Optical and radiation shielding characteristics of tellurite glass doped with different rare-earth oxides

Abstract

Shielding glass materials doped with heavy metal oxides show an improvement in the effectiveness of the materials used in radiation shielding. In this work, the photon shielding parameters of six tellurite glass systems doped with several metal oxides namely, 70TeO₂-10P₂O₅- 10ZnO- 5.0PbF₂- 0.0024Er₂O₃- 5.0X (where X represents different doped metail oxides namely, Nb₂O₅, TiO₂, WO₃, PbO, Bi₂O₃, and CdO) in a broad energy spectrum, ranging from 0.015 MeV to 15 MeV, were evaluated. The shielding parameters were calculated using the online software Phy-X/PSD. The highest linear and mass attenuation coefficients recorded were obtaibed from the samples containing bismuth oxide (Bi₂O₃), and the lowest half-value layer and mean free path were recorded among the other samples. Furthermore, the shielding effectiveness of tellurite glass systems was compared with commercial shielding materials (RS-369, RS-253 G18, chromite, ferrite, magnetite, and barite). The optical parameters viz, dispersion energy, single-oscillator energy, molar refraction, electronic polarizability, non-linear refractive indices, n₂, and third-order susceptibility were measured and reported at a different wavelength. Bi₂O₃ has a strong effect on enhancing the optical and shielding properties. The outcome of this study suggests the potential of using the proposed glass samples as radiation-shielding materials for a broad range of imaging and therapeutic applications.

Keywords

Radiation shielding oxide glass optical parameters half value layer mean free path mass attenuation exposure buildup factor (EBF)

1 Introduction

Ionizing radiation, such as X-rays and gamma rays, is utilized in medical and technical fields. The technologies of ionization radiation are important in therapeutic procedures and radiological diagnostics as well as archaeological and environmental characterization techniques [1 –3]. Many reports have indicated that ionizing radiation is associated with distinct negative effects in humans, and several of these have shown that ionizing radiation technology may cause biological damage to living tissues exposed to it [4 –6]. As a result, validating science-based, realistic approaches that protect living tissues from harm caused by exposure to ionizing radiation is becoming a common research goal [7 –9].

The intensity of many chemical components (including lead) have been tested and evaluated with respect to a broad spectrum of ionising radiation energies [10, 11]. Lead is one of the most-used materials for radiation protection; however, there are many factors that limit its use, including cost, heavy weight, low melting point, and high toxicity [12]. As such, many researchers have been encouraged to find alternative shielding materials, such as alloy, glass, concrete, polymers, and ceramics [13 –15]. Moreover, researchers are increasingly focusing on producing materials that have high resistance to corrosion, low toxicity, minimal transparency, and high density. In recent years, glass has become a common material, as it can be produced with many compositions for radiation safety in different medical radiation applications [16 –18].

There are many properties of oxide-based glasses that make them appropriate for various medical and technical-imaging applications. Most glasses have a high thermal stability, a reasonably low glass transition, low crystallisation ability, adequate physical and chemical resistance levels, and a low melting point. Furthermore, various researchers have demonstrated the use of glasses with different compositions [19, 20]; indeed, it is now possible to develop novel compositions of advanced oxide glass to test against a broad range of ionizing radiation energies.

Various glass systems have already been developed as radiation-shielding materials [21 –32]. Many researchers have been encouraged by the shielding and optical properties of glass to test various glasses with heavy metal oxide for use as alternative shielding materials in nuclear facilities, computed tomography (CT) scan units, technical sectors, gamma camera rooms, X-ray rooms, and radiation facilities in X-ray and medical centers [10 , 19–32]. El-Sayed et al. [17] reported that the addition of bismuth (Bi) and lead (Pb) in casting glasses can provide better shielding characteristics and adequate shielding for nuclear facilities, X-ray diagnostics, and CT-scanner rooms. Singh et al. [31] reported that Bi₂O₃–SiO₂–Al₂O₃ and PbO–SiO₂–Al₂O₃ glasses can replace conventional concretes as gamma-ray shielding materials, indicating that adding heavy metals can improve the shielding properties of glasses. Chanthima et al. [32] investigated the shielding effectiveness of silicate glasses doped with heavy-metal oxides, such as Bi₂O₃, PbO, and BaO, and determined that glasses doped with heavy-metal oxides can be used as radiation-shielding materials. Most of the devloped shielding materials either contain a toxic materials such as lead or have limited density’s values due to the type of the modifiers and the dopped materials, which are usually used in the shielding materials’ development.

