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Gamma-ray shielding properties of concrete including barite at different energies
Progress in Nuclear Energy 52 (2010) 620e623
Contents lists available at ScienceDirect
Progress in Nuclear Energy journal homepage: www.elsevier.com/locate/pnucene
Gamma-ray shielding properties of concrete including barite at different energies I. Akkurt a, *, H. Akyildirim a, B. Mavi a, S. Kilincarslan b, C. Basyigit b a b
Suleyman Demirel University, Fen-Edebiyat Fakultesi Fizik Bol, Isparta, Turkey Suleyman Demirel University, Teknik Egt. Fakultesi Yapı Egt. Bol, Isparta, Turkey
a b s t r a c t Keywords: Barite Concrete Gamma-ray shielding NaI(Tl)
Radiation shielding properties of barite and concrete produced with barite have been investigated. The results have been compared with the standard shielding material of lead. The linear attenuation coefficients have been calculated 1 keVe1 GeV and compared with the measurement performed using gamma spectrometer contains NaI(Tl) detector and MCA at 662, 1173 and 1332 keV. Ó 2010 Elsevier Ltd. All rights reserved.
1. Introduction From the beginning of using radioactive sources in a variety of fields with the development of technology, radiation dosimetry becomes an important subject in physics. Because radiation is dangerous for cell and it should be protected. This can be done by three main methods namely time, distance and shielding. Heavy elements such as lead or tungsten are ideal materials to be used in radiation shielding. On the other hand such heavy elements cannot be used in building construction. Barite (BaSO4) is an alternative material can be used directly or as an aggregate in the concrete for this purposes. The radiation shielding properties of a material is presented in terms of the linear attenuation coefficient m (cm1) and it is defined as the probability of a radiation interacting with a material per unit path length (Woods, 1982). As this subject is very important for health, many different studies on the linear attenuation coefficient of different materials in the literature have been performed. This includes biological materials (Chitralekha et al., 2005; Gowda et al., 2005; Icelli et al., 2004; Manohara and Hanagodimath, 2007; Midgley, 2005; Sandhu et al., 2002), elements (Murty et al., 2001; Murty and Devan, 2001, 2004), alloys (Angelone et al., 2001; El-Kateb et al., 2000; Icelli et al., 2005a,b; Murty et al., 2000), compound (Baltas et al., 2007; Bhandal and Singh, 1995; Icelli et al., 2003, 2004, 2005a,b; Icelli and Erzeneoglu, 2004; Khanna et al., 1996; Shivaramu and Ramprasath, 2000; Singh et al., 1996; Turgut et al., 2005) and some building materials (Akkurt et al., 2004, 2005a; Kharita et al., 2008; Bashter, 1997; El-Sayed, 2002; Singh et al., 2004).
* Corresponding author. Tel.: þ90 246 211 4033; fax: þ90 246 2371106. E-mail address: [email protected] (I. Akkurt). 0149-1970/$ e see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.pnucene.2010.04.006
In this paper, the linear attenuation coefficients of barite, concrete produced with barite have been measured and compared with the standard shielding material lead. The measured results have been compared with the calculation.
2. Experimental details The concrete (BC) has been produced using Portland Cement (PC) 42.5 type of cement from Goltas plant in Isparta and barite was collected from Sarkikaragac-Isparta region at south of the Sultandagları region where the pureness of barite ore is 90% BaSO4. The water-to-cement ratio was kept constant of 0.5. The linear attenuation coefficients of barite, barite concrete and lead have been measured using the gamma spectrometer which contains 300 300 NaI(Tl) detector (Akkurt, 2009). The signals from detector were amplified and recorded by a Multi-Channel-Analyser (MCA) which communicates with the PC by Genie2000(3.0) software. The schematic view of the experimental setup is shown in Fig. 1. The spectrometer has been calibrated using g-ray sources of 137 Cs and 60Co which emit 662, 1173 and 1332 keV energies respectively. The g-ray energy spectrum obtained from those sources and related energy-to-channel fit are displayed in Fig. 2 (upper and lower respectively) (Akkurt et al., in press). The linear attenuation coefficients (m cm1) of a material is obtained by:
1 N0 x N
m ¼ In
where N and N0 are the background subtracted number of counts recorded in detector with and without material between detector and source respectively and x is the material thickness. When
I. Akkurt et al. / Progress in Nuclear Energy 52 (2010) 620e623
621
Fig. 1. Schematic view of the experimental devices.
