A comparative Monte Carlo simulation study on shielding features of the CaF2–CaO–B2O3–P2O5–SrO–Ta2O5 glass system against X-ray by GEANT4 and MCNPX codes

Regarding to their unique physical and mechanical features, glasses and glass–ceramics are suitable materials for shielding purposes. The present study evaluates the shielding properties of the CaF2–CaO–B2O3–P2O5–SrO–Ta2O5 glass system using Monte Carlo GEANT4 and MCNPX codes for X-ray radiations with an energy range of 20 to 100 keV. MAC values of the Ta0, Ta1, Ta2, Ta2.5, and Ta3 samples of the CaF2–CaO–B2O3–P2O5–SrO–Ta2O5 glass were computed using Phy-X/PSD, GEANT4, and MCNPX codes and compared. According to the results, the programs have good compatibility with each other. For instance, in the energy of 40 keV and for the Ta2 sample, GEANT4 and MCNP codes are 1.445765406 and 1.517801204 cm2/g, respectively, indicating 7.419529525 and 2.829628418% differences with 1.562 cm2/g obtained using the Phy-X/PSD software. According to recent estimations, the Ta3 sample of the CaF2–CaO–B2O3–P2O5–SrO–Ta2O5 glass system can be selected as the best shield compared with the other samples.


GEANT4 and MCNP simulation geometry
GEANT4 toolkit GEANT4 toolkit is a Monte Carlo package that uses random numbers during the calculation process.GEANT4 code can be used to simulate passing various sorts of particles either charged or non-charged with any range of energy within different types of materials.Moreover, an excellent feature of this code is the flexibility of choosing arbitrary physics lists and input, and output parameters 25,26 .In the present work, GEANT4-10.7,a version of GEANT4 code is employed to simulate the set-up of the X-ray radiations and calculate the shielding parameters.

MCNPX code
MCNPX, an improved Monte Carlo package by Los Alamos National Laboratory, is applied for calculating the shielding features of the CaF 2 -CaO-B 2 O 3 -P 2 O 5 -SrO-Ta 2 O 5 glass system against photons with an energy range of 20-100 keV.Also, the code is designed to simulate a wide range of energies for different particles (alpha, photon, proton, neutron, deuteron, electron, 3 He etc.) and various types of materials (elements, compositions, and mixtures).In MCNP code, the geometry can be illustrated in 2D and 3D dimensions, which is one of the best features of the code.The geometry part of the target, source, detector, and tally key can be defined in the input file of the code 26 .In the present study, MCNPX-2.6, a version of the MCNPX code was selected to simulate the set-up of the X-ray radiations.

The geometry details and set-up
Figure 1 displays the geometry of an X-ray machine, which was selected for evaluating of shielding properties of the CaF 2 -CaO-B 2 O 3 -P 2 O 5 -SrO-Ta 2 O 5 glass system.As shown in Fig. 1, a glass sample prepared as a disk with 2 cm radius and 3 mm thickness is placed in the middle of the photon source with an energy range from 20 to 100 keV and a cylindrical detector with 2.54 cm radius and 2.54 cm thickness.The X-ray source is simulated as a circle plane with a radius of 1.5 mm, with the sample placed 10 cm far from the source and the detector.The physics lists of GEANT4 code that applied for the calculations of this study are G4EmStandardPhysics_option2, G4PhotoNuclearProcess, G4LowEGammaNuclearModel, and G4CascadeInterface.
Moreover, a simulation setup diagram from visual editor for GEANT4 and MCNP nuclear codes is displayed in Fig. 2. Photons exit from the top (the cubic), drop on the middle cylinder (the sample), and detect by the yellow cylinder (the detector).The flow chart of the overall simulation process of using GEANT4 and MCNP codes are illustrated in Fig. 3.The two Monte Carlo input files are including materials, source, and detector details, which with defining the tally, the cell flux of the photons can be seen in the output of the codes.