In this study, we investigated the shielding properties of tellurite glass systems doped with heavy-metal oxides. The properties were investigated using shielding parameters, including the linear and mass attenuation coefficients (LAC and MAC, respectively), half-value layer (HVL), mean free path (MFP), total atom cross-section (σ_a), total electronic cross-section (σ_a), effective atomic number (Z_eff), effective electron number (N_eff), equivalent atomic number (Z_eq), and exposure buildup factor (EBF).

2 Materials and method

We developed tellurite glass systems with different compositions: 70TeO₂-10P₂O₅- 10ZnO- 5.0PbF₂- 0.0024Er₂O₃- 5.0X (Where X represent different doped metail oxides namely; Nb₂O₅, TiO₂, WO₃, PbO, Bi₂O₃, and CdO) (see Table 1). We placed the raw materials in a Pt crucible in a heating furnace at 850°C to 950°C for 30 min, depending on the composition. We then stirred the melt until the viscosity was high and then cast the melt in a brass mold. We then put the sample in an annealing furnace for 2 h at 320°C, after which we switched off the furnace.

Table 1
Codes and chemical compositions of the prepared glasses

Sample code Glass compositions (in mol %)

TeO₂ P₂O₅ ZnO PbF₂ Er₂O₃ Nb₂O₅ TiO₂ WO₃ PbO Bi₂O₃ CdO

S1 70 10 10 5 0.0024 5 – – – – –

S2 70 10 10 5 0.0024 – 5 – – – –

S3 70 10 10 5 0.0024 – – 5 – – –

S4 70 10 10 5 0.0024 – – – 5 – –

S5 70 10 10 5 0.0024 – – – – 5 –

S6 70 10 10 5 0.0024 – – – – – 5

Sample code	Glass compositions (in mol %)
S1	70	10	10	5	0.0024	5	–	–	–	–	–
S2	70	10	10	5	0.0024	–	5	–	–	–	–
S3	70	10	10	5	0.0024	–	–	5	–	–	–
S4	70	10	10	5	0.0024	–	–	–	5	–	–
S5	70	10	10	5	0.0024	–	–	–	–	5	–
S6	70	10	10	5	0.0024	–	–	–	–	–	5

Figure 1 shows the annealed highly optical glasses. Table 2 shows the fraction by weight of the constituent elements and the measured densities. The densities of the glasses were between 5.161 g/cm³ to 5.589 g/cm³. The effectiveness of the proposed shielding materials was evaluated using the calculated shielding parameters that have been computed using the online software Phy-X/PSD [19]. Phy-X/PSD software calculated the shielding paramters based on the compostion and the measured densities of the propsed glass materials. The results of the shielding parameters were compared with other commercial shielding materials commonly used in photon and neutron shielding applications.

Fig. 1

Prepared glasses after annealing at 320 °C for 2 hours.

Table 2

The fractions by weights, densities, and chemical compositions of the proposed glass samples

Sample code	Density ρ	Fractions by weights (in percentage)
		Te	O	F	P	Pb	Zn	Er	Nb	Ti	W	Bi	Cd
S1	5.422	0.5596	0.2256	0.0119	0.0388	0.0649	0.04097	5.03E-06	0.0582	0	0	0	0
S2	5.161	0.5942	0.2235	0.0126	0.0412	0.0689	0.0435	5.34E-06	0	0.01593	0	0	0
S3	5.338	0.5657	0.2178	0.012	0.0392	0.0656	0.04141	5.08E-06	0	0	0.05822	0	0
S4	5.304	0.5672	0.2083	0.0121	0.0393	0.1316	0.0415	5.10E-06	0	0	0	0	0
S5	5.589	0.5266	0.2028	0.0112	0.0365	0.06108	0.0386	4.73E-06	0	0	0	0.1232	0
S6	5.248	0.5848	0.2147	0.0124	0.0406	0.06783	0.04281	5.26E-06	0	0	0	0	0.0368

