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A new way of depositing thin targets of monolayer thickness for nuclear reaction analysis: A case of the 550 keV 13C (p,γ) 14N resonant nuclear reaction
ARTICLE IN PRESS
Nuclear Instruments and Methods in Physics Research A 555 (2005) 31–35 www.elsevier.com/locate/nima
A new way of depositing thin targets of monolayer thickness for nuclear reaction analysis: A case of the 550 keV 13C ðp; gÞ14N resonant nuclear reaction N.W. Makau,1, T.E. Derry Schonland Research Institute for Nuclear Sciences (iThemba LABS-Gauteng) and School of Physics, University of the Witwatersrand, Private Bag 3, Wits 2050, Johannesburg, South Africa Received 18 May 2005; received in revised form 22 September 2005; accepted 24 September 2005
Abstract We suggest a method by which the thinnest possible uniform isotopic targets may be produced in favourable cases, by bonding a monolayer to a diamond substrate, for use in nuclear level studies at maximum energy resolution. The need to deconvolve the target thickness contribution, or concern about its possible non-uniformity, fall away. We illustrate with a new measurement of the proton energy width of the 13 Cðp; gÞ14 N resonance at 550 keV. r 2005 Elsevier B.V. All rights reserved. PACS: 24.30.V; 29.25.t; 68.43.h; 81.05.Uw Keywords: Thin target; Nuclear reaction; Resonance width; Diamond
1. Introduction Measurements (or remeasurements) of the width, spin, parity, etc. of nuclear energy levels still occupy an important place in experimental nuclear physics. For studies at the highest possible energy resolution, allowance for the degradation of the accelerator beam energy in the target material has always been a problem. Deconvolution of the thickness contribution is only reliable if the target thickness is very uniform, which, for either supported or self-supporting targets, may well not be the case. It is important to note that uniformity errors tend to make the width too large. The ideal target from this point of view would have negligible thickness, i.e. it would be a partial or full atomic monolayer. Over the years, Nuclear Reaction Analysis has evolved to become one of the most practical analytical tools in Corresponding author. Tel.: +11 351 7050; fax: +11 351 7053.
E-mail addresses: [email protected] (N.W. Makau), [email protected] (T.E. Derry). URL: http://www.src.wits.ac.za. 1 On leave from Moi University, Eldoret, Kenya. 0168-9002/$ - see front matter r 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.nima.2005.09.034
various applications [1]. Resonant particle-induced reactions which exhibit sharp increases in cross-section at specific energies are often particularly useful for both surface and near-surface probing. An accurate knowledge of the energy width of a resonance is essential for precision depth profiling in this application [2]. While studying the adatoms which become attached to a diamond surface during standard preparation procedures based on mechanical polishing, we observed [3] that the outermost carbon atoms, approximately a monolayer, together with associated hydrogen atoms, were derived from the olive oil (principally consisting of olein) which is invariably used as a lubricant with the diamond grit which achieves the polishing. This added carbon monolayer was detected after polishing with 13C-labelled olein, using a proton beam and the 13 Cðp; gÞ14 N resonance at 550 keV. We were able to re-measure the width of this resonance, which has been subject to some disagreement, at high resolution, and report the results below. This method could be applicable in other cases where a precursor containing the desired isotope is available, e.g. a fluorinated oil for a fluorine monolayer. Covalent solids
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N.W. Makau, T.E. Derry / Nuclear Instruments and Methods in Physics Research A 555 (2005) 31–35
other than diamond may be found to bond atoms or molecular fragments in a similar way. King et al. [4] have outlined earlier attempts to establish the above reaction width. They indicated that the first reported width for this resonance was 40 keV obtained by Fowler et al. [5] which was followed quite closely by the 1951 work of Seagrave [6] who obtained a value of 32:5 1 keV. Subsequent work of Mahaux [7] gave a value of 42 keV, while Fowler et al. [8] later reported a revised value of 40.5 keV, which was very close to the one that they had obtained earlier in 1948 [5]. As a result of the rather narrow width (25 1 keV) reported by Spits et al. [9], Brune and Kavanagh [10] remeasured it, using almost the same geometry over the proton energy range of 495–605 keV and obtained a value of 37:5 0:5 keV, while King et al. [4] using the same energy interval and fitting their data to the S-factor equation obtained a value of 38:4 0:3 keV. They, however, note in their work that a fit over such a restricted range considerably overestimates the contribution from direct capture and the tail at the O1 state compared with the fit to the full range of data, but they do not mention by how much this overestimation is made. The nuclear reaction’s resonance width Gr for 13 Cðp; gÞ14 N is still being referred to as being uncertain [11], due to these emergent values of its width, which do not seem to show much agreement. Nastasi et al. [12] actually quote both the values of 32:5 1 keV and 25 1 keV that were mentioned previously. 