Tailoring bismuth borate glasses by incorporating PbO/GeO2 for protection against nuclear radiation

Nuclear radiation shielding capabilities for a glass series 20Bi2O3 − xPbO − (80 − 2x)B2O3 − xGeO2 (where x = 5, 10, 20, and 30 mol%) have been investigated using the Phy-X/PSD software and Monte Carlo N-Particle transport code. The mass attenuation coefficients (μm) of selected samples have been estimated through XCOM dependent Phy-X/PSD program and MCNP-5 code in the photon-energy range 0.015–15 MeV. So obtained μm values are used to calculate other γ-ray shielding parameters such as half-value layer (HVL), mean-free-path (MFP), etc. The calculated μm values were found to be 71.20 cm2/g, 76.03 cm2/g, 84.24 cm2/g, and 90.94 cm2/g for four glasses S1 to S4, respectively. The effective atomic number (Zeff)values vary between 69.87 and 17.11 for S1 or 75.66 and 29.11 for S4 over 0.05–15 MeV of photon-energy. Sample S4, which has a larger PbO/GeO2 of 30 mol% in the bismuth-borate glass, possesses the lowest MFP and HVL, providing higher radiation protection efficiency compared to all other combinations. It shows outperformance while compared the calculated parameters (HVL and MFP) with the commercial shielding glasses, different alloys, polymers, standard shielding concretes, and ceramics. Geometric Progression (G-P) was applied for evaluating the energy absorption and exposure buildup factors at energies 0.015–15 MeV with penetration depths up to 40 mfp. The buildup factors showed dependence on the MFP and photon-energy as well. The studied samples' neutron shielding behavior was also evaluated by calculating the fast neutron removal cross-section (ΣR), i.e. found to be 0.139 cm−1 for S1, 0.133 cm−1 for S2, 0.128 cm−1 for S3, and 0.12 cm−1 for S4. The results reveal a great potential for using a glass composite sample S4 in radiation protection applications.


Theoretical approach on attenuating γ-rays
The MFP is defined as an average distance λ (in cm) traveled by the photons before being absorbed in a particular material. It has been calculated as [31][32][33] , MFP = μ −1 , where μ (cm −1 ) denotes a linear attenuation coefficient of the medium. When a narrow beam of radiation of initial intensity I 0 moves through a specific medium of thickness t, the number of photons (I) that can transmit the medium is given by the Lambert-Beer law [34][35][36] , I = I 0 e −μt . Also, the mixture rule is a suitable relation used to determine μ m (or µ/ρ, where ρ is the material density) for an absorber 27,28 , µ m = ∑ω i (µ m ) i . The HVL used to describe the material thickness diminishes the intensity I to be 0.5 I 0 13 , HVL = 0.693 µ −1 . The μ m quantities helps in evaluating the total molecular cross-section (σ t,m ) 13,36 , σ t,m = µ m (M/N A ), N A is the Avogadros' number. The σ t,m used to calculate the average atomic crosssection (σ t,a ) 12,36 , σ t,a = σ t,m (∑n j ) −1 . The fractional abundance f i , atomic mass A i , and atomic weight Z i were used to calculate the average electronic cross-section (σ t,el ), where σ t,el = (N A ) −1 ∑f i A i (µ m ) (Z i ) −1 . The calculated quantities σ t,a and σ t,el utilized to calculate Z eff , Zeff = σ t,a (σ t,el ) −1 . The radiation protection efficiency (RPE) of an attenuator is determined in a relation, RPE = (1 − e −µt ) × 100.
The equivalent atomic number (Z eq ) is interpolated by matching the ratio, R = (μ m ) comp /(μ m ) total . Beside, the Z eq , geometric progression (G-P) fitting parameters (b, c, a, X k and d), (EABF), and (EBF) were calculated using the Phy-X/PSD program 37 .
On the other hand, a (∑ R ) represents the probability of a neutron undergoing certain reaction per unit length of moving through a certain medium, which can be calculated using the mass removal cross-section (∑ ER ) and fractional abundance ω for i th constituent, ∑ R (cm −1 ) = ∑ω i (∑ ER ) i .

Simulations of shielding parameters
The shielding parameters have been obtained using the user-friendly online Photon Shielding and Dosimetry (Phys-X/PSD) software. Several articles recently reported shielding properties against γ-rays, X-rays, and neutrons using simulation codes such as Geant, Fluka, and MCNP [38][39][40] . Previously mentioned codes were used as alternative methods for the experimental measurements. The shielding parameters were evaluated using MCNP-5  2 , with x = 5, 10, 20, and 30 mol %. As presented in Fig. 1, the simulation processes started with creating an input file, containing all information required to introduce the shielding material (density and chemical composition), γ-rays source (energy and its distribution), detector, and the geometry (cell and surface cards). A disk γ-source with a diameter of 2 cm and thickness of 0.5 cm was placed inside a lead collimator. The NPS card is set to stop running the simulation after 10 6 particle. The sample was placed at mid-distance between the collimator and γ-rays detector, so that the γ-rays transmit via the sample and transmited part is directed to the detector. The simulation process aims to estimate the average track length (ATL) of γ-photons; thus, Tally (F4) was used. MCNP-5 is a helpful code supported by continuousenergy nuclear and atomic data libraries. The cross-section data sources used in the MCNP-5 nuclear database are ENDF/B-VI.8, ACTI, ENDL, ACTI, and T-16 files 41 .

