Journal of the Korean Physical Society, Vol. 61, No. 3, August 2012, pp. 336∼341
Comparison between Different Models for Alpha-particle Range Determination and a New Approach to CR-39 Detector M. El Ghazaly∗ Department of Physics, Faculty of Science, PO 44519, Zagazig, Zagazig University, Egypt and Department of Physiology, College of Medicine, Tiaf University, Al-Hawiah, PO 21974, Taif, Saudi Arabia
T. T. Salama and E. I. Khalil Department of Physics, Faculty of Science, Zagazig University, PO 44519, Zagazig, Egypt
Kh. M. Abd El Raouf Radiology Department, Faculty of Medicine, Zagazig University, PO 44519, Zagazig, Egypt and College of Men in Alqunfudah, Umm Al-Qura University, Saudi Arabia (Received 14 October 2011, in final form 1 June 2012) An extensive study was carried out to compare different models and a new approach for measuring the alpha-particle range in the CR-39 detector. The CR-39 samples were exposed perpendicularly to alpha particles with energies ranging from 2.5 MeV to 5.5 MeV emitted from 241 Am. The CR39 samples were etched in 7.25 N NaOH at (70 ± 0.5) ◦ C for different durations. Both the track diameters and the track cone lengths were measured under an optical microscope. The new approach is based on measurement of the track etch rate along the particle’s trajectory as a function of the removal thickness (h). A correlation was found to exist between the removal thickness at the maximum track etch rate (VT max ) and the range of alpha particles in the CR-39 detector. The track etch rate data were fitted using the function VT (h) = a1 + [a2 − a3 h] exp[a4 h]. The ranges of alpha particles were determined by setting the first order derivative of the fitting function equal to zero, where h is equal to the range of the alpha particles (R) in the CR-39 detector. Furthermore, the range of the alpha particle in the CR-39 detector was measured using the over-etched track diameter and the track cone length. The theoretical predictions of the alpha-particle ranges were calculated using the SRIM software. A well-known function, R(E) = b1 E b2 , was used to fit the experimental results and the theoretical predictions. Experiments showed that the determination of the alpha-particle range based on the cone length model was in a good agreement with the theoretical calculations, where the discrepancy was less than that for the over-etched track diameter and the maximum track etch rate models. PACS numbers: 29.40.Gx, 29.40.Wk, 79.60.Fr, 07.77.Ka, 61.82.-d Keywords: Poly allyl diglycol carbonate (CR-39), Alpha particle, Range, Track etch rate, SRIM DOI: 10.3938/jkps.61.336
I. INTRODUCTION
parameters are the key characteristics in the use of the CR-39 detector for alpha-particle range determination. With respect to the track opening, the diameter of the mouth opening is used to measure the alpha-particle’s energy via a calibration curve between the diameter and the energy of the alpha particle. This technique, however, has some disadvantage for practical utilization over a wide range of alpha-particle energies; this is the degeneracy of the alpha-particle diameter. In other words, the alpha-particle track diameter is a non-monotonic function of the alpha-particle energy [10]. A track profile technique is used to identify and determine the energy of charged particles and to measure the track cone length or track cone depth L [11]. The track profile is revealed by observation either of the track perpendicularly to its
Poly allyl digloycol carbonate (PADC), commercially known as CR-39 detector, is being used to register and identify charged particles [1–4]. Nevertheless, its wide scientific and technological applications are growing rapidly in several different fields including materials science, micro mapping of radioactive elements in rocks, radon monitoring, neutron radiography, particle identification, cosmic-ray measurements, radiation dosimetry, X-ray reflectivity, and eyeglass lenses [5–9]. Both the track opening parameters and track profile ∗ E-mail:
[email protected]; Fax: +2055-2303252
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Comparison between Different Models for Alpha-particle Range · · · – M. El Ghazaly et al.