2. Experimental 2.1. Sample preparation Most of the work reported in the literature regarding the Cðp; gÞ14 N nuclear reaction deals primarily with either supported thin targets which are obtained by evaporating the species of interest onto a suitable substrate, or alternatively implanting the species into some matrix. Each of these two methods may have its own drawbacks, since the thickness and hence uniformity of the target may vary, thus being put into question. In this study we discuss a method of depositing thin monolayer targets by polishing diamond surfaces with olive oil labelled with 13C atoms. It is important to note that many other labelled oils and even solvents do exist nowadays [13,14], among them being the chlorinated and fluorinated oils, etc. In this work, six natural diamond samples of sizes ranging between 3 mm 3 mm 4 mm and 3 mm 3 mm 2 mm were initially polished mechanically following the procedure described previously in Ref. [15]. They were then repolished manually on a highly polished cast iron block, using diamond pastes of 1=4 and 1=10 mm, together with olein that was labelled with 99% 13C atoms [14]. The oil acted as both a lubricant and a donor for the 13C atoms required to bond with the dangling carbon bonds that are created on the diamond surfaces while polishing. Each polishing process lasted for about 30 min, after which the surfaces were cleaned in a 13
solution of Contrad (a surface decontamination detergent), followed by an ultrasonic rinsing thrice using deionized water. The surfaces were dried by blowing dry nitrogen gas over them. 2.2. Irradiation process The 1.4 MeV Cockcroft–Walton proton accelerator based at the Schonland Research Institute was used to provide the energetic protons needed to probe for the 13C atoms via the 13 Cðp; gÞ14 N nuclear resonance at 550 keV. Fig. 1 shows the target–detector geometry. A 10 cm 10 cm Bicron NaI(Tl) detector having a resolution of about 60 keV was positioned outside the vacuum, at 10 mm right in front of the beam stub where the target was mounted as shown in Fig. 1, and this arrangement was used for the collection of the gamma-ray yield in all cases. This geometry ensured that almost a 2p steradian solid angle was subtended at the target, maximizing the gammaray collection efficiency [16]. Absorption by the sample holder was negligible. The detector was placed within a lead annulus measuring 6.8 cm in thickness, and this contributed greatly towards the minimization of the background radiation. The vacuum within the target chamber was maintained at better than 106 Torr. The target chamber was isolated from the beam line, and acted as a Faraday cup for current integration. This avoids the need for secondary electron suppression. We used 137Cs and 60Co standard sources, for setting up the experiment. This ensured that the collected (8.06 MeV) [12] gamma-rays were identified and recorded into reasonable channels by the multichannel analyzer (MCA). The entire spectrum was collected, and our setup ensured that the gamma-rays of interest were deposited well away from the low-energy background. We then selected the region of interest containing the 8.06 MeV gamma-rays to work with. In order to ensure that the deposited layer of 13C atoms remained the same, before and after the irradiation process, a Transport and Range of Ions in Matter (TRIM) simulation using the 2004 Stopping and Range of Ions in Matter (SRIM) computer code [17] was done, and this showed that no sputtering would occur during the entire irradiation process within the chosen energy range. This was further confirmed by making an initial short run involving a few energy steps about the resonance energy, where it was expected that if no sputtering occurred, the
γ
Proton beam
Target
Detector
Fig. 1. A schematic diagram of the target–detector arrangement. The distance between them is exaggerated here.
ARTICLE IN PRESS N.W. Makau, T.E. Derry / Nuclear Instruments and Methods in Physics Research A 555 (2005) 31–35
Fig. 2. Three gamma-ray peaks emitted from the 13 Cðp; gÞ14 N nuclear reaction at 560 keV. They represent the single and double escape peaks as well as the full energy peak.
number of gamma-ray counts at a given energy would remain the same when repeated, to within the statistical errors. The long runs were then made between 475 and 670 keV using energy steps of 10 keV in the off-resonance region, and 5 keV in the resonance one, a range chosen because of its proximity to the resonance energy (all the energy values are in the laboratory system). The previously measured beam energy spread was 4 keV, making the chosen energy stepping of 5 keV ideal. The beam energy fluctuation during the runs was controlled by the use of a helipot that controlled the amount of current to the accelerator’s 90 analyzing magnet, and a rotating coil flux meter. These two ensured that the beam energy was kept constant at a given energy value during the irradiation process. The runs were made in such a way that enough counts were obtained per run as seen from Fig. 2, with beam currents as high as 500 nA often being used. Such high beams ensured that the exposure times were minimized. The current was normalized through a current integrator by setting a fixed value of the charge, which ensured that the counts were independent of the amount of beam current. 3. Results and discussion By varying the beam energy between 475 and 670 keV at the energy intervals mentioned previously, gamma-ray peaks similar to the one shown in Fig. 2 were obtained at each of the proton energy steps. After a linear background subtraction, the area under these peaks (i.e. between channels x and y as shown in Fig. 2) was taken to represent the number of gamma-ray counts which was directly related to the number of 13C atoms that
33
Fig. 3. A typical gamma-ray yield profile of a 13C-treated diamond (1 1 1) surface.
