J Radioanal Nucl Chem (2013) 298:1303–1307 DOI 10.1007/s10967-013-2494-y
Investigation of mass attenuation coefficients of water, concrete and bakelite at different energies using the FLUKA Monte Carlo code Nilgun Demir • Urkiye Akar Tarim • Maria-Ana Popovici • Zehra Nur Demirci Orhan Gurler • Iskender Akkurt
•
Received: 13 February 2013 / Published online: 4 April 2013 Ó Akade´miai Kiado´, Budapest, Hungary 2013
Abstract The mass attenuation coefficients of water, bakelite and concrete sample defined in the simulation package were obtained using the FLUKA Monte Carlo code at 59.5, 80.9, 140.5, 356.5, 661.6, 1173.2 and 1332.5 keV photon energies. The results for the mass attenuation coefficients obtained by simulation have been compared with experimental and the theoretical ones and good agreement has been observed. The results indicate that this process can be followed to determine the data on the attenuation of gamma-rays with the several energies in other materials. Also, the deposited energy by 661.6 keV photons at several thicknesses of each media was determined as being an important data for radiation shielding studies. Keywords Water Bakelite Concrete FLUKA Energy deposition Mass attenuation coefficient
Introduction The mass attenuation coefficient (l/q) is one of the most important quantities characterizing the penetration and
N. Demir (&) U. A. Tarim O. Gurler Physics Department, Faculty of Arts and Sciences, Uludag University, Gorukle Campus, 16059 Bursa, Turkey e-mail:
[email protected] M.-A. Popovici Physics Department, Politehnica University of Bucharest, Bucharest, Romania Z. N. Demirci I. Akkurt Suleyman Demirel University, Fen-Edebiyat Fakultesi Fizik Bol., Isparta, Turkey
diffusion of gamma-rays in any target material [1, 2]. Knowledge of mass attenuation coefficients of gamma-rays in several materials is essential requirement for nuclear diagnostics, radiation protection, nuclear medicine, radiation dosimetry, radiation biophysics and etc. [3]. In recent years many researchers have been studied on determination of mass attenuation coefficients theoretically and experimentally for different materials. Such as, some experiments have been performed by Demir and Keles¸ [4] for mass attenuation coefficients of concrete including boron waste. Mass attenuation coefficients of the 12 concrete samples with and without supplementary cementitious materials have been measured by Yılmaz et al. [5]. Measurements of the mass attenuation coefficients of water [6–8] and bakelite [9] have been also carried out for different photon energies by Ramachandran et al. [6], Akar et al. [7], I˙shakog˘lu and Baytas¸ [8] and Sidhu et al. [9]. Similarly reports on the theoretical computation of the mass attenuation coefficients of ordinary, hematite-serpentine, ilmenite-limonite, basalt-magnetite, ilmenite, steel-scrap and steel-magnetite concretes by Bashter [10], concretes containing marble by Akkurt and El-Khayatt [11] are also available in the literature. Additionally, some recent works also performed for calculation of the mass attenuation coefficients by Gurler and Akar Tarim [12] and Stankovic et al. [13] using the Monte Carlo code written by themselves and the photon transport Monte Carlo software, respectively. In this work, we have tried to estimate the mass attenuation coefficients of water, bakelite and concrete samples for the photons with the energies of 59.5, 80.9, 140.5, 356.5, 661.6, 1173.2 and 1332.5 keV by using the FLUKA Monte Carlo code due to its event-by-event tracking feature. FLUKA is a Monte Carlo simulation package for a variety of models of particle transport and interaction with
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Table 1 Elemental composition by relative weight of the investigated concrete sample; density of the concrete is 2.3 g cm-3 [14] Element
H
C
O
Na
Mg
Al
Si
K
Ca
Fe
Weight (%)
1.0
0.1
52.9107
1.6
0.2
3.3872
33.7021
1.3
4.4
1.4
Materials and method In this study, we carried out an investigation on availability of FLUKA Monte Carlo code for calculation of gamma-ray attenuation coefficients of several materials and for determination of the deposited energy into them. Water (H2O), bakelite (C9H9O) with the density of 1.45 g cm-3 and concrete pre-defined in FLUKA [14] as a compound were used as the attenuator. The density and the chemical composition of the investigated concrete sample are given in Table 1. Calculation of the mass attenuation coefficients were performed by the implementation of the simulation model for the seven incident photon energies 59.5, 80.9, 140.5, 356.5, 661.6, 1173.2 and 1332.5 keV. The mass attenuation coefficients (l/q) were calculated by the following equation that is based on the Lambert–Beer law: 1 I0 l=q ¼ ln qt I where q is the density of medium, I0 and I are incident and transmitted intensities and t is thickness of the sample. For
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14 12 10
ln(I 0 /I)
matter. FLUKA can simulate the interaction and propagation in matter of more than 60 different particles—such as heavy-ions, electrons, neutrons, photons, neutrinos, and muons—in many types of research fields: shielding design, detector response studies, cosmic ray studies, medical physics, and dosimetry calculations [14, 15]. Use of this method requires knowledge of the chemical or elemental composition and density of the material and its physical characteristics as input information for performing these calculations [16]. In FLUKA, for most applications, no programming is required from the user. However, a number of user interface routines are available for users with special requirements. Another feature of FLUKA, probably not found in any other Monte Carlo program, is its double capability to be used in a biased mode as well as fully analogue code [14]. The purposes of the present work are to determine the mass attenuation coefficients of investigated materials by the FLUKA Monte Carlo code and to evaluate the code’s availability on this subject by comparison of simulation results with the theoretical values and the available experimental ones. In addition to the results for attenuation coefficients, distributions of deposited energy into investigated materials are presented as contour in this study.
