- Email: [email protected]
Determination of mass attenuation coefficients, effective atomic numbers and effective electron numbers for heavy-weight and normal-weight concretes
Applied Radiation and Isotopes 80 (2013) 73–77
Contents lists available at SciVerse ScienceDirect
Applied Radiation and Isotopes journal homepage: www.elsevier.com/locate/apradiso
Determination of mass attenuation coefficients, effective atomic numbers and effective electron numbers for heavy-weight and normal-weight concretes Adem Un a, Faruk Demir b,n a b
Arts and Sciences Faculty, Physics Department, Ağrı İbrahim Çeçen University, 04000 Agri, Turkey Nature Sciences, Architecture and Engineering Faculty, Metallurgy and Materials Engineering, Bursa Technical University, 16190 Bursa, Turkey
H I G H L I G H T S
The effective atomic number Zeff and the effective electron number Neff depend on the elemental compositions of the heavy-weight and normal-weight concretes. The iron, barium and calcium concentration of the concretes is more effective than the other elemental concentrations for the mass attenuation coefficients. The Zeff and Neff values of heavy-weight concretes are found to be higher than the Zeff and Neff values of the normal-weight concretes.
art ic l e i nf o
a b s t r a c t
Article history: Received 16 April 2013 Accepted 13 June 2013 Available online 21 June 2013
Total mass attenuation coefficients, effective atomic numbers and effective electron numbers values for different 16 heavy-weight and normal-weight concretes are calculated in the energy range from 1 keV to 100 GeV. The values of mass attenuation coefficients used in calculations are taken from the WinXCom computer program. The obtained results for heavy-weight concretes are compared with the results for normal-weight concretes. The results of heavy-weight concretes fairly differ from results for normalweight concretes. & 2013 Elsevier Ltd. All rights reserved.
Keywords: Attenuation coefficients Effective atomic numbers Effective electron numbers Heavy-weight concrete
1. Introduction Concrete is a widespread material for radiation shielding. Heavyweight concrete is defined as concrete with unit weight ranging from about 2900 and 6000 kg/m3 while unit weight of conventional concrete (i.e. normal-weight concrete) varied between 2200 and 2450 kg/m3 (Nawy, 1997; Erdoğan, 2003). As reported by Demir et al. (2011), a great number of experimental or theoretical researches have been conducted on concretes recently (Abdo, 2002; Abdo et al., 2002; Akkurt et al., 2005, 2006; Bashter et al., 1996a, 1996b, 1997; Bashter, 1997; Dealmeid et al., 1974; Demir et al., 2010, 2011; Kaplan, 1989, Kitis et al., 1993; Mollah et al., 1992; Yarar and Bayülken, 1994). Abdo (2002) and Abdo et al. (2002) theoretically calculated and determined attenuation by using XCom computer program for
n
Corresponding author. Tel.: +905306096581; fax:+902243141628. E-mail addresses: [email protected], [email protected] (F. Demir). 0969-8043/$ - see front matter & 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.apradiso.2013.06.015
photon radiations shielding. In these studies, the mass attenuation (m/ρ) was found to decrease with increasing the photon energy from 0.1 and to 100 MeV for barite concretes. According to these papers, the decrease of m/ρ with increasing photon energy is almost the same for all studied concretes, and this may be attributed to the fact that the Compton scattering and pair production are the predominant reactions. Akkurt et al. (2005, 2006) measured radiation transmission of heavyweight concretes including normal and barite aggregates for different γ-ray energies and calculated linear attenuation coefficients. These results were found to be about 0.138–0.157 cm−1 for barite concretes and about 0.102–0.107 cm−1 at 1.25 and 1.33 MeV, respectively. Bashter et al. (1996a, 1996b) studied heavyweight concretes including hematiteserpentite, ilmenite-limonite as control absorber in nuclear reactors γ-rays and neutron particles shielding. Bashter (1997) and Bashter et al. (1997) studied heavyweight concretes including hematite-serpentite, ilmenite-limonite, basalt-magnetite, ilmenite, basalt, steel and magnetite for only photon radiation shielding and calculated linear and mass attenuation coefficients from 10 keV to 1 GeV. Kaplan (1989) reported many studies on heavyweight
74
A. Un, F. Demir / Applied Radiation and Isotopes 80 (2013) 73–77
concretes in his book. Kitis et al. (1993) studied heavyweight concretes including barite aggregates for cyclotron shielding. Mass attenuation coefficients of the given materials have been calculated by the WinXCom program (Gerward et al., 2001, 2004). This program which is based on the DOS-based compilation XCom (Berger and Hubbell, 1987; Hubbell and Seltzer, 1995) provides total mass attenuation coefficient and total attenuation cross section data for about 100 elements as well as partial cross sections for incoherent and coherent scattering, photoelectric absorption and pair production at energies from 1 keV to 100 GeV. For composite materials such as concrete, composition of concrete is related to effective atomic number, Zeff. Because partial interaction cross-section depends on the composite materials of elements, a single atomic number being a characteristic of element will not describe the atomic number of composite material in the all energy range. This number is called to be Zeff that varies with energy and theoretical expressions to evaluate Zeff values for individual partial photon interaction processes have been suggested by Hine (1952). Some works on the determination of the Zeff values of composite materials various alloys (Kurudirek et al., 2010; Han and Demir, 2009; Un and Sahin, 2011, 2012) have been reported in the literature. In this work, it is aimed to calculate – the total mass attenuation coefficient, Zeff and Neff – for energies in the range from 1 keV to 100 GeV. The total mass attenuation coefficient, Zeff and Neff of 16 different heavy-weight and normal-weight concretes have been reported by using WinXCom and our excel program. The calculated values of heavy-weight and normal-weight concretes have also been compared. To our best knowledge, the investigation of the Zeff and Neff for normal-weight and heavy-weight concretes in the studied energies is not available in the literature.
