Gamma-ray shielding study of light to heavyweight concretes using MCNP-4C code

Gamma-ray shielding study of light to heavyweight concretes using MCNP-4C code 1 corresp first-author Corresponding author, reza_bagheri@aut.ac.ir Corresponding author, reza_bagheri@aut.ac.ir reza_bagheri@aut.ac.ir 2 1 Nuclear Fuel Cycle Research School (NFCRS), Nuclear Science and Technology Research Institute (NSTRI), Tehran, Iran, 14155-1339 Nuclear Fuel Cycle Research School (NFCRS), Nuclear Science and Technology Research Institute (NSTRI), Tehran, Iran, 14155-1339 Radiology Department, Paramedical Faculty, Mazandaran University of Medical Sciences, Mazandaran, Iran, 14536-33143 Radiology Department, Paramedical Faculty, Mazandaran University of Medical Sciences, Mazandaran, Iran, 14536-33143 In this work, linear and mass attenuation coefficients, half and tenth value layers, effective atomic number and electron density of different types of concretes were determined at 316.51, 468.07, 511, 662, 1173 and 1332 keV using MCNP-4C code and WinXCom program. The MCNP-4C and WinXCom results agreed well with each other, with differences of < ±1.9%. The results agreed with available experimental data, too, with differences of < ±6%. The MCNP-4C results showed better agreement with the experimental data than the WinXCom results. Also it was found that the effective electron density of studied concretes varies in the range of (2.83–3.2) ×10 23 electron/g. Concrete Shielding MCNP-4C WinXCom Mass attenuation coefficient Effective atomic number and electron density 1 Introduction 1 Today, utilization of gamma-ray sources with care and safety is essential [ 1 1 - 3 3 1-3 ] . Concrete, a common construction material, is widely used against ionizing radiations [ 4 4 - 7 7 4-7 ] . For this purpose, various types of heavy density concretes have been developed, consisting of heavy elements like iron, barium and titanium in their structure [ 8 8 - 12 12 8-12 ] . Extensive studies on radiation shielding characteristics of various concretes and aggregates were published by Bashter and coworkers. [ 6 6 - 9 9 6-9 ] . They calculated the linear and mass attenuation coefficients of seven types of concretes at photon energies from 10 keV to 1 GeV [ 6 6 ] . Akkurt et al . used 137 Cs and 60 Co gamma-ray sources to measure photon attenuation coefficients of barite and concrete produced with barite in different rates [ 2 2 ] . Han et al . determined mass attenuation coefficients, effective atomic and electron numbers for some natural minerals usable in concretes [ 5 5 ] . Stankovic et al . calculated the transmission factor and the mass attenuation coefficients in ordinary and barite concretes for 511 and 662 keV photons by the FOTELP-2K6 Monte Carlo code [ 10 10 ] . The shielding of gamma rays and fast neutrons were studied for concretes containing different lime/silica ratios using WinXCom and MERCSF-N program by El-Khayatt [ 11 11 ] . Using the Monte Carlo code of MCNP-4B, Singh et al . simulated the linear and mass attenuation coefficients of photons at 1.5–6 MeV and the tenth value layer thickness of seven types of concretes used in nuclear