties in the SðEÞ data were evaluated following the same method used in Ref. [12]. They were derived from errors associated with quantities involved in the determination of stopping powers (mean peak positions, energy-channel calibration slope, target sample thickness) and propagated in the above SðEÞ expression. 4. Discussion and conclusion
Fig. 1. Typical energy loss spectra recorded with and without the formvar sample in place for 1 MeV incident protons using a 2048-channel portion of an Ortec MCB Card.
In Fig. 2, our SðEÞ experimental data are compared to only previous ones reported by Munnik et al. [7] and to values calculated by the SRIM-2008 computer code [11] assuming Bragg-Kleeman’s additivity of stopping powers. As can be seen, while for the proton data (Fig. 2(a)) an overall agreement with previous measurements
S. Damache et al. / Nuclear Instruments and Methods in Physics Research B 268 (2010) 1759–1762
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Table 1 Energy loss fractions DE/E (%) for back-scattered ions transmitted through the target sample (column 2) and corresponding measured SðEÞ data (column 3) versus the projectile mean energies E (column 1) in the polyvinyl formal resin: (a) for protons, (b) for alpha particles. (a) Protons results 193.4 234.2 313.6 370.3 425 478.5 478.5 531.6 584 687.6 738.7 789.6 840.7 891.1 941.7 1042.3 1142.5 1242.6 1342.3 1441.7 1540.5 1640.3 1739.2 1838.3 1937.4 2134.6 2331.7 2529 2726.3 2923.8 3120.1 3316.7
68.42 56.45 40.01 32.06 26.53 22.46 22.4 19.18 16.65 12.92 11.57 10.43 9.38 8.6 7.84 6.63 5.71 4.94 4.35 3.87 3.52 3.1 2.82 2.56 2.33 2 1.75 1.51 1.31 1.12 1.03 0.93
725.0 ± 17.4 664.1 ± 16.0 565.3 ± 13.6 509.6 ± 12.3 468.6 ± 11.3 436.3 ± 10.5 435.2 ± 10.5 406.6 ± 09.8 382.4 ± 09.2 342.4 ± 08.2 327.1 ± 07.9 313.2 ± 07.5 298.3 ± 07.2 288.5 ± 06.9 277.0 ± 06.7 257.7 ± 06.2 242.2 ± 05.8 226.9 ± 05.5 215.0 ± 05.2 204.8 ± 04.2 199.2 ± 04.8 186.0 ± 04.5 179.5 ± 04.3 172.0 ± 04.1 164.3 ± 04.0 155.4 ± 03.7 148.0 ± 03.6 138.6 ± 03.4 129.2 ± 03.1 118.4 ± 02.9 116.5 ± 02.8 112.0 ± 02.8
(b) Alpha particles results 605.7 694.5 786.4 883.6 982.6 1084 1185.2 1287.3 1388.5 1490.2 1591.1 1791.7 1990.3 2188.1 2379.7
68.78 63.23 58.02 52.75 47.94 43.45 39.53 35.95 32.89 30.09 27.65 23.57 20.34 17.69 15.88
2288.6 ± 55.0 2314.3 ± 55.6 2316.7 ± 55.7 2281.8 ± 54.8 2233.3 ± 53.7 2168.5 ± 52.1 2104.3 ± 50.6 2033.8 ± 48.9 1969.7 ± 47.3 1902.5 ± 45.7 1840.1 ± 44.2 1725.2 ± 41.5 1624.3 ± 39.0 1530.1 ± 36.8 1479.3 ± 35.5
[7] is observed, within experimental uncertainties, over the whole explored common energy range, in case of the alpha particle data (see Fig. 2(b)) the measured previous values (Ref. [7]) clearly lie above our own data points mainly in the energy region around the stopping power maximum where the increasing deviation amounts up to 9%. One can also notice that the stopping power maximum for previous alpha particle data [7] is shifted by 40 keV towards low energies relative to our data. Besides, our SðEÞ data show to be in fair agreement with values derived by the SRIM-2008 code over the energy range Ep J 1:8 MeV in case of protons and at Ea J 1:8 MeV in case of alpha particles. In the remaining lower energy regions explored, however, the SRIM-2008 calculation increasingly underestimates our data for both two projectile types as one goes down towards the stopping power maximum. The observed deviations are significant, amounting to 5.5% and 3.0%, in average, for the proton and alpha particle data, respectively. Therefore, one can conclude that the measured stopping powers of both protons and alpha
Fig. 2. Measured stopping powers (solid circles) in polyvinyl formal versus ion mean energy compared to previous experimental data (open triangles, [7]) and to values derived by the SRIM-2008 computer code (solid curve, [11]) assuming BraggKleeman’s additivity rule: (a) for protons, (b) for alpha particles.
