Calculation of photon attenuation coefficient and dose rate in concrete with the addition of SiO₂ and MnFe₂O₄ nanoparticles using MCNPX code and comparison with experimental results

Calculation of photon attenuation coefficient and dose rate in concrete with the addition of SiO 2 and MnFe 2 O 4 nanoparticles using MCNPX code and comparison with experimental results 1 corresp first-author Corresponding Author: E-mail:m_hassanzadeh1354@yahoo.com, Corresponding Author: E-mail:m_hassanzadeh1354@yahoo.com, m_hassanzadeh1354@yahoo.com 2 Nuclear Science and Technology Research Institute (NSTRI), Reactor & Nuclear Safety School, Tehran-Iran Nuclear Science and Technology Research Institute (NSTRI), Reactor & Nuclear Safety School, Tehran-Iran Nuclear Science and Technology Research Institute (NSTRI), Plasma and Nuclear Fusion Research School, Tehran-Iran Nuclear Science and Technology Research Institute (NSTRI), Plasma and Nuclear Fusion Research School, Tehran-Iran One of the most important safety features of nuclear facilities is the shielding material used to protect the operating personnel from radiation exposure. The most common materials used in radiation shielding are concretes. In this study, a Monte Carlo N-Particle eXtended (MCNPX) code is used to calculate the gamma-ray attenuation coefficients and dose rates for a new concrete material composed of MnFe 2 O 4 nanoparticles, which is then compared with the theoretical and experimental results obtained for a SiO 2 nanoparticle concrete material. According to the results, the average relative differences between the simulations and the theoretical and experimental results for the linear attenuation coefficient ( μ ) in the SiO 2 nanoparticle materials are 6.4% and 5.5%, respectively. By increasing the SiO 2 content up to 1.5% and the temperature of MnFe 2 O 4 up to 673 K, μ is increased for all energies. In addition, the photon dose rate decreases up to 9.2% and 3.7% for MnFe 2 O 4 and SiO 2 for gamma-ray energies of 0.511 and 1.274 MeV, respectively. Therefore, it was concluded that the addition of SiO 2 and MnFe 2 O 4 nanoparticles to concrete improves its nuclear properties and could lead to it being more useful in radiation shielding. Shielding Radiation Concrete Attenuation coefficient Photon dose MCNPX code SiO 2 and MnFe 2 O 4 nanoparticles 1. Introduction 1 Concrete has been used in nuclear facilities for its physical strength and radiation shielding capability. It contains a mixture of low and high atomic number elements, and is therefore effective in shielding photons and neutrons. Lead is found to be another suitable option for shielding against X-rays and gamma-rays [ 1 1 - 3 3 1-3 ]. Nowadays, the use of nanoparticles in materials has attracted attention from researchers owing to a variety of features that have led to its use in a large number of applications [ 3 3 - 5 5 3-5 ]. Nanoparticles are used as a mixture to improve the mechanical and structural strengths of concrete. In general, the physical properties of nanomaterial are different from those of their bulk counterparts, and frequently display new and surprising phenomena, including the hardening of concrete [ 6 6 - 8 8 6-8 ]. Tao studied the microstructure and water permeability of concrete incorporated with SiO 2 nanoparticles, herein referred to as Nano SiO 2 . He stated that the presence of nanoparticles can improve the resistance to water penetration in concrete specimens [ 9 9 ]. Moreover, an investigation using environmental scanning electron microscopy (ESEM) demonstrated that the concrete microstructure including Nano SiO 2 led to a denser concrete microstructure and improved pore structure [ 7 7 , 10 10 ]. In this study, for the first time, MnFe 2 O 4 nanoparticles [ 11 11 - 12 12 11-12 ] are added to concrete to improve its nuclear properties. The linear and mass attenuation coefficients are calculated using point isotropic gamma-ray sources based on the Monte Carlo N-Particle eXtended (MCNPX) code, and the results obtained were compared with the experimental and theoretical results. In addition, the configuration and materials are simulated using the MCNPX code [ 13 13 , 14 14 ]. Finally, the photon dose rate is calculated for a system of concrete and MnFe 2 O 4 nanoparticles, herein referred to as Nano MnFe 2 O 4 and compared to Nano SiO 2 for different gamma-ray energies and weight percentages. 