reactor technology, and by comparing the simulation results with experimental data and XCOM photon cross section database, they showed that simulation produced reliable shielding data for this use of concretes. [ 12 12 ] In this research, eight types of concretes including ordinary(O), hematite-serpentine(HS), serpentine(S), ilmenite-limonite (IL), basalt-magnetite(BM), barite(B), steel-scrap(SS) and steel-magnetite(SM) were considered as shielding against gamma-rays. The linear and mass attenuation coefficients ( µ and µ m ), effective atomic number and electron density ( Z eff and N eff ), total atomic and electronic cross sections ( σ a and σ e ), half value layer (HVL) and tenth value layer (TVL) were calculated on basis of elemental compositions of the concretes using MCNP-4C Monte Carlo code and WinXCom program. Percentage composition of mentioned concretes and their densities are given in Table 1 Table 1 [ 2 2 , 6 6 - 9 9 6-9 ] . 1 1 Concrete types 1 1 Ordinary 1 1 Hematite–serpentine 1 1 Serpentine 1 1 Ilmenite–limonite 1 1 Basalt–magnetite 1 1 Barite 1 1 Steel-scrap 1 1 Steel–magnetite 1 1 Portland cement 1 1 11.82 1 1 13.19 1 1 15.94 1 1 12.44 1 1 12.42 1 1 10.77 1 1 8.81 1 1 7.55 1 1 Sand 1 1 26.71 1 1 ― 1 1 27.35 1 1 ― 1 1 ― 1 1 ― 1 1 26.08 1 1 ― 1 1 Gravel 1 1 54.96 1 1 ― 1 1 ― 1 1 ― 1 1 ― 1 1 ― 1 1 ― 1 1 ― 1 1 Ilmenite 1 1 ― 1 1 ― 1 1 ― 1 1 68.5 1 1 ― 1 1 ― 1 1 ― 1 1 ― 1 1 Limonite 1 1 ― 1 1 ― 1 1 ― 1 1 14.75 1 1 ― 1 1 ― 1 1 ― 1 1 ― 1 1 Hematite 1 1 ― 1 1 56.88 1 1 ― 1 1 ― 1 1 ― 1 1 ― 1 1 ― 1 1 ― 1 1 Barite 1 1 ― 1 1 ― 1 1 ― 1 1 ― 1 1 ― 1 1 83.75 1 1 ― 1 1 ― 1 1 Basalt 1 1 ― 1 1 ― 1 1 ― 1 1 ― 1 1 38.51 1 1 ― 1 1 ― 1 1 ― 1 1 Serpentine 1 1 ― 1 1 21.03 1 1 48.33 1 1 ― 1 1 ― 1 1 ― 1 1 ― 1 1 ― 1 1 Magnetite 1 1 ― 1 1 ― 1 1 ― 1 1 ― 1 1 41.62 1 1 ― 1 1 ― 1 1 26.19 1 1 Steel scrap 1 1 ― 1 1 ― 1 1 ― 1 1 ― 1 1 ― 1 1 ― 1 1 60.70 1 1 61.73 1 1 Water 1 1 6.51 1 1 8.90 1 1 8.38 1 1 4.30 1 1 7.45 1 1 5.48 1 1 4.41 1 1 4.53 1 1 Density(g cm -3 ) 1 1 2.3 1 1 2.5 1 1 2.6 1 1 2.9 1 1 3.05 1 1 3.35 1 1 4 1 1 5.1 Gamma-ray sources of 192 Ir (316.51 keV, 82.81%; 468.07 keV, 47.83%), 60 Co (1173 keV,100%; 1332 keV, 100%), and 137 Cs (662 keV, 94.6%), together with 511 keV gamma-ray of positron annihilation, were used in the simulation [ 10 10 , 13 13 - 16 16 13-16 ] . On the other hand, the theoretical values of mass attenuation coefficients for different elements, compounds and mixtures over wide range of photon energy have been tabulated by Hubbell and Seltzer [ 17 17 ] . Using such tables, mass attenuation coefficients at energies of 1 keV to 100 GeV [ 18 18 , 19 19 ] can be calculated by the WinXCom program. So, we used it to determine shielding characteristics of the concretes, and compared them with MCNP results. Also, our results were compared with available experimental data [ 2 2 , 6 6 , 20 20 ] . 2 Materials and methods 1 2.1 Geometry of concretes 2 Cylindrical geometries were employed for modeling of concrete samples. Eight sections of sub-cylinders of Φ 30 cm×5 cm were considered for every type of concretes and set on Z axis in tandem. Figure 1 Figure 1 shows the simulated geometry. 