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

Abstract

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 (μ_m) 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 μ_m values are used to calculate other γ-ray shielding parameters such as half-value layer (HVL), mean-free-path (MFP), etc. The calculated μ_m 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 (Z_eff)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 (Σ_R), i.e. found to be 0.139 cm⁻¹ for S₁, 0.133 cm⁻¹ for S₂, 0.128 cm⁻¹ for S_3, and 0.12 cm⁻¹ for S₄. The results reveal a great potential for using a glass composite sample S4 in radiation protection applications.

Introduction

γ-Rays emitting radionuclides are found to be useful in many fields like industrial (to detect defects in metal casting), medical (to treat malignant and cancerous tumors), agriculture (to control the degree of ripeness and extend the shelf life of fruits and vegetables) and space applications, etc.^1–3. γ-Rays are high-frequency electromagnetic radiation that easily transmit through a thick wall, which may produce greater occupational exposures in nuclear facilities if not shielded adequately. Using suitable shielding may ensure better safety of radiation workers against its harmful dosages. Consequently, many researchers have been paid a great effort to develop and design well-formed radiation shielding materials^4–6.

In this view, a range of materials, including concrete, lead, oxide glass, etc., have been developed and used to shield radiation^1,2,4. Concrete has been formed from a loosely compacted mass of small fragments or particles^4,7. It has several limitations to be used as shielding in a nuclear reactor. Due to its non-transparent characteristics, it is not possible to observe/monitor the internal environment. Moreover, variation in water quantity in concrete often exhibits unwanted fluctuations in attenuation coefficients^8,9. To overcome such limitations, several glass-based materials have been processed. Being transparent in visible light, their properties can be modified by changing the components and preparation methods^8,10,11. As a result, a number of researchers studied the γ-rays attenuation parameters for a variety of glasses like bismuth borate glasses¹², lead borate glasses¹³, lead fluoroborate glasses¹⁴, bismuth borosilicate glasses¹⁵, alkali borosilicate glasses¹⁶, barium borosilicate glasses¹⁷, calcium–strontium-borate glasses¹⁸, lead silicate glasses¹⁹ and lead/barium phosphate glasses²⁰, etc. In these glasses^12–20, B₂O₃ is a common component that gives glass-forming of a lower melting point with good thermal stability and transparency. Smaller B³⁺ ionic size provides high bond strength^3,11. Heavier cations used in different dosages promote glasses of varied shielding capabilities. Radiation shielding of glass structures can be developed by adding some high-density materials like heavy metal oxides (HMO).

The glass structures made with HMO (Pb, Ba, and Bi) show characteristics like high refractive index, high infrared transparency, and high nonlinear optical susceptibility^21–23, all of which are favorable for a material to be used as an effective γ-rays shielding. Heavy metal oxides PbO, Bi₂O_3, BaO, etc. play a key role in enhancing an average product density. A required characteristic of a good radiation shielding material is its chemical homogeneity made over its high density^24–26. Generally, PbO containing high-density glasses offer high optical nonlinearity. A reasonably high PbO solubility is required to make a suitable glass for γ-rays' attenuation²⁷. Bi₂O₃ doped borate glasses find wide applications in various fields like fast optical switching, photonic devices, and infrared transmission components, with high refractive index, large optical susceptibility, large polarizability, and high optical basicity²⁸. Boro-germanate glasses offer high solubility to dissolve heavy metals, extending resistance to moisture, low melting point, good transparency, and excellent thermal stability²⁹.

The main goal of this work is to evaluate the γ-rays shielding parameters of glasses 0.2Bi₂O₃ − xPbO − (0.8 − 2x)B₂O₃ − xGeO₂, x = 0.05, 0.1, 0.2 and 0.3 mol %, as given in Table 1. The densities of the present samples have been taken from Knoblochova et al.³⁰. The μ_m values, as determined using the XCOM dependent Phy-X/PSD program and MCNP computer code, were used to calculate the other shielding parameters like linear attenuation coefficient (µ), electron density, mean-free-path (MFP), half-value layer (HVL), and radiation protection efficiency (RPE). The exposure buildup factor (EBF) and energy absorption buildup factor (EABF) were evaluated using the geometric progression (GP) fitting method within a 0.015–10 MeV energy range. The interaction of the neutrons with the present glasses is studied in terms of fast neutron removal cross-sections.

