Measurements of the elastic recoil cross-section for 1H(12C, 1H)12C

Nuclear Instruments and Methods in Physics Research B 346 (2015) 17–20

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Measurements of the elastic recoil cross-section for 1H(12C, 1H)12C Yang Zhang, Hongliang Zhang, Zhibin Han, Liqun Shi ⇑ Applied Ion Beam Physics Laboratory, Institute of Modern Physics, Fudan University, Shanghai 200433, PR China Department of Nuclear Science and Technology, Fudan University, Shanghai 200433, PR China

a r t i c l e

i n f o

Article history: Received 11 July 2014 Received in revised form 23 December 2014 Accepted 25 December 2014 Available online 2 February 2015 Keywords: Elastic recoil cross section Hydrogen Carbon

a b s t r a c t The elastic recoil cross section for 1H(12C, 1H)12C was determined at a recoil angle of 30° over an incident carbon energy range from 4.0 to 8.0 MeV. The thin solid film target Pd/TiHx/Si used for cross section measurement was prepared by direct current (DC) magnetron sputtering. The measured cross-section data are compared with records available in literature and a similar trend over the energy range was shown. The total uncertainty in the present cross-section data is less than 7%. Ó 2014 Elsevier B.V. All rights reserved.

1. Introduction Hydrogen and its storage in materials are of importance to a variety of domains, especially in the fusion field. For better understanding of hydrogen’s behavior in materials, an accurate measurement of its concentration is mandatory, using techniques such as elastic recoil detection analysis (ERDA), proton backscattering (PBS) [1–3] and nuclear reaction analysis. ERDA analysis is a method for depth profiling light elements, and ERDA using a He beam has been widely used for hydrogen profiling [4–9]. However, as hydrogen usually co-exists with helium in nuclear materials [10] simultaneous analysis of H and He becomes necessary, using heavy ion scattering for example. Heavy ion scattering also improves depth resolution and sensitivity (down to the ppm level) because of higher stopping power and higher scattering cross-sections, while being rather unaffected by the substrate’s atomic number. In order to get larger detection depths with a limited ion energy, a C ion beam is often used for H and He depth profiling. But, there is only one set of experimental data for H–C-backscattering from the literature [11] for ion energies above the Rutherford energy region, which can be used as recoil analysis by conversion of incident ion-target atom system via kinematically reversed process. In this work, the cross-section for the interaction of carbon with hydrogen at a recoil angle of 30° over the energy range from 4.0 to 8.0 MeV were measured. The main source of the experimental error in the ⇑ Corresponding author at: Applied Ion Beam Physics Laboratory, Institute of Modern Physics, Fudan University, Shanghai 200433, PR China. Tel.: +86 21 65642292; fax: +86 21 65642787. E-mail address: [email protected] (L. Shi). http://dx.doi.org/10.1016/j.nimb.2014.12.075 0168-583X/Ó 2014 Elsevier B.V. All rights reserved.

accurate determination of the cross sections is to make sure the certain of the H content of the target during the entire measurement because of hydrogen loss from the target caused by the ion bombardment. In our measurements, the content of H in the target could be measured by using the 12C–1H Rutherford cross section in a certain energy region. We show that Pd/TiHx/Si target, prepared by magnetron sputtering, shows almost no hydrogen loss during C ion bombardment and so is a suitable substrate for these cross-section measurements. 2. Experimental techniques 2.1. Experimental apparatus The incident carbon beam used in these cross-section measurements, with energies ranging between 4.0 and 8.0 MeV was provided by the NEC 9SDH-2 2  3 MV tandem accelerator at Fudan University. The accelerator energy was calibrated using nuclear resonance reactions such as 27Al(p, c)28Si at 992 keV, and 19F(p, c)16O at 872 keV. After calibration the beam energy had a precision better than ±6 keV and energy spread of around 1 keV. The beam was confined to a diameter of 1 mm with a full width angular divergence of 0.05° before bombarding the target. An Au/Si surface barrier detector, which was placed at a backscattering angle, subtended a solid angle of 1.12  103 sr defined by a 3  4 mm slit. The angular resolution of this detector was 1° and the energy resolution of the detection system was typically 30 keV for carbon. The beam currents were limited to less than 30 nA, and such low currents minimized pulse pile-up so that the dead time of analyzer was negligible in this experiment. In the measurement, the beam energy was varied in 100 keV or 250 keV intervals over the energy