plotting each Ln(N0/N) versus different x a straight line can be obtained. This is shown in Fig. 3 where the value of the slope can give m of the material. The error on the measured m was determined from errors in number of counts reading by software and measuring thickness of concrete and it is given:
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2 DN0 2 DN 2 Dx 1 N Dm ¼ þ þLn 0 x N x N0 N
on a PC. It uses pre-existing data bases for coherent and incoherent scattering, photoelectric absorption, and pair production cross sections to calculate mass attenuation coefficients at photon energies of 1 keVe1 GeV (Berger and Hubbell, 1987). The mean free path (cm) of a material is different way of expressing radiation shielding properties of a material and is
The error on linear attenuation coefficients was found within 5% in this measurement. The measurement of the linear attenuation coefficients (m) were compared with the calculation. It has been evaluated via the mass attenuation coefficients (m/r) which were obtained using XCOM computer code which is a database, can run
Fig. 3. A linear fit to obtain the linear attenuation coefficients (data obtained for BC at 662 keV).
Fig. 2. The g-ray energy spectrum obtained from related fit channel versus energy (keV).
137
Cs and
60
Co sources (upper) and
Fig. 4. The linear attenuation coefficients of barite, BC and Pb (Akkurt et al. in press) as a function of photon energies.
622
I. Akkurt et al. / Progress in Nuclear Energy 52 (2010) 620e623
Fig. 5. Variation of mean free path with the photon energies for barite, BC and Pb.
defined as the average distance between two successive interactions of photons and it is given as:
mfp ¼
1
m
The half value layer (HVL) or the tenth value layer (TVL) of a material is used to describe the effectiveness of g-ray shielding
Fig. 7. The transmission rate of barite, BC and Pb as a function of thickness at different photon energies (The HVL and TVL have been indicated).
and the HVL is the thicknesses of an absorber that will reduce the g-radiation to half, and the TVL is the thicknesses of an absorber that will reduce the g-radiation to tenth of its intensity. Those can be calculated:
x1=2 ¼ In2 m ; x1=10 ¼ In10 m
3. Results and discussions
Fig. 6. Variation of the linear attenuation coefficients for material’s density.
The linear attenuation coefficients for barite have been measured at photon energy of 662, 1173 and 1332 keV and the results were compared with the barite concrete and lead (Akkurt et al., in press). The measured and calculated results are compared in Fig. 4 where it can be seen that there is a good
I. Akkurt et al. / Progress in Nuclear Energy 52 (2010) 620e623
agreement between experimental and calculated results. It is also clear that the linear attenuation coefficients are the highest for lead as expected. It can also be seen that the linear attenuation coefficients of barite are higher than barite concrete. The energy dependence of photon interaction with the material is also seen from this figure. This could be due to different photon absorption mechanism for different energy range. The photon absorption processes is mainly dominant as photoelectric effect at low energy, Compton scattering low and mid-energy range and pair production process after 1022 keV energy (Akkurt et al., 2005b). The mean free path (mfp) have been extracted from the measured and calculated results of linear attenuation coefficients of concrete, barite and lead at photon energies of 662, 1173 and 1332 keV. The results of mfp as a function of photon energy are displayed in Fig. 5 where it can be seen that the low energy photon can lost its energy in short distance while high energy photons needs long distance. It is also clear that photons lost its energy in short distance for leads medium than others for all energy. As the linear attenuation coefficients depend on the material density it is interesting to plot obtained linear attenuation coefficients as a