2. Theory The mass attenuation coefficients of the different materials such as concretes can be determined by the transmission. It can be described by the following equation I ¼ exp −ðμ=ρÞx I0
ð1Þ
where I0 denotes the number of photons incoming in unit time with energy E, incoming intensity; I the number of outgoing in unit time photons with energy E, outgoing intensity after attenuation; μ/ρ (cm2/g) is the mass attenuation coefficient and x (g/cm2)
is the sample mass thickness (the mass per unit area). The total μ/ρ values for concretes composed of multi elements are the sum of the (μ/ρ)i values of each constituent element by the following mixture rule Hubbell and Seltzer (1995); μ=ρ ¼ ∑ W i ðμ=ρÞi
ð2Þ
i
where Wi is the weight fraction and (μ/ρ) is the mass attenuation coefficient of the ith element. The theoretical (μ/ρ) values for present samples were calculated by WinXCom program (Gerward et al., 2001, 2004). More detailed information about the calculation of Zeff and Neff for some concretes used in this work has been given in previous studies (Un and Sahin, 2011). In this work, the chemical compositions of concretes are taken from ICRU (1989) for ordinary (http://physics.nist.gov/PhysRef Data/XrayMassCoef/Table2.html) and barite; NIST listings, “Compositions of Materials used in STAR Databases” webpage for Portland (http://physics.nist.gov/cgi-bin/Star/compos.pl?matno=144) concretes; book of Reppond (1977) for Type 04, limestone–silicate, limestone, silicate and rocky flats; book of Hungerford (1960) for magnetite, ferro–phosphorus, iron–limonite, iron–portland, colemanite–baryte, boron–frits–baryte, and lumnite–portland–baryte–colemanite concretes.
3. Results and discussion The chemical content of the concretes are tabulated in Tables 1 and 2. It can be seen from Tables 1 and 2 that the chemical contents of the normal-weight concretes resemble to the chemical contents of the heavy-weight concretes. The total mass attenuation coefficients via energy of the heavy-weight and normal-weight concretes are presented in Fig. 1. Mass attenuation coefficients decrease with increasing the photon energy from 10−3 MeV to 1 MeV for these concretes. But the mass attenuation coefficients increase with increasing the photon energy from 1 MeV to 103 MeV. The mass attenuation coefficients are constant with increasing the photon energy from 103 MeV to 1 GeV. Although the concretes have a wide variety of elements, the main influence on the results in this work is the amount of iron and barium in the heavy-weights concretes. The higher concentration of iron in the chemical composition of the heavy-weight concrete H-IP in comparison to that of the other heavy-weight concretes and the higher concentration of calcium in the chemical composition of normal-weight concrete N-L in comparison to that of other
Table 1 Elemental composition of the normal-weight concretes. Concrete name Concrete short name Concrete density (g/cm3) Element
Silicatesc Limestone and silicatesc N-S N-LS 2.220 2.278 Weight Fraction
Ordinarya N-OC 2.300
Portlandb N-PC 2.300
Rocky flatsc N-RF 2.321
Type 04c N-T04 2.336
Limestonec N-L 2.337
H C O Na Mg Al Si K S Ca Fe
0.006488
0.022100 0.002484 0.574930 0.015208 0.001266 0.010045 0.304627 0.010045
0.010000 0.001000 0.529107 0.016000 0.002000 0.033872 0.337021 0.013000
0.007500 0.055502 0.492926
0.005567
0.005135 0.100250 0.485288
0.035137 0.015324
0.006262 0.177318 0.403413 0.000335 0.032954 0.011112 0.034804 0.001140
0.045057 0.014411
0.325043 0.007735
0.042951
0.044000 0.014000
a
0.518069 0.016577
0.007497 0.179258 0.229502 0.008191
0.498825 0.017159 0.002592 0.045840 0.315439 0.019177 0.082904 0.012306
0.001710 0.005138 0.011974
0.382590 0.008134
Composition of ordinary concrete taken from ICRU (1989) (http://physics.nist.gov/PhysRefData/XrayMassCoef/tab2.html). Composition of Portland concrete taken from NIST listings, “Compositions of Materials used in STAR Databases” webpage (http://physics.nist.gov/cgi-bin/Star/compos. pl?matno=144). c Composition of Type 04 concrete taken from Reppond (1977). b