particles in the investigated formvar polymer deviate from Bragg-Kleeman’s additivity rule at moderate projectile velocities when evolving down towards the stopping power maximum dominated by charge exchange processes. Notice that we have also pointed out such deviations relative to the SRIM 2003 calculation based on Bragg-Kleeman’s additivity rule in a previous study [12] of the stopping powers of polypropylene and mylar polymers for (0.236–3.019) MeV protons. Previously, these trends of stopping powers have been reported by several groups ([21–26] and references cited therein) for various projectile-compound target combinations exhibiting deviations up to 25%. The observed increasing departures of S(E) data from the stopping power linear additivity assumption as the projectile velocity decreases seem to be due to a rather complex interplay between various effects such as shell correction, Barkas effect and valence structure [25,27] among which the latter likely plays a dominant role. Consequently, they mainly relate to differences in chemical bonding and physical phase state of the compound target electronic structure characterizing the moderate and low ion velocity regimes. Chemical binding effects become more significant for stopping materials of low atomic number constituents mainly as the projectile velocity approaches the transition region [28]. In this respect, the contribution to the stopping process of the C5H8O2 molecule outermost electrons is presumably expected to become more and more pronounced with decreasing projectile velocity due to the increasing non-participation (or even the closing) of the molecule inner shell excitation channels. More precisely, the observed effect mainly implies valence electrons of the C–H bonds that represent half of the
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total chemical bonds of the (C5H8O2)n investigated polymer compound. The transitions of 1s electrons of H atoms to 2p-like states of C atoms likely lead to the formation of relatively strong C–H bonds and to drastic changes of their orbital velocities and excitation spectra. In contrast, the electrons of C–C and C–O bonds remain practically unchanged in comparison to their states in isolated C and O atoms, and therefore presumably do not have a significant influence on the linear additivity rule of stopping powers. As stated, it is found that the departure from the S(E) additivity rule is more pronounced in case of the proton data than for alpha particle ones. It can be noted, moreover, that the proton kinetic energy limit, E=A ffi 0:94 MeV/amu, at which the Bragg-Kleeman rule breaks down is about twice than for alpha particles (E=A ffi 0:45 MeV/amu). This distinctive feature can be related to the projectile electronic screening that occurs at low velocities tending to reduce the strength of Coulomb attraction between incident 4 He+ ions and target valence electrons. Indeed, at low projectile velocities the screening by electrons moving with the ion is more important for heavier ions and is then surely more significant for alpha particles than for protons.
References [1] H. Paul, O. Geithner, O. Jäkel, Nucl. Instrum. Methods Phys. Res., Sect. B 256 (2007) 561. [2] J. Sisterson, Nucl. Instrum. Methods Phys. Res., Sect. B 241 (2005) 713. [3] J.R. Tesmer, M. Nastasi (Eds.), Handbook of Modern Ion Beam Materials Analysis, Materials Research Society, Pittsburgh, Pennsylvania, 1995. [4] Y. El Masri, Ch. Heitz, Th. Keutgen, C. Dufauquez, R. Prieels, J. Van Mol, J.B. Natowitz, Nucl. Instrum. Methods Phys. Res., Sect. B 267 (2009) 1158. [5] J.F. Ziegler (Ed.), Ion Implantation – Science and Technology, Ion Implantation Technology co., Chester, Maryland, USA, 2008. [6] W.H. Bragg, R. Kleeman, Phil. Mag. 10 (1905) 318. [7] F. Munnik, A.J.M. Plompen, J. Räisänen, U. Wätjen, AIP Conf. Proc. 392 (1997) 1385.