function of materials density. This has been obtained and displayed in Fig. 6. It is clearly seen from this figure that the linear attenuation coefficients increased with the increasing density of the material. The transmission rate of the gamma ray can give an important message about the thickness of the material to stop gamma-ray in same energy. These obtained results were displayed for all materials in Fig. 7 where the comparison of the thickness for lead, barite and concrete has been done. It can be seen from this figure that the shortest distance required for lead and longest distance required for concrete. This can also be seen from the HVL and TVL of materials which are also indicated in same figure. It is concluded from this work that while the lead is an ideal shielding materials, barite itself and using it in concrete as an aggregate can be an alternative shielding materials to be used in building construction. Acknowledgement The authors wish to thank the TUBITAK (Turkiye Bilimsel ve Teknik Aras¸tırma Kurumu) for partly supporting this work with the project number of 106M127. References Akkurt, I., Basyigit, C., Kilincarslan, S., 2004. The photon attenuation coefficients of barite, Marble and Limra. Ann. Nucl. Energy 31 (5), 577e582. Akkurt, I., Basyigit, C., Kilincarslan, S., Mavi, B., 2005a. The shielding of g-rays by concrete produced with barite. Prog. Nucl. Energy 46 (1), 1e11. Akkurt, I., Mavi, B., Akkurt, A., Basyigit, C., Kilincarslan, S., Yalim, H.A., 2005b. Study on Z-dependence of partial and total mass attenuation coefficients. J. Quant. Spectrosc. Radiat. Transfer 94 (3e4), 379e385. Akkurt, I., 2009. Effective atomic and electron numbers of some steels at different energies. Ann. Nucl. Energy 36 (11e12), 1702e1705. Akkurt, I., Akyildirim, H., Mavi, B., Kilincarslan, S., Basyigit, C. Photon attenuation coefficients of concrete includes barite in different rate. Ann. Nucl. Energy, in press, doi:10.1016/j.anucene.2010.04.001. Angelone, M., Espostito, A., Chiti, M., Gentile, A., 2001. Measurements of mass attenuation coefficients for four mixtures using X-rays from 13 keV up to 40 keV. Radiat. Phys. Chem. 61, 547e548.
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Baltas, H., Celik, S., Cevik, U., Yanmaz, E., 2007. Measurement of mass attenuation coefficients and effective atomic numbers for MgB2 superconductor using X-ray energies. Radiat. Meas. 42, 55e60. Bashter, I.I., 1997. Calculation of radiation attenuation coefficients for shielding concretes. Ann. Nucl. Energy 24, 1389. Bhandal, G.S., Singh, K., 1995. Total and partial mass attenuation coefficients and effective atomic number studies in different solid state nuclear track detectors. Radiat. Phys. Chem. 47, 109e116. Berger, M.J., Hubbell, J.H., 1987. Photon Cross Sections on a Personal Computer. NBSIR 87-3597. National Institute of Standards, Gaithersburg. http://physics. nist.gov/PhysRefData/Xcom/Text/XCOM.html MD 20899 USA. Chitralekha, Kerur, B.R., Lagare, M.T., Nathuram, R., Sharma, D.N., 2005. Mass attenuation coefficients of saccharides for low-energy X-rays. Radiat. Phys. Chem. 72, 1e5. El-Kateb, A.H., Rizk, R.A.M., Abdul-Kader, A.M., 2000. Determination of atomic crosssections and effective atomic numbers for some alloys. Ann. Nucl. Energy 27, 1333e1343. El-Sayed, A., 2002. Calculation of the cross-sections for fast neutrons and gammarays in concrete shields. Ann. Nucl. Energy 29, 1977. Gowda, S., Krishnaveni, S., Gowda, R., 2005. Studies on effective atomic numbers and electron densities in amino acids and sugars in the energy range 30e1333 keV. Nucl. Instrum. Methods Phys. Res. B 239, 361e369. Icelli, O., Erzeneoglu, S., 2004. The mass attenuation coefficients in some vanadium and nickel compounds. J. Quant. Spectrosc. Radiat. Transf. 88, 519e524. Icelli, O., Erzeneoglu, S., Boncukcuoglu, R., 2003. Measurement of mass attenuation coefficients of some boron compounds and the trommel sieve waste in the energy range 15.746e40.930 keV. J. Quant. Spectrosc. Radiat. Transf. 