Table 1.

Chemical compositions and densities of studied samples.

Sample	Mole wight (mol%) of ingradients				Weight of elements (wt%)					Density (g/cm 3)
	Bi2O3	PbO	B2O3	GeO2	Bi	O	Pb	B	Ge
S1	20	5	70	5	52.80	28.80	06.54	09.56	02.29	5.85
S2	20	10	60	10	49.83	25.75	12.35	07.73	04.33	6.01
S3	20	20	40	20	44.80	20.58	22.21	04.63	07.78	6.64
S4	20	30	20	30	40.69	16.35	30.25	02.10	10.60	7.02

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^31–33, MFP = μ⁻¹, where μ (cm⁻¹) denotes a linear attenuation coefficient of the medium. When a narrow beam of radiation of initial intensity I₀ 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^34–36, I = I₀e^−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 I₀¹³, 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 cross-section (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 program³⁷.

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 ^38–40. Previously mentioned codes were used as alternative methods for the experimental measurements. The shielding parameters were evaluated using MCNP-5 code for the glasses 20 Bi₂O₃ − xPbO − (80 − 2x)B₂O₃ − xGeO₂, 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 10⁶ 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 continuous-energy 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 files⁴¹.

Figure 1.

Schematic geometrical set-up for MCNP simulations.

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. The μ_m values for sample S₁ (71.20–1.288 cm²/g), S₂ (76.03–1.34 cm²/g), S₃ (84.24–1.43 cm²/g) and S₄ (90.94–1.50 cm²/g) decrease sharply up to 15 keV, with a maximum over 71.20–90.94 cm²/g.

Table 2.

Mass attenuation coefficients for the present glasses.

Energy (MeV)	Mass attenuation coefficient (cm2 g−1)
	S1			S2			S3			S4
	MCNP	Phy-X/PSD	Diff (%)	MCNP	Phy-X/PSD	Diff (%)	MCNP	Phy-X/PSD	Diff (%)	MCNP	Phy-X/PSD	Diff (%)
0.015	71.1273	71.2000	0.1023	75.9491	76.0400	0.1196	84.1213	84.2500	0.1530	90.7962	90.9500	0.1694
0.02	53.9431	54.1600	0.4022	57.1215	57.3500	0.3999	62.5140	62.7600	0.3936	66.9188	67.1800	0.3903
0.03	19.0596	19.0700	0.0544	20.1513	20.1600	0.0431	22.0034	22.0200	0.0754	23.5159	23.5300	0.0598
0.04	9.0488	9.0690	0.2237	9.5533	9.5740	0.2170	10.4101	10.4300	0.1915	11.1090	11.1300	0.1894
0.05	5.0815	5.1040	0.4437	5.3572	5.3810	0.4442	5.8249	5.8510	0.4483	6.2067	6.2340	0.4397
0.06	3.1842	3.2080	0.7477	3.3519	3.3770	0.7502	3.6362	3.6630	0.7358	3.8686	3.8970	0.7337
0.08	1.5461	1.5740	1.8025	1.6219	1.6510	1.7950	1.7505	1.7820	1.8007	1.8555	1.8890	1.8043
0.15	1.3769	1.2880	6.4555	1.4341	1.3420	6.4250	1.5733	1.4330	8.9194	1.6087	1.5080	6.2585
0.3	0.3092	0.2891	6.5102	0.3176	0.2974	6.3684	0.3318	0.3115	6.1109	0.3435	0.3230	5.9775
0.4	0.1792	0.1796	0.2351	0.1829	0.1834	0.2790	0.1892	0.1898	0.3265	0.1944	0.1950	0.3130
0.5	0.1324	0.1327	0.2585	0.1343	0.1347	0.2948	0.1430	0.1381	3.4599	0.1451	0.1409	2.8795
0.6	0.1071	0.1077	0.5552	0.1082	0.1088	0.5222	0.1102	0.1108	0.5792	0.1154	0.1124	2.6157
0.8	0.0813	0.0817	0.4701	0.0817	0.0821	0.4828	0.0824	0.0828	0.5075	0.0829	0.0834	0.5242
1.5	0.0510	0.0519	1.8278	0.0509	0.0519	1.9002	0.0507	0.0518	2.0549	0.0506	0.0517	2.1780
2	0.0448	0.0453	1.2209	0.0448	0.0453	1.2858	0.0447	0.0454	1.3656	0.0447	0.0454	1.4383
3	0.0394	0.0397	0.7390	0.0396	0.0399	0.7634	0.0399	0.0402	0.8121	0.0402	0.0405	0.8426
4	0.0373	0.0375	0.4957	0.0377	0.0379	0.5083	0.0383	0.0386	0.5253	0.0389	0.0391	0.5417
5	0.0365	0.0367	0.3667	0.0371	0.0372	0.3617	0.0380	0.0382	0.3891	0.0388	0.0389	0.3862
6	0.0364	0.0365	0.3241	0.0371	0.0372	0.3077	0.0382	0.0383	0.3112	0.0392	0.0393	0.3190
8	0.0370	0.0371	0.2181	0.0379	0.0380	0.2200	0.0394	0.0395	0.2023	0.0407	0.0408	0.2120
10	0.0381	0.0382	0.1788	0.0392	0.0393	0.1723	0.0411	0.0411	0.1554	0.0426	0.0426	0.1576
15	0.0414	0.0415	0.1328	0.0429	0.0429	0.1124	0.0453	0.0453	0.1277	0.0472	0.0473	0.1119