Phy-X/PSD
The Phy-X/PSD software can determine shielding values for photon energies between 1 keV and 100 GeV for any materials in single elementals or mixture composites.This program illustrates the chemical compositions and density of the materials.Besides, it calculates various shielding parameters such as MAC, LAC, MFP, Z eff , HVL, and TVL using theoretical MAC values 27,28 .In this study, Phy-X/PSD software was selected to calculate the shielding features of the CaF 2 -CaO-B 2 O 3 -P 2 O 5 -SrO-Ta 2 O 5 glass system and compare with it GEANT4 and MCNPX simulated values.www.nature.com/scientificreports/

Linear attenuation coefficient (LAC)
The linear attenuation coefficient (µ) is the number of particles or photons reflected from the beam per unit thickness of the sample surface.This coefficient is calculated in a unit of cm −1 using Eq.(1) 29 : (1) LAC = −  where LAC is the linear attenuation coefficient (cm −1 ), N and N 0 are primary and ultimate particle or photon numbers, respectively, and x is the thickness of the glass sample (cm).

Mass attenuation coefficient (MAC)
The mass attenuation coefficient is the probability of photons or particles that interact in a unit of mass of the glass sample.It can be computed using Eq. ( 2) 30 : where LAC is the linear attenuation coefficient (cm −1 ), MAC is the mass attenuation coefficient (cm 2 /g), W i is the weight fraction, and ρ denotes the glass sample density (g/cm 3 ).

Half-value layer (HVL)
The thickness of the glass sample that cut the power of the particle or photon beam in half is defined as the halfvalue layer.Equation ( 3) is used to evaluate HVL 31 : where HVL is the half-value layer (cm) and LAC is the linear attenuation coefficient (cm −1 ).

Tenth-value layer (TVL)
The tenth-value layer of the sample glass is the thickness of the glass that attenuates the intensity of the beam to one-tenth of its primary strength.The TVL is calculated by Eq. ( 4) 31 : where TVL is the tenth-value layer (cm) and the LAC is the linear attenuation coefficient (cm −1 ).

Mean free path (MFP)
The distance between two successive interactions of the particles or photons through the glass sample is defined as the mean free path, which can be estimated by Eq. ( 5) 31 : where MFP is the mean free path (cm) and LAC denotes the linear attenuation coefficient (cm −1 ).

Effective atomic number
The effective atomic number (Z eff ) of the samples is expressed by Eq. (6) 32 : (2) www.nature.com/scientificreports/MAC values of the GEANT4 code and Phys-x software were compared using Eq. ( 7) 32 :