Fig. 4. A typical gamma-ray yield profile of a 13C-treated diamond (1 1 0) surface.
were excited. All the three peaks had to be included because we wished to count all the gamma rays originating at 8.06 MeV. A plot of these counts as the proton energy was swept below and above the resonance energy resulted in gamma-ray yield profiles similar to the ones shown in Figs. 3 and 4. For an untreated diamond surface, this profile is a step-function convolved with the resonance width, represented by the solid line shown in Figs. 3 and 4. Such a profile originates from the (1:10% 0:03Þ% bulk 13C atoms contained in all natural carbons [18,19], among them diamond, and it represents the ‘‘background’’ spectrum which was used for the quantitative calibration of
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N.W. Makau, T.E. Derry / Nuclear Instruments and Methods in Physics Research A 555 (2005) 31–35
the experiment. The presence of natural 13C atoms in diamond makes it self-calibrating with respect to 13C. For all 13C-treated diamond faces that were irradiated (some not shown here), profiles similar to the ones shown by the points in Figs. 3 and 4 were always obtained. They all exhibited almost similar shapes and appearances that had a tiny parasitic peak superimposed on the background profile. This was the peak due to the 13C layer that was deposited on the diamond surfaces during the polishing, and it was found in all cases involving diamond faces whose polishing was finished with the labelled olive oil. By fitting and subtracting the background, the yield profile produces 13C surface peaks similar to the ones shown in Figs. 5 and 6. Data points from the extracted surface peaks were then fitted with the Breit–Wigner distribution function using the Origin V.6.1 [20] computer program, where the yield was approximated as Y ðEÞ b
Gp Gg ðE E r Þ2 þ G2 =4
Fig. 6. An illustration of the extracted 13C surface peak from Fig. 4. The solid line is the Breit–Wigner fit using Eq. (1).
(1)
where b is a scaling factor, E is the incident proton’s energy, E r is the nuclear reaction’s resonance energy, Gp and Gg are the proton and gamma ray’s partial widths and G is the reaction’s width (full-width at half-maximum (FWHM)). All the parameters shown in Eq. (1) were used as fitting variables except the proton’s energy E and the resonance energy E r . These were allowed to vary in turn, until the best least-squares fit to the data was achieved. From these fits, the value of the FWHM of the nuclear reaction at the resonance energy of 0.55 MeV was extracted for all the three low-index diamond faces that were investigated, and the values obtained are shown in Table 1. From the integrated peaks, the areal densities of the 13C atoms on the respective surfaces were calculated by comparing the
Fig. 5. An illustration of an extracted 13C surface peak from Fig. 3. The solid line indicates the Breit–Wigner fit using Eq. (1).
Table 1 FWHM values for the 550 keV 13 Cðp; gÞ14 N resonant nuclear reaction, with the corresponding 13C areal densities taken from Ref. [21] Face
FWHM (keV)
13 C areal densities (monolayers)
(1 0 0)
25.0 24.6 25.0 25.0 25.0 25.0 24.0 26.0
0.9 1.3 1.3 0.8 0.9 0.8 1.2 1.1
(1 1 0)
(1 1 1)
counts under the extracted peaks with the ‘‘background’’ representing a known 13C density according to a standard procedure which is detailed in Ref. [12]; they were found to be about one monolayer [21]. Our findings show that it is unlikely that clumping would occur on strongly covalent surfaces, while previous works indicate that there is no exchange of labelled carbon atoms at a diamond surface [22]. For this reason, a distribution in depth is clearly ruled out. Averaging the values of the FWHM shown in Table 1 gave the nuclear reaction’s width at 550 keV of 25 1 keV. The error was one standard deviation of the values shown in Table 1, and it arises from fitting errors as well as errors propagated from the uncertainties in determining the areas under the gamma ray peaks (Fig. 2), especially the amount of linear background to subtract. Since this was clearly the thinnest layer one can possibly make, we believe that the reaction width was indeed accurate. This ties in well with Spits et al.’s. [9] definition of a thin target as one whose
ARTICLE IN PRESS N.W. Makau, T.E. Derry / Nuclear Instruments and Methods in Physics Research A 555 (2005) 31–35