Figure 2.

Variation of mass attenuation coefficient with energy in 20Bi₂O₃ − xPbO − (80 − 2x)B₂O₃ − xGeO₂ (x = 5, 10, 20, and 30 mol%) glasses.

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 S₄ 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 cm²/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 Z². It is found to be 0.037–0.041 cm²/g in S₁, 0.038–0.043 cm²/g in S₂, 0.039–0.045 cm²/g in S₃, and 0.039–0.047 cm²/g in S₄ 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. 3⁴². Table 2 shows a comparison of these values closely lying one another. The diff (%) calculated between the two programs is ≤ 5%.

Figure 3.

Variation of linear attenuation coefficient with energy in 20Bi₂O₃ − xPbO − (80 − 2x)B₂O₃ − xGeO₂ (x = 5, 10, 20, and 30 mol%) glasses.

Figure 4 plots the Z_eff changes with the energy in the different samples, varied over 69.87–17.11 for S₁ and 75.66–29.11 for S₄ 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 Z². At 15 MeV, it is found to be 29.83 for S₁, 32.86 for S₂ 39.01 for S₃, and 45.30 for S₄. A maximum value are used in S₄ over S₁ in a duly increased PbO dose. A low value 17.11–17.60 for S₁ and 29.11–29.89 for S₄ 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 regions⁴³.

Figure 4.

Variation of the effective atomic number with energy in 20Bi₂O₃ − xPbO − (80 − 2x)B₂O₃ − xGeO₂ (x = 5, 10, 20, and 30 mol%) glasses.

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 × 10²⁴ e/g (i.e. electrons/g) for S₁ and 7.05 × 10²³ e/g for S₄ at 15 keV. The values of S₁ (2.94 × 10²³ e/g) and S₄ (2.84 × 10²³ e/g), with a minimum at 1.5 MeV, fall down sharply up to 1 MeV. A pretty smaller value is found for S₁ of 3.09 × 10²³–3.18 × 10²³ e/g, while 2.99 × 10²³–3.07 × 10²³ e/g for S₄ in the medium 1–3 MeV energy region, and then increases beyond 3 MeV. The Z_eff values at 15 MeV are 5.39 × 10²³ and 4.65 × 10²³ e/g for glass samples S₁ and S₄, respectively.