2.2 Source specification 2 Sources were considered as planar, collimated and monoenergetic with uniform distribution of radioactive material that emits gamma-ray beams perpendicular to front face of the samples (in direction of Z axis). A disc source of Φ 2 cm, parallel to the X - Y plane and origin on Z axis was defined in data card of the MCNP code with ERG, PAR, POS, and DIR commands for energy and type of particle, position and direction of source respectively. 2.3 Materials specification of concretes 2 Elemental composition of concrete depends mainly on the mix proportions and chemical composition of the materials. The percentages by weight of the elements in the concretes are presented in Table 2 Table 2 [ 6 6 , 10 10 ] . 1 1 Elements 1 1 O 1 1 HS 1 1 S 1 1 IL 1 1 BM 1 1 B 1 1 SS 1 1 SM 1 1 1 H 1 1 0.94 1 1 1.29 1 1 7.20 1 1 0.66 1 1 0.83 1 1 0.36 1 1 0.7 1 1 0.51 1 1 6 C 1 1 0.09 1 1 ― 1 1 0.15 1 1 ― 1 1 ― 1 1 ― 1 1 0.09 1 1 ― 1 1 8 O 1 1 53.66 1 1 43.51 1 1 55.6 1 1 36.45 1 1 42.3 1 1 31.16 1 1 21.09 1 1 15.7 1 1 11 Na 1 1 0.46 1 1 ― 1 1 ― 1 1 ― 1 1 1.06 1 1 ― 1 1 0.45 1 1 ― 1 1 12 Mg 1 1 0.12 1 1 6.64 1 1 10.20 1 1 0.15 1 1 2.2 1 1 0.12 1 1 0.09 1 1 0.58 1 1 13 Al 1 1 1.32 1 1 1.67 1 1 2.50 1 1 0.8 1 1 4.22 1 1 0.42 1 1 1.2 1 1 0.66 1 1 14 Si 1 1 36.74 1 1 10.53 1 1 17.55 1 1 3.06 1 1 13.2 1 1 1.05 1 1 10.49 1 1 2.68 1 1 15 P 1 1 ― 1 1 ― 1 1 ― 1 1 ― 1 1 0.2 1 1 ― 1 1 ― 1 1 0.08 1 1 16 S 1 1 0.08 1 1 0.09 1 1 ― 1 1 0.08 1 1 0.09 1 1 10.78 1 1 0.06 1 1 0.06 1 1 19 K 1 1 0.31 1 1 ― 1 1 0.08 1 1 ― 1 1 0.29 1 1 ― 1 1 0.3 1 1 ― 1 1 20 Ca 1 1 5.65 1 1 5.97 1 1 5.64 1 1 5.83 1 1 8.88 1 1 5.02 1 1 4.28 1 1 3.95 1 1 22 Ti 1 1 ― 1 1 ― 1 1 ― 1 1 16.04 1 1 0.6 1 1 ― 1 1 ― 1 1 ― 1 1 25 Mm 1 1 ― 1 1 ― 1 1 ― 1 1 ― 1 1 0.12 1 1 ― 1 1 ― 1 1 0.07 1 1 26 Fe 1 1 0.63 1 1 30.30 1 1 1.08 1 1 36.93 1 1 26.01 1 1 4.75 1 1 61.25 1 1 75.71 1 1 56 Ba 1 1 ― 1 1 ― 1 1 ― 1 1 ― 1 1 ― 1 1 46.34 1 1 ― 1 1 ― 2.4 Detector geometry and tally definition 2 A small cylinder of Φ 2 cm ×2 cm was considered as detector volume and set inside the collimator at 58 cm from the source. A Φ 22 cm ×10 cm lead cylinder with a Φ 2 cm ×10 cm hole was used as the collimator ( Fig. 1 Fig. 1 ). Tally F4 was used to obtain MCNP-4C simulated data. This tally calculates average flux in a cell (detector volume) for only one incident gamma photon. The simulations were performed with 1 to 10 million histories depending on type and thickness of concrete specimens. All simulated results were reported with less than 0.1% error. 3 Results and discussion 1 3.1 Transmission factor 2 The transmission factors of a concrete type, can be defined by Eq.(1) <math display="block" id="M1"><mrow><mi>T</mi><mrow><mo>(</mo><mrow><mi>E</mi><mo>,</mo><mi>d</mi></mrow><mo>)</mo></mrow><mo>=</mo><mi>Φ</mi><mrow><mo>(</mo><mrow><mi>E</mi><mo>,</mo><mi>d</mi></mrow><mo>)</mo></mrow><mo>/</mo><mi>Φ</mi><mrow><mo>(</mo><mrow><mi>E</mi><mo>,</mo><mn>0</mn></mrow><mo>)</mo></mrow><mo>,</mo></mrow></math> where, E is the gamma-ray energy (keV), d is thickness (cm) of shielding concrete, Φ ( E , d ) is the flux in the detector attained by the Tally F4, and Φ ( E ,0) is the flux in absence of