[8] G. Both, E.P. Kanter, Z. Vager, B.J. Zabransky, D. Zajfman, Rev. Sci. Instrum. 58 (1987) 424. [9] R. Bimbot, D. Gardès, H. Geissel, K.H. Schmidt, Z. Phys. A: Hadrons Nucl. 286 (1978) 327. [10] P. Greene, C.J. Lister, P. Reiter, G.E. Thomas, K.L. Unterzuber, Nucl. Instrum. Methods Phys. Res., Sect. A 459 (2001) 334. [11] J.F. Ziegler, M.D. Ziegler, J.P. Biersack, SRIM-2008 Computer Code, Version SRIM-2008.03, 2008. [12] S. Damache, S. Ouichaoui, A. Belhout, A. Midouni, I. Toumert, Nucl. Instrum. Methods Phys. Res., Sect. B 225 (2004) 449. [13] S. Damache, S. Ouichaoui, D. Moussa, A. Dib, Nucl. Instrum. Methods Phys. Res., Sect. B 249 (2006) 22. [14] C. Pascual-Izarra, N.P. Barradas, Nucl. Instrum. Methods Phys. Res., Sect. B 266 (2008) 1866; N.P. Barradas, A.R. Ramos, E. Alves, Nucl. Instrum. Methods Phys. Res., Sect. B 266 (2008) 1180. [15] http://www.ortec-online.com/detectrors/chargedparticle/ultra.htm. [16] S. Ouichaoui, L. Rosier, E. Hourany, R. Bimbot, N. Redjdal, H. Beaumevieille, Nucl. Instrum. Methods Phys. Res., Sect. B 95 (1995) 463. [17] D. Moussa, S. Damache, S. Ouichaoui, in: Proceedings of the 19th International Conference on Ion Beam Analysis (IBA 2009), Cambridge, UK, September 07– 11. Nucl. Instrum. Methods B 268 (2010) 1754. [18] Lev. G. Glazov, Nucl. Instrum. Methods Phys. Res., Sect. B 192 (2002) 239. [19] P. Sigmund, K.B. Winterbon, Nucl. Instrum. Methods Phys. Res., Sect. B 12 (1985) 1. [20] H.H. Andersen, A.F. Garfinkel, C.C. Hanke, H. Sorensen, Mat. Fys. Medd. Dan. Vidensk. Selsk. 35 (4) (1966). [21] D.I. Thwaites, Nucl. Instrum. Methods Phys. Res., Sect. B 27 (1987) 293. [22] J.F. Ziegler, J.M. Manoyan, Nucl. Instrum. Methods Phys. Res., Sect. B 35 (1988) 215. [23] H. Ammi, M. Chekirine, A. Adjerad, Radiat. Meas. 28 (1997) 1. [24] Helmut Paul, Andreas Paul, Nucl. Instrum. Methods Phys. Res., Sect. B 249 (2006) 1. [25] A. Sharma, A. Fettouhi, A. Schinner, P. Sigmund, Nucl. Instrum. Methods Phys. Res., Sect. B 218 (2004) 19. [26] Y.C. Yu, J.Y. Hsu, K.M. Chen, Nucl. Instrum. Methods Phys. Res., Sect. B 261 (2007) 1184. [27] P. Sigmund, A. Sharma, A. Schinner, A. Fettouhi, Nucl. Instrum. Methods Phys. Res., Sect. B 230 (2005) 1. [28] D.I. Thwaites, Radiat. Res. 95 (1983) 495.