Figure 5.

Variation of electron density with energy in 20Bi₂O₃ − xPbO − (80 − 2x)B₂O₃ − xGeO₂ (x = 5, 10, 20, and 30 mol%) glasses.

Figure 6 presents how HVL is varied with photon energy. It is significantly lower and stationary below 0.1 MeV and then arises sharply above 0.1 MeV, having the values 0.002 and 0.001 cm at 15 keV, while 0.034 and 0.024 cm at 0.1 MeV for S₁ and S₄, respectively. It becomes 3.24, 3.01, 2.73 and 2.51 cm at 6 MeV, while 2.857, 2.688, 2.303 and 2.088 cm at 15 MeV for S₁, S₂, S₃ and S₄, respectively. A minimum value shown in glass S₄ thus characterizing it to be the best shielding material^42,43 among all the four glasses studied here.

Figure 6.

Variation of the half-value layer with energy in 20Bi₂O₃ − xPbO − (80 − 2x)B₂O₃ − xGeO₂ (x = 5, 10, 20, and 30 mol%) glasses.

The MFP values, as calculated from μ at several energies, vary from 0.015 to 15 MeV, as plotted in Fig. 7. Evidently, MFP varies with energy due to dominance of photons interactions. All the four S₁–S₄ glasses have a value 0.02 cm at 15 keV energy. A sharp peak is marked at 80 keV, showing 0.109, 0.101, 0.085 and 0.075 cm values (MFP) for S₁, S₂, S₃, S₄, respectively. Significantly lower (nearly steady) values stand below 0.1 MeV, namely, 0.04 cm, 0.04 cm, 0.03 cm and 0.03 cm at 0.1 MeV for the respective samples, following the dominance of photoelectric effect, and quickly arise over 0.3–6 MeV energy on Compton scattering dominates. Those become 4.681 cm, 4.474 cm, 3.928 cm, and 3.626 cm respectively at 6 MeV. Above 6 MeV, almost constant MFP prolongs on dominance of pair production, namely, 4.121 cm, 3.878 cm, 3.323 cm and 3.012 cm, respectively, at 15 MeV⁴². The shielding effectiveness is thus better in the lower energies, i.e. glass S₄ is the best attenuator.

Figure 7.

Variation of the mean free path with energy in 20Bi₂O₃ − xPbO − (80 − 2x)B₂O₃ − xGeO₂ (x = 5, 10, 20, and 30 mol%) glasses.

Further, the HVL and MFP of sample S₄ have been compared to that of traditionally used shielding materials such as five types of glasses fabricated by SCHOTT AG, steels such as stainless steel-403 (SS403), cupero-nickel (CN), carbon steel-516 (CS516), inconel-600 (IL600), and monel-400 (MN400) alloys⁴⁴, several types of concretes⁴⁵ and ceramics such as CaSi₂, Mg₂Si, MgB₂, CaB₆, Al₂O₃, or TiO₂, as shown in Figs. 8a–e and 9a–e respectively. Usefully, our glass S₄ possesses better HVL and MFP values compared to that of traditionally used shielding materials. Values of both HVL and MFP for alloys are higher than the sample S₄ values, except at 1.5 and 2 MeV (Figs. 8b and 9b). Moreover, Figs. 8c,d and 9c,d show lower HVL and MFP values of sample S4 as compared to alloys and concretes. Thus, S₄ possess better shielding ability compared to the commercial glasses, concretes, alloys (excluding at 1.5 and 2 MeV energies), or ceramics.

Figure 8.

Comparison of HVL values of glass S4 with those in (a) commercial shielding glasses, (b) alloys, (b) alloys, (c) concretes and lead, and (d) ceramics materials.

Figure 9.

Comparison of MFP values of glass S4 with those in (a) commercial shielding glasses, (b) alloys, (c) concretes and lead, and (d) ceramics materials.