any shielding material. The transmission factors for selected gamma-rays as a function of concrete thickness are shown in Fig. 2 Fig. 2 . Of all the concrete types, the ordinary concrete with the least density has the least amount of attenuation (the most amount of transmission); while the steel-magnetite concrete with the greatest density has the greatest amount of attenuation (the least amount of transmission), even though the barite and ilmenite-limonite concretes contain high atomic number elements (Ba, Ti). Also, the transmission factors of concretes span from 1 to less than 10 −9 . 3.2 Linear and mass attenuation coefficients, HVL and TVL values of concretes 2 Linear and mass attenuation coefficients of the concretes ( µ and µ m ) were derived from transmission factor curves through fitting Lambert law ( I = I 0 e − μt ) using MATLAB version 7.10.0.499. The results are given in Table 3 Table 3 . 1 1 Concrete type 1 1 Density (g·cm −3 ) 2 1 316.51 keV 2 1 468.07 keV 2 1 511 keV 2 1 662 keV 2 1 1173 keV 2 1 1332 keV 1 1   1 1   1 1 μ 1 1 µ m 1 1 μ 1 1 µ m 1 1 μ 1 1 µ m 1 1 μ 1 1 µ m 1 1 μ 1 1 µ m 1 1 μ 1 1 µ m 1 1 Ordinary 1 1 2.3 1 1 0.244 1 1 0.106 1 1 0.208 1 1 0.090 1 1 0.200 1 1 0.087 1 1 0.179 1 1 0.078 1 1 0.136 1 1 0.059 1 1 0.127 1 1 0.055 1 1 Hematite-serpentine 1 1 2.5 1 1 0.266 1 1 0.107 1 1 0.224 1 1 0.090 1 1 0.216 1 1 0.086 1 1 0.192 1 1 0.077 1 1 0.145 1 1 0.059 1 1 0.136 1 1 0.054 1 1 Serpentine 1 1 2.6 1 1 0.291 1 1 0.112 1 1 0.249 1 1 0.096 1 1 0.240 1 1 0.092 1 1 0.214 1 1 0.082 1 1 0.163 1 1 0.062 1 1 0.152 1 1 0.059 1 1 Ilmenite-limonite 1 1 2.9 1 1 0.306 1 1 0.105 1 1 0.255 1 1 0.088 1 1 0.246 1 1 0.085 1 1 0.218 1 1 0.075 1 1 0.165 1 1 0.057 1 1 0.154 1 1 0.053 1 1 Basalt-magnetite 1 1 3.05 1 1 0.323 1 1 0.106 1 1 0.272 1 1 0.089 1 1 0.262 1 1 0.086 1 1 0.233 1 1 0.076 1 1 0.176 1 1 0.058 1 1 0.165 1 1 0.054 1 1 Barite 1 1 3.35 1 1 0.456 1 1 0.136 1 1 0.324 1 1 0.097 1 1 0.305 1 1 0.091 1 1 0.258 1 1 0.077 1 1 0.186 1 1 0.055 1 1 0.173 1 1 0.052 1 1 Steel-scrap 1 1 4 1 1 0.426 1 1 0.106 1 1 0.353 1 1 0.088 1 1 0.340 1 1 0.085 1 1 0.300 1 1 0.075 1 1 0.227 1 1 0.057 1 1 0.212 1 1 0.053 1 1 Steel-magnetite 1 1 5.11 1 1 0.542 1 1 0.106 1 1 0.447 1 1 0.087 1 1 0.429 1 1 0.084 1 1 0.379 1 1 0.074 1 1 0.285 1 1 0.056 1 1 0.268 1 1 0.052 The mass attenuation coefficients of concretes were also calculated using WinXCom program data using Eq.(2) <math display="block" id="M2"><mrow><msub><mo>µ</mo><mtext>m</mtext></msub><mo>=</mo><mo>∑</mo><msub><mi>w</mi><mi>i</mi></msub><msub><mo>µ</mo><mrow><mtext>m</mtext><mo>,</mo><mi>i</mi></mrow></msub><mo>,</mo><mo stretchy="false">(</mo><mi>i</mi><mo>=</mo><mn>1</mn><mo>→</mo><mi>n</mi><mo stretchy="false">)</mo></mrow></math> where, w i and µ m, i (obtained directly from WinXCom program) are percentage by weight and mass attenuation coefficient of i th element in the concrete, respectively. The linear attenuation coefficients were calculated by multiplying mass attenuation coefficient of each type of concrete by its density. The linear and mass attenuation coefficients of concretes obtained by WinXCom program for different photon energies are presented in Table 4 Table 4 . 