2.1 Physical and shielding properties

The effectiveness of shielding material can be determined by physical properties and radiation shielding parameters, the most important of which are the cross section for scattering and absorption, effective atomic number, electron density, and HVL. The cross section for scattering and absorption can be characterized by the total MAC (μ/ρ), which can be computed using WinXcom [25]. The MAC of a mixture and compound can be calculated according to the following relation [10 –24]: $\frac{μ}{ρ} = \sum_{i} w_{i} {(\frac{μ}{ρ})}_{i}$ (1)

where w_i is the fraction by weight of the i^th atomic element, and ${(\frac{μ}{ρ})}_{i}$ is the MAC of the of the i^th atomic element.

The probability of photon interaction with a material can be characterized by the total atom cross section (σ_a) and total electronic cross section (σ_a), using the following relations [26]: $σ_{a} = \frac{1}{N_{A}} \sum_{i} f_{i} A_{i} {(\frac{μ}{ρ})}_{i}$ (2) $σ_{e} = \frac{1}{N_{A}} \sum_{j} f_{j} \frac{A_{i}}{Z_{j}} {(\frac{μ}{ρ})}_{j}$ (3)

where f_i is the fraction by mole of the i^th atomic element, A_i is the atomic weight of the i^th atomic element, Z_j is the atomic number, and N_A is Avogadro’s constant.

The effective atomic number characterizes the properties of the shielding material; it varies with energies and can be calculated from the ratio of atomic and electronic cross-sections by the following relation [26]: $Z_{eff} = \frac{σ_{a}}{σ_{e}}$ (4)

The electron density, which represents the number of electrons per unit mass of the shielding material, can be calculated using the following relation [26]: $N_{e} = \frac{N_{A}}{A} Z_{eff}$ (5)

where A is the mean atomic mass equal to ∑_if_iA_i, f_i is the fraction by mole of the i^th element, and A_i is the molecular weight of the i^th element.

The HVL and MFP are parameters for characterizing the effectiveness of the radiation-shielding material. The HVL is the thickness that reduces the intensity of the mono-energetic beam to half of its value, while the MFP is the average distance between two successive interactions. These parameters can defined by the following relations: $HVL = \frac{0.693}{μ}$ (6) $MFP = \frac{1}{μ}$ (7)

where μ is the LAC.

The equivalent atomic number (Z_eq) for the proposed shielding material is calculated by matching the ratio MACs of the Compton component to the total MACs at selected energies with a ratio of an element at the same energy. If the ratio lies between two elements, then the equivalent atomic number (Z_eq) can be calculated using the following interpolation procedure [27, 28]: $Z_{eq} = \frac{(Z_{1} \log R_{2} - logR) + (logR - \log R_{1})}{\log R_{2} - \log R_{2}}$ (8)

where Z₁ and Z₂ are the atomic numbers of two elements corresponding to ratios R₁ and R₂, and R is the ratio of the proposed material.

We used the Lambert-Beer law to estimate the physical properties of the proposed shielding material is limit for a thin absorbing material and a narrow-collimated beam geometry. For broad beams and thick shields, a correction factor needs to be introduced to account for scattering photons reaching the point of interest. This factor is known as the buildup factor, which is ratio of the total radiation quantity at any point to the quantity value of the un-collided photons reaching the same point; the lower the value of the buildup factors, the lower the amount of scattering photons reaching the point of interest. Two types of buildup factors are used to study the behavior of the shielding materials—namely, the energy absorption buildup factor (EABF) and the exposure buildup factor (EBF) [29]. These factors depend on the atomic number of the shielding material, photon energy, and the MFP of mono-energetic beams. The buildup factors can be calculated using the geometric progression (GP) technique developed by Harima et al. [29].