Results and discussion
In this research, the shielding parameters of the CaF 2 -CaO-B 2 O 3 -P 2 O 5 -SrO-Ta 2 O 5 glass were computed for X-ray energies from 20 to 100 keV by the GEANT4 toolkit and MCNPX code.2. Due to the higher atomic number of Ta than P, with increasing the amount of Ta 2 O 5 , the density of the samples rises from 2.57 to 2.903 g/cm 3 for the Ta 0 , Ta 1 , Ta 2 , Ta 2,5 , and Ta 3 samples.As can be seen from Table 2, increasing the density has raised the value of the LAC parameter.Ta 3 with the highest density value compared to other samples is the best shield against incident photons.Therefore, the behavior of the LAC is depended on the density and chemical composition of the samples, and the energy of photons.Furthermore, Fig. 5 presents a 3D comparison of LAC results between the five samples of the CaF 2 -CaO-B 2 O 3 -P 2 O 5 -SrO-Ta 2 O 5 glass system.Figure 6.exhibits mass attenuation coefficient values estimated by MCNPX and GEANT4 codes for the Ta 0 , Ta 1 , Ta 2 , Ta 2,5 , and Ta 3 samples of the CaF 2 -CaO-B 2 O 3 -P 2 O 5 -SrO-Ta 2 O 5 glass.According to this figure, MAC values for the mentioned samples decline continuously from 20 to 100 keV.The values of MAC for the GEANT4 toolkit in energy of 40 keV for the Ta 0 , Ta 1 , Ta 2 , Ta 2,5 , and Ta 3 samples are 1.303098, 1.386764, 1.445765, 1.485121, and 1.531128 cm 2 /g, respectively.Also, the simulation outputs by MAC for MCNP code for the glass samples were reported to be 1.363301651, 1.440249708, 1.517801204, 1.555898155, and 1.594936203 cm 2 /g, respectively, which are in good agreement with the GEANT4 values.Table 3 lists the values of MAC for five mentioned samples obtained using GEANT4 and MCNP codes and Phy-X/PSD program in the energy range of 20 to 100 keV.Table 3 presents the differences between GEANT4 and MCNPX codes, and the Phy-X/PSD program.As can be seen, the outputs of these three software are in good agreement for all energy range and the five samples of the glass system.( 6)   Figure 12 exhibits the mean free path values computed by GEANT4 and MCNPX codes for five samples of the CaF 2 -CaO-B 2 O 3 -P 2 O 5 -SrO-Ta 2 O 5 glass system in the photon energy range between 20 and 100 keV.As can be seen, the MFP values for each sample gradually decrease from 20 to 100 keV.According to Fig. 13, the MFP values decline by increasing the Ta 2 O 5 content of the samples.The distance between to interacting of photons with energy of 40 keV estimated by GEANT4 toolkit in the Ta 0 , Ta 1 , Ta 2 , Ta 2,5 , and Ta 3 samples are 0.2986, 0.262029, 0.244408, 0.23676, and 0.224979 cm, and for MCNP code are 0.285413766, 0.252297981, 0.232808414, 0.22599001, and 0.215978066 cm, respectively.Table 6 presents more values of the MFP for photon energy in the range of 20 to 100 keV.
Figure 14 demonstrates the effective atomic number of the five samples of the CaF 2 -CaO-B 2 O 3 -P 2 O 5 -SrO-Ta 2 O 5 glass.The values of Z eff have the highest at 20 keV photon energy, which are 23.78,24.76, 25.72, 26.18, and 26.64 for the Ta 0 , Ta 1 , Ta 2 , Ta 2.5 , and Ta 3 samples, respectively.In this respect, the Z eff values decrease with increasing photon energy and such that lowest result belongs to 100 keV energy.Also, the Ta 3 sample with the highest density has the highest Z eff value among the five samples.A comparison of Z eff for the five samples of the CaF 2 -CaO-B 2 O 3 -P 2 O 5 -SrO-Ta 2 O 5 glass system is given in Fig. 15.As can be noticed, the value of Z eff rise with increasing the density of samples.

Conclusion
This research explored the shielding properties of the CaF 2 -CaO-B 2 O 3 -P 2 O 5 -SrO-Ta 2 O 5 glass system with five different molar fractions of Ta 2 O 5 using GEANT4 and MCNPX nuclear codes, and PhyX/PSD program.The density of the five samples was different from 2.57 to 2.903 g/cm 3 , depending on the amount of Ta 2 O 5 .The parameter of MAC for each sample was determined using the GEANT4 and MCNP codes for photons with an energy range between 20 and 100 keV and compared with the values of Phy-X/PSD software.In the energy of 40 keV and for the sample of Ta 3 , the values of Phy-X/PSD, GEANT4, and MCNP were estimated as 1.641, 1.531127875, and 1.594936203 cm 2 /g, respectively.In contrast, the Monte Carlo codes have 6.700746492 and 2.807056518% discrepancy with the online software.Besides, the value of MAC rises by increasing the Ta 2 O 5 content.In the mentioned energy, for Ta 0 , Ta 1 , Ta 2 , Ta 2.5 , and Ta 3 samples, the MAC values of the Phy-X/PSD program are 1.403, 1.482, 1.562, 1.601, and 1.641 cm 2 /g.Therefore, according to the results, the Ta 3 sample was selected as the best shield against photons in comparison with the other samples.