1 1 Concrete type 1 1 Density (g·cm −3 ) 2 1 316.51 keV 2 1 468.07 keV 2 1 511 keV 2 1 662 keV 2 1 1173 keV 2 1 1332 keV 1 1   1 1   1 1 μ 1 1 µ m 1 1 μ 1 1 µ m 1 1 μ 1 1 µ m 1 1 μ 1 1 µ m 1 1 μ 1 1 µ m 1 1 μ 1 1 µ m 1 1 Ordinary 1 1 2.3 1 1 0.245 1 1 0.106 1 1 0.208 1 1 0.090 1 1 0.201 1 1 0.087 1 1 0.179 1 1 0.078 1 1 0.136 1 1 0.059 1 1 0.128 1 1 0.056 1 1 H ematite-serpentine 1 1 2.5 1 1 0.267 1 1 0.107 1 1 0.224 1 1 0.089 1 1 0.216 1 1 0.087 1 1 0.193 1 1 0.077 1 1 0.146 1 1 0.058 1 1 0.137 1 1 0.055 1 1 Serpentine 1 1 2.6 1 1 0.292 1 1 0.112 1 1 0.247 1 1 0.095 1 1 0.241 1 1 0.093 1 1 0.215 1 1 0.083 1 1 0.163 1 1 0.063 1 1 0.153 1 1 0.059 1 1 I lmenite-limonite 1 1 2.9 1 1 0.307 1 1 0.106 1 1 0.256 1 1 0.088 1 1 0.247 1 1 0.086 1 1 0.219 1 1 0.076 1 1 0.166 1 1 0.057 1 1 0.155 1 1 0.054 1 1 B asalt-magnetite 1 1 3.05 1 1 0.324 1 1 0.106 1 1 0.269 1 1 0.088 1 1 0.263 1 1 0.086 1 1 0.234 1 1 0.077 1 1 0.177 1 1 0.058 1 1 0.166 1 1 0.054 1 1 Barite 1 1 3.35 1 1 0.461 1 1 0.138 1 1 0.327 1 1 0.098 1 1 0.307 1 1 0.092 1 1 0.260 1 1 0.078 1 1 0.187 1 1 0.056 1 1 0.175 1 1 0.052 1 1 Steel-scrap 1 1 4 1 1 0.427 1 1 0.107 1 1 0.353 1 1 0.088 1 1 0.340 1 1 0.086 1 1 0.302 1 1 0.075 1 1 0.228 1 1 0.057 1 1 0.214 1 1 0.053 1 1 Steel-magnetite 1 1 5.11 1 1 0.544 1 1 0.107 1 1 0.448 1 1 0.088 1 1 0.432 1 1 0.085 1 1 0.381 1 1 0.075 1 1 0.288 1 1 0.056 1 1 0.270 1 1 0.053 It is completely clear from both tables that the MC-simulated data and WinXCom-calculated data are very close to each other. The percentage differences between the MCNP and WinXCom results of mass attenuation coefficients for all gamma rays and concrete types range from −1.89% to 1.72%, averaged at 0.53%. In Tables 3 Tables 3 and 4 4 , at 316.51 keV, the linear attenuation coefficient of barite concrete (density=3.35 g·cm −3 ) is greater than steel-scrap value (density = 4 g·cm −3 ), unlike the general tendency that the linear attenuation coefficient increases with the density. This discrepancy could be due to the photoelectric effect. This effect is favored by low energy photons and high atomic number absorbers, so that cross section for this reaction varies approximately as Z n / E 3.5 , where the exponent n varies between 4 and 5 over the gamma-ray energy region of interest [ 21 21 ] . According to this fraction, at low energetic gamma rays, barite concrete with components of high atomic number elements (especially barium) has greater linear attenuation coefficient than those of the other concretes. This makes barite aggregate a good material for shielding against gamma-rays. Figure 3 Figure 3 shows the half value layer (HVL= ln2/ μ ) and tenth value layer (TVL= ln10/ μ ) of the concretes, i.e. the HVL and TVL quantities are defined as the concrete thickness which reduces photon intensity to half and tenth of its initial value, respectively. Of cause, the HVL and TVL values decrease with increasing density and increase with the incident photon energy, but at 316.51 keV the values of barite concrete are smaller than those of steel-scrap, due to the photoelectric effect of barite concrete, as mentioned