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 S₄, while minimum in S₁. 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 glasses⁴⁶. 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 S₁, S₂, S_3, and S₄ samples for penetration depth at 40 mfp. But, the buildup factors are maximum/minimum for S₁/S₄ 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, S₄ has maximum EBF and S₁ has the least EBF.

Table 3.

Equivalent atomic numbers and G-P fitting parameters for EBF and EABF for sample S₄.

Energy (MeV)	Zeq	G-P fitting parameters—EBF					G-P fitting parameters—EABF
		a	B	c	d	Xk	a	b	c	d	Xk
1.50E−02	33.41	− 0.106	1.004	1.402	0.114	11.712	− 0.115	1.004	1.408	0.124	12.378
2.00E−02	40.01	0.120	2.353	1.775	− 0.150	12.970	0.075	1.198	1.807	− 0.074	17.415
3.00E−02	40.20	0.120	3.331	1.005	− 0.198	29.753	0.123	1.455	1.013	− 0.126	26.025
4.00E−02	40.47	0.103	3.651	0.323	− 0.039	22.476	0.116	1.444	0.327	− 0.069	23.443
5.00E−02	40.76	− 0.272	2.944	0.064	0.040	12.036	− 0.122	1.358	0.076	0.100	8.673
6.00E−02	41.02	1.048	2.325	0.027	− 0.147	17.265	0.764	1.314	0.043	− 0.188	14.886
8.00E−02	41.50	0.748	1.646	0.046	− 0.251	14.386	0.561	1.298	0.091	− 0.225	14.051
1.00E−01	69.94	0.095	1.707	0.624	− 0.060	17.221	0.100	1.733	0.603	− 0.063	17.125
1.50E−01	71.19	0.385	1.238	0.146	− 0.131	14.776	0.410	1.560	0.094	− 0.097	21.530
2.00E−01	71.86	0.323	1.156	0.277	− 0.181	13.781	0.602	1.514	0.088	− 0.295	13.912
3.00E−01	72.61	0.165	1.178	0.494	− 0.079	13.645	0.386	1.572	0.214	− 0.213	13.319
4.00E−01	73.04	0.121	1.242	0.607	− 0.064	14.148	0.289	1.696	0.334	− 0.182	13.716
5.00E−01	73.32	0.097	1.299	0.677	− 0.053	14.131	0.232	1.808	0.424	− 0.151	13.747
6.00E−01	73.51	0.079	1.343	0.726	− 0.043	13.693	0.165	1.727	0.541	− 0.105	13.584
8.00E−01	73.71	0.056	1.405	0.799	− 0.033	13.709	0.127	1.840	0.629	− 0.085	13.581
1.00E+00	73.80	0.042	1.438	0.854	− 0.028	13.343	0.105	1.876	0.693	− 0.076	13.530
1.50E+00	73.17	0.012	1.427	0.981	− 0.020	14.278	0.058	1.793	0.845	− 0.056	13.837
2.00E+00	71.22	0.005	1.446	1.020	− 0.020	13.334	0.064	1.796	0.848	− 0.069	13.422
3.00E+00	66.69	0.017	1.465	1.017	− 0.042	13.305	0.091	1.749	0.804	− 0.109	13.533
4.00E+00	63.56	0.033	1.469	0.986	− 0.057	13.740	0.104	1.659	0.787	− 0.122	13.869
5.00E+00	61.62	0.065	1.559	0.906	− 0.085	13.973	0.138	1.728	0.718	− 0.153	14.137
6.00E+00	60.44	0.072	1.606	0.900	− 0.090	14.175	0.140	1.726	0.725	− 0.153	14.285
8.00E+00	59.02	0.071	1.811	0.940	− 0.089	14.165	0.126	1.828	0.788	− 0.142	14.280
1.00E+01	58.25	0.035	1.895	1.103	− 0.058	14.041	0.085	1.831	0.939	− 0.109	14.075
1.50E+01	57.42	0.008	2.169	1.319	− 0.039	13.682	0.047	1.999	1.161	− 0.082	13.764

Figure 10.