A. Un, F. Demir / Applied Radiation and Isotopes 80 (2013) 73–77
75
Table 2 Elemental composition of the heavy-weight concretes. Concrete name Concrete short name Concrete density (g/cm3) H B C O F Na Mg Al Si P S K Ca Ti Mn Fe Zn Ba a d
H-B
Magnetited Iron– limonited H-M H-IL
Ferro– Phosphorusd H-FP
Iron– Portlandd H-IP
3.20
3.350
3.450
4.27
4.80
5.80
0.001100 0.010200
0.008500 0.009800
0.003585 0.003000
0.000500
0.005000
0.003300
0.369500
0.369800
0.348900
0.180000
0.104000
0.058200
0.001100 0.001400 0.017600 0.009600
0.001100 0.002000 0.013200 0.014900
0.001100 0.002200 0.006100 0.017600
0.002000 0.005000 0.014000
0.002000 0.004000 0.034000 0.197000
0.001300 0.003300 0.009100
0.090600
0.089700
0.096300
0.054800 0.012700 0.001200 0.030700
0.076700 0.000710 0.000400 0.018700
0.084600 0.000100 0.010300
0.001195 0.006000 0.004183 0.029000 0.010457 0.035000 0.001700 0.010700 0.107858 0.050194 0.000700 0.028000 0.000700 0.047505 0.505000
0.385900
0.380300
0.407000
0.463400
Boron Frits– Baryted H-BFB
Lumnite– Colemanite–Baryted H-LCB
Lumnite–Portland– Colemanite–Baryted H-LPCB
Colemanite– Baryted H-CB
3.10
3.10
3.10
0.005600 0.010400
0.010900 0.008800
0.338000 0.002300 0.012100 0.002300 0.006400 0.033100
Barytea
0.311622
0.091500 0.001000 0.062600 0.000200 0.021900 0.006600 0.401300
0.320000
0.001000
0.000500
0.061000
0.042000
0.039600
0.016000 0.721000
0.612000
0.003500 0.875000
Composition of ordinary concrete taken from ICRU (1989). (http://physics.nist.gov/PhysRefData/XrayMassCoef/tab2.html). Composition of ordinary concrete taken from Hungerford (1960).
103
µ (cm2/g)
102
100 10-1 10-2
10-1 E (MeV)
100 0.08
101 µ (cm2/g)
µ (cm2/g)
102
101
100
N-S N-LS N-OC N-PC N-RF N-T04 N-L H-BFB H-LCB H-LPCB H-CB H-B H-M H-IL H-FP H-IP
0.06 0.04 0.02
10-1
10-2 10-3
10-2
10-1
100
101 E (MeV)
E (MeV)
102
103
104
105
102
103
104
105
Fig. 1. Total mass attenuation coefficients versus photon energy for the heavy-weight and normal-weight concretes.
normal-weight concretes as seen in the Table 1 and 2 explain the greater value of μ/ρ for the heavy-weight concrete H-IP in comparison to values of μ/ρ for other heavy-weight concretes and the greater value of μ/ρ for normal-weight concrete N-L in comparison to values of μ/ρ for other normal-weight concretes as shown in Fig. 1. Heavy elements there is a fairly sharp maximum in the absorption cross section. The Zeff values of concretes were determined by using the values of μ/ρ. The variations of Zeff values versus photon energy for heavy-weight and normal-weight concretes are shown in Fig. 2. In Fig. 2, three energy regions E o0.01 MeV, 0.05 MeV oE o 10 MeV and E 4100 MeV can be clearly seen. In the low energy region, main interaction is photoelectric interaction which is proportional to Z4. Because of the Z4 dependency of photoelectric
interaction, maximum values of Zeff have been found in low-energy region for the concretes. Because of the Z4 dependence of photoelectric interaction and the photoelectric interaction near the K-edge of the elements with the high Z numbers, Zeff values of heavy-weight concretes are higher than those of the normal-weight concretes, as seen in Fig. 2. Zeff values of heavy-weight concrete H-B are higher than those of the other heavy-weight concretes as seen in Fig. 2. Zeff values of normal-weight concrete N-L are also higher than those of the other normal-weight concretes (Fig. 2). At the second energy region, Compton scattering is the main photon interaction. In this energy region, Zeff values are almost constant for the given samples. Because of the Compton scattering proportional to Z, minimum value of Zeff is found for the concretes in this energy region. Because of the Z dependence of Compton
76
A. Un, F. Demir / Applied Radiation and Isotopes 80 (2013) 73–77 N-S N-LS N-OC N-PC N-RF N-T04 N-L H-BFB H-LCB H-LPCB H-CB H-B H-M H-IL H-FP H-IP
54 48 42
Zeff
36 30 24 18 12 6 10-2
10-1
100
101 102 E (MeV)
103
104
105
Fig. 2. Effective atomic number versus photon energy for the heavy-weight and normal-weight concretes.