above The calculated data were compared with available experimental results of some concretes [ 2 2 , 6 6 , 20 20 ] ( Tables 5 Tables 5 and 6 6 ). Generally, the calculation results are in accordance with the experimental data. The percentage differences between calculated and experimental data of HVL and TVL range from −2.94% to 15.45%, being < 5% for ordinary concrete at 662 keV and < 3% for barite concrete at 1332 keV. The percentage differences between calculated and experimental data of linear attenuation coefficients at 1.5 MeV range from −26.83% to 15.45% ( Table 6 Table 6 ). Due to differences in the densities and elemental compositions among the concretes in this work and Refs.[ 2 2 , 6 6 , 20 20 ], some inequalities between experimental and calculated data were observed. Differences in geometry of simulation relative to experiment, lead to little discrepancy in calculated and measured values. Reported error of experimental work in Table 6 Table 6 is < ±10% [ 6 6 ] . * Densities of the ordinary concrete samples in Refs.[ 2 2 , 20 20 ] and this work are 2.46, 2.31 and 2.30 g·cm −3 , respectively; while they are 3.46, 3.45 and 3.35 g·cm −3 for the barite concrete samples in in Refs.[ 2 2 , 20 20 ], respectively 2 1 Concrete type 2 1 Ordinary 2 1 Barite 2 1 Gamma energy (keV) 1 1 662 1 1 1332 1 1 662 1 1 1332 2 1 HVL (cm) 1 1   1 1 Ref. [ 2 2 , 20 20 ] 1 1 3.71 1 1 ― 1 1 2.33 1 1 4.08 1 1   1 1 MCNP-4C(percentage difference) 1 1 3.88(4.58%) 1 1 5.46 1 1 2.69(15.45%) 1 1 4.00(−2.00%) 1 1   1 1 WinXCom(percentage difference) 1 1 3.87(4.31%) 1 1 5.42 1 1 2.67(14.59%) 1 1 3.96(−2.94%) 2 1 TVL (cm) 1 1   1 1 Refs. [ 2 2 , 20 20 ] 1 1 12.31 1 1 ― 1 1 7.75 1 1 13.54 1 1   1 1 MCNP-4C(percentage difference) 1 1 12.89(4.71%) 1 1 18.13 1 1 8.94(15.35%) 1 1 13.30(−1.77) 1 1   1 1 WinXCom(percentage difference) 1 1 12.86(4.46%) 1 1 17.99 1 1 8.86(14.32%) 1 1 13.16(−2.81%) 1 1 Concrete type 1 1 Ref.[ 6 6 ] 1 1 MCNP-4C(percentage difference) 1 1 WinXCom(percentage difference) 1 1 Ordinary 1 1 0.164 1 1 0.121 (−26.22%) 1 1 0.120 (−26.83%) 1 1 Hematite-serpentine 1 1 0.124 1 1 0.128 (3.23%) 1 1 0.129 (4.03%) 1 1 Ilmenite-limonite 1 1 0.159 1 1 0.146 (−8.18%) 1 1 0.146 (−8.18%) 1 1 Basalt-magnetite 1 1 0.139 1 1 0.156 (12.23%) 1 1 0.157 (12.95%) 1 1 Steel-scrap 1 1 0.196 1 1 0.201 (2.55%) 1 1 0.201 (2.55%) 1 1 Steel-magnetite 1 1 0.220 1 1 0.253 (15.00%) 1 1 0.254 (15.45%) 3.3 Effective atomic number and electron density of concretes 2 The total atomic cross sections for concretes are calculated from the simulated values of µ m using Eq.(3) [ 22 22 ] : <math display="block" id="M3"><mrow><msub><mi>σ</mi><mtext>a</mtext></msub><mo>=</mo><msub><mi>μ</mi><mtext>m</mtext></msub><mi>N</mi><mo>/</mo><msub><mi>N</mi><mtext>A</mtext></msub><mo>,</mo></mrow></math> where N is the atomic mass of concrete and N A is the Avogadro’s number. Also the σ a and the total electronic cross sections, σ e , for WinXCom program can be calculated from Eqs. (4) and (5) [ 23 23 ] : <math display="block" id="M4"><mrow><msub><mi>σ</mi><mtext>a</mtext></msub><mo>=</mo><mo