path [11–13] or with a confocal optical microscope [14, 15]. The energy-range relationship of a charged particle in the CR-39 detector offers a good opportunity for charged-particle identification and energy determination. This is only possible because the range is a monotonic function of the alpha-particle energy [16, 17]. In addition, particle identification based on the energy-range relationship may supply a better detector energy resolution than one based on the track opening diameter measurement simply because the variation in the track etch rate VT along the particle’s trajectory is faster than the variation in the direction perpendicular to the particle’s trajectory [2]. The updated software provided by the (SRIM) software with a quantum mechanical treatment of ion-atoms collisions has been used in a theoretical calculation of the stopping power and the range of alpha particle in the range of 10 eV-2 GeV in matter [18,19]. Experimentally, two techniques are used to determine the alpha-particle range in the CR-39 detector. The overetched track profile that depends mainly on a measure of the over-etched track diameter after the range [16, 17] and the track profile cone length that is based on a measure of the track profile parameters and the removal thickness of the charged-particle’s track [11]. In the present work, a new approach to measure the range of an alpha particle in the CR-39 detector by studying the variation in the track etch rate as a function of removal thickness will be proposed. A comparison between the well-known models that have met with a considerable success will be reported. The experimental results from three models will be compared with the theoretical calculation by using the SRIM software.
II. EXPERIMENTS AND DISCUSSION CR-39 plastic detector sheets, Tastrack, with a density of 1.32 g/cm3 , a molecular composition C12 H18 O7 and a thickness of (1000 ± 4) µm were cut into pieces of 2 cm2 from a large sheet. The CR-39 detector samples were produced in the same year to avoid the aging effect [20]. CR-39 samples were exposed to alpha particles from 241 Am (E = 5.49 MeV) with an activity of 9 µCi. Figure 1 illustrates the experimental setup for alpha-particle irradiation with perpendicular incidence. Energy degradation was carried out in air by using collimators of different thicknesses with a diameters of 1 mm by change the air column length in accordance with an energy-distance calibration curve [21]. CR-39 samples were etched in an aqueous solution of 7.25 N NaOH at (70 ± 1) ◦ C for different durations. The bulk etch rate VB was measured using the mass decrement method. The bulk etch rate VB amounted to VB = (1.80 ± 0.05) µm/h. Finally, the track openings and the track cone lengths were measured under an optical microscope. To measure the track profile, we broken CR-39 samples in small
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Fig. 1. (Color online) Experimental setup for alphaparticle irradiation with perpendicular incidence. The alphaparticle energy was selected by using several collimators of different thicknesses [21].
pieces that were carefully polished. Thereafter, the CR39 samples were irradiated laterally and then etched and inspected carefully under an optical microscope to select better samples for followup. Every datum point represents a mean value of about 50 measurements associated with a relative standard deviation of 6 – 10%. The theoretical values of the alpha-particle range were calculated using the SRIM software [22].
1. Alpha-particle Range Determination Based on the Maximum Track Etch Rate
The track etch rate VT varies along the trajectory of the charged particle in the detector’s material, but the track etch rate VT reflects the value of the linear energy transfer (LET) within the detector’s material in accordance with the Bragg curve [22]. As a consequence, the track etch rate VT varies as a function of the removal thickness h and should have a similar behavior to the linear energy transfer curve along the particle’s path in the detector material; it has a Bragg’s peak as well [10]. The track etch rate VT is given by [24] VT = dL/dte + VB ,
(1)
where L is the track cone length and te refers to the etching time measured in hours. The behavior of the track etch rate (VT ) using the track profile has been carefully studied to understand its dependence on the alpha-particle energy and the removal layer and in order to find its maximum value as a function of the alpha energy [11]. Figure 2(a) illustrates the maximum track etch rate VT max as a function of the alpha energy. For a definite alpha-particle energy, the track etch rate increases smoothly prior to the end of the range of the alpha particle. Then, it increases sharply and reaches a maximum value. Thereafter, it falls rapidly. For all examined alpha-particle energies, the maximum track etch rate has approximately a constant maximum value of 11.5 µm/h with a slight deviation of ±0.05, which is within the experimental errors. The current results confirm the fact that the maximum energy deposition at the
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Journal of the Korean Physical Society, Vol. 61, No. 3, August 2012
be considered in such measurements. When the track etch rate starts to increase sharply, the etching time interval should be reduced to avoid loss of the Bragg peak. Figure 3(a) illustrates the variation of the track etch rate along trajectory of a 3.5 MeV alpha particle. This is found in the upper left left corner on the Fig. 3(a) the energy loss calculated using the SRIM software [22]. Both curves show that the energy loss reaches it’s maximum approximately at the end of the particle’s range in the CR-39 detector. The data were fitted with a suitable function expressing the track etch rate as a function of the removal thickness: VT (h) = a1 + [a2 − a3 h] exp[a4 h],
Fig. 2. (a) Dependence of the maximum track etch rate (VT max ) on the alpha-particle energy in CR-39 detector etched in 7.25 N NaOH at (70 ± 1) ◦ C. (b) Dependence of the maximum linear energy transfer (LET) on the depth, which is calculated as in Ref. 22 for alpha particles of different energies in the CR-39 detector.
