Differential cross-section of D(12C,D)12C elastic recoil reaction

Nuclear Instruments and Methods in Physics Research B 412 (2017) 54–57

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Differential cross-section of D(12C,D)12C elastic recoil reaction Yiming Duan, Hanjun Tu, Zhibin Han, Wei Zhang, Liqun Shi ⇑ Key Laboratory of Nuclear Physics and Ion-beam Application (MOE), Institute of Modern Physics, Fudan University, Shanghai 200433, China

a r t i c l e

i n f o

Article history: Received 28 July 2017 Received in revised form 11 September 2017 Accepted 11 September 2017

a b s t r a c t In this paper, the differential cross-section of D(12C,D)12C elastic recoil reaction at a recoil angle of 30° in the energy region of 3.4–9.0 MeV was measured. The sample Pd/TiDx/Si was prepared by magnetron sputtering, and a relative determination method was employed to avoid the uncertainties in solid angle and the number of the incident ions. The uncertainty of measured data is approximately 4.4%. Ó 2017 Elsevier B.V. All rights reserved.

Keywords: Differential cross-section Deuterium Elastic recoil reaction

1. Introduction The understanding of the behavior of hydrogen and its isotopes in materials is becoming more important, especially in the neutron generator. It has been used in industrial and agricultural production widely, such as neutron logging [1], neutron radiography [2], radiation medicine [3]. The depth profile of deuterium and tritium in the metallic target is an important issue on the performance of neutron generator. There are several methods currently available to determine the deuterium and tritium depth profile in the materials including nuclear reaction analysis (NRA) [4,5], proton backscattering spectrometry (PBS) [6], elastic recoil detection analysis (ERD) [7,8] and secondary ion mass spectroscopy (SIMS) [9]. Among these methods, SIMS is time consuming, destructive and not quantitative by itself. NRA can provide a good resolution to a very large depth by multi-energy analysis [10], but ERD has a better resolution than NRA at the near-surface. An even better depth resolution and sensitivity of ERD can be obtained using a heavier incident ion because of its higher stopping power and higher scattering and recoil cross-sections. The projectile 12C was chosen as it. Gives good depth resolution while also providing a distinguishable energy difference between deuterium and tritium recoils. In this study, the cross-section of D(12C,D)12C elastic recoil reaction at a recoil angle of 30° over the energy region of 3.4–9.0 MeV was measured. The most significant challenge in the determination of the C-D elastic recoil cross-section is ensuring that there is a minimum loss of D atoms during the ion bombardment which is the dominant source of uncertainty on the cross section determi⇑ Corresponding author. E-mail address: [email protected] (L. Shi). http://dx.doi.org/10.1016/j.nimb.2017.09.007 0168-583X/Ó 2017 Elsevier B.V. All rights reserved.

nation. The target samples Pd/TiDx/Si were prepared by magnetron sputtering and the Pd overlayer trapped any diffusing deuterium to ensure a minimal loss of D during the measurement. The determination of solid angle and the total number of the incident ions are potentially a major cause of experimental errors, however their impact was minimized by employing a relative determination method. To convert from a relative to absolute cross section measurement a calibration point is required. This calibration point was determined by inverse kinematics. From a previous determination of the 12C(D,D)12C scattering cross-section it is possible to use inverse kinematics to determine the range region of D(12C,D)12C over which the Rutherford cross-section is valid and thus sets the energy range over with the Rutherford formula can be used as a standard for the cross section.

2. Experimental 2.1. Experimental system The measurements were carried out in a high vacuum chamber with pressure less than 5.0
105 Pa. The incident 12C ion beam was provided by the NEC 9SDH-2 2
3 MV tandem accelerator at Fudan University. In this study, the 12C incident energy region is 3.4–9.0 MeV, with a precision better than +6 keV and energy spread of about +1 keV, which has been calibrated by nuclear resonance reactions 13C(p,c)14N at 1.748 MeV and 16O(a,a)16O at 3.045 MeV. The ion beam was confined by a set of 1 mm collimating slits, while the current, which was measured with a faraday cup, was limited to less than 30 nA so that dead time effects of the analyzer were negligible. The RBS and ERD spectra were deter-