stretchy="false">(</mo><mo>∑</mo><msub><mi>f</mi><mi>i</mi></msub><msub><mi>N</mi><mi>i</mi></msub><msub><mi>μ</mi><mrow><mtext>m</mtext><mo>,</mo><mi>i</mi></mrow></msub><mo stretchy="false">)</mo><mo>/</mo><msub><mi>N</mi><mtext>A</mtext></msub><mo>,</mo><mo stretchy="false">(</mo><mi>i</mi><mo>=</mo><mn>1</mn><mo>→</mo><mi>n</mi><mo stretchy="false">)</mo><mo>,</mo></mrow></math> <math display="block" id="M5"><mrow><msub><mi>σ</mi><mtext>e</mtext></msub><mo>=</mo><mo stretchy="false">(</mo><mo>∑</mo><msub><mi>f</mi><mi>i</mi></msub><msub><mi>N</mi><mi>i</mi></msub><msub><mi>μ</mi><mrow><mtext>m</mtext><mo>,</mo><mi>i</mi></mrow></msub><mo>/</mo><msub><mi>Z</mi><mi>i</mi></msub><mo stretchy="false">)</mo><mo>/</mo><msub><mi>N</mi><mtext>A</mtext></msub><mo>,</mo><mo stretchy="false">(</mo><mi>i</mi><mo>=</mo><mn>1</mn><mo>→</mo><mi>n</mi><mo stretchy="false">)</mo><mo>,</mo></mrow></math> where f i denotes the fractional abundance of the i th element with respect to the number of atoms such that f 1 + f 2 + f 3 +…+ f i = 1, and Z i and N i are the atomic number and atomic mass of the i th element, respectively. Finally, effective atomic number ( Z eff ) and effective electron density ( N eff ) of the concretes are calculated by Eqs. (6) and (7) [ 3 3 ] ( Tables 7 Tables 7 and 8 8 ): 1 1 Concrete types 1 1 Density (g·cm −3 ) 2 1 316.51 keV 2 1 468.07 keV 2 1 511 keV 2 1 662 keV 2 1 1173 keV 2 1 1332 keV 1 1   1 1   1 1 MC 1 1 WXC 1 1 MC 1 1 WXC 1 1 MC 1 1 WX 1 1 MC 1 1 WXC 1 1 MC 1 1 WXC 1 1 MC 1 1 WXC 1 1 Ordinary 1 1 2.3 1 1 8.62 1 1 8.66 1 1 8.64 1 1 8.62 1 1 8.63 1 1 8.61 1 1 8.60 1 1 8.63 1 1 8.58 1 1 8.63 1 1 8.57 1 1 8.64 1 1 Hematite-serpentine 1 1 2.5 1 1 9.31 1 1 9.34 1 1 9.24 1 1 9.22 1 1 9.25 1 1 9.16 1 1 9.17 1 1 9.20 1 1 9.12 1 1 9.18 1 1 9.11 1 1 9.18 1 1 Serpentine 1 1 2.6 1 1 4.48 1 1 4.50 1 1 4.49 1 1 4.46 1 1 4.47 1 1 4.47 1 1 4.47 1 1 4.48 1 1 4.45 1 1 4.48 1 1 4.45 1 1 4.48 1 1 Ilmenite-limonite 1 1 2.9 1 1 11.68 1 1 11.73 1 1 11.56 1 1 11.57 1 1 11.56 1 1 11.50 1 1 11.47 1 1 11.52 1 1 11.42 1 1 11.48 1 1 11.41 1 1 11.49 1 1 Basalt-magnetite 1 1 3.05 1 1 10.09 1 1 10.14 1 1 10.13 1 1 10.01 1 1 10.07 1 1 9.96 1 1 9.97 1 1 10.01 1 1 9.93 1 1 9.98 1 1 9.93 1 1 9.99 1 1 Barite 1 1 3.35 1 1 17.99 1 1 18.18 1 1 15.85 1 1 15.98 1 1 15.92 1 1 14.88 1 1 14.95 1 1 15.08 1 1 14.39 1 1 14.49 1 1 14.30 1 1 14.46 1 1 Steel-scrap 1 1 4 1 1 13.43 1 1 13.47 1 1 13.28 1 1 13.27 1 1 13.35 1 1 13.13 1 1 13.12 1 1 13.20 1 1 13.06 1 1 13.15 1 1 13.05 1 1 13.15 1 1 Steel-magnetite 1 1 5.11 1 1 15.73 1 1 15.83 1 1 15.53 1 1 15.60 1 1 15.69 1 1 15.43 1 1 15.40 1 1 15.51 1 1 15.30 1 1 15.45 1 1 15.31 1 1 15.45 1 1 Concrete type 2 1 316.51 keV 2 1 468.07 keV 2 1 511 keV 2 1 662 keV 2 1 1173 keV 2 1 1332 keV 1 1   1 1 MC 1 1 WXC 1 1 MC 1 1 WXC 1 1 MC 1 1 WXC 1 1 MC 1 1 WXC 1 1 MC 1 1 WXC 1 1 MC 1 1 WXC 1 1 Ordinary 1 1 3.03 1 1 3.04 1 1 3.04 1 1 3.03 1 1 3.04 1 1 3.03 1 1 3.02 1 1 3.03 1 1 3.02 1 1 3.03 1 1 3.01 1 1 3.03 1 1 Hematite-serpentine 1 1 3.03 1 1 3.04 1 1 3.01 1 1 3.00 1 1 3.01 1 1 3.00 1 1 2.98 1 1 2.99 1 1 2.97 1 1 2.99 1 1 2.97 1 1 2.99 1 1 Serpentine 1 1 3.22 1 1 3.23 1 1 3.22 1 1 3.20 1 1 3.22 1 1 3.20 1 1 3.21 1 1 3.22 1 1 3.20 1 1 3.22 1 1 3.20 1 1 3.22 