The GP fitting parameters for the proposed materials can be interpolated using the same formula: $C = \frac{C_{1} (\log Z_{2} - \log Z_{eq}) + C_{2} (\log Z_{eq} - \log Z_{1})}{\log Z_{2} - \log Z_{1}}$ (9)

where C₁ and C₂ are the values of the GP fitting parameters, which correspond to the atomic numbers Z₁ and Z₂, respectively.

Using the GP fitting parameters at a selected energy range, the buildup factors can be estimated from the following equations [30]: $B (E, X) = 1 + \frac{b - 1}{K - 1} (K^{x} - 1) for K \neq 1$ (10) $B (E, X) = 1 + (b - 1) X for K = 1$ (11) $K (E, X) = C X^{a} + d \frac{\tanh (\frac{X}{X_{K}} - 2) - \tanh (- 2)}{1 - \tanh (- 2)} for x ⩽ 40 mfp$ (12)

where x represents the source-detector distance (SDD), in MFP units; E represents the energy of the incident photons; X_K, a, b, and d represent the GP fitting parameters; and K(E, x) refers to the dose multiplicative factor.

The chemical compositions of the prepared glasses are mainly depend on optical parameters, such as dispersion energy, E_d, single-oscillator energy, E_s, magnetic oscillator strength electronics, linear refractive indices, n, non-linear refractive indices, n₂, and third-order susceptibility χ⁽³⁾. Via the single-oscillator model which can be calculated according to the relation adopted by DiDomenico and Wimple [31], E_d and E_s can be calculated as follows: $\frac{E_{d} E_{s}}{n^{2} - 1} = E_{s}^{2} - E^{2},$ (13)

The molar refraction of R_m can be calculated using the following equation [32]: $R_{M} = \frac{M \cdot [n^{2} - 1]}{ρ \cdot [n^{2} + 2]}$ (14)

where M is the average molar weight of the sample, ρ is the density of the sample and n is the refractive index of the glass materials. The molar electronic polarizability (α_m) can be calculated using the following equation [32]: $α_{M} = \frac{3 R_{M}}{4 π N_{A}}$ (15)

where N_A represents Avogadro’s number and M expresses the molecular weight of the prepared glasses.

The metallization criterion M_c of the prototyped samples at various wavelengths can be estimated using the following relation: $M_{c} = \frac{3}{n^{2} + 2}$ (16)

3 Results and discussion

Figure 2 shows a plot of [n² –1]^–1 versus E² for samples S1, S2, S3, S4, S5, and S6. E_s was between 6.7 eV and 7.33 eV, and E_d changed from 18.42 eV to 21.45 eV, which change was dependent on the type of modifier in the host glass matrix, as shown in Table 3.

Fig. 2

The variation of 1/(1-n²) with (h ν)² in (eV)² of the prepared glasses.

Table 3

The density (ρ), molar volume (V_m), oscillator energy (E₀), dispersion energy (E_d), and third-order susceptibility (χ⁽³⁾) of the prepared glasses

Sample code	Density in g/cm³	Molar volume [cm³·mol^–1]	E_s [eV]	E_d [eV]	χ⁽³⁾ at 1700 nm [× 10^–13 esu]
S1	5.422	29.431	6.70	19.32	4.79
S2	5.161	29.118	6.75	19.96	5.74
S3	5.338	29.576	6.70	18.42	3.96
S4	5.304	29.684	7.33	21.32	5.19
S5	5.589	30.342	7.02	21.45	6.36
S6	5.248	29.098	7.27	21.45	5.86

The R_M and α_M values at 1700 nm were between 14.17 and 15.43 in cm³×mol^–1, and 6.117 and 5.618 in A⁰³, respectively, as shown in Table 4. Sample S5 (Bi2O3) had the highest linear refractive index, as reported in [38], and the highest molar polarizability. Sample 3 (WO₃) had the lowest value of both R_M and α_M at 1700 nm.