2. Materials and methods 1 2.1 Materials 2 2.1.1 Nano SiO 2 3 The chemical analysis of Portland concrete and Nano SiO 2 is given by Elsharkawy and Sadawy [ 1 1 ]. Nano concrete is formed by grinding the commercially available grade Portland concrete at a high energy [ 7 7 ]. Tables 1 Tables 1 and 2 2 show the concrete sample without Nano SiO 2 and the concrete mixed with a weight percentage of 0.5% CaO in Nano SiO 2 , respectively. Table 3 Table 3 shows the densities of Nano SiO 2 at different weight percentages of SiO 2 nanoparticles [ 1 1 ]. 1 1 Chemical composition 1 1 Weight (%) 1 1 SiO 2 1 1 23.7 1 1 Al 2 O 3 1 1 5.6 1 1 Fe 2 O 3 1 1 3.3 1 1 CaO 1 1 63.7 1 1 MgO 1 1 1.4 1 1 SO 3 1 1 0.2 1 1 K 2 O 1 1 1.2 1 1 Chemical composition 1 1 Weight (%) 1 1 CaO 1 1 0.5 1 1 SiO 2 1 1 93.3 1 1 Al 2 O 3 1 1 3.2 1 1 Fe 2 O 3 1 1 1.7 1 1 MgO 1 1 0.3 1 1 SO 3 1 1 0.1 1 1 K 2 O 1 1 0.1 1 1 N 2 O 1 1 0.1 1 1 SiO 2 nanoparticle percentage addition 1 1 Density (ρ) (g/cm 3 ) 1 1 0.0 1 1 2.15 1 1 0.5 1 1 2.17 1 1 1.5 1 1 2.30 1 1 2.0 1 1 2.26 To study the nuclear attenuation properties, the compressive strength of hardened concrete cubic samples (7×7×7 cm 3 ) is considered. A beam from both point and disk isotropic gamma-ray sources of 137 Cs, with one line of energy of 0.662 MeV, 60 Co, with two lines of energy of 1.17 and 1.33 MeV, and 22 Na, with two lines of energy of 0.511 and 1.274 MeV, was used in the MCNPX code. Figure 1 Figure 1 shows the disk gamma-ray source and cubic concrete sample simulated by the MCNPX code. Figures 2a and b Figures 2a and b show the tracks of photons obtained from this code for the point and disk gamma-ray sources, respectively. 2.1.2 Nano MnFe 2 O 4 3 We have added MnFe 2 O 4 nanoparticles to concrete with a weight percentage of 2.0% CaO at different temperatures, as shown in Tables 4 Tables 4 and 5 5 . MnFe 2 O 4 is a magnetic oxide, in which oxygen has a close packing structure with the Mn 2+ and Fe 3+ ions. These spinel ferrites are very promising candidates for understanding and controlling the magnetic properties of nanoparticles at the atomic level [ 11 11 - 12 12 11-12 ]. 1 1 Composition 1 1 Weight (%) 1 1 CaO 1 1 2.0 1 1 SiO 2 1 1 23.7 1 1 Al 2 O 3 1 1 3.2 1 1 Fe 2 O 3 1 1 1.7 1 1 MgO 1 1 0.3 1 1 SO 3 1 1 0.1 1 1 K 2 O 1 1 0.1 1 1 N 2 O 1 1 0.1 1 1 MnFe 2 O 4 1 1 68.8 1 1 Temperature (K) 1 1 Density (ρ) (g/cm 3 ) 1 1 300 1 1 4.373 1 1 573 1 1 4.773 1 1 673 1 1 5.194 1 1 773 1 1 4.745 2.2 Methods 2 2.2.1 MCNPX code 3 The shielding material parameters are the most important for characterizing the penetration and diffusion of gamma-rays [ 15 15 ]. Theoretical modeling of the photon attenuation coefficients of the materials permits more flexibility and simplicity compared to experimental studies. The linear attenuation coefficients, μ , in materials are determined by the transmission method according to Beer- Lambert’s law [ 1 1 , 15 15 - 17 17 15-17 ]: <math display="block" id="M1"><mrow><mi>μ</mi><mo>.