Contents lists available at ScienceDirect
Nuclear Instruments and Methods in Physics Research B journal homepage: www.elsevier.com/locate/nimb
Stopping of 0.2–3.4 MeV/amu 1H+ and 4He+ ions in polyvinyl formal S. Damache a, D. Moussa b, S. Ouichaoui b,* a b
Division de Physique, CRNA, 02 Bd. Frantz Fanon, B.P. 399 Alger-gare, Algiers, Algeria USTHB, Faculté de Physique, B.P. 32, 16111 Bab-Ezzouar, Algiers, Algeria
a r t i c l e
i n f o
Article history: Available online 26 February 2010 Keywords: Stopping power Bragg’s additivity rule Polymer compound
a b s t r a c t The stopping powers of polyvinyl formal resin for protons and alpha particles have been measured over the energy range (0.2–3.4) MeV/amu with an overall relative uncertainty of less than 2.5% using the ion beam transmission method. The obtained results are discussed in comparison to scarce experimental data from the literature and to values calculated by the SRIM-2008 computer code assuming Bragg-Kleeman’s additivity rule of stopping powers. Departures from additivity attaining 5.5% and 3.0% for the proton and alpha particle data, respectively, are observed at moderate projectile velocities, increasingly as one evolves towards the stopping power maximum dominated by charge exchange effects. They are presumed to be mainly due to valence structure effects involving the C–H bonds of the studied polymer compound. The less pronounced deviation for alpha particles is probably due to the projectile screening effect that occurs in distant collisions tending to reduce the contribution of valence electrons in the low projectile velocity regime. Ó 2010 Elsevier B.V. All rights reserved.
1. Introduction The stopping of light charged particles in matter (either elemental or composite) is of considerable interest both from the fundamental and practical points of view. Besides providing valuable information on energy-loss mechanisms, it is widely exploited in many applications involving ion-beam bombardment such as, e.g., radiation therapy [1,2], materials analysis [3,4] and ion implantation technology [5]. Most of ion beam applications use compound materials for which the accurate knowledge of stopping powers for protons and alpha particles is essential for investigating, e.g., materials aggregation effects that may induce significant departures from the Bragg-Kleeman linear additivity rule [6] assuming that the interaction between the projectile and a target atom is independent of its environment within the compound. However, in the case of polymer compounds like polyvinyl formal resin (or formvar), stopping power experimental data for protons and alpha particles are very scarce. To our knowledge, the only available ones are those reported by the Belgian-Finnish group in Ref. [7] taken, in case of protons, over the energy range 0:55 MeV 6 E 6 1:75 MeV, far above the energy region corresponding to the stopping power maximum expected to occur around 100 keV. Besides, thin films of formvar are potentially used in nuclear physics experiments where stopping power data both for H+ and 4He+ are needed. Thus, formvar is used as ultra thin * Corresponding author. Fax: +213 21 24 73 44. E-mail addresses: [email protected] (S. Damache), [email protected] (S. Ouichaoui). 0168-583X/$ - see front matter Ó 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.nimb.2010.02.068
film targets in Coulomb-explosion experiments [8] as well as in heavy ion energy measurements using the proton recoil technique [9]. Among polymer materials, formvar is known for its high resistance to heat and radiation effects, and as plastic conductive foils, it is very suitable for position sensitive micro-channel plate detector systems [10]. The present paper reports on our measurements of formvar stopping powers for E (0.2–3.4) MeV/amu 1H+ and 4He+ projectiles using the transmission method where an overall relative uncertainty of less than 2.5% was achieved. The obtained S(E) data are thus reported and discussed in comparison to scarce previous ones [7] from the literature and to values generated by the SRIM2008 semi-empirical computer code [11] assuming the validity of Bragg-Kleeman’s additivity rule for stopping powers. 2. Experimental þ Incident H+ and 4He+ ion beams as well as molecular Hþ 2 and H3 ones were generated by the CRN Algiers 3.75 MV Van de Graaff accelerator with optimum energy resolution DE/E 0.1% and current intensity I 30 nA. The experimental set up and procedure used for energy loss measurements were described in details elsewhere [12,13]. In brief, primary beams collimated by 1.5 mm diameter slits were first directed onto a very thin Au layer evaporated onto a Si substrate. Then, secondary back-scattered beams of considerably reduced intensity were used in the energy loss measurements by means of a 500 lm-thick ULTRA ion implanted Si detector (Ortec U-011-025-500) placed at a laboratory angle of 165° relative to the incident primary beam direction. The detector,