end of alpha-particle track doesn’t depend on the incident energy of the alpha particle. The data presented in Fig. 2(a) is fitted with a linear function: VT max = a + bE,
(2)
where the fitting parameters values are a = 11.4 ± 0.4 and b = 0.02 ± 0.09, respectively. Considering the linear energy transfer (LET) curves that are calculated using the SRIM software for the alpha particles within the CR-39 detector, it is easy to recognize that the Bragg peak has approximately the same values of the maximum energy loss of 27.7 ± 0.1 eV/˚ A at the end of the range [22]. The maximum energy loss is independent of the alpha-particle energy, as illustrated in Fig. 2(b). These results confirm the current investigation and the result reported by D¨ orschel et al. [23]. As pointed out by D¨ orschel et al. [24], this fact holds just for light charged projectiles like protons, deuterons and alpha particles, but it doesn’t hold for the heavy charged projectiles including nitrogen and oxygen ions in the CR39 detector, where the maximum track etch rete VT max depends on the energy of the projectiles. For the alpha-particle range determination with the aid of the track profile, an important precaution should
(3)
where the best fit parameters are a1 = 4.45, a2 = 0.0003, a3 = 0.00001, and a4 = 3.12. In principle, at maximum value of the track etch rate, the following condition must hold, dVT /dh = 0. Therefore, the range is determined by differentiating Eq. (3) and setting the results equal to zero. This procedure is applied to other alpha-particle energies to extract the range of the alpha particle in the same way. The track etch rate of the 3.5 MeV alpha particle reaches its maximum value at a removal thickness 15.7 µm while the theoretical value according to the SRIM software is 17.2 µm; the discrepancy is less than 10%. The relative gradual decrease in the track etch rate after the range may be attributed to δ-ray electrons, which propagate for some distance after the complete stopping of the alpha particle in the CR-39 detector. This discrepancy may be attributed to the density variation of the CR-39 sdetector resulting from the swelling during the chemical etching or to the alpha particle energy uncertainty or to the track length measurement uncertainty. Figure 3(b) depicts a comparison between the alphaparticle range within the CR-39 detector, which was theoretically calculated by using the SRIM software [22], and the experimental range based on the track etch rate variation. The experimental and the theoretical data for the alpha-particle range in the CR-39 detector are fitted with function R(E) = b1 E b2 .
(4)
The fitting parameters b1 and b2 have been determined for each model and compared with the theoretical fitting parameters. Equation (4) will be used to fit the data on the alpha-particle range in the current work. The difference between the experimental and the theoretical values of the alpha particles ranges was about 3.5%, for alpha particles with energy of 5.48 MeV, whereas for a lower alpha-particle energy of 2.5 MeV the difference amounted to 20%. For a high-alpha particle energy of 5.49 MeV, the deviation is within the experimental error as shown from Fig. 3(b), which means this method can be suitable for high-energy alpha particles.
Comparison between Different Models for Alpha-particle Range · · · – M. El Ghazaly et al.
Fig. 3. (a) Variation of the track etch rate VT along the trajectory of an alpha particle with an energy of 3.5 MeV in the CR-39 detector etched in 7.25 N NaOH at (70 ± 1) ◦ C. The upper left side of the graph shown the corresponding energy loss curve as calculated by using SRIM [22]. (b) Ranges of alpha particles as a function of the alpha-particle energy at the maximum track etch rate (VT max ) show a relative small deviation from the predicted values of the range, especially at high energy.
2. Alpha-particle Range Determination Based on the Over-etched Track Diameter
The easiest model, but the most sophisticated one, used to measure the range of alpha particles in the CR39 detector depends on the measure of the over-etched track diameter [17]. In this model, the track etch rate VT doesn’t take this into consideration and is considered a constant. For an over-etched track, te tR , where tR is the time needed to etch the track to its end range (R), a plot of the diameter squared D2 versus the etching time te will show a linear relationship. By a determination of the linear regression (S) of the straight line segment, and the intersection of the straight line (I) with the D2 axis, the range of alpha particles can be determined experimentally with the aide of the following equation [10, 16]:
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Fig. 4. Determination of the alpha-particle range in the CR-39 detector is shown after Somogyi [16] for alpha particles of 5 MeV. The CR-39 detector is etched in 7.25 N NaOH at (70 ± 1) ◦ C. (a) The linear segment of the curve is fitted to extract the tR , the linear regression, and the intersection I. (b) Range of alpha particles in the CR-39 detector as a function of alpha-particle energy based on the over-etched track diameter.