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range between 4.0 and 8.0 MeV. The accumulated charge per energy interval was usually 20lC. It was found that the Pd/TiHx/ Si target was stable under the carbon beam bombardment and no hydrogen losses were observed during the 20 lC runs. 2.2. Sample preparation The common methods for introducing hydrogen into a material are ion implantation [12] or hydrogenation from a hydrogen atmosphere [13]. In both cases it is hard to achieve a uniform distribution and desired concentrations because of the Gaussian depth distribution of the implanted particles or the exponential distribution of the diffused particles. Such targets are also difficult to reproduce and to prepare for quick thin target production. In this work, a new preparation method for Pd/TiHx/Si called magnetron sputtering [14,15] was employed, and a uniform and surprisingly high concentration (1.8  1017 atoms/cm2 H atoms in a 1.2  1017 atoms/cm2 Ti film) hydrogen–titanium target was achieved. The hydrogen content in the Ti film was controlled by adjusting the ratio of the hydrogen and argon fluxes from the working gas mixture so that a uniform Ti–H film with 1.2  1017 atoms/cm2 Ti atoms was sputtered onto a Si substrate. Following this a Pd overlayer of 2.4  1016 atoms/cm2 was deposited onto the Ti film. The Pd here is used both as an internal ion dose reference, and a layer to prevent titanium from oxidizing and to prevent H atoms from coming out of the sample during the ion bombardment. The concentration of hydrogen in the target was measured by elastic recoil detection analysis (ERDA) using a beam of 4.35 MeV 12C ions (after subtracting the energy loss of C ion in the Pd and Ti films). At this energy, the Rutherford cross-section can be used to determine concentrations. This measurement was done by employing two detectors simultaneously, one to detect the H recoils at a recoil angle of 30° and the other to measure the backscattered yield of the incident 12C particles at a scattering angle of 165°. The peak area of the Pd backscattered signal was also used as an ion dose calibration for the ERD measurement. In this way, we measured an atomic ratio of H to Ti to be above 150%.

where

1 ERuth ¼ E0Ruth  DEPd  DETiH1:5 2

ð4Þ

All Rutherford scattering cross-sections used here have been corrected for electron screening effects [16]. It is known that Rutherford-like cross-sections for H recoil by heavier ions only exist in certain low energy regions for different scattering angles. This is because, at such incidence energies, the particle nucleus is prevented by the Coulomb barrier from approaching the target H nucleus, and the contribution from the nuclear potential are negligible. However, at particle energies which are too low, deviations from Rutherford scattering can also occur because the nuclear charge is partially screened by the inner shell electrons. In order to find the carbon ion energy region where the scattering is Rutherford, the literature values of r=rRuth , the ratio of the scattering cross section to the Rutherford cross section, are shown in Fig. 1 for proton scattering from the carbon at angles of 115–170°, together with the corresponding recoil cross section ratios for the angles of 4.6–30°. All available data [11,17,18] are shown in Fig. 1, in the laboratory frame of reference. The conversion on the ion-target system in backscattering process to the recoil process can be made by kinematically reversing the reaction which has been described everywhere [19]. Although the data of Liu et al. [17] show good, i.e. to within 3%, agreement with a Rutherford cross section over a wide incident ion energy region, most of the crosssection data measured by Mazzoni [11] and Milne [18] only fit the Rutherford values to within 3% in a narrow C ion energy region around 4.35 MeV. No large effects on scattering angle are found in this angle region. When the C ion energy is larger than 4.48 MeV or less than 4.24 MeV the measured data significantly deviates from the Rutherford values, and the difference between the measured values and Rutherford values at these two energies can reach 7%. Thus, a C ion energy of 4.35 MeV was taken to ensure a crosssection closest to Rutherford to allow calibration of measurements. To make sure that the hydrogen content is constant over the whole experiment, the sample was measured using elastic recoil detection at both the beginning and the end of the measurement