N-S N-LS N-OC N-PC N-RF N-T04 N-L H-BFB H-LCB H-LPCB H-CB H-B H-M H-IL H-FP H-IP
14 13 12 11 10 Neff
9 8 7 5 4 3 10-1
100
101 102 E (MeV)
103
104
The mass attenuation of high energy X or γ-ray photons is governed primarily by the atomic number and density of the concrete as a shielding material. Mass attenuation coefficients depend on pair production, photoelectric effect and Compton scattering. It is indicated that the effective atomic number Zeff and the effective electron number Neff are useful parameter for radiation shielding. The effective atomic number Zeff and the effective electron number Neff depend on the elemental compositions of the heavy-weight and normal-weight concretes. The iron, barium and calcium concentration of the concretes is more effective than the other elemental concentrations according to the results analyzed. The Zeff and Neff values of heavy-weight concretes are found to be higher than the Zeff and Neff values of the normal-weight concretes.
Acknowledgment The authors would like to thank Professor L. Gerward of the Department of Physics, Technical University of Denmark for providing with the WinXCom program. References
6
2 10-2
4. Conclusion
105
Fig. 3. Effective electron number versus photon energy for the heavy-weight and normal-weight concretes.
interaction, Zeff values of heavy-weight concretes are higher than the normal-weight concretes as seen in Fig. 2. The value of Zeff is also constant in the high energy region in which the pair production is the main interaction. Because of proportionality of the pair production with Z2, the value of Zeff for high energy region is smaller than the value obtained for photoelectric interaction and higher than the value obtained for Compton scattering. The variation of effective electron number Neff values versus photon energy for heavy-weight and normal-weight concretes soils is plotted in Fig. 3. In Fig. 3, three energy regions are clearly seen. The energy dependence of the effective electron number, Neff, is similar to the effective atomic numbers, Zeff. The effective electron numbers for the heavy-weight concretes are compared with the Neff value of the median value of normal-weight concretes in Fig. 3. As can be seen in Fig. 3, the Neff values of normalweight concretes are the same for the Neff values of heavy-weight concretes. However, the Neff values of heavy-weight concretes are higher than those of normal-weight concretes for the other region.
Abdo, A.E., 2002. Calculation of the cross-sections for fast neutrons and gammarays in concrete shields. Ann. Nucl. Energy 29, 1977–1988. Abdo, A.E., Kansouh, W.A., Megahid, R.M., 2002. Investigation of radiation attenuation properties for barite concrete. Jpn. J. Appl. Phys. 41, 7512–7517. Akkurt, I., Basyigit, C., Kilincarslan, S., Mavi, B., 2005. The shielding of γ-rays by concretes produced with barite. Prog. Nucl. Energy 46 (l), 1–11. Akkurt, I., Basyigit, C., Kilincarslan, S., Mavi, B., Akkurt, A., 2006. Radiation shielding of concretes containing different aggregates. Cem Concr. Compos. 28, 153–157. Bashter, I.I., 1997. Calculation of radiation attenuation coefficients for shielding concretes. Ann. Nucl. Energy 24 (17), 1389–1401. Bashter, I.I., Makarious, A.S., Abdo, A.E., 1996a. Investigation of hematite-serpentine andilmenite–limonite concretes for reactor radiation shielding. Ann. Nucl. Energy 23 (1), 65–71. Bashter, I.I., Abdo, A.E., Makarious, A.S., 1996b. A comparative study of the attenuation of reactor thermal neutrons in different types of concrete. Ann. Nucl. Energy 23 (14), 1189–1195. Bashter, I.I., Abdo, A.E., Abdel-Azim, M.S., 1997. Magnetite ores with steel or basalt for concrete radiation shielding. Jpn. J. Appl. Phys. Part 1 36 (6A), 3692–3696. Berger, M.J., Hubbell, J.H., 1987. XCOM: Photon Cross Sections on a Personal Computer. MD, National Bureau of Standards (former name of NIST), Gaithersburg p. 3597. Dealmeid, C.E., Almond, P.R., Rosansky, S.L., 1974. Transmission in concrete and scatter angular distribution of 25 MV X-rays for a betatron and a LINAC. Health. Phys. 27 (6), 652. Demir, F., Budak, G., Sahin, R., Karabulut, A., Oltulu, M., Serifoglu, K., Un, A., 2010. Radiation transmission of heavyweight- and normal-weight concretes containing colemanite for 6 MV and 18 MV X-rays using linear accelerator. Ann. Nucl. Energy 37, 339–344. Demir, F., Budak, G., Sahin, R., Karabulut, A., Oltulu, M., Un, A., 2011. Determination of radiation attenuation coefficients of heavyweight- and normal-weight concretes containing colemanite and barite for 0.663 MeV γ-rays. Ann. Nucl. Energy 38, 1274–1278. Erdoğan, T.Y., 2003. Concrete. METU PRESS, Ankara, Turkey. (in Turkish). Gerward, L., Guilbert, N., Jensen, K.B., Levring, H., 2001. X-ray absorption in matter. reengineering XCom. Radiat. Phys. Chem. 60, 23–24. Gerward, L., Guilbert, N., Jensen, K.B., Levring, H., 2004. WinXCom—a program for calculating X-ray attenuation coefficients. Radiat. Phys. Chem. 71, 653–654. Han, I., Demir, L., 2009. Mass attenuation coefficients, effective atomic and electron numbers of Ti and Ni alloys. Radiat. Meas. 44, 289–294. Hine, G.J., 1952. The effective atomic numbers of materials for various gamma ray interactions. Phys. Rev. 85, 725–737. Hubbell, J.H., Seltzer, S.M., 1995. Tables of X-Ray Mass Attenuation Coefficients and Mass Energy-Absorption Coefficients from 1 keV to 20 MeV for Elements Z¼ 1 to 92 and 48 Additional Substances of Dosimetric Interest. MD, National Institute of Standards and Technology, Gaithersburg. Hungerford, H.E., 1960. Reactor Handbook, Volume I, Materials. In: Tipton Jr., C.R. (Ed.), Interscience Publishers, a division of John Wiley and Sons, Inc. ICRU, 1989. Tissue Substitutes in Radiation Dosimetry and Measurement. Report 44 of the International Commission on Radiation Units and Measurements (Bethesda, MD). Kaplan, M.F., 1989. Concrete radiation shielding. Longman Scientific and Technology, Longman Group UK Limited Essex England.