78, 203e210. Icelli, O., Erzeneoglu, S., Boncukcuoglu, R., 2004. Experimental studies on measurements of mass attenuation coefficients of boric acid at different concentration. Ann. Nucl. Energy 31, 97e106. Icelli, O., Erzeneoglu, S., Gurbulak, B., 2005a. Mass attenuation coefficients for ntype InSe InSe:Gd InSe:Ho and InSe:Er single crystal. J. Quant. Spectrosc. Radiat. Transf. 90, 399e407. Icelli, O., Erzeneoglu, S., Karahan, I.H., Cankaya, G., 2005b. Effective atomic numbers for CoCuNi alloys using transmission experiments. J. Quant. Spectrosc. Radiat. Transf. 91, 485e491. Khanna, A., Bhatti, S.S., Singh, K.J., Thind, K.S., 1996. Gamma-ray attenuation coefficients in some heavy metal oxide borate glasses at 662 keV. Nucl. Instrum. Methods Phys. Res. B 114, 217e220. Kharita, M.H., Takeyeddin, M., Alnassar, M., Yousef, S., 2008. Development of special radiation shielding concretes using natural local materials and evaluation of their shielding characteristics. Prog. Nucl. Energy 50, 33e36. Manohara, S.R., Hanagodimath, S.M., 2007. Studies on effective atomic numbers and electron densities of essential amino acids in the energy range 1 keVe100 keV. Nucl. Instrum. Methods Phys. Res. B 258, 321e328. Midgley, S.M., 2005. Measurements of the X-ray linear attenuation coefficient for low atomic number materials at energies 32e66 and 140 keV. Radiat. Phys. Chem. 72, 525e535. Murty, V.R.K., Devan, K.R.S., 2001. On the suitability of Peltier cooled Si-PIN detectors in transmission experiments. Radiat. Phys. Chem. 61, 495e496. Murty, V.R.K., Devan, K.R.S., 2004. Photon interaction cross sections in the low energy region in Mg and V. Radiat. Phys. Chem. 71, 671e672. Murty, V.R.K., Winkoun, D.P., Devan, K.R.S., 2000. Effective atomic numbers for W/ Cu alloy using transmission experiments. Appl. Radiat. Isot. 53, 945e948. Murty, V.R.K., Winkoun, D.P., Devan, K.R.S., 2001. Total photoelectric cross sections close to absorption edges. Radiat. Phys. Chem. 51, 361e362. Sandhu, G.K., Singh, K., Lark, B.S., Gerward, L., 2002. Molar extinction coefficients of some fatty acids. Radiat. Phys. Chem. 65, 211e215. Shivaramu, Ramprasath, V., 2000. Effective atomic numbers for photon energy absorption and energy dependence of some thermoluminescent dosimetric compound. Nucl. Instrum. Methods Phys. Res. B 168, 294e304. Singh, Charanjeet, Singh, Tejbir, Kumar, Ashok, Mudahar, Gurmel S., 2004. Energy and chemical composition dependence of mass attenuation coefficients of building materials. Ann. Nucl. Energy 31, 1199e1205. Singh, K., Kaur, R., Vandana, V., Kumar, V., 1996. Study of effective atomic numbers and mass attenuations coefficients in some compound. Radiat. Phys. Chem. 47, 535e541. Turgut, U., Buyukkasap, E., Simsek, O., Ertugrul, M., 2005. X-ray attenuation coefficients of Fe compounds in the K-edge region at different energies and the validity of the mixture rule. J. Quant. Spectrosc. Radiat. Transf. 92, 143e151. Woods, J., 1982. Computational Methods in Reactor Shielding. Pergamon, New York.
Contents lists available at ScienceDirect
Progress in Nuclear Energy journal homepage: www.elsevier.com/locate/pnucene
Gamma-ray shielding properties of concrete including barite at different energies I. Akkurt a, *, H. Akyildirim a, B. Mavi a, S. Kilincarslan b, C. Basyigit b a b
Suleyman Demirel University, Fen-Edebiyat Fakultesi Fizik Bol, Isparta, Turkey Suleyman Demirel University, Teknik Egt. Fakultesi Yapı Egt. Bol, Isparta, Turkey
a b s t r a c t Keywords: Barite Concrete Gamma-ray shielding NaI(Tl)
Radiation shielding properties of barite and concrete produced with barite have been investigated. The results have been compared with the standard shielding material of lead. The linear attenuation coefficients have been calculated 1 keVe1 GeV and compared with the measurement performed using gamma spectrometer contains NaI(Tl) detector and MCA at 662, 1173 and 1332 keV. Ó 2010 Elsevier Ltd. All rights reserved.