Table 4

The molar refraction (R_m), polarizability (α_M), and metallization (M_C) of the prepared glasses at a different wavelengths

Sample code	R_M [cm³·mol^–1]			α_M [Å]			M_C
	400 nm	633 nm	1700 nm	400 nm	633 nm	1700 nm	400 nm	633 nm	1700 nm
S1	16.20	15.08	14.45	6.423	5.979	5.727	0.449	0.488	0.509
S2	16.20	15.11	14.63	6.421	5.990	5.799	0.444	0.481	0.498
S3	15.93	14.81	14.17	6.316	5.870	5.618	0.461	0.499	0.521
S4	16.09	15.16	14.72	6.378	6.012	5.837	0.458	0.489	0.504
S5	16.97	15.93	15.43	6.729	6.317	6.117	0.441	0.475	0.491
S6	15.91	14.99	14.66	6.306	5.941	5.810	0.453	0.485	0.496

The M_c value was from 0.491 to 0.521 at 1700 nm (see Table 4). The third-order nonlinear optical susceptibility χ⁽³⁾ could be determined using linear optical susceptibility χ⁽¹⁾ by χ⁽³⁾ = 1.7 · [χ⁽¹⁾] ⁴ × 10^-10 esu, where χ⁽¹⁾ = (1/ 12.56) × (n² - 1). The value of χ⁽³⁾ of the prototyped glasses were from 6.36 to 3.96×10^–13 esu (Table 3).

Sample 5 (70TeO₂- 10P₂O₅- 10ZnO- 5PbF₂- 0.0024Er₂O₃- 5.0Bi₂O₃) had the largest value; Sample 3 (70TeO₂- 10P₂O₅- 10ZnO- 5PbF₂- 0.0024Er₂O₃- 5.0WO₃) had the smallest χ⁽³⁾ value. The increase in the molar volume R_M and electronic polarzibilty α_M for the glasses took place in sequence (WO₃ < CdO < Nb₂O₅ < TiO₂ < PbO < Bi₂O₃) at 633 nm; otherwise, the metallization decreased in the same sequence. The polarizability and refractive index of the glass containing bismuth oxide Bi₂O₃ were the highest and led to an increase in the dispersion energy, E_d, R_M, α_M, and χ⁽³⁾; in particular, the explanation of the change is based on the number of oxygen atoms incorporated by individual oxides into the glass matrix. The introduction of tungsten oxide (W:O = 1:3) into the glass with the electronic polarizability was calculated from the energy gap (α_O2– (Eg) = 2.670 A⁰³), while bismuth oxide (Bi:O = 2:3) has α_O2– (Eg) = 3.507 A⁰³ and caused an increase in E_d, R_M, and α_M, and a decrease in M_c. Moreover, Bi₂O₃ oxide had a large optical basicity of Λ(Eg) = 1.19 and hence led to an increase in E_d, R_M, α_M, and χ⁽³⁾ with Bi2O3 content, and a decrease with WO₃ content.

Figures 3A and 3B show the computed LACs and MACs of the samples at energies between 0.015 MeV and 15 MeV. The decrease in attenuation coefficients with increased photon energy is due to the contribution of the photoelectric effect and Compton scattering, which are the predominant interactions in the diagnostic energies range. The superiority of the mass attenuation of Samples 3, 5, and 6 are due to the heavy-metal oxide materials doped on each sample. For example, Sample 6, which contained Cadmium oxide (CdO), recorded slightly higher values at energies above the K-edge absorption energy of Cadmium (32 keV to 68 keV). Sample 3, which contained tungsten oxide (WO3), recorded slightly higher values at energies above the K-edge absorption energy of tungsten (70 keV to 90 keV). Sample 5, which contained bismuth oxide (Bi₂O₃), recorded higher values among the other samples for energies above the K-edge absorption energy of bismuth (> 90.5 keV). As shown in Fig. 1B, the LACs of Sample 5 were superior to the other samples in all energies due to the sample’s higher density. For example, the value of LACs recorded for Sample 5 was 4.275 cm^–1 compared to 3.064 cm^–1, 2.97 cm^–1, 3.406 cm^–1, 3.6 cm^–1, and 3.06 cm^–1 at 0.15 MeV, with percentage differences of 28.3%, 30.5%, 20.3%, 15.7%, and 28.3% for Samples 1, 2, 3, 4, and 6, respectively.