Y. Duan et al. / Nuclear Instruments and Methods in Physics Research B 412 (2017) 54–57

mined simultaneously by two fixed detectors. The backscattering spectra were detected at a laboratory angle of 165° by an Au/Si surface barrier detector with a solid angle of 1.83
103 sr. The elastic recoil spectra were detected at 30° by another Au/Si surface barrier detector with a solid angle of 1.12
103 sr and a 10 lm mylar foil was placed before the ERD detector to stop the scattered C ions. The typical backscattering spectrum and elastic recoil spectrum are shown in Fig. 1 and Fig. 2. The angular resolution of both detectors were approximately ±0.5° and the energy resolution of the detection system was about 30 keV for C ions. During the measurement, the incident energy was stepped in increments of 200–250 keV over the energy range between 3.4 and 9.0 MeV. The ion beam was incident at an angle of 15° to the sample surface. It was found that the D content in the sample was stable under the C beam bombardment over the duration of the measurements and so its loss can be ignored. 2.2. Sample preparation The samples used in this measurements were Pd/TiDx/Si which were made by magnetron sputtering. A uniform TiDx film with the thickness of about 20 nm was first sputtered onto a Si substrate then an approximately 3 nm Pd overlayer was deposited on the TiDx film. This overlayer acts to protect the TiDx film from being

oxidized, is an internal ion dose reference for the calculation of cross-section, and prevents D atoms from escaping the sample during the ion bombardment. The D concentration in the TiDx film can be controlled by varying the ratio of Ar to D and by varying the working pressure of the gas in the magnetron. The working gas used was a mixture of 99.99% purity argon and 99.999% deuterium. A series of experiments at different ratios of the argon and deuterium and different working pressure identified the conditions to achieve a uniform, high concentration TiDx film. The areal densities of Ti atoms were 1.0
1017 atoms/cm2 and D atoms were 0.7
1017 atoms/cm2. The content of D in the TiDx film was determined by ERD analysis with a 2.0 MeV 4He ion beam using the two Au/Si surface barrier detectors simultaneously. One detector monitored the scattering C ions at a scattering angle of 165°, and other monitored the recoiling D ions at an angle of 30°. The detected spectrum simulated by SIMNRA and ALEGRIA revealed that the ratio of D to Ti was approximately 70%. 2.3. Cross-section determination It is know that the cross-section for D recoil by heavier ions is a Rutherford cross-section over a range of energies where the pure Coulomb potential applies. There are departures to this behavior at higher incident energies when the effect of the nuclear potential impacts on the scattering and at lower incident energies where the nuclear charge is partially screened by the inner shell electrons. The latter effect occurs at an energy below the range used in this study. To find the energy regions where the Rutherford cross-section for the reaction D(12C,D)12C was valid, we calculated the ratio of recoil cross-section to Rutherford cross-section through inverse kinematics of the previously determined 12C(D,D)12C scattering cross section [11–13]. The inversion process involves the following steps [14]:

tan h ¼ M

sin 2u

 COS2u M1

E2 ¼

Fig. 1. The typical RBS spectrum of Pd/TiDx/Si by 4.5 MeV

12

C ion beam.

55

2

M2 E1 M1

ð1Þ

ð2Þ

where the h is scattering angle and the E2 is the incident energy in the inverse scattering reaction, the u is the recoil angle and the E1 is the incident energy in the recoil reaction, the M 1 and M 2 is the mass of incident ion and recoil ion in the recoil reaction. The ratio of recoil cross-section to Rutherford cross-section deduced from all available data are show in Fig. 3. The scattering angle of available data varied from 111° to 165°, with the corresponding recoil angle varied from 30° to 6.3°. It is evident that the ratio is near 1.0 over the incident C ion energy range from 3.0 to 4.2 MeV. As a consequence incident C ion energy of 3.8 MeV was chosen to calibrate the measured data. At this energy, the peak areas of RBS (A’Pd-C) and ERD (A’D-C) signals are related by the equation:

A0DC ND rDC ðER ÞXERD ¼ A0PdC NPd rPdC ðER0 ÞXRBS

ð3Þ

At this energy, the recoil cross-section rDC ðER Þ and the scattering cross-section rPdC ðER0 Þ are given by the Rutherford cross-section, where ER0 is the incident energy and ER ¼ ER0  DEPd  12 DETiDx . In which DEPd and DETiDx are the energy losses of incident C ion in Pd overlayer and TiDx layer, calculated by SRIM. At higher incident energies, the RBS and ERD yields are given by:

Fig. 2. The typical ERD spectrum of Pd/TiDx/Si by 4.5 MeV

12

C ion beam.