1 1 Ilmenite-limonite 1 1 2.97 1 1 2.98 1 1 2.94 1 1 2.94 1 1 2.94 1 1 2.94 1 1 2.92 1 1 2.93 1 1 2.90 1 1 2.92 1 1 2.90 1 1 2.92 1 1 Basalt-magnetite 1 1 3.01 1 1 3.02 1 1 3.02 1 1 2.98 1 1 3.02 1 1 2.98 1 1 2.97 1 1 2.98 1 1 2.96 1 1 2.98 1 1 2.96 1 1 2.98 1 1 Barite 1 1 3.52 1 1 3.55 1 1 3.10 1 1 3.12 1 1 3.10 1 1 3.12 1 1 2.92 1 1 2.95 1 1 2.81 1 1 2.83 1 1 2.80 1 1 2.83 1 1 Steel-scrap 1 1 2.97 1 1 2.98 1 1 2.94 1 1 2.94 1 1 2.94 1 1 2.94 1 1 2.90 1 1 2.92 1 1 2.89 1 1 2.91 1 1 2.89 1 1 2.91 1 1 Steel-magnetite 1 1 2.93 1 1 2.95 1 1 2.89 1 1 2.90 1 1 2.89 1 1 2.90 1 1 2.87 1 1 2.89 1 1 2.85 1 1 2.88 1 1 2.85 1 1 2.88 <math display="block" id="M6"><mrow><msub><mi>Z</mi><mrow><mtext>eff</mtext></mrow></msub><mo>=</mo><msub><mi>σ</mi><mtext>a</mtext></msub><mo>/</mo><msub><mi>σ</mi><mtext>e</mtext></msub><mo>,</mo></mrow></math> <math display="block" id="M7"><mrow><msub><mi>N</mi><mrow><mtext>eff</mtext></mrow></msub><mo>=</mo><msub><mo>µ</mo><mtext>m</mtext></msub><mo>/</mo><msub><mi>σ</mi><mtext>e</mtext></msub><mo>.</mo></mrow></math> Both tables show good agreement between MCNP-4C code and WinXCom program results. In Table 7 Table 7 , the Z eff value approximately increases with the concrete density, and decreases with increasing photon energy. This is due to high atomic number elements ratio in material (especially barium in barite concrete), and concretes of high Z eff values will effectively absorb incoming photons. Of all the concretes, the effective atomic number of steel-magnetite is the greatest, while that of serpentine concretes is the lowest. Iron ( Z =26) and oxygen ( Z =8) as heavy and light weight elements constitute the greatest elemental portion in these concretes (about 76 and 56% respectively). In Table 8 Table 8 , the effective electron density of studied concretes varies from 2.83×10 23 to 3.2×10 23 electron/g. It is decreases slowly with increasing photon energy, and serpentine and barite concretes have the greatest and the lowest values of effective electron densities, respectively. 4 Conclusion 1 Transmission factors, linear and mass attenuation coefficients, HVL and TVL values, effective atomic numbers and electron densities for ordinary, hematite–serpentine, serpentine, ilmenite–limonite, basalt–magnetite, barite, steel-scrap and steel–magnetite concretes at 316.51, 468.07, 511, 662, 1173 and 1332 keV gamma ray energies were simulated and calculated using MCNP-4C Code and WinXCom program and were compared with available experimental data. It was found that results by MCNP code and WinXCom program were in good agreement with each other. Effective electron density of studied concretes was about 3×10 23 electron/g and steel-magnetite and barite concretes have got the greatest value of effective atomic number. 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(Science Press), Shanghai Institute of Applied Physics, the Chinese Academy of Sciences, ChineseNuclear Society and Springer Nature Singapore Pte Ltd. 2017 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/s41365-016-0167-6 http://dx.doi.org/10.1007/s41365-016-0167-6 . 2017 Nuclear Science and Techniques 02 28