Fig. 3

Line graphs of the computed MACs (A) and LACs (B) for six radiation-shielding sample materials.

The half-value layer (HVL) is the thickness required to reduce the intensity of the radiation beam to its half value. HVL is commonly used to estimate the required shielding thickness for the specific energy range. Figure 4A show the computed half-value layers of the samples in a broad energy spectrum, ranging from 0.015 MeV to 15 MeV. Sample 5 recorded the lowest HVL, which was consistent with its high linear attenuation value. This high attenuation value was due to the high atomic of the doped heavy-metal oxide (Bi₂O₃) and higher density, which increased the possibility of photon interaction and decreased the possibility of photon transmission. For example, the HVL of Sample 5 was 0.162 cm, compared to 0.226 cm, 0.233 cm, 0.204 cm, 0.193 cm, and 0.226 cm at 0.15 MeV, with percentage differences of 28.34%, 30.5%, 20.32%, 15.8%, and 28.34% for Samples 1, 2, 3, 4, and 6, respectively. The superior performance of Sample 5 is mainly due to the contribution of the photoelectric effect and Compton scattering, which are the predominant interactions in low and medium energies; and in high energy, the performance is due to the pair production interaction process. The low HVL of Sample 5 indicates the presence of heavy-metal oxide materials that result in high average molecular weight. These findings are consistent with other findings [17 , 40].

Fig. 4

Line graphs of the computed HVLs for the proposed shielding materials (A), and a comparison of the outcomes with other HVLs for different radiation-shielding materials (B).

Furthermore, the half-value layer (HVL) of the samples were compared with the most common commercial materials [34, 35]. Figure 4B shows the values of the samples compared to the most common commercial shielding glass materials developed by de Schott Co., Germany (RS-253 G18, RS-520, and RS-360) [41] as well as common oxide used with concrete materials, such as barite, chromite, ferrite, and magnetite [42]. The samples performed better, with lower HVL than RS-360, RS-253 G18, barite, chromite, ferrite, and magnetite, at all energies. This indicates that the samples had better shielding characteristics than the commercial materials. Compared to RS-369, Sample 5 had slightly higher HVL in the energy range of 90 keV to 300 keV, and better shielding performance with photon energies above 300 keV. For example, the HVL at 0.5 MeV of Sample 5, RS-360, chromite, and RS-253 G18 were 1.19 cm, 1.39 cm, 1.65 cm, and 3.12 cm, respectively, with percentage differences of 15%, 28%, and 62%, respectively. Nevertheless, RS-520 shielding materials has better performance than the samples, at all energies, due to the presence of highly weighted lead oxide (71%).

MFP determines the average distance between two successive interactions; the lower the MFP, the more effective the shielding material. Figure 5A illustrates the MFP as a function of the photon energy of the samples. Sample 5 recorded the lowest MFP, consistent with findings recorded for its HVL, as both are strongly dependent on the attenuation coefficients. For example, at 0.15 MeV, the MFP of Sample 5 was 0.234 cm, compared to 0.326 cm, 0.337 cm, 0.294 cm, 0.278 cm, and 0.326 cm, with percentage differences of 28.34%, 30.5%, 20.32%, 15.8%, and 28.34% for Sample 1, 2, 3, 4, and 6, respectively.

Fig. 5

Line graphs of the MFPs for the proposed shielding materials (A), and a comparison of the outcomes with other MFPs for various radiation-shielding materials (B).

Furthermore, the MFPs of the samples were compared with other shielding materials (RS-253 G18, RS-520, RS-369, chromite, and ferrite), as shown in Fig. 5B. Similar findings to the HVLs were noticed; the higher the density and photon attenuation of the shielding material, the lower the MFP.

Figure 6 shows the values of the total atom cross-section (σ_a) and total electronic cross-section (σ_a) as a function of photon energy between 15 keV and 15 MeV; the higher the values of atomic and electronic cross-sections, the more effective the shielding material. Sample 5 had the highest atomic and electronic cross-section values. These results are consistent with the values recorded for the attenuation coefficients.