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Kitis, G., Charalambous, S., Tuyn, J.W.N., 1993. Thermo luminescence response of heavyweight concrete used in the shielding of the CERN 600 MeV. Synchrocyclotron Radiat. Prot. Dos 47 (1/4), 589–593. Kurudirek, M., Buyukyildiz, M., Ozdemir, Y., 2010. Effective atomic number study of various alloys for total photon interaction in the energy region of 1 keV– 100 GeV. Nucl. Instrum. Methods A 613, 251–256. Mollah, A.S., Ahmad, G.U., Husain, S.R., 1992. Measurements of neutron shielding properties of heavyweight concretes using a Cf-252 source. Nucl. Eng. Des. 135 (3), 321–325. NIST listings, Compositions of Materials used in STAR Databeses, 〈http://physics. nist.gov/cgi-bin/Star/compos.pl?matno=144〉. Nawy, E.G., 1997. Concrete Construction Engineering Handbook. CRC Press, Florida, US, pp. 1–17.
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Reppond, E.B., 1977. Criticality Safety Analysis Resource Book, Part II: Atom Densities and Dimensional Parameters. Un, A., Sahin, Y., 2011. Determination of mass attenuation coefficients, effective atomic and electron numbers, mean free paths and kermas for PbO, barite and some boron ores. Nucl. Instrum. Methods B 269, 1506–1511. Un, A., Sahin, Y., 2012. Determination of mass attenuation coefficients, effective atomic and electron numbers, mean free paths and kermas for Earth and Martian soils. Nucl. Instrum. Methods B 288, 42–47. Yarar, Y., Bayülken, A., 1994. Investigation of neutron shielding efficiency and radioactivity of concrete shields containing colemanite. J. Nucl. Mater. 212, 1720.
Contents lists available at SciVerse ScienceDirect
Applied Radiation and Isotopes journal homepage: www.elsevier.com/locate/apradiso
Determination of mass attenuation coefficients, effective atomic numbers and effective electron numbers for heavy-weight and normal-weight concretes Adem Un a, Faruk Demir b,n a b
Arts and Sciences Faculty, Physics Department, Ağrı İbrahim Çeçen University, 04000 Agri, Turkey Nature Sciences, Architecture and Engineering Faculty, Metallurgy and Materials Engineering, Bursa Technical University, 16190 Bursa, Turkey
H I G H L I G H T S
The effective atomic number Zeff and the effective electron number Neff depend on the elemental compositions of the heavy-weight and normal-weight concretes. The iron, barium and calcium concentration of the concretes is more effective than the other elemental concentrations for the mass attenuation coefficients. The Zeff and Neff values of heavy-weight concretes are found to be higher than the Zeff and Neff values of the normal-weight concretes.
art ic l e i nf o
a b s t r a c t
Article history: Received 16 April 2013 Accepted 13 June 2013 Available online 21 June 2013
Total mass attenuation coefficients, effective atomic numbers and effective electron numbers values for different 16 heavy-weight and normal-weight concretes are calculated in the energy range from 1 keV to 100 GeV. The values of mass attenuation coefficients used in calculations are taken from the WinXCom computer program. The obtained results for heavy-weight concretes are compared with the results for normal-weight concretes. The results of heavy-weight concretes fairly differ from results for normalweight concretes. & 2013 Elsevier Ltd. All rights reserved.