Variation of exposure buildup factor with energy for 20Bi₂O₃ − xPbO − (80 − 2x)B₂O₃ − xGeO₂ (x = 5) glass (S₁).

Figure 11.

Variation of exposure buildup factor with energy for 20Bi₂O₃ − xPbO − (80 − 2x)B₂O₃ − xGeO₂ (x = 10) glass (S₂).

Figure 12.

Variation of exposure buildup factor with energy for 20Bi₂O₃ − xPbO − (80 − 2x)B₂O₃ − xGeO₂ (x = 20) glass (S₃).

Figure 13.

Variation of exposure buildup factor with energy for 20Bi₂O₃ − xPbO − (80 − 2x)B₂O₃ − xGeO₂ (x = 30) glass (S₄).

Figure 14.

Variation of energy absorption buildup factor with energy for 20Bi₂O₃ − xPbO − (80 − 2x)B₂O₃ − xGeO₂ (x = 5) glass (S₁).

Figure 15.

Variation of energy absorption buildup factor with energy for 20Bi₂O₃ − xPbO − (80 − 2x)B₂O₃ − xGeO₂ (x = 10) glass (S₂).

Figure 16.

Variation of energy absorption buildup factor with energy for 20Bi₂O₃ − xPbO − (80 − 2x)B₂O₃ − xGeO₂ (x = 20) glass (S₃).

Figure 17.

Variation of energy absorption buildup factor with energy for 20Bi₂O₃ − xPbO − (80 − 2x)B₂O₃ − xGeO₂ (x = 30) glass (S₄).

Calculated RPE for S₁-S₄ glasses and their variation with energy is portrayed in Fig. 18, where RPE is stationary up to 0.1 MeV. This means the incident photons can totally penetrate at 0.1 MeV, then RPE sharply decreases over 0.1 to 3 MeV energies, showing 23.29, 23.58, 26.00, and 27.28% residual values in respective glasses, which stay constant up to 8 MeV. About 21% of incident photons penetrate at 15 MeV. Glasses S₁ and S₄ have 32.83% and 38.20% values at 1 MeV, respectively, in a due effect of PbO–GeO₂ 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.

Figure 18.

Variation of the radiation protection efficiency with energy for 20Bi₂O₃ − xPbO − (80 − 2x)B₂O₃ − xGeO₂ glasses.

Figure 19.

The fast neutron removal cross-section for 20Bi₂O₃ − xPbO − (80 − 2x)B₂O₃ − xGeO₂ glasses.

Conclusions

Major γ-rays shielding parameters are studied over a multicomponent glass series, 20Bi₂O₃ − xPbO − (80 − 2x)B₂O₃ − xGeO₂, with x-values varied in small steps up to 30 mol%, in precisely determining how sensitively the PbO/GeO₂ additives tailor the features. The additives promptly facilitate proportional behavior for µ, Z_eff and RPE in the doped glasses on duly suppressed HVL and MFP values. A sample S₄ is found to possess the highest value of the effective atomic number and the sample S₁ is found to possess the lower values of effective atomic number among the selected glasses beyond 0.05 MeV, anticipating a synergic PbO role of improving the shielding capability in this series. The HVL and MFP of this sample S₄ have been compared to those of traditionally used shielding glasses, such as SCHOTT AG glasses, steels, polymers, concretes, and ceramics. This specific glass S₄ 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.

Author contributions

Conceptualization, A.K.; methodology, A.J.; software, F.L.; validation, M.I.S. and K.A.M.; formal analysis, A.K.; investigation, A.K. and A.J.; resources, M.I.S.; data curation, M.I.S.; writing—original draft preparation, A.K., A.J. and M.I.S.; writing—review and editing, M.U.K.; visualization, F.L.; supervision, M.I.S.; project administration, M.R.I.F.; funding acquisition, M.R.I.F. All authors have read and agreed to the published version of the manuscript.

Competing interests

The authors declare no competing interests.