Heat energy produced in nuclear reactors and nuclear fuel cycle facilities interactions modifies the physical properties of the shielding materials containing water content. Therefore, in the present paper, effect of the heat on shielding effectiveness of the concretes is investigated for gamma and neutron. The mass attenuation coefficients, effective atomic numbers, fast neutron removal crosssection and exposure buildup factors.
The mass attenuation coefficients, effective atomic numbers, fast neutron removal crosssection and exposure buildup factors of ordinary and heavy concretes were investigated using NIST data of XCOM program and Geometric Progression method.
The improvement in shielding effectiveness for photon and reduction in fast neutron for ordinary concrete was observed. The change in the neutron shielding effectiveness was insignificant.
The present investigation on interaction of gamma and neutron radiation would be very useful for assessment of shielding efficiency of the concrete used in high temperature applications such as reactors.
Wide varieties of radiation shielding materials are being used in nuclear technology for exposure control of occupational radiation workers. The shielding materials are being chosen based on the requirements, application, feasibility, type of radiation, cost, availability, etc. Concrete is one of the most suitable shielding materials in view of cost effective, easily available, easy fabrication of different densities for stopping both the gamma and neutron. The concrete has combination of low as well as high atomic number elements (H, C, O, S, Ca, Fe) to reduce gamma as well as neutron radiations, which is the most necessary for a nuclear facility. The aggregates increase the density of concrete which results in improvement of shielding efficiency [
The concrete is being used for biological shielding of the reactor core and other applications for exposure control. Thermal energy is transferred to the concrete from directly from reactor core as well as radiation interacting with it. Exposure of the concrete with thermal energy modifies physical properties as a result of which elemental composition of the concrete vary. Due envisagement of thermal energy transfers to the biological shielding, the concrete is being cooled by flowing water in contact with it to reduce the temperature. However, the heat transferred to the concrete induces thermal expansion, defects in addition to dehydration of concretes. These effects of heat transferred into the concrete alter chemical compositions of the concrete [
The aim of present study is to investigate shielding effectiveness of heat treated ordinary and high density concretes for gamma and neutron radiations. In present study, shielding parameters viz. mass attenuation coefficients, effective atomic numbers, fast neutron removal crosssection and exposure buildup factors were computed [
The concrete samples for the present investigation are ordinary concrete (density: 2.3 g/cm^{3}) and high density concrete (density: 3.6 g/cm^{3}). These samples were heated up to 120°C to investigate the effect of heat on shielding properties. Elemental compositions of the concretes before and after the heat treatment are given in
Nowadays, it is becoming very popular to investigate the shielding properties of a material by using the Monte Carlo method. Gamma ray transmission method based on calculating the photon attenuation for a material is applied for evaluation of shielding. Thus, we have applied Monte Carlo NParticle Transport Code Systemextended (MCNPX) version 2.4.0 of Los Alamos national lab (Los Alamos, NM) for investigation of mass attenuation coefficients of investigated concrete samples. MCNPX is a Monte Carlo code for simulation of radiation interactions at wide energy range. MCNPX is fully threedimensional and it operates extended nuclear cross section libraries and uses certain physics models for different particle types. MCNPX is a major and powerful code for photon attenuation and energy deposition studies. The mass attenuation coefficients for the concrete samples have been calculated for both conditions before and after heating. Similar to the present study, various simulation studies using MCNPX for different radiation applications are found in the literature [
In this study, material features have been employed twice. In the first case, elemental mass fractions and density was taken into consideration for the situation before the heating. Secondly, the same calculation has been done for the situation after the heating. In this study, gamma ray sources with various energies were considered as a point isotropic source. The source has been defined in the mode card of MCNPX input file as a point isotropic source at photon energies of 1, 2, 3, 4, 5, 6, 7, and 8 MeV. The absorbed dose amount in the detection field have been obtained by using the average flux tally F4 has been employed. This type of tally in MCNPX scores average flux in a point or cell. In addition, 10^{8} particles have been tracked as the number of particle (NPS variable). MCNPX calculations were done by using Intel^{®} Core^{TM} i7 CPU 2.80 GHz computer hardware. During the simulation study, the relative error rate has been observed less than 1% of the output file.
When a beam of monochromatic gamma ray is attenuated on matter according to LambertBeer law:
Where,
Considering density for gamma interaction, the mass attenuation coefficient is defined and is calculated using the following equation.
Where,
Where,
Effective atomic cross section, σ
Total electronic cross section, σ
where
Exposure buildup factor (EBF) values and the Geometric Progression (GP) fitting parameters of the concrete samples were computed by method of logarithmic interpolation using the equivalent atomic number (
Calculation of equivalent atomic number
Calculation of GP fitting parameters
Calculation of buildup factors
The
where
The GP fitting parameters are calculated in the similar fashion of logarithmic interpolation procedure for
Third and final step is buildup factors estimation by GP fitting parameters (
where
The effective removal crosssection for fast neutron (2–12 MeV) for compounds and homogenous mixtures may be calculated by mixture rule.
The mass attenuation coefficients, effective atomic numbers, neutron removal crosssections and exposure buildup factors for ordinary and high density concrete samples are shown in
In
It is to be noted that the
In
It is to be noted that the
The low atomic number elements are dominant conscientious for shielding of fast neutrons (2–12 MeV). Therefore, significant reduction of chemical composition of low atomic number elements (H and O) after heat treatment (see
The variation of exposure buildup factor (EBF) of the concrete samples with photon energy at different mean free paths before and after heat treatment is shown in
The reasons for such variation of EBF can be explained by basic interaction processes i.e. photoelectric effect, Compton scattering and pair production [
The change in EBF due to heat treatment is shown in
In the present investigation on gamma and neutron shielding effectiveness for the ordinary and high density concretes before and after heat treatment, mass attenuation coefficients, effective atomic numbers, and exposure buildup factors are found to be dependent heat treatment. The mass attenuation coefficients for the ordinary and high density concretes are lesser before heat treatment and increases after the heat treatment. The heat treatment of the concrete marginally increases gamma shielding effectiveness. The neutron removal cross section of the ordinary concrete reduces after heat treatment whereas it is independent for the high density concrete. Also, the MCNPX is capable of simulation mass attenuation coefficients for radiation interaction in presence of heat treatment.
The experimental investigation on shielding effectiveness of the ordinary and high density concretes in under process.
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Trubey DK, Eisenhauer CM, Foderaro A, Gopinath DV, Harima Y, Hubbell JH, Shure K, Su S. Gamma Ray Attenuation Coefficient and Buildup Factors for Engineering Materials. American Nuclear Society. ANSI/ANS6.4.3, 1991.
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Experimental setup for simulation of mass attenuation coefficients of concretes.
Mass attenuation coefficients of ordinary and high density concretes before and after heat treatment.
Effective atomic numbers of ordinary and high density concretes before and after heat treatment.
Fast neutron removal crosssection of ordinary and high density concretes before and after heat treatment.
Exposure buildup factors of ordinary and high density concretes before and after heat treatment (A) 5 mfp (B) 10 mfp (C) 20 mfp (D) 40 mfp.
Ratio of exposure buildup factors for before to after heat treatment for (A) ordinary concrete (B) high density concrete.
Elemental Composition of Ordinary and High Density Concretes before and after Heat Treatment
Elements  Ordinary concrete (2,300 kg/m^{3})  High density concrete (3,600 kg/m^{3})  