Keywords: Attenuation coefficients Effective atomic numbers Effective electron numbers Heavy-weight concrete
1. Introduction Concrete is a widespread material for radiation shielding. Heavyweight concrete is defined as concrete with unit weight ranging from about 2900 and 6000 kg/m3 while unit weight of conventional concrete (i.e. normal-weight concrete) varied between 2200 and 2450 kg/m3 (Nawy, 1997; Erdoğan, 2003). As reported by Demir et al. (2011), a great number of experimental or theoretical researches have been conducted on concretes recently (Abdo, 2002; Abdo et al., 2002; Akkurt et al., 2005, 2006; Bashter et al., 1996a, 1996b, 1997; Bashter, 1997; Dealmeid et al., 1974; Demir et al., 2010, 2011; Kaplan, 1989, Kitis et al., 1993; Mollah et al., 1992; Yarar and Bayülken, 1994). Abdo (2002) and Abdo et al. (2002) theoretically calculated and determined attenuation by using XCom computer program for
n
Corresponding author. Tel.: +905306096581; fax:+902243141628. E-mail addresses: [email protected], [email protected] (F. Demir). 0969-8043/$ - see front matter & 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.apradiso.2013.06.015
photon radiations shielding. In these studies, the mass attenuation (m/ρ) was found to decrease with increasing the photon energy from 0.1 and to 100 MeV for barite concretes. According to these papers, the decrease of m/ρ with increasing photon energy is almost the same for all studied concretes, and this may be attributed to the fact that the Compton scattering and pair production are the predominant reactions. Akkurt et al. (2005, 2006) measured radiation transmission of heavyweight concretes including normal and barite aggregates for different γ-ray energies and calculated linear attenuation coefficients. These results were found to be about 0.138–0.157 cm−1 for barite concretes and about 0.102–0.107 cm−1 at 1.25 and 1.33 MeV, respectively. Bashter et al. (1996a, 1996b) studied heavyweight concretes including hematiteserpentite, ilmenite-limonite as control absorber in nuclear reactors γ-rays and neutron particles shielding. Bashter (1997) and Bashter et al. (1997) studied heavyweight concretes including hematite-serpentite, ilmenite-limonite, basalt-magnetite, ilmenite, basalt, steel and magnetite for only photon radiation shielding and calculated linear and mass attenuation coefficients from 10 keV to 1 GeV. Kaplan (1989) reported many studies on heavyweight
74
A. Un, F. Demir / Applied Radiation and Isotopes 80 (2013) 73–77
concretes in his book. Kitis et al. (1993) studied heavyweight concretes including barite aggregates for cyclotron shielding. Mass attenuation coefficients of the given materials have been calculated by the WinXCom program (Gerward et al., 2001, 2004). This program which is based on the DOS-based compilation XCom (Berger and Hubbell, 1987; Hubbell and Seltzer, 1995) provides total mass attenuation coefficient and total attenuation cross section data for about 100 elements as well as partial cross sections for incoherent and coherent scattering, photoelectric absorption and pair production at energies from 1 keV to 100 GeV. For composite materials such as concrete, composition of concrete is related to effective atomic number, Zeff. Because partial interaction cross-section depends on the composite materials of elements, a single atomic number being a characteristic of element will not describe the atomic number of composite material in the all energy range. This number is called to be Zeff that varies with energy and theoretical expressions to evaluate Zeff values for individual partial photon interaction processes have been suggested by Hine (1952). Some works on the determination of the Zeff values of composite materials various alloys (Kurudirek et al., 2010; Han and Demir, 2009; Un and Sahin, 2011, 2012) have been reported in the literature. In this work, it is aimed to calculate – the total mass attenuation coefficient, Zeff and Neff – for energies in the range from 1 keV to 100 GeV. The total mass attenuation coefficient, Zeff and Neff of 16 different heavy-weight and normal-weight concretes have been reported by using WinXCom and our excel program. The calculated values of heavy-weight and normal-weight concretes have also been compared. To our best knowledge, the investigation of the Zeff and Neff for normal-weight and heavy-weight concretes in the studied energies is not available in the literature.
2. Theory The mass attenuation coefficients of the different materials such as concretes can be determined by the transmission. It can be described by the following equation I ¼ exp −ðμ=ρÞx I0
ð1Þ
where I0 denotes the number of photons incoming in unit time with energy E, incoming intensity; I the number of outgoing in unit time photons with energy E, outgoing intensity after attenuation; μ/ρ (cm2/g) is the mass attenuation coefficient and x (g/cm2)
is the sample mass thickness (the mass per unit area). The total μ/ρ values for concretes composed of multi elements are the sum of the (μ/ρ)i values of each constituent element by the following mixture rule Hubbell and Seltzer (1995); μ=ρ ¼ ∑ W i ðμ=ρÞi
ð2Þ
i
where Wi is the weight fraction and (μ/ρ) is the mass attenuation coefficient of the ith element. The theoretical (μ/ρ) values for present samples were calculated by WinXCom program (Gerward et al., 2001, 2004). More detailed information about the calculation of Zeff and Neff for some concretes used in this work has been given in previous studies (Un and Sahin, 2011). In this work, the chemical compositions of concretes are taken from ICRU (1989) for ordinary (http://physics.nist.gov/PhysRef Data/XrayMassCoef/Table2.html) and barite; NIST listings, “Compositions of Materials used in STAR Databases” webpage for Portland (http://physics.nist.gov/cgi-bin/Star/compos.pl?matno=144) concretes; book of Reppond (1977) for Type 04, limestone–silicate, limestone, silicate and rocky flats; book of Hungerford (1960) for magnetite, ferro–phosphorus, iron–limonite, iron–portland, colemanite–baryte, boron–frits–baryte, and lumnite–portland–baryte–colemanite concretes.