thickness is less than that for which the average proton energy loss is equal to the FWHM width of the reaction, a criterion that was very well satisfied by the 13C layer that was deposited in this work. The average value of the FWHM obtained agrees very well with that obtained by Spits et al. [9], but again showing some deviation from those obtained by others [4,5,7,8,10]. This is a rather interesting result because in spite of using an approach different from Spits et al. [9], we still obtained the same low value as them. We note that 13 Cðp; gÞ14 N is a low-energy reaction that takes place via the compound nucleus. It has been said [23] that the compound nuclear levels are fragments of simpler states that have been split by the residual interactions, so that the strength function will show characteristic maxima whenever one of the states is measured. We therefore speculate that because of the geometry of the sampledetector among other factors, the width observed in this study may be one that is mainly dominated by contributions arising from the isotropic s-wave, while others observe both the s-wave plus other contributions. In their fitting algorithm, Galster et al. [24] observe that the total width is composed of partial proton widths that are constituted of an s-wave contribution measuring 26 keV which is very close to the value that we report in our study, and a d-wave contribution of 7 keV. In general, we find this new technique ideal for depositing monolayer targets for determining nuclear reaction widths. The success demonstrated with 13Clabelled oil means that it might be used with similar results for other labelled oils too. 4. Conclusion A small parasitic peak corresponding to the 13C layer residing on polished diamond surfaces was observed on all faces whose polishing was finished with the labelled oil, showing this to be an ideal way of preparing monolayer thick targets. The peak was observed to occur at a resonance energy of 550 keV, where it was superimposed on the background spectrum. Subtraction of the latter gives the surface peaks fitted with the Breit–Wigner distribution. From these fits, an average value of 25 1 keV was extracted for the width of the 13 Cðp; gÞ14 N reaction. This value was in surprisingly good agreement with that obtained by Spits et al. [9] of 25 1 keV, as well as the one obtained for the s-wave contribution by Galster et al. [24] of 26 1 keV. It was at variance with those obtained by others [4,5,7,8,10], as outlined in the Introduction, and it may well be that, because of our geometry, our result of the FWHM is predominantly due to the isotropic s-wave contribution as reported by Ref. [24]. The results also confirm that the 13C layer formed on the diamond surfaces after polishing was very thin, and hence the value of the reaction width that is established is likely to be
35
accurate to within the errors mentioned previously. It would therefore be interesting to observe whether this method can be useful in other cases. Acknowledgements The authors would like to thank Mick Rebak for the mechanical polishing of the diamond samples, and the DAAD for financial support of one of the authors, N.W. Makau. The contribution of vacation students, Keri Pickster and Chris Freemantle, in extracting the initial data is also acknowledged. References [1] L. Wei, in: AIP Conference Proceedings, New York, vol. 680, 2003, pp. 464. [2] T.E. Derry, R.A. Spits, J.P.F. Sellschop, Mater. Sci. Eng. B 11 (1992) 249. [3] T.E. Derry, N.W. Makau, in: Y. Ballim, A.G. Avery, S. Luyckx, D.C. Levendis (Eds.), Proceedings of second International Conference of the African Material Research Society. Johannesburg, South Africa, 8–11 December 2003, University of the Witwatersrand (ISBN: 0-620-31513-X), 255–256. [4] J.D. King, R.E. Azuma, J. Vise, J. Gorres, C. Rolfs, H.P. Trautvetter, A.E. Vlieks, Nucl. Phys. A 567 (1994) 354. [5] W. Fowler, C. Lauritsen, T. Lauritsen, Rev. Mod. Phys. 20 (1948) 236. [6] J.D. Seagrave, Phys. Rev. 85 (1951) 197. [7] C.M. Mahaux, Nucl. Phys. 71 (1965) 241. [8] W.A. Fowler, G.R. Caughlan, B.A. Zimmermann, Ann. Rev. Astrophys. 5 (1967) 525. [9] R.A. Spits, W. Baloyi, T.E. Derry, Phys. Rev. C 41 (5) (1990) 2429. [10] C.R. Brune, R.W. Kavanagh, Phys. Rev. C 44 (4) (1991) 1665. [11] J. Kiener, M. Gros, V. Tatischeff, D. Attie, I. Bailley, A. Bauchet, C. Chapuis, B. Cordier, I. Deloncle, M.G. Porquet, et al., Nucl. Instr. and Meth. A 519 (2) (2004) 623. [12] M. Nastasi, J.R. Tesmer (Eds.), Handbook of Ion Beam Materials Analysis, Materials Research Society, Pittsburg, Pennyslvania, 1995, pp. 576 and 586. [13] Cambridge Isotope Laboratories, Stable Isotopes Catalog, Andover, MA, USA, 2003. [14] Aldrich Chemical Company Inc., Stable Isotopes Catalog, Milwaukee, USA, 2003. [15] N.W. Makau, T.E. Derry, Surf. Rev. Lett. 10 (2,3) (2003) 295. [16] G.F. Knoll, Radiation Detection and Measurement, third ed., Wiley, New York, 2000, pp. 116–119. [17] J.F. Ziegler, The Stopping and Ranges of Ions in Matter, vol. 5, Pergamon, New York, 1980. [18] D.R. Lide (Ed.), CRC Handbook of Chemistry and Physics, CRC Press, Boston, 1992, pp. 11–34. [19] H.J. Ro¨sler, H. Lange (Eds.), Geochemical Tables, Elsevier Publishing Company, Amsterdam, 1972, pp. 405. [20] OriginLab Corporation, One Roundhouse Plaza, Northampton, MA O1060, USA, 2004, www.OriginLab.com [21] T.E. Derry, N.W. Makau, Diamond Related. Mater. (2005), in press. [22] J. Perrie`re, A. Laurent, J.P. Enard, Mater. Sci. Eng. B 11 (1992) 347. [23] P.E. Hodgson, Nuclear Reactions and Nuclear Structure, Oxford University Press, London, 1971, pp. 195. [24] W. Galster, P. Leleux, I. Licot, E. Lienard, P. Lipnik, D. Mertens, P. Decrock, M. Huyse, P. van Duppen, P. Duhamel, et al., Phys. Rev. C 44 (6) (1991) 2776.