 
Before HT  After HT  Before HT  After HT  
Si  15.95  19.46  2.57  2.3 
 
Ca  19.28  22.25  8.63  8.84 
 
Al  1.853  1.99  0.714  0.572 
 
Fe  3.81  4.35  52.16  53.42 
 
Mg  1.7  2.26  1.33  1.42 
 
S  0.46  0.46  0.23  0.24 
 
Na  0.89  1.54  0.21  0.15 
 
K  0.79  0.8  0.094  0.084 
 
P  0.03  0.06  0.0021  0.002 
 
H  4.55  2.51  3.74  2 
 
O  50.6  44.35  31  31 
Mass Attenuation Coefficients of Ordinary and High Density Concretes before and after Heat Treatment Using MCNP Simulation and XCOM
Energy (MeV)  Ordinary concrete  High density concrete  


 
Before HT  After HT  Before HT  After HT  



 
MCNPX  XCOM  MCNPX  XCOM  MCNPX  XCOM  MCNPX  XCOM  
1  0.06535  0.06635  0.06413  0.06502  0.06347  0.06407  0.06144  0.06294 
 
2  0.04552  0.04659  0.04452  0.04571  0.04442  0.04523  0.04217  0.04446 
 
3  0.03696  0.03797  0.03630  0.03737  0.03628  0.03751  0.03508  0.03694 
 
4  0.03187  0.03314  0.03143  0.03273  0.03286  0.03340  0.03131  0.03298 
 
5  0.02857  0.03007  0.02874  0.02981  0.02922  0.03094  0.02922  0.03061 
 
6  0.02665  0.02799  0.02648  0.02786  0.02806  0.02937  0.02794  0.02912 
 
7  0.02535  0.02652  0.02522  0.02648  0.02767  0.02833  0.02728  0.02815 
 
8  0.02413  0.02542  0.02430  0.02547  0.02628  0.02763  0.02653  0.02750 
Equivalent Atomic Numbers of Ordinary and High Density Concretes before and after Heat Treatment
Energy (MeV)  Ordinary concrete  High density concrete  


 
Before HT  After HT  Before HT  After HT  
0.015  13.83  14.53  20.28  20.70 
 
0.02  14.05  14.77  20.56  20.94 
 
0.03  14.28  14.97  20.86  21.21 
 
0.04  14.43  15.10  21.03  21.37 
 
0.05  14.53  15.19  21.15  21.48 
 
0.06  14.60  15.27  21.25  21.57 
 
0.08  14.70  15.36  21.38  21.69 
 
0.1  14.77  15.42  21.46  21.76 
 
0.15  14.88  15.51  21.58  21.88 
 
0.2  14.95  15.57  21.64  21.94 
 
0.3  15.02  15.63  21.72  22.02 
 
0.4  15.06  15.67  21.76  22.05 
 
0.5  15.09  15.69  21.79  22.07 
 
0.6  15.09  15.70  21.80  22.09 
 
0.8  15.09  15.71  21.82  22.10 
 
1  15.09  15.71  21.82  22.10 
 
1.5  12.49  13.50  19.85  20.51 
 
2  11.74  12.77  18.28  18.93 
 
3  11.54  12.57  17.73  18.42 
 
4  11.47  12.51  17.57  18.27 
 
5  11.45  12.49  17.50  18.18 
 
6  11.44  12.47  17.46  18.13 
 
8  11.42  12.46  17.41  18.09 
 
10  11.41  12.45  17.38  18.06 
 
15  11.39  12.43  17.35  18.02 