</mo><mi>X</mi><mo>=</mo><mtext>Ln</mtext><mo stretchy="false">(</mo><mfrac><mrow><msub><mi>I</mi><mn>0</mn></msub></mrow><mi>I</mi></mfrac><mo stretchy="false">)</mo><mo>,</mo></mrow></math> where I 0 and I are the incident and attenuation photon intensities, respectively, μ (cm −1 ) is the linear attenuation coefficient, and X is the thickness of the slab. The mass attenuation coefficient is defined as μ m (cm 2 g -1 ) = μ (cm −1 )/ρ (g/cm 3 ). In this work, the μ and μ m coefficients are obtained by the MCNPX code at various photon energies: 511, 662, 1170, 1274, and 1332.5 keV. The concrete material content ratios have been defined relative to a sample material in this code. Calculations were performed for one million histories per run using Intel Core i7 CPU 3.40 GHz computers. The obtained statistical errors were less than 1% for a long run time. The flux integrated over a surface tally ( F2 ) has been used in the μ and μ m calculations [ 3 3 , 17 17 - 19 19 17-19 ]. One of two methods can be used for the calculation of the photon dose rate in concrete samples that are useful for converting the flounce quantities to units of dose. The choice is between using a heating number method or one or more flounces-to-dose conversion functions. Both approaches are valid for photon dose rate calculations, but the use of conversion functions is recommended for dose equivalent and effective dose calculations [ 14 14 , 20 20 ]. In the heating number method, the code calculates the absorbed dose on the basis of the KERMA approximation, which is locally deposited [ 14 14 ]. The KERMA approximation dose can be represented using the following equations: <math display="block" id="M2"><mrow><mi>D</mi><mrow><mo>(</mo><mrow><mfrac><mrow><mtext>Gy</mtext></mrow><mrow><mtext>Source</mtext><mo>−</mo><mtext>particle</mtext></mrow></mfrac></mrow><mo>)</mo></mrow><mo>=</mo><mfrac><mi>C</mi><mi>N</mi></mfrac><munderover><mstyle mathsize="140%" displaystyle="true"><mo>∑</mo></mstyle><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mi>N</mi></munderover><munderover><mstyle mathsize="140%" displaystyle="true"><mo>∑</mo></mstyle><mrow><mi>j</mi><mo>=</mo><mn>1</mn></mrow><mi>T</mi></munderover><mo>∅</mo><msub><mi>σ</mi><mtext>T</mtext></msub><mrow><mo>(</mo><mi>E</mi><mo>)</mo></mrow><mi>H</mi><mrow><mo>(</mo><mi>E</mi><mo>)</mo></mrow><mo>,</mo></mrow></math> <math display="block" id="M3"><mrow><mi>C</mi><mo>=</mo><mrow><mo>(</mo><mrow><mn>1.602</mn><mo>×</mo><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>10</mn></mrow></msup><mfrac><mrow><mtext>Gy</mtext></mrow><mrow><mtext>Mev</mtext><mo>/</mo><mtext>g</mtext></mrow></mfrac></mrow><mo>)</mo></mrow><mrow><mo>(</mo><mrow><mn>1</mn><mo>×</mo><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>24</mn></mrow></msup><mfrac><mrow><msup><mrow><mtext>cm</mtext></mrow><mn>2</mn></msup></mrow><mrow><mtext>barn</mtext></mrow></mfrac></mrow><mo>)</mo></mrow><mrow><mo>(</mo><mrow><mfrac><mrow><msub><mi>N</mi><mtext>a</mtext></msub><mi>η</mi></mrow><mi>M</mi></mfrac></mrow><mo>)</mo></mrow><mo>,</mo></mrow></math> where <math id="M4"><mrow><msub><mi>N</mi><mtext>a</mtext></msub></mrow></math> is Avogadro’s number (6.022×10 23 mol -1 ), <math id="M5"><mi>η</mi></math> is the number of atoms per molecule, <math id="M6"><mi>M</mi></math> is the molar mass in grams, <math id="M7"><mo>∅</mo></math> is the fluence score in particles/cm 2 , <math id="M8"><mrow><msub><mi>σ</mi><mtext>T</mtext></msub></mrow></math> is the total atomic cross section at energy of scoring track in barns, <math id="M9"><mi>H</mi></math> is the heating number in MeV per collision, <math id="M10"><mi>T</mi></math> is the number of scoring source particle tracks and <math id="M11"><mi>N</mi></math> is the number of source particles. The second method is the flounce-to-dose conversion function. In this method, the absorbed dose rate is calculated by using DF n (Dose Function) and tally F4 operations. Suppose one wanted to compute the dose rate of some type of flux tally, either total or by energy group. This feature allows you to enter a point wise response