Results and discussion
The μ m values of the glasses simulated utilizing MCNP-5 code and calculated using the Phy-X/PSD in the energy range 0.015-15 MeV, as presented in Table 2. Both the μ m values (MCNP-5 and Phy-X/PSD) are found to be in good agreement. Their variations with incident photon energies for all the glasses are displayed in Fig. 2   www.nature.com/scientificreports/ An abrupt change in μ m is observed in the lower energy region in the Pb/Bi modified glasses, which have their K-absorption edges. The highest μ m value is shown in S 4 what is it required for a good shielding. In this energy region, the photoelectric process (PE) is the dominant process, which has the Z-dependence of Z 4-5 . The μ m values for all samples (~ 0.08 cm 2 /g) are found to be nearly constant in the energy range 0.08 MeV on predominating Compton scattering, which varies linearly with Z, falling down on higher energies. The μ m is found to increase slowly above 1 MeV on prevailing pair production process in this region, i.e., an order of Z 2 . It is found to be 0.037-0.041 cm 2 /g in S 1 , 0.038-0.043 cm 2 /g in S 2 , 0.039-0.045 cm 2 /g in S 3 , and 0.039-0.047 cm 2 /g in S 4 in the energy range of 4-15 MeV. The linear attenuation coefficients can easily be obtained from the μ m values, following a similar trend with the energy as presented in Fig. 3 42 . Table 2 shows a comparison of these values closely lying one another. The diff (%) calculated between the two programs is ≤ 5%. Figure 4 plots the Z eff changes with the energy in the different samples, varied over 69.87-17.11 for S 1 and 75.66-29.11 for S 4 in the energy range of 0.05-15 MeV. The Z eff is found to decrease up to 1.5 MeV on dominance of the photoelectric absorption process in this region, which has Z-dependence of Z 4-5 . It arises sharply beyond 3 MeV, attributing to dominance of pair production process, which depends on Z 2 . At 15 MeV, it is found to be 29.83 for S 1 , 32.86 for S 2 39.01 for S 3 , and 45.30 for S 4 . A maximum value are used in S 4 over S 1 in a duly increased PbO dose. A low value 17.11-17.60 for S 1 and 29.11-29.89 for S 4 in a medium 1-3 MeV energy region is contributed by the dominant Compton scattering in this region, which has a linear Z-dependence responsible for duly increased Z eff in the high-energy regions 43 .
The N e values, calculated for present samples at different γ-rays energies using Eq. (9), are ploted with energy in Fig. 5. These are 1.33 × 10 24 e/g (i.e. electrons/g) for S 1 and 7.05 × 10 23 e/g for S 4 at 15 keV. The values of S 1 (2.94 × 10 23 e/g) and S 4 (2.84 × 10 23 e/g), with a minimum at 1.5 MeV, fall down sharply up to 1 MeV. A pretty smaller value is found for S 1 of 3.09 × 10 23 -3.18 × 10 23 e/g, while 2.99 × 10 23 -3.07 × 10 23 e/g for S 4 in the  The values of other parameters studied for the present glasses are given in Table 3. The changes in EBF and EABF studied with energy at several penetration depths of 1, 2, 5, 10, 15, 20, 25, 30, 35 and 40 mfp are plotted in Figs. 10, 11, 12 and 13, 14, 15, 16 and 17 respectively. Both EBF and EABF of the studied samples possess low values in low and high-energy regions, but assume higher values in the moderate energy regions. At 0.015 and 0.15 MeV energies, EBF and EABF values are more dependent on sample contents and increase with decreasing Z eq in these glasses. The Z eq is maximum in S 4 , while minimum in S 1 . Both EBF and EABF in low-energies of 0.015-0.3 MeV are small and nearly equal to one for all penetration depths since the photons are totally absorbed/removed through photoelectric absorption in dominant interaction process up to 0.3 MeV. Those progressively increase with energy due to multiple Compton scattering (the degradation of photon energy), which dominates in the intermediate-energies (0.3-3 MeV). The EABF reduces in high-energy region (E > 3 MeV) in absorption behavior of the pair production process. After that, for gamma photon energies higher than 3 MeV, the buildup factors have high increase with increasing the incident energy. Also, EBF has a peak at 0.02 MeV in the K-absorption edge of high Z-elements present in these glasses 46 . The EBF values are the highest for 40 mfp and lowest for the penetration depth of 1 mfp due to the multiple scattering events for large penetration depths. Therefore, both EBF and EABF are increasing to reach a maximum for all S 1 , S 2 , S 3, and S 4 samples for penetration depth at 40 mfp. But, the buildup factors are maximum/minimum for S 1 /S 4 at penetration depths of 1, 2, 5, 10, 15, 20, 25, 30, 35 and 40 mfp for incident energies up to 3 MeV. By contrast, at E > 3 MeV, S 4 has maximum EBF and S 1 has the least EBF. .20% values at 1 MeV, respectively, in a due effect of PbO-GeO 2 additives of suppressing the attenuation properties. Thus, sample S4 can shield better than the other glasses. A composite glass has the property of removing more neutrons if it owes high Z elements. Low-Z elements may also remove neutrons if one using a combination of high-Z elements with low-Z elements. As portrayed in Fig. 19, the Σ R value varies as 0.139, 0.133, 0.128 and 0.12 cm −1 in the respective glasses. There is only a minor variation in this parameter. The amount of Z-elements like B and O may increase the neutron shielding capability in such glasses. shielding glasses, such as SCHOTT AG glasses, steels, polymers, concretes, and ceramics. This specific glass S 4 possesses suitably lowered HVL and MFP values (excluding at 1.5 and 2 MeV energies), over all these traditionally materials being used for this purpose. This work reveals a great potential of selected lead borate glasses to shield ionizing radiations in nuclear environment. The future scope of the presently selected glass series is to explore the structural and the mechanical properties. www.nature.com/scientificreports/