Nuclear Instruments and Methods in Physics Research A 555 (2005) 31–35 www.elsevier.com/locate/nima
A new way of depositing thin targets of monolayer thickness for nuclear reaction analysis: A case of the 550 keV 13C ðp; gÞ14N resonant nuclear reaction N.W. Makau,1, T.E. Derry Schonland Research Institute for Nuclear Sciences (iThemba LABS-Gauteng) and School of Physics, University of the Witwatersrand, Private Bag 3, Wits 2050, Johannesburg, South Africa Received 18 May 2005; received in revised form 22 September 2005; accepted 24 September 2005
Abstract We suggest a method by which the thinnest possible uniform isotopic targets may be produced in favourable cases, by bonding a monolayer to a diamond substrate, for use in nuclear level studies at maximum energy resolution. The need to deconvolve the target thickness contribution, or concern about its possible non-uniformity, fall away. We illustrate with a new measurement of the proton energy width of the 13 Cðp; gÞ14 N resonance at 550 keV. r 2005 Elsevier B.V. All rights reserved. PACS: 24.30.V; 29.25.t; 68.43.h; 81.05.Uw Keywords: Thin target; Nuclear reaction; Resonance width; Diamond
1. Introduction Measurements (or remeasurements) of the width, spin, parity, etc. of nuclear energy levels still occupy an important place in experimental nuclear physics. For studies at the highest possible energy resolution, allowance for the degradation of the accelerator beam energy in the target material has always been a problem. Deconvolution of the thickness contribution is only reliable if the target thickness is very uniform, which, for either supported or self-supporting targets, may well not be the case. It is important to note that uniformity errors tend to make the width too large. The ideal target from this point of view would have negligible thickness, i.e. it would be a partial or full atomic monolayer. Over the years, Nuclear Reaction Analysis has evolved to become one of the most practical analytical tools in Corresponding author. Tel.: +11 351 7050; fax: +11 351 7053.
E-mail addresses: [email protected] (N.W. Makau), [email protected] (T.E. Derry). URL: http://www.src.wits.ac.za. 1 On leave from Moi University, Eldoret, Kenya. 0168-9002/$ - see front matter r 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.nima.2005.09.034
various applications [1]. Resonant particle-induced reactions which exhibit sharp increases in cross-section at specific energies are often particularly useful for both surface and near-surface probing. An accurate knowledge of the energy width of a resonance is essential for precision depth profiling in this application [2]. While studying the adatoms which become attached to a diamond surface during standard preparation procedures based on mechanical polishing, we observed [3] that the outermost carbon atoms, approximately a monolayer, together with associated hydrogen atoms, were derived from the olive oil (principally consisting of olein) which is invariably used as a lubricant with the diamond grit which achieves the polishing. This added carbon monolayer was detected after polishing with 13C-labelled olein, using a proton beam and the 13 Cðp; gÞ14 N resonance at 550 keV. We were able to re-measure the width of this resonance, which has been subject to some disagreement, at high resolution, and report the results below. This method could be applicable in other cases where a precursor containing the desired isotope is available, e.g. a fluorinated oil for a fluorine monolayer. Covalent solids
ARTICLE IN PRESS 32
N.W. Makau, T.E. Derry / Nuclear Instruments and Methods in Physics Research A 555 (2005) 31–35
other than diamond may be found to bond atoms or molecular fragments in a similar way. King et al. [4] have outlined earlier attempts to establish the above reaction width. They indicated that the first reported width for this resonance was 40 keV obtained by Fowler et al. [5] which was followed quite closely by the 1951 work of Seagrave [6] who obtained a value of 32:5 1 keV. Subsequent work of Mahaux [7] gave a value of 42 keV, while Fowler et al. [8] later reported a revised value of 40.5 keV, which was very close to the one that they had obtained earlier in 1948 [5]. As a result of the rather narrow width (25 1 keV) reported by Spits et al. [9], Brune and Kavanagh [10] remeasured it, using almost the same geometry over the proton energy range of 495–605 keV and obtained a value of 37:5 0:5 keV, while King et al. [4] using the same energy interval and fitting their data to the S-factor equation obtained a value of 38:4 0:3 keV. They, however, note in their work that a fit over such a restricted range considerably overestimates the contribution from direct capture and the tail at the O1 state compared with the fit to the full range of data, but they do not mention by how much this overestimation is made. The nuclear reaction’s resonance width Gr for 13 Cðp; gÞ14 N is still being referred to as being uncertain [11], due to these emergent values of its width, which do not seem to show much agreement. Nastasi et al. [12] actually quote both the values of 32:5 1 keV and 25 1 keV that were mentioned previously. 