3. Results and discussion The chemical content of the concretes are tabulated in Tables 1 and 2. It can be seen from Tables 1 and 2 that the chemical contents of the normal-weight concretes resemble to the chemical contents of the heavy-weight concretes. The total mass attenuation coefficients via energy of the heavy-weight and normal-weight concretes are presented in Fig. 1. Mass attenuation coefficients decrease with increasing the photon energy from 10−3 MeV to 1 MeV for these concretes. But the mass attenuation coefficients increase with increasing the photon energy from 1 MeV to 103 MeV. The mass attenuation coefficients are constant with increasing the photon energy from 103 MeV to 1 GeV. Although the concretes have a wide variety of elements, the main influence on the results in this work is the amount of iron and barium in the heavy-weights concretes. The higher concentration of iron in the chemical composition of the heavy-weight concrete H-IP in comparison to that of the other heavy-weight concretes and the higher concentration of calcium in the chemical composition of normal-weight concrete N-L in comparison to that of other
Table 1 Elemental composition of the normal-weight concretes. Concrete name Concrete short name Concrete density (g/cm3) Element
Silicatesc Limestone and silicatesc N-S N-LS 2.220 2.278 Weight Fraction
Ordinarya N-OC 2.300
Portlandb N-PC 2.300
Rocky flatsc N-RF 2.321
Type 04c N-T04 2.336
Limestonec N-L 2.337
H C O Na Mg Al Si K S Ca Fe
0.006488
0.022100 0.002484 0.574930 0.015208 0.001266 0.010045 0.304627 0.010045
0.010000 0.001000 0.529107 0.016000 0.002000 0.033872 0.337021 0.013000
0.007500 0.055502 0.492926
0.005567
0.005135 0.100250 0.485288
0.035137 0.015324
0.006262 0.177318 0.403413 0.000335 0.032954 0.011112 0.034804 0.001140
0.045057 0.014411
0.325043 0.007735
0.042951
0.044000 0.014000
a
0.518069 0.016577
0.007497 0.179258 0.229502 0.008191
0.498825 0.017159 0.002592 0.045840 0.315439 0.019177 0.082904 0.012306
0.001710 0.005138 0.011974
0.382590 0.008134
Composition of ordinary concrete taken from ICRU (1989) (http://physics.nist.gov/PhysRefData/XrayMassCoef/tab2.html). Composition of Portland concrete taken from NIST listings, “Compositions of Materials used in STAR Databases” webpage (http://physics.nist.gov/cgi-bin/Star/compos. pl?matno=144). c Composition of Type 04 concrete taken from Reppond (1977). b
A. Un, F. Demir / Applied Radiation and Isotopes 80 (2013) 73–77
75
Table 2 Elemental composition of the heavy-weight concretes. Concrete name Concrete short name Concrete density (g/cm3) H B C O F Na Mg Al Si P S K Ca Ti Mn Fe Zn Ba a d
H-B
Magnetited Iron– limonited H-M H-IL
Ferro– Phosphorusd H-FP
Iron– Portlandd H-IP
3.20
3.350
3.450
4.27
4.80
5.80
0.001100 0.010200
0.008500 0.009800
0.003585 0.003000
0.000500
0.005000
0.003300
0.369500
0.369800
0.348900
0.180000
0.104000
0.058200
0.001100 0.001400 0.017600 0.009600
0.001100 0.002000 0.013200 0.014900
0.001100 0.002200 0.006100 0.017600
0.002000 0.005000 0.014000
0.002000 0.004000 0.034000 0.197000
0.001300 0.003300 0.009100
0.090600
0.089700
0.096300
0.054800 0.012700 0.001200 0.030700
0.076700 0.000710 0.000400 0.018700
0.084600 0.000100 0.010300
0.001195 0.006000 0.004183 0.029000 0.010457 0.035000 0.001700 0.010700 0.107858 0.050194 0.000700 0.028000 0.000700 0.047505 0.505000
0.385900
0.380300
0.407000
0.463400
Boron Frits– Baryted H-BFB
Lumnite– Colemanite–Baryted H-LCB
Lumnite–Portland– Colemanite–Baryted H-LPCB
Colemanite– Baryted H-CB
3.10
3.10
3.10
0.005600 0.010400
0.010900 0.008800
0.338000 0.002300 0.012100 0.002300 0.006400 0.033100
Barytea
0.311622
0.091500 0.001000 0.062600 0.000200 0.021900 0.006600 0.401300
0.320000
0.001000
0.000500
0.061000
0.042000
0.039600
0.016000 0.721000
0.612000
0.003500 0.875000
Composition of ordinary concrete taken from ICRU (1989). (http://physics.nist.gov/PhysRefData/XrayMassCoef/tab2.html). Composition of ordinary concrete taken from Hungerford (1960).