R=
S I − VB . 16VB S
(5)
Figure 4(a) shows an example for such measurements, with the linear best fit function of D2 = −2880 ± 284te . The range of alpha particles can be measured experimentally by applying Eq. (5). For the alpha particle with an energy of 5 MeV, the measured range is 28.1 ± 0.8 µm. The same procedure was applied for different alphaparticle energies to get the range in the CR-39 detector.
3. Alpha-particle Range Determination Based on the Track Cone Length
The range of charged particle was determined by measuring the track cone length L directly, where the range
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Journal of the Korean Physical Society, Vol. 61, No. 3, August 2012
Table 1. Best fit parameters of the alpha particle range in a CR-39 detector deduced from the different models and from a theoretical calculation based on Eq. (4). Model Theoretical by SRIM Over-etched track diameter Track profile cone length Maximum track etch rate
2.99 3.75 2.97 1.92
b1 ± ± ± ±
0.07 0.15 0.33 0.02
1.40 1.25 1.44 1.64
b2 ± ± ± ±
0.02 0.03 0.07 0.01
of alpha particles could be determined experimentally by using Eq. (6) [23]. R = VB te + Lmax = h + Lmax ,
(6)
where h = VB te is the removal thickness measured in microns. However, Eq. (6) holds when dL dx = 0, i.e., when L = constant, i.e., at the end of the range of alphaparticle track within the CR-39 detector. Figure 5(a) shows the dependence of the cone track length on the removal thickness. After the range of alpha particle, the track cone length has a constant value. The measured ranges of the alpha particles Fig. 5(b) are compared with the theoretical values of the dashed line. The experimental and the theoretical data were fitted with Eq. (4). The fitting parameters b1 and b2 are summarized in Table 1. The good agreement at higher energies may be attributed to the δ-ray electrons.
4. Comparison between the Different Models to Determine the Alpha-particle Range in a CR-39 Detector
This section is devoted to comparing quantitatively the different models to determine the alpha-particle range in the CR-39 detector where the comparison is based on Eq. (4). The experimental and the theoretical data on the alpha-particle range in the CR-39 are fitted with Eq. (4); the fitting parameters b1 and b2 are summarized in Table 1. Concerning the maximum track etch rate approach, the fitting parameters deviate from the theoretical values by factors of 35.8% for b1 and 17.1% for b2 . Considering the over-etched track profile, the fitting parameters deviate from the theoretical values by a factor of 25.4% for b1 and 10.7% for b2 . The reasonable experimental measurements, on the other hand, are given by the track profile cone length, where the fitting parameters deviate by a factor of 0.66% for b1 and 2.9% for b2 . The over-etched technique is the preferred method to measure the range of alpha particles in the CR-39 detector. On the other hand, its drawback is that needs many of measurements after the range of the alpha particle. The track profile and the maximum track etch rate techniques are faster techniques, but following the track exactly to the end of
Fig. 5. (a) Variation of the track cone length as a function of removal thickness for 5 MeV alpha-particle in a CR-39 detector etched in 7.25 N NaOH at (70 ± 1) ◦ C. (b) The range of alpha particles as a function of alpha-particle energy in a CR-39 detector by using a track cone length L and a removal thickness h (track profile technique) [11].
its range’s is difficult because of the fast track etch rate in that region. In conclusion, the track profile cone length method gives reasonable results in comparison with the theoretical calculation.
III. CONCLUSION Taking into account the results obtained in the present paper, a new approach that is based on the measurement of the maximum track etch rate has been proposed for measuring the alpha-particle range experimentally in the CR-39 detector. This approach is found to be suitable for high-energy alpha particles, where the range for alpha particles having an energy of 5 MeV is less than the theoretical value by a factor of 3.5%, whereas for alpha particles with an energy of 2.5 MeV, the discrepancy was about 24.1%. As to other techniques, the over-etched technique is the preferred method to measure the range of the particles in the CR-39 detector. The track cone profile, on the other hand, also gives reasonable results in a short time; furthermore, the results are in a good agreement with the theoretical predictions made by using the SRIM software.
Comparison between Different Models for Alpha-particle Range · · · – M. El Ghazaly et al.
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