2. Experimental 2.1. Sample preparation Most of the work reported in the literature regarding the Cðp; gÞ14 N nuclear reaction deals primarily with either supported thin targets which are obtained by evaporating the species of interest onto a suitable substrate, or alternatively implanting the species into some matrix. Each of these two methods may have its own drawbacks, since the thickness and hence uniformity of the target may vary, thus being put into question. In this study we discuss a method of depositing thin monolayer targets by polishing diamond surfaces with olive oil labelled with 13C atoms. It is important to note that many other labelled oils and even solvents do exist nowadays [13,14], among them being the chlorinated and fluorinated oils, etc. In this work, six natural diamond samples of sizes ranging between 3 mm 3 mm 4 mm and 3 mm 3 mm 2 mm were initially polished mechanically following the procedure described previously in Ref. [15]. They were then repolished manually on a highly polished cast iron block, using diamond pastes of 1=4 and 1=10 mm, together with olein that was labelled with 99% 13C atoms [14]. The oil acted as both a lubricant and a donor for the 13C atoms required to bond with the dangling carbon bonds that are created on the diamond surfaces while polishing. Each polishing process lasted for about 30 min, after which the surfaces were cleaned in a 13
solution of Contrad (a surface decontamination detergent), followed by an ultrasonic rinsing thrice using deionized water. The surfaces were dried by blowing dry nitrogen gas over them. 2.2. Irradiation process The 1.4 MeV Cockcroft–Walton proton accelerator based at the Schonland Research Institute was used to provide the energetic protons needed to probe for the 13C atoms via the 13 Cðp; gÞ14 N nuclear resonance at 550 keV. Fig. 1 shows the target–detector geometry. A 10 cm 10 cm Bicron NaI(Tl) detector having a resolution of about 60 keV was positioned outside the vacuum, at 10 mm right in front of the beam stub where the target was mounted as shown in Fig. 1, and this arrangement was used for the collection of the gamma-ray yield in all cases. This geometry ensured that almost a 2p steradian solid angle was subtended at the target, maximizing the gammaray collection efficiency [16]. Absorption by the sample holder was negligible. The detector was placed within a lead annulus measuring 6.8 cm in thickness, and this contributed greatly towards the minimization of the background radiation. The vacuum within the target chamber was maintained at better than 106 Torr. The target chamber was isolated from the beam line, and acted as a Faraday cup for current integration. This avoids the need for secondary electron suppression. We used 137Cs and 60Co standard sources, for setting up the experiment. This ensured that the collected (8.06 MeV) [12] gamma-rays were identified and recorded into reasonable channels by the multichannel analyzer (MCA). The entire spectrum was collected, and our setup ensured that the gamma-rays of interest were deposited well away from the low-energy background. We then selected the region of interest containing the 8.06 MeV gamma-rays to work with. In order to ensure that the deposited layer of 13C atoms remained the same, before and after the irradiation process, a Transport and Range of Ions in Matter (TRIM) simulation using the 2004 Stopping and Range of Ions in Matter (SRIM) computer code [17] was done, and this showed that no sputtering would occur during the entire irradiation process within the chosen energy range. This was further confirmed by making an initial short run involving a few energy steps about the resonance energy, where it was expected that if no sputtering occurred, the
γ
Proton beam
Target
Detector
Fig. 1. A schematic diagram of the target–detector arrangement. The distance between them is exaggerated here.
ARTICLE IN PRESS N.W. Makau, T.E. Derry / Nuclear Instruments and Methods in Physics Research A 555 (2005) 31–35
Fig. 2. Three gamma-ray peaks emitted from the 13 Cðp; gÞ14 N nuclear reaction at 560 keV. They represent the single and double escape peaks as well as the full energy peak.
number of gamma-ray counts at a given energy would remain the same when repeated, to within the statistical errors. The long runs were then made between 475 and 670 keV using energy steps of 10 keV in the off-resonance region, and 5 keV in the resonance one, a range chosen because of its proximity to the resonance energy (all the energy values are in the laboratory system). The previously measured beam energy spread was 4 keV, making the chosen energy stepping of 5 keV ideal. The beam energy fluctuation during the runs was controlled by the use of a helipot that controlled the amount of current to the accelerator’s 90 analyzing magnet, and a rotating coil flux meter. These two ensured that the beam energy was kept constant at a given energy value during the irradiation process. The runs were made in such a way that enough counts were obtained per run as seen from Fig. 2, with beam currents as high as 500 nA often being used. Such high beams ensured that the exposure times were minimized. The current was normalized through a current integrator by setting a fixed value of the charge, which ensured that the counts were independent of the amount of beam current. 3. Results and discussion By varying the beam energy between 475 and 670 keV at the energy intervals mentioned previously, gamma-ray peaks similar to the one shown in Fig. 2 were obtained at each of the proton energy steps. After a linear background subtraction, the area under these peaks (i.e. between channels x and y as shown in Fig. 2) was taken to represent the number of gamma-ray counts which was directly related to the number of 13C atoms that
33
Fig. 3. A typical gamma-ray yield profile of a 13C-treated diamond (1 1 1) surface.