Fig. 6

Line graphs illustrating the total atom cross-sections (σ_a; A) and total electronic cross-sections (σ_a; B) as a function of photon energy for the proposed shielding materials.

The effectiveness of the shielding material on the atomic number as well as the density; the higher the atomic number and density of the shielding material, the more effective in reducing the intensity of the radiation. The atomic number and number of electrons are defined as Z_eff and N_eff, which can be computed from the MACs of the compound elements. Figures 7A and 7B illustrate Z_eff and N_eff as a function of photon energy between 15 keV and 15 MeV. Sample 5 recorded the highest Z_eff and N_eff, which is consistent with the values recorded for the attenuation coefficients.

Fig. 7

Line graphs demonstrating the variations in effective atomic number (A) and effective electron density (B) as a function of photon energy.

Figure 8 shows the values of Z_eq calculated for the proposed shielding materials, between 15 keV and 15 MeV. The Z_eq was estimated from the ratio of the MACs of the Compton component to the total MACs. Sample 5 recorded the highest values. As shown in Fig. 8, the highest equivalent atomic numbers were recorded at the intermediate energies. These values are mainly a consequence of the Compton scatter process, which is the predominate process in this region.

Fig. 8

The equivalent atomic number (Z_eq) of the proposed samples as a function of photon energy.

Figures 9A, 9B, 9C, 9D, 9E, and 9F illustrate the EBFs for the proposed samples as a function of MFP calculated using the GP fitting coefficients (a, b, c, d, and X_k); the EBFs for all samples increase gradually as the penetration depth increases due to the more energetic Compton scattering photons and the annihilation gamma photons. The EBFs as a function of photon energy increase as the energy increases, and then flattens; this is because, at low energy, photo-electric absorption is the predominate interaction process, in which all photons are absorbed. Samples 4, 5, and 6, which contained PbO, Bi2O3, and CdO, recorded higher values at low photon energies, compared to Samples 1, 2, and 3. This sharp increase was a consequence of doping these heavy-metal oxides with high atomic numbers.

Fig. 9

Line graphs of the EBFs for the proposed shielding materials as a function of penetration depth.

4 Conclusion

The effectiveness of a material as a shielding material depends on its physical properties and shielding parameters, such as density, linear and mass attenuation coefficients, half-value layer, mean free path, effective atomic number, effective electron number, equivalent atomic number, and exposure buildup factors. The glass that contained bismuth oxide (Bi2O3) recorded the highest LACs and MACs and showed better shielding performance, with the lowest HVL and MFP and higher Z_eff and Z_eq. Furthermore, the effectiveness of the proposed samples was compared with common commercial materials and oxides used with concrete materials, and the proposed Sample 5 showed better shielding effectiveness than almost all of the materials, at all energies, while RS-520 performed best overall. Finally, Bi₂O₃ enhances electronic polarizability and molar volume, suggesting high values of HVL, MFP, Z_eff, N_eff, Z_eq, and EBF. These results indicate that the proposed samples have good characteristics as radiation-shielding materials, which can be use in various diagnostic and therapeutic applications. The standard materials RS520 recoded higher values due to the high concentration of lead oxide, while the proposed novel glass materials considered as alternative radiation shielding materials; these glass compositions could provide a good add to the market in terms of providing non-toxic, dense, and transparent radiation shielding glass.

Footnotes

Acknowledgments

The authors extend their appreciation to the Deanship of Scientific Research at King Khalid University (KKU) for funding this research project Number (R.G. P2/79/41).

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Sample code	Glass compositions (in mol %)
	TeO₂	P₂O₅	ZnO	PbF₂	Er₂O₃	Nb₂O₅	TiO₂	WO₃	PbO	Bi₂O₃	CdO
S1	70	10	10	5	0.0024	5	–	–	–	–	–
S2	70	10	10	5	0.0024	–	5	–	–	–	–
S3	70	10	10	5	0.0024	–	–	5	–	–	–
S4	70	10	10	5	0.0024	–	–	–	5	–	–
S5	70	10	10	5	0.0024	–	–	–	–	5	–
S6	70	10	10	5	0.0024	–	–	–	–	–	5