3. Measurement and analysis Proton Energy(keV)

Using the Pd/TiHx/Si sample, the elastic scattering differential cross-section in the laboratory frame of reference can be calculated from:

rPd—C ðE0 ÞAH ðNtÞPd APd ðNtÞH

ð1Þ

where rPd—C is the Rutherford scattering cross-section for C from Pd and

1 E ¼ E0  DEPd  DETiH1:5 2

ð2Þ

where E0 is the incident carbon projectile energy and DEPd and DETiH1:5 are the energy losses of the carbon projectile in the Pd and TiHx layer, respectively. The signal peak area ratio AH =APd was determined from the measured spectrum. The ratio ðNtÞPd =ðNtÞH , where N is the film atom density and t is the layer thickness, was determined from the measured peak areas AH and APd by using sufficiently low C ion energies to ensure Rutherford-like scattering during the simultaneous ERD and Rutherford backscattering (RBS) measurements of the areal densities (Nt)H and (Nt)Pd. Thus, the recoil cross section rH—C could be obtained by adopting a given C ion energy E0Ruth which allows Rutherford scattering for C in the TiH1.5 film, so that:

rH—C ¼ rPd—C ðE0 Þ

AH—C rH—C ðERuth ÞAPd—C ðE0Ruth Þ APd—C rPd—C ðE0Ruth ÞAH—C ðERuth Þ

ð3Þ

360

380

400

420

1.2

Cross section relative to Rutherford

rH—C ðEÞ ¼

340

440 o 115 , S.Mazzoni+[11]

1.2

o 120 ,S.Mazzoni+[11] o 160 S.Mazzoni+[11]

, , , o 160 ,E.A.Milne[18] o 170 ,Zhengmin Liu{17] o 170 S.Mazzoni+[11]

1.0

o 120 E.A.Milne[18]

0.8

0.6

0.4

0.2 4000

1.0

0.8 Scattering angle o 115 o 120 o 160 o 170

Recoil angle o 30.3 o 27.9 o 9.2 o 4.6

0.6

0.4

0.2 4200

4400

4600

4800

5000

5200

5400

12

C Ion Energy(keV)

Fig. 1. Measured cross-section divided by the Rutherford cross-section at different scattering angles, obtained from previous data. The top axis represents the incident energy for proton backscattering geometry and the bottom axis represents the carbon ion energy deduced from the kinematically reversed 12C(p, p)12C reaction. The recoil angles corresponding to the different scattering angles are also listed in the figure.

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0

200

400

600

800

1000

5000

6000

7000

3500

8000 measurement data

9000

3500

S.Mazzoni et al

3000

SigmaCalc

3000

2500

2500

2000

2000

1500

1500

1000

1000

500

500

0 4000

5000 12

6000

7000

8000

0 9000

C Ion Energy(keV)

Fig. 3. The 1H(12C, 1H)12C differential cross section at a recoil angle of 30o as a function of energy, compared to the data deduced from kinematically reversed 12 C(p, p)12C scattering cross-section and the value obtained from SigmaCalc.