Fig. 4. A typical gamma-ray yield profile of a 13C-treated diamond (1 1 0) surface.
were excited. All the three peaks had to be included because we wished to count all the gamma rays originating at 8.06 MeV. A plot of these counts as the proton energy was swept below and above the resonance energy resulted in gamma-ray yield profiles similar to the ones shown in Figs. 3 and 4. For an untreated diamond surface, this profile is a step-function convolved with the resonance width, represented by the solid line shown in Figs. 3 and 4. Such a profile originates from the (1:10% 0:03Þ% bulk 13C atoms contained in all natural carbons [18,19], among them diamond, and it represents the ‘‘background’’ spectrum which was used for the quantitative calibration of
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the experiment. The presence of natural 13C atoms in diamond makes it self-calibrating with respect to 13C. For all 13C-treated diamond faces that were irradiated (some not shown here), profiles similar to the ones shown by the points in Figs. 3 and 4 were always obtained. They all exhibited almost similar shapes and appearances that had a tiny parasitic peak superimposed on the background profile. This was the peak due to the 13C layer that was deposited on the diamond surfaces during the polishing, and it was found in all cases involving diamond faces whose polishing was finished with the labelled olive oil. By fitting and subtracting the background, the yield profile produces 13C surface peaks similar to the ones shown in Figs. 5 and 6. Data points from the extracted surface peaks were then fitted with the Breit–Wigner distribution function using the Origin V.6.1 [20] computer program, where the yield was approximated as Y ðEÞ b
Gp Gg ðE E r Þ2 þ G2 =4
Fig. 6. An illustration of the extracted 13C surface peak from Fig. 4. The solid line is the Breit–Wigner fit using Eq. (1).
(1)
where b is a scaling factor, E is the incident proton’s energy, E r is the nuclear reaction’s resonance energy, Gp and Gg are the proton and gamma ray’s partial widths and G is the reaction’s width (full-width at half-maximum (FWHM)). All the parameters shown in Eq. (1) were used as fitting variables except the proton’s energy E and the resonance energy E r . These were allowed to vary in turn, until the best least-squares fit to the data was achieved. From these fits, the value of the FWHM of the nuclear reaction at the resonance energy of 0.55 MeV was extracted for all the three low-index diamond faces that were investigated, and the values obtained are shown in Table 1. From the integrated peaks, the areal densities of the 13C atoms on the respective surfaces were calculated by comparing the
Fig. 5. An illustration of an extracted 13C surface peak from Fig. 3. The solid line indicates the Breit–Wigner fit using Eq. (1).
Table 1 FWHM values for the 550 keV 13 Cðp; gÞ14 N resonant nuclear reaction, with the corresponding 13C areal densities taken from Ref. [21] Face
FWHM (keV)
13 C areal densities (monolayers)
(1 0 0)
25.0 24.6 25.0 25.0 25.0 25.0 24.0 26.0
0.9 1.3 1.3 0.8 0.9 0.8 1.2 1.1
(1 1 0)
(1 1 1)
counts under the extracted peaks with the ‘‘background’’ representing a known 13C density according to a standard procedure which is detailed in Ref. [12]; they were found to be about one monolayer [21]. Our findings show that it is unlikely that clumping would occur on strongly covalent surfaces, while previous works indicate that there is no exchange of labelled carbon atoms at a diamond surface [22]. For this reason, a distribution in depth is clearly ruled out. Averaging the values of the FWHM shown in Table 1 gave the nuclear reaction’s width at 550 keV of 25 1 keV. The error was one standard deviation of the values shown in Table 1, and it arises from fitting errors as well as errors propagated from the uncertainties in determining the areas under the gamma ray peaks (Fig. 2), especially the amount of linear background to subtract. Since this was clearly the thinnest layer one can possibly make, we believe that the reaction width was indeed accurate. This ties in well with Spits et al.’s. [9] definition of a thin target as one whose
ARTICLE IN PRESS N.W. Makau, T.E. Derry / Nuclear Instruments and Methods in Physics Research A 555 (2005) 31–35
thickness is less than that for which the average proton energy loss is equal to the FWHM width of the reaction, a criterion that was very well satisfied by the 13C layer that was deposited in this work. The average value of the FWHM obtained agrees very well with that obtained by Spits et al. [9], but again showing some deviation from those obtained by others [4,5,7,8,10]. This is a rather interesting result because in spite of using an approach different from Spits et al. [9], we still obtained the same low value as them. We note that 13 Cðp; gÞ14 N is a low-energy reaction that takes place via the compound nucleus. It has been said [23] that the compound nuclear levels are fragments of simpler states that have been split by the residual interactions, so