function (such as flux-to-dose conversion factors) as a function of energy to modify a regular tally. Therefore, the absorbed dose rate is calculated by combining the DF n and F4 cards. Finally, the DF n card is defined as follows: <math display="block" id="M12"><mrow><mi>D</mi><msub><mi>F</mi><mi>n</mi></msub><mi>I</mi><mi>U</mi><mtext> </mtext><mi>F</mi><mi>A</mi><mi>C</mi><mtext> </mtext><mi>I</mi><mi>C</mi><mtext> </mtext><mi>I</mi><mi>N</mi><mi>T</mi></mrow></math> where IU , FAC , IC and INT are the controls units, normalization factor for dose, standard dose function, and energy interpolation, respectively [ 14 14 , 20 20 ]. 3. Simulation, experimental, and theoretical results 1 3.1 Calculation of attenuation coefficients 2 3.1.1 Calculation of attenuation coefficients in Nano SiO 2 3 The μ value was calculated by the MCNPX code, and is shown in Fig. 3 Fig. 3 . This figure presents the effects of varying gamma-ray energy with μ at weight percentages of 0.0%, 0.5%, 1.5% and 2.0% SiO 2 in Nano SiO 2 , and compares these to the experimental results of ref. 1. Calculations have been carried out using a beam of point isotropic gamma-ray sources of 137 Cs, with one line of energy of 0.662 MeV, 60 Co, with two lines of energy of 1.17 and 1.33 MeV, and 22 Na, with two lines of energy of 0.511 and 1.274 MeV. This figure illustrates that the values of μ decrease with increasing gamma-ray energies and that the maximum and minimum values of are found at the energies of 0.511 and 1.33 MeV, respectively. In addition, these parameters increase with increasing weight percentage of SiO 2 nanoparticles until 1.5%, after which they decrease due to decreasing density. In general, the relative error in all these calculations is less than 1.0%. 3.1.2 Calculation of attenuation coefficients of Nano MnFe 2 O 4 3 Figure 4 Figure 4 shows the effect of gamma-ray energy on μ for Nano MnFe 2 O 4 with 2.0% CaO at 300, 573, 673, and 773 K. Figure 5 Figure 5 presents the same effect for Nano MnFe 2 O 4 at different temperatures, as calculated by the MCNPX code. As shown in Figs. 4 Figs. 4 and 5 5 , the values of μ decrease with increasing gamma-ray energies and the maximum and minimum values of μ are found at 0.511 and 1.33 MeV, respectively. In addition, this parameter can be increased by increasing the density up to 5.194 g/cm 3 , as seen for the Nano MnFe 2 O 4 temperature of 673 K. 3.1.3 Comparison of SiO 2 and MnFe 2 O 4 nanoparticles 3 Figure 6 Figure 6 shows the μ m of the SiO 2 and MnFe 2 O 4 nanoparticles constituting 2.0 wt.% in concrete for different gamma-ray energies. According to Fig. 6 Fig. 6 a fairly good agreement with the experimental results was observed, notably in the simulation of Nano SiO 2 with a density of 2.26 g/cm 3 , whereas for the theoretical results, a good agreement was obtained at the density of 2.47 g/cm 3 . The average relative differences between the simulation results and the experimental and theoretical results are 6.4%, 5.5% and 2.1% for the densities of 2.26 g/cm 3 and 2.47 g/cm 3 , respectively. Moreover, as seen in this figure, the μ m of the MnFe 2 O 4 nanoparticles is much higher compared to that of the SiO 2 nanoparticles, which is attributed to a higher density. As listed below, there are sources of uncertainty in the results of the MCNPX code in comparison to the experimental and theoretical results: 1. Inherent error in the probabilistic method of the MCNPX code, 2. Inherent error in this code due to the libraries used, especially the inability to define the cross-section of the nanoparticles, 3. Physical models used in the MCNPX code. 3.2 Calculation of dose rate 2 3.2.1 Calculation of dose rate in Nano SiO 2 and MnFe 2 O 4 nanoparticles 3 Table 6 Table 6 and figure 7 figure 7 show the effect of adding 2.0 wt.