Figure 1 .
Figure 1.Geometry of X-ray radiation shielding simulated using MCNPX and GEANT4 codes: (a) before irradiating the samples, (b) during irradiating the sample.

Figure 2 .
Figure 2. The simulation setup diagram from Visual Editor for both GEANT4 and MCNP codes.

Figure 3 .
Figure 3. Operation of the simulation process of GEANT4 and MCNP codes.

Figure 4
indicates the linear attenuation coefficient simulated results of five samples of the CaF 2 -CaO-B 2 O 3 -P 2 O 5 -SrO-Ta 2 O 5 glass.According to Fig. 4a, LAC values at 20 keV are 22.07342 and 22.42434066 cm −1 for GEANT4 and MCNP codes, respectively, while decline to 0.514242 and 0.553058358 cm −1 in the energy of 100 keV.Moreover, by increasing the percentages of Ta 2 O 5 in samples, the values of LAC rise for the Ta 0 , Ta 1 , Ta 2 , Ta 2.5 , and Ta 3 glass samples.For example, in the energy of 40 keV, the GEANT4 value of LAC reported in this study for the mentioned samples are 3.348961, 3.816376, 4.091516, 4.223683, and 4.444864 cm −1 , while they are 3.503685242, 3.963567196, 4.295377408, 4.424974352, and 4.630099796 cm −1 for MCNP code, respectively.The measured values for other energies are summarized in Table

Figure 5 .
Figure 5.A comparison of linear attenuation coefficient parameter of the five samples of the CaF 2 -CaO-B 2 O 3 -P 2 O 5 -SrO-Ta 2 O 5 glass that evaluated by MCNPX and GEANT4 codes.

Figure 7 .
Figure 7.A comparison of mass attenuation coefficient parameter of the five samples of the CaF 2 -CaO-B 2 O 3 -P 2 O 5 -SrO-Ta 2 O 5 glass that evaluated by GEANT4 and MCNPX codes.

Figure 9 .
Figure 9.A comparison of half-value layer parameter of the five samples of the CaF 2 -CaO-B 2 O 3 -P 2 O 5 -SrO-Ta 2 O 5 glass that evaluated by MCNPX and GEANT4 codes.

Figure 11 .
Figure 11.A comparison of the TVL GEANT4 and MCNPX simulated values for samples of the CaF 2 -CaO-B 2 O 3 -P 2 O 5 -SrO-Ta 2 O 5 glass.

Figure 13 .
Figure 13.A comparison of the MFP GEANT4 and MCNPX simulated values for samples of the CaF 2 -CaO-B 2 O 3 -P 2 O 5 -SrO-Ta 2 O 5 glass.

Figure 15 .
Figure 15.A comparison of effective atomic number for the five samples of the CaF 2 -CaO-B 2 O 3 -P 2 O 5 -SrO-Ta 2 O 5 glass.

Table 1 .
Chemical composition (mole %) and density details of the glass samples.

Table 3 .
GEANT4 and MCNPX simulated values of MAC for the samples of the CaF 2 -CaO-B 2 O 3 -P 2 O 5 -SrO-Ta 2 O 5 glass.

Table 4 .
GEANT4 and MCNPX simulated values of HVL for the samples of the CaF 2 -CaO-B 2 O 3 -P 2 O 5 -SrO-Ta 2 O 5 glass.

Table 5 .
GEANT4 and MCNPX simulated values of TVL for the samples of the CaF 2 -CaO-B 2 O 3 -P 2 O 5 -SrO-Ta 2 O 5 glass.

Table 6 .
GEANT4 and MCNPX simulated values of MFP for the samples of the CaF 2 -CaO-B 2 O 3 -P 2 O 5 -SrO-Ta 2 O 5 glass.