ADC ND rDC ðEÞXERD ¼ APdC NPd rPdC ðE0 ÞXRBS

ð4Þ

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Y. Duan et al. / Nuclear Instruments and Methods in Physics Research B 412 (2017) 54–57

Fig. 4. The recoil cross-section data determined at a recoil angle of 30°, and the comparison of the data deduced from 12C(D,D)12C scattering cross-section. Fig. 3. The ratio of recoil cross-section to Rutherford cross-section deduced from all available data.

where, E ¼ E0  DEPd  12 DETiDx , the parameters ADC and APdC are the measured peak areas by incident C ions, N D and N Pd are the areal density of D and Pd, XERD and XRBS are the solid angle of detectors. From Eq. (3) and Eq. (4) an expression for the recoil cross section can be derived as:

rDC ðEÞ ¼ rPdC ðE0 Þ

ADC A0PdC rDC ðER Þ APdC A0DC rPdC ðER0 Þ

ð5Þ

Employing this relative determination method, a calibration point at 3.8 MeV was been used. The rDC ðEÞ can be derived from known Rutherford cross-sections at 3.8 MeV, measured yields and Rutherford scattering cross-section rPdC ðE0 Þ. The experimental errors associated with of the solid angle and the total number of the incident ions were eliminated. 3. Results and discussion The measured recoil cross-sections are presented in Fig. 4 and Table 1. The recoil cross-section data were determined at a recoil angle of 30° for C ion energies of 3.4–9.0 MeV, the scattering angle of 111° and the deuterium energy varies from 0.57 to 1.5 MeV. A comparison of the measured 12C(D,D)12C scattering cross-section with the measurements by E. Kashy [11] and that calculated by SigmaCalc [13] is presented in Fig. 4. Overall the data agree with previous measurements and with the SigmaCalc prediction however the location of the maxima and minima in the cross section are at higher energies for this study that for the others. Our measured values can be expected to deviate from the data deduced from scattering data measured by E. Kashy, as the recoil angle is 27.4° at scattering angle 116.7°, while our experimental angle is 30° which will have some impact on the cross section. The measured data are close to the calculated data by SigmaCalc at low energy (<5.2 MeV) and high energy (>6.7 MeV) although it does not reproduce the sharp resonance at 8680 keV, however this is probably a result of the experimental method used. Rather than using a monoenergetic ion beam the projectiles will have a range of energies caused by the energy straggling in incident path. The energy spread due to energy straggling processes is approximately 23 keV at the half depth of the TiDx layer and the largest energy spread of Pd/TiDx/Si can reach to about 40 keV at full depth. While

Table 1 The recoil cross-section data determined at a recoil angle of 30°. E/keV

(dr/dX)/(mb/sr)

E/keV

(dr/dX)/(mb/sr)

3315 3515 3713 3913 4112 4411 4690 4911 5111 5311 5511 5711 5911 6161 6412 6563 6662 6713 6813 6913

1252 1163 1021 927 838 695 586 478 411 334 297 350 414 443 413 378 326 312 269 245

7163 7413 7665 7715 7765 7815 7915 8015 8165 8419 8515 8619 8629 8639 8649 8659 8669 8719 8819 8919

203 200 243 270 301 314 302 283 217 177 187 221 256 249 254 251 211 188 157 137

the full width at half maximum (FWHM) of the sharp resonance peak is about 50 keV, the yield of energy spread function convoluted with the true resonance was smaller than theoretical calculation, thus resulting in a much less prominent resonance peak. The loss of D atoms resulting from the ion bombardment was potentially the main contribution to the experimental error in the cross section determination. The content of D was determined repeatedly as reported by the ratio of the D to Pd in Table 2, and it can be concluded that the loss of D can be ignored. The uncertainty in the measured recoil cross-section data were caused by the errors of all the parameters in Eq. (5). The errors of