that the strength function will show characteristic maxima whenever one of the states is measured. We therefore speculate that because of the geometry of the sampledetector among other factors, the width observed in this study may be one that is mainly dominated by contributions arising from the isotropic s-wave, while others observe both the s-wave plus other contributions. In their fitting algorithm, Galster et al. [24] observe that the total width is composed of partial proton widths that are constituted of an s-wave contribution measuring 26 keV which is very close to the value that we report in our study, and a d-wave contribution of 7 keV. In general, we find this new technique ideal for depositing monolayer targets for determining nuclear reaction widths. The success demonstrated with 13Clabelled oil means that it might be used with similar results for other labelled oils too. 4. Conclusion A small parasitic peak corresponding to the 13C layer residing on polished diamond surfaces was observed on all faces whose polishing was finished with the labelled oil, showing this to be an ideal way of preparing monolayer thick targets. The peak was observed to occur at a resonance energy of 550 keV, where it was superimposed on the background spectrum. Subtraction of the latter gives the surface peaks fitted with the Breit–Wigner distribution. From these fits, an average value of 25 1 keV was extracted for the width of the 13 Cðp; gÞ14 N reaction. This value was in surprisingly good agreement with that obtained by Spits et al. [9] of 25 1 keV, as well as the one obtained for the s-wave contribution by Galster et al. [24] of 26 1 keV. It was at variance with those obtained by others [4,5,7,8,10], as outlined in the Introduction, and it may well be that, because of our geometry, our result of the FWHM is predominantly due to the isotropic s-wave contribution as reported by Ref. [24]. The results also confirm that the 13C layer formed on the diamond surfaces after polishing was very thin, and hence the value of the reaction width that is established is likely to be
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accurate to within the errors mentioned previously. It would therefore be interesting to observe whether this method can be useful in other cases. Acknowledgements The authors would like to thank Mick Rebak for the mechanical polishing of the diamond samples, and the DAAD for financial support of one of the authors, N.W. Makau. The contribution of vacation students, Keri Pickster and Chris Freemantle, in extracting the initial data is also acknowledged. References [1] L. Wei, in: AIP Conference Proceedings, New York, vol. 680, 2003, pp. 464. [2] T.E. Derry, R.A. Spits, J.P.F. Sellschop, Mater. Sci. Eng. B 11 (1992) 249. [3] T.E. Derry, N.W. Makau, in: Y. Ballim, A.G. Avery, S. Luyckx, D.C. Levendis (Eds.), Proceedings of second International Conference of the African Material Research Society. Johannesburg, South Africa, 8–11 December 2003, University of the Witwatersrand (ISBN: 0-620-31513-X), 255–256. [4] J.D. King, R.E. Azuma, J. Vise, J. Gorres, C. Rolfs, H.P. Trautvetter, A.E. Vlieks, Nucl. Phys. A 567 (1994) 354. [5] W. Fowler, C. Lauritsen, T. Lauritsen, Rev. Mod. Phys. 20 (1948) 236. [6] J.D. Seagrave, Phys. Rev. 85 (1951) 197. [7] C.M. Mahaux, Nucl. Phys. 71 (1965) 241. [8] W.A. Fowler, G.R. Caughlan, B.A. Zimmermann, Ann. Rev. Astrophys. 5 (1967) 525. [9] R.A. Spits, W. Baloyi, T.E. Derry, Phys. Rev. C 41 (5) (1990) 2429. [10] C.R. Brune, R.W. Kavanagh, Phys. Rev. C 44 (4) (1991) 1665. [11] J. Kiener, M. Gros, V. Tatischeff, D. Attie, I. Bailley, A. Bauchet, C. Chapuis, B. Cordier, I. Deloncle, M.G. Porquet, et al., Nucl. Instr. and Meth. A 519 (2) (2004) 623. [12] M. Nastasi, J.R. Tesmer (Eds.), Handbook of Ion Beam Materials Analysis, Materials Research Society, Pittsburg, Pennyslvania, 1995, pp. 576 and 586. [13] Cambridge Isotope Laboratories, Stable Isotopes Catalog, Andover, MA, USA, 2003. [14] Aldrich Chemical Company Inc., Stable Isotopes Catalog, Milwaukee, USA, 2003. [15] N.W. Makau, T.E. Derry, Surf. Rev. Lett. 10 (2,3) (2003) 295. [16] G.F. Knoll, Radiation Detection and Measurement, third ed., Wiley, New York, 2000, pp. 116–119. [17] J.F. Ziegler, The Stopping and Ranges of Ions in Matter, vol. 5, Pergamon, New York, 1980. [18] D.R. Lide (Ed.), CRC Handbook of Chemistry and Physics, CRC Press, Boston, 1992, pp. 11–34. [19] H.J. Ro¨sler, H. Lange (Eds.), Geochemical Tables, Elsevier Publishing Company, Amsterdam, 1972, pp. 405. [20] OriginLab Corporation, One Roundhouse Plaza, Northampton, MA O1060, USA, 2004, www.OriginLab.com [21] T.E. Derry, N.W. Makau, Diamond Related. Mater. (2005), in press. [22] J. Perrie`re, A. Laurent, J.P. Enard, Mater. Sci. Eng. B 11 (1992) 347. [23] P.E. Hodgson, Nuclear Reactions and Nuclear Structure, Oxford University Press, London, 1971, pp. 195. [24] W. Galster, P. Leleux, I. Licot, E. Lienard, P. Lipnik, D. Mertens, P. Decrock, M. Huyse, P. van Duppen, P. Duhamel, et al., Phys. Rev. C 44 (6) (1991) 2776.