1. Introduction From the beginning of using radioactive sources in a variety of fields with the development of technology, radiation dosimetry becomes an important subject in physics. Because radiation is dangerous for cell and it should be protected. This can be done by three main methods namely time, distance and shielding. Heavy elements such as lead or tungsten are ideal materials to be used in radiation shielding. On the other hand such heavy elements cannot be used in building construction. Barite (BaSO4) is an alternative material can be used directly or as an aggregate in the concrete for this purposes. The radiation shielding properties of a material is presented in terms of the linear attenuation coefficient m (cm1) and it is defined as the probability of a radiation interacting with a material per unit path length (Woods, 1982). As this subject is very important for health, many different studies on the linear attenuation coefficient of different materials in the literature have been performed. This includes biological materials (Chitralekha et al., 2005; Gowda et al., 2005; Icelli et al., 2004; Manohara and Hanagodimath, 2007; Midgley, 2005; Sandhu et al., 2002), elements (Murty et al., 2001; Murty and Devan, 2001, 2004), alloys (Angelone et al., 2001; El-Kateb et al., 2000; Icelli et al., 2005a,b; Murty et al., 2000), compound (Baltas et al., 2007; Bhandal and Singh, 1995; Icelli et al., 2003, 2004, 2005a,b; Icelli and Erzeneoglu, 2004; Khanna et al., 1996; Shivaramu and Ramprasath, 2000; Singh et al., 1996; Turgut et al., 2005) and some building materials (Akkurt et al., 2004, 2005a; Kharita et al., 2008; Bashter, 1997; El-Sayed, 2002; Singh et al., 2004).
* Corresponding author. Tel.: þ90 246 211 4033; fax: þ90 246 2371106. E-mail address: [email protected] (I. Akkurt). 0149-1970/$ e see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.pnucene.2010.04.006
In this paper, the linear attenuation coefficients of barite, concrete produced with barite have been measured and compared with the standard shielding material lead. The measured results have been compared with the calculation.
2. Experimental details The concrete (BC) has been produced using Portland Cement (PC) 42.5 type of cement from Goltas plant in Isparta and barite was collected from Sarkikaragac-Isparta region at south of the Sultandagları region where the pureness of barite ore is 90% BaSO4. The water-to-cement ratio was kept constant of 0.5. The linear attenuation coefficients of barite, barite concrete and lead have been measured using the gamma spectrometer which contains 300 300 NaI(Tl) detector (Akkurt, 2009). The signals from detector were amplified and recorded by a Multi-Channel-Analyser (MCA) which communicates with the PC by Genie2000(3.0) software. The schematic view of the experimental setup is shown in Fig. 1. The spectrometer has been calibrated using g-ray sources of 137 Cs and 60Co which emit 662, 1173 and 1332 keV energies respectively. The g-ray energy spectrum obtained from those sources and related energy-to-channel fit are displayed in Fig. 2 (upper and lower respectively) (Akkurt et al., in press). The linear attenuation coefficients (m cm1) of a material is obtained by:
1 N0 x N
m ¼ In
where N and N0 are the background subtracted number of counts recorded in detector with and without material between detector and source respectively and x is the material thickness. When
I. Akkurt et al. / Progress in Nuclear Energy 52 (2010) 620e623
621
Fig. 1. Schematic view of the experimental devices.
plotting each Ln(N0/N) versus different x a straight line can be obtained. This is shown in Fig. 3 where the value of the slope can give m of the material. The error on the measured m was determined from errors in number of counts reading by software and measuring thickness of concrete and it is given:
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2 DN0 2 DN 2 Dx 1 N Dm ¼ þ þLn 0 x N x N0 N
on a PC. It uses pre-existing data bases for coherent and incoherent scattering, photoelectric absorption, and pair production cross sections to calculate mass attenuation coefficients at photon energies of 1 keVe1 GeV (Berger and Hubbell, 1987). The mean free path (cm) of a material is different way of expressing radiation shielding properties of a material and is
The error on linear attenuation coefficients was found within 5% in this measurement. The measurement of the linear attenuation coefficients (m) were compared with the calculation. It has been evaluated via the mass attenuation coefficients (m/r) which were obtained using XCOM computer code which is a database, can run
Fig. 3. A linear fit to obtain the linear attenuation coefficients (data obtained for BC at 662 keV).
Fig. 2. The g-ray energy spectrum obtained from related fit channel versus energy (keV).
137
Cs and
60
Co sources (upper) and
Fig. 4. The linear attenuation coefficients of barite, BC and Pb (Akkurt et al. in press) as a function of photon energies.