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collimated with a 3 mm diameter slit and set 1.5 cm apart from the formvar stopping sample, was associated to standard Ortec data acquisition electronics comprising a charge pre-amplifier (Ortec A142), a pulse height amplifier (Ortec 572) and an advanced multichannel analyzer (Ortec 4096 MCB Card). During all experimental runs, a maximum bias voltage was applied to the detector while the electronic gain of the pulse processing chain was set to fixed, adequately chosen values for all used projectile species in order to minimize pulse high defects (PHDs) that are the main cause of non linearity in the detector energy response ([14] and references cited therein). These conditions corresponded to a minimum level of the dead time, permanently checked during the experiment. A detailed energy-channel calibration curve was accurately determined for each projectile specie with recording data points without the target sample in place that was found to be essentially linear. Notice that the maximum uncertainty (0.31%) in the calibration slope was obtained in the case of alpha particles. It mainly arose from neglected ion energy losses within the detector entrance window (dead layer of 50 nm of equivalent Si [15]) that represents the main contribution to PHDs [14]. Indeed, e.g., the calculated energy loss, DEDL [14], in this inactive region of the detector for the considered alpha particle energies ranged between 10.68 keV and 16.01 keV (corresponding relative energy losses of 1.66% and 7.01%, respectively), and therefore the absolute uncertainty thus introduced in the calibration slope amounted to a value of 0.01 keV/channel. The measured energy resolution of the detection system was found to be of 0.2% (i.e., 11 keV FWHM of the 5.486 MeV alpha particle peak from a 241Am radioactive source). In each experimental run, ion energy spectra obtained with and without the target sample in place were successively recorded without breaking the high vacuum (pressure of 2 106 Torr) inside the scattering chamber by using a special target holder as detailed in Ref. [12]. Fig. 1 reports a typical energy loss spectrum with and without the formvar film installed, recorded only over a portion of 2048 channels of the multichannel analyzer for 1 MeV primary protons. Notice that, the detector PHDs should not induce a significant uncertainty in the deduced energy loss measurements (see section below) over the investigated ion energy ranges since they are practically compensated. Indeed, the dead layer PHDs (DEDL), calculated with and without formvar sample in place, are practically of the same magnitude (the difference amounts to, at most, 1.95 keV) and no noticeable error is thus introduced on the obtained ion energy losses (relative uncer-
tainty < 0.35%). The formvar foil used was supplied by the Chemistry laboratory of the InESS/CRNS Strasbourg (France) with a specified thickness of 2.5 lm. It is a single-bonded polymer compound with chemical formula (C5H8O2)n having 8 C–H bonds, 4 C–C bonds (with 2 12 ones from the bonding to neighboring molecules), and 4 C–O bonds per molecule. Its elemental composition expressed in weight fraction is: C: 59.98%, H: 8.05% and O: 31.97%. The foil thickness and non-uniformity was investigated following the method described in [12,16] using a very thin mixed 241 Am–239Pu–233U radioactive source and standard alpha particle stopping powers from the SRIM-2008 computer code assuming Bragg-Kleeman’s additivity rule. The details of this procedure are reported in Ref. [17] devoted to light particle stopping in Ag. A thickness value x ffi (277.46 ± 6.66) lg/cm2 was derived on the basis of the 2% accuracy of the SRIM-2008 S(E) computed values. 