% SiO 2 and MnFe 2 O 4 nanoparticles to concrete on the photon dose rate at different distances from the point source for gamma-ray energies of 0.511 and 1.274 MeV. According to Table 6 Table 6 , the photon dose rate decreases at the average values of about 9.2% and 3.7% for the gamma-ray energies of 0.511 and 1.274 MeV, respectively. This difference is due to the larger μ in Nano MnFe 2 O 4 in comparison to Nano SiO 2 (as seen in Fig. 6 Fig. 6 ). 1 1 X (cm) 1 1 MnFe 2 O 4 -0.511 MeV 1 1 SiO 2 -0.511 MeV 1 1 Relative difference % 1 1 MnFe 2 O 4 -1.274 MeV 1 1 SiO 2 -1.274 MeV 1 1 Relative difference % 1 1 4.0 1 1 1.30E-03 1 1 1.45E-03 1 1 -11.5 1 1 1.75E-03 1 1 1.81E-03 1 1 -3.4 1 1 5.0 1 1 9.76E-04 1 1 1.07E-03 1 1 -9.6 1 1 1.32E-03 1 1 1.37E-03 1 1 -3.8 1 1 6.0 1 1 7.59E-04 1 1 8.27E-04 1 1 -9.0 1 1 1.04E-03 1 1 1.08E-03 1 1 -3.8 1 1 7.0 1 1 6.07E-04 1 1 6.60E-04 1 1 -8.7 1 1 8.40E-04 1 1 8.72E-04 1 1 -3.8 1 1 8.0 1 1 4.98E-04 1 1 5.40E-04 1 1 -8.4 1 1 6.93E-04 1 1 7.19E-04 1 1 -3.8 1 1 9.0 1 1 4.15E-04 1 1 4.50E-04 1 1 -8.4 1 1 5.81E-04 1 1 6.03E-04 1 1 -3.8 1 1 10.0 1 1 3.52E-04 1 1 3.83E-04 1 1 -8.8 1 1 4.95E-04 1 1 5.14E-04 1 1 -3.8 4. Discussion and conclusion 1 Generally speaking, the linear mass attenuation coefficients and photon dose rate of a shielding material depends on the quantity, type, and energy of radiation. It can be shown that most interactions of high energy photons with atoms occur through the Compton Effect, the strength of which depends on the atomic number and amount of primary energy of the gamma source. An increase in photon dose rate can occur owing to Compton reactions involving the photons and the concrete atoms. In addition, photoelectric interactions occur in low energy photons, which is a major mechanism of photon interactions with atoms. Furthermore, there is a greater probability of photon interaction at energies much greater than the K- and L-edge energies. When small quantities of nanoparticles are uniformly dispersed in concrete, they act as a nucleus to strongly bind with the concrete hydrates. This leads to a boost in concrete hydration due to their high activity, which is beneficial for the strength of the concrete. Whilst these nanoparticles are bound to the hydrates, they also prevent the crystals from growing, which could lead to a decrease in concrete strength. The loading of the concrete pores with nanoparticles therefore leads to an increase in the strength. Finally, Nano SiO 2 can offer to the hydration process, producing more C-S-H via the formation of Ca(OH) 2 . In this study, the interaction between a concrete material in a cubic sample configuration and a point isotropic beam for a range of gamma-ray sources has been considered and simulated using the MCNPX code. The μ, μ m , and photon dose rates have been calculated by this code, from which the statistical errors of the obtained parameters were determined to be less than 1%. According to the obtained μ results, the average relative differences between simulations and the theoretical and experimental results for Nano MnFe 2 O 4 and Nano SiO 2 were 6.4% and 5.5%, respectively. In addition, the photon dose rate decreases up to 9.2% for Nano MnFe 2 O 4 and 3.7% for Nano SiO 2 for gamma-ray energies of 0.511 and 1.274 MeV, respectively. Finally, the obtained results are in close agreement with both the experimental and theoretical data. Therefore, it can be stated that the obtained data from this code is a strong tool not only for obtaining μ and μ m but also for calculating the photon dose rate. It can also be used for future work such as gamma spectroscopy in material characterization, detector design, and especially in investigations of shielding materials for nuclear reactors and high energy therapy facilities. References E. R. Elsharkawy , M. M. Sadawy , Effect of gamma ray energies and addition