Table 1 The differential cross-sections for the recoil process 1H(12C, 1H)12C at the recoil angle of 30° as a function of 12C ion energy. All the values refer to the laboratory frame of reference. Beam energy E (keV)

dr=dX (mb/sr) (165°)

4030 4278 4352 4527 4626 4726 4826 4926 5026 5126 5226 5326 5426 5526 5626 5726 5826 5926 6026 6279 6531 6782 7034 7286 7538 7790 8044

3205.44 2650.40 2535.10 2263.47 2067.03 1825.72 1564.49 1333.84 921.52 757.53 505.17 401.91 1477.76 2324.21 2914.70 3201.07 3320.94 3208.84 2820.58 2820.58 2540.54 2321.45 2112.11 1952.28 1864.15 1758.87 1711.25

1200 1000

1000

800

800 Pd

Counts

4000

Differential cross-section(mb/sr)

in two energy regions, i.e. from 4.0 to 6.0 MeV and from 6.0 to 8.0 MeV. From this analysis the hydrogen content is shown to be almost constant throughout the series of experiments, and the total hydrogen loss for each energy region is found to be less than 0.8% with the loss for each run of 20 lC less than 0.05%. A typical backscattering spectrum for carbon incident on the Pd/TiHx/Si sample is shown in Fig. 2. In the present range of energies, i.e. from 4.0 to 8.0 MeV, carbon elastic scattering from Pd is purely Rutherford in nature. The differential cross-sections for the direct scattering process 1H(12C, 1H)12C at the recoil angle of 30° are presented in Fig. 3 and given in Table 1. Fig. 3 also gives data calculated from the kinematically reversed measured values of the 12C(p, p)12C scattering cross-section [11] and from the SigmaCalc [20]. The experimental C ion energies EC = 4.2–8 MeV and a proton recoil angle of 30° correspond to calculated proton energies EH = 0.35–0.6667 MeV and a scattering angle of 115.7°. The accuracy of the carbon elastic recoil cross-sections measured here is limited by the uncertainties in all parameters used in Eq. (2). The errors in APd and AH result from statistical errors and background subtraction uncertainties in the determination of Pd and H peak areas and they are typically ±2–3%. The error in rPd associated with uncertainties in the scattering angle (±1°) and the carbon beam energy (±6 keV) is less than ±1% in the measured energy region. Thus, when we consider the maximum possible error of 3% due to using the Rutherford cross-section value on 4.35 MeV, the total error associated with the measured crosssection is about 7%. As expected from the Fig. 1, the measured cross-section data in Fig. 3 agrees with the Rutherford calculated values only in a narrow energy region around 4.35 MeV beyond which the values deviate from Rutherford values. When the incident C ion energy is larger than 4.35 MeV the cross-section value decreases and reaches a minimum at 5.32 MeV. But, it then rises rapidly to a maximum at about 5.76 MeV. As the incident C ion energy further increases, the cross-section decreases almost linearly. It is noted that there are large differences in energy for the minimum and maximum cross-sections among different data sets. The energy values obtained from the kinematically reversed scattering cross-section of 12C(p, p)12C measured by Mazzoni et al. [11] are, for example, larger than that calculated from both SigmaCal and our direct recoil measurement. This is can be explained by the energy loss through the thickness of thin self-supporting carbon foils (with an areal density of 13 lg/cm2, corresponding to a proton energy loss of 6–4 keV for the proton energies from 350 to 700 keV respectively in [11]) that is not deducted from the given proton energy in Mazzoni et al.’s measurements. This small energy difference, about 5 keV, will convert to a 60 keV

600

600 Si

400

400

Ti

200

200 0 0

200

400

600

800

1000

0 1200

Channel Fig. 2. The spectrum of 8.0 MeV C ions backscattered from the Pd/TiHx/Si sample. The scattering angle is 165°.