3. Stopping power determination and results The difference in mean peak positions of the recorded particle spectra without and with the polyvinyl formal target in place (see Fig. 1) yields the mean energy loss, DE, of secondary backscattered ions across the latter. The peak positions were obtained from Gaussian fits to the measured energy loss distributions over energy intervals defined by about 4 times the standard deviation, r, around the mean value [12]. First, the experimental distributions have been inspected for their Gaussian shapes by computing their overall dimensionless path-length parameters [18,19] that were found to exceed unity for both used projectiles, i.e., X2 X2 1:32 P T 2t P 323:58 for H+ and 210 P T 2t P 1624:81 for 4He+ (with m m 2 Xt and Tm denoting respectively the total straggling variance and the maximum energy transferred in a single collision). Therefore, neglecting single and free Coulomb collisions, the Gaussian character of the measured energy loss distributions was thus checked. According to Andersen et al. [20], the target sample average stopping power, SðEÞ, at the mean energy E ¼ E D2E (with E denoting the energy of backscattered projectiles off the Au–Si target) can be determined to within 0.05% by the ratio DE=x, provided that the energy loss fraction, DE/E amounts to less than 20%. In cases where this condition is not fulfilled, our calculated SðEÞ values were corrected by adding a quadratic correction term derived from an expansion of the SðEÞ function as in Ref. [20]. Besides, the average path lengths of the H+ and 4He+ ions within the formvar target sample were assumed to be equal to the sample mean thickness value x determined above. Indeed, this polymer material is constituted of light elements and therefore the increase of both proton and alpha particle path lengths within the target due to multiple scattering was neglected. The maximum error introduced by this assumption is of less than 0.1%. The derived SðEÞ results are reported in Table 1 together with corresponding relative uncertainties and ion energy loss fractions, and plotted in Fig. 2(a) for protons and (b) for alpha particles. The overall relative uncertainties in the SðEÞ data were evaluated following the same method used in Ref. [12]. They were derived from errors associated with quantities involved in the determination of stopping powers (mean peak positions, energy-channel calibration slope, target sample thickness) and propagated in the above SðEÞ expression. 4. Discussion and conclusion
Fig. 1. Typical energy loss spectra recorded with and without the formvar sample in place for 1 MeV incident protons using a 2048-channel portion of an Ortec MCB Card.
In Fig. 2, our SðEÞ experimental data are compared to only previous ones reported by Munnik et al. [7] and to values calculated by the SRIM-2008 computer code [11] assuming Bragg-Kleeman’s additivity of stopping powers. As can be seen, while for the proton data (Fig. 2(a)) an overall agreement with previous measurements
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Table 1 Energy loss fractions DE/E (%) for back-scattered ions transmitted through the target sample (column 2) and corresponding measured SðEÞ data (column 3) versus the projectile mean energies E (column 1) in the polyvinyl formal resin: (a) for protons, (b) for alpha particles. (a) Protons results 193.4 234.2 313.6 370.3 425 478.5 478.5 531.6 584 687.6 738.7 789.6 840.7 891.1 941.7 1042.3 1142.5 1242.6 1342.3 1441.7 1540.5 1640.3 1739.2 1838.3 1937.4 2134.6 2331.7 2529 2726.3 2923.8 3120.1 3316.7
68.42 56.45 40.01 32.06 26.53 22.46 22.4 19.18 16.65 12.92 11.57 10.43 9.38 8.6 7.84 6.63 5.71 4.94 4.35 3.87 3.52 3.1 2.82 2.56 2.33 2 1.75 1.51 1.31 1.12 1.03 0.93
725.0 ± 17.4 664.1 ± 16.0 565.3 ± 13.6 509.6 ± 12.3 468.6 ± 11.3 436.3 ± 10.5 435.2 ± 10.5 406.6 ± 09.8 382.4 ± 09.2 342.4 ± 08.2 327.1 ± 07.9 313.2 ± 07.5 298.3 ± 07.2 288.5 ± 06.9 277.0 ± 06.7 257.7 ± 06.2 242.2 ± 05.8 226.9 ± 05.5 215.0 ± 05.2 204.8 ± 04.2 199.2 ± 04.8 186.0 ± 04.5 179.5 ± 04.3 172.0 ± 04.1 164.3 ± 04.0 155.4 ± 03.7 148.0 ± 03.6 138.6 ± 03.4 129.2 ± 03.1 118.4 ± 02.9 116.5 ± 02.8 112.0 ± 02.8
(b) Alpha particles results 605.7 694.5 786.4 883.6 982.6 1084 1185.2 1287.3 1388.5 1490.2 1591.1 1791.7 1990.3 2188.1 2379.7
68.78 63.23 58.02 52.75 47.94 43.45 39.53 35.95 32.89 30.09 27.65 23.57 20.34 17.69 15.88
2288.6 ± 55.0 2314.3 ± 55.6 2316.7 ± 55.7 2281.8 ± 54.8 2233.3 ± 53.7 2168.5 ± 52.1 2104.3 ± 50.6 2033.8 ± 48.9 1969.7 ± 47.3 1902.5 ± 45.7 1840.1 ± 44.2 1725.2 ± 41.5 1624.3 ± 39.0 1530.1 ± 36.8 1479.3 ± 35.5