of nano- SiO2 to concrete on mechanical properties and mass attenuation coefficient , IOSR Journal of Mechanical and Civil Engineering , 13 , 17 - 22 , 2016 , doi: 10.9790/1684-1306061722 http://doi.org/10.9790/1684-1306061722 . Effect of gamma ray energies and addition of nano- SiO2 to concrete on mechanical properties and mass attenuation coefficient I. I. Bashter , Effect of silica fume addition to concrete mixes on Radiation Attenuation Properties , Arab Journal of Nuclear Science and Applications , vol. 34 , pp. 179 - 189 , 2001 . Effect of silica fume addition to concrete mixes on Radiation Attenuation Properties H. Tekin , V.P. Singh , T. Manici , Effects of micro-sized and nano-sized WO3 on mass attenauation coefficients of concrete by using MCNPX code , Appl. Radiat. Isot ., 121 : 122 - 125 ., 2017 , doi: 10.1016/j.apradiso.2016.12.040 http://doi.org/10.1016/j.apradiso.2016.12.040 . Effects of micro-sized and nano-sized WO3 on mass attenauation coefficients of concrete by using MCNPX code R. S. Chen , Q. Ye , Research on the comparison of properties of hardened concrete paste between Nano-SiO2 and silica fume added , Concrete Journal , No. 1 , 7 - 10 , 2002 . Research on the comparison of properties of hardened concrete paste between Nano-SiO2 and silica fume added Q. Ye , Research on the comparison of pozzolanic activity between Nano-SiO2 and silica fume , Concrete Journal , No. 1 , 3, 19-22 , 2001 . Research on the comparison of pozzolanic activity between Nano-SiO2 and silica fume S. Gopinath , P. C. Mouli , A. R. Murthy , et al ., Effect of nano silica on mechanical properties and durability of normal strength concrete . Arch. Civ. Eng ., 4 , 433 - 444 , 2012 . doi: 10.2478/v.10169-012-0023-y http://doi.org/10.2478/v.10169-012-0023-y Effect of nano silica on mechanical properties and durability of normal strength concrete M. J. Carmichae , G. P. Arulraj , Strength and permeability studies on concrete with nano-cement , volume 8 , issue 1 , January 2017 , pp. 132 - 139 , 2017 , ID: IJCIET_08_01_014 . Strength and permeability studies on concrete with nano-cement S. Gopinath , P. C. Mouli , A. R. Murthy , et al ., Effect of nano silica on mechanical properties and durability of normal strength concrete . Arch. Civ. Eng ., 2012 , 4 , 433 - 444 . doi: 10.2478/v.10169-012-0023-y http://doi.org/10.2478/v.10169-012-0023-y Effect of nano silica on mechanical properties and durability of normal strength concrete J. Tao , Preliminary study on the water permeability and microstructure of concrete incorporating Nano-Sio2 , Concrete and Concrete Research , No. 10 , 35 , 1943 - 7 , 2005 , doi: 10.1016/j.cemconres.2005.07.004 http://doi.org/10.1016/j.cemconres.2005.07.004 . Preliminary study on the water permeability and microstructure of concrete incorporating Nano-Sio2 I. I. Bashter , A. El-Sayed Abdo , A.S. Makarious , et al ., A comparative study of the attenuation of reactor thermal neutrons in different types of concrete , Ann. Nucl. Energy , 23 , 1189 - 1195 , ( 1996 ). doi: 10.1016/0306-4549(95)00122-0 http://doi.org/10.1016/0306-4549(95)00122-0 A comparative study of the attenuation of reactor thermal neutrons in different types of concrete Z. Surowiec , M. Wiertel , W. Gac , et al ., Influence of annealing temperature on structural and magnetic properties of MnFe2O4 nanoparticles , NUKLEONIKA , 60 : 137 - 141 , 2015 , doi: 10.1515/nuka-2015-0029 http://doi.org/10.1515/nuka-2015-0029 . Influence of annealing temperature on structural and magnetic properties of MnFe2O4 nanoparticles S. Kanagesan , S. B.A. Aziz , M. Hashim , et al ., Synthesis, Characterization and in Vitro Evaluation of Manganese Ferrite (MnFe2O4) Nanoparticles for Their Biocompatibility with Murine Breast Cancer Cells (4T1) , Molecules 2016 , doi: 10.3390/molecules21030312 