8 6 4 2 0 0
20
40
60
80
Thickness (cm)
Fig. 1 Plotting of ln(I0/I) values versus attenuator medium thickness (for water at energy of 80.9 keV)
the simulation of transmission value, I/I0, an input file has been prepared. In this input file, beam properties, irradiation geometry, material definition, physical settings, and score options have been represented in a sequential order. A simple cylindrical geometry with the axis along the z-direction was described in the code. A beam of 1 9 105 gamma-rays were directed toward the materials in the z-direction and attenuated in cylindrical samples with a diameter of 10 cm and several centimeters in thickness. The code was run for 10 cycles. USRBDX score card has been used to obtain the transmission values, I/I0, for each of material thickness. Photon transmission results of simulations have been read from output files. By plotting ln(I0/I) versus t as shown in Fig. 1, the slope is calculated and this value is used in equation for Lambert–Beer law. USRBIN score card has also been included to input file and the deposited energy by the 661.6 keV photons into each material has been obtained as contour by using FLAIR which is a data analysis interface compatible with FLUKA. The volume decided on for all investigated samples was divided into 50 bins and binnings was defined with the shape of R-U-Z (3-D cylindrical) in the card. Binning data (deposited energy) in each bin was obtained and expressed in GeV per cm3.
Results and discussion The mass attenuation coefficients of water, bakelite and concrete sample defined in FLUKA code were determined for the seven incident photon energies in the range of 59.5–1332.5 keV. A simple geometry was used to estimate
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Table 2 Calculated and measured mass attenuation coefficients for the investigated materials with given densities Energy (keV)
Mass attenuation coefficients l/q (cm2 g) Water (q = 1.0 g cm-3) Calculated
XCOM
Experimental
Bakelite (q = 1.45 g cm-3)
Concrete (q = 2.3 g cm-3)
Calculated
Calculated
XCOM
Experimental
XCOM
Experimental
59.5
0.203
0.207
0.206 [6]
0.180
0.188
[0.190 [1]
0.246
0.284
–
80.9
0.179
0.183
–
0.161
0.171
–
0.187
0.204
–
140.5 356.5
0.144 0.110
0.154 0.112
0.125 [7] –
0.137 0.104
0.147 0.107
– –
0.132 0.096
0.149 0.102
– –
661.6
0.082
0.086
0.077 [7]
0.078
0.083
0.081 [9]
0.074
0.073
–
1173.2
0.064
0.066
–
0.060
0.063
–
0.056
0.059
–
1332.5
0.058
0.061
0.066 [8]
0.054
0.059
–
0.051
0.056
–
Mass attenuation coefficient (cm 2/g)
the experimental ones. Discrepancy in the values of the calculated and the experimental mass attenuation coefficients could be due to deviations from narrow beam geometry in the source-detector arrangements as expressed by Medhat [18] and Gurler and Akar Tarim [12]. Figure 2 shows the representative plot of the Monte Carlo generated data for mass attenuation coefficients as a function of incident photon energy. It is clear in this figure, the values of mass attenuation coefficient decrease sharply in the low energy region, then becomes constant in the medium energy region. This trend was observed for each material and this signifies that if we increase the energy of the incident photons we would obtain smaller attenuation, and therefore more penetration of the photons in the attenuator.
0,25 0,2 0,15 0,1 0,05
(a) 0 0
500
1000
1500
0,2 0,15 0,1 0,05
(b)
0 0
500
Energy (keV) Mass attenuation coefficient (cm 2/g)
Fig. 2 Calculated mass attenuation coefficients of water (a), bakelite (b) and concrete (c) versus photon energies
Mass attenuation coefficient (cm 2/g)
the transmission of photons through the targets with the different thicknesses. It was considered that the monoenergetic gamma-rays incident on circular surface area of the cylindrical attenuator material with the diameter of 10 cm. The results of our presented calculations were compared with the theoretical values calculated using the photon cross section database and with the experimental results obtained by other researchers. Table 2 shows the calculated mass attenuation coefficients versus photon energy together with theoretical values, calculated by the XCOM database [17] and previously reported experimental values [1, 6–9]. It was found that the mass attenuation coefficients of each material for the different photon energies were very close to the XCOM calculated mass attenuation coefficients and
1000
1500
Energy (keV)
0,3 0,25 0,2 0,15 0,1 0,05
(c)
0 0
500
1000
1500
Energy (keV)
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Fig. 3 Distribution of deposited energy into 24 cm thick water by 661.6 keV photons
Fig. 4 Distribution of deposited energy into 24 cm thick bakelite by 661.6 keV photons
Fig. 5 Distribution of deposited energy into 24 cm thick concrete by 661.6 keV photons
We have also obtained the deposited energy into each material at several thicknesses. Figures 3, 4 and 5 show the distributions of deposited energy by the incident photons with the energy of 661.6 keV into 24 cm thick water, bakelite and concrete, respectively. One can say that the energy deposited into the concrete medium which is one of the investigated materials with the same volumes (bodies) is greater than the energy deposited into other media as an expected result.
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Conclusions The Monte Carlo calculated mass attenuation coefficients of water, bakelite and concrete in the 59.5–1332.5 keV photon energy range was found to be very close to the calculated XCOM values. These results indicate to the conclusion that this application is suitable to be used as an alternative way to experiment for this kind of studies and it
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can be used for various attenuator and energies. On the other hand, obtained energy distributions provide useful information for the studies of radiation dosimetry and radiation shielding.
1307
9.
10.
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