103
µ (cm2/g)
102
100 10-1 10-2
10-1 E (MeV)
100 0.08
101 µ (cm2/g)
µ (cm2/g)
102
101
100
N-S N-LS N-OC N-PC N-RF N-T04 N-L H-BFB H-LCB H-LPCB H-CB H-B H-M H-IL H-FP H-IP
0.06 0.04 0.02
10-1
10-2 10-3
10-2
10-1
100
101 E (MeV)
E (MeV)
102
103
104
105
102
103
104
105
Fig. 1. Total mass attenuation coefficients versus photon energy for the heavy-weight and normal-weight concretes.
normal-weight concretes as seen in the Table 1 and 2 explain the greater value of μ/ρ for the heavy-weight concrete H-IP in comparison to values of μ/ρ for other heavy-weight concretes and the greater value of μ/ρ for normal-weight concrete N-L in comparison to values of μ/ρ for other normal-weight concretes as shown in Fig. 1. Heavy elements there is a fairly sharp maximum in the absorption cross section. The Zeff values of concretes were determined by using the values of μ/ρ. The variations of Zeff values versus photon energy for heavy-weight and normal-weight concretes are shown in Fig. 2. In Fig. 2, three energy regions E o0.01 MeV, 0.05 MeV oE o 10 MeV and E 4100 MeV can be clearly seen. In the low energy region, main interaction is photoelectric interaction which is proportional to Z4. Because of the Z4 dependency of photoelectric
interaction, maximum values of Zeff have been found in low-energy region for the concretes. Because of the Z4 dependence of photoelectric interaction and the photoelectric interaction near the K-edge of the elements with the high Z numbers, Zeff values of heavy-weight concretes are higher than those of the normal-weight concretes, as seen in Fig. 2. Zeff values of heavy-weight concrete H-B are higher than those of the other heavy-weight concretes as seen in Fig. 2. Zeff values of normal-weight concrete N-L are also higher than those of the other normal-weight concretes (Fig. 2). At the second energy region, Compton scattering is the main photon interaction. In this energy region, Zeff values are almost constant for the given samples. Because of the Compton scattering proportional to Z, minimum value of Zeff is found for the concretes in this energy region. Because of the Z dependence of Compton
76
A. Un, F. Demir / Applied Radiation and Isotopes 80 (2013) 73–77 N-S N-LS N-OC N-PC N-RF N-T04 N-L H-BFB H-LCB H-LPCB H-CB H-B H-M H-IL H-FP H-IP
54 48 42
Zeff
36 30 24 18 12 6 10-2
10-1
100
101 102 E (MeV)
103
104
105
Fig. 2. Effective atomic number versus photon energy for the heavy-weight and normal-weight concretes.
N-S N-LS N-OC N-PC N-RF N-T04 N-L H-BFB H-LCB H-LPCB H-CB H-B H-M H-IL H-FP H-IP
14 13 12 11 10 Neff
9 8 7 5 4 3 10-1
100
101 102 E (MeV)
103
104
The mass attenuation of high energy X or γ-ray photons is governed primarily by the atomic number and density of the concrete as a shielding material. Mass attenuation coefficients depend on pair production, photoelectric effect and Compton scattering. It is indicated that the effective atomic number Zeff and the effective electron number Neff are useful parameter for radiation shielding. The effective atomic number Zeff and the effective electron number Neff depend on the elemental compositions of the heavy-weight and normal-weight concretes. The iron, barium and calcium concentration of the concretes is more effective than the other elemental concentrations according to the results analyzed. The Zeff and Neff values of heavy-weight concretes are found to be higher than the Zeff and Neff values of the normal-weight concretes.
Acknowledgment The authors would like to thank Professor L. Gerward of the Department of Physics, Technical University of Denmark for providing with the WinXCom program. References
6
2 10-2
4. Conclusion
105
Fig. 3. Effective electron number versus photon energy for the heavy-weight and normal-weight concretes.
interaction, Zeff values of heavy-weight concretes are higher than the normal-weight concretes as seen in Fig. 2. The value of Zeff is also constant in the high energy region in which the pair production is the main interaction. Because of proportionality of the pair production with Z2, the value of Zeff for high energy region is smaller than the value obtained for photoelectric interaction and higher than the value obtained for Compton scattering. The variation of effective electron number Neff values versus photon energy for heavy-weight and normal-weight concretes soils is plotted in Fig. 3. In Fig. 3, three energy regions are clearly seen. The energy dependence of the effective electron number, Neff, is similar to the effective atomic numbers, Zeff. The effective electron numbers for the heavy-weight concretes are compared with the Neff value of the median value of normal-weight concretes in Fig. 3. As can be seen in Fig. 3, the Neff values of normalweight concretes are the same for the Neff values of heavy-weight concretes. However, the Neff values of heavy-weight concretes are higher than those of normal-weight concretes for the other region.
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