http://doi.org/10.3390/molecules21030312 Synthesis, Characterization and in Vitro Evaluation of Manganese Ferrite (MnFe2O4) Nanoparticles for Their Biocompatibility with Murine Breast Cancer Cells (4T1) H. O. Tekin , MCNP-X Monte Carlo Code Application for Mass Attenuation Coefficients of Concrete at Different Energies by Modeling 3 × 3 Inch NaI (Tl) Detector and Comparison with XCOM and Monte Carlo Data , Hindawi Publishing Corporation Science and Technology of Nuclear Installations , 2016 , doi: 10.1155/2016/6547318 http://doi.org/10.1155/2016/6547318 . MCNP-X Monte Carlo Code Application for Mass Attenuation Coefficients of Concrete at Different Energies by Modeling 3 × 3 Inch NaI (Tl) Detector and Comparison with XCOM and Monte Carlo Data D. B. Pelowitz , MCNPX User’s Manual, Version 2.6.0, LA-CP-07-1473 , Los Alamos National Laboratory , 2008 . MCNPX User’s Manual, Version 2.6.0, LA-CP-07-1473 V.P. Singh , S.P. Shirmardi , M.E. Medhat , et al ., Determination of mass attenuation coefficient for some polymers using Monte Carlo simulation , Vacuum 119 , 1 - 5 , 2015 , doi: 10.1016/j.vacuum.2016.11.011 http://doi.org/10.1016/j.vacuum.2016.11.011 . Determination of mass attenuation coefficient for some polymers using Monte Carlo simulation M. A. Abdel-Rahman , E. A. Badawi , Y. L. Abdel-Hady , et al ., Effect of sample thickness on the measured mass attenuation coefficients of some compounds and elements for 59.54, 661.6 and 1332.5 keV γ-rays , Nucl. Instrum. Meth. A 447 , 432 - 436 , ( 2000 ). doi: 10.1016/S0168-9002(99)01257-7 http://doi.org/10.1016/S0168-9002(99)01257-7 Effect of sample thickness on the measured mass attenuation coefficients of some compounds and elements for 59.54, 661.6 and 1332.5 keV γ-rays S. M. Vahabi , M. Bahreinipour , M. Shamsaie , A comparison study for mass attenuation coefficients of some amino acids using MCNP code , Kerntechnik , 82 , 339 - 343 , 2017 , doi: 10.3139/124.110678 http://doi.org/10.3139/124.110678 . A comparison study for mass attenuation coefficients of some amino acids using MCNP code Y. C. Kam , Kuang-Chih Pei , Chien-Lung Chang , et al ., Strength and fracture toughness of heavy concrete with various iron aggregate inclusions , Nucl. Eng. Des ., 228 , 119 - 127 , 2004 . doi: 10.1016/j.nucengdes.2003.06.008 http://doi.org/10.1016/j.nucengdes.2003.06.008 Strength and fracture toughness of heavy concrete with various iron aggregate inclusions A. Mesbahi , F. Jamali , N. Gharehaghaji , Effect of Photon Beam Energy, Gold Nanoparticle Size and Concentration on the Dose Enhanconcrete in Radiation Therapy , BioImpacts , 3 , 29 - 35 , 2013 , doi: 10.5681/bi.2013.002 http://doi.org/10.5681/bi.2013.002 . Effect of Photon Beam Energy, Gold Nanoparticle Size and Concentration on the Dose Enhanconcrete in Radiation Therapy A. Abbasi , M. Hassanzadeh , Measurement and Monte Carlo simulation of γ-ray dose rate in high-exposure building materials , Nucl. Sci. Tech . 28 : 20 , ( 2016 ), doi: 10.1007/s41365-016-0171-x http://doi.org/10.1007/s41365-016-0171-x Measurement and Monte Carlo simulation of γ-ray dose rate in high-exposure building materials The authors are thankful to Dr. Ashoor in the Department of NSTRI for helping to provide the MnFe 2 O 4 and SiO 2 nanoparticle data. 10.1007/s41365-018-0493-y 2018-01-03 2018-02-10 2018-03-19 2018-09-26 2018-11-01 2021-04-11 © China Science Publishing & Media Ltd. (Science Press), Shanghai Institute of Applied Physics, the Chinese Academy of Sciences, ChineseNuclear Society and Springer Nature Singapore Pte Ltd. 2018 This is a post-peer-review, pre-copyedit version of an article published in Nuclear Science and Techniques. The final authenticated version is available online at: http://dx.doi.org/10.1007/s41365-018-0493-y http://dx.doi.org/10.1007/s41365-018-0493-y . 2018 Nuclear Science and Techniques 11 29