622
I. Akkurt et al. / Progress in Nuclear Energy 52 (2010) 620e623
Fig. 5. Variation of mean free path with the photon energies for barite, BC and Pb.
defined as the average distance between two successive interactions of photons and it is given as:
mfp ¼
1
m
The half value layer (HVL) or the tenth value layer (TVL) of a material is used to describe the effectiveness of g-ray shielding
Fig. 7. The transmission rate of barite, BC and Pb as a function of thickness at different photon energies (The HVL and TVL have been indicated).
and the HVL is the thicknesses of an absorber that will reduce the g-radiation to half, and the TVL is the thicknesses of an absorber that will reduce the g-radiation to tenth of its intensity. Those can be calculated:
x1=2 ¼ In2 m ; x1=10 ¼ In10 m
3. Results and discussions
Fig. 6. Variation of the linear attenuation coefficients for material’s density.
The linear attenuation coefficients for barite have been measured at photon energy of 662, 1173 and 1332 keV and the results were compared with the barite concrete and lead (Akkurt et al., in press). The measured and calculated results are compared in Fig. 4 where it can be seen that there is a good
I. Akkurt et al. / Progress in Nuclear Energy 52 (2010) 620e623
agreement between experimental and calculated results. It is also clear that the linear attenuation coefficients are the highest for lead as expected. It can also be seen that the linear attenuation coefficients of barite are higher than barite concrete. The energy dependence of photon interaction with the material is also seen from this figure. This could be due to different photon absorption mechanism for different energy range. The photon absorption processes is mainly dominant as photoelectric effect at low energy, Compton scattering low and mid-energy range and pair production process after 1022 keV energy (Akkurt et al., 2005b). The mean free path (mfp) have been extracted from the measured and calculated results of linear attenuation coefficients of concrete, barite and lead at photon energies of 662, 1173 and 1332 keV. The results of mfp as a function of photon energy are displayed in Fig. 5 where it can be seen that the low energy photon can lost its energy in short distance while high energy photons needs long distance. It is also clear that photons lost its energy in short distance for leads medium than others for all energy. As the linear attenuation coefficients depend on the material density it is interesting to plot obtained linear attenuation coefficients as a function of materials density. This has been obtained and displayed in Fig. 6. It is clearly seen from this figure that the linear attenuation coefficients increased with the increasing density of the material. The transmission rate of the gamma ray can give an important message about the thickness of the material to stop gamma-ray in same energy. These obtained results were displayed for all materials in Fig. 7 where the comparison of the thickness for lead, barite and concrete has been done. It can be seen from this figure that the shortest distance required for lead and longest distance required for concrete. This can also be seen from the HVL and TVL of materials which are also indicated in same figure. It is concluded from this work that while the lead is an ideal shielding materials, barite itself and using it in concrete as an aggregate can be an alternative shielding materials to be used in building construction. Acknowledgement The authors wish to thank the TUBITAK (Turkiye Bilimsel ve Teknik Aras¸tırma Kurumu) for partly supporting this work with the project number of 106M127. References Akkurt, I., Basyigit, C., Kilincarslan, S., 2004. The photon attenuation coefficients of barite, Marble and Limra. Ann. Nucl. Energy 31 (5), 577e582. Akkurt, I., Basyigit, C., Kilincarslan, S., Mavi, B., 2005a. The shielding of g-rays by concrete produced with barite. Prog. Nucl. Energy 46 (1), 1e11. Akkurt, I., Mavi, B., Akkurt, A., Basyigit, C., Kilincarslan, S., Yalim, H.A., 2005b. Study on Z-dependence of partial and total mass attenuation coefficients. J. Quant. Spectrosc. Radiat. Transfer 94 (3e4), 379e385. Akkurt, I., 2009. Effective atomic and electron numbers of some steels at different energies. Ann. Nucl. Energy 36 (11e12), 1702e1705. Akkurt, I., Akyildirim, H., Mavi, B., Kilincarslan, S., Basyigit, C. Photon attenuation coefficients of concrete includes barite in different rate. Ann. Nucl. Energy, in press, doi:10.1016/j.anucene.2010.04.001. Angelone, M., Espostito, A., Chiti, M., Gentile, A., 2001. Measurements of mass attenuation coefficients for four mixtures using X-rays from 13 keV up to 40 keV. Radiat. Phys. Chem. 61, 547e548.
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