Table 2 Comparison of peak area of D to Pd during the measurement. C ion energy/keV

ADC

APdC

ADC =APdC

4000 4000 4000 4000 4000

4824 4642 5123 5890 7706

10236 9749 10849 12373 16256

0.471 0.476 0.472 0.476 0.474

Y. Duan et al. / Nuclear Instruments and Methods in Physics Research B 412 (2017) 54–57

the peak areas were caused by the statistics and background, those are within 2.4% for APdC , 1.9% for ADC , 1.4% for A0PdC and 1.1% for A0DC . The uncertainty of rPdC resulting from the contributions of the scattering angle (<±1°), the energy straggling and energy dispersion of C ion beam (<±17.5 keV in Pd overlayer), and the error of cross-section at 3.8 MeV deviate from Rutherford cross-section (2.1%), results in the uncertainties of less than 0.72% for rPdC ðE0 Þ, 0.55% for rPdC ðER0 Þ and 2.5% for rDC ðER Þ. After considering all the uncertainties during measurements, the total error of the measured recoil cross-section is estimated to be 4.4%. 4. Conclusions The differential cross-section for the elastic recoil reaction D (12C,D)12C were measured at a recoil angle of 30° in the C ion energy range of 3.4–9.0 MeV. The sample Pd/TiDx/Si was prepared by magnetron sputtering, and a relative determination method was employed to avoid the experimental uncertainties arising from an error of solid angle and the total number of the incident ions. To convert the relative measurements to absolute values, a calibration was performed at an energy where the scattering has previously been shown to be in the Rutherford regime. In general the results agree with previous measurements taken at a different recoil angle though the local maxima and minima in this study has shifted to

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higher energy relative to that at a smaller recoil angle. There is in good agreement with the Sigmacalc program however a sharp resonance at 8670 keV was not observed in the experimental results because there is an inherent energy spread of the incident energy after passing through a thin film which broadens the energy range at the scattering event. References [1] A.X. Chen, A.J. Antolak, K.-N. Leung, Nucl. Instr. Meth. A 684 (2012) 52–56. [2] E. Lehmann, G. Frei, A. Nordlund, B. Dahl, IEEE Trans. Nucl. Sci. 52 (2005). [3] S.V. Syromukov, V.V. Stepnov, R.V. Dobrov, V.I. Sysoev, A.V. Mel’nik, K.V. Bogatikov, A.N. Starostin, R.D. Letichevskii, Atomic Energy 119 (2015). [4] I.G. Hughes, R. Behrisch, A.P. Martinelli, Nucl. Instr. Meth. B 79 (1993) 487–489. [5] V.Kh. Alimov, J. Roth, M. Mayer, J. Nucl. Mater. 337–339 (2005) 619–623, 267 (2009) 506–512. [6] Hongliang Zhang, Wei Ding, Ranran Su, Yang Zhang, Liqun Shi, Nucl. Instr. Meth. B 371 (2016) 174–177. [7] M. Wielunski, M. Mayer, R. Behrisch, J. Roth, B.M.U. Schuerzer, Nucl. Instr. Meth. B 122 (1993) 113–120. [8] S. Markelj, I. Cadez, P. Pelicon, Z. Rupnik, Nucl. Instr. Meth. B 259 (2007) 989– 996. [9] J. Likonen, J.P. Coad, E. Vainonen-Ahlgren, T. Renvall, D.E. Hole, M. Rubel, A. Widdowson, JET-EFDA Contributors, J. Nucl. Mater. 363–365 (2007) 190–195. [10] M. Mayer, E. Gauthier, K. Sugiyama, U. von Toussaint, Nucl. Instr. Meth. B. [11] E. Kashy, R.R. Perry, J.R. Risser, J. Phys. Rev. (1960). [12] H.J. Kim, W.T. Milner, F.K. McGowan, Nuclear Data Tables v.A2, 1966, p. 353. [13] SigmaCalc from IBANDL web site, http://www-nds.iaea.org/sigmacalc/. [14] E. Marlina, M. Mayer, H.T. Lee, Nucl. Instr. Meth. B 269 (2011) 3094–3097.