decrease in the C ion energy from the kinematically reversed scattering reaction 12C(p, p)12C, approximately the energy difference observed. Also the present measured values of cross-section are larger than other values found from SigmaCalc especially but also from Mazzoni at carbon energies above 6 MeV. It can be seen that our cross-section data in 7.2 MeV is very close to that of Mazzoni. 4. Conclusions The cross-section, at a laboratory angle of 30°, for elastic recoil reaction 1H(12C, 1H)12C over an energy range from 4.0 to 8.0 MeV was measured using a Pd/TiHx/Si solid target, made by magnetron sputtering. The measured cross-section values have two turning points in the measured carbon energy range, first decreasing with energy increasing to 5.4 MeV, then increasing linearly in the

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energy range from 5 to 6 MeV, achieving a maximum value at the energy of 5.8 MeV, and then rapidly reducing as the incident carbon energy increases. The present data agrees well in the lower energy range with other data calculated from the kinematically reversed scattering reaction 12C(p, p)12C from the Mazzoni et al., but differences up to 18% in the cross sections were found when the carbon energy was larger than 6 MeV. Acknowledgements This work was supported by the National Natural Science Foundation of China under Grant Nos. 91126019 and 11375046. The authors are also grateful to the staff of the tandem accelerator of the Institute of Modern Physics at Fudan University. References [1] J.A. Sawicki, H.H. Plattner, I.V. Mitchell, J. Gallant, Nucl. Instr. Meth. B 15 (1986) 475. [2] J.F. Browning, J.C. Banks, W.R. Wampler, B.L. Doyle, Nucl. Instr. Meth. B 15 (2004) 317.

[3] R.A. Langley, in: J.S. Walson, F.W. Wiffen (Eds.), Proc. Int. Conf on Radiation Effect and Tritium Technology for Fusion Reactors, vol IV, 1976, 158. [4] E. Szilagyi, F. Paszti, G. Amsel, Nucl. Instr. Meth. B 100 (1995) 103. [5] J.F. Browning, R.A. Langley, B.L. Doyle, J.C. Banks, W.R. Wampler, Nucl. Instr. Meth. 161–163 (2000) 211. [6] I. Bogdanovic´ Radovic´, O. Benka, Nucl. Instr. Meth. B 174 (2001) 25. [7] J.C. Keay, D.C. Ingram, Nucl. Instr. Meth. B 211 (2003) 305. [8] J.F. Browning, J.C. Banks, W.R. Wampler, B.L. Doyle, Nucl. Instr. Meth. B 219– 220 (2004) 317. [9] C.-S. Kim, S.-K. Kim, H.D. Choi, Nucl. Instr. Meth. B 155 (1999) 229. [10] E. Markina, M. Mayer, H.T. Lee, Nucl. Instr. Meth. B 269 (2011) 3094. [11] S. Mazzoni, M. Chiari, L. Giuntini, P.A. Mandò, N. Taccetti, Nucl. Instr. Meth. B 136–138 (1998) 86. [12] P.X. Wang, J.S. Song, Helium in Materials and Permeation of Tritium, National Defense Industry Press, Beijing, 2002. [13] L.Q. Shi, Z.Y. Zhou, G.Q. Zhao, J. Vac. Sci. Technol. A 18 (5) (2000) 2262. [14] L.Q. Shi, C.Z. Liu, S.L. Xu, Z.Y. Zhou, Thin Solid Films 479 (2005) 52. [15] Y.F. Lu, L.Q. Shi, Z.J. He, L. Zhang, B. Zhang, R. Hutton, Nucl. Instr. Meth. Phys. Res. B 267 (2009) 760. [16] H.H. Andersen, F. Besenbacher, P. Loftager, W. Möller, Phys. Rev. A 21 (1980) 1891. [17] Z. Liu, B. Li, Z. Duan, H. He, Nucl. Instr. Meth. B 74 (1993) 439. [18] E.A. Milne, Phys. Rev. 93 (1954) 762. [19] A. Nurmela, Non-Rutherford elastic scattering cross sections, University of Helsinki, 2001, 34p. + appendices, ISBN 951-45-9894-6. [20] SigmaCalc from IBANDL web site (http://www-nds.iaea.org/sigmacalc/).