[7] is observed, within experimental uncertainties, over the whole explored common energy range, in case of the alpha particle data (see Fig. 2(b)) the measured previous values (Ref. [7]) clearly lie above our own data points mainly in the energy region around the stopping power maximum where the increasing deviation amounts up to 9%. One can also notice that the stopping power maximum for previous alpha particle data [7] is shifted by 40 keV towards low energies relative to our data. Besides, our SðEÞ data show to be in fair agreement with values derived by the SRIM-2008 code over the energy range Ep J 1:8 MeV in case of protons and at Ea J 1:8 MeV in case of alpha particles. In the remaining lower energy regions explored, however, the SRIM-2008 calculation increasingly underestimates our data for both two projectile types as one goes down towards the stopping power maximum. The observed deviations are significant, amounting to 5.5% and 3.0%, in average, for the proton and alpha particle data, respectively. Therefore, one can conclude that the measured stopping powers of both protons and alpha
Fig. 2. Measured stopping powers (solid circles) in polyvinyl formal versus ion mean energy compared to previous experimental data (open triangles, [7]) and to values derived by the SRIM-2008 computer code (solid curve, [11]) assuming BraggKleeman’s additivity rule: (a) for protons, (b) for alpha particles.
particles in the investigated formvar polymer deviate from Bragg-Kleeman’s additivity rule at moderate projectile velocities when evolving down towards the stopping power maximum dominated by charge exchange processes. Notice that we have also pointed out such deviations relative to the SRIM 2003 calculation based on Bragg-Kleeman’s additivity rule in a previous study [12] of the stopping powers of polypropylene and mylar polymers for (0.236–3.019) MeV protons. Previously, these trends of stopping powers have been reported by several groups ([21–26] and references cited therein) for various projectile-compound target combinations exhibiting deviations up to 25%. The observed increasing departures of S(E) data from the stopping power linear additivity assumption as the projectile velocity decreases seem to be due to a rather complex interplay between various effects such as shell correction, Barkas effect and valence structure [25,27] among which the latter likely plays a dominant role. Consequently, they mainly relate to differences in chemical bonding and physical phase state of the compound target electronic structure characterizing the moderate and low ion velocity regimes. Chemical binding effects become more significant for stopping materials of low atomic number constituents mainly as the projectile velocity approaches the transition region [28]. In this respect, the contribution to the stopping process of the C5H8O2 molecule outermost electrons is presumably expected to become more and more pronounced with decreasing projectile velocity due to the increasing non-participation (or even the closing) of the molecule inner shell excitation channels. More precisely, the observed effect mainly implies valence electrons of the C–H bonds that represent half of the
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total chemical bonds of the (C5H8O2)n investigated polymer compound. The transitions of 1s electrons of H atoms to 2p-like states of C atoms likely lead to the formation of relatively strong C–H bonds and to drastic changes of their orbital velocities and excitation spectra. In contrast, the electrons of C–C and C–O bonds remain practically unchanged in comparison to their states in isolated C and O atoms, and therefore presumably do not have a significant influence on the linear additivity rule of stopping powers. As stated, it is found that the departure from the S(E) additivity rule is more pronounced in case of the proton data than for alpha particle ones. It can be noted, moreover, that the proton kinetic energy limit, E=A ffi 0:94 MeV/amu, at which the Bragg-Kleeman rule breaks down is about twice than for alpha particles (E=A ffi 0:45 MeV/amu). This distinctive feature can be related to the projectile electronic screening that occurs at low velocities tending to reduce the strength of Coulomb attraction between incident 4 He+ ions and target valence electrons. Indeed, at low projectile velocities the screening by electrons moving with the ion is more important for heavier ions and is then surely more significant for alpha particles than for protons.
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